0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : do_CVC4 %s 0.03/0.24 % Computer : n023.star.cs.uiowa.edu 0.03/0.24 % Model : x86_64 x86_64 0.03/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.24 % Memory : 32218.625MB 0.03/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.24 % CPULimit : 300 0.03/0.24 % DateTime : Sat Jul 14 05:50:24 CDT 2018 0.03/0.24 % CPUTime : 1.10/1.35 %----Proving without arithmetic mode 1.10/1.35 ------- cvc4-fof casc j9 : /export/starexec/sandbox2/benchmark/theBenchmark.p at ... 1.10/1.35 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20... 15.71/15.97 % SZS status Theorem for theBenchmark 15.71/15.97 % SZS output start Proof for theBenchmark 15.71/15.97 (skolem (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_4 (one_one int))) (forall ((T_4 $$unsorted)) (not (= (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_3))) m)) _let_4)) T_4) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) _let_3))) _let_4))) )))))) 15.71/15.97 ( skv_1 ) 15.71/15.97 ) 15.71/15.97 (skolem (let ((_let_0 (fun real bool))) (forall ((K_2 $$unsorted)) (or (not (forall ((X_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real im X_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_2)) K_2))) )) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) K_2)))) )) 15.71/15.97 ( skv_2 ) 15.71/15.97 ) 15.71/15.97 (skolem (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) (forall ((S_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) S_1) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) S_1) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) S_1)))) )))) 15.71/15.97 ( skv_3 ) 15.71/15.97 ) 15.71/15.97 (skolem (forall ((K_2 $$unsorted)) (not (forall ((X_2 $$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_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_2)) K_2))) )) ) 15.71/15.97 ( skv_4 ) 15.71/15.97 ) 15.71/15.97 (skolem (let ((_let_0 (norm_norm complex))) (forall ((K_2 $$unsorted)) (not (forall ((X_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP complex real _let_0 (hAPP complex complex cnj X_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_0 X_2)) K_2))) )) )) 15.71/15.97 ( skv_5 ) 15.71/15.97 ) 15.71/15.97 (skolem (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (norm_norm complex))) (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) K_2))) (not (forall ((X_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP complex real _let_2 (hAPP complex complex cnj X_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_2 X_2)) K_2))) ))) )))) 15.71/15.97 ( skv_6 ) 15.71/15.97 ) 15.71/15.97 (skolem (forall ((K_2 $$unsorted)) (not (forall ((X_2 $$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_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_2)) K_2))) )) ) 15.71/15.97 ( skv_7 ) 15.71/15.97 ) 15.71/15.97 (skolem (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (number_number_of int))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (forall ((S1 $$unsorted)) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) S1) (hAPP int nat (number_number_of nat) _let_3))) (hAPP int int _let_2 min_1)) (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int _let_2 (hAPP int int bit0 _let_3))) m)) (one_one int))))) ))))) 15.71/15.97 ( skv_8 ) 15.71/15.97 ) 15.71/15.97 (skolem (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int _let_0 (ord_less_eq int) (zero_zero int)))) (let ((_let_2 (fun int int))) (let ((_let_3 (hAPP int int (hAPP int _let_2 (plus_plus int) (hAPP int int (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) (let ((_let_4 (ord_less int))) (let ((_let_5 (hAPP int (fun int _let_0) zcong s1))) (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_1 X_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 X_2) _let_3))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_5 X_2) _let_3))) (not (forall ((Y_2 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_1 Y_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_5 Y_2) _let_3))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 Y_2) _let_3))) (= (ti int X_2) (ti int Y_2))) ))) ))))))) 15.71/15.97 ( skv_9 ) 15.71/15.97 ) 15.71/15.97 (skolem (let ((_let_0 (fun real bool))) (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) K_2))) (not (forall ((X_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real re X_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_2)) K_2))) ))) )) 15.71/15.97 ( skv_10 ) 15.71/15.97 ) 15.71/15.97 (skolem (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((K_2 $$unsorted)) (or (not (forall ((X_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (norm_norm real) (hAPP complex real re X_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_2)) K_2))) )) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) K_2)))) ))) 15.71/15.97 ( skv_11 ) 15.71/15.97 ) 15.71/15.97 (skolem (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((K_2 $$unsorted)) (or (not (forall ((X_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (norm_norm real) (hAPP complex real im X_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_2)) K_2))) )) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) K_2)))) ))) 15.71/15.97 ( skv_12 ) 15.71/15.97 ) 15.71/15.97 (skolem (let ((_let_0 (fun real bool))) (let ((_let_1 (norm_norm complex))) (forall ((K_2 $$unsorted)) (or (not (forall ((X_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP complex real _let_1 (hAPP complex complex cnj X_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_1 X_2)) K_2))) )) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) K_2)))) ))) 15.71/15.97 ( skv_13 ) 15.71/15.97 ) 15.71/15.97 (skolem (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (hAPP real _let_1 _let_2 _let_0))) (let ((_let_4 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X_2) _let_4))) (not (= _let_0 (hAPP real real cos X_2))) (not (forall ((Y_2 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_3 Y_2))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Y_2) _let_4))) (not (= _let_0 (hAPP real real cos Y_2))) (= X_2 Y_2)) )) (not (hBOOL (hAPP real bool _let_3 X_2)))) )))))) 15.71/15.97 ( skv_14 ) 15.71/15.97 ) 15.71/15.97 (skolem (forall ((P_1 $$unsorted)) (hBOOL P_1) ) 15.71/15.97 ( skv_15 ) 15.71/15.97 ) 15.71/15.97 (instantiation (forall ((N $$unsorted)) (not (= N (hAPP nat nat suc N))) ) 15.71/15.97 ( (zero_zero nat) ) 15.71/15.97 ( (hAPP nat nat suc (zero_zero nat)) ) 15.71/15.97 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.71/15.97 ) 15.71/15.97 (instantiation (let ((_let_0 (combi X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun X_a X_a) _let_0)) )) 15.71/15.97 ( bool ) 15.71/15.97 ( real ) 15.71/15.97 ( nat ) 15.71/15.97 ( (fun nat bool) ) 15.71/15.97 ( int ) 15.71/15.97 ( (fun int bool) ) 15.71/15.97 ( (fun real bool) ) 15.71/15.97 ( (fun real real) ) 15.71/15.97 ( complex ) 15.71/15.97 ( (fun nat real) ) 15.71/15.97 ( (fun int int) ) 15.71/15.97 ( (fun int (fun int bool)) ) 15.71/15.97 ( (product_prod int int) ) 15.71/15.97 ( (fun (product_prod int int) bool) ) 15.71/15.97 ( code_code_numeral ) 15.71/15.97 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.71/15.97 ( (fun (product_prod int int) int) ) 15.71/15.97 ( (fun int (fun int (fun int bool))) ) 15.71/15.97 ( (fun int real) ) 15.71/15.97 ) 15.71/15.97 (instantiation (let ((_let_0 (fun int bool))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) K1) K2)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (hAPP int int bit0 K1)) (hAPP int int bit1 K2)))) )) 15.71/15.98 ( (zero_zero int), (one_one int) ) 15.71/15.98 ( (zero_zero int), min_1 ) 15.71/15.98 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.71/15.98 ( (zero_zero int), s ) 15.71/15.98 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.71/15.98 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.71/15.98 ( (zero_zero int), skv_3 ) 15.71/15.98 ( (zero_zero int), skv_9 ) 15.71/15.98 ( pls, min_1 ) 15.71/15.98 ( (one_one int), t ) 15.71/15.98 ( min_1, pls ) 15.71/15.98 ( min_1, min_1 ) 15.71/15.98 ) 15.71/15.98 (instantiation (let ((_let_0 (fun int bool))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) pls) (hAPP int int bit1 K))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) pls) K))) )) 15.71/15.98 ( pls ) 15.71/15.98 ( (hAPP int int bit1 pls) ) 15.71/15.98 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.71/15.98 ( (one_one int) ) 15.71/15.98 ( min_1 ) 15.71/15.98 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.71/15.98 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.71/15.98 ( s ) 15.71/15.98 ( (hAPP int int (number_number_of int) pls) ) 15.71/15.98 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.71/15.98 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.71/15.98 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.71/15.98 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.71/15.98 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.71/15.98 ( skv_3 ) 15.71/15.98 ( skv_9 ) 15.71/15.98 ) 15.71/15.98 (instantiation (let ((_let_0 (product_prod X_a X_a))) (let ((_let_1 (fun _let_0 bool))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP X_a nat F X_1)) (hAPP X_a nat F Y_1))) (hBOOL (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) (hAPP X_a _let_0 (hAPP X_a (fun X_a _let_0) (product_Pair X_a X_a) X_1) Y_1)) (hAPP (fun X_a nat) _let_1 (measure X_a) F)))) ))) 15.71/15.98 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), nat_1 ) 15.71/15.98 ) 15.71/15.98 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_1))) (let ((_let_3 (times_times real))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs real real real) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_1 real) _let_3) cos)) cos)) X_1) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real _let_1 _let_3 (hAPP real real (hAPP real _let_1 _let_3 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real cos X_1))) (hAPP real real sin X_1))))) ))))) 15.71/15.98 ( (zero_zero real) ) 15.71/15.98 ( pi ) 15.71/15.98 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.71/15.98 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.71/15.98 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.71/15.98 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.71/15.98 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.71/15.98 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.71/15.98 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.71/15.98 ( skv_14 ) 15.71/15.98 ) 15.71/15.98 (instantiation (let ((_let_0 (if X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun bool (fun X_a (fun X_a X_a))) _let_0)) )) 15.71/15.98 ( bool ) 15.71/15.98 ( real ) 15.71/15.98 ( nat ) 15.71/15.98 ( (fun nat bool) ) 15.71/15.98 ( int ) 15.71/15.98 ( (fun int bool) ) 15.71/15.98 ( (fun real bool) ) 15.71/15.98 ( (fun real real) ) 15.71/15.98 ( complex ) 15.71/15.98 ( (fun nat real) ) 15.71/15.98 ( (fun int int) ) 15.71/15.98 ( (fun int (fun int bool)) ) 15.71/15.98 ( (product_prod int int) ) 15.71/15.98 ( (fun (product_prod int int) bool) ) 15.71/15.98 ( code_code_numeral ) 15.71/15.98 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.71/15.98 ( (fun (product_prod int int) int) ) 15.71/15.98 ( (fun int (fun int (fun int bool))) ) 15.71/15.98 ( (fun int real) ) 15.71/15.98 ) 15.71/15.98 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun int bool))) (forall ((A_3 $$unsorted)) (= (hBOOL (hAPP _let_1 bool (finite_finite_1 int) (hAPP _let_0 _let_1 (hAPP (fun nat int) (fun _let_0 _let_1) (image nat int) (semiring_1_of_nat int)) A_3))) (hBOOL (hAPP _let_0 bool (finite_finite_1 nat) A_3))) ))) 15.71/15.98 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 15.71/15.98 ) 15.71/15.98 (instantiation (forall ((Y $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP real real arctan Y)) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.71/15.98 ( (zero_zero real) ) 15.71/15.98 ( (one_one real) ) 15.71/15.98 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.71/15.98 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 15.71/15.98 ) 15.71/15.98 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun real _let_1))) (let ((_let_3 (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real (uminus_uminus real) (hAPP real real sin X_1))) (hAPP real real cos X_1)))) (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_0 (fun real _let_0) (deriv real) (hAPP nat _let_0 (hAPP _let_2 (fun nat _let_0) (combc real nat real) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_1 real) (power_power real)) cos)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) X_1) (hAPP real real (hAPP real _let_0 (plus_plus real) _let_3) _let_3)))) ))))) 15.71/15.98 ( (zero_zero real) ) 15.71/15.98 ( pi ) 15.71/15.98 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.71/15.98 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.71/15.98 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.71/15.98 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.71/15.98 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.71/15.98 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.71/15.98 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.71/15.98 ( skv_14 ) 15.71/15.98 ) 15.71/15.98 (instantiation (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) (hAPP int real (real_1 int) N_1))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) N_1))) ) 15.71/15.98 ( (zero_zero int) ) 15.71/15.98 ( (one_one int) ) 15.71/15.98 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.71/15.98 ( min_1 ) 15.71/15.98 ) 15.71/15.98 (instantiation (let ((_let_0 (semiring_1_of_nat int))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP nat int _let_0 Ma)) (hAPP nat int _let_0 N_1))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) Ma) N_1))) )) 15.71/15.98 ( (zero_zero nat), (zero_zero nat) ) 15.71/15.98 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.71/15.98 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.71/15.98 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.71/15.98 ) 15.71/15.98 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (ord_less int))) (forall ((W_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 W_1) _let_1)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (hAPP int int bit1 W_1)) _let_1))) )))) 15.71/15.98 ( pls ) 15.71/15.98 ( (hAPP int int bit1 pls) ) 15.71/15.98 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.71/15.98 ( min_1 ) 15.71/15.98 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.71/15.98 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.71/15.98 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.71/15.98 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.71/15.98 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.71/15.98 ) 15.71/15.98 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (one_one nat)) (hAPP nat nat (fact_fact nat) N))) ) 15.71/15.98 ( (zero_zero nat) ) 15.71/15.98 ( (hAPP nat nat suc (zero_zero nat)) ) 15.71/15.98 ) 15.71/15.98 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit0 K)) pls)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) pls))) ))) 15.71/15.98 ( pls ) 15.71/15.98 ( (hAPP int int bit1 pls) ) 15.71/15.98 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.71/15.98 ( min_1 ) 15.71/15.98 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.71/15.98 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.71/15.98 ) 15.71/15.98 (instantiation (let ((_let_0 (finite_finite_1 X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun (fun X_a bool) bool) _let_0)) )) 15.71/15.98 ( nat ) 15.71/15.98 ( int ) 15.71/15.98 ) 15.71/15.98 (instantiation (forall ((X_1 $$unsorted) (A_2 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP real int (archim2085082626_floor real) X_1)) A_2)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) X_1) (hAPP int real (real_1 int) A_2)))) ) 15.71/15.98 ( pi, (zero_zero int) ) 15.71/15.98 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero int) ) 15.71/15.98 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 15.71/15.98 ) 15.71/15.98 (instantiation (let ((_let_0 (fun real bool))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP _let_0 bool (hAPP real (fun _let_0 bool) (member real) (hAPP int real (real_1 int) X_1)) (ring_1_Ints real))) )) 15.71/15.98 ( (zero_zero int) ) 15.71/15.98 ( (one_one int) ) 15.71/15.98 ) 15.71/15.98 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((W_1 $$unsorted) (Z $$unsorted)) (= (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 W_1) Z))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP int nat nat_1 W_1)) (hAPP int nat nat_1 Z)))) ))) 15.71/15.98 ( (zero_zero int), (zero_zero int) ) 15.71/15.98 ( (zero_zero int), (one_one int) ) 15.71/15.98 ( (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.71/15.98 ( (zero_zero int), min_1 ) 15.71/15.98 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.71/15.98 ( min_1, (zero_zero int) ) 15.71/15.98 ( min_1, min_1 ) 15.71/15.98 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.71/15.98 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 15.71/15.98 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 15.71/15.98 ( t, (zero_zero int) ) 15.71/15.98 ( t, (one_one int) ) 15.71/15.98 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.71/15.98 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.71/15.98 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.71/15.98 ) 15.71/15.98 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less int) pls))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool _let_0 (hAPP int int bit0 K))) (hBOOL (hAPP int bool _let_0 K))) )) 15.71/15.98 ( pls ) 15.71/15.98 ( (hAPP int int bit1 pls) ) 15.71/15.98 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.71/15.98 ( min_1 ) 15.71/15.98 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.71/15.98 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.71/15.98 ) 15.71/15.98 (instantiation (forall ((L_4 $$unsorted)) (not (= min_1 (hAPP int int bit0 L_4))) ) 15.71/15.98 ( pls ) 15.71/15.98 ( (hAPP int int bit1 pls) ) 15.71/15.98 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.71/15.98 ( min_1 ) 15.71/15.98 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.71/15.98 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.71/15.98 ) 15.71/15.98 (instantiation (forall ((Ma $$unsorted) (Z $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Ma) (hAPP int nat nat_1 Z))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP nat int (semiring_1_of_nat int) Ma)) Z))) ) 15.71/15.98 ( (zero_zero nat), (zero_zero int) ) 15.71/15.98 ( (zero_zero nat), (one_one int) ) 15.71/15.98 ( (zero_zero nat), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.71/15.98 ( (zero_zero nat), min_1 ) 15.71/15.98 ( (zero_zero nat), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.71/15.98 ) 15.71/15.98 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int (fun _let_0 bool) (member int) X_1))) (forall ((X_1 $$unsorted)) (or (hBOOL (hAPP _let_0 bool _let_1 zOdd)) (hBOOL (hAPP _let_0 bool _let_1 zEven))) ))) 15.71/15.99 ( (one_one int) ) 15.71/15.99 ) 15.71/15.99 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) Y_1)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real sqrt X_1)) (hAPP real real sqrt Y_1)))) ))) 15.71/15.99 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.71/15.99 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.71/15.99 ) 15.71/15.99 (instantiation (let ((_let_0 (real_1 nat))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N_1) Ma)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP nat real _let_0 N_1)) (hAPP nat real _let_0 Ma)))) )) 15.71/15.99 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.71/15.99 ) 15.71/15.99 (instantiation (forall ((X $$unsorted)) (not (= (zero_zero real) (hAPP real real cos (hAPP real real arctan X)))) ) 15.71/15.99 ( (zero_zero real) ) 15.71/15.99 ( (one_one real) ) 15.71/15.99 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.71/15.99 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 15.71/15.99 ) 15.71/15.99 (instantiation (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP int bool (even_odd_even int) (hAPP nat int (semiring_1_of_nat int) X_1))) (hBOOL (hAPP nat bool (even_odd_even nat) X_1))) ) 15.71/15.99 ( (zero_zero nat) ) 15.71/15.99 ( (hAPP nat nat suc (zero_zero nat)) ) 15.71/15.99 ( (one_one nat) ) 15.71/15.99 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.71/15.99 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.71/15.99 ) 15.71/15.99 (instantiation (let ((_let_0 (product_snd X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (= _let_0 (ti (fun (product_prod X_a X_b) X_b) _let_0)) )) 15.71/15.99 ( real, real ) 15.71/15.99 ( nat, nat ) 15.71/15.99 ( int, int ) 15.71/15.99 ( int, (product_prod int int) ) 15.71/15.99 ( quickcheck_code_int, quickcheck_code_int ) 15.71/15.99 ( (product_prod int int), (product_prod int int) ) 15.71/15.99 ( (product_prod nat nat), (product_prod nat nat) ) 15.71/15.99 ( code_code_numeral, code_code_numeral ) 15.71/15.99 ) 15.71/15.99 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 N_1) (hAPP nat nat suc Ma))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Ma) N_1)))) ))) 15.71/15.99 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.71/15.99 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 15.71/15.99 ) 15.71/15.99 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (fun nat _let_1))) (let ((_let_4 (fun _let_2 _let_2))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP _let_2 bool (summable real) (hAPP _let_2 _let_2 (hAPP _let_3 _let_4 (combs nat real real) (hAPP _let_2 _let_3 (hAPP (fun real _let_1) (fun _let_2 _let_3) (combb real _let_1 nat) (times_times real)) (hAPP _let_2 _let_2 (hAPP _let_1 _let_4 (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb nat real nat) (real_1 nat)) (fact_fact nat))))) (hAPP real _let_2 (power_power real) X_1)))) )))))) 15.71/15.99 ( (hAPP int real (number_number_of real) min_1) ) 15.80/15.99 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/15.99 ) 15.80/15.99 (instantiation (let ((_let_0 (hAPP nat nat suc (zero_zero nat)))) (forall ((X_1 $$unsorted)) (= (not (hBOOL (hAPP nat bool (even_odd_even nat) X_1))) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) X_1) (hAPP nat nat suc _let_0)))) )) 15.80/15.99 ( (zero_zero nat) ) 15.80/15.99 ( (one_one nat) ) 15.80/15.99 ) 15.80/15.99 (instantiation (let ((_let_0 (complex_case X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun (fun real (fun real X_a)) (fun complex X_a)) _let_0)) )) 15.80/15.99 ( bool ) 15.80/15.99 ( real ) 15.80/15.99 ( nat ) 15.80/15.99 ( complex ) 15.80/15.99 ( (fun nat (product_prod real real)) ) 15.80/15.99 ) 15.80/15.99 (instantiation (let ((_let_0 (ti bool P))) (forall ((P $$unsorted)) (or (= fFalse _let_0) (= fTrue _let_0)) )) 15.80/15.99 ( fTrue ) 15.80/15.99 ) 15.80/15.99 (instantiation (forall ((A_2 $$unsorted) (X_1 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real (real_1 int) A_2)) X_1)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) A_2) (hAPP real int (archimedean_ceiling real) X_1)))) ) 15.80/15.99 ( (zero_zero int), pi ) 15.80/15.99 ( (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/15.99 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/15.99 ( (zero_zero int), skv_2 ) 15.80/15.99 ( (zero_zero int), skv_10 ) 15.80/15.99 ( (zero_zero int), skv_13 ) 15.80/15.99 ( (one_one int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/15.99 ) 15.80/15.99 (instantiation (forall ((N $$unsorted)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP nat real (real_1 nat) N)) (zero_zero real)))) ) 15.80/15.99 ( (zero_zero nat) ) 15.80/15.99 ( (one_one nat) ) 15.80/15.99 ) 15.80/15.99 (instantiation (forall ((K_4 $$unsorted)) (not (= pls (hAPP int int bit1 K_4))) ) 15.80/15.99 ( pls ) 15.80/15.99 ( (hAPP int int bit1 pls) ) 15.80/15.99 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/15.99 ( min_1 ) 15.80/15.99 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.80/15.99 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/15.99 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/15.99 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.80/15.99 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.80/15.99 ) 15.80/15.99 (instantiation (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (iszero int) (hAPP int int (number_number_of int) K))) (hBOOL (hAPP rat bool (iszero rat) (hAPP int rat (number_number_of rat) K)))) ) 15.80/15.99 ( pls ) 15.80/15.99 ( (hAPP int int bit1 pls) ) 15.80/15.99 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/15.99 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/15.99 ( min_1 ) 15.80/15.99 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.80/15.99 ) 15.80/15.99 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) arctan) X_1) (hAPP real real (inverse_inverse real) (hAPP real real (hAPP real _let_1 (plus_plus real) (one_one real)) (hAPP nat real (hAPP real (fun nat real) (power_power real) X_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ))) 15.80/15.99 ( (hAPP int real (number_number_of real) min_1) ) 15.80/15.99 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/15.99 ) 15.80/15.99 (instantiation (let ((_let_0 (one_one int))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) X_1) _let_0)) (= _let_0 (hAPP int int (abs_abs int) X_1))) )) 15.80/15.99 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/15.99 ) 15.80/15.99 (instantiation (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP quickcheck_code_int bool (hAPP quickcheck_code_int (fun quickcheck_code_int bool) (ord_less quickcheck_code_int) N_1) Ma)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP quickcheck_code_int int quickcheck_int_of N_1)) (hAPP quickcheck_code_int int quickcheck_int_of Ma)))) ) 15.80/15.99 ( (zero_zero quickcheck_code_int), (zero_zero quickcheck_code_int) ) 15.80/15.99 ) 15.80/15.99 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (power_power real))) (let ((_let_3 (plus_plus real))) (let ((_let_4 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_5 (hAPP real real (uminus_uminus real) X))) (forall ((X $$unsorted)) (= (zero_zero real) (hAPP real real (hAPP real _let_0 _let_3 (hAPP nat real (hAPP real _let_1 _let_2 (hAPP real real (hAPP real _let_0 _let_3 (hAPP real real sin _let_5)) (hAPP real real sin X))) _let_4)) (hAPP nat real (hAPP real _let_1 _let_2 (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real cos _let_5)) (hAPP real real cos X))) _let_4))) ))))))) 15.80/15.99 ( (one_one real) ) 15.80/15.99 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/15.99 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.80/15.99 ) 15.80/15.99 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) cos_coeff)) (hAPP real _let_1 (power_power real) X_1))) (hAPP real real cos X_1))) )))) 15.80/15.99 ( (zero_zero real) ) 15.80/15.99 ( pi ) 15.80/15.99 ( (hAPP int real (number_number_of real) min_1) ) 15.80/15.99 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/15.99 ( (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 pls)))) ) 15.80/15.99 ( (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) ) 15.80/15.99 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/15.99 ( (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))))) ) 15.80/15.99 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/15.99 ( (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))))) ) 15.80/15.99 ( (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)))) ) 15.80/15.99 ( skv_14 ) 15.80/15.99 ) 15.80/15.99 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) pls))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool _let_0 K)) (hBOOL (hAPP int bool _let_0 (hAPP int int bit0 K)))) )) 15.80/15.99 ( pls ) 15.80/15.99 ( (hAPP int int bit1 pls) ) 15.80/15.99 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/15.99 ( min_1 ) 15.80/15.99 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.80/15.99 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/15.99 ) 15.80/15.99 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) pls))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool _let_0 (hAPP int int bit1 K))) (hBOOL (hAPP int bool _let_0 K))) )) 15.80/15.99 ( pls ) 15.80/15.99 ( (hAPP int int bit1 pls) ) 15.80/15.99 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/15.99 ( min_1 ) 15.80/15.99 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.80/15.99 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/15.99 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/15.99 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.80/15.99 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.80/15.99 ) 15.80/15.99 (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))) ) 15.80/15.99 ( (one_one nat), (one_one nat) ) 15.80/15.99 ) 15.80/15.99 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (hAPP nat int (semiring_1_of_nat int) N))) ) 15.80/15.99 ( (zero_zero nat) ) 15.80/15.99 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/15.99 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/15.99 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/15.99 ) 15.80/15.99 (instantiation (let ((_let_0 (fun int bool))) (forall ((M $$unsorted)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong M) (zero_zero int)) M)) )) 15.80/15.99 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/15.99 ( s1 ) 15.80/15.99 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/15.99 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/15.99 ) 15.80/15.99 (instantiation (forall ((R_4 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) R_4) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real (real_1 int) (hAPP real int (archim2085082626_floor real) R_4))) (one_one real)))) ) 15.80/15.99 ( (zero_zero real) ) 15.80/15.99 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/15.99 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/15.99 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/15.99 ( skv_14 ) 15.80/15.99 ) 15.80/15.99 (instantiation (forall ((N $$unsorted)) (= N (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP nat nat suc N)) (one_one nat))) ) 15.80/15.99 ( (zero_zero nat) ) 15.80/15.99 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/15.99 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.80/15.99 ) 15.80/15.99 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less int) min_1))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool _let_0 (hAPP int int bit0 K))) (hBOOL (hAPP int bool _let_0 K))) )) 15.80/15.99 ( pls ) 15.80/15.99 ( (hAPP int int bit1 pls) ) 15.80/15.99 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/15.99 ( min_1 ) 15.80/15.99 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.80/15.99 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/15.99 ) 15.80/15.99 (instantiation (forall ((X $$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)))) ) 15.80/15.99 ( (zero_zero real) ) 15.80/15.99 ( (one_one real) ) 15.80/15.99 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/15.99 ( (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 pls)))) ) 15.80/15.99 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/15.99 ( skv_14 ) 15.80/15.99 ) 15.80/15.99 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((K $$unsorted) (L $$unsorted)) (= (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))) ))) 15.80/15.99 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.80/15.99 ) 15.80/15.99 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP real (fun real real) (minus_minus real) X_1) Y_1)) (zero_zero real))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) Y_1))) ))) 15.80/16.00 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.80/16.00 ) 15.80/16.00 (instantiation (let ((_let_0 (hilbert_Eps X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun (fun X_a bool) X_a) _let_0)) )) 15.80/16.00 ( bool ) 15.80/16.00 ( real ) 15.80/16.00 ( nat ) 15.80/16.00 ( (fun nat bool) ) 15.80/16.00 ( int ) 15.80/16.00 ( (fun int bool) ) 15.80/16.00 ( (product_prod real real) ) 15.80/16.00 ( (product_prod int int) ) 15.80/16.00 ( (filter real) ) 15.80/16.00 ( (filter nat) ) 15.80/16.00 ( (product_prod nat nat) ) 15.80/16.00 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.80/16.00 ( (fun nat rat) ) 15.80/16.00 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.80/16.00 ) 15.80/16.00 (instantiation (let ((_let_0 (even_odd_even int))) (let ((_let_1 (hBOOL (hAPP int bool _let_0 Y_1)))) (let ((_let_2 (hBOOL (hAPP int bool _let_0 X_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (minus_minus int) X_1) Y_1))) (or (and (not _let_1) (not _let_2)) (and _let_2 _let_1))) )))) 15.80/16.00 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.80/16.00 ) 15.80/16.00 (instantiation (forall ((X_1 $$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)))) X_1)) (hBOOL (hAPP nat bool (even_odd_even nat) X_1))) ) 15.80/16.00 ( (zero_zero nat) ) 15.80/16.00 ( (one_one nat) ) 15.80/16.00 ) 15.80/16.00 (instantiation (forall ((W $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) W) W)) ) 15.80/16.00 ( (zero_zero real) ) 15.80/16.00 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.00 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.00 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.00 ( skv_14 ) 15.80/16.00 ) 15.80/16.00 (instantiation (forall ((Z_1 $$unsorted)) (= Z_1 (hAPP real complex (hAPP real (fun real complex) complex_1 (hAPP complex real re Z_1)) (hAPP complex real im Z_1))) ) 15.80/16.00 ( ii ) 15.80/16.00 ( (zero_zero complex) ) 15.80/16.00 ( (one_one complex) ) 15.80/16.00 ) 15.80/16.00 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) (hAPP nat nat suc N)))) (zero_zero int))) ) 15.80/16.00 ( (zero_zero nat) ) 15.80/16.00 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.00 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.80/16.00 ) 15.80/16.00 (instantiation (let ((_let_0 (even_odd_even int))) (let ((_let_1 (hBOOL (hAPP int bool _let_0 Y_1)))) (let ((_let_2 (hBOOL (hAPP int bool _let_0 X_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) X_1) Y_1))) (or (and (not _let_1) (not _let_2)) (and _let_2 _let_1))) )))) 15.80/16.00 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.80/16.00 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.80/16.00 ) 15.80/16.00 (instantiation (let ((_let_0 (in_rel X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (= _let_0 (ti (fun (fun (product_prod X_a X_b) bool) (fun X_a (fun X_b bool))) _let_0)) )) 15.80/16.00 ( bool, bool ) 15.80/16.00 ( real, bool ) 15.80/16.00 ( real, real ) 15.80/16.00 ( real, int ) 15.80/16.00 ( real, (filter real) ) 15.80/16.00 ( real, (filter nat) ) 15.80/16.00 ( nat, bool ) 15.80/16.00 ( nat, nat ) 15.80/16.00 ( nat, (product_prod nat nat) ) 15.80/16.00 ( (fun nat bool), nat ) 15.80/16.00 ( int, bool ) 15.80/16.00 ( int, nat ) 15.80/16.00 ( int, int ) 15.80/16.00 ( int, (fun int bool) ) 15.80/16.00 ( int, (product_prod int int) ) 15.80/16.00 ( (fun int bool), int ) 15.80/16.00 ( (fun real bool), real ) 15.80/16.00 ( (fun nat real), nat ) 15.80/16.00 ( (fun int int), int ) 15.80/16.00 ( (fun int (fun int bool)), int ) 15.80/16.00 ( quickcheck_code_int, quickcheck_code_int ) 15.80/16.00 ( (product_prod int int), bool ) 15.80/16.00 ( (product_prod int int), int ) 15.80/16.00 ( (product_prod int int), (product_prod int int) ) 15.80/16.00 ( (product_prod nat nat), (product_prod nat nat) ) 15.80/16.00 ( (fun (product_prod int int) bool), (product_prod int int) ) 15.80/16.00 ( code_code_numeral, code_code_numeral ) 15.80/16.00 ( (fun (product_prod int int) int), (product_prod int int) ) 15.80/16.00 ( (fun int real), int ) 15.80/16.00 ( (fun real (fun int bool)), real ) 15.80/16.00 ( (fun int (fun nat bool)), int ) 15.80/16.00 ) 15.80/16.00 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (power_power real))) (let ((_let_4 (fun nat _let_0))) (let ((_let_5 (fun nat _let_1))) (let ((_let_6 (fun _let_2 _let_2))) (let ((_let_7 (combs nat real real))) (let ((_let_8 (fun real _let_1))) (let ((_let_9 (fun _let_2 _let_5))) (let ((_let_10 (combb real _let_1 nat))) (let ((_let_11 (fun _let_0 _let_2))) (let ((_let_12 (combb nat real nat))) (let ((_let_13 (hAPP nat _let_0 (hAPP _let_4 _let_4 (combc nat nat nat) (hAPP _let_0 _let_4 (hAPP _let_4 (fun _let_0 _let_4) (combb nat _let_0 nat) (plus_plus nat)) (hAPP nat _let_0 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP _let_2 (fun real bool) (sums real) (hAPP _let_2 _let_2 (hAPP _let_5 _let_6 _let_7 (hAPP _let_2 _let_5 (hAPP _let_8 _let_9 _let_10 (times_times real)) (hAPP _let_2 _let_2 (hAPP _let_5 _let_6 _let_7 (hAPP _let_2 _let_5 (hAPP _let_8 _let_9 _let_10 (inverse_divide real)) (hAPP real _let_2 _let_3 (hAPP int real (number_number_of real) min_1)))) (hAPP _let_0 _let_2 (hAPP _let_2 _let_11 _let_12 (real_1 nat)) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb nat nat nat) (fact_fact nat)) _let_13))))) (hAPP _let_0 _let_2 (hAPP _let_2 _let_11 _let_12 (hAPP real _let_2 _let_3 X_1)) _let_13))) (hAPP real real sin X_1))) ))))))))))))))) 15.80/16.00 ( (zero_zero real) ) 15.80/16.00 ( pi ) 15.80/16.00 ( (hAPP int real (number_number_of real) min_1) ) 15.80/16.00 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.00 ( (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) ) 15.80/16.00 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.00 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.00 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/16.00 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.00 ( (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)))) ) 15.80/16.00 ) 15.80/16.00 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (one_one real))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) _let_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real sqrt X_1)) _let_2))) )))) 15.80/16.00 ( (zero_zero real) ) 15.80/16.00 ( (one_one real) ) 15.80/16.00 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.00 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.00 ) 15.80/16.00 (instantiation (forall ((X $$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))) ) 15.80/16.00 ( (zero_zero real) ) 15.80/16.00 ( pi ) 15.80/16.00 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.00 ( (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) ) 15.80/16.00 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.00 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/16.00 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.00 ( (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)))) ) 15.80/16.00 ) 15.80/16.00 (instantiation (let ((_let_0 (semiring_1_of_nat int))) (forall ((N $$unsorted) (M $$unsorted)) (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))))) )) 15.80/16.00 ( (zero_zero nat), (zero_zero nat) ) 15.80/16.00 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.00 ) 15.80/16.00 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (one_one nat)) (hAPP nat nat fact N))) ) 15.80/16.00 ( (zero_zero nat) ) 15.80/16.00 ) 15.80/16.00 (instantiation (let ((_let_0 (fun int bool))) (forall ((W_1 $$unsorted) (Z $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) W_1) (hAPP int int (hAPP int (fun int int) (minus_minus int) Z) (one_one int)))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W_1) Z))) )) 15.80/16.00 ( (zero_zero int), (zero_zero int) ) 15.80/16.00 ( (zero_zero int), (one_one int) ) 15.80/16.00 ( (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.00 ( (zero_zero int), min_1 ) 15.80/16.00 ( min_1, (zero_zero int) ) 15.80/16.00 ( min_1, min_1 ) 15.80/16.00 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.00 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 15.80/16.00 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 15.80/16.00 ( t, (zero_zero int) ) 15.80/16.00 ( t, (one_one int) ) 15.80/16.00 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.00 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.00 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.00 ) 15.80/16.00 (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))) ) 15.80/16.00 ( (zero_zero real) ) 15.80/16.00 ( (one_one real) ) 15.80/16.00 ) 15.80/16.00 (instantiation (let ((_let_0 (product_fst X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (= _let_0 (ti (fun (product_prod X_a X_b) X_a) _let_0)) )) 15.80/16.00 ( real, real ) 15.80/16.00 ( nat, nat ) 15.80/16.00 ( int, int ) 15.80/16.00 ( int, (product_prod int int) ) 15.80/16.00 ( quickcheck_code_int, quickcheck_code_int ) 15.80/16.00 ( (product_prod int int), (product_prod int int) ) 15.80/16.00 ( (product_prod nat nat), (product_prod nat nat) ) 15.80/16.00 ( code_code_numeral, code_code_numeral ) 15.80/16.00 ) 15.80/16.00 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (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)))) ))) 15.80/16.00 ( min_1, min_1 ) 15.80/16.00 ) 15.80/16.00 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (collect X_a))) (forall ((X_a $$unsorted)) (= _let_1 (ti (fun _let_0 _let_0) _let_1)) ))) 15.80/16.00 ( bool ) 15.80/16.00 ( real ) 15.80/16.00 ( nat ) 15.80/16.00 ( (fun nat bool) ) 15.80/16.00 ( int ) 15.80/16.00 ( (fun int bool) ) 15.80/16.00 ( (product_prod real real) ) 15.80/16.00 ( (product_prod int int) ) 15.80/16.00 ( (filter real) ) 15.80/16.00 ( (filter nat) ) 15.80/16.00 ( (product_prod nat nat) ) 15.80/16.00 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.80/16.00 ( (fun nat rat) ) 15.80/16.00 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.80/16.00 ) 15.80/16.00 (instantiation (let ((_let_0 (even_odd_even int))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (= (and (hBOOL (hAPP int bool _let_0 X_1)) (not (= (zero_zero nat) N_1))) (hBOOL (hAPP int bool _let_0 (hAPP nat int (hAPP int (fun nat int) (power_power int) X_1) N_1)))) )) 15.80/16.00 ( s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.00 ( s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.00 ( skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.00 ) 15.80/16.00 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (forall ((Y_1 $$unsorted)) (= (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt Y_1))) (hBOOL (hAPP real bool _let_0 Y_1))) )) 15.80/16.00 ( (zero_zero real) ) 15.80/16.00 ( (one_one real) ) 15.80/16.00 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.00 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.00 ) 15.80/16.00 (instantiation (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real (real_1 int) N_1)) (zero_zero real))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) N_1) (zero_zero int)))) ) 15.80/16.00 ( (zero_zero int) ) 15.80/16.00 ( (one_one int) ) 15.80/16.00 ( min_1 ) 15.80/16.00 ( s ) 15.80/16.00 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.80/16.00 ( t ) 15.80/16.00 ( skv_3 ) 15.80/16.00 ( skv_9 ) 15.80/16.00 ) 15.80/16.00 (instantiation (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP int bool nat_is_nat X_1)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X_1))) ) 15.80/16.00 ( (zero_zero int) ) 15.80/16.00 ( (one_one int) ) 15.80/16.00 ( min_1 ) 15.80/16.00 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.00 ( s ) 15.80/16.00 ( (hAPP int int (number_number_of int) pls) ) 15.80/16.00 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.00 ( skv_3 ) 15.80/16.00 ( skv_9 ) 15.80/16.00 ) 15.80/16.00 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((K $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit0 K)) (hAPP int int bit0 L))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L))) ))) 15.80/16.00 ( pls, pls ) 15.80/16.00 ) 15.80/16.00 (instantiation (forall ((N $$unsorted)) (= (one_one nat) (hAPP nat nat (hAPP nat (fun nat nat) (gcd_gcd nat) (hAPP nat nat suc N)) N)) ) 15.80/16.00 ( (zero_zero nat) ) 15.80/16.01 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.01 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.80/16.01 ) 15.80/16.01 (instantiation (let ((_let_0 (fun real bool))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) sin) X_1) (hAPP real real cos X_1))) )) 15.80/16.01 ( (zero_zero real) ) 15.80/16.01 ( pi ) 15.80/16.01 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.01 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.80/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.01 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.01 ( skv_14 ) 15.80/16.01 ) 15.80/16.01 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (times_times real))) (let ((_let_4 (fun real _let_2))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) (hAPP nat _let_1 (hAPP _let_4 (fun nat _let_1) (combc real nat real) (hAPP _let_1 _let_4 (hAPP _let_4 (fun _let_1 _let_4) (combb real _let_2 real) (power_power real)) cos)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) X_1) (hAPP real real (hAPP real _let_1 _let_3 (hAPP real real (hAPP real _let_1 _let_3 (hAPP int real (number_number_of real) (hAPP int int bit0 min_1))) (hAPP real real cos X_1))) (hAPP real real sin X_1)))) )))))) 15.80/16.01 ( (zero_zero real) ) 15.80/16.01 ( pi ) 15.80/16.01 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.01 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.80/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.01 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.01 ( skv_14 ) 15.80/16.01 ) 15.80/16.01 (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))))) ) 15.80/16.01 ( (zero_zero nat) ) 15.80/16.01 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.01 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.80/16.01 ) 15.80/16.01 (instantiation (let ((_let_0 (fun nat bool))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) Ma) N_1)) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) (hAPP nat nat suc Ma)) N_1))) )) 15.80/16.01 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.01 ) 15.80/16.01 (instantiation (let ((_let_0 (trivial_limit X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun (filter X_a) bool) _let_0)) )) 15.80/16.01 ( real ) 15.80/16.01 ( nat ) 15.80/16.01 ) 15.80/16.01 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real sqrt X_1)) (hAPP real real sqrt Y_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) Y_1))) ))) 15.80/16.01 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.01 ) 15.80/16.01 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_4 (times_times real))) (let ((_let_5 (fun real _let_2))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) (hAPP nat _let_1 (hAPP _let_5 (fun nat _let_1) (combc real nat real) (hAPP _let_1 _let_5 (hAPP _let_5 (fun _let_1 _let_5) (combb real _let_2 real) (power_power real)) cos)) (hAPP int nat (number_number_of nat) _let_3))) X_1) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real _let_1 _let_4 (hAPP real real (hAPP real _let_1 _let_4 (hAPP int real (number_number_of real) _let_3)) (hAPP real real cos X_1))) (hAPP real real sin X_1))))) ))))))) 15.80/16.01 ( (zero_zero real) ) 15.80/16.01 ( pi ) 15.80/16.01 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.01 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.80/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.01 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.01 ( skv_14 ) 15.80/16.01 ) 15.80/16.01 (instantiation (forall ((K_4 $$unsorted)) (= K_4 (hAPP int quickcheck_code_int quickcheck_of_int (hAPP quickcheck_code_int int quickcheck_int_of K_4))) ) 15.80/16.01 ( (zero_zero quickcheck_code_int) ) 15.80/16.01 ) 15.80/16.01 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (fun _let_2 _let_2))) (let ((_let_4 (fun (filter nat) bool))) (let ((_let_5 (combb real real nat))) (forall ((R_1 $$unsorted)) (hBOOL (hAPP (filter nat) bool (hAPP real _let_4 (hAPP _let_2 (fun real _let_4) (tendsto nat real) (hAPP _let_2 _let_2 (hAPP _let_1 _let_3 _let_5 (hAPP real _let_1 (times_times real) R_1)) (hAPP _let_2 _let_2 (hAPP _let_1 _let_3 _let_5 (hAPP real _let_1 (plus_plus real) (one_one real))) (hAPP _let_2 _let_2 (hAPP _let_1 _let_3 _let_5 (uminus_uminus real)) (hAPP _let_2 _let_2 (hAPP _let_1 _let_3 _let_5 (inverse_inverse real)) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb nat real nat) (real_1 nat)) suc)))))) R_1) sequentially)) ))))))) 15.80/16.01 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.01 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.01 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.80/16.01 ) 15.80/16.01 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (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))) ))) 15.80/16.01 ( (zero_zero real), pi ) 15.80/16.01 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.01 ( (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.01 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.01 ( (zero_zero real), skv_6 ) 15.80/16.01 ( (zero_zero real), skv_11 ) 15.80/16.01 ( (zero_zero real), skv_12 ) 15.80/16.01 ( (zero_zero real), skv_14 ) 15.80/16.01 ( pi, (zero_zero real) ) 15.80/16.01 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.01 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.80/16.01 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.01 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 15.80/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.80/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.01 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.80/16.01 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.80/16.01 ( skv_6, (zero_zero real) ) 15.80/16.01 ( skv_11, (zero_zero real) ) 15.80/16.01 ( skv_12, (zero_zero real) ) 15.80/16.01 ( skv_14, (zero_zero real) ) 15.80/16.01 ( skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.01 ) 15.80/16.01 (instantiation (let ((_let_0 (frac X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun int (fun int X_a)) _let_0)) )) 15.80/16.01 ( bool ) 15.80/16.01 ( real ) 15.80/16.01 ( int ) 15.80/16.01 ( (fun int bool) ) 15.80/16.01 ( rat ) 15.80/16.01 ( (fun bool bool) ) 15.80/16.01 ( (fun int (fun int bool)) ) 15.80/16.01 ( (product_prod int int) ) 15.80/16.01 ( (fun (fun int bool) bool) ) 15.80/16.01 ( (fun (product_prod int int) bool) ) 15.80/16.01 ( (product_prod int (product_prod int int)) ) 15.80/16.01 ( (fun int (product_prod int (product_prod int int))) ) 15.80/16.01 ( (fun int (fun int (product_prod int (product_prod int int)))) ) 15.80/16.01 ( (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 15.80/16.01 ( (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 15.80/16.01 ( (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 15.80/16.01 ( (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 15.80/16.01 ) 15.80/16.01 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun nat real))) (let ((_let_5 (power_power real))) (let ((_let_6 (fun nat _let_2))) (let ((_let_7 (fun nat _let_3))) (let ((_let_8 (fun _let_4 _let_4))) (let ((_let_9 (combs nat real real))) (let ((_let_10 (fun real _let_3))) (let ((_let_11 (fun _let_4 _let_7))) (let ((_let_12 (combb real _let_3 nat))) (let ((_let_13 (fun _let_2 _let_4))) (let ((_let_14 (combb nat real nat))) (let ((_let_15 (fun nat _let_10))) (forall ((N_1 $$unsorted)) (= (one_one real) (hAPP _let_1 real (hAPP _let_4 (fun _let_1 real) (big_co1399186613setsum nat real) (hAPP _let_4 _let_4 (hAPP _let_7 _let_8 _let_9 (hAPP _let_4 _let_7 (hAPP _let_10 _let_11 _let_12 (times_times real)) (hAPP real _let_4 (hAPP _let_7 (fun real _let_4) (combc nat real real) (hAPP _let_4 _let_7 (hAPP _let_15 _let_11 (combs nat real _let_3) (hAPP _let_1 _let_15 (hAPP (fun bool _let_10) (fun _let_1 _let_15) (combb bool _let_10 nat) (if real)) (even_odd_even nat))) (hAPP _let_4 _let_4 (hAPP _let_7 _let_8 _let_9 (hAPP _let_4 _let_7 (hAPP _let_10 _let_11 _let_12 (inverse_divide real)) (hAPP _let_2 _let_4 (hAPP _let_4 _let_13 _let_14 (hAPP real _let_4 _let_5 (hAPP int real (number_number_of real) min_1))) (hAPP nat _let_2 (hAPP _let_6 _let_6 (combc nat nat nat) (div_div nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (hAPP _let_2 _let_4 (hAPP _let_4 _let_13 _let_14 (real_1 nat)) (fact_fact nat))))) _let_0))) (hAPP real _let_4 _let_5 _let_0))) (hAPP nat _let_1 (hAPP nat (fun nat _let_1) (ord_atLeastLessThan nat) (zero_zero nat)) (hAPP nat nat suc N_1)))) ))))))))))))))))) 15.80/16.01 ( (zero_zero nat) ) 15.80/16.01 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.01 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.80/16.01 ) 15.80/16.01 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (= (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) X_1) A_3)) (hBOOL (hAPP X_a bool A_3 X_1))) )) 15.80/16.01 ( real, (zero_zero real), (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.80/16.01 ( real, (zero_zero real), (hAPP real (fun real bool) (ord_less real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.01 ( real, (zero_zero real), (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.01 ( real, (zero_zero real), (hAPP real (fun real bool) (ord_less real) pi) ) 15.80/16.01 ( real, (one_one real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))) ) 15.80/16.01 ( real, pi, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.80/16.01 ( real, pi, (hAPP real (fun real bool) (ord_less real) (zero_zero real)) ) 15.80/16.01 ( real, pi, (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.01 ( real, pi, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi))) ) 15.80/16.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.01 ( 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_14) ) 15.80/16.01 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.80/16.01 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less real) (zero_zero real)) ) 15.80/16.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less real) pi) ) 15.80/16.01 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.80/16.01 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less real) (zero_zero real)) ) 15.80/16.01 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less real) (one_one real)) ) 15.80/16.01 ( real, skv_2, (hAPP real (fun real bool) (ord_less real) (zero_zero real)) ) 15.80/16.01 ( real, skv_6, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.80/16.02 ( real, skv_10, (hAPP real (fun real bool) (ord_less real) (zero_zero real)) ) 15.80/16.02 ( real, skv_11, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.80/16.02 ( real, skv_12, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.80/16.02 ( real, skv_13, (hAPP real (fun real bool) (ord_less real) (zero_zero real)) ) 15.80/16.02 ( real, skv_14, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.80/16.02 ( nat, (zero_zero nat), (even_odd_even nat) ) 15.80/16.02 ( nat, (zero_zero nat), prime ) 15.80/16.02 ( nat, (one_one nat), (even_odd_even nat) ) 15.80/16.02 ( nat, (one_one nat), prime ) 15.80/16.02 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) ) 15.80/16.02 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), prime ) 15.80/16.02 ( (fun nat bool), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)), (finite_finite_1 nat) ) 15.80/16.02 ( (fun nat bool), (hAPP bool (fun nat bool) (combk bool nat) fTrue), (hAPP (fun nat int) (fun (fun nat bool) bool) (nat_tr1645093318rphism nat int) (semiring_1_of_nat int)) ) 15.80/16.02 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less int) pls) ) 15.80/16.02 ( int, (zero_zero int), nat_is_nat ) 15.80/16.02 ( int, (zero_zero int), (even_odd_even int) ) 15.80/16.02 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))) ) 15.80/16.02 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less int) min_1) ) 15.80/16.02 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less int) t) ) 15.80/16.02 ( int, pls, (hAPP int (fun int bool) (ord_less_eq int) min_1) ) 15.80/16.02 ( int, (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.80/16.02 ( int, (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 15.80/16.02 ( int, (one_one int), nat_neg ) 15.80/16.02 ( int, (one_one int), zEven ) 15.80/16.02 ( int, (one_one int), nat_is_nat ) 15.80/16.02 ( int, (one_one int), (even_odd_even int) ) 15.80/16.02 ( int, (one_one int), (hAPP int (fun int bool) (ord_less int) t) ) 15.80/16.02 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), zprime ) 15.80/16.02 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 15.80/16.02 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) s) ) 15.80/16.02 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)) ) 15.80/16.02 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 15.80/16.02 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) t) ) 15.80/16.02 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 15.80/16.02 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))) ) 15.80/16.02 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) skv_3) ) 15.80/16.02 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_3)) ) 15.80/16.02 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (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_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 15.80/16.02 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) skv_9) ) 15.80/16.02 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_9)) ) 15.80/16.02 ( int, min_1, (hAPP int (fun int bool) (ord_less int) pls) ) 15.80/16.02 ( int, min_1, (hAPP int (fun int bool) (ord_less_eq int) pls) ) 15.80/16.02 ( int, min_1, (hAPP int (fun int bool) (ord_less int) min_1) ) 15.80/16.02 ( int, min_1, (hAPP int (fun int bool) (ord_less_eq int) min_1) ) 15.80/16.02 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.80/16.02 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), zprime ) 15.80/16.02 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), nat_is_nat ) 15.80/16.02 ( int, (hAPP int int (number_number_of int) min_1), nat_neg ) 15.80/16.02 ( int, (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) ) 15.80/16.02 ( int, s, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.80/16.02 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) ) 15.80/16.02 ( int, (hAPP int int (number_number_of int) pls), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.80/16.02 ( int, (hAPP int int (number_number_of int) pls), nat_neg ) 15.80/16.02 ( int, t, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) ) 15.80/16.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))), twoSqu1091635170sum2sq ) 15.80/16.02 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.80/16.02 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), nat_is_nat ) 15.80/16.02 ( 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))) (zero_zero int)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t)))) ) 15.80/16.02 ( int, skv_3, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.80/16.02 ( int, skv_9, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.80/16.02 ( (fun int bool), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1) ) 15.80/16.02 ( (fun int bool), zEven, (hAPP int (fun (fun int bool) bool) (member int) (one_one int)) ) 15.80/16.02 ( (filter real), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (filter real) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)) (zero_zero real))))) ) 15.80/16.02 ( (filter nat), sequentially, (trivial_limit nat) ) 15.80/16.02 ( (filter nat), sequentially, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))) ) 15.80/16.02 ) 15.80/16.02 (instantiation (forall ((R_4 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) R_4) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real (real_1 int) (hAPP real int (archim2085082626_floor real) R_4))) (one_one real)))) ) 15.80/16.02 ( (zero_zero real) ) 15.80/16.02 ( (one_one real) ) 15.80/16.02 ( pi ) 15.80/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.02 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.02 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.02 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.80/16.02 ) 15.80/16.02 (instantiation (let ((_let_0 (even_odd_even int))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (or (hBOOL (hAPP int bool _let_0 X_1)) (hBOOL (hAPP int bool _let_0 Y_1))) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) X_1) Y_1)))) )) 15.80/16.02 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.80/16.02 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 15.80/16.02 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.80/16.02 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1 ) 15.80/16.02 ) 15.80/16.02 (instantiation (forall ((N $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N) (zero_zero nat)))) ) 15.80/16.02 ( (zero_zero nat) ) 15.80/16.02 ) 15.80/16.02 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun _let_1 _let_1))) (let ((_let_4 (fun (fun nat nat) _let_1))) (let ((_let_5 (combb nat real nat))) (let ((_let_6 (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) (combc nat nat nat) (plus_plus nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (hBOOL (hAPP _let_1 bool (summable real) (hAPP _let_1 _let_1 (hAPP _let_2 _let_3 (combs nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP _let_1 _let_1 (hAPP _let_0 _let_3 (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_4 _let_5 (real_1 nat)) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb nat nat nat) (fact_fact nat)) _let_6))))) (hAPP _let_0 _let_1 (hAPP _let_1 _let_4 _let_5 (hAPP real _let_1 (power_power real) X_1)) _let_6))))) )))))))) 15.80/16.02 ( (hAPP int real (number_number_of real) min_1) ) 15.80/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.02 ) 15.80/16.02 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (= X (hAPP complex real re (hAPP real complex (hAPP real (fun real complex) complex_1 X) Y))) ) 15.80/16.02 ( (zero_zero real), (zero_zero real) ) 15.80/16.02 ( (zero_zero real), (one_one real) ) 15.80/16.02 ( (one_one real), (zero_zero real) ) 15.80/16.02 ) 15.80/16.02 (instantiation (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) Ma) (hAPP int int (number_number_of int) N_1))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real (real_1 int) Ma)) (hAPP int real (number_number_of real) N_1)))) ) 15.80/16.02 ( (zero_zero int), pls ) 15.80/16.02 ( (zero_zero int), (hAPP int int bit1 pls) ) 15.80/16.02 ( min_1, pls ) 15.80/16.02 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), pls ) 15.80/16.03 ( t, pls ) 15.80/16.03 ( t, (hAPP int int bit1 pls) ) 15.80/16.03 ) 15.80/16.03 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) X) (hAPP nat int (hAPP int (fun nat int) (power_power int) X) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.80/16.03 ( (zero_zero int) ) 15.80/16.03 ( (one_one int) ) 15.80/16.03 ( min_1 ) 15.80/16.03 ( s ) 15.80/16.03 ( s1 ) 15.80/16.03 ( skv_8 ) 15.80/16.03 ) 15.80/16.03 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) min_1)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit0 K)) min_1))) ))) 15.80/16.03 ( pls ) 15.80/16.03 ( (hAPP int int bit1 pls) ) 15.80/16.03 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/16.03 ( min_1 ) 15.80/16.03 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.80/16.03 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.03 ) 15.80/16.03 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_1)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) (hAPP real real (exp real) X_1)))) ))) 15.80/16.03 ( pi ) 15.80/16.03 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.03 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.03 ( skv_6 ) 15.80/16.03 ( skv_11 ) 15.80/16.03 ( skv_12 ) 15.80/16.03 ( skv_14 ) 15.80/16.03 ) 15.80/16.03 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) min_1))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool _let_0 K)) (hBOOL (hAPP int bool _let_0 (hAPP int int bit1 K)))) )) 15.80/16.03 ( pls ) 15.80/16.03 ( (hAPP int int bit1 pls) ) 15.80/16.03 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/16.03 ( min_1 ) 15.80/16.03 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.80/16.03 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.03 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.03 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.80/16.03 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.80/16.03 ) 15.80/16.03 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N) (hAPP nat nat suc N))) ) 15.80/16.03 ( (zero_zero nat) ) 15.80/16.03 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.03 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.80/16.03 ) 15.80/16.03 (instantiation (forall ((Nat_4 $$unsorted)) (not (= (zero_zero nat) (hAPP nat nat suc Nat_4))) ) 15.80/16.03 ( (zero_zero nat) ) 15.80/16.03 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.03 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.80/16.03 ) 15.80/16.03 (instantiation (forall ((N $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc N)) N))) ) 15.80/16.03 ( (zero_zero nat) ) 15.80/16.03 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.03 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.80/16.03 ) 15.80/16.03 (instantiation (forall ((B_1_1 $$unsorted)) (= (hBOOL (ti bool B_1_1)) (hBOOL B_1_1)) ) 15.80/16.03 ( fFalse ) 15.80/16.03 ( fTrue ) 15.80/16.03 ) 15.80/16.03 (instantiation (let ((_let_0 (fun int bool))) (forall ((K $$unsorted) (L $$unsorted)) (= (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))) )) 15.80/16.03 ( (zero_zero int), (one_one int) ) 15.80/16.03 ( (zero_zero int), min_1 ) 15.80/16.03 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.03 ( (zero_zero int), s ) 15.80/16.03 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.80/16.03 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.03 ( (zero_zero int), skv_3 ) 15.80/16.03 ( (zero_zero int), skv_9 ) 15.80/16.03 ( pls, (zero_zero int) ) 15.80/16.03 ( pls, min_1 ) 15.80/16.03 ( (one_one int), t ) 15.80/16.03 ( min_1, pls ) 15.80/16.03 ( min_1, min_1 ) 15.80/16.03 ) 15.80/16.03 (instantiation (let ((_let_0 (image X_b X_a))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (= _let_0 (ti (fun (fun X_b X_a) (fun (fun X_b bool) (fun X_a bool))) _let_0)) )) 15.80/16.03 ( real, real ) 15.80/16.03 ( nat, nat ) 15.80/16.03 ( int, int ) 15.80/16.03 ( (product_prod int int), (product_prod int int) ) 15.80/16.03 ) 15.80/16.03 (instantiation (let ((_let_0 (fun real bool))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) cos) X_1) (hAPP real real (uminus_uminus real) (hAPP real real sin X_1)))) )) 15.80/16.03 ( (zero_zero real) ) 15.80/16.03 ( pi ) 15.80/16.03 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.03 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.80/16.03 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.03 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/16.03 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.03 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.03 ) 15.80/16.03 (instantiation (forall ((N $$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))))) ) 15.80/16.03 ( (zero_zero nat) ) 15.80/16.03 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.03 ) 15.80/16.03 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) (hAPP real real cos X))) (one_one real))) ) 15.80/16.03 ( (zero_zero real) ) 15.80/16.03 ( pi ) 15.80/16.03 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.03 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.03 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.80/16.03 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.03 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/16.03 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.03 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.03 ( skv_14 ) 15.80/16.03 ) 15.80/16.03 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K1) K2)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K1)) (hAPP int int bit1 K2)))) ))) 15.80/16.03 ( min_1, min_1 ) 15.80/16.03 ) 15.80/16.03 (instantiation (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP int bool (even_odd_even int) X_1)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) X_1))) ) 15.80/16.03 ( (zero_zero int) ) 15.80/16.03 ( (one_one int) ) 15.80/16.03 ) 15.80/16.03 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP complex real re X)) (hAPP complex real (norm_norm complex) X))) ) 15.80/16.03 ( ii ) 15.80/16.03 ( (zero_zero complex) ) 15.80/16.03 ( (one_one complex) ) 15.80/16.03 ) 15.80/16.03 (instantiation (forall ((T_1 $$unsorted)) (ord (filter T_1)) ) 15.80/16.03 ( real ) 15.80/16.03 ( nat ) 15.80/16.03 ) 15.80/16.03 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K)) min_1)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) min_1))) ))) 15.80/16.03 ( pls ) 15.80/16.03 ( (hAPP int int bit1 pls) ) 15.80/16.03 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/16.03 ( min_1 ) 15.80/16.03 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.80/16.03 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.03 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.03 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.80/16.03 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.80/16.03 ) 15.80/16.03 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((K $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K)) (hAPP int int bit0 L))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L))) ))) 15.80/16.03 ( min_1, pls ) 15.80/16.03 ) 15.80/16.03 (instantiation (let ((_let_0 (fun nat bool))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) Ma) (hAPP nat nat suc N_1))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) Ma) N_1))) )) 15.80/16.03 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.03 ) 15.80/16.03 (instantiation (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) N_1) (zero_zero int))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (real_1 int) N_1)) (zero_zero real)))) ) 15.80/16.03 ( (zero_zero int) ) 15.80/16.03 ( (one_one int) ) 15.80/16.03 ( min_1 ) 15.80/16.03 ) 15.80/16.03 (instantiation (forall ((D $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) D) (hAPP int int (abs_abs int) D))) ) 15.80/16.03 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.03 ) 15.80/16.03 (instantiation (forall ((Z $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int (abs_abs int) Z)) (one_one int))) (= (zero_zero int) (ti int Z))) ) 15.80/16.03 ( pls ) 15.80/16.03 ( m ) 15.80/16.03 ( min_1 ) 15.80/16.03 ( s ) 15.80/16.03 ( s1 ) 15.80/16.03 ( t ) 15.80/16.03 ) 15.80/16.03 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (ord_less int))) (forall ((W_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 W_1) _let_1)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (hAPP int int bit0 W_1)) _let_1))) )))) 15.80/16.03 ( pls ) 15.80/16.03 ( (hAPP int int bit1 pls) ) 15.80/16.03 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/16.03 ( min_1 ) 15.80/16.03 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.80/16.03 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.03 ) 15.80/16.03 (instantiation (let ((_let_0 (zero_zero int))) (let ((_let_1 (fun int rat))) (forall ((A_1 $$unsorted)) (= (hAPP int rat (hAPP int _let_1 fract _let_0) (one_one int)) (hAPP int rat (hAPP int _let_1 fract A_1) _let_0)) ))) 15.80/16.03 ( (zero_zero int) ) 15.80/16.03 ( (one_one int) ) 15.80/16.03 ) 15.80/16.03 (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))) ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_6 ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_14 ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_10 ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_13 ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less real) (one_one real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))), (zero_zero real) ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.80/16.03 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi))), pi ) 15.80/16.03 ( real, (hAPP real (fun real bool) (ord_less_eq real) skv_14), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.03 ( nat, (even_odd_even nat), (zero_zero nat) ) 15.80/16.03 ( nat, (even_odd_even nat), (one_one nat) ) 15.80/16.03 ( nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.03 ( nat, prime, (zero_zero nat) ) 15.80/16.03 ( nat, prime, (one_one nat) ) 15.80/16.03 ( nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.03 ( (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 15.80/16.03 ( (fun nat bool), (hAPP (fun nat int) (fun (fun nat bool) bool) (nat_tr1645093318rphism nat int) (semiring_1_of_nat int)), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 15.80/16.03 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 15.80/16.03 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.03 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 15.80/16.03 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_3 ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_9 ) 15.80/16.04 ( int, zprime, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ( int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ( int, nat_neg, (one_one int) ) 15.80/16.04 ( int, nat_neg, (hAPP int int (number_number_of int) min_1) ) 15.80/16.04 ( int, nat_neg, (hAPP int int (number_number_of int) pls) ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less int) pls), (zero_zero int) ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 15.80/16.04 ( int, nat_is_nat, (zero_zero int) ) 15.80/16.04 ( int, nat_is_nat, (one_one int) ) 15.80/16.04 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.04 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.04 ( int, (even_odd_even int), (zero_zero int) ) 15.80/16.04 ( int, (even_odd_even int), (one_one int) ) 15.80/16.04 ( int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))), (zero_zero int) ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less int) min_1), (zero_zero int) ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 15.80/16.04 ( int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 15.80/16.04 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ( int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less int) t), (zero_zero int) ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less int) t), (one_one int) ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less int) t), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ( int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun int bool) (ord_less 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)))), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less int) skv_3), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_3)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ( 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_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ( int, (hAPP int (fun int bool) (ord_less int) skv_9), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_9)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ( (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 15.80/16.04 ( (fun int bool), (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.80/16.04 ( (filter real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (filter real) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)) (zero_zero real))))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.04 ( (filter nat), (trivial_limit nat), sequentially ) 15.80/16.04 ( (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 15.80/16.04 ) 15.80/16.04 (instantiation (let ((_let_0 (hAPP nat int (semiring_1_of_nat int) M))) (forall ((M $$unsorted)) (= _let_0 (hAPP int int (abs_abs int) _let_0)) )) 15.80/16.04 ( (zero_zero nat) ) 15.80/16.04 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.04 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.04 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.04 ) 15.80/16.04 (instantiation (forall ((N $$unsorted)) (= N (hAPP int nat nat_1 (hAPP nat int (semiring_1_of_nat int) N))) ) 15.80/16.04 ( (zero_zero nat) ) 15.80/16.04 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.04 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.04 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.04 ) 15.80/16.04 (instantiation (forall ((N $$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)))))) ) 15.80/16.04 ( (zero_zero nat) ) 15.80/16.04 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.04 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.80/16.04 ) 15.80/16.04 (instantiation (forall ((X_1 $$unsorted)) (= (not (hBOOL (hAPP int bool nat_neg X_1))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X_1))) ) 15.80/16.04 ( (one_one int) ) 15.80/16.04 ( min_1 ) 15.80/16.04 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.04 ( (hAPP int int (number_number_of int) min_1) ) 15.80/16.04 ( s ) 15.80/16.04 ( (hAPP int int (number_number_of int) pls) ) 15.80/16.04 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.04 ( skv_3 ) 15.80/16.04 ( skv_9 ) 15.80/16.04 ) 15.80/16.04 (instantiation (let ((_let_0 (one_one real))) (forall ((X_1 $$unsorted)) (= (= _let_0 (hAPP real real sqrt X_1)) (= _let_0 X_1)) )) 15.80/16.04 ( (zero_zero real) ) 15.80/16.04 ( (one_one real) ) 15.80/16.04 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.04 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.04 ) 15.80/16.04 (instantiation (let ((_let_0 (fun int bool))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) K1) K2)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int bit1 K1)) (hAPP int int bit0 K2)))) )) 15.80/16.04 ( (zero_zero int), (zero_zero int) ) 15.80/16.04 ( (zero_zero int), (one_one int) ) 15.80/16.04 ( (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ( (zero_zero int), min_1 ) 15.80/16.04 ( min_1, (zero_zero int) ) 15.80/16.04 ( min_1, pls ) 15.80/16.04 ( min_1, min_1 ) 15.80/16.04 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 15.80/16.04 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 15.80/16.04 ( t, (zero_zero int) ) 15.80/16.04 ( t, (one_one int) ) 15.80/16.04 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.04 ) 15.80/16.04 (instantiation (let ((_let_0 (fun int bool))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) min_1) K)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) min_1) (hAPP int int bit0 K)))) )) 15.80/16.04 ( (zero_zero int) ) 15.80/16.04 ( pls ) 15.80/16.04 ( (hAPP int int bit1 pls) ) 15.80/16.04 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/16.04 ( min_1 ) 15.80/16.04 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.80/16.04 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.04 ) 15.80/16.04 (instantiation (forall ((Real1_1 $$unsorted) (Real2_1 $$unsorted)) (= (zero_zero nat) (hAPP complex nat complex_size (hAPP real complex (hAPP real (fun real complex) complex_1 Real1_1) Real2_1))) ) 15.80/16.04 ( (zero_zero real), (zero_zero real) ) 15.80/16.04 ( (zero_zero real), (one_one real) ) 15.80/16.04 ( (one_one real), (zero_zero real) ) 15.80/16.04 ) 15.80/16.04 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) min_1)) (hAPP real real cos X))) ) 15.80/16.04 ( (zero_zero real) ) 15.80/16.04 ( pi ) 15.80/16.04 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.04 ( (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)))) ) 15.80/16.04 ( (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) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.05 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.05 ( skv_14 ) 15.80/16.05 ) 15.80/16.05 (instantiation (forall ((J_2 $$unsorted) (I_1 $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) J_2) I_1)) I_1))) ) 15.80/16.05 ( (one_one nat), (one_one nat) ) 15.80/16.05 ) 15.80/16.05 (instantiation (let ((_let_0 (real_1 int))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) X_1) Y_1)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real _let_0 X_1)) (hAPP int real _let_0 Y_1)))) )) 15.80/16.05 ( (zero_zero int), (one_one int) ) 15.80/16.05 ( (zero_zero int), min_1 ) 15.80/16.05 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.05 ( (zero_zero int), s ) 15.80/16.05 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.80/16.05 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.05 ( (zero_zero int), skv_3 ) 15.80/16.05 ( (zero_zero int), skv_9 ) 15.80/16.05 ( (one_one int), t ) 15.80/16.05 ( min_1, pls ) 15.80/16.05 ( min_1, min_1 ) 15.80/16.05 ) 15.80/16.05 (instantiation (forall ((I_1 $$unsorted) (M $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I_1) (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) I_1) M)))) ) 15.80/16.05 ( (one_one nat), (one_one nat) ) 15.80/16.05 ) 15.80/16.05 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (number_number_of int))) (forall ((K $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int _let_2 K)) (hAPP int int _let_2 L))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L))) )))) 15.80/16.05 ( pls, pls ) 15.80/16.05 ( pls, (hAPP int int bit1 pls) ) 15.80/16.05 ( pls, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/16.05 ( pls, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.80/16.05 ) 15.80/16.05 (instantiation (let ((_let_0 (zero_zero real))) (forall ((N $$unsorted)) (= _let_0 (hAPP real real (hAPP nat (fun real real) root N) _let_0)) )) 15.80/16.05 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.05 ) 15.80/16.05 (instantiation (let ((_let_0 (fun int bool))) (forall ((Z $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (one_one int)) Z)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) Z))) )) 15.80/16.05 ( (zero_zero int) ) 15.80/16.05 ( (one_one int) ) 15.80/16.05 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.05 ( min_1 ) 15.80/16.05 ( t ) 15.80/16.05 ) 15.80/16.05 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (power_power real))) (let ((_let_4 (fun nat _let_1))) (let ((_let_5 (fun _let_2 _let_2))) (let ((_let_6 (combs nat real real))) (let ((_let_7 (fun real _let_1))) (let ((_let_8 (fun _let_2 _let_4))) (let ((_let_9 (combb real _let_1 nat))) (let ((_let_10 (fun _let_0 _let_2))) (let ((_let_11 (combb nat real nat))) (let ((_let_12 (hAPP nat _let_0 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP _let_2 (fun real bool) (sums real) (hAPP _let_2 _let_2 (hAPP _let_4 _let_5 _let_6 (hAPP _let_2 _let_4 (hAPP _let_7 _let_8 _let_9 (times_times real)) (hAPP _let_2 _let_2 (hAPP _let_4 _let_5 _let_6 (hAPP _let_2 _let_4 (hAPP _let_7 _let_8 _let_9 (inverse_divide real)) (hAPP real _let_2 _let_3 (hAPP int real (number_number_of real) min_1)))) (hAPP _let_0 _let_2 (hAPP _let_2 _let_10 _let_11 (real_1 nat)) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb nat nat nat) (fact_fact nat)) _let_12))))) (hAPP _let_0 _let_2 (hAPP _let_2 _let_10 _let_11 (hAPP real _let_2 _let_3 X_1)) _let_12))) (hAPP real real cos X_1))) )))))))))))))) 15.80/16.05 ( (zero_zero real) ) 15.80/16.05 ( pi ) 15.80/16.05 ( (hAPP int real (number_number_of real) min_1) ) 15.80/16.05 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.05 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.05 ( skv_14 ) 15.80/16.05 ) 15.80/16.05 (instantiation (forall ((T_1 $$unsorted)) (comple44059174attice (filter T_1)) ) 15.80/16.05 ( real ) 15.80/16.05 ( nat ) 15.80/16.05 ) 15.80/16.05 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) X) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real (real_1 nat) (hAPP real nat natfloor X))) (one_one real)))) ) 15.80/16.05 ( (zero_zero real) ) 15.80/16.05 ( (one_one real) ) 15.80/16.05 ( pi ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.05 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.05 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.05 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.80/16.05 ) 15.80/16.05 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos X)) (one_one real))) ) 15.80/16.05 ( (zero_zero real) ) 15.80/16.05 ( pi ) 15.80/16.05 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.05 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.05 ( skv_14 ) 15.80/16.05 ) 15.80/16.05 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) min_1)) (hAPP real real sin X))) ) 15.80/16.05 ( (zero_zero real) ) 15.80/16.05 ( pi ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.05 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.05 ) 15.80/16.05 (instantiation (forall ((T_1 $$unsorted)) (preorder (filter T_1)) ) 15.80/16.05 ( real ) 15.80/16.05 ( nat ) 15.80/16.05 ) 15.80/16.05 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP nat real (real_1 nat) N)) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) N))) ) 15.80/16.05 ( (zero_zero nat) ) 15.80/16.05 ( (one_one nat) ) 15.80/16.05 ) 15.80/16.05 (instantiation (forall ((N $$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))) ) 15.80/16.05 ( (zero_zero nat) ) 15.80/16.05 ( (one_one nat) ) 15.80/16.05 ) 15.80/16.05 (instantiation (let ((_let_0 (even_odd_even int))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP int bool _let_0 X_1)) (hBOOL (hAPP int bool _let_0 (hAPP int int (uminus_uminus int) X_1)))) )) 15.80/16.05 ( pls ) 15.80/16.05 ( (one_one int) ) 15.80/16.05 ( min_1 ) 15.80/16.05 ) 15.80/16.05 (instantiation (forall ((Z $$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))) ) 15.80/16.05 ( (zero_zero int) ) 15.80/16.05 ( (one_one int) ) 15.80/16.05 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.05 ( min_1 ) 15.80/16.05 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.05 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.05 ) 15.80/16.05 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP _let_1 bool (summable real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) sin_coeff)) (hAPP real _let_1 (power_power real) X_1)))) )))) 15.80/16.05 ( (hAPP int real (number_number_of real) min_1) ) 15.80/16.05 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.05 ) 15.80/16.05 (instantiation (forall ((X $$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))) ) 15.80/16.05 ( ii ) 15.80/16.05 ( (zero_zero complex) ) 15.80/16.05 ( (one_one complex) ) 15.80/16.05 ) 15.80/16.05 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP nat nat suc N))) ) 15.80/16.05 ( (zero_zero nat) ) 15.80/16.05 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.05 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.80/16.05 ) 15.80/16.05 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int (fun _let_0 bool) (member int) X_1))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP _let_0 bool _let_1 zOdd)) (not (hBOOL (hAPP _let_0 bool _let_1 zEven)))) ))) 15.80/16.05 ( (one_one int) ) 15.80/16.05 ) 15.80/16.05 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((K $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit0 K)) (hAPP int int bit0 L))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L))) ))) 15.80/16.05 ( pls, pls ) 15.80/16.05 ) 15.80/16.05 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (one_one nat))) (forall ((N $$unsorted)) (= _let_1 (hAPP nat nat (hAPP nat _let_0 (gcd_gcd nat) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N) _let_1)) N)) ))) 15.80/16.05 ( (one_one nat) ) 15.80/16.05 ) 15.80/16.05 (instantiation (let ((_let_0 (fun int bool))) (forall ((A_2 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_2) (zero_zero int)) Ma)) (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) Ma) A_2))) )) 15.80/16.05 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.05 ) 15.80/16.05 (instantiation (let ((_let_0 (real_1 int))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real _let_0 N_1)) (one_one real))) (hAPP int real _let_0 Ma))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) N_1) Ma))) )) 15.80/16.05 ( (zero_zero int), (zero_zero int) ) 15.80/16.05 ( (zero_zero int), (one_one int) ) 15.80/16.05 ( (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.05 ( (zero_zero int), min_1 ) 15.80/16.05 ( min_1, (zero_zero int) ) 15.80/16.05 ( min_1, min_1 ) 15.80/16.05 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.05 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 15.80/16.05 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 15.80/16.05 ( t, (zero_zero int) ) 15.80/16.05 ( t, (one_one int) ) 15.80/16.05 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.05 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.06 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.06 ) 15.80/16.06 (instantiation (forall ((Z_1 $$unsorted)) (= (zero_zero int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP int int (uminus_uminus int) Z_1)) Z_1)) ) 15.80/16.06 ( pls ) 15.80/16.06 ( (one_one int) ) 15.80/16.06 ( min_1 ) 15.80/16.06 ) 15.80/16.06 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real sqrt X_1)) _let_0)) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X_1) _let_0))) )))) 15.80/16.06 ( (zero_zero real) ) 15.80/16.06 ( (one_one real) ) 15.80/16.06 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.06 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.06 ) 15.80/16.06 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_1))) (let ((_let_3 (times_times real))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs real real real) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_1 real) _let_3) sin)) sin)) X_1) (hAPP real real (hAPP real _let_1 _let_3 (hAPP real real (hAPP real _let_1 _let_3 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real cos X_1))) (hAPP real real sin X_1)))) ))))) 15.80/16.06 ( (zero_zero real) ) 15.80/16.06 ( pi ) 15.80/16.06 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.06 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.06 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.80/16.06 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.06 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/16.06 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.06 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.06 ( skv_14 ) 15.80/16.06 ) 15.80/16.06 (instantiation (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))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (and (or (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Y_1) _let_0)) (hBOOL (hAPP real bool _let_3 X_1))) (or (hBOOL (hAPP real bool _let_3 Y_1)) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X_1) _let_0)))) (hBOOL (hAPP real bool _let_3 (hAPP real real (hAPP real (fun real real) (inverse_divide real) X_1) Y_1)))) ))))) 15.80/16.06 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.06 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.06 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.06 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.80/16.06 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.06 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.06 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.06 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.06 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.06 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.06 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.06 ) 15.80/16.06 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X_1) _let_0)) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real sqrt X_1)) _let_0))) )))) 15.80/16.06 ( (zero_zero real) ) 15.80/16.06 ( (one_one real) ) 15.80/16.06 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.06 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.06 ) 15.80/16.06 (instantiation (let ((_let_0 (hAPP int complex (number_number_of complex) W))) (forall ((W $$unsorted)) (= _let_0 (hAPP complex complex cnj _let_0)) )) 15.80/16.06 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/16.06 ( min_1 ) 15.80/16.06 ) 15.80/16.06 (instantiation (let ((_let_0 (even_odd_even nat))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (= (hBOOL (hAPP nat bool _let_0 N_1)) (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) N_1)))) )) 15.80/16.06 ( (one_one nat), (one_one nat) ) 15.80/16.06 ) 15.80/16.06 (instantiation (let ((_let_0 (fun code_code_numeral X_a))) (let ((_let_1 (code_c600343653l_case X_a))) (forall ((X_a $$unsorted)) (= _let_1 (ti (fun X_a (fun _let_0 _let_0)) _let_1)) ))) 15.80/16.06 ( nat ) 15.80/16.06 ( (fun nat nat) ) 15.80/16.06 ( int ) 15.80/16.06 ( code_code_numeral ) 15.80/16.06 ( (product_prod code_code_numeral code_code_numeral) ) 15.80/16.06 ( (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 15.80/16.06 ) 15.80/16.06 (instantiation (let ((_let_0 (fun int bool))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (hAPP int int bit0 K)) min_1)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) K) min_1))) )) 15.80/16.06 ( (zero_zero int) ) 15.80/16.06 ( pls ) 15.80/16.06 ( (hAPP int int bit1 pls) ) 15.80/16.06 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/16.06 ( (one_one int) ) 15.80/16.06 ( min_1 ) 15.80/16.06 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.80/16.06 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.06 ) 15.80/16.06 (instantiation (forall ((M $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (hAPP int int (fact_fact int) M))) ) 15.80/16.06 ( (zero_zero int) ) 15.80/16.06 ( (one_one int) ) 15.80/16.06 ) 15.80/16.06 (instantiation (let ((_let_0 (fun int bool))) (forall ((W_1 $$unsorted) (Z $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) W_1) Z)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W_1) (hAPP int int (hAPP int (fun int int) (plus_plus int) Z) (one_one int))))) )) 15.80/16.06 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.80/16.06 ( (zero_zero int), (one_one int) ) 15.80/16.06 ( (zero_zero int), min_1 ) 15.80/16.06 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.06 ( (zero_zero int), s ) 15.80/16.06 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.80/16.06 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.06 ( (zero_zero int), skv_3 ) 15.80/16.06 ( (zero_zero int), skv_9 ) 15.80/16.06 ( (one_one int), t ) 15.80/16.06 ( min_1, pls ) 15.80/16.06 ( min_1, min_1 ) 15.80/16.06 ( s, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.80/16.06 ( t, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.80/16.06 ( skv_3, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.80/16.06 ( skv_9, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.80/16.06 ) 15.80/16.06 (instantiation (let ((_let_0 (even_odd_even nat))) (let ((_let_1 (hBOOL (hAPP nat bool _let_0 Y_1)))) (let ((_let_2 (hBOOL (hAPP nat bool _let_0 X_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (or (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) X_1) Y_1)) (and _let_1 _let_2) (and (not _let_1) (not _let_2))) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) X_1) Y_1)))) )))) 15.80/16.06 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.06 ) 15.80/16.06 (instantiation (let ((_let_0 (fun nat nat))) (forall ((N $$unsorted) (M $$unsorted)) (= (zero_zero nat) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) N) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N) M))) )) 15.80/16.06 ( (one_one nat), (one_one nat) ) 15.80/16.06 ) 15.80/16.06 (instantiation (forall ((K_4 $$unsorted)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP nat int (semiring_1_of_nat int) K_4)) (zero_zero int)))) ) 15.80/16.06 ( (zero_zero nat) ) 15.80/16.06 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.06 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.06 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.06 ) 15.80/16.06 (instantiation (let ((_let_0 (number_of_frac X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun int X_a) _let_0)) )) 15.80/16.06 ( bool ) 15.80/16.06 ( real ) 15.80/16.06 ( nat ) 15.80/16.06 ( (fun nat bool) ) 15.80/16.06 ( (fun nat nat) ) 15.80/16.06 ( int ) 15.80/16.06 ( (fun int bool) ) 15.80/16.06 ( (fun nat int) ) 15.80/16.06 ( (fun real real) ) 15.80/16.06 ( (fun nat real) ) 15.80/16.06 ( (fun int int) ) 15.80/16.06 ( rat ) 15.80/16.06 ( (fun int rat) ) 15.80/16.06 ( (fun bool bool) ) 15.80/16.06 ( (fun int (fun bool bool)) ) 15.80/16.06 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 15.80/16.06 ( (fun int (fun int bool)) ) 15.80/16.06 ( quickcheck_code_int ) 15.80/16.06 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 15.80/16.06 ( (product_prod int int) ) 15.80/16.06 ( (fun int (product_prod int int)) ) 15.80/16.06 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 15.80/16.06 ( (fun (fun int bool) bool) ) 15.80/16.06 ( (fun (product_prod int int) bool) ) 15.80/16.06 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 15.80/16.06 ( (product_prod int (product_prod int int)) ) 15.80/16.06 ( (fun int (product_prod int (product_prod int int))) ) 15.80/16.06 ( (fun (fun int int) (fun int bool)) ) 15.80/16.06 ( (fun int (fun (product_prod int int) bool)) ) 15.80/16.06 ( (fun int (fun (fun int bool) bool)) ) 15.80/16.06 ( (list int) ) 15.80/16.06 ( (fun nat (fun bool bool)) ) 15.80/16.06 ( (fun int (fun int (product_prod int (product_prod int int)))) ) 15.80/16.06 ( (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 15.80/16.06 ( (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 15.80/16.06 ( (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 15.80/16.06 ( (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 15.80/16.06 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 15.80/16.06 ( (fun (product_prod int int) int) ) 15.80/16.06 ( (fun int (fun int (fun int bool))) ) 15.80/16.06 ( (fun int real) ) 15.80/16.06 ( (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 15.80/16.06 ( (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 15.80/16.06 ) 15.80/16.06 (instantiation (let ((_let_0 (measure X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun (fun X_a nat) (fun (product_prod X_a X_a) bool)) _let_0)) )) 15.80/16.06 ( real ) 15.80/16.06 ( nat ) 15.80/16.06 ( int ) 15.80/16.06 ( complex ) 15.80/16.06 ( quickcheck_code_int ) 15.80/16.06 ( (product_prod int int) ) 15.80/16.06 ( (product_prod nat nat) ) 15.80/16.06 ( code_code_numeral ) 15.80/16.06 ) 15.80/16.06 (instantiation (forall ((R_4 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (minus_minus real) R_4) (one_one real))) (hAPP int real (real_1 int) (hAPP real int (archim2085082626_floor real) R_4)))) ) 15.80/16.06 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.80/16.06 ) 15.80/16.06 (instantiation (let ((_let_0 (real_1 nat))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real _let_0 N_1)) (one_one real))) (hAPP nat real _let_0 Ma))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N_1) Ma))) )) 15.80/16.06 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.06 ) 15.80/16.06 (instantiation (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) (hAPP nat real (real_1 nat) N_1)))) ) 15.80/16.06 ( (zero_zero nat) ) 15.80/16.06 ( (one_one nat) ) 15.80/16.06 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.06 ) 15.80/16.06 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (forall ((N $$unsorted)) (= (zero_zero real) (hAPP real real sin (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP nat real (real_1 nat) N))) pi))) ))) 15.80/16.06 ( (zero_zero nat) ) 15.80/16.06 ( (one_one nat) ) 15.80/16.06 ) 15.80/16.06 (instantiation (let ((_let_0 (prod X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (= _let_0 (ti (fun (fun X_a bool) (fun (fun X_b bool) (fun (product_prod X_a X_b) bool))) _let_0)) )) 15.80/16.06 ( real, real ) 15.80/16.06 ( nat, nat ) 15.80/16.06 ( int, int ) 15.80/16.06 ( int, (product_prod int int) ) 15.80/16.06 ( quickcheck_code_int, quickcheck_code_int ) 15.80/16.06 ( (product_prod int int), (product_prod int int) ) 15.80/16.06 ( (product_prod nat nat), (product_prod nat nat) ) 15.80/16.06 ( code_code_numeral, code_code_numeral ) 15.80/16.06 ) 15.80/16.06 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (forall ((Ma $$unsorted) (X_2 $$unsorted) (Xa $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong X_2) Xa) Ma)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcongm Ma) X_2) Xa))) ))) 15.80/16.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.80/16.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s1, s ) 15.80/16.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_3 ) 15.80/16.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_9 ) 15.80/16.07 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.80/16.07 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP 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_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.80/16.07 ) 15.80/16.07 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (or (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Z_1) W)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 W) Z_1))) ))) 15.80/16.07 ( (zero_zero int), (one_one int) ) 15.80/16.07 ( (zero_zero int), min_1 ) 15.80/16.07 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.07 ( (zero_zero int), s ) 15.80/16.07 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.80/16.07 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.07 ( (zero_zero int), skv_3 ) 15.80/16.07 ( (zero_zero int), skv_9 ) 15.80/16.07 ( pls, min_1 ) 15.80/16.07 ( (one_one int), (zero_zero int) ) 15.80/16.07 ( (one_one int), t ) 15.80/16.07 ( min_1, (zero_zero int) ) 15.80/16.07 ( min_1, pls ) 15.80/16.07 ( min_1, min_1 ) 15.80/16.07 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.80/16.07 ( s, (zero_zero int) ) 15.80/16.07 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.80/16.07 ( t, (one_one int) ) 15.80/16.07 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.80/16.07 ( skv_3, (zero_zero int) ) 15.80/16.07 ( skv_9, (zero_zero int) ) 15.80/16.07 ) 15.80/16.07 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less int) min_1))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool _let_0 K)) (hBOOL (hAPP int bool _let_0 (hAPP int int bit1 K)))) )) 15.80/16.07 ( pls ) 15.80/16.07 ( (hAPP int int bit1 pls) ) 15.80/16.07 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/16.07 ( min_1 ) 15.80/16.07 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.80/16.07 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.07 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.07 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.80/16.07 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.80/16.07 ) 15.80/16.07 (instantiation (let ((_let_0 (refl X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun (fun (product_prod X_a X_a) bool) bool) _let_0)) )) 15.80/16.07 ( real ) 15.80/16.07 ( nat ) 15.80/16.07 ( int ) 15.80/16.07 ( quickcheck_code_int ) 15.80/16.07 ( (product_prod int int) ) 15.80/16.07 ( (product_prod nat nat) ) 15.80/16.07 ( code_code_numeral ) 15.80/16.07 ) 15.80/16.07 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP _let_1 bool (summable real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) cos_coeff)) (hAPP real _let_1 (power_power real) X_1)))) )))) 15.80/16.07 ( (hAPP int real (number_number_of real) min_1) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.07 ) 15.80/16.07 (instantiation (forall ((N $$unsorted)) (not (hBOOL (hAPP int bool nat_neg (hAPP nat int (semiring_1_of_nat int) N)))) ) 15.80/16.07 ( (zero_zero nat) ) 15.80/16.07 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.07 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.07 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.07 ) 15.80/16.07 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (ord_less int))) (forall ((K $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 K) L)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (hAPP int int _let_1 K)) (hAPP int int _let_1 L)))) )))) 15.80/16.07 ( pls, pls ) 15.80/16.07 ( pls, (hAPP int int bit1 pls) ) 15.80/16.07 ) 15.80/16.07 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (powp X_a))) (forall ((X_a $$unsorted)) (= _let_1 (ti (fun _let_0 (fun _let_0 bool)) _let_1)) ))) 15.80/16.07 ( nat ) 15.80/16.07 ( int ) 15.80/16.07 ) 15.80/16.07 (instantiation (forall ((N $$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)))) ) 15.80/16.07 ( (zero_zero nat) ) 15.80/16.07 ( (one_one nat) ) 15.80/16.07 ) 15.80/16.07 (instantiation (forall ((Y $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real real arctan Y))) ) 15.80/16.07 ( (zero_zero real) ) 15.80/16.07 ( (one_one real) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 15.80/16.07 ) 15.80/16.07 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K)) pls)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) pls))) ))) 15.80/16.07 ( pls ) 15.80/16.07 ( (hAPP int int bit1 pls) ) 15.80/16.07 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/16.07 ( min_1 ) 15.80/16.07 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.80/16.07 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.07 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.07 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.80/16.07 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.80/16.07 ) 15.80/16.07 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real sin X)) (one_one real))) ) 15.80/16.07 ( (zero_zero real) ) 15.80/16.07 ( pi ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.07 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.07 ) 15.80/16.07 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_4 (times_times real))) (let ((_let_5 (fun real _let_2))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) (hAPP nat _let_1 (hAPP _let_5 (fun nat _let_1) (combc real nat real) (hAPP _let_1 _let_5 (hAPP _let_5 (fun _let_1 _let_5) (combb real _let_2 real) (power_power real)) sin)) (hAPP int nat (number_number_of nat) _let_3))) X_1) (hAPP real real (hAPP real _let_1 _let_4 (hAPP real real (hAPP real _let_1 _let_4 (hAPP int real (number_number_of real) _let_3)) (hAPP real real cos X_1))) (hAPP real real sin X_1)))) ))))))) 15.80/16.07 ( (zero_zero real) ) 15.80/16.07 ( pi ) 15.80/16.07 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.07 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.07 ( skv_14 ) 15.80/16.07 ) 15.80/16.07 (instantiation (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X_1) (one_one real))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP real nat natceiling X_1)) (one_one nat)))) ) 15.80/16.07 ( (zero_zero real) ) 15.80/16.07 ( (one_one real) ) 15.80/16.07 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.07 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.07 ( skv_14 ) 15.80/16.07 ) 15.80/16.07 (instantiation (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) N_1)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP int real (real_1 int) N_1)))) ) 15.80/16.07 ( (zero_zero int) ) 15.80/16.07 ( (one_one int) ) 15.80/16.07 ( min_1 ) 15.80/16.07 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.07 ( s ) 15.80/16.07 ( (hAPP int int (number_number_of int) pls) ) 15.80/16.07 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.07 ( skv_3 ) 15.80/16.07 ( skv_9 ) 15.80/16.07 ) 15.80/16.07 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (minus_minus real) X) (one_one real))) (hAPP nat real (real_1 nat) (hAPP real nat natfloor X)))) ) 15.80/16.07 ( (zero_zero real) ) 15.80/16.07 ( (one_one real) ) 15.80/16.07 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.80/16.07 ) 15.80/16.07 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit0 K1)) (hAPP int int bit1 K2))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K1) K2))) ))) 15.80/16.07 ( pls, min_1 ) 15.80/16.07 ) 15.80/16.07 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real (fun real real)))) (let ((_let_2 (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real (uminus_uminus real) (hAPP real real sin X_1))) (hAPP real real cos X_1)))) (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_0 (fun real _let_0) (deriv 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) (times_times real)) cos)) cos)) X_1) (hAPP real real (hAPP real _let_0 (plus_plus real) _let_2) _let_2)))) )))) 15.80/16.07 ( (zero_zero real) ) 15.80/16.07 ( pi ) 15.80/16.07 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.07 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.07 ( skv_14 ) 15.80/16.07 ) 15.80/16.07 (instantiation (forall ((X_1 $$unsorted)) (= (= X_1 (hAPP real real (exp real) (hAPP real real ln X_1))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X_1))) ) 15.80/16.07 ( (one_one real) ) 15.80/16.07 ( pi ) 15.80/16.07 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.07 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.07 ( skv_2 ) 15.80/16.07 ( skv_10 ) 15.80/16.07 ( skv_13 ) 15.80/16.07 ) 15.80/16.07 (instantiation (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP quickcheck_code_int bool (hAPP quickcheck_code_int (fun quickcheck_code_int bool) (ord_less_eq quickcheck_code_int) N_1) Ma)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP quickcheck_code_int int quickcheck_int_of N_1)) (hAPP quickcheck_code_int int quickcheck_int_of Ma)))) ) 15.80/16.07 ( (zero_zero quickcheck_code_int), (zero_zero quickcheck_code_int) ) 15.80/16.07 ) 15.80/16.07 (instantiation (forall ((X_1 $$unsorted) (A_2 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X_1) (hAPP int real (real_1 int) A_2))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP real int (archimedean_ceiling real) X_1)) A_2))) ) 15.80/16.07 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 15.80/16.07 ) 15.80/16.07 (instantiation (forall ((Z_1 $$unsorted)) (hBOOL (hAPP int bool nat_is_nat (hAPP nat int (semiring_1_of_nat int) Z_1))) ) 15.80/16.07 ( (zero_zero nat) ) 15.80/16.07 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.07 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.07 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.07 ) 15.80/16.07 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (fun nat _let_1))) (let ((_let_4 (fun real _let_1))) (let ((_let_5 (times_times real))) (let ((_let_6 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_7 (fun real _let_2))) (let ((_let_8 (combc real nat real))) (let ((_let_9 (hAPP _let_7 (fun _let_1 _let_7) (combb real _let_2 real) (power_power real)))) (let ((_let_10 (hAPP real real (hAPP real _let_1 _let_5 (hAPP real real (hAPP real _let_1 _let_5 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real cos X_2))) (hAPP real real sin X_2)))) (forall ((X_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) (hAPP _let_1 _let_1 (hAPP _let_4 (fun _let_1 _let_1) (combs real real real) (hAPP _let_1 _let_4 (hAPP _let_4 (fun _let_1 _let_4) (combb real _let_1 real) (plus_plus real)) (hAPP nat _let_1 (hAPP _let_7 _let_3 _let_8 (hAPP _let_1 _let_7 _let_9 sin)) _let_6))) (hAPP nat _let_1 (hAPP _let_7 _let_3 _let_8 (hAPP _let_1 _let_7 _let_9 cos)) _let_6))) X_2) (hAPP real real (hAPP real _let_1 (minus_minus real) _let_10) _let_10))) )))))))))))) 15.80/16.08 ( (zero_zero real) ) 15.80/16.08 ( pi ) 15.80/16.08 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.08 ( (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)))) ) 15.80/16.08 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.80/16.08 ( (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))))) ) 15.80/16.08 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/16.08 ( (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))))) ) 15.80/16.08 ( (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)))) ) 15.80/16.08 ( skv_14 ) 15.80/16.08 ) 15.80/16.08 (instantiation (let ((_let_0 (list X_a))) (let ((_let_1 (size_size _let_0))) (forall ((X_a $$unsorted)) (= _let_1 (ti (fun _let_0 nat) _let_1)) ))) 15.80/16.08 ( int ) 15.80/16.08 ) 15.80/16.08 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong A_2) B_1) Ma)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong B_1) A_2) Ma))) ))) 15.80/16.08 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.08 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.08 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.08 ( s, s1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.08 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.08 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.08 ( s1, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.08 ( s1, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.08 ( s1, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.08 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.08 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.08 ( skv_3, s1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.08 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.08 ( skv_9, s1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.08 ) 15.80/16.08 (instantiation (let ((_let_0 (zero_zero nat))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N_1) (hAPP nat nat suc _let_0))) (= _let_0 N_1)) )) 15.80/16.08 ( (zero_zero nat) ) 15.80/16.08 ) 15.80/16.08 (instantiation (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (one_one nat)) (hAPP real nat natfloor X_1))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (one_one real)) X_1))) ) 15.80/16.08 ( (zero_zero real) ) 15.80/16.08 ( (one_one real) ) 15.80/16.08 ) 15.80/16.08 (instantiation (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) Ma))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (or (hBOOL (hAPP nat bool _let_0 N_1)) (= Ma N_1)) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat suc N_1)))) )) 15.80/16.08 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.08 ) 15.80/16.08 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (accp X_a))) (forall ((X_a $$unsorted)) (= _let_1 (ti (fun (fun X_a _let_0) _let_0) _let_1)) ))) 15.80/16.08 ( bool ) 15.80/16.08 ( real ) 15.80/16.08 ( nat ) 15.80/16.08 ( (fun nat bool) ) 15.80/16.08 ( int ) 15.80/16.08 ( (fun int bool) ) 15.80/16.08 ( (product_prod real real) ) 15.80/16.08 ( (product_prod int int) ) 15.80/16.08 ( (filter real) ) 15.80/16.08 ( (filter nat) ) 15.80/16.08 ( (product_prod nat nat) ) 15.80/16.08 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.80/16.08 ( (fun nat rat) ) 15.80/16.08 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.80/16.08 ) 15.80/16.08 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP nat nat (fact_fact nat) N))) ) 15.80/16.08 ( (zero_zero nat) ) 15.80/16.08 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.08 ) 15.80/16.08 (instantiation (let ((_let_0 (finite_card X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun (fun X_a bool) nat) _let_0)) )) 15.80/16.08 ( bool ) 15.80/16.08 ( real ) 15.80/16.08 ( nat ) 15.80/16.08 ( (fun nat bool) ) 15.80/16.08 ( int ) 15.80/16.08 ( (fun int bool) ) 15.80/16.08 ( (product_prod real real) ) 15.80/16.08 ( (product_prod int int) ) 15.80/16.08 ( (filter real) ) 15.80/16.08 ( (filter nat) ) 15.80/16.08 ( (product_prod nat nat) ) 15.80/16.08 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.80/16.08 ( (fun nat rat) ) 15.80/16.08 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.80/16.08 ) 15.80/16.08 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP real real (inverse_inverse real) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) N))))) ) 15.80/16.08 ( (zero_zero nat) ) 15.80/16.08 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.08 ) 15.80/16.08 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (one_one real)))) (forall ((Y_1 $$unsorted)) (= (hBOOL (hAPP real bool _let_0 Y_1)) (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt Y_1)))) )) 15.80/16.08 ( (zero_zero real) ) 15.80/16.08 ( (one_one real) ) 15.80/16.08 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.08 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.08 ) 15.80/16.08 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) N))) (zero_zero int))) ) 15.80/16.08 ( (zero_zero nat) ) 15.80/16.08 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.08 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.08 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.08 ) 15.80/16.08 (instantiation (forall ((V_1 $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP int nat (number_number_of nat) V_1))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) V_1))) ) 15.80/16.08 ( (zero_zero int) ) 15.80/16.08 ( pls ) 15.80/16.08 ( (hAPP int int bit1 pls) ) 15.80/16.08 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/16.08 ( (one_one int) ) 15.80/16.08 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.80/16.08 ( min_1 ) 15.80/16.08 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.80/16.08 ) 15.80/16.08 (instantiation (forall ((R_4 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) R_4) (hAPP int real (real_1 int) (hAPP real int (archimedean_ceiling real) R_4)))) ) 15.80/16.08 ( (zero_zero real) ) 15.80/16.08 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.08 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.08 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.08 ( skv_14 ) 15.80/16.08 ) 15.80/16.08 (instantiation (let ((_let_0 (hAPP nat real (real_1 nat) X))) (forall ((X $$unsorted)) (= _let_0 (hAPP real real (abs_abs real) _let_0)) )) 15.80/16.08 ( (zero_zero nat) ) 15.80/16.08 ( (one_one nat) ) 15.80/16.08 ) 15.80/16.08 (instantiation (let ((_let_0 (hAPP nat (fun nat bool) (dvd_dvd nat) K))) (forall ((K $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N_1) K))) (hBOOL (hAPP nat bool _let_0 N_1))) )) 15.80/16.08 ( (one_one nat), (one_one nat) ) 15.80/16.08 ) 15.80/16.08 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) sin_coeff)) (hAPP real _let_1 (power_power real) X_1))) (hAPP real real sin X_1))) )))) 15.80/16.08 ( (zero_zero real) ) 15.80/16.08 ( pi ) 15.80/16.08 ( (hAPP int real (number_number_of real) min_1) ) 15.80/16.08 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.08 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.80/16.08 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.80/16.08 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.08 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.80/16.08 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.80/16.08 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.08 ) 15.80/16.08 (instantiation (let ((_let_0 (number_number_of int))) (forall ((W_1 $$unsorted)) (= (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 (hAPP int int bit1 W_1)))) (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 W_1)))) )) 15.80/16.08 ( pls ) 15.80/16.08 ( (hAPP int int bit1 pls) ) 15.80/16.08 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/16.08 ( min_1 ) 15.80/16.08 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.80/16.08 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.80/16.08 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.80/16.08 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.80/16.08 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.80/16.08 ) 15.80/16.08 (instantiation (forall ((V_1 $$unsorted)) (= (= (zero_zero nat) (hAPP int nat (number_number_of nat) V_1)) (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) (hAPP int int pred V_1))))) ) 15.80/16.08 ( pls ) 15.80/16.08 ( (hAPP int int bit1 pls) ) 15.80/16.08 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.80/16.08 ( min_1 ) 15.80/16.08 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.80/16.08 ) 15.80/16.08 (instantiation (forall ((N $$unsorted)) (= (zero_zero nat) (hAPP int nat nat_1 (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) N)))) ) 15.80/16.08 ( (zero_zero nat) ) 15.80/16.08 ( (hAPP nat nat suc (zero_zero nat)) ) 15.80/16.08 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.80/16.08 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.80/16.08 ) 15.80/16.08 (instantiation (forall ((I_1 $$unsorted) (M $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I_1) (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) I_1)))) ) 15.80/16.08 ( (one_one nat), (one_one nat) ) 15.80/16.08 ) 15.80/16.08 (instantiation (let ((_let_0 (filter complex))) (let ((_let_1 (fun _let_0 bool))) (forall ((A_2 $$unsorted)) (hBOOL (hAPP _let_0 bool (hAPP complex _let_1 (hAPP (fun complex complex) (fun complex _let_1) (tendsto complex complex) cnj) (hAPP complex complex cnj A_2)) (hAPP complex _let_0 (at complex) A_2))) ))) 15.89/16.08 ( ii ) 15.89/16.08 ( (zero_zero complex) ) 15.89/16.08 ( (one_one complex) ) 15.89/16.08 ) 15.89/16.08 (instantiation (forall ((N $$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))) ) 15.89/16.08 ( (zero_zero nat) ) 15.89/16.08 ( (hAPP nat nat suc (zero_zero nat)) ) 15.89/16.08 ) 15.89/16.08 (instantiation (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) N_1))) (or (hBOOL (hAPP nat bool _let_0 Ma)) (hBOOL (hAPP nat bool _let_0 N_1)))) )) 15.89/16.09 ( (one_one nat), (one_one nat) ) 15.89/16.09 ) 15.89/16.09 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (hBOOL (hAPP _let_0 bool (hAPP (fun X_a X_b) (fun _let_0 bool) (nat_tr1645093318rphism X_a X_b) F) A_3)) )) 15.89/16.09 ( nat, int, (semiring_1_of_nat int), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 15.89/16.09 ( int, nat, nat_1, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.89/16.09 ) 15.89/16.09 (instantiation (let ((_let_0 (filter complex))) (let ((_let_1 (fun _let_0 bool))) (forall ((A_2 $$unsorted)) (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP (fun complex real) (fun real _let_1) (tendsto complex real) im) (hAPP complex real im A_2)) (hAPP complex _let_0 (at complex) A_2))) ))) 15.89/16.09 ( ii ) 15.89/16.09 ( (zero_zero complex) ) 15.89/16.09 ( (one_one complex) ) 15.89/16.09 ) 15.89/16.09 (instantiation (forall ((W $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) W) W)) ) 15.89/16.09 ( (zero_zero int) ) 15.89/16.09 ( (one_one int) ) 15.89/16.09 ( min_1 ) 15.89/16.09 ) 15.89/16.09 (instantiation (let ((_let_0 (fun int bool))) (forall ((W_1 $$unsorted) (Z $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W_1) Z)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int (hAPP int (fun int int) (plus_plus int) W_1) (one_one int))) Z))) )) 15.89/16.09 ( (zero_zero int), (zero_zero int) ) 15.89/16.09 ( (zero_zero int), (one_one int) ) 15.89/16.09 ( (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.89/16.09 ( (zero_zero int), min_1 ) 15.89/16.09 ( min_1, (zero_zero int) ) 15.89/16.09 ( min_1, min_1 ) 15.89/16.09 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.89/16.09 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 15.89/16.09 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 15.89/16.09 ( t, (zero_zero int) ) 15.89/16.09 ( t, (one_one int) ) 15.89/16.09 ( 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))) ) 15.89/16.09 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.89/16.09 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.89/16.09 ) 15.89/16.09 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP nat real (real_1 nat) N))) ) 15.89/16.09 ( (zero_zero nat) ) 15.89/16.09 ( (one_one nat) ) 15.89/16.09 ) 15.89/16.09 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (one_one real)))) (forall ((Y_1 $$unsorted)) (= (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt Y_1))) (hBOOL (hAPP real bool _let_0 Y_1))) )) 15.89/16.09 ( (zero_zero real) ) 15.89/16.09 ( (one_one real) ) 15.89/16.09 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.89/16.09 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.89/16.09 ) 15.89/16.09 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (power_power real))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_4 (inverse_divide real))) (let ((_let_5 (hAPP int real (number_number_of real) _let_3))) (let ((_let_6 (hAPP nat real (hAPP real _let_1 _let_2 X_1) (hAPP int nat (number_number_of nat) _let_3)))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (combb real real nat) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 _let_4 _let_6) _let_5))) (hAPP real _let_1 _let_2 (hAPP real real (hAPP real _let_0 _let_4 (one_one real)) _let_5)))) _let_6)) )))))))) 15.89/16.09 ( (hAPP int real (number_number_of real) min_1) ) 15.89/16.09 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.89/16.09 ) 15.89/16.09 (instantiation (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) Ma) (hAPP int int (number_number_of int) N_1))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (real_1 int) Ma)) (hAPP int real (number_number_of real) N_1)))) ) 15.89/16.09 ( (zero_zero int), pls ) 15.89/16.09 ( (zero_zero int), (hAPP int int bit1 pls) ) 15.89/16.09 ( (zero_zero int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.89/16.09 ( (zero_zero int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.89/16.09 ( min_1, pls ) 15.89/16.09 ) 15.89/16.09 (instantiation (let ((_let_0 (fun real bool))) (forall ((N_1 $$unsorted)) (hBOOL (hAPP _let_0 bool (hAPP real (fun _let_0 bool) (member real) (hAPP nat real (real_1 nat) N_1)) (ring_1_Ints real))) )) 15.89/16.09 ( (zero_zero nat) ) 15.89/16.09 ( (one_one nat) ) 15.89/16.09 ) 15.89/16.09 (instantiation (let ((_let_0 (number_number_of int))) (forall ((W_1 $$unsorted)) (= (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 W_1))) (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 (hAPP int int bit0 W_1))))) )) 15.89/16.09 ( pls ) 15.89/16.09 ( (hAPP int int bit1 pls) ) 15.89/16.09 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.89/16.09 ( min_1 ) 15.89/16.09 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.89/16.09 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.89/16.09 ) 15.89/16.09 (instantiation (let ((_let_0 (fun real bool))) (forall ((N_1 $$unsorted)) (hBOOL (hAPP _let_0 bool (hAPP real (fun _let_0 bool) (member real) (hAPP nat real (real_1 nat) N_1)) (field_char_0_Rats real))) )) 15.89/16.09 ( (zero_zero nat) ) 15.89/16.09 ( (one_one nat) ) 15.89/16.09 ) 15.89/16.09 (instantiation (let ((_let_0 (even_odd_even nat))) (let ((_let_1 (hBOOL (hAPP nat bool _let_0 Y_1)))) (let ((_let_2 (hBOOL (hAPP nat bool _let_0 X_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) X_1) Y_1))) (or (and _let_1 _let_2) (and (not _let_2) (not _let_1)))) )))) 15.89/16.09 ( (one_one nat), (one_one nat) ) 15.89/16.09 ) 15.89/16.09 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP nat nat fact N))) ) 15.89/16.09 ( (zero_zero nat) ) 15.89/16.09 ) 15.89/16.09 (instantiation (forall ((X $$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))) ) 15.89/16.09 ( ii ) 15.89/16.09 ( (zero_zero complex) ) 15.89/16.09 ( (one_one complex) ) 15.89/16.09 ) 15.89/16.09 (instantiation (let ((_let_0 (fun nat nat))) (forall ((M $$unsorted)) (= M (hAPP nat nat (hAPP nat _let_0 (div_div nat) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) M) M)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) )) 15.89/16.09 ( (one_one nat) ) 15.89/16.09 ) 15.89/16.09 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) X_1) Y_1)) zEven)) (= (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Y_1) zEven)) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_1) zEven)))) )))) 15.89/16.09 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.89/16.09 ) 15.89/16.09 (instantiation (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (hAPP nat int (semiring_1_of_nat int) N_1)))) ) 15.89/16.09 ( (zero_zero nat) ) 15.89/16.09 ( (hAPP nat nat suc (zero_zero nat)) ) 15.89/16.09 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.89/16.09 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.89/16.09 ) 15.89/16.09 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (one_one real))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real sqrt X_1)) _let_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) _let_2))) )))) 15.89/16.09 ( (zero_zero real) ) 15.89/16.09 ( (one_one real) ) 15.89/16.09 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.89/16.09 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.89/16.09 ) 15.89/16.09 (instantiation (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (the _let_0))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (= _let_1 (ti (fun (fun _let_0 bool) _let_0) _let_1)) ))) 15.89/16.09 ( real, real ) 15.89/16.09 ( nat, nat ) 15.89/16.09 ( int, int ) 15.89/16.09 ( int, (product_prod int int) ) 15.89/16.09 ( quickcheck_code_int, quickcheck_code_int ) 15.89/16.09 ( (product_prod int int), (product_prod int int) ) 15.89/16.09 ( (product_prod nat nat), (product_prod nat nat) ) 15.89/16.09 ( code_code_numeral, code_code_numeral ) 15.89/16.09 ) 15.89/16.09 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun real _let_1))) (let ((_let_3 (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real cos X_1)) (hAPP real real sin X_1)))) (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_0 (fun real _let_0) (deriv real) (hAPP nat _let_0 (hAPP _let_2 (fun nat _let_0) (combc real nat real) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_1 real) (power_power real)) sin)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) X_1) (hAPP real real (hAPP real _let_0 (plus_plus real) _let_3) _let_3)))) ))))) 15.89/16.09 ( (zero_zero real) ) 15.89/16.09 ( pi ) 15.89/16.09 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.89/16.09 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.89/16.09 ( (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) ) 15.89/16.09 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.89/16.09 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.89/16.09 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.89/16.09 ( (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)))) ) 15.89/16.09 ( skv_14 ) 15.89/16.09 ) 15.89/16.09 (instantiation (let ((_let_0 (real_1 int))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) X_1) Y_1)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real _let_0 X_1)) (hAPP int real _let_0 Y_1)))) )) 15.89/16.09 ( (zero_zero int), (zero_zero int) ) 15.89/16.09 ( (zero_zero int), (one_one int) ) 15.89/16.09 ( (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.89/16.09 ( (zero_zero int), min_1 ) 15.89/16.09 ( min_1, (zero_zero int) ) 15.89/16.09 ( min_1, min_1 ) 15.89/16.09 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.89/16.09 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 15.89/16.09 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 15.90/16.09 ( t, (zero_zero int) ) 15.90/16.09 ( t, (one_one int) ) 15.90/16.09 ( 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))) ) 15.90/16.09 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.90/16.09 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.90/16.09 ) 15.90/16.09 (instantiation (let ((_let_0 (power_1 X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun X_a (fun (fun X_a (fun X_a X_a)) (fun X_a (fun nat X_a)))) _let_0)) )) 15.90/16.09 ( bool ) 15.90/16.09 ( real ) 15.90/16.09 ( nat ) 15.90/16.09 ( (fun nat bool) ) 15.90/16.09 ( (fun nat nat) ) 15.90/16.09 ( int ) 15.90/16.09 ( (fun int bool) ) 15.90/16.09 ( (fun real bool) ) 15.90/16.09 ( (fun real real) ) 15.90/16.09 ( complex ) 15.90/16.09 ( (fun nat real) ) 15.90/16.09 ( (fun int int) ) 15.90/16.09 ( rat ) 15.90/16.09 ( (fun bool bool) ) 15.90/16.09 ( (fun int (fun int bool)) ) 15.90/16.09 ( (fun nat (fun nat bool)) ) 15.90/16.09 ( (product_prod real real) ) 15.90/16.09 ( (product_prod int int) ) 15.90/16.09 ( (fun nat (product_prod int int)) ) 15.90/16.09 ( (product_prod nat nat) ) 15.90/16.09 ( (fun (product_prod nat nat) bool) ) 15.90/16.09 ( (fun nat (fun (product_prod nat nat) bool)) ) 15.90/16.09 ( (fun nat (product_prod nat nat)) ) 15.90/16.09 ( (fun (product_prod int int) bool) ) 15.90/16.09 ( code_code_numeral ) 15.90/16.09 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.90/16.09 ( (fun (product_prod int int) int) ) 15.90/16.09 ( (fun int (fun int (fun int bool))) ) 15.90/16.09 ( (fun int real) ) 15.90/16.09 ) 15.90/16.09 (instantiation (forall ((I_1 $$unsorted) (J_2 $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) I_1) J_2)) I_1))) ) 15.90/16.09 ( (one_one nat), (one_one nat) ) 15.90/16.09 ) 15.90/16.09 (instantiation (let ((_let_0 (even_odd_even nat))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP nat bool _let_0 (hAPP nat nat suc X_1))) (not (hBOOL (hAPP nat bool _let_0 X_1)))) )) 15.90/16.09 ( (zero_zero nat) ) 15.90/16.09 ( (hAPP nat nat suc (zero_zero nat)) ) 15.90/16.09 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.90/16.09 ) 15.90/16.09 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_1)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) (hAPP real real (exp real) X_1)))) ))) 15.90/16.10 ( pi ) 15.90/16.10 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.90/16.10 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.90/16.10 ( skv_2 ) 15.90/16.10 ( skv_10 ) 15.90/16.10 ( skv_13 ) 15.90/16.10 ) 15.90/16.10 (instantiation (forall ((A_2 $$unsorted) (X_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) A_2) (hAPP real int (archim2085082626_floor real) X_1))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (real_1 int) A_2)) X_1))) ) 15.90/16.10 ( (zero_zero int), pi ) 15.90/16.10 ( (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.90/16.10 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.90/16.10 ( (zero_zero int), skv_6 ) 15.90/16.10 ( (zero_zero int), skv_11 ) 15.90/16.10 ( (zero_zero int), skv_12 ) 15.90/16.10 ( (zero_zero int), skv_14 ) 15.90/16.10 ) 15.90/16.10 (instantiation (let ((_let_0 (nat_tr1645093318rphism X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (= _let_0 (ti (fun (fun X_a X_b) (fun (fun X_a bool) bool)) _let_0)) )) 15.90/16.10 ( nat, int ) 15.90/16.10 ( int, nat ) 15.90/16.10 ) 15.90/16.10 (instantiation (let ((_let_0 (semiring_1_of_nat int))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP nat int _let_0 Ma)) (hAPP nat int _let_0 N_1))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Ma) N_1))) )) 15.90/16.10 ( (zero_zero nat), (zero_zero nat) ) 15.90/16.10 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.90/16.10 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.90/16.10 ) 15.90/16.10 (instantiation (forall ((N $$unsorted) (M $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N) M))) ) 15.90/16.10 ( (one_one nat), (one_one nat) ) 15.90/16.10 ) 15.90/16.10 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K)) min_1)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) min_1))) ))) 15.90/16.10 ( pls ) 15.90/16.10 ( (hAPP int int bit1 pls) ) 15.90/16.10 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.90/16.10 ( min_1 ) 15.90/16.10 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.90/16.10 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.90/16.10 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.90/16.10 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.90/16.10 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.90/16.10 ) 15.90/16.10 (instantiation (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) N_1)) (hAPP int real (real_1 int) Ma))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (number_number_of int) N_1)) Ma))) ) 15.90/16.10 ( pls, (one_one int) ) 15.90/16.10 ( pls, min_1 ) 15.90/16.10 ( pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.90/16.10 ( pls, s ) 15.90/16.10 ( pls, (hAPP int int (number_number_of int) pls) ) 15.90/16.10 ( pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.90/16.10 ( pls, skv_3 ) 15.90/16.10 ( pls, skv_9 ) 15.90/16.10 ( (hAPP int int bit1 pls), t ) 15.90/16.10 ) 15.90/16.10 (instantiation (let ((_let_0 (semiring_1_of_nat int))) (forall ((N $$unsorted) (M $$unsorted)) (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))) )) 15.90/16.10 ( (zero_zero nat), (zero_zero nat) ) 15.90/16.10 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.90/16.10 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.90/16.10 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.90/16.10 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 15.90/16.10 ) 15.90/16.10 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (exp real) X_1)) (one_one real))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (zero_zero real)))) ))) 15.90/16.10 ( pi ) 15.90/16.10 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.90/16.10 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.90/16.10 ) 15.90/16.10 (instantiation (forall ((R_4 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (minus_minus real) R_4) (one_one real))) (hAPP int real (real_1 int) (hAPP real int (archim2085082626_floor real) R_4)))) ) 15.90/16.10 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.90/16.10 ) 15.90/16.10 (instantiation (forall ((Z $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP nat nat suc (zero_zero nat))) (hAPP int nat nat_1 Z))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (one_one int)) Z))) ) 15.90/16.10 ( (zero_zero int) ) 15.90/16.10 ( (one_one int) ) 15.90/16.10 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.90/16.10 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.90/16.10 ) 15.90/16.10 (instantiation (forall ((N $$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)) ) 15.90/16.10 ( (one_one nat) ) 15.90/16.10 ) 15.90/16.10 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) pls)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit0 K)) pls))) ))) 15.90/16.10 ( pls ) 15.90/16.10 ( (hAPP int int bit1 pls) ) 15.90/16.10 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.90/16.10 ( min_1 ) 15.90/16.10 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.90/16.10 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.90/16.10 ) 15.90/16.10 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (forall ((N $$unsorted)) (= _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)) ))) 15.90/16.10 ( (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)))) ) 15.90/16.10 ) 15.90/16.10 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real (fun real real)))) (let ((_let_2 (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real cos X_1)) (hAPP real real sin X_1)))) (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_0 (fun real _let_0) (deriv real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (times_times real)) sin)) sin)) X_1) (hAPP real real (hAPP real _let_0 (plus_plus real) _let_2) _let_2)))) )))) 15.90/16.10 ( (zero_zero real) ) 15.90/16.10 ( pi ) 15.90/16.10 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.90/16.10 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.90/16.10 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.90/16.10 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.90/16.10 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.90/16.10 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.90/16.10 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.90/16.10 ( skv_14 ) 15.90/16.10 ) 15.90/16.10 (instantiation (let ((_let_0 (fun nat nat))) (forall ((M $$unsorted) (N $$unsorted)) (= M (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) M) N)) N)) )) 15.90/16.10 ( (one_one nat), (one_one nat) ) 15.90/16.10 ) 15.90/16.10 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) (hAPP real real (hAPP real (fun real real) (plus_plus real) X_1) Y_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) X_1)) Y_1))) ))) 15.90/16.10 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.90/16.10 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), pi ) 15.90/16.10 ) 15.90/16.10 (instantiation (forall ((Z_5 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) Z_5) (zero_zero int))) (hBOOL (hAPP int bool nat_neg Z_5))) ) 15.90/16.10 ( (zero_zero int) ) 15.90/16.10 ( (one_one int) ) 15.90/16.10 ( min_1 ) 15.90/16.10 ( (hAPP int int (number_number_of int) min_1) ) 15.90/16.10 ( s ) 15.90/16.10 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.90/16.10 ( (hAPP int int (number_number_of int) pls) ) 15.90/16.10 ( t ) 15.90/16.10 ( skv_3 ) 15.90/16.10 ( skv_9 ) 15.90/16.10 ) 15.90/16.10 (instantiation (let ((_let_0 (fun int bool))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) Ma) (hAPP int int (hAPP int (fun int int) (minus_minus int) A_2) B_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_2) B_1) Ma))) )) 15.90/16.10 ( (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_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.90/16.10 ( (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 nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.90/16.10 ( s1, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.90/16.10 ( s1, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.90/16.10 ( s1, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.90/16.10 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.90/16.10 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.90/16.10 ) 15.90/16.10 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (exp real) X_1)) (one_one real))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (zero_zero real)))) ))) 15.90/16.10 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.90/16.10 ) 15.90/16.10 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (zero_zero nat)) (hAPP real nat natceiling X))) ) 15.90/16.10 ( (zero_zero real) ) 15.90/16.10 ( (one_one real) ) 15.90/16.10 ) 15.90/16.10 (instantiation (let ((_let_0 (hAPP nat int (semiring_1_of_nat int) N))) (forall ((N $$unsorted)) (= _let_0 (hAPP int int (ring_1_of_int int) _let_0)) )) 15.90/16.10 ( (zero_zero nat) ) 15.90/16.10 ( (hAPP nat nat suc (zero_zero nat)) ) 15.90/16.10 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.90/16.10 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.90/16.10 ) 15.90/16.10 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_1))) (let ((_let_3 (times_times real))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs real real real) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_1 real) _let_3) cos)) cos)) X_1) (hAPP real real (hAPP real _let_1 _let_3 (hAPP real real (hAPP real _let_1 _let_3 (hAPP int real (number_number_of real) (hAPP int int bit0 min_1))) (hAPP real real cos X_1))) (hAPP real real sin X_1)))) ))))) 15.91/16.10 ( (zero_zero real) ) 15.91/16.10 ( pi ) 15.91/16.10 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.10 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.10 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.91/16.10 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.91/16.10 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.91/16.10 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.91/16.10 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.91/16.10 ( skv_14 ) 15.91/16.10 ) 15.91/16.10 (instantiation (forall ((N $$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)))) ) 15.91/16.11 ( (zero_zero nat) ) 15.91/16.11 ( (hAPP nat nat suc (zero_zero nat)) ) 15.91/16.11 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.91/16.11 ) 15.91/16.11 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) N)))) ) 15.91/16.11 ( (zero_zero nat) ) 15.91/16.11 ( (hAPP nat nat suc (zero_zero nat)) ) 15.91/16.11 ) 15.91/16.11 (instantiation (let ((_let_0 (filter complex))) (let ((_let_1 (fun _let_0 bool))) (forall ((A_2 $$unsorted)) (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP (fun complex real) (fun real _let_1) (tendsto complex real) re) (hAPP complex real re A_2)) (hAPP complex _let_0 (at complex) A_2))) ))) 15.91/16.11 ( ii ) 15.91/16.11 ( (zero_zero complex) ) 15.91/16.11 ( (one_one complex) ) 15.91/16.11 ) 15.91/16.11 (instantiation (let ((_let_0 (fun int bool))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) K) pls)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int bit1 K)) pls))) )) 15.91/16.11 ( (zero_zero int) ) 15.91/16.11 ( pls ) 15.91/16.11 ( (hAPP int int bit1 pls) ) 15.91/16.11 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.91/16.11 ( min_1 ) 15.91/16.11 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.91/16.11 ( s ) 15.91/16.11 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.91/16.11 ( t ) 15.91/16.11 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.91/16.11 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.91/16.11 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.91/16.11 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.91/16.11 ( skv_3 ) 15.91/16.11 ( skv_9 ) 15.91/16.11 ) 15.91/16.11 (instantiation (let ((_let_0 (semiring_1_of_nat int))) (forall ((N $$unsorted) (M $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int (uminus_uminus int) (hAPP nat int _let_0 (hAPP nat nat suc N)))) (hAPP nat int _let_0 M))) )) 15.91/16.11 ( (zero_zero nat), (zero_zero nat) ) 15.91/16.11 ) 15.91/16.11 (instantiation (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real (number_number_of real) N_1)) (hAPP int real (real_1 int) Ma))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int (number_number_of int) N_1)) Ma))) ) 15.91/16.11 ( pls, (zero_zero int) ) 15.91/16.11 ( pls, (one_one int) ) 15.91/16.11 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.11 ( pls, min_1 ) 15.91/16.11 ) 15.91/16.11 (instantiation (forall ((T_1 $$unsorted)) (order (filter T_1)) ) 15.91/16.11 ( real ) 15.91/16.11 ( nat ) 15.91/16.11 ) 15.91/16.11 (instantiation (forall ((N_1 $$unsorted)) (= (= (zero_zero nat) N_1) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP nat int (semiring_1_of_nat int) N_1)) (zero_zero int)))) ) 15.91/16.11 ( (zero_zero nat) ) 15.91/16.11 ( (hAPP nat nat suc (zero_zero nat)) ) 15.91/16.11 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.11 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.11 ) 15.91/16.11 (instantiation (let ((_let_0 (real_1 int))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) N_1) Ma)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real _let_0 N_1)) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real _let_0 Ma)) (one_one real))))) )) 15.91/16.11 ( (zero_zero int), (one_one int) ) 15.91/16.11 ( (zero_zero int), min_1 ) 15.91/16.11 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.11 ( (zero_zero int), s ) 15.91/16.11 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.91/16.11 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.11 ( (zero_zero int), skv_3 ) 15.91/16.11 ( (zero_zero int), skv_9 ) 15.91/16.11 ( (one_one int), t ) 15.91/16.11 ( min_1, pls ) 15.91/16.11 ( min_1, min_1 ) 15.91/16.11 ) 15.91/16.11 (instantiation (forall ((N $$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)))) ) 15.91/16.11 ( (zero_zero nat) ) 15.91/16.11 ( (hAPP nat nat suc (zero_zero nat)) ) 15.91/16.11 ) 15.91/16.11 (instantiation (let ((_let_0 (fun int bool))) (forall ((A_1 $$unsorted) (B $$unsorted)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_1) B) (one_one int))) )) 15.91/16.11 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.91/16.11 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.11 ( s1, s ) 15.91/16.11 ( s1, skv_3 ) 15.91/16.11 ( s1, skv_9 ) 15.91/16.11 ( (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_1) ) 15.91/16.11 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.91/16.11 ) 15.91/16.11 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)))) (forall ((Y_1 $$unsorted)) (= (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt Y_1))) (hBOOL (hAPP real bool _let_0 Y_1))) )) 15.91/16.11 ( (zero_zero real) ) 15.91/16.11 ( (one_one real) ) 15.91/16.11 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.11 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.11 ) 15.91/16.11 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_101752))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_101750 $$unsorted) (BOUND_VARIABLE_101751 $$unsorted) (BOUND_VARIABLE_101752 $$unsorted)) (or (not (linord581940658strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_101752))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_101750)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_101751))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_101750) BOUND_VARIABLE_101751)))) )))) 15.91/16.11 ( int, skv_1, (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.11 ) 15.91/16.11 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_0 X_1))) (not (hBOOL (hAPP int bool _let_0 Y_1))) (= (= (hAPP int nat nat_1 X_1) (hAPP int nat nat_1 Y_1)) (= (ti int Y_1) (ti int X_1)))) )) 15.91/16.11 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.11 ( pls, pls ) 15.91/16.11 ( pls, (one_one int) ) 15.91/16.11 ( (one_one int), pls ) 15.91/16.11 ( min_1, (hAPP int int (number_number_of int) pls) ) 15.91/16.11 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 15.91/16.11 ( s, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.11 ( s, s ) 15.91/16.11 ( (hAPP int int (number_number_of int) pls), min_1 ) 15.91/16.11 ( (hAPP int int (number_number_of int) pls), (hAPP int int (number_number_of int) pls) ) 15.91/16.11 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.91/16.11 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.11 ( skv_3, skv_3 ) 15.91/16.11 ( skv_3, skv_9 ) 15.91/16.11 ( skv_9, skv_3 ) 15.91/16.11 ) 15.91/16.11 (instantiation (let ((_let_0 (plus_plus X_a))) (forall ((X_a $$unsorted)) (or (not (cancel_semigroup_add X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0))) )) 15.91/16.11 ( bool ) 15.91/16.11 ( real ) 15.91/16.11 ( nat ) 15.91/16.11 ( (fun nat bool) ) 15.91/16.11 ( int ) 15.91/16.11 ( (fun int bool) ) 15.91/16.11 ( (fun real bool) ) 15.91/16.11 ( (fun real real) ) 15.91/16.11 ( complex ) 15.91/16.11 ( (fun nat real) ) 15.91/16.11 ( (fun int int) ) 15.91/16.11 ( rat ) 15.91/16.11 ( (fun int (fun int bool)) ) 15.91/16.11 ( quickcheck_code_int ) 15.91/16.11 ( (product_prod int int) ) 15.91/16.11 ( (fun (product_prod int int) bool) ) 15.91/16.11 ( code_code_numeral ) 15.91/16.11 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.91/16.11 ( (fun (product_prod int int) int) ) 15.91/16.11 ( (fun int (fun int (fun int bool))) ) 15.91/16.11 ( (fun int real) ) 15.91/16.11 ) 15.91/16.11 (instantiation (let ((_let_0 (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_101896))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_101896 $$unsorted) (BOUND_VARIABLE_101897 $$unsorted) (BOUND_VARIABLE_101898 $$unsorted)) (or (not (cancel_semigroup_add X_a)) (not (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_101897) (hAPP X_a X_a _let_0 BOUND_VARIABLE_101898))) (= (ti X_a BOUND_VARIABLE_101897) (ti X_a BOUND_VARIABLE_101898))) )) 15.91/16.11 ( nat, (one_one nat), (one_one nat), (one_one nat) ) 15.91/16.11 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), (one_one int) ) 15.91/16.11 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int), (one_one int) ) 15.91/16.11 ) 15.91/16.11 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less int) (zero_zero int)))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_0 B_1))) (= (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less rat) (zero_zero rat)) (hAPP int rat (hAPP int (fun int rat) fract A_2) B_1))) (hBOOL (hAPP int bool _let_0 A_2)))) )) 15.91/16.11 ( (zero_zero int), (one_one int) ) 15.91/16.11 ( (one_one int), (one_one int) ) 15.91/16.11 ) 15.91/16.11 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_101933 $$unsorted) (BOUND_VARIABLE_101934 $$unsorted)) (or (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_101934) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_101934) BOUND_VARIABLE_101933)) _let_3))) ))))) 15.91/16.11 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 15.91/16.11 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 15.91/16.11 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 15.91/16.11 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 15.91/16.11 ) 15.91/16.11 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_101960 $$unsorted) (BOUND_VARIABLE_101961 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_101961))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_101960))) (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_101961) BOUND_VARIABLE_101960)))) )) 15.91/16.11 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.11 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.91/16.11 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.11 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.11 ( int, (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.11 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.11 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.11 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.11 ( complex, ii, ii ) 15.91/16.11 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.91/16.11 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.11 ) 15.91/16.11 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool _let_0 X))) (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt X)))) )) 15.91/16.11 ( (zero_zero real) ) 15.91/16.11 ( (one_one real) ) 15.91/16.11 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.11 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.11 ) 15.91/16.11 (instantiation (forall ((I_1 $$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))) ) 15.91/16.11 ( (zero_zero int) ) 15.91/16.11 ( pls ) 15.91/16.11 ( m ) 15.91/16.11 ( min_1 ) 15.91/16.11 ( s ) 15.91/16.11 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.91/16.11 ( s1 ) 15.91/16.11 ( t ) 15.91/16.11 ( skv_3 ) 15.91/16.11 ( skv_9 ) 15.91/16.11 ) 15.91/16.11 (instantiation (forall ((I_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) I_1) (zero_zero int)))) (= (hAPP int int (abs_abs int) I_1) (hAPP int int (uminus_uminus int) I_1))) ) 15.91/16.11 ( (zero_zero int) ) 15.91/16.11 ( pls ) 15.91/16.11 ( (one_one int) ) 15.91/16.11 ( min_1 ) 15.91/16.11 ( s ) 15.91/16.11 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.91/16.11 ( t ) 15.91/16.11 ( skv_3 ) 15.91/16.11 ( skv_9 ) 15.91/16.11 ) 15.91/16.11 (instantiation (let ((_let_0 (norm_norm X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_102018 $$unsorted) (BOUND_VARIABLE_102019 $$unsorted)) (or (not (real_normed_field X_a)) (not (field_inverse_zero 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_102018) BOUND_VARIABLE_102019)) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP X_a real _let_0 BOUND_VARIABLE_102018)) (hAPP X_a real _let_0 BOUND_VARIABLE_102019)))) )) 15.91/16.11 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.11 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.91/16.11 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.11 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.91/16.12 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.12 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.12 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.91/16.12 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.12 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.12 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.12 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.12 ) 15.91/16.12 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_102048 $$unsorted) (BOUND_VARIABLE_102049 $$unsorted) (BOUND_VARIABLE_102050 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_102050)) (= (= (ti X_a BOUND_VARIABLE_102049) (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_102048) BOUND_VARIABLE_102050)) (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_102049) BOUND_VARIABLE_102050) (ti X_a BOUND_VARIABLE_102048)))) )) 15.91/16.12 ( real, pi, pi, pi ) 15.91/16.12 ) 15.91/16.12 (instantiation (let ((_let_0 (uminus_uminus real))) (forall ((X $$unsorted)) (= (hAPP real real tan (hAPP real real _let_0 X)) (hAPP real real _let_0 (hAPP real real tan X))) )) 15.91/16.12 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.91/16.12 ) 15.91/16.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102135 $$unsorted)) (or (not (real_algebra_1 X_a)) (= (hAPP real X_a (of_real X_a) (hAPP int real (ring_1_of_int real) BOUND_VARIABLE_102135)) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_102135))) ) 15.91/16.12 ( real, (zero_zero int) ) 15.91/16.12 ( real, (one_one int) ) 15.91/16.12 ) 15.91/16.12 (instantiation (let ((_let_0 (hAPP int int (number_number_of int) (hAPP int int pred V_1)))) (let ((_let_1 (hBOOL (hAPP int bool nat_neg _let_0)))) (forall ((V_1 $$unsorted) (N_1 $$unsorted)) (= (= (hAPP int nat (number_number_of nat) V_1) (hAPP nat nat suc N_1)) (and (or _let_1 (= N_1 (hAPP int nat nat_1 _let_0))) (not _let_1))) ))) 15.91/16.12 ( pls, (hAPP nat nat suc (zero_zero nat)) ) 15.91/16.12 ( (hAPP int int bit1 pls), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.91/16.12 ( (hAPP int int bit0 (hAPP int int bit1 pls)), (zero_zero nat) ) 15.91/16.12 ) 15.91/16.12 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) 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)))) ))) 15.91/16.12 ( (zero_zero real) ) 15.91/16.12 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.12 ( (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)))) ) 15.91/16.12 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.12 ( skv_14 ) 15.91/16.12 ) 15.91/16.12 (instantiation (let ((_let_0 (norm_norm X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_102248 $$unsorted) (BOUND_VARIABLE_102249 $$unsorted)) (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_102248) BOUND_VARIABLE_102249)) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP X_a real _let_0 BOUND_VARIABLE_102248)) (hAPP X_a real _let_0 BOUND_VARIABLE_102249)))) )) 15.91/16.12 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.91/16.12 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 15.91/16.12 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.91/16.12 ( 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))))), pi ) 15.91/16.12 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.91/16.12 ( 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))), (zero_zero int) ) 15.91/16.12 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.91/16.12 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1 ) 15.91/16.12 ( complex, ii, ii ) 15.91/16.12 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.91/16.12 ( 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)), ii ) 15.91/16.12 ) 15.91/16.12 (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 X_a) (ord_less_eq X_a)))) ) 15.91/16.12 ( bool ) 15.91/16.12 ( real ) 15.91/16.12 ( nat ) 15.91/16.12 ( (fun nat bool) ) 15.91/16.12 ( int ) 15.91/16.12 ( (fun int bool) ) 15.91/16.12 ( (fun real bool) ) 15.91/16.12 ( (fun real real) ) 15.91/16.12 ( complex ) 15.91/16.12 ( (fun nat real) ) 15.91/16.12 ( (fun int int) ) 15.91/16.12 ( rat ) 15.91/16.12 ( (fun int (fun int bool)) ) 15.91/16.12 ( quickcheck_code_int ) 15.91/16.12 ( (product_prod real real) ) 15.91/16.12 ( (product_prod int int) ) 15.91/16.12 ( (filter real) ) 15.91/16.12 ( (filter nat) ) 15.91/16.12 ( (product_prod nat nat) ) 15.91/16.12 ( (fun (product_prod int int) bool) ) 15.91/16.12 ( code_code_numeral ) 15.91/16.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.91/16.12 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.91/16.12 ( (fun nat rat) ) 15.91/16.12 ( (fun (product_prod int int) int) ) 15.91/16.12 ( (fun int (fun int (fun int bool))) ) 15.91/16.12 ( (fun int real) ) 15.91/16.12 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.91/16.12 ) 15.91/16.12 (instantiation (forall ((Z_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Z_1))) (= (ti int Z_1) (hAPP nat int (semiring_1_of_nat int) (hAPP int nat nat_1 Z_1)))) ) 15.91/16.12 ( (zero_zero int) ) 15.91/16.12 ( pls ) 15.91/16.12 ( m ) 15.91/16.12 ( (one_one int) ) 15.91/16.12 ( min_1 ) 15.91/16.12 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.12 ( s ) 15.91/16.12 ( (hAPP int int (number_number_of int) pls) ) 15.91/16.12 ( s1 ) 15.91/16.12 ( t ) 15.91/16.12 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.12 ( skv_3 ) 15.91/16.12 ( skv_9 ) 15.91/16.12 ) 15.91/16.12 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (abs_abs X_a))) (let ((_let_3 (fun X_a bool))) (let ((_let_4 (ord_less_eq X_a))) (let ((_let_5 (zero_zero X_a))) (let ((_let_6 (hAPP X_a _let_3 _let_4 _let_5))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_102333 $$unsorted) (BOUND_VARIABLE_102334 $$unsorted)) (or (not (ordered_ring_abs X_a)) (and (not (hBOOL (hAPP X_a bool _let_6 BOUND_VARIABLE_102333))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_102333) _let_5)))) (and (not (hBOOL (hAPP X_a bool _let_6 BOUND_VARIABLE_102334))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_102334) _let_5)))) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_102334) BOUND_VARIABLE_102333)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_102334)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_102333)))) )))))))) 15.91/16.12 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.12 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.91/16.12 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.12 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.12 ( int, (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.12 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.12 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.12 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.12 ( complex, ii, ii ) 15.91/16.12 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.91/16.12 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.12 ) 15.91/16.12 (instantiation (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) I_1))) (forall ((I_1 $$unsorted) (K_4 $$unsorted)) (or (not (hBOOL (hAPP nat bool _let_0 K_4))) (= K_4 (hAPP nat nat suc I_1)) (not (forall ((J_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool _let_0 J_1))) (not (= K_4 (hAPP nat nat suc J_1)))) ))) )) 15.91/16.12 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.12 ) 15.91/16.12 (instantiation (let ((_let_0 (norm_norm complex))) (forall ((Z_1 $$unsorted)) (= (hAPP complex real _let_0 (hAPP complex complex cnj Z_1)) (hAPP complex real _let_0 Z_1)) )) 15.91/16.12 ( ii ) 15.91/16.12 ( (zero_zero complex) ) 15.91/16.12 ( (one_one complex) ) 15.91/16.12 ) 15.91/16.12 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (one_one X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_102500 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (= (or (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_102500) (zero_zero X_a))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_102500))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_102500)) _let_2)))) )))) 15.91/16.12 ( real, (zero_zero real) ) 15.91/16.12 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.12 ( int, (zero_zero int) ) 15.91/16.12 ( int, min_1 ) 15.91/16.12 ( int, t ) 15.91/16.12 ( complex, ii ) 15.91/16.12 ) 15.91/16.12 (instantiation (let ((_let_0 (inverse_inverse real))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X))) (= (hAPP real real _let_0 X) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real _let_0 (hAPP real real sqrt X))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) )) 15.91/16.12 ( (zero_zero real) ) 15.91/16.12 ( (one_one real) ) 15.91/16.12 ( pi ) 15.91/16.12 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.12 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.12 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.12 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.12 ( skv_2 ) 15.91/16.12 ( skv_10 ) 15.91/16.12 ( skv_13 ) 15.91/16.12 ) 15.91/16.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102550 $$unsorted)) (or (not (real_vector X_a)) (= (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_102550) (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) (hAPP int real (number_number_of real) min_1)) BOUND_VARIABLE_102550))) ) 15.91/16.12 ( real, (one_one real) ) 15.91/16.12 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.12 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.91/16.12 ( int, pls ) 15.91/16.12 ( int, (one_one int) ) 15.91/16.12 ( int, min_1 ) 15.91/16.12 ( complex, ii ) 15.91/16.12 ( complex, (one_one complex) ) 15.91/16.12 ) 15.91/16.12 (instantiation (let ((_let_0 (fun real real))) (forall ((A_1 $$unsorted) (X $$unsorted)) (= (hAPP real real (hAPP real _let_0 (times_times real) A_1) X) (hAPP real real (hAPP real _let_0 (scaleR_scaleR real) A_1) X)) )) 15.91/16.12 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.91/16.12 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 15.91/16.12 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.91/16.12 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.91/16.13 ) 15.91/16.13 (instantiation (let ((_let_0 (real_1 int))) (forall ((X $$unsorted) (N $$unsorted)) (= (hAPP int real _let_0 (hAPP nat int (hAPP int (fun nat int) (power_power int) X) N)) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP int real _let_0 X)) N)) )) 15.91/16.13 ( s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ( s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ( skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ) 15.91/16.13 (instantiation (let ((_let_0 (ord_less_eq X_b))) (forall ((X_b $$unsorted)) (or (not (ord X_b)) (= _let_0 (ti (fun X_b (fun X_b bool)) _let_0))) )) 15.91/16.13 ( bool ) 15.91/16.13 ( real ) 15.91/16.13 ( nat ) 15.91/16.13 ( (fun nat bool) ) 15.91/16.13 ( int ) 15.91/16.13 ( (fun int bool) ) 15.91/16.13 ( rat ) 15.91/16.13 ( quickcheck_code_int ) 15.91/16.13 ( (product_prod real real) ) 15.91/16.13 ( (product_prod int int) ) 15.91/16.13 ( (filter real) ) 15.91/16.13 ( (filter nat) ) 15.91/16.13 ( (product_prod nat nat) ) 15.91/16.13 ( code_code_numeral ) 15.91/16.13 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.91/16.13 ( (fun nat rat) ) 15.91/16.13 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.91/16.13 ) 15.91/16.13 (instantiation (let ((_let_0 (fun int int))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (hAPP int int (hAPP int _let_0 (plus_plus int) Z_1) (hAPP int int (uminus_uminus int) W)) (hAPP int int (hAPP int _let_0 (minus_minus int) Z_1) W)) )) 15.91/16.13 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.91/16.13 ) 15.91/16.13 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (hAPP int int _let_1 W))) (let ((_let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) _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_2) negDivAlg (one_one int)))) (let ((_let_7 (hAPP int _let_2 _let_6 _let_3))) (forall ((W $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) _let_3))) (and (or (not _let_5) (= (hAPP int _let_2 (hAPP int (fun int _let_2) (product_Pair int int) (hAPP int int _let_1 min_1)) _let_4) _let_7)) (or _let_5 (= _let_7 (hAPP _let_2 _let_2 (hAPP int (fun _let_2 _let_2) adjust _let_3) (hAPP int _let_2 _let_6 (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int _let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) _let_3))))))) ))))))))) 15.91/16.13 ( pls ) 15.91/16.13 ( (hAPP int int bit1 pls) ) 15.91/16.13 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.91/16.13 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ( min_1 ) 15.91/16.13 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.91/16.13 ) 15.91/16.13 (instantiation (let ((_let_0 (fun X_c X_a))) (let ((_let_1 (product_prod X_b X_c))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (= (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) F) (hAPP X_c _let_1 (hAPP X_b (fun X_c _let_1) (product_Pair X_b X_c) A_2) B_1)) (hAPP X_c X_a (hAPP X_b _let_0 F A_2) B_1)) ))) 15.91/16.13 ( real, real, bool, (ord_less_eq real), (zero_zero real), pi ) 15.91/16.13 ( real, real, bool, (ord_less_eq real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.13 ( real, real, bool, (ord_less_eq real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.13 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_6 ) 15.91/16.13 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_11 ) 15.91/16.13 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_12 ) 15.91/16.13 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_14 ) 15.91/16.13 ( real, real, bool, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.91/16.13 ( real, real, bool, (ord_less_eq real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ( real, real, bool, (ord_less_eq real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.91/16.13 ( real, real, bool, (ord_less_eq real), skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ( real, real, bool, (ord_less real), (zero_zero real), pi ) 15.91/16.13 ( real, real, bool, (ord_less real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.13 ( real, real, bool, (ord_less real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.13 ( real, real, bool, (ord_less real), (zero_zero real), skv_2 ) 15.91/16.13 ( real, real, bool, (ord_less real), (zero_zero real), skv_10 ) 15.91/16.13 ( real, real, bool, (ord_less real), (zero_zero real), skv_13 ) 15.91/16.13 ( real, real, bool, (ord_less real), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.13 ( real, real, bool, (ord_less real), pi, (zero_zero real) ) 15.91/16.13 ( real, real, bool, (ord_less real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.13 ( real, real, bool, (ord_less real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ( real, real, bool, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.91/16.13 ( real, real, bool, (ord_less real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.91/16.13 ( real, real, bool, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.91/16.13 ( real, real, real, (minus_minus real), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.91/16.13 ( real, real, real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ( real, real, real, (inverse_divide real), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.91/16.13 ( real, real, real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.13 ( real, real, real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.91/16.13 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.13 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.91/16.13 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.13 ( real, real, real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ( real, real, real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ( real, real, real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ( real, real, real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.91/16.13 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 15.91/16.13 ( real, real, real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.91/16.13 ( real, real, real, (times_times real), (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.91/16.13 ( real, real, complex, complex_1, (zero_zero real), (zero_zero real) ) 15.91/16.13 ( real, real, complex, complex_1, (zero_zero real), (one_one real) ) 15.91/16.13 ( real, real, complex, complex_1, (one_one real), (zero_zero real) ) 15.91/16.13 ( real, (filter real), bool, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 (fun real (fun (filter real) bool)) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)))), (zero_zero real), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.91/16.13 ( real, (filter nat), bool, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real (fun (filter nat) bool)) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real), sequentially ) 15.91/16.13 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 15.91/16.13 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 15.91/16.13 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.13 ( nat, nat, bool, (ord_less nat), (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ( nat, nat, nat, (plus_plus nat), (one_one nat), (one_one nat) ) 15.91/16.13 ( int, nat, int, (power_power int), s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ( int, nat, int, (power_power int), s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ( int, nat, int, (power_power int), skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ( int, int, bool, (ord_less_eq int), (zero_zero int), (one_one int) ) 15.91/16.13 ( int, int, bool, (ord_less_eq int), (zero_zero int), min_1 ) 15.91/16.13 ( int, int, bool, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.13 ( int, int, bool, (ord_less_eq int), (zero_zero int), s ) 15.91/16.13 ( int, int, bool, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.91/16.13 ( int, int, bool, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.13 ( int, int, bool, (ord_less_eq int), (zero_zero int), skv_3 ) 15.91/16.13 ( int, int, bool, (ord_less_eq int), (zero_zero int), skv_9 ) 15.91/16.13 ( int, int, bool, (ord_less_eq int), (one_one int), t ) 15.91/16.13 ( int, int, bool, (ord_less_eq int), min_1, pls ) 15.91/16.13 ( int, int, bool, (ord_less_eq int), min_1, min_1 ) 15.91/16.13 ( int, int, bool, (ord_less int), (zero_zero int), (zero_zero int) ) 15.91/16.13 ( int, int, bool, (ord_less int), (zero_zero int), (one_one int) ) 15.91/16.13 ( 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))) ) 15.91/16.13 ( int, int, bool, (ord_less int), (zero_zero int), min_1 ) 15.91/16.13 ( int, int, bool, (ord_less int), min_1, (zero_zero int) ) 15.91/16.13 ( int, int, bool, (ord_less int), min_1, min_1 ) 15.91/16.13 ( int, int, bool, (ord_less int), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.13 ( int, int, bool, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 15.91/16.13 ( int, int, bool, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 15.91/16.13 ( int, int, bool, (ord_less int), t, (zero_zero int) ) 15.91/16.13 ( int, int, bool, (ord_less int), t, (one_one int) ) 15.91/16.13 ( int, int, bool, (ord_less int), t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.13 ( int, int, bool, (ord_less int), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.13 ( int, int, bool, (ord_less int), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.13 ( int, int, bool, (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.91/16.14 ( int, int, bool, quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 15.91/16.14 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong s1), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.14 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong s1), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.14 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong s1), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.14 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.14 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.14 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.14 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.14 ( int, int, int, (plus_plus int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.91/16.14 ( int, int, int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.91/16.14 ( int, int, int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.91/16.14 ( 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))), (zero_zero int) ) 15.91/16.14 ( int, int, int, (times_times int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.91/16.14 ( 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_1 ) 15.91/16.14 ( int, int, int, (minus_minus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.91/16.14 ( int, int, int, legendre, (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.14 ( int, int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP _let_0 _let_1 (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))), s, (one_one int) ) 15.91/16.14 ( int, int, (fun int bool), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.91/16.14 ( int, int, (fun int bool), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.14 ( int, int, (fun int bool), zcong, s1, s ) 15.91/16.14 ( int, int, (fun int bool), zcong, s1, skv_3 ) 15.91/16.14 ( int, int, (fun int bool), zcong, s1, skv_9 ) 15.91/16.14 ( int, int, (fun int bool), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.91/16.14 ( int, int, (fun int bool), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.91/16.14 ( int, int, rat, fract, (zero_zero int), (one_one int) ) 15.91/16.14 ( int, int, rat, fract, (one_one int), (one_one int) ) 15.91/16.14 ( int, int, (product_prod int int), (product_Pair int int), (zero_zero int), (one_one int) ) 15.91/16.14 ( int, int, (product_prod int int), (product_Pair int int), (one_one int), (one_one int) ) 15.91/16.14 ( int, int, (product_prod int int), (product_Pair int int), s, (one_one int) ) 15.91/16.14 ( int, (fun int bool), bool, (member int), (one_one int), zEven ) 15.91/16.14 ( (fun int nat), (fun int bool), bool, (nat_tr1645093318rphism int nat), nat_1, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.91/16.14 ( (fun nat int), (fun nat bool), bool, (nat_tr1645093318rphism nat int), (semiring_1_of_nat int), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 15.91/16.14 ( (fun real real), real, (fun (filter real) bool), (tendsto real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real) ) 15.91/16.14 ( (fun real real), (fun nat real), (fun nat real), (combb real real nat), (inverse_inverse real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) ) 15.91/16.14 ( complex, nat, complex, (power_power complex), ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.14 ( complex, complex, complex, (times_times complex), ii, ii ) 15.91/16.14 ( complex, complex, complex, (times_times complex), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.91/16.14 ( complex, complex, complex, (times_times complex), (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.91/16.14 ( (fun nat real), real, bool, (sums real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 15.91/16.14 ( (fun nat real), real, (fun (filter nat) bool), (tendsto nat real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 15.91/16.14 ( (fun nat real), (fun nat nat), (fun nat real), (combb nat real nat), (real_1 nat), suc ) 15.91/16.14 ( (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)))) ) 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_let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool nat)) (fequal real))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int (fun nat real)))) (let ((_let_5 (fun int _let_1))) (hAPP (fun nat real) _let_4 (hAPP _let_5 (fun (fun nat real) _let_4) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_5 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_5) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))) ) 16.00/16.22 ( (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (fun (fun _let_1 _let_0) (fun (fun int _let_1) (fun int 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real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))), (real_1 nat) ) 16.00/16.22 ( (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))))) ) 16.00/16.22 ) 16.00/16.22 (instantiation (let ((_let_0 (fun X_c X_a))) (let ((_let_1 (product_prod X_b X_c))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (= (hAPP _let_1 X_a (hAPP (fun X_b _let_0) (fun _let_1 X_a) (product_prod_rec X_b X_c X_a) F1) (hAPP X_c _let_1 (hAPP X_b (fun X_c _let_1) (product_Pair X_b X_c) A_2) B_1)) (hAPP X_c X_a (hAPP X_b _let_0 F1 A_2) B_1)) ))) 16.00/16.22 ( real, real, bool, (ord_less_eq real), (zero_zero real), pi ) 16.00/16.22 ( 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)))) ) 16.00/16.22 ( 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)))) ) 16.00/16.22 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_6 ) 16.00/16.22 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_11 ) 16.00/16.22 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_12 ) 16.00/16.22 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_14 ) 16.00/16.22 ( real, real, bool, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.00/16.22 ( 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))) ) 16.00/16.22 ( 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) ) 16.00/16.22 ( real, real, bool, (ord_less_eq real), skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.22 ( real, real, bool, (ord_less real), (zero_zero real), pi ) 16.00/16.22 ( 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)))) ) 16.00/16.22 ( 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)))) ) 16.00/16.22 ( real, real, bool, (ord_less real), (zero_zero real), skv_2 ) 16.00/16.22 ( real, real, bool, (ord_less real), (zero_zero real), skv_10 ) 16.00/16.22 ( real, real, bool, (ord_less real), (zero_zero real), skv_13 ) 16.00/16.22 ( 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)))) ) 16.00/16.22 ( real, real, bool, (ord_less real), pi, (zero_zero real) ) 16.00/16.22 ( 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)))) ) 16.00/16.22 ( 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))) ) 16.00/16.22 ( 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) ) 16.00/16.23 ( 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) ) 16.00/16.23 ( 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 ) 16.00/16.23 ( real, real, real, (minus_minus real), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.00/16.23 ( 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))) ) 16.00/16.23 ( 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)))) ) 16.00/16.23 ( 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)))) ) 16.00/16.23 ( 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))))))))) ) 16.00/16.23 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.23 ( 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)))) ) 16.00/16.23 ( 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)))) ) 16.00/16.23 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.00/16.23 ( 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))) ) 16.00/16.23 ( 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))) ) 16.00/16.23 ( 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))) ) 16.00/16.23 ( real, real, real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.00/16.23 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 16.00/16.23 ( 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)))))) ) 16.00/16.23 ( 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 ) 16.00/16.23 ( real, real, complex, complex_1, (zero_zero real), (zero_zero real) ) 16.00/16.23 ( real, real, complex, complex_1, (zero_zero real), (one_one real) ) 16.00/16.23 ( real, real, complex, complex_1, (one_one real), (zero_zero real) ) 16.00/16.23 ( 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))))) ) 16.00/16.23 ( real, (filter nat), bool, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real (fun (filter nat) bool)) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real), sequentially ) 16.00/16.23 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 16.00/16.23 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 16.00/16.23 ( 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))) ) 16.00/16.23 ( 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))) ) 16.00/16.23 ( 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))) ) 16.00/16.23 ( nat, nat, nat, (plus_plus nat), (one_one nat), (one_one nat) ) 16.00/16.23 ( int, nat, int, (power_power int), s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.23 ( int, nat, int, (power_power int), s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.23 ( int, nat, int, (power_power int), skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.23 ( int, int, bool, (ord_less_eq int), (zero_zero int), (one_one int) ) 16.00/16.23 ( int, int, bool, (ord_less_eq int), (zero_zero int), min_1 ) 16.00/16.23 ( 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))) ) 16.00/16.23 ( int, int, bool, (ord_less_eq int), (zero_zero int), s ) 16.00/16.23 ( int, int, bool, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.00/16.23 ( 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))) ) 16.00/16.23 ( int, int, bool, (ord_less_eq int), (zero_zero int), skv_3 ) 16.00/16.23 ( int, int, bool, (ord_less_eq int), (zero_zero int), skv_9 ) 16.00/16.23 ( int, int, bool, (ord_less_eq int), (one_one int), t ) 16.00/16.23 ( int, int, bool, (ord_less_eq int), min_1, pls ) 16.00/16.23 ( int, int, bool, (ord_less_eq int), min_1, min_1 ) 16.00/16.23 ( int, int, bool, (ord_less int), (zero_zero int), (zero_zero int) ) 16.00/16.23 ( int, int, bool, (ord_less int), (zero_zero int), (one_one int) ) 16.00/16.23 ( 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))) ) 16.00/16.23 ( int, int, bool, (ord_less int), (zero_zero int), min_1 ) 16.00/16.23 ( int, int, bool, (ord_less int), min_1, (zero_zero int) ) 16.00/16.23 ( int, int, bool, (ord_less int), min_1, min_1 ) 16.00/16.23 ( 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))) ) 16.00/16.23 ( int, int, bool, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 16.00/16.23 ( int, int, bool, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 16.00/16.23 ( int, int, bool, (ord_less int), t, (zero_zero int) ) 16.00/16.23 ( int, int, bool, (ord_less int), t, (one_one int) ) 16.00/16.23 ( 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))) ) 16.00/16.23 ( int, int, bool, (ord_less int), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.00/16.23 ( int, int, bool, (ord_less int), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.00/16.23 ( int, int, bool, (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.00/16.23 ( int, int, bool, quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 16.00/16.23 ( 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))) ) 16.00/16.23 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong s1), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.00/16.23 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong s1), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP 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(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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_102768 $$unsorted) (BOUND_VARIABLE_102769 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_102768) BOUND_VARIABLE_102769)) _let_2)) (or (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_102768) _let_2)) (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_102769))) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_102769) _let_2)) (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_102768)))))) ))))) 16.00/16.28 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.28 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.00/16.28 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.00/16.28 ( 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))))))))) ) 16.00/16.28 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.28 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.00/16.28 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.00/16.28 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.00/16.28 ( 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))) ) 16.00/16.28 ( 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))) ) 16.00/16.28 ( 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))) ) 16.00/16.28 ) 16.00/16.28 (instantiation (let ((_let_0 (fun int int))) (forall ((B $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) B))) (= (hAPP int int (hAPP int _let_0 (div_mod int) (hAPP int int (number_number_of int) min_1)) B) (hAPP int int (hAPP int _let_0 (minus_minus int) B) (one_one int)))) )) 16.00/16.28 ( (zero_zero int) ) 16.00/16.28 ( (one_one int) ) 16.00/16.28 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.00/16.28 ( min_1 ) 16.00/16.28 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.00/16.28 ) 16.00/16.28 (instantiation (let ((_let_0 (fun real real))) (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (hBOOL (hAPP real bool (hAPP _let_0 (fun real bool) (isCont real real) (hAPP nat _let_0 root N_1)) (zero_zero real)))) )) 16.00/16.28 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.28 ) 16.00/16.28 (instantiation (let ((_let_0 (norm_norm X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_102811 $$unsorted) (BOUND_VARIABLE_102812 $$unsorted)) (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_102811) BOUND_VARIABLE_102812))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP X_a real _let_0 BOUND_VARIABLE_102811)) (hAPP X_a real _let_0 BOUND_VARIABLE_102812))))) )) 16.00/16.28 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.00/16.28 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 16.00/16.28 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.00/16.28 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.00/16.28 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.00/16.28 ( 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))), (zero_zero int) ) 16.00/16.28 ( 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 ) 16.00/16.29 ( 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_1 ) 16.00/16.29 ( complex, ii, ii ) 16.00/16.29 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 16.00/16.29 ( 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 ) 16.00/16.29 ) 16.00/16.29 (instantiation (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_102833 $$unsorted) (BOUND_VARIABLE_102834 $$unsorted)) (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_102833)) BOUND_VARIABLE_102834)) (hAPP X_a X_a _let_0 (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_102833) BOUND_VARIABLE_102834)))) )))) 16.00/16.29 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.29 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.29 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.29 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.29 ) 16.00/16.29 (instantiation (let ((_let_0 (product_prod_size X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (= _let_0 (ti (fun (fun X_a nat) (fun (fun X_b nat) (fun (product_prod X_a X_b) nat))) _let_0)) )) 16.00/16.29 ( real, real ) 16.00/16.29 ( nat, nat ) 16.00/16.29 ( int, int ) 16.00/16.29 ( int, (product_prod int int) ) 16.00/16.29 ( quickcheck_code_int, quickcheck_code_int ) 16.00/16.29 ( (product_prod int int), (product_prod int int) ) 16.00/16.29 ( (product_prod nat nat), (product_prod nat nat) ) 16.00/16.29 ( code_code_numeral, code_code_numeral ) 16.00/16.29 ) 16.00/16.29 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_102864 $$unsorted) (BOUND_VARIABLE_102865 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (not (forall ((Z_2 $$unsorted)) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 (zero_zero X_a)) Z_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 Z_2) (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) Z_2) BOUND_VARIABLE_102864)) BOUND_VARIABLE_102865))) )) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_102864) BOUND_VARIABLE_102865))) )))) 16.00/16.29 ( real, (zero_zero real), pi ) 16.00/16.29 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.00/16.29 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.00/16.29 ( real, (zero_zero real), skv_6 ) 16.00/16.29 ( real, (zero_zero real), skv_11 ) 16.00/16.29 ( real, (zero_zero real), skv_12 ) 16.00/16.29 ( real, (zero_zero real), skv_14 ) 16.00/16.29 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.00/16.29 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.29 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.00/16.29 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.29 ( int, (zero_zero int), (one_one int) ) 16.00/16.29 ( int, (zero_zero int), min_1 ) 16.00/16.29 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.29 ( int, (zero_zero int), s ) 16.00/16.29 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.00/16.29 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.00/16.29 ( int, (zero_zero int), skv_3 ) 16.00/16.29 ( int, (zero_zero int), skv_9 ) 16.00/16.29 ( int, (one_one int), t ) 16.00/16.29 ( int, min_1, pls ) 16.00/16.29 ( int, min_1, min_1 ) 16.00/16.29 ) 16.00/16.29 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (plus_plus nat))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP nat nat (hAPP nat _let_0 _let_1 M) N) (hAPP nat nat (hAPP nat _let_0 _let_1 N) M)) ))) 16.00/16.29 ( (one_one nat), (one_one nat) ) 16.00/16.29 ) 16.00/16.29 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_102983 $$unsorted) (BOUND_VARIABLE_102984 $$unsorted)) (or (not (field X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_102983) BOUND_VARIABLE_102984) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_102983) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_102984)))) )) 16.00/16.29 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.29 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.00/16.29 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.00/16.29 ( 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))))))))) ) 16.00/16.29 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.29 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.00/16.29 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.00/16.29 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.00/16.29 ( 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))) ) 16.00/16.29 ( 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))) ) 16.00/16.29 ( 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))) ) 16.00/16.29 ) 16.00/16.29 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102997 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_102997) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_102997)))) ) 16.00/16.29 ( real, (zero_zero real) ) 16.00/16.29 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.29 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.00/16.29 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.00/16.29 ( real, skv_14 ) 16.00/16.29 ( int, (zero_zero int) ) 16.00/16.29 ( int, (one_one int) ) 16.00/16.29 ( int, min_1 ) 16.00/16.29 ) 16.00/16.29 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103062 $$unsorted)) (or (not (linordered_field X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP X_a X_a (inverse_inverse X_a) (hAPP nat X_a (semiring_1_of_nat X_a) (hAPP nat nat (fact_fact nat) BOUND_VARIABLE_103062)))))) ) 16.00/16.29 ( real, (hAPP nat nat suc (zero_zero nat)) ) 16.00/16.29 ( int, (hAPP nat nat suc (zero_zero nat)) ) 16.00/16.29 ) 16.00/16.29 (instantiation (let ((_let_0 (fun nat nat))) (forall ((Z_1 $$unsorted)) (= (hAPP nat nat (hAPP nat _let_0 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) Z_1) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) Z_1) Z_1)) )) 16.00/16.29 ( (one_one nat) ) 16.00/16.29 ) 16.00/16.29 (instantiation (let ((_let_0 (inverse_inverse X_a))) (let ((_let_1 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_103279 $$unsorted)) (or (not (divisi14063676e_zero X_a)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_103279)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_103279)))) ))) 16.00/16.29 ( real, (zero_zero real) ) 16.00/16.29 ( real, (one_one real) ) 16.00/16.29 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.00/16.29 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.00/16.29 ( int, pls ) 16.00/16.29 ( int, (one_one int) ) 16.00/16.29 ( int, min_1 ) 16.00/16.29 ( complex, ii ) 16.00/16.29 ( complex, (one_one complex) ) 16.00/16.29 ) 16.00/16.29 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real real))) (let ((_let_6 (fun nat real))) (let ((_let_7 (fun _let_1 real))) (let ((_let_8 (fun nat _let_5))) (let ((_let_9 (fun nat _let_1))) (let ((_let_10 (fun (filter nat) bool))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (tendsto nat real))) (let ((_let_13 (hAPP _let_6 _let_6 (hAPP _let_8 (fun _let_6 _let_6) (combs nat real real) (hAPP _let_6 _let_8 (hAPP (fun real _let_5) (fun _let_6 _let_8) (combb real _let_5 nat) (times_times real)) (hAPP real _let_6 (power_power real) (hAPP int real (number_number_of real) min_1)))) A_2))) (forall ((A_2 $$unsorted)) (let ((_let_0 (filter nat))) (or (not (hBOOL (hAPP _let_0 bool (hAPP real _let_10 (hAPP _let_6 _let_11 _let_12 A_2) _let_0) sequentially))) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_3 _let_4 _let_0) (hAPP nat real A_2 N_2))) )) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_3 _let_4 (hAPP nat real A_2 (hAPP nat nat suc N_2))) (hAPP nat real A_2 N_2))) )) (hBOOL (hAPP _let_0 bool (hAPP real _let_10 (hAPP _let_6 _let_11 _let_12 (hAPP _let_9 _let_6 (hAPP _let_7 (fun _let_9 _let_6) (combb _let_1 real nat) (hAPP _let_6 _let_7 (big_co1399186613setsum nat real) _let_13)) (hAPP _let_2 _let_9 (hAPP _let_9 (fun _let_2 _let_9) (combb nat _let_1 nat) (hAPP nat _let_9 (ord_atLeastLessThan nat) (zero_zero nat))) (hAPP nat _let_2 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (hAPP _let_6 real (suminf real) _let_13)) sequentially)))) ))))))))))))))) 16.00/16.29 ( (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 16.00/16.29 ) 16.00/16.29 (instantiation (let ((_let_0 (fun X_a X_b))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (isCont X_a X_b))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_103312 $$unsorted) (BOUND_VARIABLE_103313 $$unsorted)) (or (not (topological_space X_a)) (not (real_n1866405975lgebra X_b)) (not (hBOOL (hAPP X_a bool (hAPP _let_0 _let_1 _let_2 BOUND_VARIABLE_103312) BOUND_VARIABLE_103313))) (= (zero_zero X_b) (hAPP X_a X_b BOUND_VARIABLE_103312 BOUND_VARIABLE_103313)) (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_103312)) BOUND_VARIABLE_103313))) )))) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_6 ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_14 ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_10 ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_13 ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less real) (one_one real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))), (zero_zero real) ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.00/16.29 ( bool, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi))), pi ) 16.00/16.29 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) skv_14), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.29 ( bool, nat, (even_odd_even nat), (zero_zero nat) ) 16.00/16.29 ( bool, nat, (even_odd_even nat), (one_one nat) ) 16.00/16.29 ( bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.29 ( bool, nat, prime, (zero_zero nat) ) 16.00/16.29 ( bool, nat, prime, (one_one nat) ) 16.00/16.29 ( bool, nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.29 ( bool, (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 16.00/16.29 ( bool, (fun nat bool), (hAPP (fun nat int) (fun (fun nat bool) bool) (nat_tr1645093318rphism nat int) (semiring_1_of_nat int)), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 16.00/16.29 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 16.00/16.29 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.00/16.29 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 16.00/16.29 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 16.00/16.29 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.00/16.29 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_3 ) 16.00/16.29 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_9 ) 16.00/16.29 ( bool, int, zprime, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.30/16.30 ( bool, int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.30/16.30 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 16.30/16.30 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.30/16.30 ( bool, int, nat_neg, (one_one int) ) 16.30/16.30 ( bool, int, nat_neg, (hAPP int int (number_number_of int) min_1) ) 16.30/16.30 ( bool, int, nat_neg, (hAPP int int (number_number_of int) pls) ) 16.30/16.30 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), (zero_zero int) ) 16.30/16.30 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 16.30/16.30 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 16.30/16.30 ( bool, int, nat_is_nat, (zero_zero int) ) 16.30/16.30 ( bool, int, nat_is_nat, (one_one int) ) 16.30/16.30 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.30/16.30 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.30/16.30 ( bool, int, (even_odd_even int), (zero_zero int) ) 16.30/16.30 ( bool, int, (even_odd_even int), (one_one int) ) 16.30/16.30 ( bool, int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 16.30/16.30 ( bool, int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))), (zero_zero int) ) 16.30/16.30 ( bool, int, (hAPP int (fun int bool) (ord_less int) min_1), (zero_zero int) ) 16.30/16.30 ( bool, int, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 16.30/16.30 ( bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 16.30/16.30 ( bool, int, (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.30/16.30 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.30/16.30 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 16.30/16.30 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 16.30/16.30 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 16.30/16.30 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.30/16.30 ( bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.30/16.30 ( bool, int, (hAPP int (fun int bool) (ord_less int) t), (zero_zero int) ) 16.30/16.30 ( bool, int, (hAPP int (fun int bool) (ord_less int) t), (one_one int) ) 16.30/16.30 ( bool, int, (hAPP int (fun int bool) (ord_less int) t), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.30/16.30 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.30/16.30 ( bool, int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.30/16.30 ( bool, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun int bool) (ord_less 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)))), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 16.30/16.30 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_3), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.30/16.30 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_3)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.30/16.30 ( 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_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.30/16.30 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_9), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.30/16.30 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_9)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.30/16.30 ( bool, (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 16.30/16.30 ( bool, (fun int bool), (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 16.30/16.30 ( bool, (filter real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (filter real) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)) (zero_zero real))))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.30/16.30 ( bool, (filter nat), (trivial_limit nat), sequentially ) 16.30/16.30 ( bool, (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 16.30/16.30 ( real, real, sqrt, (zero_zero real) ) 16.30/16.30 ( real, real, sqrt, (one_one real) ) 16.30/16.30 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.30/16.30 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.30/16.30 ( real, real, (uminus_uminus real), (one_one real) ) 16.30/16.30 ( real, real, (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.30/16.30 ( real, real, (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.30/16.30 ( real, real, tan, (zero_zero real) ) 16.30/16.30 ( real, real, tan, pi ) 16.30/16.30 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.30/16.30 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.30/16.30 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.30/16.30 ( real, real, cos, (zero_zero real) ) 16.30/16.30 ( real, real, cos, pi ) 16.30/16.30 ( real, real, cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.30/16.30 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.30/16.30 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.30/16.30 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.30/16.30 ( real, real, cos, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.30/16.30 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.30/16.30 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.30/16.30 ( real, real, cos, skv_14 ) 16.30/16.30 ( real, real, ln, (one_one real) ) 16.30/16.30 ( real, real, (inverse_inverse real), (zero_zero real) ) 16.30/16.30 ( real, real, sin, (zero_zero real) ) 16.30/16.30 ( real, real, sin, pi ) 16.30/16.30 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.30/16.30 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.30/16.30 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.30/16.30 ( real, real, sin, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.30/16.30 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.30/16.30 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.30/16.30 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.30/16.30 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.30/16.30 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.30/16.30 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.30/16.30 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.30/16.30 ( real, real, (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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 16.30/16.30 ( real, real, arctan, (zero_zero real) ) 16.30/16.30 ( real, real, arctan, (one_one real) ) 16.30/16.30 ( real, real, arctan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.30/16.30 ( real, real, arctan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 16.30/16.30 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.30/16.31 ( real, real, (sgn_sgn real), (zero_zero real) ) 16.30/16.31 ( 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))) ) 16.30/16.31 ( 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)))) ) 16.30/16.31 ( 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)))) ) 16.30/16.31 ( 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))))))))) ) 16.30/16.31 ( 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))) ) 16.30/16.31 ( 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))) ) 16.30/16.31 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), pi ) 16.30/16.31 ( 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))) ) 16.30/16.31 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1))))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.30/16.31 ( real, nat, (real_1 nat), (zero_zero nat) ) 16.30/16.31 ( real, nat, (real_1 nat), (one_one nat) ) 16.30/16.31 ( real, int, (real_1 int), (zero_zero int) ) 16.30/16.31 ( real, int, (real_1 int), (one_one int) ) 16.30/16.31 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.30/16.31 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.30/16.31 ( real, int, (number_number_of real), min_1 ) 16.30/16.31 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.30/16.31 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.30/16.31 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.30/16.31 ( 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)))))))) ) 16.30/16.31 ( real, (fun real bool), (the real), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0)))))))))))))) ) 16.30/16.31 ( real, complex, im, ii ) 16.30/16.31 ( real, complex, im, (zero_zero complex) ) 16.30/16.31 ( real, complex, im, (one_one complex) ) 16.30/16.31 ( real, complex, re, ii ) 16.30/16.31 ( real, complex, re, (zero_zero complex) ) 16.30/16.31 ( real, complex, re, (one_one complex) ) 16.30/16.31 ( real, (fun nat real), (suminf real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (combc nat nat nat))) (let ((_let_4 (fun nat _let_0))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun _let_1 _let_4))) (let ((_let_7 (combb real _let_0 nat))) (hAPP _let_1 _let_1 (hAPP _let_4 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_4 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 16.30/16.31 ( real, rat, ratreal, (zero_zero rat) ) 16.30/16.31 ( real, rat, ratreal, (one_one rat) ) 16.30/16.31 ( nat, real, natfloor, (zero_zero real) ) 16.30/16.31 ( nat, real, natfloor, (one_one real) ) 16.30/16.31 ( nat, real, natceiling, (zero_zero real) ) 16.30/16.31 ( nat, real, natceiling, (one_one real) ) 16.30/16.31 ( nat, nat, suc, (zero_zero nat) ) 16.30/16.31 ( nat, nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 16.30/16.31 ( nat, nat, suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 16.30/16.31 ( nat, nat, (fact_fact nat), (zero_zero nat) ) 16.30/16.31 ( nat, nat, (fact_fact nat), (hAPP nat nat suc (zero_zero nat)) ) 16.30/16.31 ( nat, nat, (size_size nat), (zero_zero nat) ) 16.30/16.31 ( nat, nat, fact, (zero_zero nat) ) 16.30/16.31 ( nat, nat, nat_size, (zero_zero nat) ) 16.30/16.31 ( nat, nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (one_one nat) ) 16.30/16.31 ( nat, int, nat_1, (zero_zero int) ) 16.30/16.31 ( nat, int, nat_1, (one_one int) ) 16.30/16.31 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.30/16.31 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.30/16.31 ( nat, int, (number_number_of nat), pls ) 16.30/16.31 ( nat, int, (number_number_of nat), (hAPP int int bit1 pls) ) 16.30/16.31 ( nat, int, (number_number_of nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.30/16.31 ( nat, int, (number_number_of nat), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.30/16.31 ( nat, code_code_numeral, (size_size code_code_numeral), (zero_zero code_code_numeral) ) 16.30/16.31 ( nat, code_code_numeral, code_c271388182l_size, (zero_zero code_code_numeral) ) 16.30/16.31 ( (fun nat bool), bool, (combk bool nat), fTrue ) 16.30/16.31 ( (fun nat bool), nat, (ord_less nat), (zero_zero nat) ) 16.30/16.31 ( (fun nat bool), nat, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))), (zero_zero nat) ) 16.30/16.31 ( (fun nat bool), (fun nat bool), (collect nat), prime ) 16.30/16.31 ( (fun nat bool), (fun nat bool), (let ((_let_0 (fun nat bool))) (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool nat) fNot)), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat))) ) 16.30/16.31 ( (fun nat nat), nat, (plus_plus nat), (one_one nat) ) 16.30/16.31 ( (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))) ) 16.30/16.31 ( (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) ) 16.30/16.31 ( int, nat, (semiring_1_of_nat int), (zero_zero nat) ) 16.30/16.31 ( int, nat, (semiring_1_of_nat int), (hAPP nat nat suc (zero_zero nat)) ) 16.30/16.31 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.30/16.31 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.30/16.31 ( int, nat, (hAPP int (fun nat int) (power_power int) s), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.30/16.31 ( int, nat, (hAPP int (fun nat int) (power_power int) s1), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.30/16.31 ( int, nat, (hAPP int (fun nat int) (power_power int) skv_8), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.30/16.31 ( int, int, (number_number_of int), pls ) 16.30/16.31 ( int, int, (number_number_of int), (hAPP int int bit1 pls) ) 16.30/16.31 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.30/16.31 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.30/16.31 ( int, int, (number_number_of int), min_1 ) 16.30/16.31 ( int, int, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.30/16.31 ( int, int, bit0, pls ) 16.30/16.31 ( int, int, bit0, (hAPP int int bit1 pls) ) 16.30/16.31 ( int, int, bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.30/16.31 ( int, int, bit0, min_1 ) 16.30/16.31 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.30/16.31 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.30/16.31 ( int, int, bit1, pls ) 16.30/16.31 ( int, int, bit1, (hAPP int int bit1 pls) ) 16.30/16.31 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.30/16.31 ( int, int, bit1, min_1 ) 16.30/16.31 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.30/16.31 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.30/16.31 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.30/16.31 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 16.30/16.31 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 16.30/16.31 ( int, int, (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), m ) 16.30/16.31 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 16.30/16.31 ( int, int, (uminus_uminus int), pls ) 16.30/16.31 ( int, int, (uminus_uminus int), (one_one int) ) 16.30/16.31 ( int, int, (uminus_uminus int), min_1 ) 16.30/16.31 ( int, int, pred, pls ) 16.30/16.31 ( int, int, pred, min_1 ) 16.30/16.31 ( int, int, (hAPP int (fun int int) legendre (hAPP int int (number_number_of int) min_1)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.30/16.31 ( int, int, succ, pls ) 16.30/16.31 ( int, int, succ, min_1 ) 16.30/16.31 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (one_one int) ) 16.30/16.31 ( 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))))), (zero_zero int) ) 16.30/16.31 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), t ) 16.30/16.31 ( 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_1 ) 16.30/16.31 ( int, int, (hAPP int (fun int int) (minus_minus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 16.30/16.31 ( int, int, (fact_fact int), (zero_zero int) ) 16.30/16.31 ( int, int, (fact_fact int), (one_one int) ) 16.30/16.31 ( int, quickcheck_code_int, quickcheck_int_of, (zero_zero quickcheck_code_int) ) 16.30/16.31 ( 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))) ) 16.30/16.31 ( int, code_code_numeral, code_int_of, (zero_zero code_code_numeral) ) 16.30/16.31 ( (fun int bool), int, (ord_less_eq int), (zero_zero int) ) 16.30/16.31 ( (fun int bool), int, (ord_less_eq int), (one_one int) ) 16.30/16.31 ( (fun int bool), int, (ord_less_eq int), min_1 ) 16.30/16.31 ( (fun int bool), int, (ord_less int), (zero_zero int) ) 16.30/16.31 ( (fun int bool), int, (ord_less int), min_1 ) 16.30/16.31 ( (fun int bool), int, (ord_less int), s ) 16.30/16.31 ( (fun int bool), int, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.30/16.31 ( (fun int bool), int, (ord_less int), t ) 16.30/16.31 ( (fun int bool), int, (ord_less int), skv_3 ) 16.30/16.31 ( (fun int bool), int, (ord_less int), skv_9 ) 16.30/16.31 ( (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))) ) 16.30/16.31 ( (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))) ) 16.30/16.31 ( (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) ) 16.30/16.31 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), s ) 16.30/16.31 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), skv_3 ) 16.30/16.31 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), skv_9 ) 16.30/16.31 ( (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_1) ) 16.30/16.31 ( (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)))) ) 16.30/16.31 ( (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_1) ) 16.30/16.31 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 16.30/16.31 ( (fun int bool), (fun int bool), (collect int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (fun int _let_1))) (hAPP _let_2 _let_0 (hAPP (fun _let_0 bool) (fun _let_2 _let_0) (combb _let_0 bool int) (fEx int)) (hAPP _let_1 _let_2 (hAPP _let_4 (fun _let_1 _let_2) (combc int _let_1 _let_0) (hAPP _let_2 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_2 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_1 (hAPP _let_5 _let_5 (combc int int int) (hAPP _let_1 _let_5 (hAPP _let_5 (fun _let_1 _let_5) (combb int _let_1 int) (plus_plus int)) (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int)))))))))) ) 16.30/16.32 ( (fun int bool), (fun int bool), (collect int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_2 _let_0 (hAPP (fun _let_0 bool) (fun _let_2 _let_0) (combb _let_0 bool int) (fEx int)) (hAPP _let_1 _let_2 (hAPP _let_4 (fun _let_1 _let_2) (combc int _let_1 _let_0) (hAPP _let_2 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_2 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))) ) 16.30/16.32 ( (fun int bool), (fun int bool), (let ((_let_0 (fun int bool))) (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool int) fNot)), (let ((_let_0 (fun int (fun int bool)))) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))) ) 16.30/16.32 ( (fun int bool), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (fun int _let_1))) (hAPP _let_1 _let_2 (hAPP _let_4 (fun _let_1 _let_2) (combc int _let_1 _let_0) (hAPP _let_2 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_2 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_1 (hAPP _let_5 _let_5 (combc int int int) (hAPP _let_1 _let_5 (hAPP _let_5 (fun _let_1 _let_5) (combb int _let_1 int) (plus_plus int)) (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int))))))))) ) 16.30/16.32 ( (fun int bool), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 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real, (ord_less_eq real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.30/16.32 ( (fun real bool), real, (ord_less_eq real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.30/16.32 ( (fun real bool), real, (ord_less_eq real), skv_14 ) 16.30/16.32 ( (fun real bool), real, (ord_less real), (zero_zero real) ) 16.30/16.32 ( (fun real bool), real, (ord_less real), (one_one real) ) 16.30/16.32 ( (fun real bool), real, (ord_less real), pi ) 16.30/16.32 ( (fun real bool), real, (ord_less real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.30/16.32 ( (fun real bool), real, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.30/16.32 ( (fun real bool), real, (ord_less real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.30/16.32 ( (fun real bool), real, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.30/16.32 ( (fun real bool), real, (let ((_let_0 (fun real (fun real bool)))) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.30/16.32 ( (fun real bool), real, (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos))))), (zero_zero real) ) 16.30/16.32 ( (fun real bool), (fun real bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_2 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 real) fconj) (hAPP real _let_0 (ord_less_eq real) (zero_zero real))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun real _let_2))) (let ((_let_5 (combc real real bool))) (hAPP _let_0 _let_0 (hAPP _let_4 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_4 (hAPP (fun bool _let_2) (fun _let_0 _let_4) (combb bool _let_2 real) fconj) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))))))) ) 16.30/16.32 ( (fun real bool), (fun real bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun real (fun real bool)))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 (fun (fun real bool) (fun real bool)) (combs real bool bool) (hAPP (fun real bool) _let_2 (hAPP (fun bool _let_0) (fun (fun real bool) _let_2) (combb bool _let_0 real) fconj) (hAPP real (fun real bool) (hAPP _let_1 _let_1 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP real _let_0 (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))) ) 16.30/16.32 ( (fun real bool), (fun real bool), (collect real), (let ((_let_0 (fun real bool))) (let ((_let_1 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((_let_28 (fun _let_13 _let_13))) (let ((_let_29 (fun int _let_28))) (let ((_let_30 (fun int _let_1))) (hAPP _let_14 _let_0 (hAPP _let_8 (fun _let_14 _let_0) (combb (fun int bool) bool real) _let_11) (hAPP _let_15 _let_14 (hAPP _let_10 (fun _let_15 _let_14) (combb _let_7 (fun int bool) real) (hAPP _let_8 _let_10 (combb (fun int bool) bool int) _let_11)) (hAPP (fun int bool) _let_15 (hAPP _let_17 (fun (fun int bool) _let_15) (combc real (fun int bool) _let_7) (hAPP _let_18 _let_17 (hAPP (fun _let_12 _let_16) (fun _let_18 _let_17) (combb _let_12 _let_16 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_20 _let_18 (hAPP _let_21 (fun _let_20 _let_18) (combb _let_19 _let_12 real) (hAPP (fun _let_4 _let_5) _let_21 (combb _let_4 _let_5 int) (combs int bool bool))) (hAPP _let_15 _let_20 (hAPP _let_22 (fun _let_15 _let_20) (combb _let_7 _let_19 real) (hAPP _let_6 _let_22 (combb (fun int bool) _let_4 int) (hAPP (fun bool _let_3) _let_6 (combb bool _let_3 int) fconj))) (hAPP _let_23 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(let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun (fun nat real) (fun nat bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun int _let_4))) (hAPP _let_11 _let_1 (hAPP (fun _let_0 bool) (fun _let_11 _let_1) (combb _let_0 bool real) (fEx int)) (hAPP _let_13 _let_11 (hAPP _let_14 (fun _let_13 _let_11) (combb (fun int (fun nat bool)) _let_0 real) (hAPP (fun (fun nat bool) bool) _let_14 (combb (fun nat bool) bool int) (fEx nat))) (hAPP (fun nat bool) _let_13 (hAPP _let_16 (fun (fun nat bool) _let_13) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_18 _let_16 (hAPP (fun _let_17 _let_15) (fun _let_18 _let_16) (combb _let_17 _let_15 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_20 _let_18 (hAPP _let_21 (fun _let_20 _let_18) (combb _let_19 _let_17 real) (hAPP (fun _let_8 _let_7) _let_21 (combb _let_8 _let_7 int) (combs nat bool bool))) (hAPP _let_13 _let_20 (hAPP _let_22 (fun _let_13 _let_20) (combb (fun int (fun nat bool)) _let_19 real) (hAPP 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(fun (fun int bool) _let_13) (combc real (fun int bool) _let_7) (hAPP _let_16 _let_15 (hAPP (fun _let_10 _let_14) (fun _let_16 _let_15) (combb _let_10 _let_14 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_18 _let_16 (hAPP _let_19 (fun _let_18 _let_16) (combb _let_17 _let_10 real) (hAPP (fun _let_4 _let_5) _let_19 (combb _let_4 _let_5 int) (combs int bool bool))) (hAPP _let_13 _let_18 (hAPP _let_20 (fun _let_13 _let_18) (combb _let_7 _let_17 real) (hAPP _let_6 _let_20 (combb (fun int bool) _let_4 int) (hAPP (fun bool _let_3) _let_6 (combb bool _let_3 int) fconj))) (hAPP _let_21 _let_13 (hAPP _let_23 (fun _let_21 _let_13) (combc real _let_21 _let_7) (hAPP _let_25 _let_23 (hAPP (fun _let_24 _let_22) (fun _let_25 _let_23) (combb _let_24 _let_22 real) (combb _let_11 (fun int bool) int)) (hAPP _let_8 _let_25 (hAPP (fun _let_0 _let_24) (fun _let_8 _let_25) (combb _let_0 _let_24 real) (combb real bool int)) (fequal real)))) (hAPP _let_11 _let_21 (hAPP _let_27 (fun _let_11 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bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 16.30/16.33 ( (fun real real), real, (inverse_divide real), (one_one real) ) 16.30/16.33 ( (fun real real), real, (inverse_divide real), pi ) 16.30/16.33 ( (fun real real), real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.30/16.33 ( (fun real real), real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.30/16.33 ( (fun real real), real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.30/16.33 ( (fun real real), real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.30/16.33 ( (fun real real), real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.30/16.33 ( (fun real real), real, (times_times real), (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.30/16.33 ( (fun real real), nat, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.30/16.33 ( (fun real real), (fun real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)))), sin ) 16.30/16.33 ( complex, real, (of_real complex), pi ) 16.30/16.33 ( complex, real, (of_real complex), (hAPP int real (number_number_of real) min_1) ) 16.30/16.33 ( complex, real, 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complex, complex, cnj, (one_one complex) ) 16.30/16.33 ( complex, complex, (uminus_uminus complex), ii ) 16.30/16.33 ( complex, complex, (uminus_uminus complex), (one_one complex) ) 16.30/16.33 ( complex, complex, (inverse_inverse complex), ii ) 16.30/16.33 ( complex, complex, expi, (zero_zero complex) ) 16.30/16.33 ( complex, complex, expi, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))) ii))) ) 16.30/16.33 ( complex, complex, (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real complex (of_real complex) pi) ) 16.30/16.33 ( complex, complex, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP 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((_let_5 (fun int _let_1))) (let ((_let_6 (fun real (fun int (fun nat bool))))) (let ((_let_7 (fun int (fun nat real)))) (let ((_let_8 (fun _let_7 (fun int (fun nat bool))))) (let ((_let_9 (fun real _let_8))) (let ((_let_10 (fun (fun nat real) (fun nat bool)))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun int _let_2))) (hAPP _let_7 _let_6 (hAPP _let_9 (fun _let_7 _let_6) (combc real _let_7 (fun int (fun nat bool))) (hAPP _let_11 _let_9 (hAPP (fun _let_10 _let_8) (fun _let_11 _let_9) (combb _let_10 _let_8 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_3 _let_11 (hAPP (fun _let_0 _let_10) (fun _let_3 _let_11) (combb _let_0 _let_10 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_7 (hAPP _let_12 (fun (fun nat real) _let_7) (combc int (fun nat real) (fun nat real)) (hAPP _let_5 _let_12 (hAPP (fun _let_1 _let_2) (fun _let_5 _let_12) (combb _let_1 _let_2 int) (combb real real nat)) (hAPP _let_4 _let_5 (hAPP (fun real _let_1) (fun _let_4 _let_5) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))) ) 16.30/16.39 ( (let ((_let_0 (fun nat bool))) (fun (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun (fun nat (fun bool bool)) (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (combb (fun nat (fun bool bool)) (fun _let_0 _let_0) int)), (combs nat bool bool) ) 16.30/16.39 ( (let ((_let_0 (fun nat bool))) (fun (fun real (fun int (fun nat (fun bool bool)))) (fun real (fun int (fun _let_0 _let_0))))), (let ((_let_0 (fun nat bool))) (fun (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (combb (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)) real)), (let ((_let_0 (fun (fun nat bool) (fun nat bool)))) (let ((_let_1 (fun nat (fun bool bool)))) (hAPP (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) (combb _let_1 _let_0 int) (combs nat bool bool)))) ) 16.47/16.39 ( (fun (fun int (fun nat bool)) (fun int (fun nat (fun bool bool)))), (fun (fun nat bool) (fun nat (fun bool bool))), (combb (fun nat bool) (fun nat (fun bool bool)) int), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun nat bool) (fun nat _let_0)) (combb bool _let_0 nat) fconj)) ) 16.47/16.39 ( (fun (fun real (fun int (fun nat bool))) (fun real (fun int (fun nat (fun bool bool))))), (fun (fun int (fun nat bool)) (fun int (fun nat (fun bool bool)))), (combb (fun int (fun nat bool)) (fun int (fun nat (fun bool bool))) real), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 nat) fconj)))))) ) 16.47/16.39 ( (fun int (fun nat real)), (fun nat real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_4 (fun (fun nat real) (fun int (fun nat real))) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 nat) ) 16.47/16.39 ( (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (fun real (fun (fun nat real) (fun nat bool))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (fun int _let_1) (fun int _let_0)))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP (fun _let_3 _let_2) (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (combb _let_1 _let_0 int)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun nat real) (fun nat bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool nat)) (fequal real)))))) ) 16.47/16.39 ( (fun (fun int (fun nat real)) (fun real (fun int (fun nat bool)))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (combc real (fun int (fun nat real)) (fun int (fun nat bool))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun nat real)) (fun int (fun nat bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool nat)) (fequal real))))))))) ) 16.47/16.39 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun real bool)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun (fun nat real) (fun nat bool)))) (hAPP (fun _let_0 _let_1) (fun (fun real _let_0) (fun real _let_1)) (combb _let_0 _let_1 real) (combb real bool nat)))), (fequal real) ) 16.47/16.39 ( (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (fun (fun real (fun _let_1 _let_0)) (fun real (fun (fun int _let_1) (fun int _let_0)))))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (fun (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0))))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (combb (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) real))), (combb (fun nat real) (fun nat bool) int) ) 16.47/16.39 ( (fun (fun real (fun real bool)) (fun real (fun (fun nat real) (fun nat bool)))), (fun (fun real bool) (fun (fun nat real) (fun nat bool))), (combb (fun real bool) (fun (fun nat real) (fun nat bool)) real), (combb real bool nat) ) 16.47/16.39 ( (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb real real nat)))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))) ) 16.47/16.39 ( (let ((_let_0 (fun nat real))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))) ) 16.47/16.40 ( (let ((_let_0 (fun nat real))) (fun (fun int (fun real real)) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat real))) (fun (fun real real) (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (combb (fun real real) (fun _let_0 _let_0) int)), (combb real real nat) ) 16.47/16.40 ) 16.47/16.40 (instantiation (let ((_let_0 (plus_plus X_a))) (forall ((X_a $$unsorted)) (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))) )) 16.47/16.40 ( bool ) 16.47/16.40 ( real ) 16.47/16.40 ( nat ) 16.47/16.40 ( (fun nat bool) ) 16.47/16.40 ( int ) 16.47/16.40 ( (fun int bool) ) 16.47/16.40 ( (fun real bool) ) 16.47/16.40 ( (fun real real) ) 16.47/16.40 ( complex ) 16.47/16.40 ( (fun nat real) ) 16.47/16.40 ( (fun int int) ) 16.47/16.40 ( rat ) 16.47/16.40 ( (fun int (fun int bool)) ) 16.47/16.40 ( quickcheck_code_int ) 16.47/16.40 ( (product_prod int int) ) 16.47/16.40 ( (fun (product_prod int int) bool) ) 16.47/16.40 ( code_code_numeral ) 16.47/16.40 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.47/16.40 ( (fun (product_prod int int) int) ) 16.47/16.40 ( (fun int (fun int (fun int bool))) ) 16.47/16.40 ( (fun int real) ) 16.47/16.40 ) 16.47/16.40 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= (hAPP complex complex cnj X_1) (hAPP complex complex cnj Y_1)) (= X_1 Y_1)) ) 16.47/16.40 ( ii, (one_one complex) ) 16.47/16.40 ( (zero_zero complex), ii ) 16.47/16.40 ( (zero_zero complex), (one_one complex) ) 16.47/16.40 ( (one_one complex), (zero_zero complex) ) 16.47/16.40 ( (one_one complex), (one_one complex) ) 16.47/16.40 ) 16.47/16.40 (instantiation (let ((_let_0 (semiring_1_of_nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_103427 $$unsorted) (BOUND_VARIABLE_103428 $$unsorted)) (or (not (linordered_semidom X_a)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_103427) BOUND_VARIABLE_103428)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_103427)) (hAPP nat X_a _let_0 BOUND_VARIABLE_103428))))) )) 16.47/16.40 ( int, (zero_zero nat), (zero_zero nat) ) 16.47/16.40 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 16.47/16.40 ) 16.47/16.40 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) K_4) K_4) (hAPP int int bit0 K_4)) ) 16.47/16.40 ( pls ) 16.47/16.40 ( (hAPP int int bit1 pls) ) 16.47/16.40 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.47/16.40 ( (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) ) 16.47/16.40 ( min_1 ) 16.47/16.40 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.47/16.40 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.47/16.40 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.47/16.40 ) 16.47/16.40 (instantiation (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_103458))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_103456 $$unsorted) (BOUND_VARIABLE_103457 $$unsorted) (BOUND_VARIABLE_103458 $$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)) BOUND_VARIABLE_103458))) (= (= BOUND_VARIABLE_103456 BOUND_VARIABLE_103457) (= (hAPP nat X_a _let_0 BOUND_VARIABLE_103456) (hAPP nat X_a _let_0 BOUND_VARIABLE_103457)))) )) 16.47/16.40 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 16.47/16.40 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 16.47/16.40 ( 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_8 ) 16.47/16.40 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 16.47/16.40 ) 16.47/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103516 $$unsorted)) (or (not (ring_char_0 X_a)) (= (= (zero_zero int) (ti int BOUND_VARIABLE_103516)) (= (zero_zero X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_103516)))) ) 16.47/16.40 ( real, (zero_zero int) ) 16.47/16.40 ( real, (one_one int) ) 16.47/16.40 ) 16.47/16.40 (instantiation (forall ((N $$unsorted)) (or (hBOOL (hAPP nat bool (even_odd_even nat) N)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) ) 16.47/16.40 ( (zero_zero nat) ) 16.47/16.40 ( (one_one nat) ) 16.47/16.40 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.47/16.40 ) 16.47/16.40 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_103554 $$unsorted) (BOUND_VARIABLE_103555 $$unsorted)) (or (not (comm_ring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_103554) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_103555)) (hAPP X_a X_a (hAPP X_a _let_0 (minus_minus X_a) BOUND_VARIABLE_103554) BOUND_VARIABLE_103555))) )) 16.47/16.40 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.47/16.40 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.47/16.40 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.47/16.40 ) 16.47/16.40 (instantiation (let ((_let_0 (semiring_1_of_nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_103625 $$unsorted) (BOUND_VARIABLE_103626 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_103625)) (hAPP nat X_a _let_0 BOUND_VARIABLE_103626)))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_103625) BOUND_VARIABLE_103626))) )) 16.47/16.40 ( int, (zero_zero nat), (zero_zero nat) ) 16.47/16.40 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 16.47/16.40 ) 16.47/16.40 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) (one_one real)))) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) pi))) (not (= Y (hAPP real real cos X_2))) (not (forall ((Y_2 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 Y_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_2) pi))) (not (= Y (hAPP real real cos Y_2))) (= X_2 Y_2)) )) (not (hBOOL (hAPP real bool _let_2 X_2)))) ))) )))) 16.47/16.40 ( (zero_zero real) ) 16.47/16.40 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.47/16.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.47/16.40 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.47/16.40 ( skv_14 ) 16.47/16.40 ) 16.47/16.40 (instantiation (let ((_let_0 (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_103710))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_103710 $$unsorted)) (or (not (linordered_idom X_a)) (= _let_0 (hAPP X_a X_a (abs_abs X_a) _let_0))) )) 16.47/16.40 ( real, (zero_zero nat) ) 16.47/16.40 ( real, (one_one nat) ) 16.47/16.40 ( int, (zero_zero nat) ) 16.47/16.40 ( int, (hAPP nat nat suc (zero_zero nat)) ) 16.47/16.40 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.47/16.40 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.47/16.40 ) 16.47/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103724 $$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_103724)) (hAPP int int (number_number_of int) BOUND_VARIABLE_103724))) ) 16.47/16.40 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.47/16.40 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.47/16.40 ( real, min_1 ) 16.47/16.40 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.47/16.40 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.47/16.40 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.47/16.40 ( 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)))))))) ) 16.47/16.40 ( nat, pls ) 16.47/16.40 ( nat, (hAPP int int bit1 pls) ) 16.47/16.40 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.47/16.40 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.47/16.40 ( int, pls ) 16.47/16.40 ( int, (hAPP int int bit1 pls) ) 16.47/16.40 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.47/16.40 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.47/16.40 ( int, min_1 ) 16.47/16.40 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.47/16.40 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.47/16.40 ( complex, min_1 ) 16.47/16.40 ( quickcheck_code_int, (zero_zero int) ) 16.47/16.40 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 16.47/16.40 ( quickcheck_code_int, (one_one int) ) 16.47/16.40 ( code_code_numeral, pls ) 16.47/16.40 ( code_code_numeral, (hAPP int int bit1 pls) ) 16.47/16.40 ) 16.47/16.40 (instantiation (let ((_let_0 (ord_atLeastLessThan X_a))) (forall ((X_a $$unsorted)) (or (not (ord X_a)) (= _let_0 (ti (fun X_a (fun X_a (fun X_a bool))) _let_0))) )) 16.47/16.40 ( bool ) 16.47/16.40 ( real ) 16.47/16.40 ( nat ) 16.47/16.40 ( (fun nat bool) ) 16.47/16.40 ( int ) 16.47/16.40 ( (fun int bool) ) 16.47/16.40 ( rat ) 16.47/16.40 ( quickcheck_code_int ) 16.47/16.40 ( (product_prod real real) ) 16.47/16.40 ( (product_prod int int) ) 16.47/16.40 ( (filter real) ) 16.47/16.40 ( (filter nat) ) 16.47/16.40 ( (product_prod nat nat) ) 16.47/16.40 ( code_code_numeral ) 16.47/16.40 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.47/16.40 ( (fun nat rat) ) 16.48/16.40 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.48/16.40 ) 16.48/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103782 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP int X_a (number_number_of X_a) min_1)) BOUND_VARIABLE_103782) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_103782))) ) 16.48/16.40 ( real, (one_one real) ) 16.48/16.40 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.48/16.40 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.48/16.40 ( int, pls ) 16.48/16.40 ( int, (one_one int) ) 16.48/16.40 ( int, min_1 ) 16.48/16.40 ( complex, ii ) 16.48/16.40 ( complex, (one_one complex) ) 16.48/16.40 ) 16.48/16.40 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP rat rat (hAPP rat (fun rat rat) (inverse_divide rat) (one_one rat)) (hAPP int rat (number_number_of rat) K_4)) (hAPP int rat (hAPP int (fun int rat) fract (one_one int)) (hAPP int int (number_number_of int) K_4))) ) 16.48/16.40 ( pls ) 16.48/16.40 ( (hAPP int int bit1 pls) ) 16.48/16.40 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.48/16.40 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.48/16.40 ( min_1 ) 16.48/16.40 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.48/16.40 ) 16.48/16.40 (instantiation (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_103798))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_103798 $$unsorted) (BOUND_VARIABLE_103799 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_103798) (hAPP nat X_a _let_0 BOUND_VARIABLE_103799)) (hAPP nat X_a _let_0 (hAPP nat nat suc BOUND_VARIABLE_103799)))) )) 16.48/16.40 ( int, s, (hAPP nat nat suc (zero_zero nat)) ) 16.48/16.40 ( int, s1, (hAPP nat nat suc (zero_zero nat)) ) 16.48/16.40 ( int, skv_8, (hAPP nat nat suc (zero_zero nat)) ) 16.48/16.40 ( complex, ii, (hAPP nat nat suc (zero_zero nat)) ) 16.48/16.40 ) 16.48/16.40 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_103822 $$unsorted) (BOUND_VARIABLE_103823 $$unsorted)) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_103823))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_103822))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_103822) (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_103822) BOUND_VARIABLE_103823)) BOUND_VARIABLE_103823))) )))) 16.48/16.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.48/16.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 16.48/16.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.48/16.40 ( 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))))), pi ) 16.48/16.40 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.48/16.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 16.48/16.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.48/16.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1 ) 16.48/16.40 ( complex, ii, ii ) 16.48/16.40 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 16.48/16.40 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 16.48/16.40 ) 16.49/16.40 (instantiation (let ((_let_0 (hAPP real real sqrt X))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X))) (= (hAPP real real (inverse_inverse real) _let_0) (hAPP real real (hAPP real (fun real real) (inverse_divide real) _let_0) X))) )) 16.49/16.40 ( (zero_zero real) ) 16.49/16.40 ( (one_one real) ) 16.49/16.40 ( pi ) 16.49/16.40 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.40 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.49/16.40 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.40 ( skv_6 ) 16.49/16.40 ( skv_11 ) 16.49/16.40 ( skv_12 ) 16.49/16.40 ( skv_14 ) 16.49/16.40 ) 16.49/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103936 $$unsorted)) (or (not (real_vector X_a)) (= (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) (one_one real)) BOUND_VARIABLE_103936) (ti X_a BOUND_VARIABLE_103936))) ) 16.49/16.40 ( bool, fFalse ) 16.49/16.40 ( bool, fTrue ) 16.49/16.40 ( real, pi ) 16.49/16.40 ( (fun nat bool), (even_odd_even nat) ) 16.49/16.40 ( (fun nat bool), prime ) 16.49/16.40 ( (fun nat nat), suc ) 16.49/16.40 ( (fun nat nat), (fact_fact nat) ) 16.49/16.40 ( (fun nat nat), (size_size nat) ) 16.49/16.40 ( (fun nat nat), fact ) 16.49/16.40 ( (fun nat nat), nat_size ) 16.49/16.40 ( int, pls ) 16.49/16.40 ( int, m ) 16.49/16.40 ( int, min_1 ) 16.49/16.40 ( int, s ) 16.49/16.40 ( int, s1 ) 16.49/16.40 ( int, t ) 16.49/16.40 ( (fun int bool), zprime ) 16.49/16.40 ( (fun int bool), nat_neg ) 16.49/16.40 ( (fun int bool), zEven ) 16.49/16.40 ( (fun int bool), nat_is_nat ) 16.49/16.41 ( (fun int bool), zOdd ) 16.49/16.41 ( (fun int bool), (even_odd_even int) ) 16.49/16.41 ( (fun int bool), twoSqu1091635170sum2sq ) 16.49/16.41 ( (fun int nat), nat_1 ) 16.49/16.41 ( (fun int nat), phi ) 16.49/16.41 ( (fun real real), sqrt ) 16.49/16.41 ( (fun real real), tan ) 16.49/16.41 ( (fun real real), cos ) 16.49/16.41 ( (fun real real), arccos ) 16.49/16.41 ( (fun real real), ln ) 16.49/16.41 ( (fun real real), sin ) 16.49/16.41 ( (fun real real), arctan ) 16.49/16.41 ( (fun real real), arcsin ) 16.49/16.41 ( complex, ii ) 16.49/16.41 ( (fun complex complex), cnj ) 16.49/16.41 ( (fun complex complex), expi ) 16.49/16.41 ( (fun nat real), (real_1 nat) ) 16.49/16.41 ( (fun nat real), cos_coeff ) 16.49/16.41 ( (fun nat real), sin_coeff ) 16.49/16.41 ( (fun int int), bit0 ) 16.49/16.41 ( (fun int int), bit1 ) 16.49/16.41 ( (fun int int), pred ) 16.49/16.41 ( (fun int int), succ ) 16.49/16.41 ( (fun int int), (fact_fact int) ) 16.49/16.41 ( (fun int int), zfact ) 16.49/16.41 ( (fun bool bool), fNot ) 16.49/16.41 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.49/16.41 ( (fun bool (fun bool bool)), fconj ) 16.49/16.41 ( (fun bool (fun bool bool)), fdisj ) 16.49/16.41 ( (fun bool (fun bool bool)), fimplies ) 16.49/16.41 ( (fun int (fun int bool)), sRStar ) 16.49/16.41 ( (fun int (fun int bool)), quadRes ) 16.49/16.41 ( (fun int (fun int bool)), norRRset ) 16.49/16.41 ( (fun int (fun int bool)), d22set ) 16.49/16.41 ( (fun int (fun int bool)), sr ) 16.49/16.41 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.49/16.41 ( (fun nat (fun nat nat)), nat_gcd ) 16.49/16.41 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.49/16.41 ( (fun nat (fun nat nat)), nat_lcm ) 16.49/16.41 ( (fun nat (fun real real)), root ) 16.49/16.41 ( (fun real (fun real real)), log ) 16.49/16.41 ( (fun real (fun real real)), powr ) 16.49/16.41 ( (fun nat (fun nat bool)), coprime ) 16.49/16.41 ( (fun (fun int bool) int), (the int) ) 16.49/16.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.49/16.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.49/16.41 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.49/16.41 ( (fun (fun int bool) bool), nat_nat_set ) 16.49/16.41 ( (filter nat), sequentially ) 16.49/16.41 ( (fun (product_prod nat nat) bool), pred_nat ) 16.49/16.41 ( (fun (product_prod int int) bool), frac_1 ) 16.49/16.41 ( (fun real complex), cis ) 16.49/16.41 ( (fun complex real), im ) 16.49/16.41 ( (fun complex real), re ) 16.49/16.41 ( (fun complex real), arg ) 16.49/16.41 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.49/16.41 ( (fun int (fun int int)), int_gcd ) 16.49/16.41 ( (fun int (fun int int)), multInv ) 16.49/16.41 ( (fun int (fun int int)), legacy_zgcd ) 16.49/16.41 ( (fun int (fun int int)), z3mod ) 16.49/16.41 ( (fun int (fun int int)), inv ) 16.49/16.41 ( (fun int (fun int int)), (gcd_gcd int) ) 16.49/16.41 ( (fun int (fun int int)), standardRes ) 16.49/16.41 ( (fun int (fun int int)), legendre ) 16.49/16.41 ( (fun int (fun int int)), nat_tsub ) 16.49/16.41 ( (fun int (fun int int)), z3div ) 16.49/16.41 ( (fun int (fun int int)), int_lcm ) 16.49/16.41 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.49/16.41 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.49/16.41 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.49/16.41 ( (fun int (fun (fun int bool) bool)), resSet ) 16.49/16.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.49/16.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.49/16.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.49/16.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.49/16.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.49/16.41 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.49/16.41 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.49/16.41 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.49/16.41 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.49/16.41 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.49/16.41 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.49/16.41 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.49/16.41 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.49/16.41 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.49/16.41 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.49/16.41 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.49/16.41 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.49/16.41 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.49/16.41 ( (fun real nat), natfloor ) 16.49/16.41 ( (fun real nat), natceiling ) 16.49/16.41 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.49/16.41 ( (fun int (fun int (fun int bool))), wset ) 16.49/16.41 ( (fun int (fun int (fun int bool))), bnorRset ) 16.49/16.41 ( (fun int (fun int (fun int bool))), zcong ) 16.49/16.41 ( (fun int (fun int (fun int bool))), noXRRset ) 16.49/16.41 ( (fun int (fun int (fun int bool))), zcongm ) 16.49/16.41 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.49/16.41 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.49/16.41 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.49/16.41 ( (fun int real), (real_1 int) ) 16.49/16.41 ( (fun complex nat), (size_size complex) ) 16.49/16.41 ( (fun complex nat), complex_size ) 16.49/16.41 ( (fun int (list int)), quickc666637781d_zero ) 16.49/16.41 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.49/16.41 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.49/16.41 ( (fun (product_prod int int) rat), frct ) 16.49/16.41 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.49/16.41 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.49/16.41 ( (fun (fun nat rat) bool), vanishes ) 16.49/16.41 ( (fun int (fun int rat)), fract ) 16.49/16.41 ( (fun code_code_numeral int), code_int_of ) 16.49/16.41 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.49/16.41 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.49/16.41 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.49/16.41 ( (fun real (fun real complex)), complex_1 ) 16.49/16.41 ( (fun real (fun real complex)), rcis ) 16.49/16.41 ( (fun int (fun nat nat)), nat_aux ) 16.49/16.41 ( (fun rat real), ratreal ) 16.49/16.41 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.49/16.41 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.49/16.41 ( (fun rat (product_prod int int)), quotient_of ) 16.49/16.41 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.49/16.41 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.49/16.41 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.49/16.41 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.49/16.41 ) 16.49/16.41 (instantiation (let ((_let_0 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_103950 $$unsorted) (BOUND_VARIABLE_103951 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_103950) BOUND_VARIABLE_103951)) (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_103950)) (hAPP int X_a _let_0 BOUND_VARIABLE_103951)))) )) 16.49/16.41 ( nat, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 16.49/16.41 ) 16.49/16.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103966 $$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_103966)) (zero_zero int))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_103966) (zero_zero X_a))))) ) 16.49/16.41 ( real, (zero_zero real) ) 16.49/16.41 ( real, (one_one real) ) 16.49/16.41 ( real, pi ) 16.49/16.41 ( 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)))) ) 16.49/16.41 ( 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))))) ) 16.49/16.41 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.41 ( 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)) ) 16.49/16.41 ( nat, (zero_zero nat) ) 16.49/16.41 ( int, (zero_zero int) ) 16.49/16.41 ( int, min_1 ) 16.49/16.41 ( int, s ) 16.49/16.41 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.49/16.41 ( int, t ) 16.49/16.41 ( int, skv_3 ) 16.49/16.41 ( int, skv_9 ) 16.49/16.41 ) 16.49/16.41 (instantiation (let ((_let_0 (summable X_a))) (forall ((X_a $$unsorted)) (or (not (topological_space X_a)) (not (comm_monoid_add X_a)) (= _let_0 (ti (fun (fun nat X_a) bool) _let_0))) )) 16.49/16.41 ( bool ) 16.49/16.41 ( real ) 16.49/16.41 ( nat ) 16.49/16.41 ( (fun nat bool) ) 16.49/16.41 ( (fun nat nat) ) 16.49/16.41 ( int ) 16.49/16.41 ( (fun real real) ) 16.49/16.41 ( complex ) 16.49/16.41 ( (fun int int) ) 16.49/16.41 ( rat ) 16.49/16.41 ( (fun bool bool) ) 16.49/16.41 ( quickcheck_code_int ) 16.49/16.41 ( (fun nat (fun nat bool)) ) 16.49/16.41 ( (product_prod real real) ) 16.49/16.41 ( (product_prod int int) ) 16.49/16.41 ( (fun nat (product_prod int int)) ) 16.49/16.41 ( (product_prod nat nat) ) 16.49/16.41 ( (fun (product_prod nat nat) bool) ) 16.49/16.41 ( (fun nat (fun (product_prod nat nat) bool)) ) 16.49/16.41 ( (fun nat (product_prod nat nat)) ) 16.49/16.41 ( code_code_numeral ) 16.49/16.41 ) 16.49/16.41 (instantiation (forall ((X $$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)) ) 16.49/16.41 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.41 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.41 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.49/16.41 ) 16.49/16.41 (instantiation (let ((_let_0 (fun X_b X_c))) (let ((_let_1 (fun X_a X_b))) (let ((_let_2 (fun X_a X_c))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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))) )))) 16.49/16.41 ( real, bool, real, (ord_less real), tan, pi ) 16.49/16.41 ( 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))) ) 16.49/16.41 ( real, complex, real, complex_1, cos, (zero_zero real) ) 16.49/16.41 ( real, complex, real, complex_1, ln, (one_one real) ) 16.49/16.41 ( real, complex, real, complex_1, (inverse_inverse real), (zero_zero real) ) 16.49/16.41 ( nat, nat, nat, (plus_plus nat), (fact_fact nat), (one_one nat) ) 16.49/16.41 ( int, bool, int, (ord_less_eq int), (number_number_of int), (zero_zero int) ) 16.49/16.41 ( int, bool, int, (ord_less_eq int), bit1, min_1 ) 16.49/16.41 ( int, bool, int, (ord_less_eq int), pred, (zero_zero int) ) 16.49/16.41 ( int, bool, int, (ord_less_eq int), succ, min_1 ) 16.49/16.41 ( int, bool, int, (ord_less_eq int), (fact_fact int), (zero_zero int) ) 16.49/16.41 ( int, bool, int, (ord_less int), (number_number_of int), (zero_zero int) ) 16.49/16.41 ( int, bool, int, (ord_less int), bit1, min_1 ) 16.49/16.41 ( int, bool, int, (ord_less int), pred, (zero_zero int) ) 16.49/16.41 ( int, bool, int, (ord_less int), succ, min_1 ) 16.49/16.41 ( int, bool, int, (ord_less int), (fact_fact int), (zero_zero int) ) 16.49/16.41 ( int, rat, int, fract, (fact_fact int), (zero_zero int) ) 16.49/16.41 ( int, rat, int, fract, (fact_fact int), (one_one int) ) 16.49/16.41 ( int, (product_prod int int), int, (product_Pair int int), (fact_fact int), (zero_zero int) ) 16.49/16.41 ( int, (product_prod int int), int, (product_Pair int int), (fact_fact int), (one_one int) ) 16.49/16.41 ) 16.49/16.41 (instantiation (forall ((W $$unsorted)) (= (hAPP int nat (number_number_of nat) W) (hAPP int nat nat_1 (hAPP int int (number_number_of int) W))) ) 16.49/16.41 ( pls ) 16.49/16.41 ( (hAPP int int bit1 pls) ) 16.49/16.41 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.49/16.41 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.41 ( min_1 ) 16.49/16.41 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.49/16.41 ) 16.49/16.41 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_104063))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_104063 $$unsorted) (BOUND_VARIABLE_104064 $$unsorted) (BOUND_VARIABLE_104065 $$unsorted)) (or (not (linord581940658strict X_a)) (= (or (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104064) BOUND_VARIABLE_104065)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_104063))) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104063) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104065) BOUND_VARIABLE_104064)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_3 BOUND_VARIABLE_104064)) (hAPP X_a X_a _let_3 BOUND_VARIABLE_104065))))) ))))) 16.49/16.41 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1, (zero_zero int) ) 16.49/16.41 ) 16.49/16.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104100 $$unsorted)) (or (not (field X_a)) (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_104100) (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 pls))) (ti X_a BOUND_VARIABLE_104100))) ) 16.49/16.41 ( bool, fFalse ) 16.49/16.41 ( bool, fTrue ) 16.49/16.41 ( real, (one_one real) ) 16.49/16.41 ( real, pi ) 16.49/16.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.49/16.41 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.49/16.41 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.41 ( (fun nat bool), (even_odd_even nat) ) 16.49/16.41 ( (fun nat bool), prime ) 16.49/16.41 ( (fun nat nat), suc ) 16.49/16.41 ( (fun nat nat), (fact_fact nat) ) 16.49/16.41 ( (fun nat nat), (size_size nat) ) 16.49/16.41 ( (fun nat nat), fact ) 16.49/16.41 ( (fun nat nat), nat_size ) 16.49/16.41 ( int, pls ) 16.49/16.41 ( int, m ) 16.49/16.41 ( int, min_1 ) 16.49/16.41 ( int, s ) 16.49/16.41 ( int, s1 ) 16.49/16.41 ( int, t ) 16.49/16.41 ( (fun int bool), zprime ) 16.49/16.41 ( (fun int bool), nat_neg ) 16.49/16.41 ( (fun int bool), zEven ) 16.49/16.41 ( (fun int bool), nat_is_nat ) 16.49/16.41 ( (fun int bool), zOdd ) 16.49/16.41 ( (fun int bool), (even_odd_even int) ) 16.49/16.41 ( (fun int bool), twoSqu1091635170sum2sq ) 16.49/16.41 ( (fun int nat), nat_1 ) 16.49/16.41 ( (fun int nat), phi ) 16.49/16.41 ( (fun real real), sqrt ) 16.49/16.41 ( (fun real real), tan ) 16.49/16.41 ( (fun real real), cos ) 16.49/16.41 ( (fun real real), arccos ) 16.49/16.41 ( (fun real real), ln ) 16.49/16.41 ( (fun real real), sin ) 16.49/16.41 ( (fun real real), arctan ) 16.49/16.41 ( (fun real real), arcsin ) 16.49/16.41 ( complex, ii ) 16.49/16.41 ( (fun complex complex), cnj ) 16.49/16.41 ( (fun complex complex), expi ) 16.49/16.41 ( (fun nat real), (real_1 nat) ) 16.49/16.41 ( (fun nat real), cos_coeff ) 16.49/16.41 ( (fun nat real), sin_coeff ) 16.49/16.41 ( (fun int int), bit0 ) 16.49/16.41 ( (fun int int), bit1 ) 16.49/16.41 ( (fun int int), pred ) 16.49/16.41 ( (fun int int), succ ) 16.49/16.41 ( (fun int int), (fact_fact int) ) 16.49/16.41 ( (fun int int), zfact ) 16.49/16.41 ( (fun bool bool), fNot ) 16.49/16.41 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.49/16.41 ( (fun bool (fun bool bool)), fconj ) 16.49/16.41 ( (fun bool (fun bool bool)), fdisj ) 16.49/16.41 ( (fun bool (fun bool bool)), fimplies ) 16.49/16.41 ( (fun int (fun int bool)), sRStar ) 16.49/16.41 ( (fun int (fun int bool)), quadRes ) 16.49/16.41 ( (fun int (fun int bool)), norRRset ) 16.49/16.41 ( (fun int (fun int bool)), d22set ) 16.49/16.41 ( (fun int (fun int bool)), sr ) 16.49/16.41 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.49/16.41 ( (fun nat (fun nat nat)), nat_gcd ) 16.49/16.41 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.49/16.41 ( (fun nat (fun nat nat)), nat_lcm ) 16.49/16.41 ( (fun nat (fun real real)), root ) 16.49/16.41 ( (fun real (fun real real)), log ) 16.49/16.41 ( (fun real (fun real real)), powr ) 16.49/16.41 ( (fun nat (fun nat bool)), coprime ) 16.49/16.41 ( (fun (fun int bool) int), (the int) ) 16.49/16.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.49/16.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.49/16.41 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.49/16.41 ( (fun (fun int bool) bool), nat_nat_set ) 16.49/16.41 ( (filter nat), sequentially ) 16.49/16.41 ( (fun (product_prod nat nat) bool), pred_nat ) 16.49/16.41 ( (fun (product_prod int int) bool), frac_1 ) 16.49/16.41 ( (fun real complex), cis ) 16.49/16.41 ( (fun complex real), im ) 16.49/16.41 ( (fun complex real), re ) 16.49/16.41 ( (fun complex real), arg ) 16.49/16.41 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.49/16.41 ( (fun int (fun int int)), int_gcd ) 16.49/16.41 ( (fun int (fun int int)), multInv ) 16.49/16.41 ( (fun int (fun int int)), legacy_zgcd ) 16.49/16.41 ( (fun int (fun int int)), z3mod ) 16.49/16.41 ( (fun int (fun int int)), inv ) 16.49/16.41 ( (fun int (fun int int)), (gcd_gcd int) ) 16.49/16.41 ( (fun int (fun int int)), standardRes ) 16.49/16.41 ( (fun int (fun int int)), legendre ) 16.49/16.41 ( (fun int (fun int int)), nat_tsub ) 16.49/16.41 ( (fun int (fun int int)), z3div ) 16.49/16.41 ( (fun int (fun int int)), int_lcm ) 16.49/16.41 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.49/16.41 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.49/16.41 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.49/16.41 ( (fun int (fun (fun int bool) bool)), resSet ) 16.49/16.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.49/16.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.49/16.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.49/16.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.49/16.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.49/16.41 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.49/16.41 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.49/16.41 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.49/16.41 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.49/16.41 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.49/16.41 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.49/16.41 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.49/16.41 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.49/16.41 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.49/16.42 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.49/16.42 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.49/16.42 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.49/16.42 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.49/16.42 ( (fun real nat), natfloor ) 16.49/16.42 ( (fun real nat), natceiling ) 16.49/16.42 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.49/16.42 ( (fun int (fun int (fun int bool))), wset ) 16.49/16.42 ( (fun int (fun int (fun int bool))), bnorRset ) 16.49/16.42 ( (fun int (fun int (fun int bool))), zcong ) 16.49/16.42 ( (fun int (fun int (fun int bool))), noXRRset ) 16.49/16.42 ( (fun int (fun int (fun int bool))), zcongm ) 16.49/16.42 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.49/16.42 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.49/16.42 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.49/16.42 ( (fun int real), (real_1 int) ) 16.49/16.42 ( (fun complex nat), (size_size complex) ) 16.49/16.42 ( (fun complex nat), complex_size ) 16.49/16.42 ( (fun int (list int)), quickc666637781d_zero ) 16.49/16.42 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.49/16.42 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.49/16.42 ( (fun (product_prod int int) rat), frct ) 16.49/16.42 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.49/16.42 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.49/16.42 ( (fun (fun nat rat) bool), vanishes ) 16.49/16.42 ( (fun int (fun int rat)), fract ) 16.49/16.42 ( (fun code_code_numeral int), code_int_of ) 16.49/16.42 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.49/16.42 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.49/16.42 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.49/16.42 ( (fun real (fun real complex)), complex_1 ) 16.49/16.42 ( (fun real (fun real complex)), rcis ) 16.49/16.42 ( (fun int (fun nat nat)), nat_aux ) 16.49/16.42 ( (fun rat real), ratreal ) 16.49/16.42 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.49/16.42 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.49/16.42 ( (fun rat (product_prod int int)), quotient_of ) 16.49/16.42 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.49/16.42 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.49/16.42 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.49/16.42 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.49/16.42 ) 16.49/16.42 (instantiation (let ((_let_0 (cauchy X_a))) (forall ((X_a $$unsorted)) (or (not (metric_space X_a)) (= _let_0 (ti (fun (fun nat X_a) bool) _let_0))) )) 16.49/16.42 ( bool ) 16.49/16.42 ( real ) 16.49/16.42 ( nat ) 16.49/16.42 ( (fun nat bool) ) 16.49/16.42 ( (fun nat nat) ) 16.49/16.42 ( int ) 16.49/16.42 ( (fun real real) ) 16.49/16.42 ( complex ) 16.49/16.42 ( (fun int int) ) 16.49/16.42 ( rat ) 16.49/16.42 ( (fun bool bool) ) 16.49/16.42 ( (fun nat (fun nat bool)) ) 16.49/16.42 ( (product_prod real real) ) 16.49/16.42 ( (product_prod int int) ) 16.49/16.42 ( (fun nat (product_prod int int)) ) 16.49/16.42 ( (product_prod nat nat) ) 16.49/16.42 ( (fun (product_prod nat nat) bool) ) 16.49/16.42 ( (fun nat (fun (product_prod nat nat) bool)) ) 16.49/16.42 ( (fun nat (product_prod nat nat)) ) 16.49/16.42 ) 16.49/16.42 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (one_one X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_104174 $$unsorted) (BOUND_VARIABLE_104175 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_104175))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104175) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_104175) (hAPP nat nat suc BOUND_VARIABLE_104174))) _let_2))) )))) 16.49/16.42 ( int, (hAPP nat nat suc (zero_zero nat)), s ) 16.49/16.42 ( int, (hAPP nat nat suc (zero_zero nat)), s1 ) 16.49/16.42 ( int, (hAPP nat nat suc (zero_zero nat)), skv_8 ) 16.49/16.42 ( complex, (hAPP nat nat suc (zero_zero nat)), ii ) 16.49/16.42 ) 16.49/16.42 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (div_mod nat))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (forall ((M $$unsorted)) (= (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat suc (hAPP nat nat suc M))) _let_2) (hAPP nat nat (hAPP nat _let_0 _let_1 M) _let_2)) )))) 16.49/16.42 ( (zero_zero nat) ) 16.49/16.42 ( (hAPP nat nat suc (zero_zero nat)) ) 16.49/16.42 ) 16.49/16.42 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (forall ((X $$unsorted) (Y $$unsorted)) (= (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))) ))) 16.49/16.42 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.49/16.42 ) 16.49/16.42 (instantiation (let ((_let_0 (ord_lessThan X_a))) (forall ((X_a $$unsorted)) (or (not (ord X_a)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0))) )) 16.49/16.42 ( bool ) 16.49/16.42 ( real ) 16.49/16.42 ( nat ) 16.49/16.42 ( (fun nat bool) ) 16.49/16.42 ( int ) 16.49/16.42 ( (fun int bool) ) 16.49/16.42 ( rat ) 16.49/16.42 ( quickcheck_code_int ) 16.49/16.42 ( (product_prod real real) ) 16.49/16.42 ( (product_prod int int) ) 16.49/16.42 ( (filter real) ) 16.49/16.42 ( (filter nat) ) 16.49/16.42 ( (product_prod nat nat) ) 16.49/16.42 ( code_code_numeral ) 16.49/16.42 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.49/16.42 ( (fun nat rat) ) 16.49/16.42 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.49/16.42 ) 16.49/16.42 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_104410 $$unsorted) (BOUND_VARIABLE_104411 $$unsorted)) (or (not (ordere453448008miring X_a)) (and (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104410) _let_2))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_104411)))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104411) _let_2))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_104410))))) (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_104411) BOUND_VARIABLE_104410)) _let_2))) ))))) 16.49/16.42 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.42 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.49/16.42 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.42 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.42 ( int, (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.42 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.42 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.42 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.42 ( complex, ii, ii ) 16.49/16.42 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.49/16.42 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.42 ) 16.49/16.42 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (forall ((N $$unsorted) (X $$unsorted)) (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)))) )) 16.49/16.42 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 16.49/16.42 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 16.49/16.42 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 16.49/16.42 ) 16.49/16.42 (instantiation (let ((_let_0 (fun int bool))) (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_4))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_2) P_4))) (= (hAPP int nat nat_1 A_2) (hAPP _let_0 nat (finite_card int) (hAPP int _let_0 (hAPP int (fun int _let_0) bnorRset A_2) P_4)))) )) 16.49/16.42 ( (zero_zero int), (zero_zero int) ) 16.49/16.42 ( (zero_zero int), (one_one int) ) 16.49/16.42 ( (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))) ) 16.49/16.42 ( (zero_zero int), min_1 ) 16.49/16.42 ( min_1, (zero_zero int) ) 16.49/16.42 ( min_1, min_1 ) 16.49/16.42 ( 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))) ) 16.49/16.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 16.49/16.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 16.49/16.42 ( t, (zero_zero int) ) 16.49/16.42 ( t, (one_one int) ) 16.49/16.42 ( 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))) ) 16.49/16.42 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.42 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.42 ) 16.49/16.42 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_104600 $$unsorted) (BOUND_VARIABLE_104601 $$unsorted) (BOUND_VARIABLE_104602 $$unsorted) (BOUND_VARIABLE_104603 $$unsorted)) (or (not (ab_group_add X_a)) (not (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104600) BOUND_VARIABLE_104601) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104602) BOUND_VARIABLE_104603))) (= (= (ti X_a BOUND_VARIABLE_104603) (ti X_a BOUND_VARIABLE_104602)) (= (ti X_a BOUND_VARIABLE_104601) (ti X_a BOUND_VARIABLE_104600)))) ))) 16.49/16.42 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.49/16.42 ( 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)))), (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.49/16.42 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral), (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.49/16.42 ) 16.49/16.42 (instantiation (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 (product_prod int int))) (let ((_let_6 (fun _let_5 bool))) (forall ((D_1 $$unsorted)) (= (hAPP int _let_6 int_ge_less_than2 D_1) (hAPP _let_6 _let_6 (collect _let_5) (hAPP _let_4 _let_6 (product_prod_case int int bool) (hAPP _let_4 _let_4 (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_eq int) D_1)))) (ord_less int))))) )))))))) 16.49/16.42 ( (zero_zero int) ) 16.49/16.42 ( (one_one int) ) 16.49/16.42 ( min_1 ) 16.49/16.42 ) 16.49/16.42 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int real (number_number_of real) K_4) (hAPP rat real ratreal (hAPP int rat (number_number_of rat) K_4))) ) 16.49/16.42 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.49/16.42 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.42 ( min_1 ) 16.49/16.42 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.42 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.49/16.42 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.49/16.42 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.49/16.42 ) 16.49/16.42 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (fun int int))) (let ((_let_3 (one_one int))) (forall ((I $$unsorted) (P_1 $$unsorted) (K $$unsorted)) (or (not (hBOOL (hAPP int bool P_1 K))) (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) I_2))) (not (hBOOL (hAPP int bool P_1 I_2))) (hBOOL (hAPP int bool P_1 (hAPP int int (hAPP int _let_2 (plus_plus int) I_2) _let_3)))) )) (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 I_2) K))) (not (hBOOL (hAPP int bool P_1 I_2))) (hBOOL (hAPP int bool P_1 (hAPP int int (hAPP int _let_2 (minus_minus int) I_2) _let_3)))) )) (hBOOL (hAPP int bool P_1 I))) ))))) 16.49/16.43 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) pls), (zero_zero int) ) 16.49/16.43 ( (zero_zero int), nat_is_nat, (zero_zero int) ) 16.49/16.43 ( (zero_zero int), (even_odd_even int), (zero_zero int) ) 16.49/16.43 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))), (zero_zero int) ) 16.49/16.43 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) min_1), (zero_zero int) ) 16.49/16.43 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) t), (zero_zero int) ) 16.49/16.43 ( pls, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 16.49/16.43 ( (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 16.49/16.43 ( (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 16.49/16.43 ( (one_one int), nat_neg, (one_one int) ) 16.49/16.43 ( (one_one int), nat_is_nat, (one_one int) ) 16.49/16.43 ( (one_one int), (even_odd_even int), (one_one int) ) 16.49/16.43 ( (one_one int), (hAPP int (fun int bool) (ord_less int) t), (one_one int) ) 16.49/16.43 ( (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))), zprime, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.43 ( (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 (fun int bool) (ord_less int) (zero_zero int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.43 ( (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 (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.43 ( (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))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.43 ( (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))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.43 ( (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 (fun int bool) (ord_less int) t), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.43 ( (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))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.43 ( (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))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.43 ( (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 (fun int bool) (ord_less int) skv_3), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.43 ( (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))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_3)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.43 ( (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))), (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_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.43 ( (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 (fun int bool) (ord_less int) skv_9), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.43 ( (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))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_9)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.43 ( min_1, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 16.49/16.43 ( min_1, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 16.49/16.43 ( min_1, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 16.49/16.43 ( min_1, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 16.49/16.43 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.43 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.43 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.43 ( (hAPP int int (number_number_of int) min_1), nat_neg, (hAPP int int (number_number_of int) min_1) ) 16.49/16.43 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 16.49/16.43 ( s, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 16.49/16.43 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.49/16.43 ( (hAPP int int (number_number_of int) pls), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 16.49/16.43 ( (hAPP int int (number_number_of int) pls), nat_neg, (hAPP int int (number_number_of int) pls) ) 16.49/16.43 ( t, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 16.49/16.43 ( (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))) t))), twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 16.49/16.43 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.49/16.43 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.49/16.43 ( (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))) (zero_zero int)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun int bool) (ord_less 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)))), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 16.49/16.43 ( skv_3, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_3 ) 16.49/16.43 ( skv_9, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_9 ) 16.49/16.43 ) 16.49/16.43 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (filter X_a))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun X_a X_b))) (let ((_let_5 (fun X_b _let_3))) (let ((_let_6 (tendsto X_a X_b))) (let ((_let_7 (hAPP X_a _let_2 (at X_a) BOUND_VARIABLE_104686))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_104683 $$unsorted) (BOUND_VARIABLE_104684 $$unsorted) (BOUND_VARIABLE_104685 $$unsorted) (BOUND_VARIABLE_104686 $$unsorted) (BOUND_VARIABLE_104687 $$unsorted)) (or (not (metric_space X_a)) (not (topological_space X_b)) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) BOUND_VARIABLE_104687))) (not (forall ((X_2 $$unsorted)) (or (= (ti X_a X_2) (ti X_a BOUND_VARIABLE_104686)) (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_2) BOUND_VARIABLE_104686)) BOUND_VARIABLE_104687))) (= (hAPP X_a X_b BOUND_VARIABLE_104684 X_2) (hAPP X_a X_b BOUND_VARIABLE_104685 X_2))) )) (not (hBOOL (hAPP _let_2 bool (hAPP X_b _let_3 (hAPP _let_4 _let_5 _let_6 BOUND_VARIABLE_104685) BOUND_VARIABLE_104683) _let_7))) (hBOOL (hAPP _let_2 bool (hAPP X_b _let_3 (hAPP _let_4 _let_5 _let_6 BOUND_VARIABLE_104684) BOUND_VARIABLE_104683) _let_7))) ))))))))) 16.49/16.43 ( real, real, (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.44 ) 16.49/16.44 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP nat (fun real real) root N))) (forall ((Y $$unsorted) (X $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (zero_zero real)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) Y))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real _let_2 X)) (hAPP real real _let_2 Y)))) )))) 16.49/16.44 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.44 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.44 ) 16.49/16.44 (instantiation (let ((_let_0 (combs X_a X_b X_c))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (= _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)) )) 16.49/16.44 ( real, bool, bool ) 16.49/16.44 ( real, bool, (fun bool bool) ) 16.49/16.44 ( real, real, real ) 16.49/16.44 ( real, real, (fun real bool) ) 16.49/16.44 ( real, real, (fun real real) ) 16.49/16.44 ( real, (fun int bool), bool ) 16.49/16.44 ( real, (fun real bool), (fun (fun int real) (fun int bool)) ) 16.49/16.44 ( real, (fun real bool), (fun (fun nat real) (fun nat bool)) ) 16.49/16.44 ( real, (fun int (fun int bool)), (fun int bool) ) 16.49/16.44 ( real, (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 16.49/16.44 ( 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))) ) 16.49/16.44 ( real, (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 16.49/16.44 ( real, (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 16.49/16.44 ( real, (fun int (fun nat bool)), (fun int bool) ) 16.49/16.44 ( real, (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 16.49/16.44 ( 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))) ) 16.49/16.44 ( real, (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 16.49/16.44 ( real, (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 16.49/16.44 ( nat, bool, bool ) 16.49/16.44 ( nat, bool, (fun bool bool) ) 16.49/16.44 ( nat, real, bool ) 16.49/16.44 ( nat, real, real ) 16.49/16.44 ( nat, real, (fun real real) ) 16.49/16.44 ( nat, nat, real ) 16.49/16.44 ( nat, nat, (fun nat bool) ) 16.49/16.44 ( nat, nat, (fun nat nat) ) 16.49/16.44 ( int, bool, bool ) 16.49/16.44 ( int, bool, (fun int bool) ) 16.49/16.44 ( int, bool, (fun int int) ) 16.49/16.44 ( int, bool, (fun bool bool) ) 16.49/16.44 ( int, real, bool ) 16.49/16.44 ( int, real, real ) 16.49/16.44 ( int, real, (fun real real) ) 16.49/16.44 ( int, real, (fun int real) ) 16.49/16.44 ( int, (fun nat bool), bool ) 16.49/16.44 ( int, (fun nat bool), (fun nat (fun bool bool)) ) 16.49/16.44 ( int, int, bool ) 16.49/16.44 ( int, int, int ) 16.49/16.44 ( int, int, (fun int bool) ) 16.49/16.44 ( int, int, (fun int int) ) 16.49/16.44 ( int, (fun int bool), bool ) 16.49/16.44 ( int, (fun int bool), (fun int bool) ) 16.49/16.44 ( int, (fun int bool), (fun int (fun bool bool)) ) 16.49/16.44 ( int, (fun int bool), (fun (fun int int) (fun int bool)) ) 16.49/16.44 ( int, (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 16.49/16.44 ( int, (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 16.49/16.44 ( int, (fun nat real), (fun nat bool) ) 16.49/16.44 ( int, (fun int int), (fun int (fun int bool)) ) 16.49/16.44 ( int, (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 16.49/16.44 ( int, (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 16.49/16.44 ( int, (fun int (fun int bool)), (fun int (fun int bool)) ) 16.49/16.44 ( int, (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 16.49/16.44 ( int, (fun int real), (fun int bool) ) 16.49/16.44 ( (product_prod int int), bool, bool ) 16.49/16.44 ( (product_prod int int), bool, (fun bool bool) ) 16.49/16.44 ( (product_prod int int), int, bool ) 16.49/16.44 ( (product_prod int int), int, int ) 16.49/16.44 ( (product_prod int int), int, (fun int bool) ) 16.49/16.44 ( (product_prod int int), int, (fun int int) ) 16.49/16.44 ( (product_prod int int), int, (fun (product_prod int int) int) ) 16.49/16.44 ( (product_prod int int), (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 16.49/16.44 ( (product_prod int int), (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 16.49/16.44 ( (product_prod int int), (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 16.49/16.44 ( (product_prod int int), (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 16.49/16.44 ( (product_prod int int), (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 16.49/16.44 ( (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))) ) 16.49/16.44 ) 16.49/16.44 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_104784 $$unsorted) (BOUND_VARIABLE_104785 $$unsorted)) (or (not (division_ring X_a)) (= _let_3 (ti X_a BOUND_VARIABLE_104785)) (= _let_3 (ti X_a BOUND_VARIABLE_104784)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104785) BOUND_VARIABLE_104784)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_104784)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_104785)))) ))))) 16.49/16.44 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.44 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.49/16.44 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.44 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.44 ( int, (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.44 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.44 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.44 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.44 ( complex, ii, ii ) 16.49/16.44 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.49/16.44 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.44 ) 16.49/16.44 (instantiation (let ((_let_0 (hBOOL (hAPP int bool (hAPP int (fun int bool) quadRes P_5) A_1)))) (let ((_let_1 (hAPP int int (hAPP int (fun int int) legendre A_1) P_5))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int bool))) (or (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_1) (zero_zero int)) P_5)) (and (or (not _let_0) (= (one_one int) _let_1)) (or _let_0 (= (hAPP int int (number_number_of int) min_1) _let_1))))) ))) 16.49/16.44 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.44 ) 16.49/16.44 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_1) _let_1) P_5))) (= _let_1 (hAPP int int (hAPP int (fun int int) legendre A_1) P_5))) ))) 16.49/16.44 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.44 ) 16.49/16.44 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) Y) X))) (= (hAPP int int (hAPP int (fun int int) (gcd_gcd int) X) Y) (hAPP int int (abs_abs int) Y))) ) 16.49/16.44 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.49/16.44 ) 16.49/16.44 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (one_one real))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (abs_abs real) X)) _let_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (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_2))) )))) 16.49/16.44 ( (hAPP int real (number_number_of real) min_1) ) 16.49/16.44 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.44 ) 16.49/16.44 (instantiation (forall ((X $$unsorted)) (= (hAPP real real (uminus_uminus real) (hAPP real real cos X)) (hAPP real real cos (hAPP real real (hAPP real (fun real real) (plus_plus real) X) pi))) ) 16.49/16.44 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.49/16.44 ) 16.49/16.44 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_104972 $$unsorted) (BOUND_VARIABLE_104973 $$unsorted) (BOUND_VARIABLE_104974 $$unsorted)) (or (not (ord X_a)) (not (= (ti X_a BOUND_VARIABLE_104974) (ti X_a BOUND_VARIABLE_104973))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104974) BOUND_VARIABLE_104972))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104973) BOUND_VARIABLE_104972))) ))) 16.49/16.44 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi, (zero_zero real) ) 16.49/16.44 ( int, (one_one int), pls, (zero_zero int) ) 16.49/16.44 ( int, min_1, s, (zero_zero int) ) 16.49/16.44 ( int, min_1, t, min_1 ) 16.49/16.44 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), s1, (zero_zero int) ) 16.49/16.44 ( int, s, m, (zero_zero int) ) 16.49/16.44 ( int, (hAPP int int (number_number_of int) pls), min_1, (zero_zero int) ) 16.49/16.44 ) 16.49/16.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105002 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int (archimedean_ceiling X_a) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_105002)) (hAPP nat int (semiring_1_of_nat int) BOUND_VARIABLE_105002))) ) 16.49/16.44 ( real, (zero_zero nat) ) 16.49/16.44 ( real, (one_one nat) ) 16.49/16.44 ( int, (zero_zero nat) ) 16.49/16.44 ( int, (hAPP nat nat suc (zero_zero nat)) ) 16.49/16.44 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.44 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.49/16.44 ) 16.49/16.44 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_105013 $$unsorted)) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_105013) BOUND_VARIABLE_105013)) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_105013) _let_2)))) )))) 16.49/16.44 ( nat, (one_one nat) ) 16.49/16.44 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.49/16.44 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.44 ) 16.49/16.44 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_105088))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_105088 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_105088))) (hBOOL (hAPP X_a bool _let_0 (zero_zero X_a))))) )) 16.49/16.44 ( real, (zero_zero real) ) 16.49/16.44 ( real, (one_one real) ) 16.49/16.44 ( real, pi ) 16.49/16.44 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.44 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.49/16.44 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.49/16.44 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.44 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.49/16.44 ( nat, (zero_zero nat) ) 16.49/16.44 ( int, (zero_zero int) ) 16.49/16.44 ( int, pls ) 16.49/16.44 ( int, (one_one int) ) 16.49/16.44 ( int, min_1 ) 16.49/16.44 ( int, s ) 16.49/16.44 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.49/16.44 ( int, t ) 16.49/16.44 ( int, skv_3 ) 16.49/16.44 ( int, skv_9 ) 16.49/16.44 ( complex, ii ) 16.49/16.44 ( complex, (one_one complex) ) 16.49/16.44 ) 16.49/16.44 (instantiation (let ((_let_0 (product_prod int int))) (forall ((R_4 $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (or (not (= (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) P_5) Q_3) (hAPP rat _let_0 quotient_of R_4))) (= (one_one int) (hAPP int int (hAPP int (fun int int) (gcd_gcd int) P_5) Q_3))) )) 16.49/16.44 ( (zero_zero rat), (zero_zero int), (one_one int) ) 16.49/16.44 ( (one_one rat), (one_one int), (one_one int) ) 16.49/16.44 ) 16.49/16.44 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (not (hBOOL (hAPP X_a bool (iszero X_a) (hAPP int X_a (number_number_of X_a) min_1))))) ) 16.49/16.44 ( real ) 16.49/16.44 ( nat ) 16.49/16.44 ( int ) 16.49/16.44 ( complex ) 16.49/16.44 ( rat ) 16.49/16.44 ( quickcheck_code_int ) 16.49/16.44 ( code_code_numeral ) 16.49/16.44 ) 16.49/16.44 (instantiation (forall ((T_5 $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) T_5) T_5))) ) 16.49/16.44 ( (zero_zero nat) ) 16.49/16.44 ) 16.49/16.44 (instantiation (forall ((N $$unsorted)) (= (hAPP real nat natfloor (hAPP int real (number_number_of real) N)) (hAPP int nat (number_number_of nat) N)) ) 16.49/16.44 ( pls ) 16.49/16.44 ( (hAPP int int bit1 pls) ) 16.49/16.44 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.49/16.44 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.44 ( min_1 ) 16.49/16.44 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.44 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.49/16.44 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.49/16.44 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.49/16.45 ) 16.49/16.45 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_105283 $$unsorted)) (or (not (archim1804426504_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_105283))) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (inverse_inverse X_a) (hAPP nat X_a (semiring_1_of_nat X_a) N_2))) BOUND_VARIABLE_105283)))) ))) ))) 16.49/16.45 ( real, pi ) 16.49/16.45 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.45 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.45 ( real, skv_2 ) 16.49/16.45 ( real, skv_10 ) 16.49/16.45 ( real, skv_13 ) 16.49/16.45 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.45 ( int, (zero_zero int) ) 16.49/16.45 ( int, (one_one int) ) 16.49/16.45 ( 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))) ) 16.49/16.45 ( int, min_1 ) 16.49/16.45 ) 16.49/16.45 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_b bool))) (let ((_let_3 (ord_less_eq X_b))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_105321 $$unsorted) (BOUND_VARIABLE_105322 $$unsorted) (BOUND_VARIABLE_105323 $$unsorted) (BOUND_VARIABLE_105324 $$unsorted)) (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_105322 BOUND_VARIABLE_105323)) BOUND_VARIABLE_105324))) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_2 _let_3 BOUND_VARIABLE_105321) BOUND_VARIABLE_105323))) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (or (not (hBOOL (hAPP X_b bool (hAPP X_b _let_2 _let_3 Y_2) X_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (hAPP X_b X_a BOUND_VARIABLE_105322 Y_2)) (hAPP X_b X_a BOUND_VARIABLE_105322 X_2)))) )) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_b X_a BOUND_VARIABLE_105322 BOUND_VARIABLE_105321)) BOUND_VARIABLE_105324))) ))))) 16.49/16.45 ( real, 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))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.45 ( real, real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), cos, skv_14, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.45 ( real, real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), cos, skv_14, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.45 ( real, real, (hAPP real real cos (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) ) 16.49/16.45 ( real, nat, skv_14, natceiling, (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.45 ( int, real, (one_one int), (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)))) ) 16.49/16.45 ( int, int, (zero_zero 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), (zero_zero int) ) 16.49/16.45 ( int, int, min_1, (number_number_of int), pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.45 ) 16.49/16.45 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (forall ((Y $$unsorted) (X $$unsorted)) (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)))) )) 16.49/16.45 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.45 ( pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.49/16.45 ( (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.45 ( (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.45 ) 16.49/16.45 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (plus_plus nat))) (forall ((Ma $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (= (= (hAPP nat nat (hAPP nat _let_0 _let_1 N_1) K) (hAPP nat nat (hAPP nat _let_0 _let_1 Ma) K)) (= Ma N_1)) ))) 16.49/16.45 ( (one_one nat), (one_one nat), (one_one nat) ) 16.49/16.45 ) 16.49/16.45 (instantiation (let ((_let_0 (fun nat X_a))) (let ((_let_1 (power_power X_a))) (let ((_let_2 (inverse_inverse X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_105400 $$unsorted) (BOUND_VARIABLE_105401 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_105401)) (= (hAPP X_a X_a _let_2 (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_105401) BOUND_VARIABLE_105400)) (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_105401)) BOUND_VARIABLE_105400))) )))) 16.49/16.45 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 16.49/16.45 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 16.49/16.45 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 16.49/16.45 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 16.49/16.45 ) 16.49/16.45 (instantiation (let ((_let_0 (fun nat X_a))) (let ((_let_1 (power_power X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_105515 $$unsorted) (BOUND_VARIABLE_105516 $$unsorted)) (or (not (comm_ring_1 X_a)) (not (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_105516))) (= (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_105515)) BOUND_VARIABLE_105516) (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_105515) BOUND_VARIABLE_105516))) ))) 16.49/16.45 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.45 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.45 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.45 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.45 ) 16.49/16.45 (instantiation (let ((_let_0 (real_1 nat))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (= (hAPP nat real _let_0 N_1) (hAPP nat real _let_0 Ma)) (= N_1 Ma)) )) 16.49/16.45 ( (zero_zero nat), (one_one nat) ) 16.49/16.45 ( (one_one nat), (zero_zero nat) ) 16.49/16.45 ( (one_one nat), (one_one nat) ) 16.49/16.45 ) 16.49/16.45 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted)) (or (not (group_add X_a)) (= _let_0 (hAPP X_a X_a (uminus_uminus X_a) _let_0))) )) 16.49/16.45 ( real ) 16.49/16.45 ( nat ) 16.49/16.45 ( int ) 16.49/16.45 ( complex ) 16.49/16.45 ( rat ) 16.49/16.45 ( quickcheck_code_int ) 16.49/16.45 ( code_code_numeral ) 16.49/16.45 ) 16.49/16.45 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_105646 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_105646) _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_105646)) _let_2)))) )))) 16.49/16.45 ( real, (zero_zero real) ) 16.49/16.45 ( real, pi ) 16.49/16.45 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.49/16.45 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.45 ( int, (zero_zero int) ) 16.49/16.45 ( int, min_1 ) 16.49/16.45 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.49/16.45 ( int, t ) 16.49/16.45 ( complex, ii ) 16.49/16.45 ) 16.49/16.45 (instantiation (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP int nat _let_0 W))) (forall ((W $$unsorted)) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) W))) (= (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) _let_1) _let_1)) (hAPP int nat _let_0 (hAPP int int bit1 W)))) ))) 16.49/16.45 ( pls ) 16.49/16.45 ( (hAPP int int bit1 pls) ) 16.49/16.45 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.49/16.45 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.45 ( min_1 ) 16.49/16.45 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.49/16.45 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.49/16.45 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.49/16.45 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 16.49/16.45 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 16.49/16.45 ) 16.49/16.45 (instantiation (forall ((W $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) W)))) (= (zero_zero nat) (hAPP int nat (number_number_of nat) (hAPP int int bit1 W)))) ) 16.49/16.45 ( pls ) 16.49/16.45 ( (hAPP int int bit1 pls) ) 16.49/16.45 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.49/16.45 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.45 ( min_1 ) 16.49/16.45 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.49/16.45 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.49/16.45 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.49/16.45 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 16.49/16.45 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 16.49/16.45 ) 16.49/16.45 (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))) ) 16.49/16.45 ( (zero_zero real), (zero_zero real) ) 16.49/16.45 ( (zero_zero real), (one_one real) ) 16.49/16.45 ( (one_one real), (zero_zero real) ) 16.49/16.45 ) 16.49/16.45 (instantiation (let ((_let_0 (hAPP int nat (number_number_of nat) V))) (forall ((V $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) _let_0))) (= _let_0 (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) _let_0) (one_one nat))))) )) 16.49/16.45 ( pls ) 16.49/16.45 ( (hAPP int int bit1 pls) ) 16.49/16.45 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.49/16.45 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.49/16.45 ) 16.49/16.45 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (let ((_let_2 (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_105692))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_105692 $$unsorted) (BOUND_VARIABLE_105693 $$unsorted) (BOUND_VARIABLE_105694 $$unsorted)) (or (not (division_ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_105693)) BOUND_VARIABLE_105694) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_105693) BOUND_VARIABLE_105694)))) )))) 16.49/16.45 ( 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))) ) 16.49/16.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.49/16.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.49/16.46 ) 16.49/16.46 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_105712 $$unsorted) (BOUND_VARIABLE_105713 $$unsorted)) (or (not (linorder X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_105713) BOUND_VARIABLE_105712)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_105712) BOUND_VARIABLE_105713))))) )) 16.49/16.46 ( real, (zero_zero real), pi ) 16.49/16.46 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.46 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.49/16.46 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.46 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.46 ( real, (zero_zero real), skv_6 ) 16.49/16.46 ( real, (zero_zero real), skv_11 ) 16.49/16.46 ( real, (zero_zero real), skv_12 ) 16.49/16.46 ( real, (zero_zero real), skv_14 ) 16.49/16.46 ( real, pi, (zero_zero real) ) 16.49/16.46 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.49/16.46 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.49/16.46 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.46 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.49/16.46 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.46 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.49/16.46 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.49/16.46 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.49/16.46 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 16.49/16.46 ( real, skv_2, (zero_zero real) ) 16.49/16.46 ( real, skv_10, (zero_zero real) ) 16.49/16.46 ( real, skv_13, (zero_zero real) ) 16.49/16.46 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.46 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 16.49/16.46 ( int, (zero_zero int), (zero_zero int) ) 16.49/16.46 ( int, (zero_zero int), (one_one int) ) 16.49/16.46 ( int, (zero_zero int), min_1 ) 16.49/16.46 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.46 ( int, (zero_zero int), s ) 16.49/16.46 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.49/16.46 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.49/16.46 ( int, (zero_zero int), t ) 16.49/16.46 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.49/16.46 ( int, (zero_zero int), skv_3 ) 16.49/16.46 ( int, (zero_zero int), skv_9 ) 16.49/16.46 ( int, (one_one int), (zero_zero int) ) 16.49/16.46 ( int, (one_one int), t ) 16.49/16.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 16.49/16.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 16.49/16.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.49/16.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_3 ) 16.49/16.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_9 ) 16.49/16.46 ( int, min_1, (zero_zero int) ) 16.49/16.46 ( int, min_1, pls ) 16.49/16.46 ( int, min_1, min_1 ) 16.49/16.46 ( 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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.49/16.46 ) 16.49/16.46 (instantiation (let ((_let_0 (hAPP int X_b (number_number_of X_b) BOUND_VARIABLE_105735))) (forall ((X_b $$unsorted) (BOUND_VARIABLE_105735 $$unsorted)) (or (not (number X_b)) (not (monoid_mult X_b)) (= (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (times_times X_b) _let_0) _let_0) (hAPP nat X_b (hAPP X_b (fun nat X_b) (power_power X_b) _let_0) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) )) 16.49/16.46 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.49/16.46 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.46 ( real, min_1 ) 16.49/16.46 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.46 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.49/16.46 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.49/16.46 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.49/16.46 ( nat, pls ) 16.49/16.46 ( nat, (hAPP int int bit1 pls) ) 16.49/16.46 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.49/16.46 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.49/16.46 ( int, pls ) 16.49/16.46 ( int, (hAPP int int bit1 pls) ) 16.49/16.46 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.49/16.46 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.46 ( int, min_1 ) 16.49/16.46 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.49/16.46 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.49/16.46 ( complex, min_1 ) 16.49/16.46 ( quickcheck_code_int, (zero_zero int) ) 16.49/16.46 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 16.49/16.46 ( quickcheck_code_int, (one_one int) ) 16.49/16.46 ( code_code_numeral, pls ) 16.49/16.46 ( code_code_numeral, (hAPP int int bit1 pls) ) 16.49/16.46 ) 16.49/16.46 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (minus_minus real))) (let ((_let_2 (times_times real))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP real real sin (hAPP real real (hAPP real _let_0 _let_1 X) Y)) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_2 (hAPP real real cos Y)) (hAPP real real sin X))) (hAPP real real (hAPP real _let_0 _let_2 (hAPP real real sin Y)) (hAPP real real cos X)))) )))) 16.49/16.46 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.49/16.46 ) 16.49/16.46 (instantiation (let ((_let_0 (filter nat))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (fun X_a bool))) (let ((_let_3 (fun X_a (fun _let_0 bool)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_105787 $$unsorted)) (or (not (metric_space X_a)) (= (hAPP _let_2 X_a (the X_a) (hAPP _let_0 _let_2 (hAPP _let_3 (fun _let_0 _let_2) (combc X_a _let_0 bool) (hAPP _let_1 _let_3 (tendsto nat X_a) BOUND_VARIABLE_105787)) sequentially)) (hAPP _let_1 X_a (lim X_a) BOUND_VARIABLE_105787))) ))))) 16.49/16.46 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 16.49/16.46 ) 16.49/16.46 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (one_one X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_105861 $$unsorted) (BOUND_VARIABLE_105862 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_105862))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_105862) BOUND_VARIABLE_105861)))) )) 16.49/16.46 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 16.49/16.46 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 16.49/16.46 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 16.49/16.46 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 16.49/16.46 ) 16.49/16.46 (instantiation (let ((_let_0 (div_mod X_a))) (forall ((X_a $$unsorted)) (or (not (semiring_div X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0))) )) 16.49/16.46 ( bool ) 16.49/16.46 ( real ) 16.49/16.46 ( nat ) 16.49/16.46 ( (fun nat bool) ) 16.49/16.46 ( int ) 16.49/16.46 ( (fun int bool) ) 16.49/16.46 ( (fun real bool) ) 16.49/16.46 ( (fun real real) ) 16.49/16.46 ( complex ) 16.49/16.46 ( (fun nat real) ) 16.49/16.46 ( (fun int int) ) 16.49/16.46 ( (fun int (fun int bool)) ) 16.49/16.46 ( quickcheck_code_int ) 16.49/16.46 ( (product_prod int int) ) 16.49/16.46 ( (fun (product_prod int int) bool) ) 16.49/16.46 ( code_code_numeral ) 16.49/16.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.49/16.46 ( (fun (product_prod int int) int) ) 16.49/16.46 ( (fun int (fun int (fun int bool))) ) 16.49/16.46 ( (fun int real) ) 16.49/16.46 ) 16.49/16.46 (instantiation (let ((_let_0 (size_size nat))) (forall ((Nat_1 $$unsorted)) (= (hAPP nat nat _let_0 (hAPP nat nat suc Nat_1)) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP nat nat _let_0 Nat_1)) (hAPP nat nat suc (zero_zero nat)))) )) 16.49/16.46 ( (zero_zero nat) ) 16.49/16.46 ( (hAPP nat nat suc (zero_zero nat)) ) 16.49/16.46 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 16.49/16.46 ) 16.49/16.46 (instantiation (let ((_let_0 (fun (filter X_a) bool))) (let ((_let_1 (fun X_a real))) (let ((_let_2 (fun X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_106026 $$unsorted) (BOUND_VARIABLE_106027 $$unsorted)) (let ((_let_0 (filter X_a))) (or (not (real_normed_vector X_b)) (= (hBOOL (hAPP _let_0 bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (tendsto X_a real) (hAPP _let_2 _let_1 (hAPP (fun X_b real) (fun _let_2 _let_1) (combb X_b real X_a) (norm_norm X_b)) BOUND_VARIABLE_106026)) (zero_zero real)) BOUND_VARIABLE_106027)) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_0 (hAPP _let_2 (fun X_b _let_0) (tendsto X_a X_b) BOUND_VARIABLE_106026) (zero_zero X_b)) BOUND_VARIABLE_106027))))) )))) 16.49/16.46 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.49/16.46 ( nat, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), sequentially ) 16.49/16.46 ) 16.49/16.46 (instantiation (let ((_let_0 (number_number_of int))) (let ((_let_1 (number_number_of nat))) (let ((_let_2 (semiring_1_of_nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_106059 $$unsorted) (BOUND_VARIABLE_106068 $$unsorted)) (or (not (number_ring X_a)) (and (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 BOUND_VARIABLE_106059)))) (= (zero_zero X_a) (hAPP nat X_a _let_2 (hAPP int nat _let_1 BOUND_VARIABLE_106059)))) (or (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 BOUND_VARIABLE_106068))) (= (hAPP nat X_a _let_2 (hAPP int nat _let_1 BOUND_VARIABLE_106068)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_106068))))) )))) 16.49/16.46 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.49/16.46 ( int, min_1, min_1 ) 16.49/16.46 ( complex, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.46 ( rat, pls, pls ) 16.49/16.46 ) 16.49/16.46 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_106089 $$unsorted) (BOUND_VARIABLE_106090 $$unsorted)) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_106090) (hAPP X_a X_a _let_2 BOUND_VARIABLE_106089))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_106089) (hAPP X_a X_a _let_2 BOUND_VARIABLE_106090))))) )))) 16.49/16.46 ( int, (zero_zero int), pls ) 16.49/16.46 ( int, (zero_zero int), (one_one int) ) 16.49/16.46 ( int, pls, (zero_zero int) ) 16.49/16.46 ( int, pls, min_1 ) 16.49/16.46 ( int, (one_one int), (zero_zero int) ) 16.49/16.46 ( int, (one_one int), min_1 ) 16.49/16.46 ( int, min_1, pls ) 16.49/16.46 ( int, min_1, (one_one int) ) 16.49/16.46 ) 16.49/16.46 (instantiation (let ((_let_0 (zero_zero int))) (let ((_let_1 (fun int (fun int bool)))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (ring_1_of_int X_a))) (let ((_let_4 (fun int X_a))) (let ((_let_5 (fun int _let_4))) (let ((_let_6 (fun X_a _let_4))) (let ((_let_7 (fun int _let_6))) (let ((_let_8 (fun X_a X_a))) (let ((_let_9 (fun int _let_8))) (let ((_let_10 (fun int _let_9))) (let ((_let_11 (combc int X_a X_a))) (let ((_let_12 (fun X_a _let_9))) (let ((_let_13 (fun int (fun X_a _let_8)))) (let ((_let_14 (hAPP (fun X_a _let_8) (fun _let_4 _let_9) (combb X_a _let_8 int) (plus_plus X_a)))) (let ((_let_15 (hAPP _let_4 _let_4 (hAPP _let_9 (fun _let_4 _let_4) (combs int X_a X_a) (hAPP _let_4 _let_9 _let_14 _let_3)) _let_3))) (let ((_let_16 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_106168) _let_0)))) (let ((_let_17 (hAPP int X_a _let_3 BOUND_VARIABLE_106168))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_106161 $$unsorted) (BOUND_VARIABLE_106168 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun X_a _let_8))) (or (not (ring_1 X_a)) (and (or (not (= _let_0 (ti int BOUND_VARIABLE_106161))) (= (zero_zero X_a) (hAPP int X_a _let_3 BOUND_VARIABLE_106161))) (or (= _let_0 (ti int BOUND_VARIABLE_106168)) (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_106168))))) (or _let_16 (= _let_17 (hAPP _let_2 X_a (hAPP _let_5 (fun _let_2 X_a) (product_prod_case int int X_a) (hAPP _let_4 _let_5 (hAPP _let_7 (fun _let_4 _let_5) (combs int X_a _let_4) (hAPP _let_10 _let_7 (hAPP (fun _let_9 _let_6) (fun _let_10 _let_7) (combb _let_9 _let_6 int) _let_11) (hAPP _let_4 _let_10 (hAPP _let_12 (fun _let_4 _let_10) (combb X_a _let_9 int) (hAPP _let_13 _let_12 (combc int X_a _let_8) (hAPP _let_0 _let_13 (hAPP (fun bool _let_1) (fun _let_0 _let_13) (combb bool _let_1 int) (if X_a)) (hAPP int _let_0 (hAPP _let_1 _let_1 (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_2 (hAPP int (fun int _let_2) divmod_int BOUND_VARIABLE_106168) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))))) ))))))))))))))))))) 16.49/16.46 ( real, t, t ) 16.49/16.46 ( int, m, m ) 16.49/16.46 ( complex, min_1, min_1 ) 16.49/16.46 ( rat, s, s ) 16.49/16.46 ) 16.49/16.46 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) X) (zero_zero int)))) (not (forall ((N_2 $$unsorted)) (not (= (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) (hAPP nat nat suc N_2))) (ti int X))) ))) ) 16.49/16.47 ( (zero_zero int) ) 16.49/16.47 ( min_1 ) 16.49/16.47 ( s ) 16.49/16.47 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.49/16.47 ( t ) 16.49/16.47 ( skv_3 ) 16.49/16.47 ( skv_9 ) 16.49/16.47 ) 16.49/16.47 (instantiation (forall ((X_a $$unsorted)) (or (not (ring_1 X_a)) (= (hAPP int X_a (ring_1_of_int X_a) (one_one int)) (one_one X_a))) ) 16.49/16.47 ( real ) 16.49/16.47 ( nat ) 16.49/16.47 ( int ) 16.49/16.47 ( complex ) 16.49/16.47 ( rat ) 16.49/16.47 ( quickcheck_code_int ) 16.49/16.47 ( code_code_numeral ) 16.49/16.47 ) 16.49/16.47 (instantiation (let ((_let_0 (hAPP complex (fun complex complex) (times_times complex) ii))) (forall ((X $$unsorted)) (= (hAPP complex complex (uminus_uminus complex) X) (hAPP complex complex _let_0 (hAPP complex complex _let_0 X))) )) 16.49/16.47 ( ii ) 16.49/16.47 ( (one_one complex) ) 16.49/16.47 ) 16.49/16.47 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (not (linord1117847801e_zero X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) (one_one X_a)) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 16.49/16.47 ( bool ) 16.49/16.47 ( real ) 16.49/16.47 ( nat ) 16.49/16.47 ( (fun nat bool) ) 16.49/16.47 ( int ) 16.49/16.47 ( (fun int bool) ) 16.49/16.47 ( (fun real bool) ) 16.49/16.47 ( (fun real real) ) 16.49/16.47 ( complex ) 16.49/16.47 ( (fun nat real) ) 16.49/16.47 ( (fun int int) ) 16.49/16.47 ( rat ) 16.49/16.47 ( (fun int (fun int bool)) ) 16.49/16.47 ( quickcheck_code_int ) 16.49/16.47 ( (product_prod real real) ) 16.49/16.47 ( (product_prod int int) ) 16.49/16.47 ( (filter real) ) 16.49/16.47 ( (filter nat) ) 16.49/16.47 ( (product_prod nat nat) ) 16.49/16.47 ( (fun (product_prod int int) bool) ) 16.49/16.47 ( code_code_numeral ) 16.49/16.47 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.49/16.47 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.49/16.47 ( (fun nat rat) ) 16.49/16.47 ( (fun (product_prod int int) int) ) 16.49/16.47 ( (fun int (fun int (fun int bool))) ) 16.49/16.47 ( (fun int real) ) 16.49/16.47 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.49/16.47 ) 16.49/16.47 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_106264 $$unsorted)) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_106264))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_106264) _let_2)))) )))) 16.49/16.47 ( real, (zero_zero real) ) 16.49/16.47 ( real, (one_one real) ) 16.49/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.47 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.47 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.49/16.47 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.47 ( real, skv_14 ) 16.49/16.47 ( int, (zero_zero int) ) 16.49/16.47 ( int, pls ) 16.49/16.47 ( int, (one_one int) ) 16.49/16.47 ( int, min_1 ) 16.49/16.47 ( complex, ii ) 16.49/16.47 ( complex, (one_one complex) ) 16.49/16.47 ) 16.49/16.47 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (power_power real))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_4 (times_times real))) (let ((_let_5 (number_number_of real))) (let ((_let_6 (hAPP int nat (number_number_of nat) _let_3))) (forall ((X $$unsorted)) (= (hAPP real real (hAPP real _let_0 _let_4 (hAPP int real _let_5 (hAPP int int bit0 _let_3))) (hAPP nat real (hAPP real _let_1 _let_2 X) _let_6)) (hAPP nat real (hAPP real _let_1 _let_2 (hAPP real real (hAPP real _let_0 _let_4 (hAPP int real _let_5 _let_3)) X)) _let_6)) )))))))) 16.49/16.47 ( pi ) 16.49/16.47 ( (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 16.49/16.47 ) 16.49/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106301 $$unsorted) (BOUND_VARIABLE_106302 $$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_106301) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_106301) BOUND_VARIABLE_106302)))) ) 16.49/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.49/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 16.49/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.49/16.47 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.49/16.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.49/16.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 16.49/16.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.49/16.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1 ) 16.49/16.47 ( complex, ii, ii ) 16.49/16.47 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 16.49/16.47 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 16.49/16.47 ) 16.49/16.47 (instantiation (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_106356))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_106356 $$unsorted) (BOUND_VARIABLE_106357 $$unsorted)) (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_106357)) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_106357)))) )))) 16.49/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.49/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 16.49/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.49/16.47 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.49/16.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.49/16.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 16.49/16.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.49/16.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1 ) 16.49/16.47 ( complex, ii, ii ) 16.49/16.47 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 16.49/16.47 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 16.49/16.47 ) 16.49/16.47 (instantiation (forall ((N $$unsorted)) (= N (hAPP real nat natfloor (hAPP nat real (real_1 nat) N))) ) 16.49/16.47 ( (zero_zero nat) ) 16.49/16.47 ( (one_one nat) ) 16.49/16.47 ) 16.49/16.47 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_106387 $$unsorted) (BOUND_VARIABLE_106388 $$unsorted)) (or (not (ordered_ring X_a)) (and (or (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_106387))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_106388)))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_106388) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_106387) _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_106388) BOUND_VARIABLE_106387)))) ))))) 16.49/16.47 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.47 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.49/16.47 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.47 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.47 ( int, (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.47 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.47 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.47 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.47 ( complex, ii, ii ) 16.49/16.47 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.49/16.47 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.47 ) 16.49/16.47 (instantiation (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (not (hBOOL (hAPP X_a bool (iszero X_a) (one_one X_a))))) ) 16.49/16.47 ( real ) 16.49/16.47 ( nat ) 16.49/16.47 ( int ) 16.49/16.47 ( complex ) 16.49/16.47 ( rat ) 16.49/16.47 ( quickcheck_code_int ) 16.49/16.47 ( code_code_numeral ) 16.49/16.47 ) 16.49/16.47 (instantiation (let ((_let_0 (product_prod int int))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (hAPP _let_0 _let_0 normalize (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) A_1) B)) (hAPP rat _let_0 quotient_of (hAPP int rat (hAPP int (fun int rat) fract A_1) B))) )) 16.49/16.47 ( (zero_zero int), (one_one int) ) 16.49/16.47 ( (one_one int), (one_one int) ) 16.49/16.47 ( s, (one_one int) ) 16.49/16.47 ) 16.49/16.47 (instantiation (forall ((X $$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))) ) 16.49/16.47 ( (zero_zero real) ) 16.49/16.47 ( (one_one real) ) 16.49/16.47 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.47 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.47 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.47 ( skv_14 ) 16.49/16.47 ) 16.49/16.47 (instantiation (let ((_let_0 (norm_norm X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (minus_minus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_106581 $$unsorted) (BOUND_VARIABLE_106582 $$unsorted)) (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_106582) BOUND_VARIABLE_106581)) (hAPP X_a real _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_106581) BOUND_VARIABLE_106582)))) )))) 16.49/16.47 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.49/16.48 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 16.49/16.48 ( int, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.48 ( 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)))), (hAPP int int (number_number_of int) min_1) ) 16.49/16.48 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.49/16.48 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 16.49/16.48 ) 16.49/16.48 (instantiation (let ((_let_0 (one_one int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (hAPP int int (number_number_of int) W))) (forall ((W $$unsorted)) (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_mod int) _let_0) _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)))) )))) 16.49/16.48 ( pls ) 16.49/16.48 ( (hAPP int int bit1 pls) ) 16.49/16.48 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.49/16.48 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.48 ( min_1 ) 16.49/16.48 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.49/16.48 ) 16.49/16.48 (instantiation (forall ((K_4 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) K_4))) (not (forall ((N_2 $$unsorted)) (not (= (ti int K_4) (hAPP nat int (semiring_1_of_nat int) N_2))) ))) ) 16.49/16.48 ( (one_one int) ) 16.49/16.48 ( min_1 ) 16.49/16.48 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.48 ( s ) 16.49/16.48 ( (hAPP int int (number_number_of int) pls) ) 16.49/16.48 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.49/16.48 ( skv_3 ) 16.49/16.48 ( skv_9 ) 16.49/16.48 ) 16.49/16.48 (instantiation (let ((_let_0 (fun nat X_a))) (let ((_let_1 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_106686 $$unsorted)) (or (not (comm_monoid_add X_a)) (not (topological_space X_a)) (= (hAPP _let_1 X_a (the X_a) (hAPP _let_0 _let_1 (sums X_a) BOUND_VARIABLE_106686)) (hAPP _let_0 X_a (suminf X_a) BOUND_VARIABLE_106686))) ))) 16.49/16.48 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))) ) 16.49/16.48 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (combc nat nat nat))) (let ((_let_4 (fun nat _let_0))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun _let_1 _let_4))) (let ((_let_7 (combb real _let_0 nat))) (hAPP _let_1 _let_1 (hAPP _let_4 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_4 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 16.49/16.48 ) 16.49/16.48 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_106735 $$unsorted)) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_106735)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_106735)) BOUND_VARIABLE_106735)))) ))) 16.49/16.48 ( real, (one_one real) ) 16.49/16.48 ( real, pi ) 16.49/16.48 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.48 ( 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) ) 16.49/16.48 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.48 ( real, skv_2 ) 16.49/16.48 ( real, skv_10 ) 16.49/16.48 ( real, skv_13 ) 16.49/16.48 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.48 ( int, (zero_zero int) ) 16.49/16.48 ( int, pls ) 16.49/16.48 ( int, (one_one int) ) 16.49/16.48 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.48 ( int, min_1 ) 16.49/16.48 ( complex, ii ) 16.49/16.48 ( complex, (one_one complex) ) 16.49/16.48 ) 16.49/16.48 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP int real (real_1 int) N))) (forall ((N $$unsorted) (X $$unsorted)) (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))) )))) 16.49/16.48 ( (zero_zero int), pi ) 16.49/16.48 ( (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.48 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.48 ( (zero_zero int), skv_2 ) 16.49/16.48 ( (zero_zero int), skv_10 ) 16.49/16.48 ( (zero_zero int), skv_13 ) 16.49/16.48 ( (one_one int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.48 ) 16.49/16.48 (instantiation (forall ((R_4 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) R_4) (zero_zero real)))) (= (hAPP real real (abs_abs real) R_4) (hAPP real real (uminus_uminus real) R_4))) ) 16.49/16.48 ( (zero_zero real) ) 16.49/16.48 ( (one_one real) ) 16.49/16.48 ( pi ) 16.49/16.48 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.48 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.49/16.48 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.49/16.48 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.48 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.49/16.48 ) 16.49/16.48 (instantiation (forall ((R_4 $$unsorted)) (or (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) R_4) (zero_zero real))) (= R_4 (hAPP real real (abs_abs real) R_4))) ) 16.49/16.48 ( (zero_zero real) ) 16.49/16.48 ( (one_one real) ) 16.49/16.48 ( pi ) 16.49/16.48 ( (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)))) ) 16.49/16.48 ( (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))))) ) 16.49/16.48 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.48 ( (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)) ) 16.49/16.48 ) 16.49/16.48 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (norm_norm X_a))) (forall ((X_a $$unsorted)) (or (not (real_normed_vector X_a)) (not (forall ((K_2 $$unsorted)) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_2 (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) A_4) B_4))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (norm_norm real) A_4)) (hAPP X_a real _let_2 B_4))) K_2))) )) ))) )))) 16.49/16.48 ( real ) 16.49/16.48 ( complex ) 16.49/16.48 ) 16.49/16.48 (instantiation (let ((_let_0 (fun X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_106799 $$unsorted) (BOUND_VARIABLE_106800 $$unsorted) (BOUND_VARIABLE_106801 $$unsorted)) (or (not (ord X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) BOUND_VARIABLE_106800) BOUND_VARIABLE_106801))) (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) (hAPP X_a X_b BOUND_VARIABLE_106800 BOUND_VARIABLE_106799)) (hAPP X_a X_b BOUND_VARIABLE_106801 BOUND_VARIABLE_106799)))) )) 16.49/16.48 ( real, real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), cos, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.48 ( int, int, (zero_zero int), (number_number_of int), (fact_fact int) ) 16.49/16.48 ( int, int, pls, (number_number_of int), (number_number_of int) ) 16.49/16.48 ( int, int, pls, pred, (number_number_of int) ) 16.49/16.48 ( int, int, min_1, bit1, bit1 ) 16.49/16.48 ( int, int, min_1, succ, bit1 ) 16.49/16.48 ) 16.49/16.48 (instantiation (forall ((P_5 $$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)) ) 16.49/16.48 ( (zero_zero nat) ) 16.49/16.48 ( (one_one nat) ) 16.49/16.48 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.48 ) 16.49/16.48 (instantiation (let ((_let_0 (ord_gr676655987ssThan X_a))) (forall ((X_a $$unsorted)) (or (not (ordered_ab_group_add X_a)) (= _let_0 (ti (fun X_a (fun X_a (fun X_a bool))) _let_0))) )) 16.49/16.48 ( bool ) 16.49/16.48 ( real ) 16.49/16.48 ( nat ) 16.49/16.48 ( (fun nat bool) ) 16.49/16.48 ( int ) 16.49/16.48 ( (fun int bool) ) 16.49/16.48 ( rat ) 16.49/16.48 ( (product_prod real real) ) 16.49/16.48 ( (product_prod int int) ) 16.49/16.48 ( (filter real) ) 16.49/16.48 ( (filter nat) ) 16.49/16.48 ( (product_prod nat nat) ) 16.49/16.48 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.49/16.48 ( (fun nat rat) ) 16.49/16.48 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.49/16.48 ) 16.49/16.48 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (or (= (zero_zero real) C_1) (= (= A_2 B_1) (= (hAPP real real (hAPP real _let_0 _let_1 A_2) C_1) (hAPP real real (hAPP real _let_0 _let_1 B_1) C_1)))) ))) 16.49/16.48 ( (hAPP int real (number_number_of 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)))), pi ) 16.49/16.48 ( (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 ) 16.49/16.48 ( (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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 16.49/16.48 ( (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 ) 16.49/16.48 ( (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 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.49/16.48 ) 16.49/16.48 (instantiation (let ((_let_0 (fun real real))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP real real (hAPP real _let_0 (minus_minus real) X) Y) (hAPP real real (hAPP real _let_0 (plus_plus real) X) (hAPP real real (uminus_uminus real) Y))) )) 16.49/16.48 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.49/16.48 ) 16.49/16.48 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_106921 $$unsorted) (BOUND_VARIABLE_106922 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_106921) BOUND_VARIABLE_106922))) (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_106921) BOUND_VARIABLE_106922)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 _let_4) _let_4))) BOUND_VARIABLE_106922))) )))))) 16.49/16.48 ( real, (zero_zero real), pi ) 16.49/16.48 ( 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)))) ) 16.49/16.48 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.48 ( real, (zero_zero real), skv_2 ) 16.49/16.48 ( real, (zero_zero real), skv_10 ) 16.49/16.48 ( real, (zero_zero real), skv_13 ) 16.49/16.48 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.49 ( real, pi, (zero_zero real) ) 16.49/16.49 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.49 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.49 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.49/16.49 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.49/16.49 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.49/16.49 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.49 ( nat, (one_one nat), (one_one nat) ) 16.49/16.49 ( int, (zero_zero int), (zero_zero int) ) 16.49/16.49 ( int, (zero_zero int), (one_one int) ) 16.49/16.49 ( int, (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.49 ( int, (zero_zero int), min_1 ) 16.49/16.49 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.49/16.49 ( int, min_1, (zero_zero int) ) 16.49/16.49 ( int, min_1, min_1 ) 16.49/16.49 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.49 ( 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)))), (one_one int) ) 16.49/16.49 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 16.49/16.49 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 16.49/16.49 ( int, t, (zero_zero int) ) 16.49/16.49 ( int, t, (one_one int) ) 16.49/16.49 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.49 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.49 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.49 ) 16.49/16.49 (instantiation (let ((_let_0 (fun real real))) (forall ((R $$unsorted) (S_5 $$unsorted)) (= (hAPP real real (hAPP real _let_0 (inverse_divide real) R) S_5) (hAPP real real (hAPP real _let_0 (times_times real) R) (hAPP real real (inverse_inverse real) S_5))) )) 16.49/16.49 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.49 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.49/16.49 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.49 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 16.49/16.49 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.49 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.49 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.49/16.49 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.49/16.49 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.49 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.49 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.49/16.49 ) 16.49/16.49 (instantiation (let ((_let_0 (real_1 int))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP int real _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) X) Y)) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real _let_0 X)) (hAPP int real _let_0 Y))) )) 16.49/16.49 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.49/16.49 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 16.49/16.49 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.49/16.49 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1 ) 16.49/16.49 ) 16.49/16.49 (instantiation (let ((_let_0 (norm_norm X_a))) (forall ((X_a $$unsorted)) (or (not (sgn_div_norm X_a)) (= _let_0 (ti (fun X_a real) _let_0))) )) 16.49/16.49 ( real ) 16.49/16.49 ( nat ) 16.49/16.49 ( int ) 16.49/16.49 ( (fun real bool) ) 16.49/16.49 ( complex ) 16.49/16.49 ( rat ) 16.49/16.49 ) 16.49/16.49 (instantiation (let ((_let_0 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_107056 $$unsorted) (BOUND_VARIABLE_107057 $$unsorted)) (or (not (group_add X_a)) (= (= (ti X_a BOUND_VARIABLE_107056) (hAPP X_a X_a _let_0 BOUND_VARIABLE_107057)) (= (ti X_a BOUND_VARIABLE_107057) (hAPP X_a X_a _let_0 BOUND_VARIABLE_107056)))) )) 16.49/16.49 ( real, pi, (one_one real) ) 16.49/16.49 ( int, m, min_1 ) 16.49/16.49 ( int, min_1, (one_one int) ) 16.49/16.49 ( int, s, pls ) 16.49/16.49 ( complex, ii, (one_one complex) ) 16.49/16.49 ) 16.49/16.49 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (let ((_let_2 (fun int bool))) (let ((_let_3 (ord_less_eq int))) (let ((_let_4 (ord_less nat))) (let ((_let_5 (hAPP nat _let_0 _let_1 Ma))) (forall ((K $$unsorted) (F $$unsorted) (N_1 $$unsorted) (Ma $$unsorted)) (or (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool _let_5 I_2))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_4 I_2) N_1))) (hBOOL (hAPP int bool (hAPP int _let_2 _let_3 (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 _let_0 _let_4 Ma) N_1))) (not (hBOOL (hAPP int bool (hAPP int _let_2 _let_3 (hAPP nat int F Ma)) K))) (not (hBOOL (hAPP int bool (hAPP int _let_2 _let_3 K) (hAPP nat int F N_1)))) (not (forall ((I_2 $$unsorted)) (or (not (= (hAPP nat int F I_2) (ti int K))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 I_2) N_1))) (not (hBOOL (hAPP nat bool _let_5 I_2)))) ))) ))))))) 16.49/16.49 ( (hAPP int int (number_number_of int) pls), (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 16.49/16.49 ) 16.49/16.49 (instantiation (forall ((Z_1 $$unsorted)) (= Z_1 (hAPP complex complex cnj (hAPP complex complex cnj Z_1))) ) 16.49/16.49 ( (zero_zero complex) ) 16.49/16.49 ( (one_one complex) ) 16.49/16.49 ) 16.49/16.49 (instantiation (let ((_let_0 (zero_zero int))) (let ((_let_1 (fun int 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))) (forall ((P_5 $$unsorted) (R_4 $$unsorted) (S_3 $$unsorted) (Q_3 $$unsorted)) (or (= _let_0 (ti int Q_3)) (= _let_0 (ti int S_3)) (not (= (hAPP _let_3 _let_3 normalize (hAPP int _let_3 (hAPP int _let_4 _let_5 P_5) Q_3)) (hAPP _let_3 _let_3 normalize (hAPP int _let_3 (hAPP int _let_4 _let_5 R_4) S_3)))) (= (hAPP int int (hAPP int _let_1 _let_2 P_5) S_3) (hAPP int int (hAPP int _let_1 _let_2 R_4) Q_3))) ))))))) 16.49/16.49 ( (zero_zero int), (zero_zero int), min_1, min_1 ) 16.49/16.49 ( (zero_zero int), (one_one int), min_1, min_1 ) 16.49/16.49 ( (one_one int), (zero_zero int), s, s ) 16.49/16.49 ( s, s, m, m ) 16.49/16.49 ( s, s, t, m ) 16.49/16.49 ) 16.49/16.49 (instantiation (forall ((X_a $$unsorted) (P $$unsorted)) (= (ti X_a P) (hAPP X_a X_a (combi X_a) P)) ) 16.49/16.49 ( bool, fFalse ) 16.49/16.49 ( bool, fTrue ) 16.49/16.49 ( real, pi ) 16.49/16.49 ( (fun nat bool), (even_odd_even nat) ) 16.49/16.49 ( (fun nat bool), prime ) 16.49/16.49 ( (fun nat nat), suc ) 16.49/16.49 ( (fun nat nat), (fact_fact nat) ) 16.49/16.49 ( (fun nat nat), (size_size nat) ) 16.49/16.49 ( (fun nat nat), fact ) 16.49/16.49 ( (fun nat nat), nat_size ) 16.49/16.49 ( int, pls ) 16.49/16.49 ( int, m ) 16.49/16.49 ( int, min_1 ) 16.49/16.49 ( int, s ) 16.49/16.49 ( int, s1 ) 16.49/16.49 ( int, t ) 16.49/16.49 ( (fun int bool), zprime ) 16.49/16.49 ( (fun int bool), nat_neg ) 16.49/16.49 ( (fun int bool), zEven ) 16.49/16.49 ( (fun int bool), nat_is_nat ) 16.49/16.49 ( (fun int bool), zOdd ) 16.49/16.49 ( (fun int bool), (even_odd_even int) ) 16.49/16.49 ( (fun int bool), twoSqu1091635170sum2sq ) 16.49/16.49 ( (fun int nat), nat_1 ) 16.49/16.49 ( (fun int nat), phi ) 16.49/16.49 ( (fun real real), sqrt ) 16.49/16.49 ( (fun real real), tan ) 16.49/16.49 ( (fun real real), cos ) 16.49/16.49 ( (fun real real), arccos ) 16.49/16.49 ( (fun real real), ln ) 16.49/16.49 ( (fun real real), sin ) 16.49/16.49 ( (fun real real), arctan ) 16.49/16.49 ( (fun real real), arcsin ) 16.49/16.49 ( complex, ii ) 16.49/16.49 ( (fun complex complex), cnj ) 16.49/16.49 ( (fun complex complex), expi ) 16.49/16.49 ( (fun nat real), (real_1 nat) ) 16.49/16.49 ( (fun nat real), cos_coeff ) 16.49/16.49 ( (fun nat real), sin_coeff ) 16.49/16.49 ( (fun int int), bit0 ) 16.49/16.49 ( (fun int int), bit1 ) 16.49/16.49 ( (fun int int), pred ) 16.49/16.49 ( (fun int int), succ ) 16.49/16.49 ( (fun int int), (fact_fact int) ) 16.49/16.49 ( (fun int int), zfact ) 16.49/16.49 ( (fun bool bool), fNot ) 16.49/16.49 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.49/16.49 ( (fun bool (fun bool bool)), fconj ) 16.49/16.49 ( (fun bool (fun bool bool)), fdisj ) 16.49/16.49 ( (fun bool (fun bool bool)), fimplies ) 16.49/16.49 ( (fun int (fun int bool)), sRStar ) 16.49/16.49 ( (fun int (fun int bool)), quadRes ) 16.49/16.49 ( (fun int (fun int bool)), norRRset ) 16.49/16.49 ( (fun int (fun int bool)), d22set ) 16.49/16.49 ( (fun int (fun int bool)), sr ) 16.49/16.49 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.49/16.49 ( (fun nat (fun nat nat)), nat_gcd ) 16.49/16.49 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.49/16.49 ( (fun nat (fun nat nat)), nat_lcm ) 16.49/16.49 ( (fun nat (fun real real)), root ) 16.49/16.49 ( (fun real (fun real real)), log ) 16.49/16.49 ( (fun real (fun real real)), powr ) 16.49/16.49 ( (fun nat (fun nat bool)), coprime ) 16.49/16.49 ( (fun (fun int bool) int), (the int) ) 16.49/16.49 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.49/16.49 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.49/16.49 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.49/16.49 ( (fun (fun int bool) bool), nat_nat_set ) 16.49/16.49 ( (filter nat), sequentially ) 16.49/16.49 ( (fun (product_prod nat nat) bool), pred_nat ) 16.49/16.49 ( (fun (product_prod int int) bool), frac_1 ) 16.49/16.49 ( (fun real complex), cis ) 16.49/16.49 ( (fun complex real), im ) 16.49/16.49 ( (fun complex real), re ) 16.49/16.49 ( (fun complex real), arg ) 16.49/16.49 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.49/16.49 ( (fun int (fun int int)), int_gcd ) 16.49/16.49 ( (fun int (fun int int)), multInv ) 16.49/16.49 ( (fun int (fun int int)), legacy_zgcd ) 16.49/16.49 ( (fun int (fun int int)), z3mod ) 16.49/16.49 ( (fun int (fun int int)), inv ) 16.49/16.49 ( (fun int (fun int int)), (gcd_gcd int) ) 16.49/16.49 ( (fun int (fun int int)), standardRes ) 16.49/16.49 ( (fun int (fun int int)), legendre ) 16.49/16.49 ( (fun int (fun int int)), nat_tsub ) 16.49/16.49 ( (fun int (fun int int)), z3div ) 16.49/16.49 ( (fun int (fun int int)), int_lcm ) 16.49/16.49 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.49/16.49 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.49/16.49 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.49/16.49 ( (fun int (fun (fun int bool) bool)), resSet ) 16.49/16.49 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.49/16.49 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.49/16.49 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.49/16.49 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.49/16.49 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.49/16.49 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.49/16.49 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.49/16.49 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.49/16.49 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.49/16.49 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.49/16.49 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.49/16.49 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.49/16.49 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.49/16.49 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.49/16.49 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.49/16.49 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.49/16.49 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.49/16.49 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.49/16.49 ( (fun real nat), natfloor ) 16.49/16.49 ( (fun real nat), natceiling ) 16.49/16.49 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.49/16.49 ( (fun int (fun int (fun int bool))), wset ) 16.49/16.49 ( (fun int (fun int (fun int bool))), bnorRset ) 16.49/16.49 ( (fun int (fun int (fun int bool))), zcong ) 16.49/16.49 ( (fun int (fun int (fun int bool))), noXRRset ) 16.49/16.49 ( (fun int (fun int (fun int bool))), zcongm ) 16.49/16.49 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.49/16.49 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.49/16.49 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.49/16.49 ( (fun int real), (real_1 int) ) 16.49/16.49 ( (fun complex nat), (size_size complex) ) 16.49/16.49 ( (fun complex nat), complex_size ) 16.49/16.49 ( (fun int (list int)), quickc666637781d_zero ) 16.49/16.49 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.49/16.49 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.49/16.49 ( (fun (product_prod int int) rat), frct ) 16.49/16.49 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.49/16.49 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.49/16.49 ( (fun (fun nat rat) bool), vanishes ) 16.49/16.49 ( (fun int (fun int rat)), fract ) 16.49/16.49 ( (fun code_code_numeral int), code_int_of ) 16.49/16.49 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.49/16.49 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.49/16.49 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.49/16.49 ( (fun real (fun real complex)), complex_1 ) 16.49/16.49 ( (fun real (fun real complex)), rcis ) 16.49/16.49 ( (fun int (fun nat nat)), nat_aux ) 16.49/16.49 ( (fun rat real), ratreal ) 16.49/16.49 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.49/16.49 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.49/16.49 ( (fun rat (product_prod int int)), quotient_of ) 16.49/16.49 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.49/16.49 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.49/16.49 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.49/16.49 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.49/16.49 ) 16.49/16.49 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107190 $$unsorted) (BOUND_VARIABLE_107191 $$unsorted)) (or (not (group_add X_a)) (= (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_107190) BOUND_VARIABLE_107191)) (= (ti X_a BOUND_VARIABLE_107190) (ti X_a BOUND_VARIABLE_107191)))) ) 16.49/16.49 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.49/16.50 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.49/16.50 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.49/16.50 ) 16.49/16.50 (instantiation (let ((_let_0 (one_one X_a))) (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) _let_0) _let_0) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls))))) )) 16.49/16.50 ( bool ) 16.49/16.50 ( real ) 16.49/16.50 ( nat ) 16.49/16.50 ( (fun nat bool) ) 16.49/16.50 ( int ) 16.49/16.50 ( (fun int bool) ) 16.49/16.50 ( (fun real bool) ) 16.49/16.50 ( (fun real real) ) 16.49/16.50 ( complex ) 16.49/16.50 ( (fun nat real) ) 16.49/16.50 ( (fun int int) ) 16.49/16.50 ( rat ) 16.49/16.50 ( (fun int (fun int bool)) ) 16.49/16.50 ( quickcheck_code_int ) 16.49/16.50 ( (product_prod int int) ) 16.49/16.50 ( (fun (product_prod int int) bool) ) 16.49/16.50 ( code_code_numeral ) 16.49/16.50 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.49/16.50 ( (fun (product_prod int int) int) ) 16.49/16.50 ( (fun int (fun int (fun int bool))) ) 16.49/16.50 ( (fun int real) ) 16.49/16.50 ) 16.49/16.50 (instantiation (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))) (forall ((X_a $$unsorted)) (= (hAPP _let_3 _let_3 (collect _let_2) (hAPP _let_5 _let_3 (product_prod_case _let_1 _let_1 bool) (hAPP _let_4 _let_5 (hAPP _let_7 (fun _let_4 _let_5) (combc _let_1 _let_4 _let_4) (hAPP _let_9 _let_7 (hAPP (fun _let_8 _let_6) (fun _let_9 _let_7) (combb _let_8 _let_6 _let_1) (combs _let_1 bool bool)) (hAPP _let_5 _let_9 (hAPP _let_10 (fun _let_5 _let_9) (combb _let_4 _let_8 _let_1) (hAPP (fun bool _let_0) _let_10 (combb bool _let_0 _let_1) fconj)) (ord_less _let_1)))) (finite_finite_1 X_a)))) (finite_psubset X_a)) )))))))))))) 16.49/16.50 ( nat ) 16.49/16.50 ( int ) 16.49/16.50 ) 16.49/16.50 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (forall ((X $$unsorted)) (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)))) ))) 16.49/16.50 ( pi ) 16.49/16.50 ( (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)))) ) 16.49/16.50 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.49/16.50 ( skv_2 ) 16.49/16.50 ( skv_10 ) 16.49/16.50 ( skv_13 ) 16.49/16.50 ) 16.49/16.50 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (ord_less int))) (forall ((I $$unsorted) (K $$unsorted)) (= (= _let_2 (hAPP int int (hAPP int (fun int int) (div_div int) I) K)) (or (and (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 K) I)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 I) _let_2))) (and (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) I)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 I) K))) (= _let_2 (ti int K)))) ))))) 16.49/16.50 ( (zero_zero int), (zero_zero int) ) 16.49/16.50 ( (zero_zero int), (one_one int) ) 16.49/16.50 ( (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.50 ( (zero_zero int), min_1 ) 16.49/16.50 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.49/16.50 ( (zero_zero int), t ) 16.49/16.50 ( (one_one int), (zero_zero int) ) 16.49/16.50 ( (one_one int), t ) 16.49/16.50 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 16.49/16.50 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 16.49/16.50 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.49/16.50 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_3 ) 16.49/16.50 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_9 ) 16.49/16.50 ( min_1, (zero_zero int) ) 16.49/16.50 ( min_1, min_1 ) 16.49/16.50 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.49/16.50 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 16.49/16.50 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 16.65/16.50 ( t, (zero_zero int) ) 16.65/16.50 ( t, (one_one int) ) 16.65/16.50 ( 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))) ) 16.65/16.50 ( (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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.65/16.50 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.50 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.50 ) 16.65/16.50 (instantiation (let ((_let_0 (fun real real))) (forall ((X $$unsorted)) (= (hAPP real real cos X) (hAPP real real sin (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) X))) )) 16.65/16.50 ( (zero_zero real) ) 16.65/16.50 ( pi ) 16.65/16.50 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.50 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.50 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.65/16.50 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.65/16.50 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.65/16.50 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.65/16.50 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.65/16.50 ( skv_14 ) 16.65/16.50 ) 16.65/16.50 (instantiation (let ((_let_0 (fun X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_107392 $$unsorted) (BOUND_VARIABLE_107393 $$unsorted)) (or (not (uminus X_b)) (= (hAPP X_a X_b (hAPP _let_0 _let_0 (uminus_uminus _let_0) BOUND_VARIABLE_107392) BOUND_VARIABLE_107393) (hAPP X_b X_b (uminus_uminus X_b) (hAPP X_a X_b BOUND_VARIABLE_107392 BOUND_VARIABLE_107393)))) )) 16.65/16.50 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.65/16.50 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.50 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.65/16.50 ( real, complex, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 16.65/16.50 ( real, complex, cis, (zero_zero real) ) 16.65/16.50 ( int, int, (number_number_of int), pls ) 16.65/16.50 ( int, int, (number_number_of int), (hAPP int int bit1 pls) ) 16.65/16.50 ( int, int, bit1, min_1 ) 16.65/16.50 ) 16.65/16.50 (instantiation (let ((_let_0 (fun int rat))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (hAPP int rat (hAPP int _let_0 fract B) A_1) (hAPP rat rat (inverse_inverse rat) (hAPP int rat (hAPP int _let_0 fract A_1) B))) )) 16.65/16.50 ( (zero_zero int), (one_one int) ) 16.65/16.50 ( (one_one int), (zero_zero int) ) 16.65/16.50 ( (one_one int), (one_one int) ) 16.65/16.50 ) 16.65/16.50 (instantiation (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (times_times X_a))) (let ((_let_3 (inverse_inverse X_a))) (let ((_let_4 (minus_minus X_a))) (let ((_let_5 (hAPP X_a X_a _let_3 BOUND_VARIABLE_107441))) (let ((_let_6 (hAPP X_a X_a _let_3 BOUND_VARIABLE_107440))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_107440 $$unsorted) (BOUND_VARIABLE_107441 $$unsorted)) (or (not (division_ring X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_107441)) (= _let_0 (ti X_a BOUND_VARIABLE_107440)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_4 _let_5) _let_6) (hAPP X_a X_a (uminus_uminus 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 _let_5) (hAPP X_a X_a (hAPP X_a _let_1 _let_4 BOUND_VARIABLE_107441) BOUND_VARIABLE_107440))) _let_6)))) )))))))) 16.65/16.50 ( 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 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 16.65/16.50 ( int, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.50 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 16.65/16.50 ) 16.65/16.50 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107518 $$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_107518) BOUND_VARIABLE_107518))) ) 16.65/16.50 ( 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))) ) 16.65/16.50 ) 16.65/16.50 (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)) ) 16.65/16.50 ( real, real, sqrt, (zero_zero real) ) 16.65/16.50 ( real, real, sqrt, (one_one real) ) 16.65/16.50 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.50 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.50 ( real, real, tan, (zero_zero real) ) 16.65/16.50 ( real, real, tan, pi ) 16.65/16.50 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.65/16.50 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.65/16.50 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.65/16.50 ( real, real, cos, (zero_zero real) ) 16.65/16.50 ( real, real, cos, pi ) 16.65/16.50 ( real, real, cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.50 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.50 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.65/16.50 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.65/16.50 ( real, real, cos, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.65/16.50 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.65/16.50 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.65/16.50 ( real, real, cos, skv_14 ) 16.65/16.50 ( real, real, ln, (one_one real) ) 16.65/16.50 ( real, real, sin, (zero_zero real) ) 16.65/16.50 ( real, real, sin, pi ) 16.65/16.50 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.50 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.65/16.50 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.65/16.50 ( real, real, sin, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.65/16.50 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.65/16.50 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.65/16.51 ( real, real, arctan, (zero_zero real) ) 16.65/16.51 ( real, real, arctan, (one_one real) ) 16.65/16.51 ( real, real, arctan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.65/16.51 ( real, real, arctan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 16.65/16.51 ( real, nat, natfloor, (zero_zero real) ) 16.65/16.51 ( real, nat, natfloor, (one_one real) ) 16.65/16.51 ( real, nat, natceiling, (zero_zero real) ) 16.65/16.51 ( real, nat, natceiling, (one_one real) ) 16.65/16.51 ( real, complex, cis, (zero_zero real) ) 16.65/16.51 ( real, (fun real complex), complex_1, (zero_zero real) ) 16.65/16.51 ( real, (fun real complex), complex_1, (one_one real) ) 16.65/16.51 ( nat, bool, (even_odd_even nat), (zero_zero nat) ) 16.65/16.51 ( nat, bool, (even_odd_even nat), (one_one nat) ) 16.65/16.51 ( nat, bool, prime, (zero_zero nat) ) 16.65/16.51 ( nat, bool, prime, (one_one nat) ) 16.65/16.51 ( nat, bool, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.51 ( nat, real, (real_1 nat), (zero_zero nat) ) 16.65/16.51 ( nat, real, (real_1 nat), (one_one nat) ) 16.65/16.51 ( nat, nat, suc, (zero_zero nat) ) 16.65/16.51 ( nat, nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 16.65/16.51 ( nat, nat, suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 16.65/16.51 ( nat, nat, (fact_fact nat), (zero_zero nat) ) 16.65/16.51 ( nat, nat, (fact_fact nat), (hAPP nat nat suc (zero_zero nat)) ) 16.65/16.51 ( nat, nat, (size_size nat), (zero_zero nat) ) 16.65/16.51 ( nat, nat, fact, (zero_zero nat) ) 16.65/16.51 ( nat, nat, nat_size, (zero_zero nat) ) 16.65/16.51 ( nat, (fun real real), root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.51 ( 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))) ) 16.65/16.51 ( int, bool, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.51 ( int, bool, nat_neg, (one_one int) ) 16.65/16.51 ( int, bool, nat_neg, (hAPP int int (number_number_of int) min_1) ) 16.65/16.51 ( int, bool, nat_neg, (hAPP int int (number_number_of int) pls) ) 16.65/16.51 ( int, bool, nat_is_nat, (zero_zero int) ) 16.65/16.51 ( int, bool, nat_is_nat, (one_one int) ) 16.65/16.51 ( int, bool, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.51 ( int, bool, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.51 ( int, bool, (even_odd_even int), (zero_zero int) ) 16.65/16.51 ( int, bool, (even_odd_even int), (one_one int) ) 16.65/16.51 ( 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))) ) 16.65/16.51 ( int, real, (real_1 int), (zero_zero int) ) 16.65/16.51 ( int, real, (real_1 int), (one_one int) ) 16.65/16.51 ( int, nat, nat_1, (zero_zero int) ) 16.65/16.51 ( int, nat, nat_1, (one_one int) ) 16.65/16.51 ( int, nat, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.51 ( int, nat, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.51 ( int, int, bit0, pls ) 16.65/16.51 ( int, int, bit0, (hAPP int int bit1 pls) ) 16.65/16.51 ( int, int, bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.65/16.51 ( int, int, bit0, min_1 ) 16.65/16.51 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.65/16.51 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.51 ( int, int, bit1, pls ) 16.65/16.51 ( int, int, bit1, (hAPP int int bit1 pls) ) 16.65/16.51 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.65/16.51 ( int, int, bit1, min_1 ) 16.65/16.51 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.65/16.51 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.65/16.51 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.65/16.51 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 16.65/16.51 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 16.65/16.51 ( int, int, pred, pls ) 16.65/16.51 ( int, int, pred, min_1 ) 16.65/16.51 ( int, int, succ, pls ) 16.65/16.51 ( int, int, succ, min_1 ) 16.65/16.51 ( int, int, (fact_fact int), (zero_zero int) ) 16.65/16.51 ( int, int, (fact_fact int), (one_one int) ) 16.65/16.51 ( 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))) ) 16.65/16.51 ( int, (fun int int), legendre, (hAPP int int (number_number_of int) min_1) ) 16.65/16.51 ( int, (fun int rat), fract, (zero_zero int) ) 16.65/16.51 ( int, (fun int rat), fract, (one_one int) ) 16.65/16.51 ( 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)))) ) 16.65/16.51 ( int, (fun int (fun int bool)), zcong, s1 ) 16.65/16.51 ( 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)))) ) 16.65/16.51 ( int, (fun int (fun int bool)), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.51 ( int, quickcheck_code_int, quickcheck_of_int, (zero_zero int) ) 16.65/16.51 ( int, quickcheck_code_int, quickcheck_of_int, (hAPP int int bit1 pls) ) 16.65/16.51 ( int, quickcheck_code_int, quickcheck_of_int, (one_one int) ) 16.65/16.51 ( complex, real, im, ii ) 16.65/16.51 ( complex, real, im, (zero_zero complex) ) 16.65/16.51 ( complex, real, im, (one_one complex) ) 16.65/16.51 ( complex, real, re, ii ) 16.65/16.51 ( complex, real, re, (zero_zero complex) ) 16.65/16.51 ( complex, real, re, (one_one complex) ) 16.65/16.51 ( complex, complex, cnj, ii ) 16.65/16.51 ( complex, complex, cnj, (zero_zero complex) ) 16.65/16.51 ( complex, complex, cnj, (one_one complex) ) 16.65/16.51 ( complex, complex, expi, (zero_zero complex) ) 16.65/16.51 ( complex, complex, expi, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))) ii))) ) 16.65/16.51 ( rat, real, ratreal, (zero_zero rat) ) 16.65/16.51 ( rat, real, ratreal, (one_one rat) ) 16.65/16.51 ( rat, (product_prod int int), quotient_of, (zero_zero rat) ) 16.65/16.51 ( rat, (product_prod int int), quotient_of, (one_one rat) ) 16.65/16.51 ( quickcheck_code_int, int, quickcheck_int_of, (zero_zero quickcheck_code_int) ) 16.65/16.51 ( (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))) ) 16.65/16.51 ( (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))) ) 16.65/16.51 ( code_code_numeral, nat, (size_size code_code_numeral), (zero_zero code_code_numeral) ) 16.65/16.51 ( code_code_numeral, nat, code_c271388182l_size, (zero_zero code_code_numeral) ) 16.65/16.51 ( code_code_numeral, int, code_int_of, (zero_zero code_code_numeral) ) 16.65/16.51 ) 16.65/16.51 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (fun (filter nat) bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_107546 $$unsorted) (BOUND_VARIABLE_107547 $$unsorted)) (or (not (real_normed_vector X_a)) (= (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) R_2))) (not (forall ((No $$unsorted)) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_2))) (hBOOL (hAPP real bool (hAPP real _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) (hAPP nat X_a BOUND_VARIABLE_107546 N_2)) BOUND_VARIABLE_107547))) R_2))) )) ))) ) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_2 (hAPP (fun nat X_a) (fun X_a _let_2) (tendsto nat X_a) BOUND_VARIABLE_107546) BOUND_VARIABLE_107547) sequentially)))) )))) 16.65/16.51 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 16.65/16.51 ) 16.65/16.51 (instantiation (forall ((N $$unsorted)) (= N (hAPP real nat natceiling (hAPP nat real (real_1 nat) N))) ) 16.65/16.51 ( (zero_zero nat) ) 16.65/16.51 ( (one_one nat) ) 16.65/16.51 ) 16.65/16.51 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107652 $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (not (number_ring X_a)) (= (hAPP real real (abs_abs real) (hAPP int real (number_number_of real) BOUND_VARIABLE_107652)) (hAPP X_a real (norm_norm X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_107652)))) ) 16.65/16.51 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.65/16.51 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.51 ( real, min_1 ) 16.65/16.51 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.51 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.65/16.51 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.51 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.65/16.51 ( nat, pls ) 16.65/16.51 ( nat, (hAPP int int bit1 pls) ) 16.65/16.51 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.65/16.51 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.65/16.51 ( int, pls ) 16.65/16.51 ( int, (hAPP int int bit1 pls) ) 16.65/16.51 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.65/16.51 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.51 ( int, min_1 ) 16.65/16.51 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.65/16.51 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.65/16.51 ( complex, min_1 ) 16.65/16.51 ( quickcheck_code_int, (zero_zero int) ) 16.65/16.51 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 16.65/16.51 ( quickcheck_code_int, (one_one int) ) 16.65/16.51 ( code_code_numeral, pls ) 16.65/16.51 ( code_code_numeral, (hAPP int int bit1 pls) ) 16.65/16.51 ) 16.65/16.51 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (let ((_let_4 (fun X_a X_a))) (let ((_let_5 (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_107678)))) (let ((_let_6 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_107679))) (let ((_let_7 (hAPP X_a X_a (hAPP X_a _let_4 (times_times X_a) _let_6) BOUND_VARIABLE_107678))) (let ((_let_8 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_107678) _let_2)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_107677 $$unsorted) (BOUND_VARIABLE_107678 $$unsorted) (BOUND_VARIABLE_107679 $$unsorted)) (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 BOUND_VARIABLE_107677) _let_7))) (or _let_5 (and (or _let_8 (hBOOL (hAPP X_a bool _let_3 _let_6))) (or (not _let_8) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_7) BOUND_VARIABLE_107677)))))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_4 (inverse_divide X_a) BOUND_VARIABLE_107677) BOUND_VARIABLE_107678)) _let_6)))) )))))))))) 16.65/16.51 ( real, (zero_zero real), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.65/16.51 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.65/16.51 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.65/16.51 ( 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)), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.65/16.51 ) 16.65/16.51 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107720 $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (= (hAPP nat real (semiring_1_of_nat real) BOUND_VARIABLE_107720) (hAPP X_a real (norm_norm X_a) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_107720)))) ) 16.65/16.51 ( real, (zero_zero nat) ) 16.65/16.51 ( real, (one_one nat) ) 16.65/16.51 ( int, (zero_zero nat) ) 16.65/16.51 ( int, (hAPP nat nat suc (zero_zero nat)) ) 16.65/16.51 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.51 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.51 ) 16.65/16.51 (instantiation (forall ((V_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) V_1) pls)) (= (zero_zero nat) (hAPP int nat (number_number_of nat) V_1))) ) 16.65/16.51 ( (zero_zero int) ) 16.65/16.51 ( pls ) 16.65/16.51 ( (hAPP int int bit1 pls) ) 16.65/16.51 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.65/16.51 ( (one_one int) ) 16.65/16.51 ( min_1 ) 16.65/16.51 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.65/16.51 ) 16.65/16.51 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (= (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 Z1) Z2)) W) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 Z1) W)) (hAPP int int (hAPP int _let_0 _let_2 Z2) W))) )))) 16.65/16.51 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), (zero_zero int) ) 16.65/16.51 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), t ) 16.65/16.51 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), skv_1 ) 16.65/16.51 ) 16.65/16.51 (instantiation (forall ((R_4 $$unsorted)) (= (hAPP real complex (hAPP real (fun real complex) complex_1 (zero_zero real)) R_4) (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) ii) (hAPP real complex (of_real complex) R_4))) ) 16.65/16.51 ( (zero_zero real) ) 16.65/16.51 ( (one_one real) ) 16.65/16.51 ( pi ) 16.65/16.51 ( (hAPP int real (number_number_of real) min_1) ) 16.65/16.51 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 16.65/16.51 ) 16.65/16.51 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_107759 $$unsorted) (BOUND_VARIABLE_107760 $$unsorted)) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_107759) BOUND_VARIABLE_107760))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_107759) BOUND_VARIABLE_107760)) (= (ti X_a BOUND_VARIABLE_107759) (ti X_a BOUND_VARIABLE_107760))) )) 16.65/16.51 ( real, (zero_zero real), pi ) 16.65/16.51 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.52 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.52 ( real, (zero_zero real), skv_2 ) 16.65/16.52 ( real, (zero_zero real), skv_6 ) 16.65/16.52 ( real, (zero_zero real), skv_10 ) 16.65/16.52 ( real, (zero_zero real), skv_11 ) 16.65/16.52 ( real, (zero_zero real), skv_12 ) 16.65/16.52 ( real, (zero_zero real), skv_13 ) 16.65/16.52 ( real, (zero_zero real), skv_14 ) 16.65/16.52 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.52 ( real, pi, (zero_zero real) ) 16.65/16.52 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.52 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.65/16.52 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.52 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.65/16.52 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.65/16.52 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.65/16.52 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.52 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.52 ( int, (zero_zero int), (zero_zero int) ) 16.65/16.52 ( int, (zero_zero int), (one_one int) ) 16.65/16.52 ( int, (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.52 ( int, (zero_zero int), min_1 ) 16.65/16.52 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.52 ( int, (zero_zero int), s ) 16.65/16.52 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.65/16.52 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.52 ( int, (zero_zero int), skv_3 ) 16.65/16.52 ( int, (zero_zero int), skv_9 ) 16.65/16.52 ( int, (one_one int), t ) 16.65/16.52 ( int, min_1, (zero_zero int) ) 16.65/16.52 ( int, min_1, pls ) 16.65/16.52 ( int, min_1, min_1 ) 16.65/16.52 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.52 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 16.65/16.52 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 16.65/16.52 ( int, t, (zero_zero int) ) 16.65/16.52 ( int, t, (one_one int) ) 16.65/16.52 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.52 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.52 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.52 ) 16.65/16.52 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (number_number_of real))) (let ((_let_3 (number_number_of rat))) (forall ((R_4 $$unsorted) (S_3 $$unsorted)) (= (hAPP real real (hAPP real _let_0 _let_1 (hAPP int real _let_2 R_4)) (hAPP int real _let_2 S_3)) (hAPP real real (hAPP real _let_0 _let_1 (hAPP rat real ratreal (hAPP int rat _let_3 R_4))) (hAPP rat real ratreal (hAPP int rat _let_3 S_3)))) ))))) 16.65/16.52 ( (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.65/16.52 ) 16.65/16.52 (instantiation (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (dvd_dvd X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (div_div X_a))) (let ((_let_5 (times_times X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_107824 $$unsorted) (BOUND_VARIABLE_107825 $$unsorted) (BOUND_VARIABLE_107826 $$unsorted) (BOUND_VARIABLE_107827 $$unsorted)) (or (not (semiring_div X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_107827)) (= _let_0 (ti X_a BOUND_VARIABLE_107826)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_107827) BOUND_VARIABLE_107825))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_107826) BOUND_VARIABLE_107824))) (= (= (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_107824) BOUND_VARIABLE_107826) (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_107825) BOUND_VARIABLE_107827)) (= (hAPP X_a X_a (hAPP X_a _let_3 _let_5 BOUND_VARIABLE_107825) BOUND_VARIABLE_107826) (hAPP X_a X_a (hAPP X_a _let_3 _let_5 BOUND_VARIABLE_107827) BOUND_VARIABLE_107824)))) ))))))) 16.65/16.52 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.52 ) 16.65/16.52 (instantiation (forall ((N $$unsorted)) (not (= (zero_zero nat) (hAPP nat nat (fact_fact nat) N))) ) 16.65/16.52 ( (zero_zero nat) ) 16.65/16.52 ( (hAPP nat nat suc (zero_zero nat)) ) 16.65/16.52 ) 16.65/16.52 (instantiation (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) N))) (forall ((N $$unsorted) (M $$unsorted)) (or (hBOOL (hAPP nat bool _let_0 M)) (not (hBOOL (hAPP nat bool _let_0 (hAPP nat nat suc M)))) (= N M)) )) 16.65/16.52 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 16.65/16.52 ) 16.65/16.52 (instantiation (let ((_let_0 (product_prod X_b X_a))) (forall ((X_b $$unsorted) (X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (ti X_a B) (hAPP _let_0 X_a (product_snd X_b X_a) (hAPP X_a _let_0 (hAPP X_b (fun X_a _let_0) (product_Pair X_b X_a) A_1) B))) )) 16.65/16.52 ( int, int, (zero_zero int), (one_one int) ) 16.65/16.52 ( int, int, (one_one int), (one_one int) ) 16.65/16.52 ( int, int, s, (one_one int) ) 16.65/16.52 ) 16.65/16.52 (instantiation (let ((_let_0 (norm_norm X_a))) (forall ((X_a $$unsorted)) (or (not (dist_norm X_a)) (= _let_0 (ti (fun X_a real) _let_0))) )) 16.65/16.52 ( real ) 16.65/16.52 ( nat ) 16.65/16.52 ( int ) 16.65/16.52 ( (fun real bool) ) 16.65/16.52 ( complex ) 16.65/16.52 ( rat ) 16.65/16.52 ) 16.65/16.52 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (one_one int))) (forall ((X $$unsorted) (P_5 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_5))) (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) P_5) X)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) X) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) P_5) _let_1)))) _let_1) P_5))) ))) 16.65/16.52 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.52 ) 16.65/16.52 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (div_mod X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_108083 $$unsorted) (BOUND_VARIABLE_108084 $$unsorted)) (or (not (semiring_div X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_108083) BOUND_VARIABLE_108084)) BOUND_VARIABLE_108083) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_108084) BOUND_VARIABLE_108083))) ))) 16.65/16.52 ( nat, (one_one nat), (one_one nat) ) 16.65/16.52 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.65/16.52 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 16.65/16.52 ) 16.65/16.52 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108098 $$unsorted) (BOUND_VARIABLE_108099 $$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_108098)) (hAPP int int (number_number_of int) BOUND_VARIABLE_108099))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_108098) (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_108099)) (one_one X_a)))))) ) 16.65/16.52 ( nat, (zero_zero nat), (hAPP int int bit1 pls) ) 16.65/16.52 ) 16.65/16.52 (instantiation (forall ((X $$unsorted)) (= (hAPP real real (inverse_inverse real) (hAPP rat real ratreal X)) (hAPP rat real ratreal (hAPP rat rat (inverse_inverse rat) X))) ) 16.65/16.52 ( (zero_zero rat) ) 16.65/16.52 ) 16.65/16.52 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP complex real re (hAPP int complex (ring_1_of_int complex) Z_1)) (hAPP int real (ring_1_of_int real) Z_1)) ) 16.65/16.52 ( (zero_zero int) ) 16.65/16.52 ( (one_one int) ) 16.65/16.52 ) 16.65/16.52 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) A_2) B_1)) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 A_2) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 B_1) zOdd))) )))) 16.65/16.52 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.65/16.52 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 16.65/16.52 ) 16.65/16.52 (instantiation (let ((_let_0 (zero_zero real))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) _let_0) X))) (not (= _let_0 (hAPP real real sqrt X))) (= _let_0 X)) )) 16.65/16.52 ( (zero_zero real) ) 16.65/16.52 ( (one_one real) ) 16.65/16.52 ( pi ) 16.65/16.52 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.52 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.52 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.52 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.52 ( skv_6 ) 16.65/16.52 ( skv_11 ) 16.65/16.52 ( skv_12 ) 16.65/16.52 ( skv_14 ) 16.65/16.52 ) 16.65/16.52 (instantiation (let ((_let_0 (zero_zero nat))) (let ((_let_1 (hAPP nat nat suc _let_0))) (forall ((X $$unsorted)) (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)) ))) 16.65/16.52 ( (zero_zero nat) ) 16.65/16.52 ) 16.65/16.52 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (forall ((N $$unsorted) (M $$unsorted)) (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)))) ))) 16.65/16.52 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 16.65/16.52 ) 16.65/16.52 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_108213 $$unsorted) (BOUND_VARIABLE_108214 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_108214))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_108213) _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_108214) BOUND_VARIABLE_108213)) _let_2))) )))) 16.65/16.52 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.52 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.65/16.52 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.52 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.52 ( int, (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.52 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.52 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.52 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.52 ( complex, ii, ii ) 16.65/16.52 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.65/16.52 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.52 ) 16.65/16.52 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP complex real im (hAPP real complex cis A_1)) (hAPP real real sin A_1)) ) 16.65/16.52 ( (zero_zero real) ) 16.65/16.52 ( pi ) 16.65/16.52 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.52 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.65/16.53 ( (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 (hAPP int int bit1 pls))))) ) 16.65/16.53 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.65/16.53 ( (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 bit0 (hAPP int int bit1 pls))))) ) 16.65/16.53 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.65/16.53 ) 16.65/16.53 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108259 $$unsorted) (BOUND_VARIABLE_108260 $$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_108259) BOUND_VARIABLE_108260))) (= (ti X_a BOUND_VARIABLE_108259) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_min X_a) BOUND_VARIABLE_108260) BOUND_VARIABLE_108259))) ) 16.65/16.53 ( real, (zero_zero real), pi ) 16.65/16.53 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.53 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.53 ( real, (zero_zero real), skv_6 ) 16.65/16.53 ( real, (zero_zero real), skv_11 ) 16.65/16.53 ( real, (zero_zero real), skv_12 ) 16.65/16.53 ( real, (zero_zero real), skv_14 ) 16.65/16.53 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.65/16.53 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.53 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.65/16.53 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.53 ( int, (zero_zero int), (one_one int) ) 16.65/16.53 ( int, (zero_zero int), min_1 ) 16.65/16.53 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.53 ( int, (zero_zero int), s ) 16.65/16.53 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.65/16.53 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.53 ( int, (zero_zero int), skv_3 ) 16.65/16.53 ( int, (zero_zero int), skv_9 ) 16.65/16.53 ( int, (one_one int), t ) 16.65/16.53 ( int, min_1, pls ) 16.65/16.53 ( int, min_1, min_1 ) 16.65/16.53 ) 16.65/16.53 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat real))) (let ((_let_4 (power_power real))) (forall ((N_1 $$unsorted)) (= _let_0 (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) N_1)) _let_0) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP nat real (hAPP real _let_3 _let_4 (hAPP int real (number_number_of real) min_1)) (hAPP nat nat (hAPP nat _let_1 (div_div nat) (hAPP nat nat (hAPP nat _let_1 (minus_minus nat) N_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) N_1))))) (hAPP nat real (hAPP real _let_3 _let_4 _let_0) N_1))) )))))) 16.65/16.53 ( (zero_zero nat) ) 16.65/16.53 ( (hAPP nat nat suc (zero_zero nat)) ) 16.65/16.53 ( (one_one nat) ) 16.65/16.53 ) 16.65/16.53 (instantiation (let ((_let_0 (one_one real))) (let ((_let_1 (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) A_1)))) (let ((_let_2 (hAPP real real (sgn_sgn real) A_1))) (forall ((A_1 $$unsorted)) (or (= (zero_zero real) A_1) (and (or _let_1 (= (hAPP real real (uminus_uminus real) _let_0) _let_2)) (or (not _let_1) (= _let_0 _let_2)))) )))) 16.65/16.53 ( (zero_zero real) ) 16.65/16.53 ( pi ) 16.65/16.53 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.53 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.53 ( skv_2 ) 16.65/16.53 ( skv_10 ) 16.65/16.53 ( skv_13 ) 16.65/16.53 ) 16.65/16.53 (instantiation (let ((_let_0 (fun nat bool))) (forall ((S $$unsorted)) (= (forall ((M_2 $$unsorted)) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP nat (fun _let_0 bool) (member nat) N_2) S))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M_2) N_2)))) )) ) (not (hBOOL (hAPP _let_0 bool (finite_finite_1 nat) S)))) )) 16.65/16.53 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 16.65/16.53 ) 16.65/16.53 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_108347 $$unsorted) (BOUND_VARIABLE_108348 $$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 (linord581940658strict X_a)) (= (or (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_108348) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_108347) _let_2))) (and (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_108347)) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_108348)))) (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_108347) BOUND_VARIABLE_108348)))))))) )) 16.65/16.53 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.65/16.53 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 16.65/16.53 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.65/16.53 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.65/16.53 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.65/16.53 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 16.65/16.53 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.65/16.53 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_1 ) 16.65/16.53 ( complex, ii, ii ) 16.65/16.53 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 16.65/16.53 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 16.65/16.53 ) 16.65/16.53 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))))) (forall ((X $$unsorted)) (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)))) ))) 16.65/16.53 ( (zero_zero nat) ) 16.65/16.53 ( (one_one nat) ) 16.65/16.53 ) 16.65/16.53 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_108383 $$unsorted) (BOUND_VARIABLE_108384 $$unsorted)) (or (not (linorder X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_108384) BOUND_VARIABLE_108383)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_108383) BOUND_VARIABLE_108384))))) )) 16.65/16.53 ( real, (zero_zero real), pi ) 16.65/16.53 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.53 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.53 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.53 ( real, (zero_zero real), skv_2 ) 16.65/16.53 ( real, (zero_zero real), skv_10 ) 16.65/16.53 ( real, (zero_zero real), skv_13 ) 16.65/16.53 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.53 ( real, pi, (zero_zero real) ) 16.65/16.53 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.53 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.53 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.53 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 16.65/16.53 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.65/16.53 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.53 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.65/16.53 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.65/16.53 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.65/16.53 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.65/16.53 ( real, skv_6, (zero_zero real) ) 16.65/16.53 ( real, skv_11, (zero_zero real) ) 16.65/16.53 ( real, skv_12, (zero_zero real) ) 16.65/16.53 ( real, skv_14, (zero_zero real) ) 16.65/16.53 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.53 ( int, (zero_zero int), (zero_zero int) ) 16.65/16.53 ( int, (zero_zero int), (one_one int) ) 16.65/16.53 ( int, (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.53 ( int, (zero_zero int), min_1 ) 16.65/16.53 ( int, pls, min_1 ) 16.65/16.53 ( int, (one_one int), (zero_zero int) ) 16.65/16.53 ( int, min_1, (zero_zero int) ) 16.65/16.53 ( int, min_1, min_1 ) 16.65/16.53 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 16.65/16.53 ( int, s, (zero_zero int) ) 16.65/16.53 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.53 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 16.65/16.53 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 16.65/16.53 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 16.65/16.53 ( int, t, (zero_zero int) ) 16.65/16.53 ( int, t, (one_one int) ) 16.65/16.53 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.53 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 16.65/16.53 ( int, skv_3, (zero_zero int) ) 16.65/16.53 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.53 ( int, skv_9, (zero_zero int) ) 16.65/16.53 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.53 ) 16.65/16.53 (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)) ) 16.65/16.53 ( bool, (fun nat bool), (combk bool nat), fTrue ) 16.65/16.53 ( real, bool, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 16.65/16.53 ( real, bool, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 16.65/16.53 ( 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 ) 16.65/16.53 ( 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 ) 16.65/16.53 ( real, real, tan, pi ) 16.65/16.53 ( real, real, cos, pi ) 16.65/16.53 ( real, real, sin, pi ) 16.65/16.53 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.65/16.53 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), pi ) 16.65/16.53 ( real, (fun real bool), (ord_less real), pi ) 16.65/16.53 ( real, (fun real real), (inverse_divide real), pi ) 16.65/16.53 ( real, complex, (of_real complex), pi ) 16.65/16.53 ( (fun nat bool), (fun nat bool), (collect nat), prime ) 16.65/16.53 ( (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 ) 16.65/16.53 ( (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 ) 16.65/16.53 ( (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 ) 16.65/16.53 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), pls ) 16.65/16.54 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 16.65/16.54 ( int, bool, nat_neg, pls ) 16.65/16.54 ( int, bool, (hAPP int (fun int bool) (ord_less int) pls), pls ) 16.65/16.54 ( int, bool, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 16.65/16.54 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 16.65/16.54 ( int, bool, nat_is_nat, pls ) 16.65/16.54 ( int, bool, (even_odd_even int), pls ) 16.65/16.54 ( int, bool, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))), pls ) 16.65/16.54 ( int, bool, (hAPP int (fun int bool) (ord_less int) min_1), pls ) 16.65/16.54 ( int, bool, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 16.65/16.54 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 16.65/16.54 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 16.65/16.54 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 16.65/16.54 ( int, bool, (hAPP int (fun int bool) (ord_less int) t), pls ) 16.65/16.54 ( int, real, (real_1 int), pls ) 16.65/16.54 ( int, real, (number_number_of real), min_1 ) 16.65/16.54 ( int, nat, nat_1, pls ) 16.65/16.54 ( int, nat, (number_number_of nat), pls ) 16.65/16.54 ( int, int, (number_number_of int), pls ) 16.65/16.54 ( int, int, (number_number_of int), min_1 ) 16.65/16.54 ( int, int, bit0, pls ) 16.65/16.54 ( int, int, bit0, min_1 ) 16.65/16.54 ( int, int, bit1, pls ) 16.65/16.54 ( int, int, bit1, min_1 ) 16.65/16.54 ( int, int, (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), m ) 16.65/16.54 ( int, int, (uminus_uminus int), pls ) 16.65/16.54 ( int, int, (uminus_uminus int), min_1 ) 16.65/16.54 ( int, int, pred, pls ) 16.65/16.54 ( int, int, pred, min_1 ) 16.65/16.54 ( int, int, succ, pls ) 16.65/16.54 ( int, int, succ, min_1 ) 16.65/16.54 ( 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))))), pls ) 16.65/16.54 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), t ) 16.65/16.54 ( int, int, (fact_fact int), pls ) 16.65/16.54 ( int, (fun int bool), (ord_less_eq int), pls ) 16.65/16.54 ( int, (fun int bool), (ord_less_eq int), min_1 ) 16.65/16.54 ( int, (fun int bool), (ord_less int), pls ) 16.65/16.54 ( int, (fun int bool), (ord_less int), min_1 ) 16.65/16.54 ( int, (fun int bool), (ord_less int), s ) 16.65/16.54 ( int, (fun int bool), (ord_less int), t ) 16.65/16.54 ( int, (fun int bool), (let ((_let_0 (fun int (fun int bool)))) (hAPP _let_0 _let_0 (combc int int bool) (fequal int))), pls ) 16.65/16.54 ( int, (fun int bool), (hAPP int (fun int (fun int bool)) zcong s1), s ) 16.65/16.54 ( int, (fun nat int), (power_power int), s ) 16.65/16.54 ( int, (fun nat int), (power_power int), s1 ) 16.65/16.54 ( int, complex, (number_number_of complex), min_1 ) 16.65/16.54 ( int, (fun int rat), fract, pls ) 16.65/16.54 ( int, (fun int (fun int bool)), zcong, s1 ) 16.65/16.54 ( int, quickcheck_code_int, quickcheck_of_int, pls ) 16.65/16.54 ( int, (fun int (product_prod int int)), (product_Pair int int), pls ) 16.65/16.54 ( int, (fun int (product_prod int int)), (product_Pair int int), s ) 16.65/16.54 ( 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 ) 16.65/16.54 ( int, code_code_numeral, (number_number_of code_code_numeral), pls ) 16.65/16.54 ( (fun int bool), bool, (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 16.65/16.54 ( (fun int nat), (fun (fun int bool) bool), (nat_tr1645093318rphism int nat), nat_1 ) 16.65/16.54 ( (fun real real), (fun real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)))), sin ) 16.65/16.54 ( (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 ) 16.65/16.54 ( (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 ) 16.65/16.54 ( complex, real, im, ii ) 16.65/16.54 ( complex, real, re, ii ) 16.65/16.54 ( complex, complex, (hAPP complex (fun complex complex) (times_times complex) ii), ii ) 16.65/16.54 ( complex, complex, cnj, ii ) 16.65/16.54 ( complex, complex, (uminus_uminus complex), ii ) 16.65/16.54 ( complex, complex, (inverse_inverse complex), ii ) 16.65/16.54 ( complex, complex, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))))), ii ) 16.65/16.54 ( complex, (fun complex complex), (times_times complex), ii ) 16.65/16.54 ( complex, (fun nat complex), (power_power complex), ii ) 16.65/16.54 ( (fun nat real), (fun nat real), (diffs real), sin_coeff ) 16.65/16.54 ( (fun nat real), (fun (fun nat nat) (fun nat real)), (combb nat real nat), (real_1 nat) ) 16.65/16.54 ( (fun nat real), (fun int (fun nat real)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_4 (fun (fun nat real) (fun int (fun nat real))) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 nat) ) 16.65/16.54 ( (fun bool bool), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (combb bool bool int), fNot ) 16.65/16.54 ( (fun bool bool), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), (combb bool bool nat), fNot ) 16.65/16.54 ( (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 ) 16.65/16.54 ( (fun bool (fun bool bool)), (fun (fun int bool) (fun int (fun bool bool))), (combb bool (fun bool bool) int), fconj ) 16.65/16.54 ( (fun bool (fun bool bool)), (fun (fun real bool) (fun real (fun bool bool))), (combb bool (fun bool bool) real), fconj ) 16.65/16.54 ( (fun bool (fun bool bool)), (fun (fun nat bool) (fun nat (fun bool bool))), (combb bool (fun bool bool) nat), fconj ) 16.65/16.54 ( (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 ) 16.65/16.54 ( (filter nat), bool, (trivial_limit nat), sequentially ) 16.65/16.54 ( (filter nat), bool, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 16.65/16.54 ( (fun int (fun int int)), (fun int (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun int _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 _let_2 _let_3 (combb int _let_0 int) (fequal int))))))), int_gcd ) 16.65/16.54 ( (fun int real), (fun int (fun int real)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_0))) (hAPP _let_3 (fun _let_1 (fun int _let_1)) (combc int _let_1 _let_1) (hAPP _let_4 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_4 _let_3) (combb _let_0 _let_2 int) (combb real real int)) (hAPP _let_1 _let_4 (hAPP (fun real _let_0) (fun _let_1 _let_4) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 int) ) 16.65/16.54 ( (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) ) 16.65/16.54 ) 16.65/16.54 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (list int))) (forall ((I_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) I_1))) (= (hAPP _let_1 nat (size_size _let_1) (hAPP int _let_1 quickc666637781d_zero I_1)) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) (hAPP nat nat (hAPP nat _let_0 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int nat nat_1 I_1))) (one_one nat)))) ))) 16.65/16.54 ( (zero_zero int) ) 16.65/16.54 ( (one_one int) ) 16.65/16.54 ( min_1 ) 16.65/16.54 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.54 ( s ) 16.65/16.54 ( (hAPP int int (number_number_of int) pls) ) 16.65/16.54 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.54 ( skv_3 ) 16.65/16.54 ( skv_9 ) 16.65/16.54 ) 16.65/16.54 (instantiation (forall ((X_a $$unsorted)) (or (not (real_algebra_1 X_a)) (= (hAPP real X_a (of_real X_a) (one_one real)) (one_one X_a))) ) 16.65/16.54 ( real ) 16.65/16.54 ( nat ) 16.65/16.54 ( int ) 16.65/16.54 ( complex ) 16.65/16.54 ( rat ) 16.65/16.54 ( quickcheck_code_int ) 16.65/16.54 ( code_code_numeral ) 16.65/16.54 ) 16.65/16.54 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (product_Pair int int))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (hAPP (fun _let_1 _let_4) _let_4 (accp _let_1) lazy_small_lazy_rel))) (let ((_let_6 (hAPP int _let_0 P_1 D_3))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool _let_5 (hAPP int _let_1 (hAPP int _let_2 _let_3 A0) A1)))) (not (forall ((D_3 $$unsorted) (I_2 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool _let_5 (hAPP int _let_1 (hAPP int _let_2 _let_3 D_3) I_2)))) (and (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) D_3) I_2))) (not (hBOOL (hAPP int bool _let_6 (hAPP int int (hAPP int (fun int int) (plus_plus int) I_2) (one_one int)))))) (hBOOL (hAPP int bool _let_6 I_2))) )) (hBOOL (hAPP int bool (hAPP int _let_0 P_1 A0) A1))) )))))))) 16.65/16.54 ( (ord_less_eq int), (zero_zero int), (one_one int) ) 16.65/16.54 ( (ord_less_eq int), (zero_zero int), min_1 ) 16.65/16.54 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.54 ( (ord_less_eq int), (zero_zero int), s ) 16.65/16.54 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.65/16.54 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.54 ( (ord_less_eq int), (zero_zero int), skv_3 ) 16.65/16.54 ( (ord_less_eq int), (zero_zero int), skv_9 ) 16.65/16.54 ( (ord_less_eq int), (one_one int), t ) 16.65/16.54 ( (ord_less_eq int), min_1, pls ) 16.65/16.54 ( (ord_less_eq int), min_1, min_1 ) 16.65/16.54 ( (ord_less int), (zero_zero int), (zero_zero int) ) 16.65/16.54 ( (ord_less int), (zero_zero int), (one_one int) ) 16.65/16.54 ( (ord_less int), (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.54 ( (ord_less int), (zero_zero int), min_1 ) 16.65/16.54 ( (ord_less int), min_1, (zero_zero int) ) 16.65/16.54 ( (ord_less int), min_1, min_1 ) 16.65/16.54 ( (ord_less int), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.54 ( (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 16.65/16.54 ( (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 16.65/16.54 ( (ord_less int), t, (zero_zero int) ) 16.65/16.54 ( (ord_less int), t, (one_one int) ) 16.65/16.54 ( (ord_less int), t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.54 ( (ord_less int), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.54 ( (ord_less int), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.54 ( (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.65/16.54 ( quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 16.65/16.54 ( (hAPP int (fun int (fun int bool)) zcong s1), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.54 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.54 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.54 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.54 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.55 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.55 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.55 ) 16.65/16.55 (instantiation (let ((_let_0 (minus_minus X_b))) (forall ((X_b $$unsorted)) (or (not (minus X_b)) (= _let_0 (ti (fun X_b (fun X_b X_b)) _let_0))) )) 16.65/16.55 ( bool ) 16.65/16.55 ( real ) 16.65/16.55 ( nat ) 16.65/16.55 ( (fun nat bool) ) 16.65/16.55 ( int ) 16.65/16.55 ( (fun int bool) ) 16.65/16.55 ( (fun real bool) ) 16.65/16.55 ( (fun real real) ) 16.65/16.55 ( complex ) 16.65/16.55 ( (fun nat real) ) 16.65/16.55 ( (fun int int) ) 16.65/16.55 ( rat ) 16.65/16.55 ( (fun int (fun int bool)) ) 16.65/16.55 ( quickcheck_code_int ) 16.65/16.55 ( (product_prod int int) ) 16.65/16.55 ( (fun (product_prod int int) bool) ) 16.65/16.55 ( code_code_numeral ) 16.65/16.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.65/16.55 ( (fun (product_prod int int) int) ) 16.65/16.55 ( (fun int (fun int (fun int bool))) ) 16.65/16.55 ( (fun int real) ) 16.65/16.55 ) 16.65/16.55 (instantiation (forall ((I_1 $$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)) ) 16.65/16.55 ( (zero_zero quickcheck_code_int) ) 16.65/16.55 ) 16.65/16.55 (instantiation (let ((_let_0 (one_one rat))) (let ((_let_1 (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less rat) (zero_zero rat)) Q_3)))) (let ((_let_2 (hAPP rat rat (sgn_sgn rat) Q_3))) (forall ((Q_3 $$unsorted)) (or (= (zero_zero rat) Q_3) (and (or _let_1 (= _let_2 (hAPP rat rat (uminus_uminus rat) _let_0))) (or (not _let_1) (= _let_0 _let_2)))) )))) 16.65/16.55 ( (zero_zero rat) ) 16.65/16.55 ) 16.65/16.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108641 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int (archimedean_ceiling X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_108641)) (ti int BOUND_VARIABLE_108641))) ) 16.65/16.55 ( real, (zero_zero int) ) 16.65/16.55 ( real, (one_one int) ) 16.65/16.55 ) 16.65/16.55 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (minus_minus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_108680 $$unsorted) (BOUND_VARIABLE_108681 $$unsorted) (BOUND_VARIABLE_108682 $$unsorted)) (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_108681) BOUND_VARIABLE_108682)) BOUND_VARIABLE_108680)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_108680) (hAPP X_a X_a (hAPP X_a _let_2 (plus_plus X_a) BOUND_VARIABLE_108681) BOUND_VARIABLE_108682)))) (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_108680) BOUND_VARIABLE_108681))) BOUND_VARIABLE_108682)))) ))))) 16.65/16.55 ( nat, (zero_zero nat), (one_one nat), (one_one nat) ) 16.65/16.55 ( 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) ) 16.65/16.55 ( int, (zero_zero int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.65/16.55 ( int, s, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.65/16.55 ( int, t, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.65/16.55 ( 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))) (zero_zero int)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.65/16.55 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.65/16.55 ( int, skv_9, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.65/16.55 ) 16.65/16.55 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X))) (= (hAPP real nat natceiling (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 natceiling X)) (one_one nat)))) ) 16.65/16.55 ( (one_one real) ) 16.65/16.55 ( pi ) 16.65/16.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.55 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.55 ( skv_6 ) 16.65/16.55 ( skv_11 ) 16.65/16.55 ( skv_12 ) 16.65/16.55 ( skv_14 ) 16.65/16.55 ) 16.65/16.55 (instantiation (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (hAPP X_a (fun X_a bool) (ord_less X_a) _let_0))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_108761 $$unsorted)) (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_108761)))) (= _let_0 (ti X_a BOUND_VARIABLE_108761)) (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_108761))) ))) 16.65/16.55 ( bool, fFalse ) 16.65/16.55 ( bool, fTrue ) 16.65/16.55 ( real, (zero_zero real) ) 16.65/16.55 ( real, pi ) 16.65/16.55 ( (fun nat bool), (even_odd_even nat) ) 16.65/16.55 ( (fun nat bool), prime ) 16.65/16.55 ( (fun nat nat), suc ) 16.65/16.55 ( (fun nat nat), (fact_fact nat) ) 16.65/16.55 ( (fun nat nat), (size_size nat) ) 16.65/16.55 ( (fun nat nat), fact ) 16.65/16.55 ( (fun nat nat), nat_size ) 16.65/16.55 ( int, pls ) 16.65/16.55 ( int, m ) 16.65/16.55 ( int, min_1 ) 16.65/16.55 ( int, s ) 16.65/16.55 ( int, s1 ) 16.65/16.55 ( int, t ) 16.65/16.55 ( (fun int bool), zprime ) 16.65/16.55 ( (fun int bool), nat_neg ) 16.65/16.55 ( (fun int bool), zEven ) 16.65/16.55 ( (fun int bool), nat_is_nat ) 16.65/16.55 ( (fun int bool), zOdd ) 16.65/16.55 ( (fun int bool), (even_odd_even int) ) 16.65/16.55 ( (fun int bool), twoSqu1091635170sum2sq ) 16.65/16.55 ( (fun int nat), nat_1 ) 16.65/16.55 ( (fun int nat), phi ) 16.65/16.55 ( (fun real real), sqrt ) 16.65/16.55 ( (fun real real), tan ) 16.65/16.55 ( (fun real real), cos ) 16.65/16.55 ( (fun real real), arccos ) 16.65/16.55 ( (fun real real), ln ) 16.65/16.55 ( (fun real real), sin ) 16.65/16.55 ( (fun real real), arctan ) 16.65/16.55 ( (fun real real), arcsin ) 16.65/16.55 ( complex, ii ) 16.65/16.55 ( (fun complex complex), cnj ) 16.65/16.55 ( (fun complex complex), expi ) 16.65/16.55 ( (fun nat real), (real_1 nat) ) 16.65/16.55 ( (fun nat real), cos_coeff ) 16.65/16.55 ( (fun nat real), sin_coeff ) 16.65/16.55 ( (fun int int), bit0 ) 16.65/16.55 ( (fun int int), bit1 ) 16.65/16.55 ( (fun int int), pred ) 16.65/16.55 ( (fun int int), succ ) 16.65/16.55 ( (fun int int), (fact_fact int) ) 16.65/16.55 ( (fun int int), zfact ) 16.65/16.55 ( (fun bool bool), fNot ) 16.65/16.55 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.65/16.55 ( (fun bool (fun bool bool)), fconj ) 16.65/16.55 ( (fun bool (fun bool bool)), fdisj ) 16.65/16.55 ( (fun bool (fun bool bool)), fimplies ) 16.65/16.55 ( (fun int (fun int bool)), sRStar ) 16.65/16.55 ( (fun int (fun int bool)), quadRes ) 16.65/16.55 ( (fun int (fun int bool)), norRRset ) 16.65/16.55 ( (fun int (fun int bool)), d22set ) 16.65/16.55 ( (fun int (fun int bool)), sr ) 16.65/16.55 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.65/16.55 ( (fun nat (fun nat nat)), nat_gcd ) 16.65/16.55 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.65/16.55 ( (fun nat (fun nat nat)), nat_lcm ) 16.65/16.55 ( (fun nat (fun real real)), root ) 16.65/16.55 ( (fun real (fun real real)), log ) 16.65/16.55 ( (fun real (fun real real)), powr ) 16.65/16.55 ( (fun nat (fun nat bool)), coprime ) 16.65/16.55 ( (fun (fun int bool) int), (the int) ) 16.65/16.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.65/16.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.65/16.55 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.65/16.55 ( (fun (fun int bool) bool), nat_nat_set ) 16.65/16.55 ( (filter nat), sequentially ) 16.65/16.55 ( (fun (product_prod nat nat) bool), pred_nat ) 16.65/16.55 ( (fun (product_prod int int) bool), frac_1 ) 16.65/16.55 ( (fun real complex), cis ) 16.65/16.55 ( (fun complex real), im ) 16.65/16.55 ( (fun complex real), re ) 16.65/16.55 ( (fun complex real), arg ) 16.65/16.55 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.65/16.55 ( (fun int (fun int int)), int_gcd ) 16.65/16.55 ( (fun int (fun int int)), multInv ) 16.65/16.55 ( (fun int (fun int int)), legacy_zgcd ) 16.65/16.55 ( (fun int (fun int int)), z3mod ) 16.65/16.55 ( (fun int (fun int int)), inv ) 16.65/16.55 ( (fun int (fun int int)), (gcd_gcd int) ) 16.65/16.55 ( (fun int (fun int int)), standardRes ) 16.65/16.55 ( (fun int (fun int int)), legendre ) 16.65/16.55 ( (fun int (fun int int)), nat_tsub ) 16.65/16.55 ( (fun int (fun int int)), z3div ) 16.65/16.55 ( (fun int (fun int int)), int_lcm ) 16.65/16.55 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.65/16.55 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.65/16.55 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.65/16.55 ( (fun int (fun (fun int bool) bool)), resSet ) 16.65/16.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.65/16.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.65/16.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.65/16.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.65/16.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.65/16.55 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.65/16.55 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.65/16.55 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.65/16.55 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.65/16.55 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.65/16.55 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.65/16.55 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.65/16.55 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.65/16.55 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.65/16.55 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.65/16.55 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.65/16.55 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.65/16.55 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.65/16.55 ( (fun real nat), natfloor ) 16.65/16.55 ( (fun real nat), natceiling ) 16.65/16.55 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.65/16.55 ( (fun int (fun int (fun int bool))), wset ) 16.65/16.55 ( (fun int (fun int (fun int bool))), bnorRset ) 16.65/16.55 ( (fun int (fun int (fun int bool))), zcong ) 16.65/16.55 ( (fun int (fun int (fun int bool))), noXRRset ) 16.65/16.55 ( (fun int (fun int (fun int bool))), zcongm ) 16.65/16.55 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.65/16.55 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.65/16.55 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.65/16.55 ( (fun int real), (real_1 int) ) 16.65/16.55 ( (fun complex nat), (size_size complex) ) 16.65/16.55 ( (fun complex nat), complex_size ) 16.65/16.55 ( (fun int (list int)), quickc666637781d_zero ) 16.65/16.55 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.65/16.55 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.65/16.55 ( (fun (product_prod int int) rat), frct ) 16.65/16.55 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.65/16.55 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.65/16.55 ( (fun (fun nat rat) bool), vanishes ) 16.65/16.55 ( (fun int (fun int rat)), fract ) 16.65/16.55 ( (fun code_code_numeral int), code_int_of ) 16.65/16.55 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.65/16.55 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.65/16.55 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.65/16.55 ( (fun real (fun real complex)), complex_1 ) 16.65/16.55 ( (fun real (fun real complex)), rcis ) 16.65/16.55 ( (fun int (fun nat nat)), nat_aux ) 16.65/16.55 ( (fun rat real), ratreal ) 16.65/16.55 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.65/16.55 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.65/16.55 ( (fun rat (product_prod int int)), quotient_of ) 16.65/16.55 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.65/16.55 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.65/16.55 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.65/16.55 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.65/16.55 ) 16.65/16.55 (instantiation (forall ((A_1 $$unsorted)) (= (one_one real) (hAPP complex real (norm_norm complex) (hAPP real complex (hAPP real (fun real complex) complex_1 (hAPP real real cos A_1)) (hAPP real real sin A_1)))) ) 16.65/16.55 ( (zero_zero real) ) 16.65/16.55 ( pi ) 16.65/16.55 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.55 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.65/16.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.65/16.55 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.65/16.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.65/16.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.65/16.55 ( skv_14 ) 16.65/16.55 ) 16.65/16.55 (instantiation (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (ord_less X_a))) (let ((_let_3 (fun nat X_a))) (let ((_let_4 (power_power X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_108836 $$unsorted) (BOUND_VARIABLE_108837 $$unsorted)) (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_108836) _let_0)) (hAPP nat X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_108837) _let_0)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_108837))) (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_108836) BOUND_VARIABLE_108837))) )))))) 16.65/16.55 ( real, (zero_zero real), pi ) 16.65/16.55 ( 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)))) ) 16.65/16.55 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.55 ( real, (zero_zero real), skv_2 ) 16.65/16.55 ( real, (zero_zero real), skv_10 ) 16.65/16.55 ( real, (zero_zero real), skv_13 ) 16.65/16.55 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.55 ( real, pi, (zero_zero real) ) 16.65/16.55 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.55 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.55 ( 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) ) 16.65/16.55 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.65/16.55 ( 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 ) 16.65/16.55 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.55 ( int, (zero_zero int), (zero_zero int) ) 16.65/16.55 ( int, (zero_zero int), (one_one int) ) 16.65/16.55 ( 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))) ) 16.65/16.55 ( int, (zero_zero int), min_1 ) 16.65/16.55 ( int, min_1, (zero_zero int) ) 16.65/16.55 ( int, min_1, min_1 ) 16.65/16.55 ( 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))) ) 16.65/16.55 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 16.65/16.56 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 16.65/16.56 ( int, t, (zero_zero int) ) 16.65/16.56 ( int, t, (one_one int) ) 16.65/16.56 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.56 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.56 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.56 ) 16.65/16.56 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_108883 $$unsorted) (BOUND_VARIABLE_108884 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_108884))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_108883))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_108884) BOUND_VARIABLE_108883)))) )) 16.65/16.56 ( nat, (one_one nat), (one_one nat) ) 16.65/16.56 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.65/16.56 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.56 ) 16.65/16.56 (instantiation (let ((_let_0 (fun nat bool))) (forall ((M $$unsorted) (N $$unsorted)) (or (and (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) N))) (not (= M N))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M) N))) )) 16.65/16.56 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.56 ) 16.65/16.56 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (one_one real))) (let ((_let_2 (hAPP real real (hAPP real _let_0 (minus_minus real) _let_1) X))) (forall ((X $$unsorted)) (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)))))) )))) 16.65/16.56 ( (zero_zero real) ) 16.65/16.56 ( (one_one real) ) 16.65/16.56 ( pi ) 16.65/16.56 ( (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)))) ) 16.65/16.56 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.65/16.56 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.56 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.65/16.56 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.56 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.56 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.65/16.56 ) 16.65/16.56 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108978 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_108978) (one_one X_a))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_108978)) (one_one int))))) ) 16.65/16.56 ( real, (zero_zero real) ) 16.65/16.56 ( real, (one_one real) ) 16.65/16.56 ( real, pi ) 16.65/16.56 ( 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)))) ) 16.65/16.56 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.65/16.56 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.56 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.65/16.56 ( nat, (zero_zero nat) ) 16.65/16.56 ( int, (zero_zero int) ) 16.65/16.56 ( int, min_1 ) 16.65/16.56 ( int, s ) 16.65/16.56 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.65/16.56 ( int, t ) 16.65/16.56 ( int, skv_3 ) 16.65/16.56 ( int, skv_9 ) 16.65/16.56 ) 16.65/16.56 (instantiation (let ((_let_0 (archimedean_ceiling X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_108997 $$unsorted)) (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_108997) (one_one X_a))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP X_a int _let_0 BOUND_VARIABLE_108997)) (one_one int)))) )) 16.65/16.56 ( nat, (one_one nat) ) 16.65/16.56 ( 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 bit0 (hAPP int int bit1 pls))))) m) ) 16.65/16.56 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.56 ) 16.65/16.56 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109039 $$unsorted) (BOUND_VARIABLE_109040 $$unsorted)) (or (not (linorder X_a)) (= (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_max X_a) BOUND_VARIABLE_109039) BOUND_VARIABLE_109040) (ti X_a BOUND_VARIABLE_109040)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_109039) BOUND_VARIABLE_109040)))) ) 16.65/16.56 ( real, (zero_zero real), pi ) 16.65/16.56 ( 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)))) ) 16.65/16.56 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.56 ( real, (zero_zero real), skv_6 ) 16.65/16.56 ( real, (zero_zero real), skv_11 ) 16.65/16.56 ( real, (zero_zero real), skv_12 ) 16.65/16.56 ( real, (zero_zero real), skv_14 ) 16.65/16.56 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.65/16.56 ( 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))) ) 16.65/16.56 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.65/16.56 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.56 ( int, (zero_zero int), (one_one int) ) 16.65/16.56 ( int, (zero_zero int), min_1 ) 16.65/16.56 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.56 ( int, (zero_zero int), s ) 16.65/16.56 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.65/16.56 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.56 ( int, (zero_zero int), skv_3 ) 16.65/16.56 ( int, (zero_zero int), skv_9 ) 16.65/16.56 ( int, (one_one int), t ) 16.65/16.56 ( int, min_1, pls ) 16.65/16.56 ( int, min_1, min_1 ) 16.65/16.56 ) 16.65/16.56 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (one_one X_a)))) ) 16.65/16.56 ( bool ) 16.65/16.56 ( real ) 16.65/16.56 ( nat ) 16.65/16.56 ( (fun nat bool) ) 16.65/16.56 ( int ) 16.65/16.56 ( (fun int bool) ) 16.65/16.56 ( complex ) 16.65/16.56 ( rat ) 16.65/16.56 ( quickcheck_code_int ) 16.65/16.56 ( (product_prod real real) ) 16.65/16.56 ( (product_prod int int) ) 16.65/16.56 ( (filter real) ) 16.65/16.56 ( (filter nat) ) 16.65/16.56 ( (product_prod nat nat) ) 16.65/16.56 ( code_code_numeral ) 16.65/16.56 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.65/16.56 ( (fun nat rat) ) 16.65/16.56 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.65/16.56 ) 16.65/16.56 (instantiation (let ((_let_0 (hAPP real complex (of_real complex) X))) (forall ((X $$unsorted)) (= _let_0 (hAPP complex complex cnj _let_0)) )) 16.65/16.56 ( pi ) 16.65/16.56 ( (hAPP int real (number_number_of real) min_1) ) 16.65/16.56 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 16.65/16.56 ) 16.65/16.56 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (hAPP int _let_1 zcong A_1))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 B) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong B) C) M))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 C) M))) )))) 16.65/16.56 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.56 ) 16.65/16.56 (instantiation (let ((_let_0 (one_one int))) (let ((_let_1 (ti int M))) (forall ((M $$unsorted) (N $$unsorted)) (or (not (= _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) M) N))) (= _let_0 _let_1) (= (hAPP int int (number_number_of int) min_1) _let_1)) ))) 16.65/16.56 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.65/16.56 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 16.65/16.56 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.65/16.56 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1 ) 16.65/16.56 ) 16.65/16.56 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))))) (forall ((X $$unsorted)) (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 log _let_1) 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)))) ))) 16.65/16.56 ( (one_one real) ) 16.65/16.56 ( pi ) 16.65/16.56 ( (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)))) ) 16.65/16.56 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.56 ( skv_2 ) 16.65/16.56 ( skv_10 ) 16.65/16.56 ( skv_13 ) 16.65/16.56 ) 16.65/16.56 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109261 $$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_109261)) (hAPP nat int (semiring_1_of_nat int) BOUND_VARIABLE_109261))) ) 16.65/16.56 ( real, (zero_zero nat) ) 16.65/16.56 ( real, (one_one nat) ) 16.65/16.56 ( int, (zero_zero nat) ) 16.65/16.56 ( int, (hAPP nat nat suc (zero_zero nat)) ) 16.65/16.56 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.56 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.56 ) 16.65/16.56 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_109314 $$unsorted)) (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_109314)) (ring_1_Ints X_a)))) )) 16.65/16.56 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.65/16.56 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.56 ( real, min_1 ) 16.65/16.56 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.56 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.65/16.56 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.56 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.65/16.56 ( nat, pls ) 16.65/16.56 ( nat, (hAPP int int bit1 pls) ) 16.65/16.56 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.65/16.56 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.65/16.56 ( int, pls ) 16.65/16.56 ( int, (hAPP int int bit1 pls) ) 16.65/16.56 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.65/16.56 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.56 ( int, min_1 ) 16.65/16.56 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.65/16.56 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.65/16.56 ( complex, min_1 ) 16.65/16.56 ( quickcheck_code_int, (zero_zero int) ) 16.65/16.56 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 16.65/16.56 ( quickcheck_code_int, (one_one int) ) 16.65/16.56 ( code_code_numeral, pls ) 16.65/16.56 ( code_code_numeral, (hAPP int int bit1 pls) ) 16.65/16.56 ) 16.65/16.56 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_1) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (times_times int) X_1) Y_1)) zEven))) )))) 16.65/16.56 ( (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.56 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.56 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.56 ( skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.56 ) 16.65/16.56 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109358 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (ti X_a BOUND_VARIABLE_109358) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_109358) (one_one nat)))) ) 16.65/16.56 ( bool, fFalse ) 16.65/16.56 ( bool, fTrue ) 16.65/16.56 ( real, pi ) 16.65/16.56 ( real, (hAPP int real (number_number_of real) min_1) ) 16.65/16.56 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.56 ( (fun nat bool), (even_odd_even nat) ) 16.65/16.56 ( (fun nat bool), prime ) 16.65/16.56 ( (fun nat nat), suc ) 16.65/16.56 ( (fun nat nat), (fact_fact nat) ) 16.65/16.56 ( (fun nat nat), (size_size nat) ) 16.65/16.56 ( (fun nat nat), fact ) 16.65/16.56 ( (fun nat nat), nat_size ) 16.65/16.56 ( int, pls ) 16.65/16.56 ( int, m ) 16.65/16.56 ( int, min_1 ) 16.65/16.56 ( int, s ) 16.65/16.56 ( int, s1 ) 16.65/16.56 ( int, t ) 16.65/16.56 ( int, skv_8 ) 16.65/16.56 ( (fun int bool), zprime ) 16.65/16.56 ( (fun int bool), nat_neg ) 16.65/16.56 ( (fun int bool), zEven ) 16.65/16.56 ( (fun int bool), nat_is_nat ) 16.65/16.56 ( (fun int bool), zOdd ) 16.65/16.56 ( (fun int bool), (even_odd_even int) ) 16.65/16.56 ( (fun int bool), twoSqu1091635170sum2sq ) 16.65/16.56 ( (fun int nat), nat_1 ) 16.65/16.56 ( (fun int nat), phi ) 16.65/16.56 ( (fun real real), sqrt ) 16.65/16.56 ( (fun real real), tan ) 16.65/16.56 ( (fun real real), cos ) 16.65/16.56 ( (fun real real), arccos ) 16.65/16.56 ( (fun real real), ln ) 16.65/16.56 ( (fun real real), sin ) 16.65/16.56 ( (fun real real), arctan ) 16.65/16.56 ( (fun real real), arcsin ) 16.65/16.56 ( complex, ii ) 16.65/16.56 ( (fun complex complex), cnj ) 16.65/16.56 ( (fun complex complex), expi ) 16.65/16.56 ( (fun nat real), (real_1 nat) ) 16.65/16.56 ( (fun nat real), cos_coeff ) 16.65/16.56 ( (fun nat real), sin_coeff ) 16.65/16.56 ( (fun int int), bit0 ) 16.65/16.56 ( (fun int int), bit1 ) 16.65/16.56 ( (fun int int), pred ) 16.65/16.57 ( (fun int int), succ ) 16.65/16.57 ( (fun int int), (fact_fact int) ) 16.65/16.57 ( (fun int int), zfact ) 16.65/16.57 ( (fun bool bool), fNot ) 16.65/16.57 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.65/16.57 ( (fun bool (fun bool bool)), fconj ) 16.65/16.57 ( (fun bool (fun bool bool)), fdisj ) 16.65/16.57 ( (fun bool (fun bool bool)), fimplies ) 16.65/16.57 ( (fun int (fun int bool)), sRStar ) 16.65/16.57 ( (fun int (fun int bool)), quadRes ) 16.65/16.57 ( (fun int (fun int bool)), norRRset ) 16.65/16.57 ( (fun int (fun int bool)), d22set ) 16.65/16.57 ( (fun int (fun int bool)), sr ) 16.65/16.57 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.65/16.57 ( (fun nat (fun nat nat)), nat_gcd ) 16.65/16.57 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.65/16.57 ( (fun nat (fun nat nat)), nat_lcm ) 16.65/16.57 ( (fun nat (fun real real)), root ) 16.65/16.57 ( (fun real (fun real real)), log ) 16.65/16.57 ( (fun real (fun real real)), powr ) 16.65/16.57 ( (fun nat (fun nat bool)), coprime ) 16.65/16.57 ( (fun (fun int bool) int), (the int) ) 16.65/16.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.65/16.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.65/16.57 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.65/16.57 ( (fun (fun int bool) bool), nat_nat_set ) 16.65/16.57 ( (filter nat), sequentially ) 16.65/16.57 ( (fun (product_prod nat nat) bool), pred_nat ) 16.65/16.57 ( (fun (product_prod int int) bool), frac_1 ) 16.65/16.57 ( (fun real complex), cis ) 16.65/16.57 ( (fun complex real), im ) 16.65/16.57 ( (fun complex real), re ) 16.65/16.57 ( (fun complex real), arg ) 16.65/16.57 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.65/16.57 ( (fun int (fun int int)), int_gcd ) 16.65/16.57 ( (fun int (fun int int)), multInv ) 16.65/16.57 ( (fun int (fun int int)), legacy_zgcd ) 16.65/16.57 ( (fun int (fun int int)), z3mod ) 16.65/16.57 ( (fun int (fun int int)), inv ) 16.65/16.57 ( (fun int (fun int int)), (gcd_gcd int) ) 16.65/16.57 ( (fun int (fun int int)), standardRes ) 16.65/16.57 ( (fun int (fun int int)), legendre ) 16.65/16.57 ( (fun int (fun int int)), nat_tsub ) 16.65/16.57 ( (fun int (fun int int)), z3div ) 16.65/16.57 ( (fun int (fun int int)), int_lcm ) 16.65/16.57 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.65/16.57 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.65/16.57 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.65/16.57 ( (fun int (fun (fun int bool) bool)), resSet ) 16.65/16.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.65/16.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.65/16.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.65/16.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.65/16.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.65/16.57 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.65/16.57 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.65/16.57 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.65/16.57 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.65/16.57 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.65/16.57 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.65/16.57 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.65/16.57 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.65/16.57 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.65/16.57 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.65/16.57 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.65/16.57 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.65/16.57 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.65/16.57 ( (fun real nat), natfloor ) 16.65/16.57 ( (fun real nat), natceiling ) 16.65/16.57 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.65/16.57 ( (fun int (fun int (fun int bool))), wset ) 16.65/16.57 ( (fun int (fun int (fun int bool))), bnorRset ) 16.65/16.57 ( (fun int (fun int (fun int bool))), zcong ) 16.65/16.57 ( (fun int (fun int (fun int bool))), noXRRset ) 16.65/16.57 ( (fun int (fun int (fun int bool))), zcongm ) 16.65/16.57 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.65/16.57 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.65/16.57 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.65/16.57 ( (fun int real), (real_1 int) ) 16.65/16.57 ( (fun complex nat), (size_size complex) ) 16.65/16.57 ( (fun complex nat), complex_size ) 16.65/16.57 ( (fun int (list int)), quickc666637781d_zero ) 16.65/16.57 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.65/16.57 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.65/16.57 ( (fun (product_prod int int) rat), frct ) 16.65/16.57 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.65/16.57 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.65/16.57 ( (fun (fun nat rat) bool), vanishes ) 16.65/16.57 ( (fun int (fun int rat)), fract ) 16.65/16.57 ( (fun code_code_numeral int), code_int_of ) 16.65/16.57 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.65/16.57 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.65/16.57 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.65/16.57 ( (fun real (fun real complex)), complex_1 ) 16.65/16.57 ( (fun real (fun real complex)), rcis ) 16.65/16.57 ( (fun int (fun nat nat)), nat_aux ) 16.65/16.57 ( (fun rat real), ratreal ) 16.65/16.57 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.65/16.57 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.65/16.57 ( (fun rat (product_prod int int)), quotient_of ) 16.65/16.57 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.65/16.57 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.65/16.57 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.65/16.57 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.65/16.57 ) 16.65/16.57 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109374 $$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_109374)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_109374) (zero_zero X_a))))) ) 16.65/16.57 ( real, (zero_zero real) ) 16.65/16.57 ( real, (one_one real) ) 16.65/16.57 ( real, pi ) 16.65/16.57 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.57 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.65/16.57 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.57 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.65/16.57 ( nat, (zero_zero nat) ) 16.65/16.57 ( int, (zero_zero int) ) 16.65/16.57 ( int, min_1 ) 16.65/16.57 ( int, s ) 16.65/16.57 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.65/16.57 ( int, t ) 16.65/16.57 ( int, skv_3 ) 16.65/16.57 ( int, skv_9 ) 16.65/16.57 ( rat, (zero_zero rat) ) 16.65/16.57 ) 16.65/16.57 (instantiation (let ((_let_0 (fun nat real))) (let ((_let_1 (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)))) (forall ((F $$unsorted)) (or (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool _let_1 (hAPP nat real F N_2))) )) (not (hBOOL (hAPP _let_0 bool (summable real) F))) (hBOOL (hAPP real bool _let_1 (hAPP _let_0 real (suminf real) F)))) ))) 16.65/16.57 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (combc nat nat nat))) (let ((_let_4 (fun nat _let_0))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun _let_1 _let_4))) (let ((_let_7 (combb real _let_0 nat))) (hAPP _let_1 _let_1 (hAPP _let_4 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_4 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 16.65/16.57 ) 16.65/16.57 (instantiation (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_109407 $$unsorted) (BOUND_VARIABLE_109408 $$unsorted)) (or (not (real_n1866405975lgebra X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_109407) BOUND_VARIABLE_109408) sequentially))) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_109408)) (hBOOL (hAPP _let_1 bool (bseq X_a) (hAPP _let_1 _let_1 (hAPP (fun X_a X_a) (fun _let_1 _let_1) (combb X_a X_a nat) (inverse_inverse X_a)) BOUND_VARIABLE_109407)))) ))) 16.65/16.57 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 16.65/16.57 ) 16.65/16.57 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (times_times X_a))) (let ((_let_3 (plus_plus X_a))) (let ((_let_4 (one_one X_a))) (let ((_let_5 (semiring_1_of_nat X_a))) (let ((_let_6 (hAPP nat X_a _let_5 BOUND_VARIABLE_109477))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_109477 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 _let_6) (hAPP X_a X_a (hAPP X_a _let_1 _let_3 _let_6) _let_4)) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a _let_1 _let_3 _let_4) _let_4)) (hAPP _let_0 X_a (hAPP (fun nat X_a) (fun _let_0 X_a) (big_co1399186613setsum nat X_a) _let_5) (hAPP nat _let_0 (hAPP nat (fun nat _let_0) (ord_atLeastAtMost nat) (one_one nat)) BOUND_VARIABLE_109477))))) )))))))) 16.65/16.57 ( real, (zero_zero nat) ) 16.65/16.57 ( real, (one_one nat) ) 16.65/16.57 ( int, (zero_zero nat) ) 16.65/16.57 ( int, (hAPP nat nat suc (zero_zero nat)) ) 16.65/16.57 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.57 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.57 ) 16.65/16.57 (instantiation (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (fun X_c bool))) (let ((_let_2 (fun X_b _let_1))) (forall ((X_c $$unsorted) (X_a $$unsorted) (X_b $$unsorted) (R_3 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (or (not (hBOOL (hAPP X_c bool (hAPP _let_0 _let_1 (hAPP (fun X_a _let_2) (fun _let_0 _let_1) (product_prod_case X_a X_b _let_1) R_3) (hAPP X_b _let_0 (hAPP X_a (fun X_b _let_0) (product_Pair X_a X_b) A_2) B_1)) C_1))) (hBOOL (hAPP X_c bool (hAPP X_b _let_1 (hAPP X_a _let_2 R_3 A_2) B_1) C_1))) )))) 16.65/16.57 ( int, int, int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.57 ( 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))) ) 16.65/16.57 ( 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))) ) 16.65/16.57 ( int, int, int, zcong, s1, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.57 ( int, int, int, zcong, s1, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.57 ( int, int, int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.57 ( int, int, int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.65/16.57 ( (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))))) ) 16.65/16.57 ( (filter nat), (fun nat real), real, (tendsto nat real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real), sequentially ) 16.65/16.57 ) 16.65/16.57 (instantiation (let ((_let_0 (archim2085082626_floor X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_109530 $$unsorted) (BOUND_VARIABLE_109531 $$unsorted)) (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_109530) BOUND_VARIABLE_109531))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int _let_0 BOUND_VARIABLE_109530)) (hAPP X_a int _let_0 BOUND_VARIABLE_109531)))) )) 16.65/16.57 ( real, (zero_zero real), pi ) 16.65/16.57 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.57 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.57 ( real, (zero_zero real), skv_6 ) 16.65/16.57 ( real, (zero_zero real), skv_11 ) 16.65/16.57 ( real, (zero_zero real), skv_12 ) 16.65/16.57 ( real, (zero_zero real), skv_14 ) 16.65/16.57 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.65/16.57 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.57 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.65/16.57 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.57 ( int, (zero_zero int), (one_one int) ) 16.65/16.57 ( int, (zero_zero int), min_1 ) 16.65/16.57 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.57 ( int, (zero_zero int), s ) 16.65/16.57 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.65/16.57 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.57 ( int, (zero_zero int), skv_3 ) 16.65/16.57 ( int, (zero_zero int), skv_9 ) 16.65/16.57 ( int, (one_one int), t ) 16.65/16.57 ( int, min_1, pls ) 16.65/16.57 ( int, min_1, min_1 ) 16.65/16.57 ) 16.65/16.57 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (times_times int) X_1) Y_1)) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_1) zOdd))) )))) 16.65/16.57 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.65/16.57 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 16.65/16.58 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.65/16.58 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1 ) 16.65/16.58 ) 16.65/16.58 (instantiation (forall ((N $$unsorted) (Z_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Z_1))) (= (hAPP nat nat (hAPP nat (fun nat nat) (power_power nat) (hAPP int nat nat_1 Z_1)) N) (hAPP int nat nat_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) Z_1) N)))) ) 16.65/16.58 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 16.65/16.58 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 16.65/16.58 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 16.65/16.58 ) 16.65/16.58 (instantiation (let ((_let_0 (zero_zero nat))) (forall ((X_1 $$unsorted)) (= (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) X_1) (hAPP nat nat suc (hAPP nat nat suc _let_0)))) (hBOOL (hAPP nat bool (even_odd_even nat) X_1))) )) 16.65/16.58 ( (zero_zero nat) ) 16.65/16.58 ( (one_one nat) ) 16.65/16.58 ) 16.65/16.58 (instantiation (let ((_let_0 (fun nat bool))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) Ma) N_1)) (or (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) Ma) N_1)) (= Ma N_1))) )) 16.65/16.58 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.58 ) 16.65/16.58 (instantiation (let ((_let_0 (fun nat bool))) (forall ((M $$unsorted) (N $$unsorted)) (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)))) )) 16.65/16.58 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 16.65/16.58 ) 16.65/16.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109681 $$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_109681) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_109681)))) ) 16.65/16.58 ( real, (one_one real) ) 16.65/16.58 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.58 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.65/16.58 ( nat, (one_one nat) ) 16.65/16.58 ( int, pls ) 16.65/16.58 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.65/16.58 ( int, (one_one int) ) 16.65/16.58 ( int, min_1 ) 16.65/16.58 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.58 ( complex, ii ) 16.65/16.58 ( complex, (one_one complex) ) 16.65/16.58 ) 16.65/16.58 (instantiation (let ((_let_0 (fun real X_a))) (forall ((X_a $$unsorted) (F1 $$unsorted) (Real1 $$unsorted) (Real2 $$unsorted)) (= (hAPP real X_a (hAPP real _let_0 F1 Real1) Real2) (hAPP complex X_a (hAPP (fun real _let_0) (fun complex X_a) (complex_case X_a) F1) (hAPP real complex (hAPP real (fun real complex) complex_1 Real1) Real2))) )) 16.65/16.58 ( bool, (ord_less_eq real), (zero_zero real), pi ) 16.65/16.58 ( bool, (ord_less_eq real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.58 ( bool, (ord_less_eq real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.58 ( bool, (ord_less_eq real), (zero_zero real), skv_6 ) 16.65/16.58 ( bool, (ord_less_eq real), (zero_zero real), skv_11 ) 16.65/16.58 ( bool, (ord_less_eq real), (zero_zero real), skv_12 ) 16.65/16.58 ( bool, (ord_less_eq real), (zero_zero real), skv_14 ) 16.65/16.58 ( bool, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.65/16.58 ( bool, (ord_less_eq real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.58 ( bool, (ord_less_eq real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.65/16.58 ( bool, (ord_less_eq real), skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.58 ( bool, (ord_less real), (zero_zero real), pi ) 16.65/16.58 ( bool, (ord_less real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.58 ( bool, (ord_less real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.58 ( bool, (ord_less real), (zero_zero real), skv_2 ) 16.65/16.58 ( bool, (ord_less real), (zero_zero real), skv_10 ) 16.65/16.58 ( bool, (ord_less real), (zero_zero real), skv_13 ) 16.65/16.58 ( bool, (ord_less real), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.58 ( bool, (ord_less real), pi, (zero_zero real) ) 16.65/16.58 ( bool, (ord_less real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.58 ( bool, (ord_less real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.58 ( bool, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.65/16.58 ( bool, (ord_less real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.65/16.58 ( bool, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.65/16.58 ( real, (minus_minus real), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.65/16.58 ( real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.58 ( real, (inverse_divide real), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.65/16.58 ( real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.58 ( real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 16.65/16.58 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.58 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.65/16.58 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.65/16.58 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.65/16.58 ( real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.58 ( real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.58 ( real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.58 ( real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.65/16.58 ( real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 16.65/16.58 ( real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.65/16.58 ( real, (times_times real), (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.65/16.58 ( complex, complex_1, (zero_zero real), (zero_zero real) ) 16.65/16.58 ( complex, complex_1, (zero_zero real), (one_one real) ) 16.65/16.58 ( complex, complex_1, (one_one real), (zero_zero real) ) 16.65/16.58 ) 16.65/16.58 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_109707 $$unsorted)) (or (not (ring_1 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_109707) (ring_1_Ints X_a)))) (not (forall ((Z_2 $$unsorted)) (not (= (hAPP int X_a (ring_1_of_int X_a) Z_2) (ti X_a BOUND_VARIABLE_109707))) ))) )) 16.65/16.58 ( int, (one_one int) ) 16.65/16.58 ) 16.65/16.58 (instantiation (let ((_let_0 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_109773 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_109773)) (one_one X_a)) (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_109773) (hAPP int int bit1 pls))))) )) 16.65/16.58 ( nat, (hAPP int int bit1 pls) ) 16.65/16.58 ) 16.65/16.58 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (fact_fact nat))) (let ((_let_2 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N) (one_one nat)))) (forall ((N $$unsorted)) (= (hAPP nat nat _let_1 _let_2) (hAPP nat nat (hAPP nat _let_0 (times_times nat) _let_2) (hAPP nat nat _let_1 N))) )))) 16.65/16.58 ( (one_one nat) ) 16.65/16.58 ) 16.65/16.58 (instantiation (forall ((N $$unsorted)) (= (hAPP int int (uminus_uminus int) N) (hAPP real int (archim2085082626_floor real) (hAPP real real (uminus_uminus real) (hAPP int real (real_1 int) N)))) ) 16.65/16.58 ( (zero_zero int) ) 16.65/16.58 ( pls ) 16.65/16.58 ( (one_one int) ) 16.65/16.58 ( min_1 ) 16.65/16.58 ) 16.65/16.58 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_0))) (let ((_let_5 (product_prod int int))) (let ((_let_6 (fun _let_5 bool))) (let ((_let_7 (fun int _let_3))) (forall ((D_1 $$unsorted)) (= (hAPP int _let_6 int_ge_less_than D_1) (hAPP _let_6 _let_6 (collect _let_5) (hAPP _let_4 _let_6 (product_prod_case int int bool) (hAPP _let_4 _let_4 (hAPP _let_7 (fun _let_4 _let_4) (combs int _let_0 _let_0) (hAPP _let_2 _let_7 (hAPP (fun _let_1 _let_3) (fun _let_2 _let_7) (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))))) ))))))))) 16.65/16.58 ( (zero_zero int) ) 16.65/16.58 ( (one_one int) ) 16.65/16.58 ( min_1 ) 16.65/16.58 ) 16.65/16.58 (instantiation (forall ((X_1 $$unsorted)) (or (= (zero_zero real) (hAPP real real cos X_1)) (hBOOL (hAPP real bool (hAPP (fun real real) (fun real bool) (isCont real real) tan) X_1))) ) 16.65/16.58 ( (zero_zero real) ) 16.65/16.58 ( pi ) 16.65/16.58 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.65/16.58 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.65/16.58 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.65/16.58 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.65/16.58 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.65/16.58 ) 16.65/16.58 (instantiation (let ((_let_0 (fun X_b X_c))) (let ((_let_1 (fun X_a _let_0))) (let ((_let_2 (product_prod X_a X_b))) (let ((_let_3 (fun _let_2 X_c))) (let ((_let_4 (fun X_a X_d))) (let ((_let_5 (fun X_d _let_0))) (let ((_let_6 (fun _let_2 X_b))) (let ((_let_7 (fun _let_2 _let_0))) (let ((_let_8 (fun _let_2 X_d))) (let ((_let_9 (fun _let_2 X_a))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (F $$unsorted) (G $$unsorted)) (= (hAPP _let_6 _let_3 (hAPP _let_7 (fun _let_6 _let_3) (combs _let_2 X_b X_c) (hAPP _let_8 _let_7 (hAPP _let_5 (fun _let_8 _let_7) (combb X_d _let_0 _let_2) F) (hAPP _let_9 _let_8 (hAPP _let_4 (fun _let_9 _let_8) (combb X_a X_d _let_2) G) (product_fst X_a X_b)))) (product_snd X_a X_b)) (hAPP _let_1 _let_3 (product_prod_case X_a X_b X_c) (hAPP _let_4 _let_1 (hAPP _let_5 (fun _let_4 _let_1) (combb X_d _let_0 X_a) F) G))) ))))))))))) 16.65/16.58 ( real, bool, bool, bool, fconj, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 16.65/16.58 ( 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))))) ) 16.65/16.58 ( real, real, bool, real, (fequal real), cos ) 16.65/16.58 ( real, real, real, real, (inverse_divide real), cos ) 16.65/16.58 ( real, (fun nat bool), (fun int (fun nat bool)), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun nat _let_2))) (let ((_let_7 (fun (fun nat bool) _let_6))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_6))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_13 _let_11))) (let ((_let_16 (fun (fun int (fun nat bool)) _let_13))) (let ((_let_17 (fun int (fun nat real)))) (let ((_let_18 (fun _let_17 (fun int (fun nat bool))))) (let ((_let_19 (fun real _let_18))) (let ((_let_20 (fun (fun nat real) (fun nat bool)))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun int _let_3))) (hAPP _let_14 _let_12 (hAPP _let_15 (fun _let_14 _let_12) (combb _let_13 _let_11 real) (hAPP (fun _let_6 _let_5) _let_15 (combb _let_6 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_14 (hAPP _let_16 (fun _let_10 _let_14) (combb (fun int (fun nat bool)) _let_13 real) (hAPP _let_7 _let_16 (combb (fun nat bool) _let_6 int) (hAPP (fun bool _let_2) _let_7 (combb bool _let_2 nat) fconj))) (hAPP _let_17 _let_10 (hAPP _let_19 (fun _let_17 _let_10) (combc real _let_17 (fun int (fun nat bool))) (hAPP _let_21 _let_19 (hAPP (fun _let_20 _let_18) (fun _let_21 _let_19) (combb _let_20 _let_18 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_21 (hAPP (fun _let_0 _let_20) (fun _let_4 _let_21) (combb _let_0 _let_20 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_17 (hAPP _let_22 (fun (fun nat real) _let_17) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_22 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_22) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_8 _let_9 (hAPP (fun real _let_1) (fun _let_8 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))))))))))))))) ) 16.65/16.59 ( 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 bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (fun (fun int bool) (fun int bool)))) (let ((_let_6 (fun (fun int bool) _let_4))) (let ((_let_7 (fun int (fun int bool)))) (let ((_let_8 (fun real _let_0))) (let ((_let_9 (fun int _let_5))) (let ((_let_10 (fun int real))) (let ((_let_11 (fun real _let_7))) (let ((_let_12 (fun (fun int bool) _let_7))) (let ((_let_13 (fun real _let_12))) (let ((_let_14 (fun real _let_9))) (let ((_let_15 (fun int _let_4))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_15 _let_9))) (let ((_let_18 (fun _let_7 _let_15))) (let ((_let_19 (fun int _let_10))) (let ((_let_20 (fun _let_19 _let_7))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun _let_10 (fun int bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_10 _let_10))) (let ((_let_25 (fun int _let_24))) (let ((_let_26 (fun int _let_1))) (hAPP (fun int bool) _let_11 (hAPP _let_13 (fun (fun int bool) _let_11) (combc real (fun int bool) _let_7) (hAPP _let_14 _let_13 (hAPP (fun _let_9 _let_12) (fun _let_14 _let_13) (combb _let_9 _let_12 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_16 _let_14 (hAPP _let_17 (fun _let_16 _let_14) (combb _let_15 _let_9 real) (hAPP (fun _let_4 _let_5) _let_17 (combb _let_4 _let_5 int) (combs int bool bool))) (hAPP _let_11 _let_16 (hAPP _let_18 (fun _let_11 _let_16) (combb _let_7 _let_15 real) (hAPP _let_6 _let_18 (combb (fun int bool) _let_4 int) (hAPP (fun bool _let_3) _let_6 (combb bool _let_3 int) fconj))) (hAPP _let_19 _let_11 (hAPP _let_21 (fun _let_19 _let_11) (combc real _let_19 _let_7) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb _let_10 (fun int bool) int)) (hAPP _let_8 _let_23 (hAPP (fun _let_0 _let_22) (fun _let_8 _let_23) (combb _let_0 _let_22 real) (combb real bool int)) (fequal real)))) (hAPP _let_10 _let_19 (hAPP _let_25 (fun _let_10 _let_19) (combc int _let_10 _let_10) (hAPP _let_26 _let_25 (hAPP (fun _let_1 _let_24) (fun _let_26 _let_25) (combb _let_1 _let_24 int) (combb real real int)) (hAPP _let_10 _let_26 (hAPP (fun real _let_1) (fun _let_10 _let_26) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_3 _let_5 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_7 _let_7 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))) ) 16.65/16.59 ( real, int, bool, (fun int (fun nat bool)), (let ((_let_0 (fun nat bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) (fun int bool)) (combb _let_0 bool int) (fEx nat))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun nat (fun nat bool)))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun (fun nat bool) (fun nat bool)))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int real))) (let ((_let_10 (fun int _let_1))) (let ((_let_11 (fun real (fun int (fun nat bool))))) (let ((_let_12 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_13 (fun real _let_12))) (let ((_let_14 (fun int _let_6))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun int _let_7))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun _let_16 _let_14))) (let ((_let_19 (fun (fun int (fun nat bool)) _let_16))) (let ((_let_20 (fun int (fun nat real)))) (let ((_let_21 (fun _let_20 (fun int (fun nat bool))))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun (fun nat real) (fun nat bool)))) (let ((_let_24 (fun real _let_23))) (let ((_let_25 (fun int _let_3))) (hAPP (fun nat bool) _let_11 (hAPP _let_13 (fun (fun nat bool) _let_11) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_15 _let_13 (hAPP (fun _let_14 _let_12) (fun _let_15 _let_13) (combb _let_14 _let_12 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_17 _let_15 (hAPP _let_18 (fun _let_17 _let_15) (combb _let_16 _let_14 real) (hAPP (fun _let_7 _let_6) _let_18 (combb _let_7 _let_6 int) (combs nat bool bool))) (hAPP _let_11 _let_17 (hAPP _let_19 (fun _let_11 _let_17) (combb (fun int (fun nat bool)) _let_16 real) (hAPP _let_8 _let_19 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_20 _let_11 (hAPP _let_22 (fun _let_20 _let_11) (combc real _let_20 (fun int (fun nat bool))) (hAPP _let_24 _let_22 (hAPP (fun _let_23 _let_21) (fun _let_24 _let_22) (combb _let_23 _let_21 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_5 _let_24 (hAPP (fun _let_0 _let_23) (fun _let_5 _let_24) (combb _let_0 _let_23 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_20 (hAPP _let_25 (fun (fun nat real) _let_20) (combc int (fun nat real) (fun nat real)) (hAPP _let_10 _let_25 (hAPP (fun _let_1 _let_3) (fun _let_10 _let_25) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_9 _let_10 (hAPP (fun real _let_1) (fun _let_9 _let_10) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_2 _let_6 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_4 _let_4 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))) ) 16.65/16.59 ( real, int, (fun int (fun bool bool)), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 int) fconj)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun real (fun int (fun int bool))))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun _let_6 (fun int (fun int bool))))) (let ((_let_8 (fun real _let_7))) (let ((_let_9 (fun _let_4 (fun int bool)))) (let ((_let_10 (fun real _let_9))) (let ((_let_11 (fun _let_4 _let_4))) (let ((_let_12 (fun int _let_11))) (let ((_let_13 (fun int _let_1))) (hAPP _let_6 _let_5 (hAPP _let_8 (fun _let_6 _let_5) (combc real _let_6 (fun int (fun int bool))) (hAPP _let_10 _let_8 (hAPP (fun _let_9 _let_7) (fun _let_10 _let_8) (combb _let_9 _let_7 real) (combb _let_4 (fun int bool) int)) (hAPP _let_3 _let_10 (hAPP (fun _let_0 _let_9) (fun _let_3 _let_10) (combb _let_0 _let_9 real) (combb real bool int)) (fequal real)))) (hAPP _let_4 _let_6 (hAPP _let_12 (fun _let_4 _let_6) (combc int _let_4 _let_4) (hAPP _let_13 _let_12 (hAPP (fun _let_1 _let_11) (fun _let_13 _let_12) (combb _let_1 _let_11 int) (combb real real int)) (hAPP _let_4 _let_13 (hAPP (fun real _let_1) (fun _let_4 _let_13) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))) ) 16.65/16.59 ( real, int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int (fun bool bool)))) (let ((_let_1 (fun (fun int bool) (fun int bool)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combs int bool bool)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (fun (fun int bool) _let_4))) (let ((_let_6 (fun real _let_0))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun real (fun int (fun int bool))))) (let ((_let_9 (fun int _let_4))) (let ((_let_10 (fun real _let_9))) (let ((_let_11 (fun (fun int (fun int bool)) _let_9))) (let ((_let_12 (fun int _let_7))) (let ((_let_13 (fun _let_12 (fun int (fun int bool))))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_7 (fun int bool)))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_7 _let_7))) (let ((_let_18 (fun int _let_17))) (let ((_let_19 (fun int _let_1))) (hAPP _let_8 _let_10 (hAPP _let_11 (fun _let_8 _let_10) (combb (fun int (fun int bool)) _let_9 real) (hAPP _let_5 _let_11 (combb (fun int bool) _let_4 int) (hAPP (fun bool _let_3) _let_5 (combb bool _let_3 int) fconj))) (hAPP _let_12 _let_8 (hAPP _let_14 (fun _let_12 _let_8) (combc real _let_12 (fun int (fun int bool))) (hAPP _let_16 _let_14 (hAPP (fun _let_15 _let_13) (fun _let_16 _let_14) (combb _let_15 _let_13 real) (combb _let_7 (fun int bool) int)) (hAPP _let_6 _let_16 (hAPP (fun _let_0 _let_15) (fun _let_6 _let_16) (combb _let_0 _let_15 real) (combb real bool int)) (fequal real)))) (hAPP _let_7 _let_12 (hAPP _let_18 (fun _let_7 _let_12) (combc int _let_7 _let_7) (hAPP _let_19 _let_18 (hAPP (fun _let_1 _let_17) (fun _let_19 _let_18) (combb _let_1 _let_17 int) (combb real real int)) (hAPP _let_7 _let_19 (hAPP (fun real _let_1) (fun _let_7 _let_19) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2))))))))))))))))))))))) ) 16.81/16.59 ( real, int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun (fun nat bool) (fun nat bool)))) (let ((_let_1 (fun nat (fun bool bool)))) (hAPP (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) (combb _let_1 _let_0 int) (combs nat bool bool)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real 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real))))) ) 16.81/16.60 ( nat, real, real, real, (times_times real), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) ) 16.81/16.60 ( nat, nat, bool, nat, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))), suc ) 16.81/16.60 ( 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))))) ) 16.81/16.60 ( int, bool, bool, bool, fconj, (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 16.81/16.60 ( int, real, real, real, (inverse_divide real), (real_1 int) ) 16.81/16.60 ( 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) 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(inverse_divide real)) (real_1 int))))) ) 16.81/16.60 ( int, (fun int int), (fun int bool), (fun int bool), (combb int bool int), (fequal int) ) 16.81/16.60 ( 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))))))) ) 16.81/16.60 ( 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))))) ) 16.81/16.60 ( (product_prod int int), bool, bool, bool, fconj, (let ((_let_0 (fun int bool))) (let 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( (product_prod int int), (product_prod int int), int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_3 (fun int _let_2) (combc _let_1 int int) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))), (product_snd int int) ) 16.81/16.60 ( (product_prod int int), (product_prod int int), (fun int bool), (fun (product_prod int int) int), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (fequal int)))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun _let_1 _let_2))) (let ((_let_6 (fun _let_1 _let_4))) (hAPP _let_2 _let_5 (hAPP _let_6 (fun _let_2 _let_5) (combc _let_1 _let_2 _let_2) (hAPP _let_3 _let_6 (hAPP (fun _let_0 _let_4) (fun _let_3 _let_6) (combb _let_0 _let_4 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int))))))))) ) 16.81/16.60 ( (product_prod int int), (fun (product_prod int int) bool), (fun (product_prod int int) bool), (fun bool bool), (combb bool bool (product_prod int int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_2 _let_1))) (let ((_let_6 (fun _let_2 _let_0))) (hAPP _let_3 _let_5 (hAPP (fun bool _let_1) (fun _let_3 _let_5) (combb bool _let_1 _let_2) fconj) (hAPP _let_3 _let_3 (hAPP _let_1 (fun _let_3 _let_3) (combb bool bool _let_2) fNot) (hAPP int _let_3 (hAPP _let_6 (fun int _let_3) (combc _let_2 int bool) (hAPP _let_4 _let_6 (hAPP (fun int _let_0) (fun _let_4 _let_6) (combb int _let_0 _let_2) (fequal int)) (product_snd int int))) (zero_zero int))))))))))) ) 16.81/16.60 ( (product_prod int int), (fun (product_prod int int) int), (fun (product_prod int int) bool), (fun (product_prod int int) (fun int bool)), (combs (product_prod int int) int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 int))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun _let_3 _let_4))) (let ((_let_6 (fun _let_2 _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (fun _let_2 _let_3))) (let ((_let_9 (fun _let_2 _let_4))) (let ((_let_10 (fun _let_2 _let_7))) (hAPP _let_8 _let_9 (hAPP _let_5 (fun _let_8 _let_9) (combb _let_3 _let_4 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_3 _let_8 (hAPP _let_10 (fun _let_3 _let_8) (combc _let_2 _let_3 _let_3) (hAPP _let_6 _let_10 (hAPP (fun _let_1 _let_7) (fun _let_6 _let_10) (combb _let_1 _let_7 _let_2) (combb int int _let_2)) (hAPP _let_3 _let_6 (hAPP (fun int _let_1) (fun _let_3 _let_6) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int)))))))))))))) ) 16.81/16.60 ( (product_prod int int), (fun (product_prod int int) int), (fun (product_prod int int) int), (fun int int), (combb int int (product_prod int int)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))) ) 16.81/16.60 ) 16.81/16.60 (instantiation (let ((_let_0 (hAPP int (fun int int) (minus_minus int) min_1))) (forall ((L_4 $$unsorted)) (= (hAPP int int bit0 (hAPP int int _let_0 L_4)) (hAPP int int _let_0 (hAPP int int bit1 L_4))) )) 16.81/16.60 ( pls ) 16.81/16.60 ( (hAPP int int bit1 pls) ) 16.81/16.60 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.81/16.60 ( min_1 ) 16.81/16.60 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.81/16.60 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.81/16.60 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.81/16.60 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 16.81/16.60 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 16.81/16.60 ) 16.81/16.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110028 $$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_110028))) (= (hAPP nat X_a (semiring_1_of_nat X_a) (hAPP int nat nat_1 BOUND_VARIABLE_110028)) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_110028))) ) 16.81/16.60 ( real, (zero_zero int) ) 16.81/16.60 ( real, (one_one int) ) 16.81/16.60 ( int, (zero_zero int) ) 16.81/16.60 ( int, (one_one int) ) 16.81/16.60 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.60 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.81/16.60 ) 16.81/16.60 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((X $$unsorted) (Y $$unsorted)) (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)))) ))) 16.81/16.60 ( skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.60 ) 16.81/16.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110104 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (ti int BOUND_VARIABLE_110104) (hAPP X_a int (archim2085082626_floor X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_110104)))) ) 16.81/16.60 ( real, (zero_zero int) ) 16.81/16.60 ( real, (one_one int) ) 16.81/16.60 ) 16.81/16.60 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_110124 $$unsorted) (BOUND_VARIABLE_110125 $$unsorted)) (or (not (semiring_div X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_110125)) (= (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_110124) BOUND_VARIABLE_110125)) BOUND_VARIABLE_110125) (ti X_a BOUND_VARIABLE_110124))) )) 16.81/16.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.81/16.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 16.81/16.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.81/16.60 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.81/16.60 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.81/16.60 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 16.81/16.60 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.81/16.60 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1 ) 16.81/16.60 ( complex, ii, ii ) 16.81/16.60 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 16.81/16.60 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 16.81/16.61 ) 16.81/16.61 (instantiation (let ((_let_0 (combk X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (= _let_0 (ti (fun X_a (fun X_b X_a)) _let_0)) )) 16.81/16.61 ( bool, bool ) 16.81/16.61 ( bool, real ) 16.81/16.61 ( bool, nat ) 16.81/16.61 ( bool, (fun nat bool) ) 16.81/16.61 ( bool, int ) 16.81/16.61 ( bool, (fun int bool) ) 16.81/16.61 ( bool, (product_prod real real) ) 16.81/16.61 ( bool, (product_prod int int) ) 16.81/16.61 ( bool, (filter real) ) 16.81/16.61 ( bool, (filter nat) ) 16.81/16.61 ( bool, (product_prod nat nat) ) 16.81/16.61 ( bool, (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.81/16.61 ( bool, (fun nat rat) ) 16.81/16.61 ( bool, (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.81/16.61 ( real, real ) 16.81/16.61 ( real, nat ) 16.81/16.61 ( real, int ) 16.81/16.61 ( real, (fun real bool) ) 16.81/16.61 ( real, complex ) 16.81/16.61 ( real, rat ) 16.81/16.61 ( nat, real ) 16.81/16.61 ( nat, nat ) 16.81/16.61 ( nat, int ) 16.81/16.61 ( nat, complex ) 16.81/16.61 ( nat, quickcheck_code_int ) 16.81/16.61 ( nat, code_code_numeral ) 16.81/16.61 ( (fun nat bool), nat ) 16.81/16.61 ( (fun nat bool), (fun nat bool) ) 16.81/16.61 ( (fun nat bool), int ) 16.81/16.61 ( (fun nat bool), (fun nat real) ) 16.81/16.61 ( (fun nat nat), nat ) 16.81/16.61 ( (fun nat nat), int ) 16.81/16.61 ( (fun nat nat), code_code_numeral ) 16.81/16.61 ( int, nat ) 16.81/16.61 ( int, int ) 16.81/16.61 ( int, (fun int bool) ) 16.81/16.61 ( int, quickcheck_code_int ) 16.81/16.61 ( int, (product_prod int int) ) 16.81/16.61 ( int, code_code_numeral ) 16.81/16.61 ( (fun int bool), real ) 16.81/16.61 ( (fun int bool), int ) 16.81/16.61 ( (fun int bool), (fun int bool) ) 16.81/16.61 ( (fun int bool), (fun int int) ) 16.81/16.61 ( (fun int bool), (fun int (fun int bool)) ) 16.81/16.61 ( (fun int bool), (product_prod int int) ) 16.81/16.61 ( (fun int bool), (fun int real) ) 16.81/16.61 ( (fun int bool), (fun int (fun nat bool)) ) 16.81/16.61 ( (fun nat int), int ) 16.81/16.61 ( (fun real bool), real ) 16.81/16.61 ( (fun real bool), (fun real bool) ) 16.81/16.61 ( (fun real bool), (fun real (fun int bool)) ) 16.81/16.61 ( (fun real real), real ) 16.81/16.61 ( (fun real real), nat ) 16.81/16.61 ( (fun real real), int ) 16.81/16.61 ( (fun real real), (fun real real) ) 16.81/16.61 ( complex, real ) 16.81/16.61 ( complex, nat ) 16.81/16.61 ( complex, complex ) 16.81/16.61 ( (fun nat real), real ) 16.81/16.61 ( (fun nat real), (fun nat nat) ) 16.81/16.61 ( (fun nat real), int ) 16.81/16.61 ( (fun nat real), (fun nat real) ) 16.81/16.61 ( (fun int int), nat ) 16.81/16.61 ( (fun int int), int ) 16.81/16.61 ( (fun int int), (fun int int) ) 16.81/16.61 ( (fun int int), (product_prod int int) ) 16.81/16.61 ( rat, nat ) 16.81/16.61 ( rat, int ) 16.81/16.61 ( rat, (product_prod int int) ) 16.81/16.61 ( (fun int rat), int ) 16.81/16.61 ( (fun bool bool), bool ) 16.81/16.61 ( (fun bool bool), real ) 16.81/16.61 ( (fun bool bool), nat ) 16.81/16.61 ( (fun bool bool), int ) 16.81/16.61 ( (fun bool bool), (product_prod int int) ) 16.81/16.61 ( (fun int (fun bool bool)), int ) 16.81/16.61 ( (fun int (fun bool bool)), (fun int bool) ) 16.81/16.61 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), int ) 16.81/16.61 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (fun int (fun bool bool)) ) 16.81/16.61 ( (fun int (fun int bool)), real ) 16.81/16.61 ( (fun int (fun int bool)), int ) 16.81/16.61 ( (fun int (fun int bool)), (fun int bool) ) 16.81/16.61 ( (fun int (fun int bool)), (fun int int) ) 16.81/16.61 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 16.81/16.61 ( (fun int (fun int bool)), (fun int (fun int real)) ) 16.81/16.61 ( quickcheck_code_int, int ) 16.81/16.61 ( (fun nat (fun nat nat)), (fun nat nat) ) 16.81/16.61 ( (fun nat (fun real real)), (fun nat real) ) 16.81/16.61 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), int ) 16.81/16.61 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), (fun real real) ) 16.81/16.61 ( (fun real (fun real real)), (fun real real) ) 16.81/16.61 ( (fun nat (fun nat bool)), nat ) 16.81/16.61 ( (fun nat (fun nat bool)), (fun nat nat) ) 16.81/16.61 ( (product_prod real real), nat ) 16.81/16.61 ( (product_prod int int), nat ) 16.81/16.61 ( (product_prod int int), int ) 16.81/16.61 ( (product_prod int int), rat ) 16.81/16.61 ( (product_prod int int), (product_prod int int) ) 16.81/16.61 ( (fun int (product_prod int int)), int ) 16.81/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), int ) 16.81/16.61 ( (fun nat (product_prod int int)), nat ) 16.81/16.61 ( (fun (filter real) bool), real ) 16.81/16.61 ( (fun (fun int bool) bool), int ) 16.81/16.61 ( (fun real (fun real bool)), (fun real real) ) 16.81/16.61 ( (fun (filter nat) bool), real ) 16.81/16.61 ( (product_prod nat nat), nat ) 16.81/16.61 ( (fun (product_prod nat nat) bool), nat ) 16.81/16.61 ( (fun (product_prod nat nat) bool), (product_prod nat nat) ) 16.81/16.61 ( (fun nat (fun (product_prod nat nat) bool)), nat ) 16.81/16.61 ( (fun nat (product_prod nat nat)), nat ) 16.81/16.61 ( (fun (product_prod int int) bool), int ) 16.81/16.61 ( (fun (product_prod int int) bool), (product_prod int int) ) 16.81/16.61 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 16.81/16.61 ( (fun (product_prod int int) bool), (fun (product_prod int int) int) ) 16.81/16.61 ( (fun real complex), real ) 16.81/16.61 ( code_code_numeral, code_code_numeral ) 16.81/16.61 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), int ) 16.81/16.61 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), (fun nat (fun bool bool)) ) 16.81/16.61 ( (fun real (fun bool bool)), (fun real bool) ) 16.81/16.61 ( (product_prod int (product_prod int int)), int ) 16.81/16.61 ( (fun int (product_prod int (product_prod int int))), int ) 16.81/16.61 ( (fun (fun int int) (fun int bool)), int ) 16.81/16.61 ( (fun (fun int int) (fun int bool)), (fun int bool) ) 16.81/16.61 ( (fun int (fun (fun int int) (fun int bool))), (fun int (fun int bool)) ) 16.81/16.61 ( (fun int (fun int int)), (fun int bool) ) 16.81/16.61 ( (fun int (fun int int)), (fun int int) ) 16.81/16.61 ( (fun int (fun (product_prod int int) bool)), int ) 16.81/16.61 ( (fun int (fun (fun int bool) bool)), int ) 16.81/16.61 ( (list int), int ) 16.81/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.81/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 16.81/16.61 ( (fun nat (fun bool bool)), (fun nat bool) ) 16.81/16.61 ( (fun nat (fun bool bool)), int ) 16.81/16.61 ( (fun int (fun int (product_prod int (product_prod int int)))), int ) 16.81/16.61 ( (fun int (fun int (fun int (product_prod int (product_prod int int))))), int ) 16.81/16.61 ( (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))), int ) 16.81/16.61 ( (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))), int ) 16.81/16.61 ( (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))), int ) 16.81/16.61 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))), int ) 16.81/16.61 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), real ) 16.81/16.61 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (fun int (fun int (fun bool bool))) ) 16.81/16.61 ( (fun nat (product_prod real real)), real ) 16.81/16.61 ( (fun real (fun nat (product_prod real real))), real ) 16.81/16.61 ( (fun real (fun real (fun nat (product_prod real real)))), (fun (product_prod real real) bool) ) 16.81/16.61 ( (fun (product_prod int int) int), int ) 16.81/16.61 ( (fun (product_prod int int) int), (product_prod int int) ) 16.81/16.61 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 16.81/16.61 ( (fun int (fun int (fun int bool))), int ) 16.81/16.61 ( (fun int (fun int (fun int bool))), (fun int (fun int int)) ) 16.81/16.61 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 16.81/16.61 ( (product_prod code_code_numeral code_code_numeral), code_code_numeral ) 16.81/16.61 ( (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)), code_code_numeral ) 16.81/16.61 ( (fun int real), int ) 16.81/16.61 ( (fun int real), (fun int real) ) 16.81/16.61 ( (fun real (fun int bool)), (fun real (fun int (fun int bool))) ) 16.81/16.61 ( (fun real (fun int bool)), (fun real (fun int (fun nat bool))) ) 16.81/16.61 ( (fun real (fun int (fun int bool))), (fun int bool) ) 16.81/16.61 ( (fun real (fun int (fun int bool))), (fun int (fun int real)) ) 16.81/16.61 ( (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))), real ) 16.81/16.61 ( (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))) ) 16.81/16.61 ( (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)))) ) 16.81/16.61 ( (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun int (fun bool bool)))) ) 16.81/16.61 ( (fun int (fun int (fun bool bool))), real ) 16.81/16.61 ( (fun int (fun int (fun bool bool))), (fun int (fun int bool)) ) 16.81/16.61 ( (fun real (fun int (fun int (fun bool bool)))), (fun real (fun int (fun int bool))) ) 16.81/16.61 ( (fun int (fun int real)), (fun int real) ) 16.81/16.61 ( (fun (fun int (fun int real)) (fun int (fun int bool))), real ) 16.81/16.61 ( (fun (fun int (fun int real)) (fun int (fun int bool))), (fun (fun int real) (fun int bool)) ) 16.81/16.61 ( (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (fun real (fun (fun int real) (fun int bool))) ) 16.81/16.61 ( (fun (fun int real) (fun int bool)), real ) 16.81/16.61 ( (fun (fun int real) (fun int bool)), (fun real bool) ) 16.81/16.61 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun real bool)) ) 16.81/16.61 ( (let ((_let_0 (fun int real))) (fun _let_0 _let_0)), int ) 16.81/16.61 ( (let ((_let_0 (fun int real))) (fun _let_0 _let_0)), (fun real real) ) 16.81/16.61 ( (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)) ) 16.81/16.61 ( (fun int (fun real real)), (fun int real) ) 16.81/16.61 ( (let ((_let_0 (fun int int))) (fun _let_0 _let_0)), int ) 16.81/16.61 ( (let ((_let_0 (fun int int))) (fun _let_0 _let_0)), (fun int int) ) 16.81/16.61 ( (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (fun int (fun int int)) ) 16.81/16.61 ( (fun (product_prod int int) (fun bool bool)), (fun (product_prod int int) bool) ) 16.81/16.61 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (fun bool bool) ) 16.81/16.61 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (product_prod int int) ) 16.81/16.61 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))), (product_prod int int) ) 16.81/16.61 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))), (fun (product_prod int int) (fun int bool)) ) 16.81/16.61 ( (fun (product_prod int int) (fun int bool)), (product_prod int int) ) 16.81/16.61 ( (fun (product_prod int int) (fun int bool)), (fun (product_prod int int) int) ) 16.81/16.61 ( (fun (product_prod int int) (fun int int)), (fun (product_prod int int) int) ) 16.81/16.61 ( (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)), (fun int int) ) 16.81/16.61 ( (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)), (product_prod int int) ) 16.81/16.61 ( (product_prod quickcheck_code_int quickcheck_code_int), quickcheck_code_int ) 16.81/16.61 ( (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)), quickcheck_code_int ) 16.81/16.61 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (fun (product_prod int int) (fun bool bool)) ) 16.81/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (fun (product_prod int int) int) ) 16.81/16.61 ( (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)))) ) 16.81/16.61 ( (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))) ) 16.81/16.61 ( (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)) ) 16.81/16.61 ( (fun int (fun nat bool)), real ) 16.81/16.61 ( (fun int (fun nat bool)), (fun nat bool) ) 16.81/16.61 ( (fun int (fun nat bool)), (fun int (fun nat real)) ) 16.81/16.61 ( (fun real (fun int (fun nat bool))), (fun nat bool) ) 16.81/16.61 ( (fun real (fun int (fun nat bool))), (fun int (fun nat real)) ) 16.81/16.61 ( (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))), real ) 16.81/16.61 ( (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 16.81/16.61 ( (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 16.81/16.61 ( (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), real ) 16.81/16.61 ( (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), (fun int (fun nat (fun bool bool))) ) 16.81/16.61 ( (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun nat (fun bool bool)))) ) 16.81/16.61 ( (fun int (fun nat (fun bool bool))), real ) 16.81/16.61 ( (fun int (fun nat (fun bool bool))), (fun int (fun nat bool)) ) 16.81/16.61 ( (fun real (fun int (fun nat (fun bool bool)))), (fun real (fun int (fun nat bool))) ) 16.81/16.61 ( (fun int (fun nat real)), (fun nat real) ) 16.81/16.61 ( (fun (fun int (fun nat real)) (fun int (fun nat bool))), real ) 16.81/16.61 ( (fun (fun int (fun nat real)) (fun int (fun nat bool))), (fun (fun nat real) (fun nat bool)) ) 16.81/16.61 ( (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (fun real (fun (fun nat real) (fun nat bool))) ) 16.81/16.61 ( (fun (fun nat real) (fun nat bool)), real ) 16.81/16.61 ( (fun (fun nat real) (fun nat bool)), (fun real bool) ) 16.81/16.61 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun real bool)) ) 16.81/16.61 ( (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)) ) 16.81/16.61 ) 16.81/16.61 (instantiation (let ((_let_0 (fun int bool))) (forall ((Ma $$unsorted)) (= (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)) )) 16.81/16.61 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.61 ) 16.81/16.61 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (hAPP real _let_0 _let_1 A_2))) (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 B_1))) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) B_1))) (not (forall ((Y_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X_2) Y_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_2) (zero_zero real))))) ))) )) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real F B_1)) (hAPP real real F A_2)))) )))) 16.81/16.61 ( sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 16.81/16.61 ( cos, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.61 ) 16.81/16.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110205 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_110205)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_110205))))) ) 16.81/16.61 ( real, pi ) 16.81/16.61 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.61 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.61 ( real, skv_2 ) 16.81/16.61 ( real, skv_10 ) 16.81/16.61 ( real, skv_13 ) 16.81/16.61 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.61 ( int, (zero_zero int) ) 16.81/16.61 ( int, (one_one int) ) 16.81/16.61 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.61 ( int, min_1 ) 16.81/16.61 ) 16.81/16.61 (instantiation (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP nat bool (even_odd_even nat) X_1)) (not (forall ((Y_2 $$unsorted)) (not (= X_1 (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat)))) Y_2))) ))) ) 16.81/16.61 ( (zero_zero nat) ) 16.81/16.61 ( (one_one nat) ) 16.81/16.61 ) 16.81/16.61 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP int bool twoSqu1091635170sum2sq X))) (not (hBOOL (hAPP int bool twoSqu1091635170sum2sq Y))) (hBOOL (hAPP int bool twoSqu1091635170sum2sq (hAPP int int (hAPP int (fun int int) (times_times int) X) Y)))) ) 16.81/16.61 ( (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.61 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.61 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.62 ( skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.62 ) 16.81/16.62 (instantiation (let ((_let_0 (hAPP real (fun real real) (times_times real) C_1))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (or (= (zero_zero real) C_1) (= (= A_2 B_1) (= (hAPP real real _let_0 B_1) (hAPP real real _let_0 A_2)))) )) 16.81/16.62 ( pi, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.62 ( pi, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.81/16.62 ( pi, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.62 ( (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.62 ( (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.62 ) 16.81/16.62 (instantiation (let ((_let_0 (archim2085082626_floor X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_110368 $$unsorted) (BOUND_VARIABLE_110369 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP X_a int _let_0 BOUND_VARIABLE_110368)) (hAPP int int (number_number_of int) BOUND_VARIABLE_110369)) (hAPP X_a int _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_110368) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_110369))))) )) 16.81/16.62 ( nat, (one_one nat), (hAPP int int bit1 pls) ) 16.81/16.62 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (hAPP int int bit1 pls) ) 16.81/16.62 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int bit1 pls) ) 16.81/16.62 ) 16.81/16.62 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_110395 $$unsorted)) (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_110395) (ring_1_Ints X_a)))) (= (= _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_110395) BOUND_VARIABLE_110395)) (= _let_1 (ti X_a BOUND_VARIABLE_110395)))) ))) 16.81/16.62 ( bool, fFalse ) 16.81/16.62 ( bool, fTrue ) 16.81/16.62 ( real, pi ) 16.81/16.62 ( nat, (one_one nat) ) 16.81/16.62 ( (fun nat bool), (even_odd_even nat) ) 16.81/16.62 ( (fun nat bool), prime ) 16.81/16.62 ( (fun nat nat), suc ) 16.81/16.62 ( (fun nat nat), (fact_fact nat) ) 16.81/16.62 ( (fun nat nat), (size_size nat) ) 16.81/16.62 ( (fun nat nat), fact ) 16.81/16.62 ( (fun nat nat), nat_size ) 16.81/16.62 ( int, pls ) 16.81/16.62 ( int, m ) 16.81/16.62 ( 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) ) 16.81/16.62 ( int, (one_one int) ) 16.81/16.62 ( int, min_1 ) 16.81/16.62 ( int, s ) 16.81/16.62 ( 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)))) ) 16.81/16.62 ( int, s1 ) 16.81/16.62 ( int, t ) 16.81/16.62 ( (fun int bool), zprime ) 16.81/16.62 ( (fun int bool), nat_neg ) 16.81/16.62 ( (fun int bool), zEven ) 16.81/16.62 ( (fun int bool), nat_is_nat ) 16.81/16.62 ( (fun int bool), zOdd ) 16.81/16.62 ( (fun int bool), (even_odd_even int) ) 16.81/16.62 ( (fun int bool), twoSqu1091635170sum2sq ) 16.81/16.62 ( (fun int nat), nat_1 ) 16.81/16.62 ( (fun int nat), phi ) 16.81/16.62 ( (fun real real), sqrt ) 16.81/16.62 ( (fun real real), tan ) 16.81/16.62 ( (fun real real), cos ) 16.81/16.62 ( (fun real real), arccos ) 16.81/16.62 ( (fun real real), ln ) 16.81/16.62 ( (fun real real), sin ) 16.81/16.62 ( (fun real real), arctan ) 16.81/16.62 ( (fun real real), arcsin ) 16.81/16.62 ( complex, ii ) 16.81/16.62 ( (fun complex complex), cnj ) 16.81/16.62 ( (fun complex complex), expi ) 16.81/16.62 ( (fun nat real), (real_1 nat) ) 16.81/16.62 ( (fun nat real), cos_coeff ) 16.81/16.62 ( (fun nat real), sin_coeff ) 16.81/16.62 ( (fun int int), bit0 ) 16.81/16.62 ( (fun int int), bit1 ) 16.81/16.62 ( (fun int int), pred ) 16.81/16.62 ( (fun int int), succ ) 16.81/16.62 ( (fun int int), (fact_fact int) ) 16.81/16.62 ( (fun int int), zfact ) 16.81/16.62 ( (fun bool bool), fNot ) 16.81/16.62 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.81/16.62 ( (fun bool (fun bool bool)), fconj ) 16.81/16.62 ( (fun bool (fun bool bool)), fdisj ) 16.81/16.62 ( (fun bool (fun bool bool)), fimplies ) 16.81/16.62 ( (fun int (fun int bool)), sRStar ) 16.81/16.62 ( (fun int (fun int bool)), quadRes ) 16.81/16.62 ( (fun int (fun int bool)), norRRset ) 16.81/16.62 ( (fun int (fun int bool)), d22set ) 16.81/16.62 ( (fun int (fun int bool)), sr ) 16.81/16.62 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.81/16.62 ( (fun nat (fun nat nat)), nat_gcd ) 16.81/16.62 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.81/16.62 ( (fun nat (fun nat nat)), nat_lcm ) 16.81/16.62 ( (fun nat (fun real real)), root ) 16.81/16.62 ( (fun real (fun real real)), log ) 16.81/16.62 ( (fun real (fun real real)), powr ) 16.81/16.62 ( (fun nat (fun nat bool)), coprime ) 16.81/16.62 ( (fun (fun int bool) int), (the int) ) 16.81/16.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.81/16.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.81/16.62 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.81/16.62 ( (fun (fun int bool) bool), nat_nat_set ) 16.81/16.62 ( (filter nat), sequentially ) 16.81/16.62 ( (fun (product_prod nat nat) bool), pred_nat ) 16.81/16.62 ( (fun (product_prod int int) bool), frac_1 ) 16.81/16.62 ( (fun real complex), cis ) 16.81/16.62 ( (fun complex real), im ) 16.81/16.62 ( (fun complex real), re ) 16.81/16.62 ( (fun complex real), arg ) 16.81/16.62 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.81/16.62 ( (fun int (fun int int)), int_gcd ) 16.81/16.62 ( (fun int (fun int int)), multInv ) 16.81/16.62 ( (fun int (fun int int)), legacy_zgcd ) 16.81/16.62 ( (fun int (fun int int)), z3mod ) 16.81/16.62 ( (fun int (fun int int)), inv ) 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(BOUND_VARIABLE_110431 $$unsorted) (BOUND_VARIABLE_110432 $$unsorted) (BOUND_VARIABLE_110433 $$unsorted)) (or (not (field_inverse_zero X_a)) (= (and (or (not _let_2) (= _let_0 _let_3)) (or _let_2 (= (ti X_a BOUND_VARIABLE_110431) (hAPP X_a X_a (hAPP X_a _let_1 (times_times X_a) BOUND_VARIABLE_110433) BOUND_VARIABLE_110432)))) (= _let_3 (hAPP X_a X_a (hAPP X_a _let_1 (inverse_divide X_a) BOUND_VARIABLE_110431) BOUND_VARIABLE_110432)))) ))))) 16.81/16.62 ( bool, fFalse, fFalse, fFalse ) 16.81/16.62 ( bool, fTrue, fTrue, fTrue ) 16.81/16.62 ( real, pi, pi, pi ) 16.81/16.62 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat), (even_odd_even nat) ) 16.81/16.62 ( (fun nat bool), prime, prime, prime ) 16.81/16.62 ( (fun nat nat), suc, suc, suc ) 16.81/16.62 ( (fun nat nat), (fact_fact nat), (fact_fact nat), (fact_fact nat) ) 16.81/16.62 ( (fun nat nat), (size_size nat), (size_size nat), (size_size nat) ) 16.81/16.62 ( (fun nat nat), fact, fact, fact ) 16.81/16.62 ( (fun nat nat), nat_size, nat_size, nat_size ) 16.81/16.62 ( int, pls, pls, pls ) 16.81/16.62 ( int, m, m, m ) 16.81/16.62 ( int, min_1, min_1, min_1 ) 16.81/16.62 ( int, s, s, s ) 16.81/16.62 ( int, s1, s1, s1 ) 16.81/16.62 ( int, t, t, t ) 16.81/16.62 ( (fun int bool), zprime, zprime, zprime ) 16.81/16.62 ( (fun int bool), nat_neg, nat_neg, nat_neg ) 16.81/16.62 ( (fun int bool), zEven, zEven, zEven ) 16.81/16.62 ( (fun int bool), nat_is_nat, nat_is_nat, nat_is_nat ) 16.81/16.62 ( (fun int bool), zOdd, zOdd, zOdd ) 16.81/16.62 ( (fun int bool), (even_odd_even int), (even_odd_even int), (even_odd_even int) ) 16.81/16.62 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 16.81/16.62 ( (fun int nat), nat_1, nat_1, nat_1 ) 16.81/16.62 ( (fun int nat), phi, phi, phi ) 16.81/16.62 ( (fun real real), sqrt, sqrt, sqrt ) 16.81/16.62 ( (fun real real), tan, tan, tan ) 16.81/16.62 ( (fun real real), cos, cos, cos ) 16.81/16.62 ( (fun real real), arccos, arccos, arccos ) 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16.81/16.62 ( (fun real (fun real real)), powr, powr, powr ) 16.81/16.62 ( (fun nat (fun nat bool)), coprime, coprime, coprime ) 16.81/16.62 ( (fun (fun int bool) int), (the int), (the int), (the int) ) 16.81/16.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, normalize, normalize ) 16.81/16.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, negateSnd, negateSnd ) 16.81/16.62 ( (fun nat (fun nat (product_prod int int))), bezw, bezw, bezw ) 16.81/16.62 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set, nat_nat_set ) 16.81/16.62 ( (filter nat), sequentially, sequentially, sequentially ) 16.81/16.62 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat, pred_nat ) 16.81/16.62 ( (fun (product_prod int int) bool), frac_1, frac_1, frac_1 ) 16.81/16.62 ( (fun real complex), cis, cis, cis ) 16.81/16.62 ( (fun complex real), im, im, im ) 16.81/16.62 ( (fun complex real), re, re, re ) 16.81/16.62 ( (fun complex real), arg, arg, arg ) 16.81/16.62 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral, code_S1047413653umeral ) 16.81/16.62 ( (fun int (fun int int)), int_gcd, int_gcd, int_gcd ) 16.81/16.62 ( (fun int (fun int int)), multInv, multInv, multInv ) 16.81/16.62 ( (fun int (fun int int)), legacy_zgcd, legacy_zgcd, legacy_zgcd ) 16.81/16.62 ( (fun int (fun int int)), z3mod, z3mod, z3mod ) 16.81/16.62 ( (fun int (fun int int)), inv, inv, inv ) 16.81/16.62 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int), (gcd_gcd int) ) 16.81/16.62 ( (fun int (fun int int)), standardRes, standardRes, standardRes ) 16.81/16.62 ( (fun int (fun int int)), legendre, legendre, legendre ) 16.81/16.62 ( (fun int (fun int int)), nat_tsub, nat_tsub, nat_tsub ) 16.81/16.62 ( (fun int (fun int int)), z3div, z3div, z3div ) 16.81/16.62 ( (fun int (fun int int)), int_lcm, int_lcm, int_lcm ) 16.81/16.62 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than2, 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(fun (product_prod _let_0 _let_0) bool)), pair_less, pair_less, pair_less ) 16.81/16.63 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_leq, pair_leq ) 16.81/16.63 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel, divmod_int_rel ) 16.81/16.63 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd, xzgcd ) 16.81/16.63 ( (fun int (fun int (product_prod int int))), negDivAlg, negDivAlg, negDivAlg ) 16.81/16.63 ( (fun int (fun int (product_prod int int))), divmod_int, divmod_int, divmod_int ) 16.81/16.63 ( (fun int (fun int (product_prod int int))), posDivAlg, posDivAlg, posDivAlg ) 16.81/16.63 ( (fun int (fun int (product_prod int int))), pdivmod, pdivmod, pdivmod ) 16.81/16.63 ( (fun int (fun int (product_prod int int))), norm_frac, norm_frac, norm_frac ) 16.81/16.63 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust, adjust ) 16.81/16.63 ( (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 ) 16.81/16.63 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 16.81/16.63 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 16.81/16.63 ( (fun real nat), natfloor, natfloor, natfloor ) 16.81/16.63 ( (fun real nat), natceiling, natceiling, natceiling ) 16.81/16.63 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int, quickcheck_of_int ) 16.81/16.63 ( (fun int (fun int (fun int bool))), wset, wset, wset ) 16.81/16.63 ( (fun int (fun int (fun int bool))), bnorRset, bnorRset, bnorRset ) 16.81/16.63 ( (fun int (fun int (fun int bool))), zcong, zcong, zcong ) 16.81/16.63 ( (fun int (fun int (fun int bool))), noXRRset, noXRRset, noXRRset ) 16.81/16.63 ( (fun int (fun int (fun int bool))), zcongm, zcongm, zcongm ) 16.81/16.63 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair, multInvPair ) 16.81/16.63 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS, setS ) 16.81/16.63 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral, code_d418564891umeral ) 16.81/16.63 ( (fun int real), (real_1 int), (real_1 int), (real_1 int) ) 16.81/16.63 ( (fun complex nat), (size_size complex), (size_size complex), (size_size complex) ) 16.81/16.63 ( (fun complex nat), complex_size, complex_size, complex_size ) 16.81/16.63 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero, quickc666637781d_zero ) 16.81/16.63 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel, divmod_nat_rel ) 16.81/16.63 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel, ratrel ) 16.81/16.63 ( (fun 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int (fun nat nat)), nat_aux, nat_aux, nat_aux ) 16.81/16.63 ( (fun rat real), ratreal, ratreal, ratreal ) 16.81/16.63 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of, quickcheck_int_of ) 16.81/16.63 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int, quickc495462417de_int ) 16.81/16.63 ( (fun rat (product_prod int int)), quotient_of, quotient_of, quotient_of ) 16.81/16.63 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR, rRset2norRR ) 16.81/16.63 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 16.81/16.63 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of, quickcheck_nat_of ) 16.81/16.63 ( (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 ) 16.81/16.63 ) 16.81/16.63 (instantiation (forall ((X_2 $$unsorted)) (or (hBOOL (hAPP nat bool (even_odd_even nat) X_2)) (= (zero_zero real) (hAPP nat real cos_coeff X_2))) ) 16.81/16.63 ( (zero_zero nat) ) 16.81/16.63 ( (one_one nat) ) 16.81/16.63 ) 16.81/16.63 (instantiation (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) X_2))) (= (hAPP nat real cos_coeff X_2) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) (hAPP nat nat (hAPP nat (fun nat nat) (div_div nat) X_2) (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_2))))) ) 16.81/16.63 ( (zero_zero nat) ) 16.81/16.63 ( (hAPP nat nat suc (zero_zero nat)) ) 16.81/16.63 ( (one_one nat) ) 16.81/16.63 ) 16.81/16.63 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110475 $$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_110475) (zero_zero X_a)))) (= (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_110475) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_110475))) ) 16.81/16.63 ( real, (zero_zero real) ) 16.81/16.63 ( real, (one_one real) ) 16.81/16.63 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.63 ( 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)))) ) 16.81/16.63 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.81/16.63 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.63 ( real, skv_14 ) 16.81/16.63 ( int, (zero_zero int) ) 16.81/16.63 ( int, pls ) 16.81/16.63 ( int, (one_one int) ) 16.81/16.63 ( int, min_1 ) 16.81/16.63 ( complex, ii ) 16.81/16.63 ( complex, (one_one complex) ) 16.81/16.63 ) 16.81/16.63 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted)) (or (not (field_inverse_zero X_a)) (= _let_0 (hAPP X_a X_a (inverse_inverse X_a) _let_0))) )) 16.81/16.63 ( real ) 16.81/16.63 ( nat ) 16.81/16.63 ( int ) 16.81/16.63 ( complex ) 16.81/16.63 ( rat ) 16.81/16.63 ( quickcheck_code_int ) 16.81/16.63 ( code_code_numeral ) 16.81/16.63 ) 16.81/16.63 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int (fun int bool) (dvd_dvd int) K))) (forall ((Ma $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (or (not (= (one_one int) (hAPP int int (hAPP int _let_0 (gcd_gcd int) K) N_1))) (= (hBOOL (hAPP int bool _let_1 Ma)) (hBOOL (hAPP int bool _let_1 (hAPP int int (hAPP int _let_0 (times_times int) Ma) N_1))))) ))) 16.81/16.63 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_1 ) 16.81/16.63 ) 16.81/16.63 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_110538 $$unsorted) (BOUND_VARIABLE_110539 $$unsorted) (BOUND_VARIABLE_110540 $$unsorted)) (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_110538) BOUND_VARIABLE_110539))) BOUND_VARIABLE_110540) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP int X_a _let_2 BOUND_VARIABLE_110538)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP int X_a _let_2 BOUND_VARIABLE_110539)) BOUND_VARIABLE_110540)))) )))) 16.81/16.63 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 16.81/16.63 ) 16.81/16.63 (instantiation (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))) (let ((_let_6 (ti X_a BOUND_VARIABLE_110588))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_110583 $$unsorted) (BOUND_VARIABLE_110584 $$unsorted) (BOUND_VARIABLE_110585 $$unsorted) (BOUND_VARIABLE_110586 $$unsorted) (BOUND_VARIABLE_110587 $$unsorted) (BOUND_VARIABLE_110588 $$unsorted)) (or (not (topological_space X_b)) (not (topological_space X_a)) (not (= _let_6 (ti X_a BOUND_VARIABLE_110587))) (not (forall ((X_2 $$unsorted)) (or (= (ti X_a X_2) _let_6) (= (hAPP X_a X_b BOUND_VARIABLE_110586 X_2) (hAPP X_a X_b BOUND_VARIABLE_110585 X_2))) )) (not (= (ti X_b BOUND_VARIABLE_110584) (ti X_b BOUND_VARIABLE_110583))) (= (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_110586) BOUND_VARIABLE_110584) (hAPP X_a _let_0 _let_5 BOUND_VARIABLE_110588))) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_110585) BOUND_VARIABLE_110583) (hAPP X_a _let_0 _let_5 BOUND_VARIABLE_110587))))) )))))))) 16.81/16.63 ( real, real, pi, pi, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), pi, pi ) 16.81/16.63 ) 16.81/16.63 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (inverse_inverse X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_110637 $$unsorted)) (or (not (real_normed_field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_110637)) (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_110637) (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_110637)) (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat)))))))) ))) 16.81/16.63 ( bool, fFalse ) 16.81/16.63 ( bool, fTrue ) 16.81/16.63 ( real, (zero_zero real) ) 16.81/16.63 ( real, pi ) 16.81/16.63 ( (fun nat bool), (even_odd_even nat) ) 16.81/16.63 ( (fun nat bool), prime ) 16.81/16.63 ( (fun nat nat), suc ) 16.81/16.63 ( (fun nat nat), (fact_fact nat) ) 16.81/16.63 ( (fun nat nat), (size_size nat) ) 16.81/16.63 ( (fun nat nat), fact ) 16.81/16.63 ( (fun nat nat), nat_size ) 16.81/16.63 ( int, pls ) 16.81/16.63 ( int, m ) 16.81/16.63 ( int, min_1 ) 16.81/16.63 ( int, s ) 16.81/16.63 ( int, s1 ) 16.81/16.63 ( int, t ) 16.81/16.63 ( (fun int bool), zprime ) 16.81/16.63 ( (fun int bool), nat_neg ) 16.81/16.63 ( (fun int bool), zEven ) 16.81/16.63 ( (fun int bool), nat_is_nat ) 16.81/16.63 ( (fun int bool), zOdd ) 16.81/16.63 ( (fun int bool), (even_odd_even int) ) 16.81/16.63 ( (fun int bool), twoSqu1091635170sum2sq ) 16.81/16.63 ( (fun int nat), nat_1 ) 16.81/16.63 ( (fun int nat), phi ) 16.81/16.63 ( (fun real real), sqrt ) 16.81/16.63 ( (fun real real), tan ) 16.81/16.63 ( (fun real real), cos ) 16.81/16.63 ( (fun real real), arccos ) 16.81/16.63 ( (fun real real), ln ) 16.81/16.63 ( (fun real real), sin ) 16.81/16.63 ( (fun real real), arctan ) 16.81/16.63 ( (fun real real), arcsin ) 16.81/16.63 ( complex, ii ) 16.81/16.63 ( (fun complex complex), cnj ) 16.81/16.63 ( (fun complex complex), expi ) 16.81/16.63 ( (fun nat real), (real_1 nat) ) 16.81/16.63 ( (fun nat real), cos_coeff ) 16.81/16.63 ( (fun nat real), sin_coeff ) 16.81/16.63 ( (fun int int), bit0 ) 16.81/16.63 ( (fun int int), bit1 ) 16.81/16.63 ( (fun int int), pred ) 16.81/16.63 ( (fun int int), succ ) 16.81/16.63 ( (fun int int), (fact_fact int) ) 16.81/16.63 ( (fun int int), zfact ) 16.81/16.63 ( (fun bool bool), fNot ) 16.81/16.63 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.81/16.63 ( (fun bool (fun bool bool)), fconj ) 16.81/16.63 ( (fun bool (fun bool bool)), fdisj ) 16.81/16.63 ( (fun bool (fun bool bool)), fimplies ) 16.81/16.63 ( (fun int (fun int bool)), sRStar ) 16.81/16.63 ( (fun int (fun int bool)), quadRes ) 16.81/16.63 ( (fun int (fun int bool)), norRRset ) 16.81/16.63 ( (fun int (fun int bool)), d22set ) 16.81/16.63 ( (fun int (fun int bool)), sr ) 16.81/16.63 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.81/16.63 ( (fun nat (fun nat nat)), nat_gcd ) 16.81/16.63 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.81/16.63 ( (fun nat (fun nat nat)), nat_lcm ) 16.81/16.63 ( (fun nat (fun real real)), root ) 16.81/16.63 ( (fun real (fun real real)), log ) 16.81/16.63 ( (fun real (fun real real)), powr ) 16.81/16.63 ( (fun nat (fun nat bool)), coprime ) 16.81/16.63 ( (fun (fun int bool) int), (the int) ) 16.81/16.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.81/16.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.81/16.63 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.81/16.63 ( (fun (fun int bool) bool), nat_nat_set ) 16.81/16.63 ( (filter nat), sequentially ) 16.81/16.63 ( (fun (product_prod nat nat) bool), pred_nat ) 16.81/16.63 ( (fun (product_prod int int) bool), frac_1 ) 16.81/16.63 ( (fun real complex), cis ) 16.81/16.63 ( (fun complex real), im ) 16.81/16.63 ( (fun complex real), re ) 16.81/16.63 ( (fun complex real), arg ) 16.81/16.63 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.81/16.63 ( (fun int (fun int int)), int_gcd ) 16.81/16.63 ( (fun int (fun int int)), multInv ) 16.81/16.63 ( (fun int (fun int int)), legacy_zgcd ) 16.81/16.63 ( (fun int (fun int int)), z3mod ) 16.81/16.63 ( (fun int (fun int int)), inv ) 16.81/16.63 ( (fun int (fun int int)), (gcd_gcd int) ) 16.81/16.63 ( (fun int (fun int int)), standardRes ) 16.81/16.63 ( (fun int (fun int int)), legendre ) 16.81/16.63 ( (fun int (fun int int)), nat_tsub ) 16.81/16.63 ( (fun int (fun int int)), z3div ) 16.81/16.63 ( (fun int (fun int int)), int_lcm ) 16.81/16.63 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.81/16.63 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.81/16.63 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.81/16.63 ( (fun int (fun (fun int bool) bool)), resSet ) 16.81/16.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.81/16.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.81/16.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.81/16.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.81/16.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.81/16.63 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.81/16.63 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.81/16.63 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.81/16.63 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.81/16.63 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.81/16.63 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.81/16.63 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.81/16.63 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.81/16.63 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.81/16.63 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.81/16.63 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.81/16.63 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.81/16.63 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.81/16.63 ( (fun real nat), natfloor ) 16.81/16.63 ( (fun real nat), natceiling ) 16.81/16.63 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.81/16.63 ( (fun int (fun int (fun int bool))), wset ) 16.81/16.63 ( (fun int (fun int (fun int bool))), bnorRset ) 16.81/16.63 ( (fun int (fun int (fun int bool))), zcong ) 16.81/16.63 ( (fun int (fun int (fun int bool))), noXRRset ) 16.81/16.63 ( (fun int (fun int (fun int bool))), zcongm ) 16.81/16.63 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.81/16.63 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.81/16.63 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.81/16.63 ( (fun int real), (real_1 int) ) 16.81/16.63 ( (fun complex nat), (size_size complex) ) 16.81/16.63 ( (fun complex nat), complex_size ) 16.81/16.63 ( (fun int (list int)), quickc666637781d_zero ) 16.81/16.63 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.81/16.63 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.81/16.63 ( (fun (product_prod int int) rat), frct ) 16.81/16.63 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.81/16.63 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.81/16.63 ( (fun (fun nat rat) bool), vanishes ) 16.81/16.63 ( (fun int (fun int rat)), fract ) 16.81/16.63 ( (fun code_code_numeral int), code_int_of ) 16.81/16.63 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.81/16.63 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.81/16.63 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.81/16.63 ( (fun real (fun real complex)), complex_1 ) 16.81/16.63 ( (fun real (fun real complex)), rcis ) 16.81/16.63 ( (fun int (fun nat nat)), nat_aux ) 16.81/16.63 ( (fun rat real), ratreal ) 16.81/16.63 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.81/16.63 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.81/16.63 ( (fun rat (product_prod int int)), quotient_of ) 16.81/16.63 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.81/16.63 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.81/16.63 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.81/16.63 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.81/16.63 ) 16.81/16.63 (instantiation (let ((_let_0 (zero_zero real))) (forall ((X $$unsorted)) (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)))) )) 16.81/16.63 ( (zero_zero real) ) 16.81/16.63 ( (one_one real) ) 16.81/16.63 ( pi ) 16.81/16.63 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.63 ( (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)))) ) 16.81/16.64 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.81/16.64 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.64 ( skv_2 ) 16.81/16.64 ( skv_10 ) 16.81/16.64 ( skv_13 ) 16.81/16.64 ) 16.81/16.64 (instantiation (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)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_110733 $$unsorted) (BOUND_VARIABLE_110734 $$unsorted)) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_110734))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_110733))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_110733) (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_110734) BOUND_VARIABLE_110733)) BOUND_VARIABLE_110734))) )))) 16.81/16.64 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.64 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.81/16.64 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.64 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.64 ( int, (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.64 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.64 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.64 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.64 ( complex, ii, ii ) 16.81/16.64 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.81/16.64 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.64 ) 16.81/16.64 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_110764 $$unsorted) (BOUND_VARIABLE_110765 $$unsorted)) (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_110764) suc)) BOUND_VARIABLE_110765))) (hBOOL (hAPP X_a bool (hAPP _let_1 _let_2 _let_3 BOUND_VARIABLE_110764) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_110765) (hAPP nat X_a BOUND_VARIABLE_110764 (zero_zero nat)))))) ))))) 16.81/16.64 ( real, (hAPP real (fun nat real) (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (one_one real) ) 16.81/16.64 ( nat, (fact_fact nat), (one_one nat) ) 16.81/16.64 ) 16.81/16.64 (instantiation (let ((_let_0 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_1 (hAPP int int (number_number_of int) _let_0))) (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_1) P_5))) (= (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) P_5) _let_1)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat nat_1 P_5)) (hAPP int nat (number_number_of nat) _let_0)))) ))) 16.81/16.64 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.64 ) 16.81/16.64 (instantiation (let ((_let_0 (fun real complex))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP real complex (hAPP real _let_0 complex_1 A_1) B)) ii) (hAPP real complex (hAPP real _let_0 complex_1 (hAPP real real (uminus_uminus real) B)) A_1)) )) 16.81/16.64 ( (zero_zero real), (zero_zero real) ) 16.81/16.64 ( (zero_zero real), (one_one real) ) 16.81/16.64 ( (one_one real), (zero_zero real) ) 16.81/16.64 ) 16.81/16.64 (instantiation (let ((_let_0 (ring_1_of_int X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_110833 $$unsorted)) (or (not (ring_1 X_a)) (= (hAPP int X_a _let_0 (hAPP int int (uminus_uminus int) BOUND_VARIABLE_110833)) (hAPP X_a X_a (uminus_uminus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_110833)))) )) 16.81/16.64 ( real, pls ) 16.81/16.64 ( real, (one_one int) ) 16.81/16.64 ) 16.81/16.64 (instantiation (let ((_let_0 (fun int bool))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (one_one int)) B_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B_1) A_2))) (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) B_1) (hAPP int _let_0 d22set A_2)))) )) 16.81/16.64 ( pls, min_1 ) 16.81/16.64 ( (one_one int), (zero_zero int) ) 16.81/16.64 ( min_1, (zero_zero int) ) 16.81/16.64 ( min_1, min_1 ) 16.81/16.64 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 16.81/16.64 ( s, (zero_zero int) ) 16.81/16.64 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 16.81/16.64 ( t, (one_one int) ) 16.81/16.64 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 16.81/16.64 ( skv_3, (zero_zero int) ) 16.81/16.64 ( skv_9, (zero_zero int) ) 16.81/16.64 ) 16.81/16.64 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_110970 $$unsorted) (BOUND_VARIABLE_110971 $$unsorted) (BOUND_VARIABLE_110972 $$unsorted)) (or (not (ord X_a)) (not (= (ti X_a BOUND_VARIABLE_110971) (ti X_a BOUND_VARIABLE_110972))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_110972) BOUND_VARIABLE_110970))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_110971) BOUND_VARIABLE_110970))) ))) 16.81/16.64 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.64 ( int, (zero_zero int), pls, (zero_zero int) ) 16.81/16.64 ( int, (zero_zero int), min_1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.81/16.64 ( int, (zero_zero int), s1, t ) 16.81/16.64 ( int, (one_one int), t, (zero_zero int) ) 16.81/16.64 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m, (zero_zero int) ) 16.81/16.64 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s, s ) 16.81/16.64 ) 16.81/16.64 (instantiation (let ((_let_0 (fun nat real))) (let ((_let_1 (fun (filter nat) bool))) (let ((_let_2 (fun nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_110995 $$unsorted)) (let ((_let_0 (filter nat))) (or (not (real_normed_vector X_a)) (= (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 (hAPP _let_2 (fun X_a _let_1) (tendsto nat X_a) BOUND_VARIABLE_110995) (zero_zero X_a)) sequentially)) (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (tendsto nat real) (hAPP _let_2 _let_0 (hAPP (fun X_a real) (fun _let_2 _let_0) (combb X_a real nat) (norm_norm X_a)) BOUND_VARIABLE_110995)) (zero_zero real)) sequentially))))) )))) 16.81/16.64 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 16.81/16.64 ) 16.81/16.64 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (forall ((X $$unsorted)) (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)))) ))) 16.81/16.64 ( (zero_zero int) ) 16.81/16.64 ( pls ) 16.81/16.64 ( m ) 16.81/16.64 ( (one_one int) ) 16.81/16.64 ( min_1 ) 16.81/16.64 ( s ) 16.81/16.64 ( s1 ) 16.81/16.64 ( t ) 16.81/16.64 ) 16.81/16.64 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP real real cos X_1))) (forall ((X_1 $$unsorted)) (or (= (zero_zero real) _let_1) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) tan) X_1) (hAPP real real (inverse_inverse real) (hAPP nat real (hAPP real (fun nat real) (power_power real) _let_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ))) 16.81/16.64 ( (zero_zero real) ) 16.81/16.64 ( pi ) 16.81/16.64 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.64 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.81/16.64 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.81/16.64 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.81/16.64 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.81/16.64 ) 16.81/16.64 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_111131 $$unsorted) (BOUND_VARIABLE_111132 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_111132) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_111131))) (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_111132) BOUND_VARIABLE_111131)) _let_2))) )))) 16.81/16.64 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.64 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.81/16.64 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.64 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.64 ( int, (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.64 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.64 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.64 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.64 ( complex, ii, ii ) 16.81/16.64 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.81/16.64 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.64 ) 16.81/16.64 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (real_1 nat))) (let ((_let_3 (fact_fact nat))) (let ((_let_4 (inverse_inverse real))) (forall ((X_2 $$unsorted)) (= (hAPP nat real (hAPP _let_1 _let_1 (diffs real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) _let_4) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) _let_2) _let_3))) X_2) (hAPP real real _let_4 (hAPP nat real _let_2 (hAPP nat nat _let_3 X_2)))) )))))) 16.81/16.64 ( (zero_zero nat) ) 16.81/16.64 ( (hAPP nat nat suc (zero_zero nat)) ) 16.81/16.64 ) 16.81/16.64 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_111165 $$unsorted) (BOUND_VARIABLE_111166 $$unsorted) (BOUND_VARIABLE_111167 $$unsorted)) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_111166) BOUND_VARIABLE_111167))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_111165) BOUND_VARIABLE_111166))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_111165) BOUND_VARIABLE_111167))) ))) 16.81/16.64 ( 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 int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.64 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.64 ( real, (hAPP real real (hAPP 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 (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.64 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.81/16.64 ( real, skv_14, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.65 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 16.81/16.65 ( int, (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))) ) 16.81/16.65 ( int, min_1, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.65 ) 16.81/16.65 (instantiation (let ((_let_0 (fun nat bool))) (forall ((M $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) N))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M) N))) )) 16.81/16.65 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ) 16.81/16.65 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (plus_plus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_111203 $$unsorted)) (or (not (ring_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_111203) (ring_1_Ints X_a)))) (not (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (one_one X_a)) BOUND_VARIABLE_111203)) BOUND_VARIABLE_111203)))) )))) 16.81/16.65 ( nat, (one_one nat) ) 16.81/16.65 ( int, (one_one int) ) 16.81/16.65 ) 16.81/16.65 (instantiation (forall ((X $$unsorted)) (= (hAPP rat int (archim2085082626_floor rat) X) (hAPP real int (archim2085082626_floor real) (hAPP rat real ratreal X))) ) 16.81/16.65 ( (zero_zero rat) ) 16.81/16.65 ( (one_one rat) ) 16.81/16.65 ) 16.81/16.65 (instantiation (let ((_let_0 (norm_norm X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_111232 $$unsorted) (BOUND_VARIABLE_111233 $$unsorted)) (or (not (real_normed_vector X_a)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_111232) BOUND_VARIABLE_111233))) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP X_a real _let_0 BOUND_VARIABLE_111232)) (hAPP X_a real _let_0 BOUND_VARIABLE_111233))))) )) 16.81/16.65 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.81/16.65 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.81/16.65 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.81/16.65 ) 16.81/16.65 (instantiation (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a real))) (let ((_let_3 (fun X_a X_b))) (let ((_let_4 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_111289))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_111288 $$unsorted) (BOUND_VARIABLE_111289 $$unsorted)) (or (not (topological_space X_a)) (not (real_normed_vector X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (tendsto X_a real) (hAPP _let_3 _let_2 (hAPP (fun X_b real) (fun _let_3 _let_2) (combb X_b real X_a) (norm_norm X_b)) BOUND_VARIABLE_111288)) (zero_zero real)) _let_4))) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_3 (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_111288) (zero_zero X_b)) _let_4))) )))))) 16.81/16.65 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.65 ) 16.81/16.65 (instantiation (forall ((R_4 $$unsorted)) (= (hAPP real complex (of_real complex) R_4) (hAPP real complex (hAPP real (fun real complex) complex_1 R_4) (zero_zero real))) ) 16.81/16.65 ( (zero_zero real) ) 16.81/16.65 ( (one_one real) ) 16.81/16.65 ( pi ) 16.81/16.65 ( (hAPP int real (number_number_of real) min_1) ) 16.81/16.65 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 16.81/16.65 ) 16.81/16.65 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_111322 $$unsorted)) (or (not (archim1804426504_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_111322))) (not (forall ((N_2 $$unsorted)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (inverse_inverse X_a) (hAPP nat X_a (semiring_1_of_nat X_a) (hAPP nat nat suc N_2)))) BOUND_VARIABLE_111322))) ))) ))) 16.81/16.65 ( real, pi ) 16.81/16.65 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.65 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.65 ( real, skv_2 ) 16.81/16.65 ( real, skv_10 ) 16.81/16.65 ( real, skv_13 ) 16.81/16.65 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ( int, (zero_zero int) ) 16.81/16.65 ( int, (one_one int) ) 16.81/16.65 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.65 ( int, min_1 ) 16.81/16.65 ) 16.81/16.65 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (ord_less X_a))) (let ((_let_3 (zero_zero X_a))) (let ((_let_4 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_111422))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_3) BOUND_VARIABLE_111421)))) (let ((_let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_111421) _let_3)))) (let ((_let_7 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) _let_4) BOUND_VARIABLE_111421))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_111420 $$unsorted) (BOUND_VARIABLE_111421 $$unsorted) (BOUND_VARIABLE_111422 $$unsorted)) (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_111420) BOUND_VARIABLE_111421)) _let_4)) (and (or _let_5 (and (or (not _let_6) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_7) BOUND_VARIABLE_111420))) (or _let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_3) _let_4))))) (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_111420) _let_7)))))) ))))))))) 16.81/16.65 ( real, (zero_zero real), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.81/16.65 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.81/16.65 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.81/16.65 ) 16.81/16.65 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (Y_3 $$unsorted)) (= (ti _let_0 Y_3) (hAPP _let_0 _let_0 (hAPP (fun X_a X_a) (fun _let_0 _let_0) (image X_a X_a) (combi X_a)) Y_3)) )) 16.81/16.65 ( bool, fNot ) 16.81/16.65 ( nat, (even_odd_even nat) ) 16.81/16.65 ( nat, prime ) 16.81/16.65 ( int, zprime ) 16.81/16.65 ( int, nat_neg ) 16.81/16.65 ( int, zEven ) 16.81/16.65 ( int, nat_is_nat ) 16.81/16.65 ( int, zOdd ) 16.81/16.65 ( int, (even_odd_even int) ) 16.81/16.65 ( int, twoSqu1091635170sum2sq ) 16.81/16.65 ( (fun int bool), nat_nat_set ) 16.81/16.65 ( (product_prod int int), frac_1 ) 16.81/16.65 ( (product_prod nat nat), pred_nat ) 16.81/16.65 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_less ) 16.81/16.65 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_leq ) 16.81/16.65 ( (fun nat rat), vanishes ) 16.81/16.65 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), ratrel ) 16.81/16.65 ) 16.81/16.65 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_111538 $$unsorted) (BOUND_VARIABLE_111539 $$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)) (= (or (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_111538) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_111539) _let_2))) (and (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_111539)) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_111538)))) (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_111538) BOUND_VARIABLE_111539)))))))) )) 16.81/16.65 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.81/16.65 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.65 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 16.81/16.65 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.65 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.81/16.65 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.81/16.65 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ) 16.81/16.65 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111590 $$unsorted) (BOUND_VARIABLE_111591 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_111590)) (hAPP int int (number_number_of int) BOUND_VARIABLE_111591))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_111590) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_111591))))) ) 16.81/16.65 ( real, pi, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.81/16.65 ( nat, (zero_zero nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.81/16.65 ( int, (zero_zero int), pls ) 16.81/16.65 ( int, (zero_zero int), (hAPP int int bit1 pls) ) 16.81/16.65 ( int, min_1, pls ) 16.81/16.65 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), pls ) 16.81/16.65 ( int, t, pls ) 16.81/16.65 ( int, t, (hAPP int int bit1 pls) ) 16.81/16.65 ) 16.81/16.65 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111626 $$unsorted)) (or (not (linordered_idom X_a)) (not (number_ring X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_111626)) (one_one X_a))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_111626) (hAPP int int bit1 pls))))) ) 16.81/16.65 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.81/16.65 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ( real, min_1 ) 16.81/16.65 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.81/16.65 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.81/16.65 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.81/16.65 ( nat, pls ) 16.81/16.65 ( nat, (hAPP int int bit1 pls) ) 16.81/16.65 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.81/16.65 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.81/16.65 ( int, pls ) 16.81/16.65 ( int, (hAPP int int bit1 pls) ) 16.81/16.65 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.81/16.65 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ( int, min_1 ) 16.81/16.65 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.81/16.65 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.81/16.65 ( complex, min_1 ) 16.81/16.65 ( quickcheck_code_int, (zero_zero int) ) 16.81/16.65 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 16.81/16.65 ( quickcheck_code_int, (one_one int) ) 16.81/16.65 ( code_code_numeral, pls ) 16.81/16.65 ( code_code_numeral, (hAPP int int bit1 pls) ) 16.81/16.65 ) 16.81/16.65 (instantiation (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_111642)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_111641 $$unsorted) (BOUND_VARIABLE_111642 $$unsorted)) (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_111641) BOUND_VARIABLE_111642))) (or _let_1 (and (not _let_1) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_111641)))))) ))) 16.81/16.65 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ) 16.81/16.65 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111853 $$unsorted) (BOUND_VARIABLE_111854 $$unsorted)) (or (not (monoid_mult X_a)) (not (linordered_ring X_a)) (not (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_111854))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_111853) BOUND_VARIABLE_111854)))) ) 16.81/16.65 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ) 16.81/16.65 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_111894 $$unsorted)) (or (not (field_char_0 X_a)) (not (number_ring X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_111894)) (field_char_0_Rats X_a)))) )) 16.81/16.65 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.81/16.65 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.65 ( real, min_1 ) 16.81/16.65 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.66 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.81/16.66 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.81/16.66 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.81/16.66 ( nat, pls ) 16.81/16.66 ( nat, (hAPP int int bit1 pls) ) 16.81/16.66 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.81/16.66 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.81/16.66 ( int, pls ) 16.81/16.66 ( int, (hAPP int int bit1 pls) ) 16.81/16.66 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.81/16.66 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.66 ( int, min_1 ) 16.81/16.66 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.81/16.66 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.81/16.66 ( complex, min_1 ) 16.81/16.66 ( quickcheck_code_int, (zero_zero int) ) 16.81/16.66 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 16.81/16.66 ( quickcheck_code_int, (one_one int) ) 16.81/16.66 ( code_code_numeral, pls ) 16.81/16.66 ( code_code_numeral, (hAPP int int bit1 pls) ) 16.81/16.66 ) 16.81/16.66 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111911 $$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_111911) BOUND_VARIABLE_111911) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_111911) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.81/16.66 ( real, (hAPP int real (number_number_of real) min_1) ) 16.81/16.66 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.66 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.66 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.66 ( 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))))) ) 16.81/16.66 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.66 ( 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))) ) 16.81/16.66 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.66 ( int, s ) 16.81/16.66 ( int, s1 ) 16.81/16.66 ( int, skv_8 ) 16.81/16.66 ( complex, ii ) 16.81/16.66 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.66 ( 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)) ) 16.81/16.66 ) 16.81/16.66 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_111952 $$unsorted) (BOUND_VARIABLE_111953 $$unsorted)) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_111952) BOUND_VARIABLE_111953)) (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_111952) BOUND_VARIABLE_111953)) (zero_zero X_a))))) ))) 16.81/16.66 ( real, (zero_zero real), pi ) 16.81/16.66 ( 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)))) ) 16.81/16.66 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.66 ( real, (zero_zero real), skv_6 ) 16.81/16.66 ( real, (zero_zero real), skv_11 ) 16.81/16.66 ( real, (zero_zero real), skv_12 ) 16.81/16.66 ( real, (zero_zero real), skv_14 ) 16.81/16.66 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.81/16.66 ( 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))) ) 16.81/16.66 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.81/16.66 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.81/16.66 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.66 ( int, (zero_zero int), (one_one int) ) 16.81/16.66 ( int, (zero_zero int), min_1 ) 16.81/16.66 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.66 ( int, (zero_zero int), s ) 16.81/16.66 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.81/16.66 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.81/16.66 ( int, (zero_zero int), skv_3 ) 16.81/16.66 ( int, (zero_zero int), skv_9 ) 16.81/16.66 ( int, (one_one int), t ) 16.81/16.66 ( int, min_1, pls ) 16.81/16.66 ( int, min_1, min_1 ) 16.81/16.66 ( 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_1) ) 16.81/16.66 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.81/16.66 ) 16.81/16.66 (instantiation (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (inverse_divide X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_111973 $$unsorted) (BOUND_VARIABLE_111974 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_111973)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_111974)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_111973) BOUND_VARIABLE_111974)))) )))) 16.81/16.66 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.66 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.81/16.66 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.66 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 16.81/16.66 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.66 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.66 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.81/16.66 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.81/16.66 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.66 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.66 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.66 ) 16.81/16.66 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111990 $$unsorted) (BOUND_VARIABLE_111991 $$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_111990) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_111991))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_111990)) BOUND_VARIABLE_111991)))) ) 16.81/16.66 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 16.81/16.66 ) 16.81/16.66 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112037 $$unsorted)) (or (not (number_ring X_a)) (= (ti X_a BOUND_VARIABLE_112037) (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_112037))) ) 16.81/16.66 ( bool, fFalse ) 16.81/16.66 ( bool, fTrue ) 16.81/16.66 ( real, pi ) 16.81/16.66 ( (fun nat bool), (even_odd_even nat) ) 16.81/16.66 ( (fun nat bool), prime ) 16.81/16.66 ( (fun nat nat), suc ) 16.81/16.66 ( (fun nat nat), (fact_fact nat) ) 16.81/16.66 ( (fun nat nat), (size_size nat) ) 16.81/16.66 ( (fun nat nat), fact ) 16.81/16.66 ( (fun nat nat), nat_size ) 16.81/16.66 ( int, pls ) 16.81/16.66 ( int, m ) 16.81/16.66 ( int, min_1 ) 16.81/16.66 ( int, s ) 16.81/16.66 ( int, s1 ) 16.81/16.66 ( int, t ) 16.81/16.66 ( (fun int bool), zprime ) 16.81/16.66 ( (fun int bool), nat_neg ) 16.81/16.66 ( (fun int bool), zEven ) 16.81/16.66 ( (fun int bool), nat_is_nat ) 16.81/16.66 ( (fun int bool), zOdd ) 16.81/16.66 ( (fun int bool), (even_odd_even int) ) 16.81/16.66 ( (fun int bool), twoSqu1091635170sum2sq ) 16.81/16.66 ( (fun int nat), nat_1 ) 16.81/16.66 ( (fun int nat), phi ) 16.81/16.66 ( (fun real real), sqrt ) 16.81/16.66 ( (fun real real), tan ) 16.81/16.66 ( (fun real real), cos ) 16.81/16.66 ( (fun real real), arccos ) 16.81/16.66 ( (fun real real), ln ) 16.81/16.66 ( (fun real real), sin ) 16.81/16.66 ( (fun real real), arctan ) 16.81/16.66 ( (fun real real), arcsin ) 16.81/16.66 ( complex, ii ) 16.81/16.66 ( (fun complex complex), cnj ) 16.81/16.66 ( (fun complex complex), expi ) 16.81/16.66 ( (fun nat real), (real_1 nat) ) 16.81/16.66 ( (fun nat real), cos_coeff ) 16.81/16.66 ( (fun nat real), sin_coeff ) 16.81/16.66 ( (fun int int), bit0 ) 16.81/16.66 ( (fun int int), bit1 ) 16.81/16.66 ( (fun int int), pred ) 16.81/16.66 ( (fun int int), succ ) 16.81/16.66 ( (fun int int), (fact_fact int) ) 16.81/16.66 ( (fun int int), zfact ) 16.81/16.66 ( (fun bool bool), fNot ) 16.81/16.66 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.81/16.66 ( (fun bool (fun bool bool)), fconj ) 16.81/16.66 ( (fun bool (fun bool bool)), fdisj ) 16.81/16.66 ( (fun bool (fun bool bool)), fimplies ) 16.81/16.66 ( (fun int (fun int bool)), sRStar ) 16.81/16.66 ( (fun int (fun int bool)), quadRes ) 16.81/16.66 ( (fun int (fun int bool)), norRRset ) 16.81/16.66 ( (fun int (fun int bool)), d22set ) 16.81/16.66 ( (fun int (fun int bool)), sr ) 16.81/16.66 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.81/16.66 ( (fun nat (fun nat nat)), nat_gcd ) 16.81/16.66 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.81/16.66 ( (fun nat (fun nat nat)), nat_lcm ) 16.81/16.66 ( (fun nat (fun real real)), root ) 16.81/16.66 ( (fun real (fun real real)), log ) 16.81/16.66 ( (fun real (fun real real)), powr ) 16.81/16.66 ( (fun nat (fun nat bool)), coprime ) 16.81/16.66 ( (fun (fun int bool) int), (the int) ) 16.81/16.66 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.81/16.66 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.81/16.66 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.81/16.66 ( (fun (fun int bool) bool), nat_nat_set ) 16.81/16.66 ( (filter nat), sequentially ) 16.81/16.66 ( (fun (product_prod nat nat) bool), pred_nat ) 16.81/16.66 ( (fun (product_prod int int) bool), frac_1 ) 16.81/16.66 ( (fun real complex), cis ) 16.81/16.66 ( (fun complex real), im ) 16.81/16.66 ( (fun complex real), re ) 16.81/16.66 ( (fun complex real), arg ) 16.81/16.66 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.81/16.66 ( (fun int (fun int int)), int_gcd ) 16.81/16.66 ( (fun int (fun int int)), multInv ) 16.81/16.66 ( (fun int (fun int int)), legacy_zgcd ) 16.81/16.66 ( (fun int (fun int int)), z3mod ) 16.81/16.66 ( (fun int (fun int int)), inv ) 16.81/16.66 ( (fun int (fun int int)), (gcd_gcd int) ) 16.81/16.66 ( (fun int (fun int int)), standardRes ) 16.81/16.66 ( (fun int (fun int int)), legendre ) 16.81/16.66 ( (fun int (fun int int)), nat_tsub ) 16.81/16.66 ( (fun int (fun int int)), z3div ) 16.81/16.66 ( (fun int (fun int int)), int_lcm ) 16.81/16.66 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.81/16.66 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.81/16.66 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.81/16.66 ( (fun int (fun (fun int bool) bool)), resSet ) 16.81/16.66 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.81/16.66 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.81/16.66 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.81/16.66 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.81/16.66 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.81/16.66 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.81/16.66 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.81/16.66 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.81/16.66 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.81/16.66 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.81/16.66 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.81/16.66 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.81/16.66 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.81/16.66 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.81/16.66 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.81/16.66 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.81/16.66 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.81/16.66 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.81/16.66 ( (fun real nat), natfloor ) 16.81/16.66 ( (fun real nat), natceiling ) 16.81/16.66 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.81/16.66 ( (fun int (fun int (fun int bool))), wset ) 16.81/16.66 ( (fun int (fun int (fun int bool))), bnorRset ) 16.81/16.66 ( (fun int (fun int (fun int bool))), zcong ) 16.81/16.66 ( (fun int (fun int (fun int bool))), noXRRset ) 16.81/16.66 ( (fun int (fun int (fun int bool))), zcongm ) 16.81/16.66 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.81/16.66 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.81/16.66 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.81/16.66 ( (fun int real), (real_1 int) ) 16.81/16.66 ( (fun complex nat), (size_size complex) ) 16.81/16.66 ( (fun complex nat), complex_size ) 16.81/16.66 ( (fun int (list int)), quickc666637781d_zero ) 16.81/16.66 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.81/16.66 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.81/16.66 ( (fun (product_prod int int) rat), frct ) 16.81/16.66 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.81/16.66 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.81/16.66 ( (fun (fun nat rat) bool), vanishes ) 16.81/16.66 ( (fun int (fun int rat)), fract ) 16.81/16.66 ( (fun code_code_numeral int), code_int_of ) 16.81/16.66 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.81/16.66 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.81/16.66 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.81/16.66 ( (fun real (fun real complex)), complex_1 ) 16.81/16.66 ( (fun real (fun real complex)), rcis ) 16.81/16.66 ( (fun int (fun nat nat)), nat_aux ) 16.81/16.66 ( (fun rat real), ratreal ) 16.81/16.66 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.81/16.66 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.81/16.66 ( (fun rat (product_prod int int)), quotient_of ) 16.81/16.66 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.81/16.66 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.81/16.66 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.81/16.66 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.81/16.66 ) 16.81/16.66 (instantiation (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (minus_minus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_112061 $$unsorted) (BOUND_VARIABLE_112062 $$unsorted)) (or (not (ab_group_add X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_112061)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_112062)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_112061) BOUND_VARIABLE_112062)))) )))) 16.81/16.66 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.81/16.66 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.81/16.66 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.81/16.66 ) 16.81/16.66 (instantiation (let ((_let_0 (ti X_a A_2))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (A_2 $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 A_2))) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 X_2))) (= _let_0 (ti X_a X_2))) )) (= (hAPP (fun X_a bool) X_a (hilbert_Eps X_a) P_1) _let_0)) )) 16.81/16.66 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 16.81/16.66 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.66 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.66 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_6 ) 16.81/16.66 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 16.81/16.66 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 16.81/16.66 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_14 ) 16.81/16.66 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 16.81/16.66 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.67 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.67 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 16.81/16.67 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_10 ) 16.81/16.67 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_13 ) 16.81/16.67 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.67 ( real, (hAPP real (fun real bool) (ord_less real) (one_one real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.67 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))), (zero_zero real) ) 16.81/16.67 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.81/16.67 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.81/16.67 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 16.81/16.67 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.67 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.81/16.67 ( real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 16.81/16.67 ( real, (hAPP real (fun real bool) (ord_less real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.67 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi))), pi ) 16.81/16.67 ( real, (hAPP real (fun real bool) (ord_less_eq real) skv_14), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.67 ( nat, (even_odd_even nat), (zero_zero nat) ) 16.81/16.67 ( nat, (even_odd_even nat), (one_one nat) ) 16.81/16.67 ( nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.67 ( nat, prime, (zero_zero nat) ) 16.81/16.67 ( nat, prime, (one_one nat) ) 16.81/16.67 ( nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.67 ( (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 16.81/16.67 ( (fun nat bool), (hAPP (fun nat int) (fun (fun nat bool) bool) (nat_tr1645093318rphism nat int) (semiring_1_of_nat int)), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_3 ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_9 ) 16.81/16.67 ( int, zprime, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.67 ( int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.67 ( int, nat_neg, (one_one int) ) 16.81/16.67 ( int, nat_neg, (hAPP int int (number_number_of int) min_1) ) 16.81/16.67 ( int, nat_neg, (hAPP int int (number_number_of int) pls) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less int) pls), (zero_zero int) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 16.81/16.67 ( int, nat_is_nat, (zero_zero int) ) 16.81/16.67 ( int, nat_is_nat, (one_one int) ) 16.81/16.67 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.67 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.81/16.67 ( int, (even_odd_even int), (zero_zero int) ) 16.81/16.67 ( int, (even_odd_even int), (one_one int) ) 16.81/16.67 ( int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))), (zero_zero int) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less int) min_1), (zero_zero int) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 16.81/16.67 ( int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.67 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 16.81/16.67 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.67 ( int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less int) t), (zero_zero int) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less int) t), (one_one int) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less int) t), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.67 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.67 ( int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.67 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun int bool) (ord_less 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)))), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less int) skv_3), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.67 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_3)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.67 ( 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_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.67 ( int, (hAPP int (fun int bool) (ord_less int) skv_9), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.67 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_9)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.67 ( (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 16.81/16.67 ( (fun int bool), (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 16.81/16.67 ( (filter real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (filter real) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)) (zero_zero real))))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.81/16.67 ( (filter nat), (trivial_limit nat), sequentially ) 16.81/16.67 ( (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 16.81/16.67 ) 16.81/16.67 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (one_one X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_112102 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_112102))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_112102) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_112102)))) )))) 16.81/16.67 ( real, (zero_zero real) ) 16.81/16.67 ( real, pi ) 16.81/16.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.67 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.67 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.67 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.67 ( real, skv_2 ) 16.81/16.67 ( real, skv_10 ) 16.81/16.67 ( real, skv_13 ) 16.81/16.67 ( real, skv_14 ) 16.81/16.67 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.67 ( int, (zero_zero int) ) 16.81/16.67 ( int, (one_one int) ) 16.81/16.67 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.67 ( int, min_1 ) 16.81/16.67 ( complex, ii ) 16.81/16.67 ) 16.81/16.67 (instantiation (forall ((A_1 $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X))) (= (hAPP real nat natceiling (hAPP real real (hAPP real (fun real real) (plus_plus real) X) (hAPP nat real (real_1 nat) A_1))) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natceiling X)) A_1))) ) 16.81/16.67 ( (one_one nat), (one_one real) ) 16.81/16.67 ) 16.81/16.67 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (product_Pair int int))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (hAPP (fun _let_1 _let_4) _let_4 (accp _let_1) posDivAlg_rel))) (let ((_let_6 (hAPP int _let_0 P_1 A_4))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool _let_5 (hAPP int _let_1 (hAPP int _let_2 _let_3 A0) A1)))) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool _let_5 (hAPP int _let_1 (hAPP int _let_2 _let_3 A_4) B_4)))) (and (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_4) B_4))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B_4) (zero_zero int)))) (not (hBOOL (hAPP int bool _let_6 (hAPP int int (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_6 B_4))) )) (hBOOL (hAPP int bool (hAPP int _let_0 P_1 A0) A1))) )))))))) 16.81/16.68 ( (ord_less_eq int), (zero_zero int), (one_one int) ) 16.81/16.68 ( (ord_less_eq int), (zero_zero int), min_1 ) 16.81/16.68 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.68 ( (ord_less_eq int), (zero_zero int), s ) 16.81/16.68 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.81/16.68 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.81/16.68 ( (ord_less_eq int), (zero_zero int), skv_3 ) 16.81/16.68 ( (ord_less_eq int), (zero_zero int), skv_9 ) 16.81/16.68 ( (ord_less_eq int), (one_one int), t ) 16.81/16.68 ( (ord_less_eq int), min_1, pls ) 16.81/16.68 ( (ord_less_eq int), min_1, min_1 ) 16.81/16.68 ( (ord_less int), (zero_zero int), (zero_zero int) ) 16.81/16.68 ( (ord_less int), (zero_zero int), (one_one int) ) 16.81/16.68 ( (ord_less int), (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.68 ( (ord_less int), (zero_zero int), min_1 ) 16.81/16.68 ( (ord_less int), min_1, (zero_zero int) ) 16.81/16.68 ( (ord_less int), min_1, min_1 ) 16.81/16.68 ( (ord_less int), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.68 ( (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 16.81/16.68 ( (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 16.81/16.68 ( (ord_less int), t, (zero_zero int) ) 16.81/16.68 ( (ord_less int), t, (one_one int) ) 16.81/16.68 ( (ord_less int), t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.68 ( (ord_less int), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.68 ( (ord_less int), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.68 ( (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.81/16.68 ( quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 16.81/16.68 ( (hAPP int (fun int (fun int bool)) zcong s1), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.68 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.68 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.68 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.68 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.68 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.68 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.68 ) 16.81/16.68 (instantiation (forall ((Z_1 $$unsorted)) (= Z_1 (hAPP complex real re (hAPP real complex (of_real complex) Z_1))) ) 16.81/16.68 ( pi ) 16.81/16.68 ( (hAPP int real (number_number_of real) min_1) ) 16.81/16.68 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 16.81/16.68 ) 16.81/16.68 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP int real (real_1 int) N))) (forall ((N $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (hAPP real real (hAPP real (fun real real) (minus_minus real) _let_1) (one_one real))) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) X) _let_1))) (= (ti int N) (hAPP real int (archimedean_ceiling real) X))) ))) 16.81/16.68 ( (zero_zero int), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.68 ) 16.81/16.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112174 $$unsorted) (BOUND_VARIABLE_112175 $$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_112174) BOUND_VARIABLE_112175))) (not (forall ((K_1 $$unsorted)) (not (= (ti X_a BOUND_VARIABLE_112175) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_112174) K_1))) ))) ) 16.81/16.68 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.81/16.68 ) 16.81/16.68 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) sqrt) X_1) (hAPP real real (hAPP real _let_1 (inverse_divide real) (hAPP real real (inverse_inverse real) (hAPP real real sqrt X_1))) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ))) 16.81/16.68 ( (zero_zero real) ) 16.81/16.68 ( (one_one real) ) 16.81/16.68 ( pi ) 16.81/16.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.68 ( (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)))) ) 16.81/16.68 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.81/16.68 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.68 ( skv_2 ) 16.81/16.68 ( skv_10 ) 16.81/16.68 ( skv_13 ) 16.81/16.68 ) 16.81/16.68 (instantiation (forall ((X_a $$unsorted) (P_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 X_1))) (hBOOL (hAPP X_a bool P_1 (hAPP (fun X_a bool) X_a (hilbert_Eps X_a) P_1)))) ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_6 ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_14 ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_10 ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_13 ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less real) (one_one real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))), (zero_zero real) ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.81/16.68 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi))), pi ) 16.81/16.68 ( real, (hAPP real (fun real bool) (ord_less_eq real) skv_14), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.68 ( nat, (even_odd_even nat), (zero_zero nat) ) 16.81/16.68 ( nat, (even_odd_even nat), (one_one nat) ) 16.81/16.68 ( nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.68 ( nat, prime, (zero_zero nat) ) 16.81/16.68 ( nat, prime, (one_one nat) ) 16.81/16.68 ( nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.68 ( (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 16.81/16.68 ( (fun nat bool), (hAPP (fun nat int) (fun (fun nat bool) bool) (nat_tr1645093318rphism nat int) (semiring_1_of_nat int)), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 16.81/16.68 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 16.81/16.68 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.68 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 16.81/16.68 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 16.81/16.68 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.81/16.68 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_3 ) 16.81/16.68 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_9 ) 16.81/16.68 ( int, zprime, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.68 ( int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.68 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 16.81/16.68 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.68 ( int, nat_neg, (one_one int) ) 16.81/16.68 ( int, nat_neg, (hAPP int int (number_number_of int) min_1) ) 16.81/16.69 ( int, nat_neg, (hAPP int int (number_number_of int) pls) ) 16.81/16.69 ( int, (hAPP int (fun int bool) (ord_less int) pls), (zero_zero int) ) 16.81/16.69 ( int, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 16.81/16.69 ( int, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 16.81/16.69 ( int, nat_is_nat, (zero_zero int) ) 16.81/16.69 ( int, nat_is_nat, (one_one int) ) 16.81/16.69 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.81/16.69 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.81/16.69 ( int, (even_odd_even int), (zero_zero int) ) 16.81/16.69 ( int, (even_odd_even int), (one_one int) ) 16.81/16.69 ( int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 16.81/16.69 ( int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))), (zero_zero int) ) 16.81/16.69 ( int, (hAPP int (fun int bool) (ord_less int) min_1), (zero_zero int) ) 16.81/16.69 ( int, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 16.81/16.69 ( int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 16.81/16.69 ( int, (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.69 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.69 ( int, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 16.81/16.69 ( int, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 16.81/16.69 ( int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 16.81/16.69 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.81/16.69 ( int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.81/16.69 ( int, (hAPP int (fun int bool) (ord_less int) t), (zero_zero int) ) 16.81/16.69 ( int, (hAPP int (fun int bool) (ord_less int) t), (one_one int) ) 16.81/16.69 ( int, (hAPP int (fun int bool) (ord_less int) t), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.98/16.69 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.98/16.69 ( int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.98/16.69 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun int bool) (ord_less 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)))), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 16.98/16.69 ( int, (hAPP int (fun int bool) (ord_less int) skv_3), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.98/16.69 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_3)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.98/16.69 ( 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_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.98/16.69 ( int, (hAPP int (fun int bool) (ord_less int) skv_9), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.98/16.69 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_9)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.98/16.69 ( (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 16.98/16.69 ( (fun int bool), (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 16.98/16.69 ( (filter real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (filter real) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)) (zero_zero real))))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.98/16.69 ( (filter nat), (trivial_limit nat), sequentially ) 16.98/16.69 ( (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 16.98/16.69 ) 16.98/16.69 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (inverse_inverse X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_112271 $$unsorted) (BOUND_VARIABLE_112272 $$unsorted)) (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_112271)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_112272)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_112271))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_112272) BOUND_VARIABLE_112271))) )))) 16.98/16.69 ( real, (zero_zero real), pi ) 16.98/16.69 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.98/16.69 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.98/16.69 ( real, pi, (zero_zero real) ) 16.98/16.69 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.98/16.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.98/16.69 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.98/16.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.98/16.69 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.98/16.69 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 16.98/16.69 ( real, skv_2, (zero_zero real) ) 16.98/16.69 ( real, skv_10, (zero_zero real) ) 16.98/16.69 ( real, skv_13, (zero_zero real) ) 16.98/16.69 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 16.98/16.69 ( int, (zero_zero int), (zero_zero int) ) 16.98/16.69 ( int, (zero_zero int), min_1 ) 16.98/16.69 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.98/16.69 ( int, (zero_zero int), t ) 16.98/16.69 ( int, (one_one int), (zero_zero int) ) 16.98/16.69 ( int, (one_one int), t ) 16.98/16.69 ( 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))), (zero_zero int) ) 16.98/16.69 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 16.98/16.69 ( 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 ) 16.98/16.69 ( 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_3 ) 16.99/16.69 ( 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_9 ) 16.99/16.69 ( int, min_1, (zero_zero int) ) 16.99/16.69 ( int, min_1, min_1 ) 16.99/16.69 ( 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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.99/16.69 ) 16.99/16.69 (instantiation (let ((_let_0 (norm_norm X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_112380 $$unsorted)) (or (not (real_n1866405975lgebra X_a)) (not (divisi14063676e_zero X_a)) (= (hAPP real real (inverse_inverse real) (hAPP X_a real _let_0 BOUND_VARIABLE_112380)) (hAPP X_a real _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_112380)))) )) 16.99/16.69 ( real, (zero_zero real) ) 16.99/16.69 ( complex, ii ) 16.99/16.69 ) 16.99/16.69 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_112392 $$unsorted) (BOUND_VARIABLE_112393 $$unsorted)) (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_112392)) (hAPP X_a X_a (hAPP X_a _let_2 _let_4 BOUND_VARIABLE_112393) BOUND_VARIABLE_112392)) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_112393)))) )))))) 16.99/16.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 16.99/16.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.99/16.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.99/16.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.99/16.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.99/16.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.99/16.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 16.99/16.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 16.99/16.69 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 16.99/16.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 16.99/16.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (one_one real) ) 16.99/16.69 ) 16.99/16.69 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) _let_2)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) _let_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) (hAPP real real cos X)))) )))) 16.99/16.70 ( (zero_zero real) ) 16.99/16.70 ( (one_one real) ) 16.99/16.70 ( pi ) 16.99/16.70 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.99/16.70 ( (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)))) ) 16.99/16.70 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.99/16.70 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.99/16.70 ( (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 (hAPP int int bit1 pls))))) ) 16.99/16.70 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.99/16.70 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.99/16.70 ( (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 bit0 (hAPP int int bit1 pls))))) ) 16.99/16.70 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.99/16.70 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.99/16.70 ( skv_14 ) 16.99/16.70 ) 16.99/16.70 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (forall ((Y $$unsorted) (X $$unsorted)) (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)))) )) 16.99/16.70 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.99/16.70 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.99/16.70 ) 16.99/16.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112597 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_112597) (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_112597)) (zero_zero int))))) ) 16.99/16.70 ( real, (zero_zero real) ) 16.99/16.70 ( real, (one_one real) ) 16.99/16.70 ( real, pi ) 16.99/16.70 ( 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)))) ) 16.99/16.70 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.99/16.70 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.99/16.70 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.99/16.70 ( nat, (zero_zero nat) ) 16.99/16.70 ( int, (zero_zero int) ) 16.99/16.70 ( int, min_1 ) 16.99/16.70 ( int, s ) 16.99/16.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.99/16.70 ( int, t ) 16.99/16.70 ( int, skv_3 ) 16.99/16.70 ( int, skv_9 ) 16.99/16.70 ) 16.99/16.70 (instantiation (let ((_let_0 (hAPP X_a (fun X_a X_a) (inverse_divide X_a) (one_one X_a)))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_112636 $$unsorted) (BOUND_VARIABLE_112637 $$unsorted)) (or (not (field_inverse_zero X_a)) (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_112636)) BOUND_VARIABLE_112637) (hAPP X_a X_a _let_0 (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_112636) BOUND_VARIABLE_112637)))) )))) 16.99/16.70 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.99/16.70 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.99/16.70 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.99/16.70 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.99/16.70 ) 16.99/16.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112699 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_112699)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_112699))))) ) 16.99/16.70 ( real, pi ) 16.99/16.70 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.99/16.70 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.99/16.70 ( real, skv_6 ) 16.99/16.70 ( real, skv_11 ) 16.99/16.70 ( real, skv_12 ) 16.99/16.70 ( real, skv_14 ) 16.99/16.70 ( int, (one_one int) ) 16.99/16.70 ( int, min_1 ) 16.99/16.70 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.99/16.70 ( int, s ) 16.99/16.70 ( int, (hAPP int int (number_number_of int) pls) ) 16.99/16.70 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.99/16.70 ( int, skv_3 ) 16.99/16.70 ( int, skv_9 ) 16.99/16.70 ) 16.99/16.70 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_1) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Y_1) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (times_times int) X_1) Y_1)) zOdd))) )))) 16.99/16.70 ( (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.99/16.70 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.99/16.70 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.99/16.70 ( skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.99/16.70 ) 16.99/16.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112777 $$unsorted)) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_112777))) (= (one_one X_a) (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_112777))) ) 16.99/16.70 ( real, (zero_zero real) ) 16.99/16.70 ( real, pi ) 16.99/16.70 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.99/16.70 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.99/16.70 ( real, skv_2 ) 16.99/16.70 ( real, skv_10 ) 16.99/16.70 ( real, skv_13 ) 16.99/16.70 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.99/16.70 ( int, (zero_zero int) ) 16.99/16.70 ( int, (one_one int) ) 16.99/16.70 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.99/16.70 ( int, min_1 ) 16.99/16.70 ( rat, (zero_zero rat) ) 16.99/16.70 ) 16.99/16.70 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (let ((_let_3 (filter X_a))) (let ((_let_4 (fun _let_3 bool))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_112832 $$unsorted) (BOUND_VARIABLE_112833 $$unsorted) (BOUND_VARIABLE_112834 $$unsorted)) (or (not (real_normed_vector X_b)) (not (real_normed_vector X_a)) (not (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 R_2))) (not (forall ((S_1 $$unsorted)) (or (not (forall ((X_2 $$unsorted)) (or (= (ti X_a X_2) (ti X_a BOUND_VARIABLE_112834)) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (norm_norm X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) X_2) BOUND_VARIABLE_112834))) S_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_b real (norm_norm X_b) (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (minus_minus X_b) (hAPP X_a X_b BOUND_VARIABLE_112832 X_2)) BOUND_VARIABLE_112833))) R_2))) )) (not (hBOOL (hAPP real bool _let_2 S_1)))) ))) )) (hBOOL (hAPP _let_3 bool (hAPP X_b _let_4 (hAPP (fun X_a X_b) (fun X_b _let_4) (tendsto X_a X_b) BOUND_VARIABLE_112832) BOUND_VARIABLE_112833) (hAPP X_a _let_3 (at X_a) BOUND_VARIABLE_112834)))) )))))) 16.99/16.70 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.99/16.70 ) 16.99/16.70 (instantiation (let ((_let_0 (fun nat int))) (let ((_let_1 (fun int int))) (let ((_let_2 (power_power int))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (N $$unsorted)) (or (not (= (hAPP nat int (hAPP int _let_0 _let_2 C) N) (hAPP int int (hAPP int _let_1 (times_times int) A_1) B))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (one_one nat)) N))) (not (= (one_one int) (hAPP int int (hAPP int _let_1 legacy_zgcd A_1) B))) (not (forall ((K_1 $$unsorted)) (not (= (hAPP nat int (hAPP int _let_0 _let_2 K_1) N) (hAPP int int (abs_abs int) A_1))) ))) )))) 17.01/16.70 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.01/16.70 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int), skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.01/16.70 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.01/16.70 ) 17.01/16.70 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_112949 $$unsorted) (BOUND_VARIABLE_112950 $$unsorted)) (or (not (ordere453448008miring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_112950) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_112949))) (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_112950) BOUND_VARIABLE_112949)) _let_2))) )))) 17.01/16.70 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.01/16.70 ( 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))))) ) 17.01/16.70 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.01/16.70 ( 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)))) ) 17.01/16.70 ( 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))) ) 17.01/16.70 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.01/16.70 ( 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))) ) 17.01/16.70 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.01/16.70 ( complex, ii, ii ) 17.01/16.70 ( 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)) ) 17.01/16.70 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.01/16.70 ) 17.01/16.70 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (inverse_inverse X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_113039 $$unsorted) (BOUND_VARIABLE_113040 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_113039) BOUND_VARIABLE_113040))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_113040) (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_113040)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_113039)))) )))) 17.01/16.70 ( real, (zero_zero real), pi ) 17.01/16.70 ( 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)))) ) 17.02/16.70 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.70 ( real, (zero_zero real), skv_2 ) 17.02/16.70 ( real, (zero_zero real), skv_10 ) 17.02/16.70 ( real, (zero_zero real), skv_13 ) 17.02/16.70 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.70 ( real, pi, (zero_zero real) ) 17.02/16.70 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.70 ( 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))) ) 17.02/16.70 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 17.02/16.70 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.02/16.70 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 17.02/16.70 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.70 ( int, (zero_zero int), (zero_zero int) ) 17.02/16.70 ( int, (zero_zero int), (one_one int) ) 17.02/16.70 ( 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))) ) 17.02/16.71 ( int, (zero_zero int), min_1 ) 17.02/16.71 ( int, min_1, (zero_zero int) ) 17.02/16.71 ( int, min_1, min_1 ) 17.02/16.71 ( 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))) ) 17.02/16.71 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.02/16.71 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.02/16.71 ( int, t, (zero_zero int) ) 17.02/16.71 ( int, t, (one_one int) ) 17.02/16.71 ( 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))) ) 17.02/16.71 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.71 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.71 ) 17.02/16.71 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_113084 $$unsorted)) (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_113084) (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_113084) BOUND_VARIABLE_113084))) )) 17.02/16.71 ( real, pi ) 17.02/16.71 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.02/16.71 ( nat, (one_one nat) ) 17.02/16.71 ( 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) ) 17.02/16.71 ( 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)))) ) 17.02/16.71 ( complex, (hAPP real complex (of_real complex) pi) ) 17.02/16.71 ) 17.02/16.71 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_1))) (let ((_let_3 (hAPP real real cos X_1))) (forall ((X_1 $$unsorted)) (or (= (zero_zero real) _let_3) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs real real real) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_1 real) (inverse_divide real)) sin)) cos)) X_1) (hAPP real real (inverse_inverse real) (hAPP nat real (hAPP real (fun nat real) (power_power real) _let_3) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ))))) 17.02/16.71 ( (zero_zero real) ) 17.02/16.71 ( pi ) 17.02/16.71 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.71 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 17.02/16.71 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 17.02/16.71 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 17.02/16.71 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 17.02/16.71 ) 17.02/16.71 (instantiation (let ((_let_0 (zero_zero real))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) _let_0) X_1))) (= (= (one_one real) X_1) (= _let_0 (hAPP real real ln X_1)))) )) 17.02/16.71 ( (one_one real) ) 17.02/16.71 ( pi ) 17.02/16.71 ( (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)))) ) 17.02/16.71 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.71 ( skv_2 ) 17.02/16.71 ( skv_10 ) 17.02/16.71 ( skv_13 ) 17.02/16.71 ) 17.02/16.71 (instantiation (let ((_let_0 (fun nat bool))) (forall ((N_1 $$unsorted) (P_1 $$unsorted)) (or (hBOOL (hAPP nat bool P_1 (zero_zero nat))) (not (hBOOL (hAPP nat bool P_1 N_1))) (not (forall ((K_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) K_1) N_1))) (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) I_2) K_1))) (not (hBOOL (hAPP nat bool P_1 I_2)))) )) (not (hBOOL (hAPP nat bool P_1 K_1)))) ))) )) 17.02/16.71 ( (zero_zero nat), (even_odd_even nat) ) 17.02/16.71 ( (zero_zero nat), prime ) 17.02/16.71 ( (one_one nat), (even_odd_even nat) ) 17.02/16.71 ( (one_one nat), prime ) 17.02/16.71 ( (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)) ) 17.02/16.71 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), prime ) 17.02/16.71 ) 17.02/16.71 (instantiation (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_113444))) (let ((_let_3 (= _let_1 (ti X_a BOUND_VARIABLE_113443)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_113442 $$unsorted) (BOUND_VARIABLE_113443 $$unsorted) (BOUND_VARIABLE_113444 $$unsorted)) (or (not (field_inverse_zero X_a)) (not (number X_a)) (= (= _let_2 (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_113442) BOUND_VARIABLE_113443)) (and (or (not _let_3) (= _let_1 _let_2)) (or _let_3 (= (ti X_a BOUND_VARIABLE_113442) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) _let_2) BOUND_VARIABLE_113443)))))) ))))) 17.02/16.71 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.71 ( 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)) ) 17.02/16.71 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), min_1 ) 17.02/16.71 ( real, pi, (hAPP int real (number_number_of 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))) ) 17.02/16.71 ( 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))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.71 ( 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))), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.02/16.71 ( 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))), (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 17.02/16.71 ) 17.02/16.71 (instantiation (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (fun X_b bool))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP X_b bool (hAPP X_a _let_1 F A_2) B_1))) (hBOOL (hAPP _let_0 bool (hAPP (fun X_a _let_1) (fun _let_0 bool) (product_prod_case X_a X_b bool) F) (hAPP X_b _let_0 (hAPP X_a (fun X_b _let_0) (product_Pair X_a X_b) A_2) B_1)))) ))) 17.02/16.71 ( real, real, (ord_less_eq real), (zero_zero real), pi ) 17.02/16.71 ( 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)))) ) 17.02/16.71 ( 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)))) ) 17.02/16.71 ( real, real, (ord_less_eq real), (zero_zero real), skv_6 ) 17.02/16.71 ( real, real, (ord_less_eq real), (zero_zero real), skv_11 ) 17.02/16.71 ( real, real, (ord_less_eq real), (zero_zero real), skv_12 ) 17.02/16.71 ( real, real, (ord_less_eq real), (zero_zero real), skv_14 ) 17.02/16.71 ( real, real, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.02/16.71 ( 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))) ) 17.02/16.71 ( 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) ) 17.02/16.71 ( real, real, (ord_less_eq real), skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.71 ( real, real, (ord_less real), (zero_zero real), pi ) 17.02/16.71 ( 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)))) ) 17.02/16.71 ( 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)))) ) 17.02/16.71 ( real, real, (ord_less real), (zero_zero real), skv_2 ) 17.02/16.71 ( real, real, (ord_less real), (zero_zero real), skv_10 ) 17.02/16.71 ( real, real, (ord_less real), (zero_zero real), skv_13 ) 17.02/16.71 ( 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)))) ) 17.02/16.71 ( real, real, (ord_less real), pi, (zero_zero real) ) 17.02/16.71 ( 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)))) ) 17.02/16.71 ( 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))) ) 17.02/16.71 ( 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) ) 17.02/16.71 ( 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) ) 17.02/16.71 ( 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 ) 17.02/16.71 ( real, (fun nat real), (sums real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 17.02/16.71 ( nat, nat, (ord_less nat), (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.71 ( (fun nat bool), (fun nat int), (nat_tr1645093318rphism nat int), (semiring_1_of_nat int), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 17.02/16.71 ( int, int, (ord_less_eq int), (zero_zero int), (one_one int) ) 17.02/16.71 ( int, int, (ord_less_eq int), (zero_zero int), min_1 ) 17.02/16.71 ( 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))) ) 17.02/16.71 ( int, int, (ord_less_eq int), (zero_zero int), s ) 17.02/16.71 ( int, int, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 17.02/16.71 ( 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))) ) 17.02/16.71 ( int, int, (ord_less_eq int), (zero_zero int), skv_3 ) 17.02/16.71 ( int, int, (ord_less_eq int), (zero_zero int), skv_9 ) 17.02/16.71 ( int, int, (ord_less_eq int), (one_one int), t ) 17.02/16.71 ( int, int, (ord_less_eq int), min_1, pls ) 17.02/16.71 ( int, int, (ord_less_eq int), min_1, min_1 ) 17.02/16.71 ( int, int, (ord_less int), (zero_zero int), (zero_zero int) ) 17.02/16.71 ( int, int, (ord_less int), (zero_zero int), (one_one int) ) 17.02/16.71 ( 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))) ) 17.02/16.71 ( int, int, (ord_less int), (zero_zero int), min_1 ) 17.02/16.71 ( int, int, (ord_less int), min_1, (zero_zero int) ) 17.02/16.71 ( int, int, (ord_less int), min_1, min_1 ) 17.02/16.71 ( 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))) ) 17.02/16.71 ( int, int, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.02/16.71 ( int, int, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.02/16.71 ( int, int, (ord_less int), t, (zero_zero int) ) 17.02/16.71 ( int, int, (ord_less int), t, (one_one int) ) 17.02/16.71 ( 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))) ) 17.02/16.71 ( int, int, (ord_less int), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.71 ( int, int, (ord_less int), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.71 ( int, int, (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.02/16.72 ( int, int, quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 17.02/16.72 ( 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))) ) 17.02/16.72 ( int, int, (hAPP int (fun int (fun int bool)) zcong s1), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.72 ( int, int, (hAPP int (fun int (fun int bool)) zcong s1), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.72 ( int, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.72 ( 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))) ) 17.02/16.72 ( int, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.72 ( int, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.72 ( (fun int bool), int, (member int), (one_one int), zEven ) 17.02/16.72 ( (fun int bool), (fun int nat), (nat_tr1645093318rphism int nat), nat_1, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 17.02/16.72 ( (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))))) ) 17.02/16.72 ( (filter nat), real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real (fun (filter nat) bool)) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real), sequentially ) 17.02/16.72 ) 17.02/16.72 (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)))) ) 17.02/16.72 ( real ) 17.02/16.72 ( nat ) 17.02/16.72 ( int ) 17.02/16.72 ( complex ) 17.02/16.72 ( rat ) 17.02/16.72 ( quickcheck_code_int ) 17.02/16.72 ( code_code_numeral ) 17.02/16.72 ) 17.02/16.72 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real (hAPP nat (fun real real) root N_1) X_1)) _let_0)) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X_1) _let_0)))) )))) 17.02/16.72 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.72 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.72 ( (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))) ) 17.02/16.72 ( (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))) ) 17.02/16.72 ) 17.02/16.72 (instantiation (let ((_let_0 (inverse_inverse X_a))) (let ((_let_1 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_113558))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_113557 $$unsorted) (BOUND_VARIABLE_113558 $$unsorted)) (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_113557)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_113558)))) (not (hBOOL (hAPP X_a bool _let_1 (zero_zero X_a)))) (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_113557))) ))) 17.02/16.72 ( real, (zero_zero real), pi ) 17.02/16.72 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 17.02/16.72 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.72 ( real, pi, (zero_zero real) ) 17.02/16.72 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 17.02/16.72 ( 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)))) ) 17.02/16.72 ( 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) ) 17.02/16.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 17.02/16.72 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.02/16.72 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 17.02/16.72 ( real, skv_2, (zero_zero real) ) 17.02/16.72 ( real, skv_10, (zero_zero real) ) 17.02/16.72 ( real, skv_13, (zero_zero real) ) 17.02/16.72 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 17.02/16.72 ( int, (zero_zero int), (zero_zero int) ) 17.02/16.72 ( int, (zero_zero int), min_1 ) 17.02/16.72 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.02/16.72 ( int, (zero_zero int), t ) 17.02/16.72 ( int, (one_one int), (zero_zero int) ) 17.02/16.72 ( int, (one_one int), t ) 17.02/16.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 17.02/16.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 17.02/16.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 17.02/16.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_3 ) 17.02/16.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_9 ) 17.02/16.72 ( int, min_1, (zero_zero int) ) 17.02/16.72 ( int, min_1, min_1 ) 17.02/16.72 ( 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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.02/16.72 ) 17.02/16.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113589 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (one_one X_a) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_113589) (zero_zero nat)))) ) 17.02/16.72 ( real, (hAPP int real (number_number_of real) min_1) ) 17.02/16.72 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.72 ( int, s ) 17.02/16.72 ( int, s1 ) 17.02/16.72 ( int, skv_8 ) 17.02/16.72 ( complex, ii ) 17.02/16.72 ) 17.02/16.72 (instantiation (let ((_let_0 (norm_norm X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_113627 $$unsorted) (BOUND_VARIABLE_113628 $$unsorted)) (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_113627)) (hAPP X_a real _let_0 BOUND_VARIABLE_113628)))) (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_113627) BOUND_VARIABLE_113628))))) )) 17.02/16.72 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 17.02/16.72 ( 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)))), (hAPP int int (number_number_of int) min_1) ) 17.02/16.72 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 17.02/16.72 ) 17.02/16.72 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (one_one real))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) _let_3))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (exp real) (hAPP real real (hAPP real _let_2 (minus_minus real) X) (hAPP nat real (hAPP real (fun nat real) (power_power real) X) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (hAPP real real (hAPP real _let_2 (plus_plus real) _let_3) X)))) ))))) 17.02/16.72 ( pi ) 17.02/16.72 ( (hAPP int real (number_number_of real) min_1) ) 17.02/16.72 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.72 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.72 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.72 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 17.02/16.72 ( skv_6 ) 17.02/16.72 ( skv_11 ) 17.02/16.72 ( skv_12 ) 17.02/16.72 ( skv_14 ) 17.02/16.72 ) 17.02/16.72 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (plus_plus nat))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_1 M) N)) (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat suc M)) N)) ))) 17.02/16.72 ( (zero_zero nat), (one_one nat) ) 17.02/16.72 ( (one_one nat), (one_one nat) ) 17.02/16.72 ) 17.02/16.72 (instantiation (let ((_let_0 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_113741 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a _let_0 (hAPP int int (uminus_uminus int) BOUND_VARIABLE_113741)) (hAPP X_a X_a (uminus_uminus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_113741)))) )) 17.02/16.72 ( real, (one_one int) ) 17.02/16.72 ( nat, pls ) 17.02/16.72 ( nat, min_1 ) 17.02/16.72 ( int, pls ) 17.02/16.72 ( int, (hAPP int int bit1 pls) ) 17.02/16.72 ( int, (one_one int) ) 17.02/16.72 ( int, min_1 ) 17.02/16.72 ( complex, (one_one int) ) 17.02/16.72 ( quickcheck_code_int, pls ) 17.02/16.72 ( quickcheck_code_int, min_1 ) 17.02/16.72 ( code_code_numeral, pls ) 17.02/16.72 ( code_code_numeral, min_1 ) 17.02/16.72 ) 17.02/16.72 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_113758 $$unsorted) (BOUND_VARIABLE_113759 $$unsorted)) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_113758) BOUND_VARIABLE_113759))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_113759) BOUND_VARIABLE_113758)))) ))) 17.02/16.72 ( real, (zero_zero real), pi ) 17.02/16.72 ( 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)))) ) 17.02/16.72 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 17.02/16.72 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.72 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.72 ( real, (zero_zero real), skv_2 ) 17.02/16.72 ( real, (zero_zero real), skv_10 ) 17.02/16.72 ( real, (zero_zero real), skv_13 ) 17.02/16.72 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.72 ( real, pi, (zero_zero real) ) 17.02/16.72 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.72 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 17.02/16.72 ( 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)))) ) 17.02/16.72 ( 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) ) 17.02/16.72 ( 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))) ) 17.02/16.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 17.02/16.72 ( 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) ) 17.02/16.73 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.02/16.73 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.02/16.73 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 17.02/16.73 ( 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 ) 17.02/16.73 ( real, skv_2, (zero_zero real) ) 17.02/16.73 ( real, skv_10, (zero_zero real) ) 17.02/16.73 ( real, skv_13, (zero_zero real) ) 17.02/16.73 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.73 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 17.02/16.73 ( int, (zero_zero int), (zero_zero int) ) 17.02/16.73 ( int, (zero_zero int), (one_one int) ) 17.02/16.73 ( 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))) ) 17.02/16.73 ( int, (zero_zero int), min_1 ) 17.02/16.73 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.02/16.73 ( int, (zero_zero int), t ) 17.02/16.73 ( int, (one_one int), (zero_zero int) ) 17.02/16.73 ( int, (one_one int), t ) 17.02/16.73 ( 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) ) 17.02/16.73 ( 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 ) 17.02/16.73 ( 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 ) 17.02/16.73 ( 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_3 ) 17.02/16.73 ( 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_9 ) 17.02/16.73 ( int, min_1, (zero_zero int) ) 17.02/16.73 ( int, min_1, min_1 ) 17.02/16.73 ( 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))) ) 17.02/16.73 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.02/16.73 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.02/16.73 ( int, t, (zero_zero int) ) 17.02/16.73 ( int, t, (one_one int) ) 17.02/16.73 ( 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))) ) 17.02/16.73 ( 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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.02/16.73 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.73 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.73 ) 17.02/16.73 (instantiation (let ((_let_0 (even_odd_even int))) (forall ((N $$unsorted) (X $$unsorted)) (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))))) )) 17.02/16.73 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 17.02/16.73 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 17.02/16.73 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 17.02/16.73 ) 17.02/16.73 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less int) W_1))) (forall ((W_1 $$unsorted) (Z $$unsorted)) (= (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) Z) (one_one int)))) (or (hBOOL (hAPP int bool _let_0 Z)) (= (ti int W_1) (ti int Z)))) )) 17.02/16.73 ( (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) ) 17.02/16.73 ( 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) ) 17.02/16.73 ( 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) ) 17.02/16.73 ( skv_3, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 17.02/16.73 ( skv_9, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 17.02/16.73 ) 17.02/16.73 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (fun int int))) (forall ((B $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int (hAPP int _let_2 (plus_plus int) A_1) B)) _let_1))) (= (hAPP int int (number_number_of int) min_1) (hAPP int int (hAPP int _let_2 (div_div int) A_1) B))) )))) 17.02/16.73 ( (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) ) 17.02/16.73 ( (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)))) ) 17.02/16.73 ) 17.02/16.73 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= X_1 Y_1) (= (hAPP real real sqrt X_1) (hAPP real real sqrt Y_1))) ) 17.02/16.73 ( (zero_zero real), (zero_zero real) ) 17.02/16.73 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.02/16.73 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 17.02/16.73 ( (hAPP int 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))) ) 17.02/16.73 ( (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))) ) 17.02/16.73 ( (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))) ) 17.02/16.73 ) 17.02/16.73 (instantiation (let ((_let_0 (even_odd_even nat))) (let ((_let_1 (hAPP int X_a (number_number_of X_a) min_1))) (let ((_let_2 (hAPP X_a (fun nat X_a) (power_power X_a) _let_1))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_113923 $$unsorted) (BOUND_VARIABLE_113930 $$unsorted)) (or (not (number_ring X_a)) (and (or (not (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_113923))) (= (one_one X_a) (hAPP nat X_a _let_2 BOUND_VARIABLE_113923))) (or (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_113930)) (= _let_1 (hAPP nat X_a _let_2 BOUND_VARIABLE_113930))))) )))) 17.02/16.73 ( real, (one_one nat), (one_one nat) ) 17.02/16.73 ( complex, (zero_zero nat), (zero_zero nat) ) 17.02/16.73 ) 17.02/16.73 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_113948 $$unsorted)) (or (not (divisi14063676e_zero X_a)) (= (= _let_0 (ti X_a BOUND_VARIABLE_113948)) (= _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_113948)))) )) 17.02/16.73 ( bool, fFalse ) 17.02/16.73 ( bool, fTrue ) 17.02/16.73 ( real, (zero_zero real) ) 17.02/16.73 ( real, pi ) 17.02/16.73 ( (fun nat bool), (even_odd_even nat) ) 17.02/16.73 ( (fun nat bool), prime ) 17.02/16.73 ( (fun nat nat), suc ) 17.02/16.73 ( (fun nat nat), (fact_fact nat) ) 17.02/16.73 ( (fun nat nat), (size_size nat) ) 17.02/16.73 ( (fun nat nat), fact ) 17.02/16.73 ( (fun nat nat), nat_size ) 17.02/16.73 ( int, pls ) 17.02/16.73 ( int, m ) 17.02/16.73 ( int, min_1 ) 17.02/16.73 ( int, s ) 17.02/16.73 ( int, s1 ) 17.02/16.73 ( int, t ) 17.02/16.73 ( (fun int bool), zprime ) 17.02/16.73 ( (fun int bool), nat_neg ) 17.02/16.73 ( (fun int bool), zEven ) 17.02/16.73 ( (fun int bool), nat_is_nat ) 17.02/16.73 ( (fun int bool), zOdd ) 17.02/16.73 ( (fun int bool), (even_odd_even int) ) 17.02/16.73 ( (fun int bool), twoSqu1091635170sum2sq ) 17.02/16.73 ( (fun int nat), nat_1 ) 17.02/16.73 ( (fun int nat), phi ) 17.02/16.73 ( (fun real real), sqrt ) 17.02/16.73 ( (fun real real), tan ) 17.02/16.73 ( (fun real real), cos ) 17.02/16.73 ( (fun real real), arccos ) 17.02/16.73 ( (fun real real), ln ) 17.02/16.73 ( (fun real real), sin ) 17.02/16.73 ( (fun real real), arctan ) 17.02/16.73 ( (fun real real), arcsin ) 17.02/16.73 ( complex, ii ) 17.02/16.73 ( (fun complex complex), cnj ) 17.02/16.73 ( (fun complex complex), expi ) 17.02/16.73 ( (fun nat real), (real_1 nat) ) 17.02/16.73 ( (fun nat real), cos_coeff ) 17.02/16.73 ( (fun nat real), sin_coeff ) 17.02/16.73 ( (fun int int), bit0 ) 17.02/16.73 ( (fun int int), bit1 ) 17.02/16.73 ( (fun int int), pred ) 17.02/16.73 ( (fun int int), succ ) 17.02/16.73 ( (fun int int), (fact_fact int) ) 17.02/16.73 ( (fun int int), zfact ) 17.02/16.73 ( (fun bool bool), fNot ) 17.02/16.73 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.02/16.73 ( (fun bool (fun bool bool)), fconj ) 17.02/16.73 ( (fun bool (fun bool bool)), fdisj ) 17.02/16.73 ( (fun bool (fun bool bool)), fimplies ) 17.02/16.73 ( (fun int (fun int bool)), sRStar ) 17.02/16.73 ( (fun int (fun int bool)), quadRes ) 17.02/16.73 ( (fun int (fun int bool)), norRRset ) 17.02/16.73 ( (fun int (fun int bool)), d22set ) 17.02/16.73 ( (fun int (fun int bool)), sr ) 17.02/16.73 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 17.02/16.73 ( (fun nat (fun nat nat)), nat_gcd ) 17.02/16.73 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 17.02/16.73 ( (fun nat (fun nat nat)), nat_lcm ) 17.02/16.73 ( (fun nat (fun real real)), root ) 17.02/16.73 ( (fun real (fun real real)), log ) 17.02/16.73 ( (fun real (fun real real)), powr ) 17.02/16.73 ( (fun nat (fun nat bool)), coprime ) 17.02/16.73 ( (fun (fun int bool) int), (the int) ) 17.02/16.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 17.02/16.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 17.02/16.73 ( (fun nat (fun nat (product_prod int int))), bezw ) 17.02/16.73 ( (fun (fun int bool) bool), nat_nat_set ) 17.02/16.73 ( (filter nat), sequentially ) 17.02/16.73 ( (fun (product_prod nat nat) bool), pred_nat ) 17.02/16.73 ( (fun (product_prod int int) bool), frac_1 ) 17.02/16.73 ( (fun real complex), cis ) 17.02/16.73 ( (fun complex real), im ) 17.02/16.73 ( (fun complex real), re ) 17.02/16.73 ( (fun complex real), arg ) 17.02/16.73 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 17.02/16.73 ( (fun int (fun int int)), int_gcd ) 17.02/16.73 ( (fun int (fun int int)), multInv ) 17.02/16.73 ( (fun int (fun int int)), legacy_zgcd ) 17.02/16.73 ( (fun int (fun int int)), z3mod ) 17.02/16.73 ( (fun int (fun int int)), inv ) 17.02/16.73 ( (fun int (fun int int)), (gcd_gcd int) ) 17.02/16.73 ( (fun int (fun int int)), standardRes ) 17.02/16.73 ( (fun int (fun int int)), legendre ) 17.02/16.73 ( (fun int (fun int int)), nat_tsub ) 17.02/16.73 ( (fun int (fun int int)), z3div ) 17.02/16.73 ( (fun int (fun int int)), int_lcm ) 17.02/16.73 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 17.02/16.73 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 17.02/16.73 ( (fun int (fun (fun int bool) bool)), rsetR ) 17.02/16.73 ( (fun int (fun (fun int bool) bool)), resSet ) 17.02/16.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 17.02/16.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 17.02/16.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 17.02/16.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.02/16.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 17.02/16.73 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 17.02/16.73 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 17.02/16.73 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 17.02/16.73 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.02/16.73 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.02/16.73 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.02/16.73 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.02/16.73 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.02/16.73 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.02/16.73 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 17.02/16.73 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 17.02/16.73 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 17.02/16.73 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 17.02/16.73 ( (fun real nat), natfloor ) 17.02/16.73 ( (fun real nat), natceiling ) 17.02/16.73 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.02/16.73 ( (fun int (fun int (fun int bool))), wset ) 17.02/16.73 ( (fun int (fun int (fun int bool))), bnorRset ) 17.02/16.73 ( (fun int (fun int (fun int bool))), zcong ) 17.02/16.73 ( (fun int (fun int (fun int bool))), noXRRset ) 17.02/16.73 ( (fun int (fun int (fun int bool))), zcongm ) 17.02/16.73 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.02/16.73 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.02/16.73 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.02/16.73 ( (fun int real), (real_1 int) ) 17.02/16.73 ( (fun complex nat), (size_size complex) ) 17.02/16.73 ( (fun complex nat), complex_size ) 17.02/16.73 ( (fun int (list int)), quickc666637781d_zero ) 17.02/16.73 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.02/16.73 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.02/16.73 ( (fun (product_prod int int) rat), frct ) 17.02/16.73 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.02/16.73 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.02/16.73 ( (fun (fun nat rat) bool), vanishes ) 17.02/16.73 ( (fun int (fun int rat)), fract ) 17.02/16.73 ( (fun code_code_numeral int), code_int_of ) 17.02/16.73 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.02/16.73 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.02/16.73 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.02/16.73 ( (fun real (fun real complex)), complex_1 ) 17.02/16.73 ( (fun real (fun real complex)), rcis ) 17.02/16.73 ( (fun int (fun nat nat)), nat_aux ) 17.02/16.73 ( (fun rat real), ratreal ) 17.02/16.73 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.02/16.73 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.02/16.73 ( (fun rat (product_prod int int)), quotient_of ) 17.02/16.73 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.02/16.73 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.02/16.73 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.02/16.73 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.02/16.73 ) 17.02/16.73 (instantiation (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)))))) (forall ((X $$unsorted)) (= X (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_0) _let_0)) )) 17.02/16.73 ( (one_one real) ) 17.02/16.73 ( pi ) 17.02/16.73 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.02/16.73 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 17.02/16.73 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.74 ) 17.02/16.74 (instantiation (let ((_let_0 (zero_zero int))) (forall ((X $$unsorted)) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) _let_0) X)) (= _let_0 (hAPP int int (fact_fact int) X))) )) 17.02/16.74 ( (zero_zero int) ) 17.02/16.74 ( (one_one int) ) 17.02/16.74 ( min_1 ) 17.02/16.74 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.74 ( s ) 17.02/16.74 ( (hAPP int int (number_number_of int) pls) ) 17.02/16.74 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.02/16.74 ( skv_3 ) 17.02/16.74 ( skv_9 ) 17.02/16.74 ) 17.02/16.74 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X))) (= (hAPP int int (fact_fact int) X) (hAPP nat int (semiring_1_of_nat int) (hAPP nat nat (fact_fact nat) (hAPP int nat nat_1 X))))) ) 17.02/16.74 ( (zero_zero int) ) 17.02/16.74 ( (one_one int) ) 17.02/16.74 ( min_1 ) 17.02/16.74 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.74 ( s ) 17.02/16.74 ( (hAPP int int (number_number_of int) pls) ) 17.02/16.74 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.02/16.74 ( skv_3 ) 17.02/16.74 ( skv_9 ) 17.02/16.74 ) 17.02/16.74 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun X_a _let_0))) (let ((_let_2 (ord_atLeastLessThan X_a))) (let ((_let_3 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_114084 $$unsorted) (BOUND_VARIABLE_114085 $$unsorted) (BOUND_VARIABLE_114086 $$unsorted) (BOUND_VARIABLE_114087 $$unsorted)) (or (not (linorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 BOUND_VARIABLE_114086) BOUND_VARIABLE_114087))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 BOUND_VARIABLE_114084) BOUND_VARIABLE_114085))) (= (and (= (ti X_a BOUND_VARIABLE_114086) (ti X_a BOUND_VARIABLE_114084)) (= (ti X_a BOUND_VARIABLE_114087) (ti X_a BOUND_VARIABLE_114085))) (= (hAPP X_a _let_0 (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_114084) BOUND_VARIABLE_114085) (hAPP X_a _let_0 (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_114086) BOUND_VARIABLE_114087)))) ))))) 17.02/16.74 ( real, (zero_zero real), pi, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.74 ( 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)))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.74 ( 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)))), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.74 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.74 ( real, (zero_zero real), skv_2, (zero_zero real), skv_2 ) 17.02/16.74 ( real, (zero_zero real), skv_2, (zero_zero real), skv_10 ) 17.02/16.74 ( real, (zero_zero real), skv_10, (zero_zero real), skv_2 ) 17.02/16.74 ( real, (zero_zero real), skv_13, (zero_zero real), skv_13 ) 17.02/16.74 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), pi ) 17.02/16.74 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.74 ( real, pi, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.74 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi, (zero_zero real) ) 17.02/16.74 ( 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)))) ) 17.02/16.74 ( 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))), (hAPP real real (hAPP real (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))) ) 17.02/16.74 ( 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))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.02/16.74 ( 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), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP 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 ) 17.02/16.74 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), (hAPP real real (hAPP real (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))) ) 17.02/16.74 ( 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, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP 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) ) 17.02/16.74 ( 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, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP 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 ) 17.02/16.74 ( 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))) ) 17.02/16.74 ( int, (zero_zero int), (zero_zero int), t, (zero_zero int) ) 17.02/16.74 ( int, (zero_zero int), (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))) ) 17.02/16.74 ( 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))), (zero_zero int), (one_one int) ) 17.02/16.74 ( 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))), (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))) ) 17.02/16.74 ( int, (zero_zero int), min_1, t, (one_one int) ) 17.02/16.74 ( int, min_1, (zero_zero int), min_1, (zero_zero int) ) 17.02/16.74 ( int, min_1, (zero_zero int), min_1, min_1 ) 17.02/16.74 ( int, min_1, min_1, min_1, (zero_zero int) ) 17.02/16.74 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.02/16.74 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero 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))) ) 17.02/16.74 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.02/16.74 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero 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))) ) 17.02/16.74 ( int, t, (zero_zero int), (zero_zero int), (zero_zero int) ) 17.02/16.74 ( int, t, (zero_zero int), t, (zero_zero int) ) 17.02/16.74 ( int, t, (one_one int), (zero_zero int), min_1 ) 17.02/16.74 ( int, t, (one_one int), t, (one_one int) ) 17.02/16.74 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.02/16.74 ( 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))), 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))) ) 17.02/16.74 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.74 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.74 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.74 ) 17.02/16.74 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (= (= K L) (= (hAPP quickcheck_code_int int quickcheck_int_of K) (hAPP quickcheck_code_int int quickcheck_int_of L))) ) 17.02/16.74 ( (zero_zero quickcheck_code_int), (zero_zero quickcheck_code_int) ) 17.02/16.74 ) 17.02/16.74 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (one_one X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_114239 $$unsorted)) (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_114239))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_114239) _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_114239)))) )))) 17.02/16.74 ( real, (zero_zero real) ) 17.02/16.74 ( real, (one_one real) ) 17.02/16.74 ( real, pi ) 17.02/16.74 ( 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)))) ) 17.02/16.74 ( 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))))) ) 17.02/16.74 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.74 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.74 ( 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)) ) 17.02/16.74 ( real, skv_2 ) 17.02/16.74 ( real, skv_10 ) 17.02/16.74 ( real, skv_13 ) 17.02/16.74 ( nat, (zero_zero nat) ) 17.02/16.74 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.74 ( int, (zero_zero int) ) 17.02/16.74 ( int, (one_one int) ) 17.02/16.74 ( 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))) ) 17.02/16.74 ( int, min_1 ) 17.02/16.74 ( int, s ) 17.02/16.74 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.02/16.74 ( int, t ) 17.02/16.74 ( int, skv_3 ) 17.02/16.74 ( int, skv_9 ) 17.02/16.74 ( complex, ii ) 17.02/16.74 ) 17.02/16.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114267 $$unsorted) (BOUND_VARIABLE_114268 $$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_114267) BOUND_VARIABLE_114268))) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_min X_a) BOUND_VARIABLE_114267) BOUND_VARIABLE_114268) (ti X_a BOUND_VARIABLE_114267))) ) 17.02/16.74 ( real, (zero_zero real), pi ) 17.02/16.74 ( 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)))) ) 17.02/16.74 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.74 ( real, (zero_zero real), skv_6 ) 17.02/16.74 ( real, (zero_zero real), skv_11 ) 17.02/16.74 ( real, (zero_zero real), skv_12 ) 17.02/16.74 ( real, (zero_zero real), skv_14 ) 17.02/16.74 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.02/16.74 ( 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))) ) 17.02/16.74 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.02/16.74 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.74 ( int, (zero_zero int), (one_one int) ) 17.02/16.74 ( int, (zero_zero int), min_1 ) 17.02/16.74 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.74 ( int, (zero_zero int), s ) 17.02/16.74 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 17.02/16.75 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.02/16.75 ( int, (zero_zero int), skv_3 ) 17.02/16.75 ( int, (zero_zero int), skv_9 ) 17.02/16.75 ( int, (one_one int), t ) 17.02/16.75 ( int, min_1, pls ) 17.02/16.75 ( int, min_1, min_1 ) 17.02/16.75 ) 17.02/16.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114329 $$unsorted) (BOUND_VARIABLE_114330 $$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_114329) BOUND_VARIABLE_114330))) (= (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_114329) (ti X_a BOUND_VARIABLE_114330))) ) 17.02/16.75 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.02/16.75 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.02/16.75 ( 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)))))) ) 17.02/16.75 ( 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 ) 17.02/16.75 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 17.02/16.75 ( 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) ) 17.02/16.75 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 17.02/16.75 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1 ) 17.02/16.75 ( complex, ii, ii ) 17.02/16.75 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 17.02/16.75 ( 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 ) 17.02/16.75 ) 17.02/16.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114378 $$unsorted)) (or (not (real_normed_vector X_a)) (= (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_114378)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real (norm_norm X_a) BOUND_VARIABLE_114378)) (zero_zero real))))) ) 17.02/16.75 ( bool, fFalse ) 17.02/16.75 ( bool, fTrue ) 17.02/16.75 ( real, pi ) 17.02/16.75 ( (fun nat bool), (even_odd_even nat) ) 17.02/16.75 ( (fun nat bool), prime ) 17.02/16.75 ( (fun nat nat), suc ) 17.02/16.75 ( (fun nat nat), (fact_fact nat) ) 17.02/16.75 ( (fun nat nat), (size_size nat) ) 17.02/16.75 ( (fun nat nat), fact ) 17.02/16.75 ( (fun nat nat), nat_size ) 17.02/16.75 ( int, pls ) 17.02/16.75 ( int, m ) 17.02/16.75 ( int, min_1 ) 17.02/16.75 ( int, s ) 17.02/16.75 ( int, s1 ) 17.02/16.75 ( int, t ) 17.02/16.75 ( (fun int bool), zprime ) 17.02/16.75 ( (fun int bool), nat_neg ) 17.02/16.75 ( (fun int bool), zEven ) 17.02/16.75 ( (fun int bool), nat_is_nat ) 17.02/16.75 ( (fun int bool), zOdd ) 17.02/16.75 ( (fun int bool), (even_odd_even int) ) 17.02/16.75 ( (fun int bool), twoSqu1091635170sum2sq ) 17.02/16.75 ( (fun int nat), nat_1 ) 17.02/16.75 ( (fun int nat), phi ) 17.02/16.75 ( (fun real real), sqrt ) 17.02/16.75 ( (fun real real), tan ) 17.02/16.75 ( (fun real real), cos ) 17.02/16.75 ( (fun real real), arccos ) 17.02/16.75 ( (fun real real), ln ) 17.02/16.75 ( (fun real real), sin ) 17.02/16.75 ( (fun real real), arctan ) 17.02/16.75 ( (fun real real), arcsin ) 17.02/16.75 ( complex, ii ) 17.02/16.75 ( (fun complex complex), cnj ) 17.02/16.75 ( (fun complex complex), expi ) 17.02/16.75 ( (fun nat real), (real_1 nat) ) 17.02/16.75 ( (fun nat real), cos_coeff ) 17.02/16.75 ( (fun nat real), sin_coeff ) 17.02/16.75 ( (fun int int), bit0 ) 17.02/16.75 ( (fun int int), bit1 ) 17.02/16.75 ( (fun int int), pred ) 17.02/16.75 ( (fun int int), succ ) 17.02/16.75 ( (fun int int), (fact_fact int) ) 17.02/16.75 ( (fun int int), zfact ) 17.02/16.75 ( (fun bool bool), fNot ) 17.02/16.75 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.02/16.75 ( (fun bool (fun bool bool)), fconj ) 17.02/16.75 ( (fun bool (fun bool bool)), fdisj ) 17.02/16.75 ( (fun bool (fun bool bool)), fimplies ) 17.02/16.75 ( (fun int (fun int bool)), sRStar ) 17.02/16.75 ( (fun int (fun int bool)), quadRes ) 17.02/16.75 ( (fun int (fun int bool)), norRRset ) 17.02/16.75 ( (fun int (fun int bool)), d22set ) 17.02/16.75 ( (fun int (fun int bool)), sr ) 17.02/16.75 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 17.02/16.75 ( (fun nat (fun nat nat)), nat_gcd ) 17.02/16.75 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 17.02/16.75 ( (fun nat (fun nat nat)), nat_lcm ) 17.02/16.75 ( (fun nat (fun real real)), root ) 17.02/16.75 ( (fun real (fun real real)), log ) 17.02/16.75 ( (fun real (fun real real)), powr ) 17.02/16.75 ( (fun nat (fun nat bool)), coprime ) 17.02/16.75 ( (fun (fun int bool) int), (the int) ) 17.02/16.75 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 17.02/16.75 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 17.02/16.75 ( (fun nat (fun nat (product_prod int int))), bezw ) 17.02/16.75 ( (fun (fun int bool) bool), nat_nat_set ) 17.02/16.75 ( (filter nat), sequentially ) 17.02/16.75 ( (fun (product_prod nat nat) bool), pred_nat ) 17.02/16.75 ( (fun (product_prod int int) bool), frac_1 ) 17.02/16.75 ( (fun real complex), cis ) 17.02/16.75 ( (fun complex real), im ) 17.02/16.75 ( (fun complex real), re ) 17.02/16.75 ( (fun complex real), arg ) 17.02/16.75 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 17.02/16.75 ( (fun int (fun int int)), int_gcd ) 17.02/16.75 ( (fun int (fun int int)), multInv ) 17.02/16.75 ( (fun int (fun int int)), legacy_zgcd ) 17.02/16.75 ( (fun int (fun int int)), z3mod ) 17.02/16.75 ( (fun int (fun int int)), inv ) 17.02/16.75 ( (fun int (fun int int)), (gcd_gcd int) ) 17.02/16.75 ( (fun int (fun int int)), standardRes ) 17.02/16.75 ( (fun int (fun int int)), legendre ) 17.02/16.75 ( (fun int (fun int int)), nat_tsub ) 17.02/16.75 ( (fun int (fun int int)), z3div ) 17.02/16.75 ( (fun int (fun int int)), int_lcm ) 17.02/16.75 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 17.02/16.75 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 17.02/16.75 ( (fun int (fun (fun int bool) bool)), rsetR ) 17.02/16.75 ( (fun int (fun (fun int bool) bool)), resSet ) 17.02/16.75 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 17.02/16.75 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 17.02/16.75 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 17.02/16.75 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.02/16.75 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 17.02/16.75 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 17.02/16.75 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 17.02/16.75 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 17.02/16.75 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.02/16.75 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.02/16.75 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.02/16.75 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.02/16.75 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.02/16.75 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.02/16.75 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 17.02/16.75 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 17.02/16.75 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 17.02/16.75 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 17.02/16.75 ( (fun real nat), natfloor ) 17.02/16.75 ( (fun real nat), natceiling ) 17.02/16.75 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.02/16.75 ( (fun int (fun int (fun int bool))), wset ) 17.02/16.75 ( (fun int (fun int (fun int bool))), bnorRset ) 17.02/16.75 ( (fun int (fun int (fun int bool))), zcong ) 17.02/16.75 ( (fun int (fun int (fun int bool))), noXRRset ) 17.02/16.75 ( (fun int (fun int (fun int bool))), zcongm ) 17.02/16.75 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.02/16.75 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.02/16.75 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.02/16.75 ( (fun int real), (real_1 int) ) 17.02/16.75 ( (fun complex nat), (size_size complex) ) 17.02/16.75 ( (fun complex nat), complex_size ) 17.02/16.75 ( (fun int (list int)), quickc666637781d_zero ) 17.02/16.75 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.02/16.75 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.02/16.75 ( (fun (product_prod int int) rat), frct ) 17.02/16.75 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.02/16.75 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.02/16.75 ( (fun (fun nat rat) bool), vanishes ) 17.02/16.75 ( (fun int (fun int rat)), fract ) 17.02/16.75 ( (fun code_code_numeral int), code_int_of ) 17.02/16.75 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.02/16.75 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.02/16.75 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.02/16.75 ( (fun real (fun real complex)), complex_1 ) 17.02/16.75 ( (fun real (fun real complex)), rcis ) 17.02/16.75 ( (fun int (fun nat nat)), nat_aux ) 17.02/16.75 ( (fun rat real), ratreal ) 17.02/16.75 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.02/16.75 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.02/16.75 ( (fun rat (product_prod int int)), quotient_of ) 17.02/16.75 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.02/16.75 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.02/16.75 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.02/16.75 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.02/16.75 ) 17.02/16.75 (instantiation (let ((_let_0 (norm_norm X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_114396 $$unsorted) (BOUND_VARIABLE_114397 $$unsorted)) (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_114396) BOUND_VARIABLE_114397)) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP X_a real _let_0 BOUND_VARIABLE_114396)) BOUND_VARIABLE_114397))) )) 17.02/16.75 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.75 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.75 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.75 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.75 ) 17.02/16.75 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted)) (or (not (field_char_0 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (one_one X_a)) (field_char_0_Rats X_a)))) )) 17.02/16.75 ( real ) 17.02/16.75 ( nat ) 17.02/16.75 ( int ) 17.02/16.75 ( complex ) 17.02/16.75 ( rat ) 17.02/16.75 ( quickcheck_code_int ) 17.02/16.75 ( code_code_numeral ) 17.02/16.75 ) 17.02/16.75 (instantiation (let ((_let_0 (fun real bool))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) ln) X_1) (hAPP real real (inverse_inverse real) X_1)))) )) 17.02/16.75 ( (zero_zero real) ) 17.02/16.75 ( pi ) 17.02/16.75 ( (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)))) ) 17.02/16.75 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.75 ( skv_2 ) 17.02/16.75 ( skv_10 ) 17.02/16.75 ( skv_13 ) 17.02/16.75 ) 17.02/16.75 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (power_power nat))) (let ((_let_2 (minus_minus nat))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP nat nat (hAPP nat _let_0 _let_1 X) _let_3)) (hAPP nat nat (hAPP nat _let_0 _let_1 Y) _let_3)) (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))) ))))) 17.02/16.75 ( (one_one nat), (one_one nat) ) 17.02/16.75 ) 17.02/16.75 (instantiation (let ((_let_0 (zero_zero int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) A_1) B)))) (let ((_let_3 (hAPP int (fun int _let_1) posDivAlg A_1))) (let ((_let_4 (hAPP int _let_1 _let_3 B))) (forall ((A_1 $$unsorted) (B $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_0) B))) (and (or (not _let_2) (= _let_4 (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) _let_0) A_1))) (or _let_2 (= _let_4 (hAPP _let_1 _let_1 (hAPP int (fun _let_1 _let_1) adjust B) (hAPP int _let_1 _let_3 (hAPP int int (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))))))) )))))) 17.02/16.75 ( (zero_zero int), (zero_zero int) ) 17.02/16.75 ( (zero_zero int), (one_one int) ) 17.02/16.75 ( (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))) ) 17.02/16.75 ( (zero_zero int), min_1 ) 17.02/16.75 ( min_1, (zero_zero int) ) 17.02/16.75 ( min_1, min_1 ) 17.02/16.75 ( 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))) ) 17.02/16.75 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.02/16.75 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.02/16.75 ( t, (zero_zero int) ) 17.02/16.75 ( t, (one_one int) ) 17.02/16.75 ( 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))) ) 17.02/16.75 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.75 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.75 ) 17.02/16.75 (instantiation (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Ma) N_1)) (not (forall ((K_1 $$unsorted)) (not (= N_1 (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) K_1)))) ))) ) 17.02/16.75 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.75 ) 17.02/16.75 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (real_1 nat))) (let ((_let_2 (times_times real))) (let ((_let_3 (even_odd_even nat))) (let ((_let_4 (hAPP real real (hAPP real _let_0 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (forall ((X_1 $$unsorted)) (= (= (zero_zero real) (hAPP real real cos X_1)) (or (not (forall ((N_2 $$unsorted)) (or (not (= X_1 (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real _let_0 _let_2 (hAPP nat real _let_1 N_2)) _let_4)))) (hBOOL (hAPP nat bool _let_3 N_2))) )) (not (forall ((N_2 $$unsorted)) (or (not (= X_1 (hAPP real real (hAPP real _let_0 _let_2 (hAPP nat real _let_1 N_2)) _let_4))) (hBOOL (hAPP nat bool _let_3 N_2))) )))) )))))) 17.02/16.76 ( (zero_zero real) ) 17.02/16.76 ( pi ) 17.02/16.76 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.76 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.76 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 17.02/16.76 ( (hAPP real real (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))))) ) 17.02/16.76 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 17.02/16.76 ( (hAPP real 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))))) ) 17.02/16.76 ( (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)))) ) 17.02/16.76 ( skv_14 ) 17.02/16.76 ) 17.02/16.76 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_114539 $$unsorted)) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_114539) _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_114539) BOUND_VARIABLE_114539)) _let_2)))) )))) 17.02/16.76 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.76 ( nat, (one_one nat) ) 17.02/16.76 ( int, (zero_zero int) ) 17.02/16.76 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 17.02/16.76 ( int, min_1 ) 17.02/16.76 ( 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)))) ) 17.02/16.76 ) 17.02/16.76 (instantiation (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (minus_minus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_114608 $$unsorted) (BOUND_VARIABLE_114609 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_114608)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_114609)))) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_114608) BOUND_VARIABLE_114609))))) )))) 17.02/16.76 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 17.02/16.76 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 17.02/16.76 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 17.02/16.76 ) 17.02/16.76 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (X_1 $$unsorted)) (= (ti X_a X_1) (hAPP _let_0 X_a (hilbert_Eps X_a) (hAPP X_a _let_0 (fequal X_a) X_1))) )) 17.02/16.76 ( bool, fFalse ) 17.02/16.76 ( bool, fTrue ) 17.02/16.76 ( real, pi ) 17.02/16.76 ( (fun nat bool), (even_odd_even nat) ) 17.02/16.76 ( (fun nat bool), prime ) 17.02/16.76 ( (fun nat nat), suc ) 17.02/16.76 ( (fun nat nat), (fact_fact nat) ) 17.02/16.76 ( (fun nat nat), (size_size nat) ) 17.02/16.76 ( (fun nat nat), fact ) 17.02/16.76 ( (fun nat nat), nat_size ) 17.02/16.76 ( int, pls ) 17.02/16.76 ( int, m ) 17.02/16.76 ( int, min_1 ) 17.02/16.76 ( int, s ) 17.02/16.76 ( int, s1 ) 17.02/16.76 ( int, t ) 17.02/16.76 ( (fun int bool), zprime ) 17.02/16.76 ( (fun int bool), nat_neg ) 17.02/16.76 ( (fun int bool), zEven ) 17.02/16.76 ( (fun int bool), nat_is_nat ) 17.02/16.76 ( (fun int bool), zOdd ) 17.02/16.76 ( (fun int bool), (even_odd_even int) ) 17.02/16.76 ( (fun int bool), twoSqu1091635170sum2sq ) 17.02/16.76 ( (fun int nat), nat_1 ) 17.02/16.76 ( (fun int nat), phi ) 17.02/16.76 ( (fun real real), sqrt ) 17.02/16.76 ( (fun real real), tan ) 17.02/16.76 ( (fun real real), cos ) 17.02/16.76 ( (fun real real), arccos ) 17.02/16.76 ( (fun real real), ln ) 17.02/16.76 ( (fun real real), sin ) 17.02/16.76 ( (fun real real), arctan ) 17.02/16.76 ( (fun real real), arcsin ) 17.02/16.76 ( complex, ii ) 17.02/16.76 ( (fun complex complex), cnj ) 17.02/16.76 ( (fun complex complex), expi ) 17.02/16.76 ( (fun nat real), (real_1 nat) ) 17.02/16.76 ( (fun nat real), cos_coeff ) 17.02/16.76 ( (fun nat real), sin_coeff ) 17.02/16.76 ( (fun int int), bit0 ) 17.02/16.76 ( (fun int int), bit1 ) 17.02/16.76 ( (fun int int), pred ) 17.02/16.76 ( (fun int int), succ ) 17.02/16.76 ( (fun int int), (fact_fact int) ) 17.02/16.76 ( (fun int int), zfact ) 17.02/16.76 ( (fun bool bool), fNot ) 17.02/16.76 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.02/16.76 ( (fun bool (fun bool bool)), fconj ) 17.02/16.76 ( (fun bool (fun bool bool)), fdisj ) 17.02/16.76 ( (fun bool (fun bool bool)), fimplies ) 17.02/16.76 ( (fun int (fun int bool)), sRStar ) 17.02/16.76 ( (fun int (fun int bool)), quadRes ) 17.02/16.76 ( (fun int (fun int bool)), norRRset ) 17.02/16.76 ( (fun int (fun int bool)), d22set ) 17.02/16.76 ( (fun int (fun int bool)), sr ) 17.02/16.76 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 17.02/16.76 ( (fun nat (fun nat nat)), nat_gcd ) 17.02/16.76 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 17.02/16.76 ( (fun nat (fun nat nat)), nat_lcm ) 17.02/16.76 ( (fun nat (fun real real)), root ) 17.02/16.76 ( (fun real (fun real real)), log ) 17.02/16.76 ( (fun real (fun real real)), powr ) 17.02/16.76 ( (fun nat (fun nat bool)), coprime ) 17.02/16.76 ( (fun (fun int bool) int), (the int) ) 17.02/16.76 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 17.02/16.76 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 17.02/16.76 ( (fun nat (fun nat (product_prod int int))), bezw ) 17.02/16.76 ( (fun (fun int bool) bool), nat_nat_set ) 17.02/16.76 ( (filter nat), sequentially ) 17.02/16.76 ( (fun (product_prod nat nat) bool), pred_nat ) 17.02/16.76 ( (fun (product_prod int int) bool), frac_1 ) 17.02/16.76 ( (fun real complex), cis ) 17.02/16.76 ( (fun complex real), im ) 17.02/16.76 ( (fun complex real), re ) 17.02/16.76 ( (fun complex real), arg ) 17.02/16.76 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 17.02/16.76 ( (fun int (fun int int)), int_gcd ) 17.02/16.76 ( (fun int (fun int int)), multInv ) 17.02/16.76 ( (fun int (fun int int)), legacy_zgcd ) 17.02/16.76 ( (fun int (fun int int)), z3mod ) 17.02/16.76 ( (fun int (fun int int)), inv ) 17.02/16.76 ( (fun int (fun int int)), (gcd_gcd int) ) 17.02/16.76 ( (fun int (fun int int)), standardRes ) 17.02/16.76 ( (fun int (fun int int)), legendre ) 17.02/16.76 ( (fun int (fun int int)), nat_tsub ) 17.02/16.76 ( (fun int (fun int int)), z3div ) 17.02/16.76 ( (fun int (fun int int)), int_lcm ) 17.02/16.76 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 17.02/16.76 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 17.02/16.76 ( (fun int (fun (fun int bool) bool)), rsetR ) 17.02/16.76 ( (fun int (fun (fun int bool) bool)), resSet ) 17.02/16.76 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 17.02/16.76 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 17.02/16.76 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 17.02/16.76 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.02/16.76 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 17.02/16.76 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 17.02/16.76 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 17.02/16.76 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 17.02/16.76 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.02/16.76 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.02/16.76 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.02/16.76 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.02/16.76 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.02/16.76 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.02/16.76 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 17.02/16.76 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 17.02/16.76 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 17.02/16.76 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 17.02/16.76 ( (fun real nat), natfloor ) 17.02/16.76 ( (fun real nat), natceiling ) 17.02/16.76 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.02/16.76 ( (fun int (fun int (fun int bool))), wset ) 17.02/16.76 ( (fun int (fun int (fun int bool))), bnorRset ) 17.02/16.76 ( (fun int (fun int (fun int bool))), zcong ) 17.02/16.76 ( (fun int (fun int (fun int bool))), noXRRset ) 17.02/16.76 ( (fun int (fun int (fun int bool))), zcongm ) 17.02/16.76 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.02/16.76 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.02/16.76 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.02/16.76 ( (fun int real), (real_1 int) ) 17.02/16.76 ( (fun complex nat), (size_size complex) ) 17.02/16.76 ( (fun complex nat), complex_size ) 17.02/16.76 ( (fun int (list int)), quickc666637781d_zero ) 17.02/16.76 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.02/16.76 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.02/16.76 ( (fun (product_prod int int) rat), frct ) 17.02/16.76 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.02/16.76 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.02/16.76 ( (fun (fun nat rat) bool), vanishes ) 17.02/16.76 ( (fun int (fun int rat)), fract ) 17.02/16.76 ( (fun code_code_numeral int), code_int_of ) 17.02/16.76 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.02/16.76 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.02/16.76 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.02/16.76 ( (fun real (fun real complex)), complex_1 ) 17.02/16.76 ( (fun real (fun real complex)), rcis ) 17.02/16.76 ( (fun int (fun nat nat)), nat_aux ) 17.02/16.76 ( (fun rat real), ratreal ) 17.02/16.76 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.02/16.76 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.02/16.76 ( (fun rat (product_prod int int)), quotient_of ) 17.02/16.76 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.02/16.76 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.02/16.76 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.02/16.76 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.02/16.76 ) 17.02/16.76 (instantiation (let ((_let_0 (hAPP int (fun int bool) (dvd_dvd int) P_5))) (forall ((N $$unsorted) (P_5 $$unsorted) (M $$unsorted)) (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 M)) (hBOOL (hAPP int bool _let_0 N))) )) 17.02/16.76 ( skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.76 ) 17.02/16.76 (instantiation (let ((_let_0 (one_one X_a))) (forall ((X_a $$unsorted)) (or (not (linordered_idom X_a)) (= _let_0 (hAPP X_a X_a (abs_abs X_a) _let_0))) )) 17.02/16.76 ( real ) 17.02/16.76 ( nat ) 17.02/16.76 ( int ) 17.02/16.76 ( complex ) 17.02/16.76 ( rat ) 17.02/16.76 ( quickcheck_code_int ) 17.02/16.76 ( code_code_numeral ) 17.02/16.76 ) 17.02/16.76 (instantiation (let ((_let_0 (fun nat nat))) (forall ((I_1 $$unsorted) (N $$unsorted)) (= (hAPP nat nat (hAPP int _let_0 nat_aux I_1) N) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) (hAPP int nat nat_1 I_1)) N)) )) 17.02/16.76 ( (one_one int), (one_one nat) ) 17.02/16.76 ) 17.02/16.76 (instantiation (forall ((X_a $$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))))) ) 17.02/16.76 ( bool ) 17.02/16.76 ( real ) 17.02/16.76 ( nat ) 17.02/16.76 ( (fun nat bool) ) 17.02/16.76 ( int ) 17.02/16.76 ( (fun int bool) ) 17.02/16.76 ( complex ) 17.02/16.76 ( rat ) 17.02/16.76 ( quickcheck_code_int ) 17.02/16.76 ( (product_prod real real) ) 17.02/16.76 ( (product_prod int int) ) 17.02/16.76 ( (filter real) ) 17.02/16.76 ( (filter nat) ) 17.02/16.76 ( (product_prod nat nat) ) 17.02/16.76 ( code_code_numeral ) 17.02/16.76 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 17.02/16.76 ( (fun nat rat) ) 17.02/16.76 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 17.02/16.76 ) 17.02/16.76 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_114836 $$unsorted)) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_114836) _let_2)) (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_114836))))) )))) 17.02/16.76 ( real, (zero_zero real) ) 17.02/16.76 ( real, (one_one real) ) 17.02/16.76 ( real, pi ) 17.02/16.76 ( 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)))) ) 17.02/16.76 ( 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) ) 17.02/16.76 ( 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))))) ) 17.02/16.76 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.76 ( 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)) ) 17.02/16.76 ( nat, (zero_zero nat) ) 17.02/16.76 ( int, (zero_zero int) ) 17.02/16.76 ( int, pls ) 17.02/16.76 ( int, (one_one int) ) 17.02/16.76 ( int, min_1 ) 17.02/16.76 ( int, s ) 17.02/16.76 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.02/16.76 ( int, t ) 17.02/16.76 ( int, skv_3 ) 17.02/16.76 ( int, skv_9 ) 17.02/16.76 ( complex, ii ) 17.02/16.76 ( complex, (one_one complex) ) 17.02/16.76 ) 17.02/16.76 (instantiation (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))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (= (hAPP _let_2 _let_1 (hilbert_Eps _let_1) (hAPP _let_4 _let_2 (product_prod_case X_a X_b bool) (hAPP _let_3 _let_4 (hAPP _let_6 (fun _let_3 _let_4) (combc X_a _let_3 _let_3) (hAPP _let_7 _let_6 (hAPP (fun _let_0 _let_5) (fun _let_7 _let_6) (combb _let_0 _let_5 X_a) (combb bool bool X_b)) (hAPP _let_8 _let_7 (hAPP (fun bool _let_0) (fun _let_8 _let_7) (combb bool _let_0 X_a) fconj) (hAPP X_a _let_8 (fequal X_a) X_1)))) (hAPP X_b _let_3 (fequal X_b) Y_1)))) (hAPP X_b _let_1 (hAPP X_a (fun X_b _let_1) (product_Pair X_a X_b) X_1) Y_1)) )))))))))) 17.02/16.76 ( int, int, (zero_zero int), (one_one int) ) 17.02/16.76 ( int, int, (one_one int), (one_one int) ) 17.02/16.76 ( int, int, s, (one_one int) ) 17.02/16.76 ) 17.02/16.76 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP _let_0 nat (finite_card X_a) A_3)))) (hBOOL (hAPP _let_0 bool (finite_finite_1 X_a) A_3))) )) 17.02/16.76 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 17.02/16.76 ) 17.02/16.76 (instantiation (let ((_let_0 (semiring_1_of_nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_114896 $$unsorted) (BOUND_VARIABLE_114897 $$unsorted)) (or (not (semiring_char_0 X_a)) (= (= (hAPP nat X_a _let_0 BOUND_VARIABLE_114896) (hAPP nat X_a _let_0 BOUND_VARIABLE_114897)) (= BOUND_VARIABLE_114896 BOUND_VARIABLE_114897))) )) 17.02/16.76 ( real, (zero_zero nat), (one_one nat) ) 17.02/16.76 ( real, (one_one nat), (zero_zero nat) ) 17.02/16.76 ( real, (one_one nat), (one_one nat) ) 17.02/16.76 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 17.02/16.76 ( int, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.02/16.76 ( int, (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 17.02/16.76 ( int, (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)) ) 17.02/16.76 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.76 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP nat nat suc (zero_zero nat)) ) 17.02/16.76 ) 17.02/16.76 (instantiation (let ((_let_0 (ord_less int))) (let ((_let_1 (hAPP int (fun int bool) _let_0 (zero_zero int)))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int (fun int bool)))) (forall ((N_1 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool _let_1 N_1))) (= (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat nat_1 N_1)) (one_one nat)) (hAPP _let_0 nat (finite_card int) (hAPP _let_0 _let_0 (collect 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) _let_1)) (hAPP int _let_0 (hAPP _let_4 _let_4 (combc int int bool) _let_0) N_1))))))) )))))) 17.02/16.77 ( (zero_zero int) ) 17.02/16.77 ( (one_one int) ) 17.02/16.77 ( (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))) ) 17.02/16.77 ( min_1 ) 17.02/16.77 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.77 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.02/16.77 ) 17.02/16.77 (instantiation (let ((_let_0 (fun real bool))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X_1) Y_1)) (and (not (= X_1 Y_1)) (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) X_1) Y_1)))) )) 17.02/16.77 ( (zero_zero real), pi ) 17.02/16.77 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.77 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.77 ( (zero_zero real), skv_2 ) 17.02/16.77 ( (zero_zero real), skv_6 ) 17.02/16.77 ( (zero_zero real), skv_10 ) 17.02/16.77 ( (zero_zero real), skv_11 ) 17.02/16.77 ( (zero_zero real), skv_12 ) 17.02/16.77 ( (zero_zero real), skv_13 ) 17.02/16.77 ( (zero_zero real), skv_14 ) 17.02/16.77 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.77 ( pi, (zero_zero real) ) 17.02/16.77 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.77 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.02/16.77 ( (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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.77 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP 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) ) 17.02/16.77 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.02/16.77 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP 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 ) 17.02/16.77 ( skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.77 ) 17.02/16.77 (instantiation (let ((_let_0 (zero_zero nat))) (let ((_let_1 (hAPP nat nat suc _let_0))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (= _let_1 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) N_1)) (or (and (= _let_0 Ma) (= _let_1 N_1)) (and (= _let_0 N_1) (= _let_1 Ma)))) ))) 17.02/16.77 ( (one_one nat), (one_one nat) ) 17.02/16.77 ) 17.02/16.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114968 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (uminus_uminus int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_114968)) (hAPP X_a int (archim2085082626_floor X_a) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_114968)))) ) 17.02/16.77 ( real, (one_one real) ) 17.02/16.77 ( 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)))) ) 17.02/16.77 ( 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) ) 17.02/16.77 ( int, pls ) 17.02/16.77 ( int, (one_one int) ) 17.02/16.77 ( int, min_1 ) 17.02/16.77 ( complex, ii ) 17.02/16.77 ( complex, (one_one complex) ) 17.02/16.77 ) 17.02/16.77 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_1) zOdd))) (not (forall ((K_1 $$unsorted)) (not (= (ti int X_1) (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) K_1)) (one_one int)))) ))) ))) 17.02/16.77 ( (one_one int) ) 17.02/16.77 ) 17.02/16.77 (instantiation (forall ((X_a $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (one_one int) (hAPP X_a int (archimedean_ceiling X_a) (one_one X_a)))) ) 17.02/16.77 ( real ) 17.02/16.77 ( nat ) 17.02/16.77 ( int ) 17.02/16.77 ( complex ) 17.02/16.77 ( rat ) 17.02/16.77 ( quickcheck_code_int ) 17.02/16.77 ( code_code_numeral ) 17.02/16.77 ) 17.02/16.77 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP nat real (real_1 nat) N))) (forall ((N $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) _let_1) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) X) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_1) (one_one real))))) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N) (one_one nat)) (hAPP real nat natceiling X))) ))) 17.02/16.77 ( (zero_zero nat), pi ) 17.02/16.77 ( (zero_zero nat), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.77 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.77 ( (zero_zero nat), skv_2 ) 17.02/16.77 ( (zero_zero nat), skv_10 ) 17.02/16.77 ( (zero_zero nat), skv_13 ) 17.02/16.77 ( (one_one nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.77 ) 17.02/16.77 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (forall ((X_5 $$unsorted) (N_6 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_6))) (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) _let_0) X_5))) (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less_eq real) _let_0) (hAPP real real (hAPP nat (fun real real) root N_6) X_5)))) ))) 17.02/16.77 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.77 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.77 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.77 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.77 ) 17.02/16.77 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (forall ((Y $$unsorted) (X $$unsorted) (P_5 $$unsorted)) (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)))) ))) 17.02/16.77 ( s, (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.77 ( 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))) ) 17.02/16.77 ( s1, (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.77 ( skv_8, (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.77 ) 17.02/16.77 (instantiation (forall ((X $$unsorted)) (= (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP real real sin X)) (hAPP real real cos X)) (hAPP real real tan X)) ) 17.02/16.77 ( (zero_zero real) ) 17.02/16.77 ( pi ) 17.02/16.77 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.77 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.77 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 17.02/16.77 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 17.02/16.77 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 17.02/16.77 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 17.02/16.77 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 17.02/16.77 ( skv_14 ) 17.02/16.77 ) 17.02/16.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115280 $$unsorted)) (or (not (power X_a)) (= (one_one X_a) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_115280) (zero_zero nat)))) ) 17.02/16.77 ( real, (hAPP int real (number_number_of real) min_1) ) 17.02/16.77 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.77 ( int, s ) 17.02/16.77 ( int, s1 ) 17.02/16.77 ( int, skv_8 ) 17.02/16.77 ( complex, ii ) 17.02/16.77 ) 17.02/16.77 (instantiation (forall ((X_a $$unsorted) (C_1 $$unsorted) (P_1 $$unsorted) (BOUND_VARIABLE_115314 $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 BOUND_VARIABLE_115314))) (not (= (ti X_a C_1) (hAPP (fun X_a bool) X_a (hilbert_Eps X_a) P_1))) (hBOOL (hAPP X_a bool P_1 C_1))) ) 17.02/16.77 ( real, pi, (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)))) ) 17.02/16.77 ( (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) ) 17.02/16.77 ( (fun nat bool), prime, (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 17.02/16.77 ( int, pls, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 17.02/16.77 ( int, m, nat_neg, (hAPP int int (number_number_of int) pls) ) 17.02/16.77 ( int, min_1, 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))) ) 17.02/16.77 ( int, s, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.77 ( int, s1, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 17.02/16.77 ( int, t, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))), (zero_zero int) ) 17.02/16.77 ( (fun int bool), nat_neg, (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)) ) 17.02/16.77 ( (fun int bool), nat_is_nat, (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 17.02/16.77 ( (filter nat), sequentially, (trivial_limit nat), sequentially ) 17.02/16.77 ) 17.02/16.77 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less_eq X_b))) (let ((_let_2 (number_number_of X_b))) (let ((_let_3 (fun X_b X_b))) (let ((_let_4 (ord_min X_b))) (let ((_let_5 (hAPP int X_b _let_2 BOUND_VARIABLE_115345))) (let ((_let_6 (hAPP int X_b _let_2 BOUND_VARIABLE_115346))) (let ((_let_7 (hAPP int X_b _let_2 BOUND_VARIABLE_115356))) (let ((_let_8 (hAPP int X_b _let_2 BOUND_VARIABLE_115357))) (forall ((X_b $$unsorted) (BOUND_VARIABLE_115345 $$unsorted) (BOUND_VARIABLE_115346 $$unsorted) (BOUND_VARIABLE_115356 $$unsorted) (BOUND_VARIABLE_115357 $$unsorted)) (or (not (number X_b)) (not (ord X_b)) (and (or (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 _let_5) _let_6)) (= _let_6 (hAPP X_b X_b (hAPP X_b _let_3 _let_4 _let_5) _let_6))) (or (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 _let_7) _let_8))) (= _let_7 (hAPP X_b X_b (hAPP X_b _let_3 _let_4 _let_7) _let_8))))) )))))))))) 17.02/16.77 ( 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)) ) 17.02/16.77 ( 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))) ) 17.02/16.77 ( real, min_1, min_1, min_1, min_1 ) 17.02/16.77 ( 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))) ) 17.02/16.77 ( 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)) ) 17.02/16.77 ( 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))) ) 17.02/16.77 ( 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)))))))), (hAPP int int bit1 (hAPP int int bit1 (hAPP 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)))))))) ) 17.02/16.77 ( nat, pls, pls, pls, pls ) 17.02/16.77 ( nat, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 17.02/16.77 ( 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)) ) 17.02/16.77 ( 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)) ) 17.02/16.77 ( int, pls, pls, pls, pls ) 17.02/16.77 ( int, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 17.02/16.77 ( 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)) ) 17.02/16.77 ( 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))) ) 17.02/16.77 ( int, min_1, min_1, min_1, min_1 ) 17.02/16.77 ( 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)) ) 17.02/16.77 ( 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)) ) 17.02/16.77 ( complex, min_1, min_1, min_1, min_1 ) 17.02/16.77 ( quickcheck_code_int, (zero_zero int), (zero_zero int), (zero_zero int), (zero_zero int) ) 17.02/16.77 ( quickcheck_code_int, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 17.02/16.78 ( quickcheck_code_int, (one_one int), (one_one int), (one_one int), (one_one int) ) 17.02/16.78 ( code_code_numeral, pls, pls, pls, pls ) 17.02/16.78 ( code_code_numeral, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 17.02/16.78 ) 17.02/16.78 (instantiation (let ((_let_0 (zero_zero int))) (forall ((N $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) _let_0) N))) (not (= _let_0 (hAPP int int (fact_fact int) N)))) )) 17.02/16.78 ( (zero_zero int) ) 17.02/16.78 ( (one_one int) ) 17.02/16.78 ( min_1 ) 17.02/16.78 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.78 ( s ) 17.02/16.78 ( (hAPP int int (number_number_of int) pls) ) 17.02/16.78 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.02/16.78 ( skv_3 ) 17.02/16.78 ( skv_9 ) 17.02/16.78 ) 17.02/16.78 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((X_a $$unsorted)) (or (not (real_algebra_1 X_a)) (not (real_normed_vector X_a)) (not (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) K_2))) (not (forall ((X_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (norm_norm X_a) (hAPP real X_a (of_real X_a) X_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real (norm_norm real) X_2)) K_2))) ))) ))) ))) 17.02/16.78 ( real ) 17.02/16.78 ( complex ) 17.02/16.78 ) 17.02/16.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115430 $$unsorted) (BOUND_VARIABLE_115431 $$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_115430) BOUND_VARIABLE_115431))) (not (= (ti X_a BOUND_VARIABLE_115431) (ti X_a BOUND_VARIABLE_115430)))) ) 17.02/16.78 ( real, (zero_zero real), pi ) 17.02/16.78 ( 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)))) ) 17.02/16.78 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.78 ( real, (zero_zero real), skv_2 ) 17.02/16.78 ( real, (zero_zero real), skv_10 ) 17.02/16.78 ( real, (zero_zero real), skv_13 ) 17.02/16.78 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.78 ( real, pi, (zero_zero real) ) 17.02/16.78 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.78 ( 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))) ) 17.02/16.78 ( 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) ) 17.02/16.78 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.02/16.78 ( 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 ) 17.02/16.78 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.78 ( int, (zero_zero int), (zero_zero int) ) 17.02/16.78 ( int, (zero_zero int), (one_one int) ) 17.02/16.78 ( 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))) ) 17.02/16.78 ( int, (zero_zero int), min_1 ) 17.02/16.78 ( int, min_1, (zero_zero int) ) 17.02/16.78 ( int, min_1, min_1 ) 17.02/16.78 ( 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))) ) 17.02/16.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.02/16.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.02/16.78 ( int, t, (zero_zero int) ) 17.02/16.78 ( int, t, (one_one int) ) 17.02/16.78 ( 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))) ) 17.02/16.78 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.78 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.78 ) 17.02/16.78 (instantiation (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (minus_minus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_115458 $$unsorted) (BOUND_VARIABLE_115459 $$unsorted)) (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_115459) BOUND_VARIABLE_115458)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_115458) BOUND_VARIABLE_115459)))) )))) 17.02/16.78 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 17.02/16.78 ( 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 bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 17.02/16.78 ( int, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.78 ( 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)))), (hAPP int int (number_number_of int) min_1) ) 17.02/16.78 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 17.02/16.78 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 17.02/16.78 ) 17.02/16.78 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_115503 $$unsorted) (BOUND_VARIABLE_115504 $$unsorted)) (or (not (linorder X_a)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_115503) BOUND_VARIABLE_115504)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_115504) BOUND_VARIABLE_115503))) ))) 17.02/16.78 ( real, (zero_zero real), pi ) 17.02/16.78 ( 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)))) ) 17.02/16.78 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.78 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.78 ( real, (zero_zero real), skv_6 ) 17.02/16.78 ( real, (zero_zero real), skv_11 ) 17.02/16.78 ( real, (zero_zero real), skv_12 ) 17.02/16.78 ( real, (zero_zero real), skv_14 ) 17.02/16.78 ( real, pi, (zero_zero real) ) 17.02/16.78 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.78 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.02/16.78 ( 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)))) ) 17.02/16.78 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 17.02/16.78 ( 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)))), (zero_zero real) ) 17.02/16.78 ( 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))) ) 17.02/16.78 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.02/16.78 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.02/16.78 ( real, skv_6, (zero_zero real) ) 17.02/16.78 ( real, skv_11, (zero_zero real) ) 17.02/16.78 ( real, skv_12, (zero_zero real) ) 17.02/16.78 ( real, skv_14, (zero_zero real) ) 17.02/16.78 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.78 ( int, (zero_zero int), (one_one int) ) 17.02/16.78 ( int, (zero_zero int), min_1 ) 17.02/16.78 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.78 ( int, (zero_zero int), s ) 17.02/16.78 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 17.02/16.78 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.02/16.78 ( int, (zero_zero int), skv_3 ) 17.02/16.78 ( int, (zero_zero int), skv_9 ) 17.02/16.78 ( int, pls, min_1 ) 17.02/16.78 ( int, (one_one int), (zero_zero int) ) 17.02/16.78 ( int, (one_one int), t ) 17.02/16.78 ( int, min_1, (zero_zero int) ) 17.02/16.78 ( int, min_1, pls ) 17.02/16.78 ( int, min_1, min_1 ) 17.02/16.78 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 17.02/16.78 ( int, s, (zero_zero int) ) 17.02/16.78 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 17.02/16.78 ( int, t, (one_one int) ) 17.02/16.78 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 17.02/16.78 ( int, skv_3, (zero_zero int) ) 17.02/16.78 ( int, skv_9, (zero_zero int) ) 17.02/16.78 ) 17.02/16.78 (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_1) (hAPP real real (sgn_sgn real) X))) ) 17.02/16.78 ( (zero_zero real) ) 17.02/16.78 ( (one_one real) ) 17.02/16.78 ( pi ) 17.02/16.78 ( (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)))) ) 17.02/16.78 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 17.02/16.78 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.78 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 17.02/16.78 ) 17.02/16.78 (instantiation (let ((_let_0 (ti X_a BOUND_VARIABLE_115531))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_115531 $$unsorted)) (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_115531)))) )) 17.02/16.78 ( bool, fFalse ) 17.02/16.78 ( bool, fTrue ) 17.02/16.78 ( real, (one_one real) ) 17.02/16.78 ( real, pi ) 17.02/16.78 ( 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)))) ) 17.02/16.78 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 17.02/16.78 ( (fun nat bool), (even_odd_even nat) ) 17.02/16.78 ( (fun nat bool), prime ) 17.02/16.78 ( (fun nat nat), suc ) 17.02/16.78 ( (fun nat nat), (fact_fact nat) ) 17.02/16.78 ( (fun nat nat), (size_size nat) ) 17.02/16.78 ( (fun nat nat), fact ) 17.02/16.78 ( (fun nat nat), nat_size ) 17.02/16.78 ( int, pls ) 17.02/16.78 ( int, m ) 17.02/16.78 ( int, (one_one int) ) 17.02/16.78 ( int, min_1 ) 17.02/16.78 ( int, s ) 17.02/16.78 ( int, s1 ) 17.02/16.78 ( int, t ) 17.02/16.78 ( (fun int bool), zprime ) 17.02/16.78 ( (fun int bool), nat_neg ) 17.02/16.78 ( (fun int bool), zEven ) 17.02/16.78 ( (fun int bool), nat_is_nat ) 17.02/16.78 ( (fun int bool), zOdd ) 17.02/16.78 ( (fun int bool), (even_odd_even int) ) 17.02/16.78 ( (fun int bool), twoSqu1091635170sum2sq ) 17.02/16.78 ( (fun int nat), nat_1 ) 17.02/16.78 ( (fun int nat), phi ) 17.02/16.78 ( (fun real real), sqrt ) 17.02/16.78 ( (fun real real), tan ) 17.02/16.78 ( (fun real real), cos ) 17.02/16.78 ( (fun real real), arccos ) 17.02/16.78 ( (fun real real), ln ) 17.02/16.78 ( (fun real real), sin ) 17.02/16.78 ( (fun real real), arctan ) 17.02/16.78 ( (fun real real), arcsin ) 17.02/16.78 ( complex, ii ) 17.02/16.78 ( complex, (one_one complex) ) 17.02/16.78 ( (fun complex complex), cnj ) 17.02/16.78 ( (fun complex complex), expi ) 17.02/16.78 ( (fun nat real), (real_1 nat) ) 17.02/16.78 ( (fun nat real), cos_coeff ) 17.02/16.78 ( (fun nat real), sin_coeff ) 17.02/16.78 ( (fun int int), bit0 ) 17.02/16.78 ( (fun int int), bit1 ) 17.02/16.78 ( (fun int int), pred ) 17.02/16.78 ( (fun int int), succ ) 17.02/16.78 ( (fun int int), (fact_fact int) ) 17.02/16.78 ( (fun int int), zfact ) 17.02/16.78 ( (fun bool bool), fNot ) 17.02/16.78 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.02/16.78 ( (fun bool (fun bool bool)), fconj ) 17.02/16.78 ( (fun bool (fun bool bool)), fdisj ) 17.02/16.78 ( (fun bool (fun bool bool)), fimplies ) 17.02/16.78 ( (fun int (fun int bool)), sRStar ) 17.02/16.78 ( (fun int (fun int bool)), quadRes ) 17.02/16.78 ( (fun int (fun int bool)), norRRset ) 17.02/16.78 ( (fun int (fun int bool)), d22set ) 17.02/16.78 ( (fun int (fun int bool)), sr ) 17.02/16.78 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 17.02/16.78 ( (fun nat (fun nat nat)), nat_gcd ) 17.02/16.78 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 17.02/16.78 ( (fun nat (fun nat nat)), nat_lcm ) 17.02/16.78 ( (fun nat (fun real real)), root ) 17.02/16.78 ( (fun real (fun real real)), log ) 17.02/16.78 ( (fun real (fun real real)), powr ) 17.02/16.78 ( (fun nat (fun nat bool)), coprime ) 17.02/16.78 ( (fun (fun int bool) int), (the int) ) 17.02/16.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 17.02/16.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 17.02/16.78 ( (fun nat (fun nat (product_prod int int))), bezw ) 17.02/16.78 ( (fun (fun int bool) bool), nat_nat_set ) 17.02/16.78 ( (filter nat), sequentially ) 17.02/16.78 ( (fun (product_prod nat nat) bool), pred_nat ) 17.02/16.78 ( (fun (product_prod int int) bool), frac_1 ) 17.02/16.78 ( (fun real complex), cis ) 17.02/16.78 ( (fun complex real), im ) 17.02/16.78 ( (fun complex real), re ) 17.02/16.78 ( (fun complex real), arg ) 17.02/16.78 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 17.02/16.78 ( (fun int (fun int int)), int_gcd ) 17.02/16.78 ( (fun int (fun int int)), multInv ) 17.02/16.78 ( (fun int (fun int int)), legacy_zgcd ) 17.02/16.78 ( (fun int (fun int int)), z3mod ) 17.02/16.78 ( (fun int (fun int int)), inv ) 17.02/16.78 ( (fun int (fun int int)), (gcd_gcd int) ) 17.02/16.78 ( (fun int (fun int int)), standardRes ) 17.02/16.78 ( (fun int (fun int int)), legendre ) 17.02/16.78 ( (fun int (fun int int)), nat_tsub ) 17.02/16.78 ( (fun int (fun int int)), z3div ) 17.02/16.78 ( (fun int (fun int int)), int_lcm ) 17.02/16.78 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 17.02/16.78 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 17.02/16.78 ( (fun int (fun (fun int bool) bool)), rsetR ) 17.02/16.78 ( (fun int (fun (fun int bool) bool)), resSet ) 17.02/16.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 17.02/16.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 17.02/16.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 17.02/16.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.02/16.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 17.02/16.78 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 17.02/16.78 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 17.02/16.78 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 17.02/16.78 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.02/16.78 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.02/16.78 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.02/16.78 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.02/16.78 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.02/16.78 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.02/16.78 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 17.02/16.78 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 17.02/16.78 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 17.02/16.79 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 17.02/16.79 ( (fun real nat), natfloor ) 17.02/16.79 ( (fun real nat), natceiling ) 17.02/16.79 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.02/16.79 ( (fun int (fun int (fun int bool))), wset ) 17.02/16.79 ( (fun int (fun int (fun int bool))), bnorRset ) 17.02/16.79 ( (fun int (fun int (fun int bool))), zcong ) 17.02/16.79 ( (fun int (fun int (fun int bool))), noXRRset ) 17.02/16.79 ( (fun int (fun int (fun int bool))), zcongm ) 17.02/16.79 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.02/16.79 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.02/16.79 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.02/16.79 ( (fun int real), (real_1 int) ) 17.02/16.79 ( (fun complex nat), (size_size complex) ) 17.02/16.79 ( (fun complex nat), complex_size ) 17.02/16.79 ( (fun int (list int)), quickc666637781d_zero ) 17.02/16.79 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.02/16.79 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.02/16.79 ( (fun (product_prod int int) rat), frct ) 17.02/16.79 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.02/16.79 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.02/16.79 ( (fun (fun nat rat) bool), vanishes ) 17.02/16.79 ( (fun int (fun int rat)), fract ) 17.02/16.79 ( (fun code_code_numeral int), code_int_of ) 17.02/16.79 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.02/16.79 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.02/16.79 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.02/16.79 ( (fun real (fun real complex)), complex_1 ) 17.02/16.79 ( (fun real (fun real complex)), rcis ) 17.02/16.79 ( (fun int (fun nat nat)), nat_aux ) 17.02/16.79 ( (fun rat real), ratreal ) 17.02/16.79 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.02/16.79 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.02/16.79 ( (fun rat (product_prod int int)), quotient_of ) 17.02/16.79 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.02/16.79 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.02/16.79 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.02/16.79 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.02/16.79 ) 17.02/16.79 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (filter X_a))) (let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun X_a real))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (tendsto X_a real))) (let ((_let_8 (hAPP X_a _let_3 (at X_a) BOUND_VARIABLE_115566))) (let ((_let_9 (ti X_a BOUND_VARIABLE_115566))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_115564 $$unsorted) (BOUND_VARIABLE_115565 $$unsorted) (BOUND_VARIABLE_115566 $$unsorted)) (or (not (topological_space X_a)) (not (hBOOL (hAPP _let_3 bool (hAPP real _let_4 (hAPP _let_5 _let_6 _let_7 BOUND_VARIABLE_115565) _let_0) _let_8))) (not (forall ((X_2 $$unsorted)) (or (= (ti X_a X_2) _let_9) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 _let_0) (hAPP X_a real BOUND_VARIABLE_115564 X_2)))) )) (not (forall ((X_2 $$unsorted)) (or (= (ti X_a X_2) _let_9) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP X_a real BOUND_VARIABLE_115564 X_2)) (hAPP X_a real BOUND_VARIABLE_115565 X_2)))) )) (hBOOL (hAPP _let_3 bool (hAPP real _let_4 (hAPP _let_5 _let_6 _let_7 BOUND_VARIABLE_115564) _let_0) _let_8))) ))))))))))) 17.02/16.79 ( 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)))) ) 17.02/16.79 ) 17.02/16.79 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (fun int int))) (let ((_let_4 (ord_less int))) (forall ((B_5 $$unsorted) (Q_5 $$unsorted) (R_5 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 (hAPP int int (hAPP int _let_3 (plus_plus int) (hAPP int int (hAPP int _let_3 (times_times int) B_5) Q_5)) R_5)) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) R_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 _let_2) B_5))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Q_5) _let_2))) )))))) 17.02/16.79 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, (one_one int) ) 17.02/16.79 ) 17.02/16.79 (instantiation (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (hAPP int int (number_number_of int) min_1))) (forall ((B $$unsorted)) (= (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)) )))) 17.02/16.79 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.79 ) 17.02/16.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115732 $$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_115732)))))) ) 17.02/16.79 ( real, (hAPP nat nat suc (zero_zero nat)) ) 17.02/16.79 ( int, (hAPP nat nat suc (zero_zero nat)) ) 17.02/16.79 ) 17.02/16.79 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 _let_0) X_1))) (= (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X_1) (one_one real))) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real ln X_1)) _let_0)))) )))) 17.02/16.79 ( (one_one real) ) 17.02/16.79 ( pi ) 17.02/16.79 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.79 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.79 ( skv_2 ) 17.02/16.79 ( skv_10 ) 17.02/16.79 ( skv_13 ) 17.02/16.79 ) 17.02/16.79 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (div_mod int))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) Ma))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_2) B_1) Ma)) (= (hAPP int int (hAPP int _let_1 _let_2 B_1) Ma) (hAPP int int (hAPP int _let_1 _let_2 A_2) Ma)))) )))) 17.02/16.79 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.79 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (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))) ) 17.02/16.79 ( 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))) ) 17.02/16.79 ( s1, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.79 ( s1, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.79 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.79 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.79 ) 17.02/16.79 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (forall ((X_2 $$unsorted)) (= (hAPP real real cos X_2) (hAPP _let_1 real (suminf real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) cos_coeff)) (hAPP real _let_1 (power_power real) X_2)))) )))) 17.02/16.79 ( (zero_zero real) ) 17.02/16.79 ( pi ) 17.02/16.79 ( (hAPP int real (number_number_of real) min_1) ) 17.02/16.79 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.79 ( (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)))) ) 17.02/16.79 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 17.02/16.79 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.79 ( (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 (hAPP int int bit1 pls))))) ) 17.02/16.79 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 17.02/16.79 ( (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 bit0 (hAPP int int bit1 pls))))) ) 17.02/16.79 ( (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)))) ) 17.02/16.79 ( skv_14 ) 17.02/16.79 ) 17.02/16.79 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (plus_plus nat))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP nat nat (hAPP nat _let_0 _let_1 M) (hAPP nat nat suc N)) (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat suc M)) N)) ))) 17.02/16.79 ( (zero_zero nat), (one_one nat) ) 17.02/16.79 ( (one_one nat), (zero_zero nat) ) 17.02/16.79 ) 17.02/16.79 (instantiation (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) X))) (forall ((Y $$unsorted) (X $$unsorted) (Z_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool _let_0 Z_1))) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Y) Z_1)))) )) 17.02/16.79 ( (one_one nat), (zero_zero nat), (one_one nat) ) 17.02/16.79 ) 17.02/16.79 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (one_one int))) (forall ((B $$unsorted) (A_1 $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) M))) (not (= _let_2 (hAPP int int (hAPP int _let_1 legacy_zgcd A_1) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_1) B) M))) (= _let_2 (hAPP int int (hAPP int _let_1 legacy_zgcd B) M))) )))) 17.02/16.79 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.79 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.79 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (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))) ) 17.02/16.79 ( s, s1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.79 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.79 ( skv_3, 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))) ) 17.02/16.79 ( skv_9, 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))) ) 17.02/16.79 ) 17.02/16.79 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_115857 $$unsorted) (BOUND_VARIABLE_115858 $$unsorted)) (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_115857)) (not (= (zero_zero nat) BOUND_VARIABLE_115858))) (= _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_115857) BOUND_VARIABLE_115858)))) )) 17.02/16.79 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.79 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.79 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.79 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.79 ) 17.02/16.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115918 $$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_115918) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_115918) (one_one X_a))))) ) 17.02/16.79 ( real, (zero_zero real) ) 17.02/16.79 ( real, (one_one real) ) 17.02/16.79 ( real, pi ) 17.02/16.79 ( 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)))) ) 17.02/16.79 ( 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))))) ) 17.02/16.79 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.79 ( 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)) ) 17.02/16.80 ( nat, (zero_zero nat) ) 17.02/16.80 ( nat, (one_one nat) ) 17.02/16.80 ( int, (zero_zero int) ) 17.02/16.80 ( 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) ) 17.02/16.80 ( int, min_1 ) 17.02/16.80 ( int, s ) 17.02/16.80 ( 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)))) ) 17.02/16.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.02/16.80 ( int, t ) 17.02/16.80 ( int, skv_3 ) 17.02/16.80 ( int, skv_9 ) 17.02/16.80 ) 17.02/16.80 (instantiation (let ((_let_0 (fun int bool))) (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_5))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP int int zfact (hAPP int int (hAPP int (fun int int) (minus_minus int) P_5) (one_one int)))) (hAPP int int (number_number_of int) min_1)) P_5))) )) 17.02/16.80 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.80 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.80 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.02/16.80 ) 17.02/16.80 (instantiation (forall ((K_4 $$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))) ) 17.02/16.80 ( (zero_zero nat) ) 17.02/16.80 ( (hAPP nat nat suc (zero_zero nat)) ) 17.02/16.80 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.02/16.80 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.02/16.80 ) 17.02/16.80 (instantiation (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP nat bool (even_odd_even nat) N_1)) (not (forall ((M_2 $$unsorted)) (not (= N_1 (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))) ))) ) 17.02/16.80 ( (zero_zero nat) ) 17.02/16.80 ( (one_one nat) ) 17.02/16.80 ) 17.02/16.80 (instantiation (let ((_let_0 (real_1 int))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= (hAPP int real _let_0 X_1) (hAPP int real _let_0 Y_1)) (= (ti int X_1) (ti int Y_1))) )) 17.02/16.80 ( (zero_zero int), (one_one int) ) 17.02/16.80 ( (one_one int), (zero_zero int) ) 17.02/16.80 ( (one_one int), (one_one int) ) 17.02/16.80 ) 17.02/16.80 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (ord_less int))) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 A_1) C))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 B) C))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 A_1) B)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B) A_1))) )))) 17.02/16.80 ( (zero_zero int), (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.80 ( min_1, t, (zero_zero int) ) 17.02/16.80 ( s, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.02/16.80 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.02/16.80 ( t, (zero_zero int), (one_one int) ) 17.02/16.80 ( skv_3, (zero_zero int), (zero_zero int) ) 17.02/16.80 ( skv_9, min_1, (zero_zero int) ) 17.02/16.80 ) 17.02/16.80 (instantiation (let ((_let_0 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_116033 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (one_one X_a)) (hAPP int X_a _let_0 BOUND_VARIABLE_116033)) (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP int int bit1 pls)) BOUND_VARIABLE_116033)))) )) 17.02/16.80 ( nat, (hAPP int int bit1 pls) ) 17.02/16.80 ) 17.02/16.80 (instantiation (let ((_let_0 (big_co302546470etprod X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (or (not (comm_monoid_mult X_b)) (= _let_0 (ti (fun (fun X_a X_b) (fun (fun X_a bool) X_b)) _let_0))) )) 17.02/16.80 ( bool, (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 17.02/16.80 ( real, real ) 17.02/16.80 ( real, (fun real bool) ) 17.02/16.80 ( real, (fun real (fun bool bool)) ) 17.02/16.80 ( real, (fun (fun int real) (fun int bool)) ) 17.02/16.80 ( real, (fun (fun nat real) (fun nat bool)) ) 17.02/16.80 ( nat, bool ) 17.02/16.80 ( nat, (fun nat bool) ) 17.02/16.80 ( nat, (fun nat (fun bool bool)) ) 17.02/16.80 ( nat, (fun int (fun nat bool)) ) 17.02/16.80 ( nat, (fun real (fun int (fun nat bool))) ) 17.02/16.80 ( int, bool ) 17.02/16.80 ( int, int ) 17.02/16.80 ( int, (fun int bool) ) 17.02/16.80 ( int, (fun int (fun bool bool)) ) 17.02/16.80 ( int, (fun int (fun int bool)) ) 17.02/16.80 ( int, (fun (fun int int) (fun int bool)) ) 17.02/16.80 ( int, (fun int (fun int int)) ) 17.02/16.80 ( int, (fun real (fun int (fun int bool))) ) 17.02/16.80 ( (product_prod real real), (fun real (fun real (fun nat (product_prod real real)))) ) 17.02/16.80 ( (product_prod int int), (fun (product_prod int int) bool) ) 17.02/16.80 ( (product_prod int int), (fun (product_prod int int) (fun bool bool)) ) 17.02/16.80 ) 17.02/16.80 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_116110 $$unsorted) (BOUND_VARIABLE_116111 $$unsorted)) (or (not (linorder X_a)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_116111) BOUND_VARIABLE_116110)) (= (ti X_a BOUND_VARIABLE_116110) (ti X_a BOUND_VARIABLE_116111)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_116110) BOUND_VARIABLE_116111))) ))) 17.02/16.80 ( real, (zero_zero real), pi ) 17.02/16.80 ( 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)))) ) 17.18/16.80 ( 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))))) ) 17.18/16.80 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.18/16.80 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.18/16.80 ( real, (zero_zero real), skv_2 ) 17.18/16.80 ( real, (zero_zero real), skv_10 ) 17.18/16.80 ( real, (zero_zero real), skv_13 ) 17.18/16.80 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.18/16.80 ( real, pi, (zero_zero real) ) 17.18/16.80 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.18/16.80 ( 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)) ) 17.18/16.80 ( 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)))) ) 17.18/16.80 ( 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)))), (zero_zero real) ) 17.18/16.80 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.80 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 17.18/16.80 ( 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) ) 17.18/16.80 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.18/16.80 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.18/16.80 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 17.18/16.80 ( 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 ) 17.18/16.80 ( real, skv_2, (zero_zero real) ) 17.18/16.80 ( real, skv_10, (zero_zero real) ) 17.18/16.80 ( real, skv_13, (zero_zero real) ) 17.18/16.80 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.80 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 17.18/16.80 ( int, (zero_zero int), (zero_zero int) ) 17.18/16.80 ( int, (zero_zero int), (one_one int) ) 17.18/16.80 ( 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))) ) 17.18/16.80 ( int, (zero_zero int), min_1 ) 17.18/16.80 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.18/16.80 ( int, (zero_zero int), t ) 17.18/16.80 ( int, (one_one int), (zero_zero int) ) 17.18/16.80 ( int, (one_one int), t ) 17.18/16.80 ( 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))), (zero_zero int) ) 17.18/16.80 ( 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))), s ) 17.18/16.80 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 17.18/16.80 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_3 ) 17.18/16.80 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_9 ) 17.18/16.80 ( int, min_1, (zero_zero int) ) 17.18/16.80 ( int, min_1, min_1 ) 17.18/16.80 ( 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))) ) 17.18/16.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.18/16.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.18/16.80 ( int, t, (zero_zero int) ) 17.18/16.80 ( int, t, (one_one int) ) 17.18/16.80 ( 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))) ) 17.18/16.80 ( 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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.18/16.80 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.18/16.80 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.18/16.80 ) 17.18/16.80 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (ord_less_eq X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_116146))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_116145 $$unsorted) (BOUND_VARIABLE_116146 $$unsorted) (BOUND_VARIABLE_116147 $$unsorted)) (or (not (dense_linorder X_a)) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_116147))) (not (forall ((W_2 $$unsorted)) (or (not (hBOOL (hAPP X_a bool _let_3 W_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 W_2) BOUND_VARIABLE_116147))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 W_2) BOUND_VARIABLE_116145))) )) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_116147) BOUND_VARIABLE_116145))) ))))) 17.18/16.80 ( real, pi, pi, (zero_zero real) ) 17.18/16.80 ( 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))) ) 17.18/16.80 ( 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)))) ) 17.18/16.80 ( 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)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.18/16.80 ( 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) ) 17.18/16.80 ( int, pls, (zero_zero int), min_1 ) 17.18/16.80 ( int, min_1, min_1, min_1 ) 17.18/16.80 ( int, min_1, t, (zero_zero int) ) 17.18/16.80 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), min_1, (zero_zero int) ) 17.18/16.80 ( int, s, (zero_zero int), (zero_zero int) ) 17.18/16.80 ( int, (hAPP int int (number_number_of int) pls), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.18/16.80 ( int, t, (zero_zero int), (one_one int) ) 17.18/16.80 ) 17.18/16.80 (instantiation (forall ((K $$unsorted)) (= (= min_1 (ti int K)) (= min_1 (hAPP int int bit1 K))) ) 17.18/16.80 ( pls ) 17.18/16.80 ( (hAPP int int bit1 pls) ) 17.18/16.80 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.18/16.80 ( m ) 17.18/16.80 ( min_1 ) 17.18/16.80 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.18/16.80 ( s ) 17.18/16.80 ( s1 ) 17.18/16.80 ( t ) 17.18/16.80 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 17.18/16.80 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 17.18/16.80 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 17.18/16.80 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 17.18/16.81 ) 17.18/16.81 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (forall ((X $$unsorted) (Y $$unsorted)) (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)))) ))) 17.18/16.81 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.81 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.81 ) 17.18/16.81 (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)))) ) 17.18/16.81 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 17.18/16.81 ) 17.18/16.81 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_116202 $$unsorted)) (or (not (ring_1 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_116202) _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_116202)) _let_3))) ))))) 17.18/16.81 ( real, (one_one real) ) 17.18/16.81 ( 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)))) ) 17.18/16.81 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 17.18/16.81 ( int, pls ) 17.18/16.81 ( int, (one_one int) ) 17.18/16.81 ( int, min_1 ) 17.18/16.81 ( complex, ii ) 17.18/16.81 ( complex, (one_one complex) ) 17.18/16.81 ) 17.18/16.81 (instantiation (let ((_let_0 (fun nat bool))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) Ma) N_1))) (= (= Ma N_1) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) N_1) (hAPP nat nat suc Ma))))) )) 17.18/16.81 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 17.18/16.81 ) 17.18/16.81 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_116239 $$unsorted) (BOUND_VARIABLE_116240 $$unsorted) (BOUND_VARIABLE_116241 $$unsorted)) (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_116241))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_116239) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_116240) BOUND_VARIABLE_116241)))) (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_116239) BOUND_VARIABLE_116241)) BOUND_VARIABLE_116240))) )))) 17.18/16.81 ( real, (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.18/16.81 ( 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))) ) 17.18/16.81 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.18/16.81 ) 17.18/16.81 (instantiation (let ((_let_0 (deriv X_a))) (forall ((X_a $$unsorted)) (or (not (real_normed_field X_a)) (= _let_0 (ti (fun (fun X_a X_a) (fun X_a (fun X_a bool))) _let_0))) )) 17.18/16.81 ( bool ) 17.18/16.81 ( real ) 17.18/16.81 ( nat ) 17.18/16.81 ( (fun nat bool) ) 17.18/16.81 ( int ) 17.18/16.81 ( (fun int bool) ) 17.18/16.81 ( (fun real bool) ) 17.18/16.81 ( (fun real real) ) 17.18/16.81 ( complex ) 17.18/16.81 ( (fun nat real) ) 17.18/16.81 ( (fun int int) ) 17.18/16.81 ( (fun int (fun int bool)) ) 17.18/16.81 ( (product_prod real real) ) 17.18/16.81 ( (product_prod int int) ) 17.18/16.81 ( (filter real) ) 17.18/16.81 ( (filter nat) ) 17.18/16.81 ( (product_prod nat nat) ) 17.18/16.81 ( (fun (product_prod int int) bool) ) 17.18/16.81 ( code_code_numeral ) 17.18/16.81 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 17.18/16.81 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 17.18/16.81 ( (fun nat rat) ) 17.18/16.81 ( (fun (product_prod int int) int) ) 17.18/16.81 ( (fun int (fun int (fun int bool))) ) 17.18/16.81 ( (fun int real) ) 17.18/16.81 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 17.18/16.81 ) 17.18/16.81 (instantiation (let ((_let_0 (fun nat real))) (let ((_let_1 (filter real))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun (filter nat) bool))) (let ((_let_4 (fun nat X_a))) (let ((_let_5 (fun real X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_116348 $$unsorted) (BOUND_VARIABLE_116349 $$unsorted) (BOUND_VARIABLE_116350 $$unsorted)) (let ((_let_0 (filter nat))) (or (not (metric_space X_a)) (not (forall ((S_2 $$unsorted)) (or (not (forall ((N_2 $$unsorted)) (not (= (hAPP nat real S_2 N_2) BOUND_VARIABLE_116350)) )) (not (hBOOL (hAPP _let_0 bool (hAPP real _let_3 (hAPP _let_0 (fun real _let_3) (tendsto nat real) S_2) BOUND_VARIABLE_116350) sequentially))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_3 (hAPP _let_4 (fun X_a _let_3) (tendsto nat X_a) (hAPP _let_0 _let_4 (hAPP _let_5 (fun _let_0 _let_4) (combb real X_a nat) BOUND_VARIABLE_116348) S_2)) BOUND_VARIABLE_116349) sequentially))) )) (hBOOL (hAPP _let_1 bool (hAPP X_a _let_2 (hAPP _let_5 (fun X_a _let_2) (tendsto real X_a) BOUND_VARIABLE_116348) BOUND_VARIABLE_116349) (hAPP real _let_1 (at real) BOUND_VARIABLE_116350))))) ))))))) 17.18/16.81 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.18/16.81 ) 17.18/16.81 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_116405))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) _let_4)))) (let ((_let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_4) _let_2)))) (let ((_let_7 (hAPP X_a X_a (hAPP X_a _let_3 (times_times X_a) BOUND_VARIABLE_116403) _let_4))) (let ((_let_8 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_116403))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_116403 $$unsorted) (BOUND_VARIABLE_116404 $$unsorted) (BOUND_VARIABLE_116405 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (not (number X_a)) (= (and (or _let_5 (and (or (not _let_6) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_116404) _let_7))) (or _let_6 (hBOOL (hAPP X_a bool _let_8 _let_2))))) (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_7) BOUND_VARIABLE_116404)))) (hBOOL (hAPP X_a bool _let_8 (hAPP X_a X_a (hAPP X_a _let_3 (inverse_divide X_a) BOUND_VARIABLE_116404) _let_4))))) )))))))))) 17.18/16.81 ( real, (zero_zero real), pi, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.18/16.81 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), pls ) 17.18/16.81 ) 17.18/16.81 (instantiation (let ((_let_0 (the X_a))) (forall ((X_a $$unsorted)) (or (not (metric_space X_a)) (= _let_0 (ti (fun (fun X_a bool) X_a) _let_0))) )) 17.18/16.81 ( bool ) 17.18/16.81 ( real ) 17.18/16.81 ( nat ) 17.18/16.81 ( (fun nat bool) ) 17.18/16.81 ( int ) 17.18/16.81 ( (fun int bool) ) 17.18/16.81 ( complex ) 17.18/16.81 ( (product_prod real real) ) 17.18/16.81 ( (product_prod int int) ) 17.18/16.81 ( (filter real) ) 17.18/16.81 ( (filter nat) ) 17.18/16.81 ( (product_prod nat nat) ) 17.18/16.81 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 17.18/16.81 ( (fun nat rat) ) 17.18/16.81 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 17.18/16.81 ) 17.18/16.81 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_116527)))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_116527) _let_2)))) (let ((_let_6 (hAPP X_a X_a (hAPP X_a _let_3 (times_times X_a) BOUND_VARIABLE_116525) BOUND_VARIABLE_116527))) (let ((_let_7 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_116525))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_116525 $$unsorted) (BOUND_VARIABLE_116526 $$unsorted) (BOUND_VARIABLE_116527 $$unsorted)) (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 BOUND_VARIABLE_116526) _let_6))) (or _let_5 (hBOOL (hAPP X_a bool _let_7 _let_2))))) (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_6) BOUND_VARIABLE_116526)))) (hBOOL (hAPP X_a bool _let_7 (hAPP X_a X_a (hAPP X_a _let_3 (inverse_divide X_a) BOUND_VARIABLE_116526) BOUND_VARIABLE_116527))))) ))))))))) 17.18/16.81 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.81 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.18/16.81 ( 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 bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.18/16.81 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.18/16.81 ( 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))), (zero_zero int), skv_1 ) 17.18/16.81 ( 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) (hAPP nat int (hAPP 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)), (zero_zero int) ) 17.18/16.81 ( 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))), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))), skv_1 ) 17.18/16.81 ) 17.18/16.81 (instantiation (let ((_let_0 (ord_less_eq int))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int (fun int bool)))) (forall ((N_1 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_0 _let_1) N_1))) (= (ti int N_1) (hAPP nat int (semiring_1_of_nat int) (hAPP _let_0 nat (finite_card int) (hAPP _let_0 _let_0 (collect int) (hAPP _let_0 _let_0 (hAPP _let_3 (fun _let_0 _let_0) (combs int bool bool) (hAPP _let_0 _let_3 (hAPP (fun bool _let_2) (fun _let_0 _let_3) (combb bool _let_2 int) fconj) (hAPP int _let_0 (ord_less int) _let_1))) (hAPP int _let_0 (hAPP _let_4 _let_4 (combc int int bool) _let_0) N_1)))))))) )))))) 17.18/16.81 ( pls ) 17.18/16.81 ( m ) 17.18/16.81 ( (one_one int) ) 17.18/16.81 ( min_1 ) 17.18/16.81 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.81 ( s ) 17.18/16.81 ( (hAPP int int (number_number_of int) pls) ) 17.18/16.81 ( s1 ) 17.18/16.81 ( t ) 17.18/16.81 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.18/16.81 ( skv_3 ) 17.18/16.81 ( skv_9 ) 17.18/16.81 ) 17.18/16.81 (instantiation (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (power_power X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_116607 $$unsorted) (BOUND_VARIABLE_116608 $$unsorted)) (or (not (linordered_semidom X_a)) (not (= (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_116608) _let_0) (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_116607) _let_0))) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_116607))) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_116608))) (= (ti X_a BOUND_VARIABLE_116607) (ti X_a BOUND_VARIABLE_116608))) ))))) 17.18/16.82 ( real, (hAPP int real (number_number_of real) min_1), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.18/16.82 ( 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)))), (hAPP int real (number_number_of real) min_1) ) 17.18/16.82 ( 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)))), (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)))) ) 17.18/16.82 ( int, s, s ) 17.18/16.82 ( int, s, s1 ) 17.18/16.82 ( int, s1, s ) 17.18/16.82 ( int, skv_8, skv_8 ) 17.18/16.82 ( complex, ii, ii ) 17.18/16.82 ) 17.18/16.82 (instantiation (forall ((X_1 $$unsorted)) (= (not (hBOOL (hAPP nat bool (even_odd_even nat) X_1))) (not (forall ((Y_2 $$unsorted)) (not (= X_1 (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_2)))) ))) ) 17.18/16.82 ( (zero_zero nat) ) 17.18/16.82 ( (one_one nat) ) 17.18/16.82 ) 17.18/16.82 (instantiation (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (inverse_divide X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_116664 $$unsorted) (BOUND_VARIABLE_116665 $$unsorted)) (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_116664)) BOUND_VARIABLE_116665) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_116664) BOUND_VARIABLE_116665)))) )))) 17.18/16.82 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.82 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 17.18/16.82 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.18/16.82 ( 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))))))))) ) 17.18/16.82 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.82 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.18/16.82 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 17.18/16.82 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.18/16.82 ( 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))) ) 17.18/16.82 ( 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))) ) 17.18/16.82 ( 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))) ) 17.18/16.82 ) 17.18/16.82 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (one_one real))) (let ((_let_4 (plus_plus real))) (forall ((X $$unsorted)) (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) _let_3))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (exp real) X)) (hAPP real real (hAPP real _let_2 _let_4 (hAPP real real (hAPP real _let_2 _let_4 _let_3) 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)))))))) )))))) 17.18/16.82 ( pi ) 17.18/16.82 ( (hAPP int real (number_number_of real) min_1) ) 17.18/16.82 ( (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)))) ) 17.18/16.82 ( (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)))) ) 17.18/16.82 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.18/16.82 ( skv_6 ) 17.18/16.82 ( skv_11 ) 17.18/16.82 ( skv_12 ) 17.18/16.82 ( skv_14 ) 17.18/16.82 ) 17.18/16.82 (instantiation (let ((_let_0 (product_prod int int))) (forall ((P_4 $$unsorted)) (= (hAPP _let_0 int (hAPP (fun int (fun int int)) (fun _let_0 int) (product_prod_case int int int) (div_div int)) (hAPP rat _let_0 quotient_of P_4)) (hAPP rat int (archim2085082626_floor rat) P_4)) )) 17.18/16.82 ( (zero_zero rat) ) 17.18/16.82 ( (one_one rat) ) 17.18/16.82 ) 17.18/16.82 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_116715 $$unsorted) (BOUND_VARIABLE_116716 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_116716))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_116716) BOUND_VARIABLE_116715)))) )) 17.18/16.82 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 17.18/16.82 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 17.18/16.82 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 17.18/16.82 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 17.18/16.82 ) 17.18/16.82 (instantiation (forall ((X $$unsorted)) (or (= (zero_zero real) X) (= (one_one real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real (inverse_inverse real) X)) X))) ) 17.18/16.82 ( (zero_zero real) ) 17.18/16.82 ) 17.18/16.82 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 A_1))) (forall ((B $$unsorted) (A_1 $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) B))) (not (forall ((D_3 $$unsorted)) (or (not (forall ((Y_2 $$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_2))) D_3))) (and (hBOOL (hAPP real bool _let_2 Y_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_2) B)))) )) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) D_3)))) ))) )))) 17.18/16.82 ( (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 ) 17.18/16.82 ( 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) ) 17.18/16.82 ( (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)))) ) 17.18/16.82 ( (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)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.18/16.82 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), pi ) 17.18/16.82 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi, (zero_zero real) ) 17.18/16.82 ) 17.18/16.82 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X))) (= (hAPP nat real (real_1 nat) (hAPP int nat nat_1 X)) (hAPP int real (real_1 int) X))) ) 17.18/16.82 ( (zero_zero int) ) 17.18/16.82 ( (one_one int) ) 17.18/16.82 ( min_1 ) 17.18/16.82 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.82 ( s ) 17.18/16.82 ( (hAPP int int (number_number_of int) pls) ) 17.18/16.82 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.18/16.82 ( skv_3 ) 17.18/16.82 ( skv_9 ) 17.18/16.82 ) 17.18/16.82 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116819 $$unsorted)) (or (not (preorder X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_116819) BOUND_VARIABLE_116819))) ) 17.18/16.82 ( real, (zero_zero real) ) 17.18/16.82 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.82 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.18/16.82 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.18/16.82 ( real, skv_14 ) 17.18/16.82 ( int, (zero_zero int) ) 17.18/16.82 ( int, (one_one int) ) 17.18/16.82 ( int, min_1 ) 17.18/16.82 ) 17.18/16.82 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116854 $$unsorted)) (or (not (linordered_ring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_116854) BOUND_VARIABLE_116854)) (zero_zero X_a))))) ) 17.18/16.82 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.82 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.18/16.82 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 17.18/16.82 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.18/16.82 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.18/16.82 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.82 ( complex, ii ) 17.18/16.82 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.82 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 17.18/16.82 ) 17.18/16.82 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (times_times X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_116871 $$unsorted) (BOUND_VARIABLE_116872 $$unsorted) (BOUND_VARIABLE_116873 $$unsorted)) (or (not (comm_semiring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_116871) BOUND_VARIABLE_116872)) BOUND_VARIABLE_116873) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_116871) BOUND_VARIABLE_116873)) (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_116872) BOUND_VARIABLE_116873)))) )))) 17.18/16.82 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), (zero_zero int) ) 17.18/16.82 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), t ) 17.18/16.82 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), skv_1 ) 17.18/16.82 ) 17.18/16.82 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_117011 $$unsorted) (BOUND_VARIABLE_117012 $$unsorted) (BOUND_VARIABLE_117013 $$unsorted)) (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_117013))) (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_117011) BOUND_VARIABLE_117013)) BOUND_VARIABLE_117012))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_117011) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_117012) BOUND_VARIABLE_117013)))) )))) 17.18/16.82 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.82 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.18/16.82 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.18/16.82 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_1 ) 17.18/16.82 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int 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))) (zero_zero int)))), skv_1 ) 17.18/16.82 ) 17.18/16.82 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (number_number_of int))) (let ((_let_3 (hAPP int int _let_2 (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_4 (fun int _let_0))) (forall ((X $$unsorted) (P_5 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_3) P_5))) (not (hBOOL (hAPP int bool zprime P_5))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_4 zcong X) (zero_zero int)) P_5)) (hBOOL (hAPP int bool (hAPP int _let_0 quadRes P_5) X)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_4 zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) X) (hAPP int nat nat_1 (hAPP int int (hAPP int _let_1 (div_div int) (hAPP int int (hAPP int _let_1 (minus_minus int) P_5) (one_one int))) _let_3)))) (hAPP int int _let_2 min_1)) P_5))) )))))) 17.18/16.82 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.18/16.82 ) 17.18/16.82 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (times_times X_a))) (let ((_let_4 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_117085) (hAPP int nat (number_number_of nat) BOUND_VARIABLE_117086)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_117074 $$unsorted) (BOUND_VARIABLE_117075 $$unsorted) (BOUND_VARIABLE_117085 $$unsorted) (BOUND_VARIABLE_117086 $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (or (not (monoid_mult X_a)) (and (or (hBOOL (hAPP int bool _let_0 (hAPP int int _let_1 BOUND_VARIABLE_117075))) (= (one_one X_a) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_117074) (hAPP int nat _let_0 (hAPP int int bit1 BOUND_VARIABLE_117075))))) (or (not (hBOOL (hAPP int bool _let_0 (hAPP int int _let_1 BOUND_VARIABLE_117086)))) (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_117085) (hAPP int nat _let_0 (hAPP int int bit1 BOUND_VARIABLE_117086))) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_117085) _let_4)) _let_4)))))))) )))))) 17.18/16.83 ( real, (hAPP int real (number_number_of real) min_1), (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int real (number_number_of real) min_1), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.18/16.83 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int 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)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.18/16.83 ( int, s, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), s, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.83 ( int, s1, pls, s1, pls ) 17.18/16.83 ( int, skv_8, (hAPP int int bit1 pls), skv_8, (hAPP int int bit1 pls) ) 17.18/16.83 ( complex, ii, min_1, ii, min_1 ) 17.18/16.83 ) 17.18/16.83 (instantiation (let ((_let_0 (one_one nat))) (forall ((V $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V) pls))) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat (number_number_of nat) V)) _let_0))) )) 17.18/16.83 ( (zero_zero int) ) 17.18/16.83 ( pls ) 17.18/16.83 ( (hAPP int int bit1 pls) ) 17.18/16.83 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.18/16.83 ( min_1 ) 17.18/16.83 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.18/16.83 ( s ) 17.18/16.83 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.18/16.83 ( t ) 17.18/16.83 ( skv_3 ) 17.18/16.83 ( skv_9 ) 17.18/16.83 ) 17.18/16.83 (instantiation (let ((_let_0 (number_number_of nat))) (forall ((V $$unsorted)) (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)))) )) 17.18/16.83 ( (zero_zero int) ) 17.18/16.83 ( pls ) 17.18/16.83 ( (hAPP int int bit1 pls) ) 17.18/16.83 ( min_1 ) 17.18/16.83 ( s ) 17.18/16.83 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.18/16.83 ( t ) 17.18/16.83 ( skv_3 ) 17.18/16.83 ( skv_9 ) 17.18/16.83 ) 17.18/16.83 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (times_times int) min_1) K_4) (hAPP int int (uminus_uminus int) K_4)) ) 17.18/16.83 ( pls ) 17.18/16.83 ( (one_one int) ) 17.18/16.83 ( min_1 ) 17.18/16.83 ) 17.18/16.83 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (forall ((M $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_1) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_1) _let_1) M))) (= _let_1 (ti int A_1))) ))) 17.18/16.83 ( (zero_zero int), (zero_zero int) ) 17.18/16.83 ( (zero_zero int), min_1 ) 17.18/16.83 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.18/16.83 ( (zero_zero int), t ) 17.18/16.83 ( (one_one int), (zero_zero int) ) 17.18/16.83 ( (one_one int), t ) 17.18/16.83 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 17.18/16.83 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 17.18/16.83 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 17.18/16.83 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_3 ) 17.18/16.83 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_9 ) 17.18/16.83 ( min_1, (zero_zero int) ) 17.18/16.83 ( min_1, min_1 ) 17.18/16.83 ( (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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.18/16.83 ) 17.18/16.83 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_117215 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_117215) BOUND_VARIABLE_117215)) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_117215) _let_2)))) )))) 17.18/16.83 ( nat, (one_one nat) ) 17.18/16.83 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 17.18/16.83 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.18/16.83 ) 17.18/16.83 (instantiation (forall ((X $$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))) ) 17.18/16.83 ( (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)))) ) 17.18/16.83 ) 17.18/16.83 (instantiation (let ((_let_0 (fun nat bool))) (forall ((S $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (finite_finite_1 nat) S))) (not (forall ((K_1 $$unsorted)) (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)))) ))) )) 17.18/16.83 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 17.18/16.83 ) 17.18/16.83 (instantiation (forall ((X_a $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (zero_zero int) (hAPP X_a int (archim2085082626_floor X_a) (zero_zero X_a)))) ) 17.18/16.83 ( real ) 17.18/16.83 ( nat ) 17.18/16.83 ( int ) 17.18/16.83 ( complex ) 17.18/16.83 ( rat ) 17.18/16.83 ( quickcheck_code_int ) 17.18/16.83 ( code_code_numeral ) 17.18/16.83 ) 17.18/16.83 (instantiation (let ((_let_0 (uminus_uminus complex))) (forall ((X $$unsorted)) (= (hAPP complex complex _let_0 (hAPP complex complex cnj X)) (hAPP complex complex cnj (hAPP complex complex _let_0 X))) )) 17.18/16.83 ( (one_one complex) ) 17.18/16.83 ) 17.18/16.83 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (filter X_a))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun X_a X_b))) (let ((_let_5 (fun X_a X_c))) (let ((_let_6 (fun X_b X_c))) (let ((_let_7 (filter X_b))) (let ((_let_8 (fun _let_7 bool))) (let ((_let_9 (hAPP X_a _let_2 (at X_a) BOUND_VARIABLE_117357))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_117353 $$unsorted) (BOUND_VARIABLE_117354 $$unsorted) (BOUND_VARIABLE_117355 $$unsorted) (BOUND_VARIABLE_117356 $$unsorted) (BOUND_VARIABLE_117357 $$unsorted) (BOUND_VARIABLE_117358 $$unsorted)) (or (not (topological_space X_c)) (not (topological_space X_b)) (not (metric_space X_a)) (not (hBOOL (hAPP _let_2 bool (hAPP X_b _let_3 (hAPP _let_4 (fun X_b _let_3) (tendsto X_a X_b) BOUND_VARIABLE_117355) BOUND_VARIABLE_117356) _let_9))) (not (hBOOL (hAPP _let_7 bool (hAPP X_c _let_8 (hAPP _let_6 (fun X_c _let_8) (tendsto X_b X_c) BOUND_VARIABLE_117353) BOUND_VARIABLE_117354) (hAPP X_b _let_7 (at X_b) BOUND_VARIABLE_117356)))) (hBOOL (hAPP _let_2 bool (hAPP X_c _let_3 (hAPP _let_5 (fun X_c _let_3) (tendsto X_a X_c) (hAPP _let_4 _let_5 (hAPP _let_6 (fun _let_4 _let_5) (combb X_b X_c X_a) BOUND_VARIABLE_117353) BOUND_VARIABLE_117355)) BOUND_VARIABLE_117354) _let_9)) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) BOUND_VARIABLE_117358))) (not (forall ((X_2 $$unsorted)) (or (= (ti X_a X_2) (ti X_a BOUND_VARIABLE_117357)) (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_2) BOUND_VARIABLE_117357)) BOUND_VARIABLE_117358))) (not (= (hAPP X_a X_b BOUND_VARIABLE_117355 X_2) (ti X_b BOUND_VARIABLE_117356)))) ))) ))))))))))) 17.18/16.83 ( real, real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.18/16.83 ) 17.18/16.83 (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)))) ) 17.18/16.83 ( (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) ) 17.18/16.83 ( (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)))) ) 17.18/16.83 ) 17.18/16.83 (instantiation (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_117433))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_117432 $$unsorted) (BOUND_VARIABLE_117433 $$unsorted) (BOUND_VARIABLE_117434 $$unsorted)) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_117434))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_117434) BOUND_VARIABLE_117432))) (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_117432))) )))) 17.18/16.83 ( 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))) ) 17.18/16.83 ( 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)))) ) 17.18/16.83 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), skv_14 ) 17.18/16.83 ( 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)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.18/16.83 ( int, pls, min_1, min_1 ) 17.18/16.83 ( int, min_1, (zero_zero int), min_1 ) 17.18/16.83 ( int, min_1, min_1, pls ) 17.18/16.83 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 17.18/16.83 ( int, t, (zero_zero int), (one_one int) ) 17.18/16.83 ) 17.18/16.83 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (boolean_algebra T_1)) (boolean_algebra (fun T_2 T_1))) ) 17.18/16.83 ( bool, bool ) 17.18/16.83 ( bool, (fun bool bool) ) 17.18/16.83 ( real, bool ) 17.18/16.83 ( real, real ) 17.18/16.83 ( real, nat ) 17.18/16.83 ( real, (fun int bool) ) 17.18/16.83 ( real, (fun real bool) ) 17.18/16.83 ( real, (fun real real) ) 17.18/16.83 ( real, complex ) 17.18/16.83 ( real, (fun nat real) ) 17.18/16.83 ( real, (fun bool bool) ) 17.18/16.83 ( real, (fun int (fun int bool)) ) 17.18/16.83 ( real, (fun (filter real) bool) ) 17.18/16.83 ( real, (fun (filter nat) bool) ) 17.18/16.83 ( real, (fun real complex) ) 17.18/16.83 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 17.18/16.83 ( real, (fun nat (product_prod real real)) ) 17.18/16.83 ( real, (fun real (fun nat (product_prod real real))) ) 17.18/16.83 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 17.18/16.83 ( real, (fun int (fun int (fun bool bool))) ) 17.18/16.83 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 17.18/16.83 ( real, (fun (fun int real) (fun int bool)) ) 17.18/16.83 ( real, (fun int (fun nat bool)) ) 17.18/16.83 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 17.18/16.83 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 17.18/16.83 ( real, (fun int (fun nat (fun bool bool))) ) 17.18/16.83 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 17.18/16.83 ( real, (fun (fun nat real) (fun nat bool)) ) 17.18/16.83 ( nat, bool ) 17.18/16.83 ( nat, real ) 17.18/16.83 ( nat, nat ) 17.18/16.83 ( nat, (fun nat bool) ) 17.18/16.83 ( nat, (fun nat nat) ) 17.18/16.83 ( nat, int ) 17.18/16.83 ( nat, (fun real real) ) 17.18/16.83 ( nat, complex ) 17.18/16.83 ( nat, (fun int int) ) 17.18/16.83 ( nat, rat ) 17.18/16.83 ( nat, (fun bool bool) ) 17.18/16.83 ( nat, (fun nat (fun nat bool)) ) 17.18/16.83 ( nat, (product_prod real real) ) 17.18/16.83 ( nat, (product_prod int int) ) 17.18/16.83 ( nat, (fun nat (product_prod int int)) ) 17.18/16.83 ( nat, (product_prod nat nat) ) 17.18/16.83 ( nat, (fun (product_prod nat nat) bool) ) 17.18/16.83 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 17.18/16.83 ( nat, (fun nat (product_prod nat nat)) ) 17.18/16.83 ( (fun nat bool), bool ) 17.18/16.83 ( (fun nat bool), (fun nat bool) ) 17.18/16.83 ( (fun nat bool), (fun nat (fun bool bool)) ) 17.18/16.83 ( (fun nat bool), (fun int (fun nat bool)) ) 17.18/16.83 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 17.18/16.83 ( (fun nat nat), (fun nat real) ) 17.18/16.83 ( (fun nat nat), (fun nat (fun nat nat)) ) 17.18/16.83 ( (fun nat nat), (fun nat (fun nat bool)) ) 17.18/16.83 ( int, bool ) 17.18/16.83 ( int, real ) 17.18/16.83 ( int, nat ) 17.18/16.83 ( int, (fun nat bool) ) 17.18/16.83 ( int, (fun nat nat) ) 17.18/16.83 ( int, int ) 17.18/16.83 ( int, (fun int bool) ) 17.18/16.83 ( int, (fun nat int) ) 17.18/16.83 ( int, (fun real real) ) 17.18/16.83 ( int, (fun nat real) ) 17.18/16.83 ( int, (fun int int) ) 17.18/16.83 ( int, rat ) 17.18/16.83 ( int, (fun int rat) ) 17.18/16.83 ( int, (fun bool bool) ) 17.18/16.83 ( int, (fun int (fun bool bool)) ) 17.18/16.83 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 17.18/16.83 ( int, (fun int (fun int bool)) ) 17.18/16.83 ( int, quickcheck_code_int ) 17.18/16.83 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 17.18/16.83 ( int, (product_prod int int) ) 17.18/16.83 ( int, (fun int (product_prod int int)) ) 17.18/16.83 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 17.18/16.83 ( int, (fun (fun int bool) bool) ) 17.18/16.83 ( int, (fun (product_prod int int) bool) ) 17.18/16.83 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 17.18/16.83 ( int, (product_prod int (product_prod int int)) ) 17.18/16.83 ( int, (fun int (product_prod int (product_prod int int))) ) 17.18/16.83 ( int, (fun (fun int int) (fun int bool)) ) 17.18/16.83 ( int, (fun int (fun (product_prod int int) bool)) ) 17.18/16.83 ( int, (fun int (fun (fun int bool) bool)) ) 17.18/16.83 ( int, (list int) ) 17.18/16.83 ( int, (fun nat (fun bool bool)) ) 17.18/16.83 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 17.18/16.83 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 17.18/16.83 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 17.18/16.83 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 17.18/16.83 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 17.18/16.83 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 17.18/16.83 ( int, (fun (product_prod int int) int) ) 17.18/16.83 ( int, (fun int (fun int (fun int bool))) ) 17.18/16.83 ( int, (fun int real) ) 17.18/16.83 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 17.18/16.88 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 17.18/16.88 ( (fun int bool), bool ) 17.18/16.88 ( (fun int bool), int ) 17.18/16.88 ( (fun int bool), (fun int bool) ) 17.18/16.88 ( (fun int bool), (fun int (fun bool bool)) ) 17.18/16.88 ( (fun int bool), (fun int (fun int bool)) ) 17.18/16.88 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 17.18/16.88 ( (fun int bool), (fun int (fun int int)) ) 17.18/16.88 ( (fun int bool), (fun real (fun int (fun int bool))) ) 17.18/16.88 ( (fun real bool), real ) 17.18/16.88 ( (fun real bool), (fun real bool) ) 17.18/16.88 ( (fun real bool), (fun real (fun bool bool)) ) 17.18/16.88 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 17.18/16.88 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 17.18/16.88 ( (fun real real), (fun real real) ) 17.18/16.88 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 17.18/16.88 ( (fun real real), (fun real (fun real real)) ) 17.18/16.88 ( (fun real real), (fun real (fun real bool)) ) 17.18/16.88 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 17.18/16.88 ( complex, real ) 17.18/16.88 ( complex, nat ) 17.18/16.88 ( complex, complex ) 17.18/16.88 ( (fun nat real), (fun nat bool) ) 17.18/16.88 ( (fun nat real), (fun nat real) ) 17.18/16.88 ( (fun nat real), (fun nat (fun real real)) ) 17.18/16.88 ( (fun nat real), (fun int (fun nat real)) ) 17.18/16.88 ( (fun int int), (fun int bool) ) 17.18/16.88 ( (fun int int), (fun int int) ) 17.18/16.88 ( (fun int int), (fun int (fun int bool)) ) 17.18/16.88 ( (fun int int), (fun int (fun int int)) ) 17.18/16.88 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 17.18/16.88 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 17.18/16.88 ( rat, real ) 17.18/16.88 ( rat, (product_prod int int) ) 17.18/16.88 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 17.18/16.88 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 17.18/16.88 ( (fun int (fun int bool)), (fun int bool) ) 17.18/16.88 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 17.18/16.88 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 17.18/16.88 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 17.18/16.88 ( quickcheck_code_int, nat ) 17.18/16.88 ( quickcheck_code_int, int ) 17.18/16.88 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 17.18/16.88 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 17.18/16.88 ( (product_prod real real), bool ) 17.18/16.88 ( (product_prod int int), bool ) 17.18/16.88 ( (product_prod int int), int ) 17.18/16.88 ( (product_prod int int), (fun int bool) ) 17.18/16.88 ( (product_prod int int), (fun int int) ) 17.18/16.88 ( (product_prod int int), rat ) 17.18/16.88 ( (product_prod int int), (fun bool bool) ) 17.18/16.88 ( (product_prod int int), (product_prod int int) ) 17.18/16.88 ( (product_prod int int), (fun (product_prod int int) bool) ) 17.18/16.88 ( (product_prod int int), (fun (product_prod int int) int) ) 17.18/16.88 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 17.18/16.88 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 17.18/16.88 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 17.18/16.88 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 17.18/16.88 ( (filter real), bool ) 17.18/16.88 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 17.18/16.88 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 17.18/16.88 ( (filter nat), bool ) 17.18/16.88 ( (product_prod nat nat), bool ) 17.18/16.88 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 17.18/16.88 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 17.18/16.88 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 17.18/16.88 ( code_code_numeral, nat ) 17.18/16.88 ( code_code_numeral, (fun nat nat) ) 17.18/16.88 ( code_code_numeral, int ) 17.18/16.88 ( code_code_numeral, code_code_numeral ) 17.18/16.88 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 17.18/16.88 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 17.18/16.88 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 17.18/16.88 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 17.18/16.88 ( (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))) ) 17.18/16.88 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 17.18/16.88 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 17.18/16.88 ( (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))) ) 17.18/16.88 ( (fun nat rat), bool ) 17.18/16.88 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 17.18/16.88 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 17.18/16.88 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 17.18/16.88 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 17.18/16.88 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 17.18/16.88 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 17.18/16.88 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 17.18/16.88 ( (fun int real), (fun int bool) ) 17.18/16.88 ( (fun int real), (fun int real) ) 17.18/16.88 ( (fun int real), (fun int (fun int real)) ) 17.18/16.88 ( (fun int real), (fun int (fun real real)) ) 17.18/16.88 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 17.18/16.88 ( (fun real (fun int bool)), (fun real bool) ) 17.18/16.88 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 17.18/16.88 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 17.18/16.88 ( (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)))) ) 17.18/16.88 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 17.18/16.88 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 17.18/16.88 ( (fun int (fun int real)), (fun int (fun int bool)) ) 17.18/16.88 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 17.18/16.88 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 17.18/16.88 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 17.18/16.88 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 17.18/16.88 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 17.18/16.88 ( (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))) ) 17.18/16.88 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 17.18/16.88 ( (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))) ) 17.18/16.88 ( (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))) ) 17.18/16.88 ( (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)))) ) 17.18/16.88 ( (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)))) ) 17.18/16.88 ( (fun int (fun nat bool)), (fun int bool) ) 17.18/16.88 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 17.18/16.88 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 17.18/16.88 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 17.18/16.88 ( (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))) ) 17.18/16.88 ( (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)))) ) 17.18/16.88 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 17.18/16.88 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 17.18/16.88 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 17.18/16.88 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 17.18/16.88 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 17.18/16.88 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 17.18/16.88 ) 17.18/16.88 (instantiation (let ((_let_0 (ring_1_of_int X_a))) (forall ((X_a $$unsorted)) (or (not (ring_1 X_a)) (= _let_0 (ti (fun int X_a) _let_0))) )) 17.18/16.88 ( bool ) 17.18/16.88 ( real ) 17.18/16.88 ( nat ) 17.18/16.88 ( (fun nat bool) ) 17.18/16.88 ( (fun nat nat) ) 17.18/16.88 ( int ) 17.18/16.88 ( (fun int bool) ) 17.18/16.88 ( (fun nat int) ) 17.18/16.88 ( (fun real real) ) 17.18/16.88 ( complex ) 17.18/16.88 ( (fun nat real) ) 17.18/16.88 ( (fun int int) ) 17.18/16.88 ( rat ) 17.18/16.88 ( (fun int rat) ) 17.18/16.88 ( (fun bool bool) ) 17.18/16.88 ( (fun int (fun bool bool)) ) 17.18/16.88 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 17.18/16.88 ( (fun int (fun int bool)) ) 17.18/16.88 ( quickcheck_code_int ) 17.18/16.88 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 17.18/16.88 ( (product_prod int int) ) 17.18/16.88 ( (fun int (product_prod int int)) ) 17.18/16.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 17.18/16.88 ( (fun (fun int bool) bool) ) 17.18/16.88 ( (fun (product_prod int int) bool) ) 17.18/16.88 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 17.18/16.88 ( (product_prod int (product_prod int int)) ) 17.18/16.88 ( (fun int (product_prod int (product_prod int int))) ) 17.18/16.88 ( (fun (fun int int) (fun int bool)) ) 17.18/16.88 ( (fun int (fun (product_prod int int) bool)) ) 17.18/16.88 ( (fun int (fun (fun int bool) bool)) ) 17.18/16.88 ( (list int) ) 17.18/16.88 ( (fun nat (fun bool bool)) ) 17.18/16.88 ( (fun int (fun int (product_prod int (product_prod int int)))) ) 17.18/16.88 ( (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 17.18/16.88 ( (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 17.18/16.88 ( (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 17.18/16.88 ( (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 17.18/16.88 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 17.18/16.88 ( (fun (product_prod int int) int) ) 17.18/16.88 ( (fun int (fun int (fun int bool))) ) 17.18/16.88 ( (fun int real) ) 17.18/16.88 ( (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 17.18/16.88 ( (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 17.18/16.88 ) 17.18/16.88 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (one_one real))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP nat (fun real real) root N_1) X_1)) _let_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) _let_2)))) )))) 17.18/16.88 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.88 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.88 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.88 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.88 ) 17.18/16.88 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP real complex (hAPP real (fun real complex) rcis (one_one real)) A_1) (hAPP real complex cis A_1)) ) 17.18/16.88 ( (zero_zero real) ) 17.18/16.88 ) 17.18/16.88 (instantiation (let ((_let_0 (fun real complex))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (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))) )) 17.18/16.88 ( (zero_zero real), (zero_zero real) ) 17.18/16.88 ( (zero_zero real), (one_one real) ) 17.18/16.88 ( (one_one real), (zero_zero real) ) 17.18/16.88 ) 17.18/16.88 (instantiation (forall ((P_1 $$unsorted) (BOUND_VARIABLE_117672 $$unsorted)) (or (hBOOL (hAPP nat bool P_1 (zero_zero nat))) (not (hBOOL (hAPP nat bool P_1 BOUND_VARIABLE_117672))) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool P_1 (hAPP nat nat suc N_2)))) (hBOOL (hAPP nat bool P_1 N_2))) ))) ) 17.18/16.88 ( (even_odd_even nat), (zero_zero nat) ) 17.18/16.88 ( (even_odd_even nat), (one_one nat) ) 17.18/16.88 ( (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.88 ( prime, (zero_zero nat) ) 17.18/16.88 ( prime, (one_one nat) ) 17.18/16.88 ( prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.88 ) 17.18/16.88 (instantiation (let ((_let_0 (fun X_a (fun X_a bool)))) (forall ((X_a $$unsorted)) (or (not (linorder X_a)) (= (hAPP _let_0 (fun X_a (fun X_a X_a)) (max X_a) (hAPP _let_0 _let_0 (combc X_a X_a bool) (ord_less_eq X_a))) (ord_min X_a))) )) 17.18/16.88 ( bool ) 17.18/16.88 ( real ) 17.18/16.88 ( nat ) 17.18/16.88 ( (fun nat bool) ) 17.18/16.88 ( int ) 17.18/16.88 ( (fun int bool) ) 17.18/16.88 ( (fun real bool) ) 17.18/16.88 ( (fun real real) ) 17.18/16.88 ( complex ) 17.18/16.88 ( (fun nat real) ) 17.18/16.88 ( (fun int int) ) 17.18/16.88 ( rat ) 17.18/16.88 ( (fun int (fun int bool)) ) 17.18/16.88 ( quickcheck_code_int ) 17.18/16.88 ( (product_prod real real) ) 17.18/16.88 ( (product_prod int int) ) 17.18/16.88 ( (filter real) ) 17.18/16.88 ( (filter nat) ) 17.18/16.88 ( (product_prod nat nat) ) 17.18/16.88 ( (fun (product_prod int int) bool) ) 17.18/16.88 ( code_code_numeral ) 17.18/16.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 17.18/16.88 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 17.18/16.88 ( (fun nat rat) ) 17.18/16.88 ( (fun (product_prod int int) int) ) 17.18/16.88 ( (fun int (fun int (fun int bool))) ) 17.18/16.88 ( (fun int real) ) 17.18/16.88 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 17.18/16.88 ) 17.18/16.88 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_117712 $$unsorted) (BOUND_VARIABLE_117713 $$unsorted)) (or (not (ring_1 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_117713) (ring_1_Ints X_a)))) (not (forall ((Z_2 $$unsorted)) (hBOOL (hAPP X_a bool BOUND_VARIABLE_117712 (hAPP int X_a (ring_1_of_int X_a) Z_2))) )) (hBOOL (hAPP X_a bool BOUND_VARIABLE_117712 BOUND_VARIABLE_117713))) )) 17.18/16.88 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 17.18/16.88 ( 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)))) ) 17.18/16.88 ( 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)))) ) 17.18/16.89 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_6 ) 17.18/16.89 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 17.18/16.89 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 17.18/16.89 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_14 ) 17.18/16.89 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 17.18/16.89 ( 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)))) ) 17.18/16.89 ( 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)))) ) 17.18/16.89 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 17.18/16.89 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_10 ) 17.18/16.89 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_13 ) 17.18/16.89 ( 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))) ) 17.18/16.89 ( 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)))) ) 17.18/16.89 ( 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) ) 17.18/16.89 ( 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) ) 17.18/16.89 ( 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) ) 17.18/16.89 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 17.18/16.89 ( 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))) ) 17.18/16.89 ( 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 ) 17.18/16.89 ( real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 17.18/16.89 ( 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)))) ) 17.18/16.89 ( 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 ) 17.18/16.89 ( real, (hAPP real (fun real bool) (ord_less_eq real) skv_14), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.89 ( nat, (even_odd_even nat), (zero_zero nat) ) 17.18/16.89 ( nat, (even_odd_even nat), (one_one nat) ) 17.18/16.89 ( 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))) ) 17.18/16.89 ( nat, prime, (zero_zero nat) ) 17.18/16.89 ( nat, prime, (one_one nat) ) 17.18/16.89 ( nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.89 ( (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 17.18/16.89 ( (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) ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 17.18/16.89 ( 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))) ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 17.18/16.89 ( 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))) ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_3 ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_9 ) 17.18/16.89 ( 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))) ) 17.18/16.89 ( int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 17.18/16.89 ( 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))) ) 17.18/16.89 ( int, nat_neg, (one_one int) ) 17.18/16.89 ( int, nat_neg, (hAPP int int (number_number_of int) min_1) ) 17.18/16.89 ( int, nat_neg, (hAPP int int (number_number_of int) pls) ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less int) pls), (zero_zero int) ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 17.18/16.89 ( int, nat_is_nat, (zero_zero int) ) 17.18/16.89 ( int, nat_is_nat, (one_one int) ) 17.18/16.89 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.89 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.18/16.89 ( int, (even_odd_even int), (zero_zero int) ) 17.18/16.89 ( int, (even_odd_even int), (one_one int) ) 17.18/16.89 ( 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))) ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))), (zero_zero int) ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less int) min_1), (zero_zero int) ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 17.18/16.89 ( int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 17.18/16.89 ( 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))) ) 17.18/16.89 ( 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))) ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 17.18/16.89 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.18/16.89 ( int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less int) t), (zero_zero int) ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less int) t), (one_one int) ) 17.18/16.89 ( 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))) ) 17.18/16.89 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.18/16.89 ( int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.18/16.89 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun int bool) (ord_less 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)))), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less int) skv_3), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.18/16.89 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_3)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.18/16.89 ( 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_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.18/16.89 ( int, (hAPP int (fun int bool) (ord_less int) skv_9), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.18/16.89 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_9)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.18/16.89 ( (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 17.18/16.89 ( (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)) ) 17.18/16.89 ( (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))))) ) 17.18/16.89 ( (filter nat), (trivial_limit nat), sequentially ) 17.18/16.89 ( (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 17.18/16.89 ) 17.18/16.89 (instantiation (let ((_let_0 (fun int int))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (= (hAPP int int (hAPP int _let_0 (minus_minus int) A_1) B) (ti int C))) (= (ti int A_1) (hAPP int int (hAPP int _let_0 (plus_plus int) C) B))) )) 17.18/16.89 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), min_1 ) 17.18/16.89 ) 17.18/16.89 (instantiation (forall ((Z_1 $$unsorted)) (= (zero_zero real) (hAPP complex real im (hAPP real complex (of_real complex) Z_1))) ) 17.18/16.89 ( pi ) 17.18/16.89 ( (hAPP int real (number_number_of real) min_1) ) 17.18/16.89 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 17.18/16.89 ) 17.18/16.89 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117825 $$unsorted)) (or (not (finite_finite X_a)) (hBOOL (hAPP (fun X_a bool) bool (finite_finite_1 X_a) BOUND_VARIABLE_117825))) ) 17.18/16.89 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 17.18/16.89 ) 17.18/16.89 (instantiation (let ((_let_0 (fun nat X_a))) (let ((_let_1 (power_power X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_117843 $$unsorted) (BOUND_VARIABLE_117844 $$unsorted)) (or (not (ring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 (one_one X_a))) BOUND_VARIABLE_117844)) (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_117843) BOUND_VARIABLE_117844)) (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_117843)) BOUND_VARIABLE_117844))) )))) 17.18/16.89 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.90 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.90 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.90 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.90 ) 17.18/16.90 (instantiation (let ((_let_0 (semiring_1_of_nat int))) (let ((_let_1 (zero_zero nat))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (and (= _let_1 N_1) (= _let_1 Ma)) (= (hAPP nat int _let_0 Ma) (hAPP int int (uminus_uminus int) (hAPP nat int _let_0 N_1)))) ))) 17.18/16.90 ( (zero_zero nat), (zero_zero nat) ) 17.18/16.90 ( (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)) ) 17.18/16.90 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.90 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.18/16.90 ) 17.18/16.90 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (hAPP complex real re X) (hAPP complex real re Y))) (not (= (hAPP complex real im Y) (hAPP complex real im X))) (= X Y)) ) 17.18/16.90 ( ii, (zero_zero complex) ) 17.18/16.90 ( ii, (one_one complex) ) 17.18/16.90 ( (zero_zero complex), (one_one complex) ) 17.18/16.90 ( (one_one complex), ii ) 17.18/16.90 ( (one_one complex), (one_one complex) ) 17.18/16.90 ) 17.18/16.90 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((N $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) N) M))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 M) (zero_zero int))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 N) M))) ))) 17.18/16.90 ( (zero_zero int), (one_one int) ) 17.18/16.90 ( (zero_zero int), min_1 ) 17.18/16.90 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.18/16.90 ( (zero_zero int), s ) 17.18/16.90 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 17.18/16.90 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.18/16.90 ( (zero_zero int), skv_3 ) 17.18/16.90 ( (zero_zero int), skv_9 ) 17.18/16.90 ( (one_one int), t ) 17.18/16.90 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.18/16.90 ( min_1, pls ) 17.18/16.90 ( min_1, min_1 ) 17.18/16.90 ) 17.18/16.90 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (= (= (ti int L) (ti int K)) (= (hAPP int int bit1 K) (hAPP int int bit1 L))) ) 17.18/16.90 ( pls, s1 ) 17.18/16.90 ( m, s ) 17.18/16.90 ( min_1, m ) 17.18/16.90 ( min_1, min_1 ) 17.18/16.90 ( min_1, s ) 17.18/16.90 ( s, min_1 ) 17.18/16.90 ( s1, t ) 17.18/16.90 ( t, pls ) 17.18/16.90 ( t, s1 ) 17.18/16.90 ( t, t ) 17.18/16.90 ) 17.18/16.90 (instantiation (let ((_let_0 (norm_norm X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_118004 $$unsorted) (BOUND_VARIABLE_118005 $$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 _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_118004) BOUND_VARIABLE_118005))) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP X_a real _let_0 BOUND_VARIABLE_118004)) (hAPP X_a real _let_0 BOUND_VARIABLE_118005))))) )) 17.18/16.90 ( nat, (one_one nat), (one_one nat) ) 17.18/16.90 ( 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), (one_one int) ) 17.18/16.90 ( 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)))), (one_one int) ) 17.18/16.90 ) 17.18/16.90 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun int bool))) (let ((_let_2 (ord_less_eq int))) (forall ((K $$unsorted) (F $$unsorted) (N_1 $$unsorted)) (or (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) I_2) N_1))) (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 (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_1 _let_2 (hAPP nat int F (zero_zero nat))) K))) (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 K) (hAPP nat int F N_1)))) (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) I_2) N_1))) (not (= (hAPP nat int F I_2) (ti int K)))) ))) )))) 17.18/16.90 ( (zero_zero int), (semiring_1_of_nat int), (zero_zero nat) ) 17.18/16.90 ( (zero_zero int), (semiring_1_of_nat int), (hAPP nat nat suc (zero_zero nat)) ) 17.32/16.90 ( (zero_zero int), (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.90 ( (zero_zero int), (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.32/16.90 ( min_1, (semiring_1_of_nat int), (zero_zero nat) ) 17.32/16.90 ) 17.32/16.90 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((A_2 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_1))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP real nat natceiling X_1)) A_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (hAPP nat real (real_1 nat) A_2))))) ))) 17.32/16.90 ( (zero_zero nat), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.90 ) 17.32/16.90 (instantiation (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_118315 $$unsorted) (BOUND_VARIABLE_118316 $$unsorted)) (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_118315) BOUND_VARIABLE_118316) sequentially))) (= (ti X_a BOUND_VARIABLE_118316) (hAPP _let_1 X_a (lim X_a) BOUND_VARIABLE_118315))) ))) 17.32/16.90 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 17.32/16.90 ) 17.32/16.90 (instantiation (let ((_let_0 (product_prod X_b X_c))) (let ((_let_1 (fun X_c X_a))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (P_1 $$unsorted) (Z $$unsorted)) (= (hAPP X_c X_a (hAPP X_b _let_1 P_1 (hAPP _let_0 X_b (product_fst X_b X_c) Z)) (hAPP _let_0 X_c (product_snd X_b X_c) Z)) (hAPP _let_0 X_a (hAPP (fun X_b _let_1) (fun _let_0 X_a) (product_prod_case X_b X_c X_a) P_1) Z)) ))) 17.32/16.90 ( int, int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP _let_0 _let_1 (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))), (let ((_let_0 (product_prod int int))) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) s) (one_one int))) ) 17.32/16.90 ) 17.32/16.90 (instantiation (let ((_let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_118394) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_118394 $$unsorted)) (or (not (linordered_idom X_a)) (= _let_0 (hAPP X_a X_a (abs_abs X_a) _let_0))) )) 17.32/16.90 ( real, (hAPP int real (number_number_of real) min_1) ) 17.32/16.90 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.90 ( int, s ) 17.32/16.90 ( int, s1 ) 17.32/16.90 ( int, skv_8 ) 17.32/16.90 ( complex, ii ) 17.32/16.90 ) 17.32/16.90 (instantiation (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_118415))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_118415 $$unsorted) (BOUND_VARIABLE_118416 $$unsorted)) (or (not (ring X_a)) (= (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_118416)) (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_118416)))) ))) 17.32/16.90 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.32/16.90 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.32/16.90 ( 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)))))) ) 17.32/16.90 ( 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))))), pi ) 17.32/16.90 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 17.32/16.90 ( 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))), (zero_zero int) ) 17.32/16.90 ( 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))), pls ) 17.32/16.90 ( 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))), t ) 17.32/16.90 ( 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))), skv_1 ) 17.32/16.90 ( complex, ii, ii ) 17.32/16.90 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 17.32/16.90 ( 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)), ii ) 17.32/16.90 ) 17.32/16.90 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118433 $$unsorted)) (or (not (number_ring X_a)) (= (ti X_a BOUND_VARIABLE_118433) (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_118433))) ) 17.32/16.90 ( bool, fFalse ) 17.32/16.90 ( bool, fTrue ) 17.32/16.90 ( real, pi ) 17.32/16.90 ( (fun nat bool), (even_odd_even nat) ) 17.32/16.90 ( (fun nat bool), prime ) 17.32/16.90 ( (fun nat nat), suc ) 17.32/16.90 ( (fun nat nat), (fact_fact nat) ) 17.32/16.90 ( (fun nat nat), (size_size nat) ) 17.32/16.90 ( (fun nat nat), fact ) 17.32/16.90 ( (fun nat nat), nat_size ) 17.32/16.90 ( int, pls ) 17.32/16.90 ( int, m ) 17.32/16.90 ( int, min_1 ) 17.32/16.90 ( int, s ) 17.32/16.90 ( int, s1 ) 17.32/16.90 ( int, t ) 17.32/16.90 ( (fun int bool), zprime ) 17.32/16.90 ( (fun int bool), nat_neg ) 17.32/16.90 ( (fun int bool), zEven ) 17.32/16.90 ( (fun int bool), nat_is_nat ) 17.32/16.90 ( (fun int bool), zOdd ) 17.32/16.90 ( (fun int bool), (even_odd_even int) ) 17.32/16.90 ( (fun int bool), twoSqu1091635170sum2sq ) 17.32/16.90 ( (fun int nat), nat_1 ) 17.32/16.90 ( (fun int nat), phi ) 17.32/16.90 ( (fun real real), sqrt ) 17.32/16.90 ( (fun real real), tan ) 17.32/16.90 ( (fun real real), cos ) 17.32/16.90 ( (fun real real), arccos ) 17.32/16.90 ( (fun real real), ln ) 17.32/16.90 ( (fun real real), sin ) 17.32/16.90 ( (fun real real), arctan ) 17.32/16.90 ( (fun real real), arcsin ) 17.32/16.90 ( complex, ii ) 17.32/16.90 ( (fun complex complex), cnj ) 17.32/16.90 ( (fun complex complex), expi ) 17.32/16.90 ( (fun nat real), (real_1 nat) ) 17.32/16.90 ( (fun nat real), cos_coeff ) 17.32/16.90 ( (fun nat real), sin_coeff ) 17.32/16.90 ( (fun int int), bit0 ) 17.32/16.90 ( (fun int int), bit1 ) 17.32/16.90 ( (fun int int), pred ) 17.32/16.90 ( (fun int int), succ ) 17.32/16.90 ( (fun int int), (fact_fact int) ) 17.32/16.90 ( (fun int int), zfact ) 17.32/16.90 ( (fun bool bool), fNot ) 17.32/16.90 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.32/16.90 ( (fun bool (fun bool bool)), fconj ) 17.32/16.90 ( (fun bool (fun bool bool)), fdisj ) 17.32/16.90 ( (fun bool (fun bool bool)), fimplies ) 17.32/16.90 ( (fun int (fun int bool)), sRStar ) 17.32/16.90 ( (fun int (fun int bool)), quadRes ) 17.32/16.90 ( (fun int (fun int bool)), norRRset ) 17.32/16.90 ( (fun int (fun int bool)), d22set ) 17.32/16.90 ( (fun int (fun int bool)), sr ) 17.32/16.90 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 17.32/16.90 ( (fun nat (fun nat nat)), nat_gcd ) 17.32/16.90 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 17.32/16.90 ( (fun nat (fun nat nat)), nat_lcm ) 17.32/16.90 ( (fun nat (fun real real)), root ) 17.32/16.90 ( (fun real (fun real real)), log ) 17.32/16.90 ( (fun real (fun real real)), powr ) 17.32/16.90 ( (fun nat (fun nat bool)), coprime ) 17.32/16.90 ( (fun (fun int bool) int), (the int) ) 17.32/16.90 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 17.32/16.90 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 17.32/16.90 ( (fun nat (fun nat (product_prod int int))), bezw ) 17.32/16.90 ( (fun (fun int bool) bool), nat_nat_set ) 17.32/16.90 ( (filter nat), sequentially ) 17.32/16.90 ( (fun (product_prod nat nat) bool), pred_nat ) 17.32/16.90 ( (fun (product_prod int int) bool), frac_1 ) 17.32/16.90 ( (fun real complex), cis ) 17.32/16.90 ( (fun complex real), im ) 17.32/16.90 ( (fun complex real), re ) 17.32/16.90 ( (fun complex real), arg ) 17.32/16.90 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 17.32/16.90 ( (fun int (fun int int)), int_gcd ) 17.32/16.90 ( (fun int (fun int int)), multInv ) 17.32/16.90 ( (fun int (fun int int)), legacy_zgcd ) 17.32/16.90 ( (fun int (fun int int)), z3mod ) 17.32/16.90 ( (fun int (fun int int)), inv ) 17.32/16.90 ( (fun int (fun int int)), (gcd_gcd int) ) 17.32/16.90 ( (fun int (fun int int)), standardRes ) 17.32/16.90 ( (fun int (fun int int)), legendre ) 17.32/16.90 ( (fun int (fun int int)), nat_tsub ) 17.32/16.90 ( (fun int (fun int int)), z3div ) 17.32/16.90 ( (fun int (fun int int)), int_lcm ) 17.32/16.90 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 17.32/16.90 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 17.32/16.90 ( (fun int (fun (fun int bool) bool)), rsetR ) 17.32/16.90 ( (fun int (fun (fun int bool) bool)), resSet ) 17.32/16.90 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 17.32/16.90 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 17.32/16.90 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 17.32/16.90 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.32/16.90 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 17.32/16.90 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 17.32/16.90 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 17.32/16.90 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 17.32/16.90 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.32/16.90 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.32/16.90 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.32/16.90 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.32/16.90 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.32/16.90 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.32/16.90 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 17.32/16.90 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 17.32/16.91 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 17.32/16.91 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 17.32/16.91 ( (fun real nat), natfloor ) 17.32/16.91 ( (fun real nat), natceiling ) 17.32/16.91 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.32/16.91 ( (fun int (fun int (fun int bool))), wset ) 17.32/16.91 ( (fun int (fun int (fun int bool))), bnorRset ) 17.32/16.91 ( (fun int (fun int (fun int bool))), zcong ) 17.32/16.91 ( (fun int (fun int (fun int bool))), noXRRset ) 17.32/16.91 ( (fun int (fun int (fun int bool))), zcongm ) 17.32/16.91 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.32/16.91 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.32/16.91 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.32/16.91 ( (fun int real), (real_1 int) ) 17.32/16.91 ( (fun complex nat), (size_size complex) ) 17.32/16.91 ( (fun complex nat), complex_size ) 17.32/16.91 ( (fun int (list int)), quickc666637781d_zero ) 17.32/16.91 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.32/16.91 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.32/16.91 ( (fun (product_prod int int) rat), frct ) 17.32/16.91 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.32/16.91 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.32/16.91 ( (fun (fun nat rat) bool), vanishes ) 17.32/16.91 ( (fun int (fun int rat)), fract ) 17.32/16.91 ( (fun code_code_numeral int), code_int_of ) 17.32/16.91 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.32/16.91 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.32/16.91 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.32/16.91 ( (fun real (fun real complex)), complex_1 ) 17.32/16.91 ( (fun real (fun real complex)), rcis ) 17.32/16.91 ( (fun int (fun nat nat)), nat_aux ) 17.32/16.91 ( (fun rat real), ratreal ) 17.32/16.91 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.32/16.91 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.32/16.91 ( (fun rat (product_prod int int)), quotient_of ) 17.32/16.91 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.32/16.91 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.32/16.91 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.32/16.91 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.32/16.91 ) 17.32/16.91 (instantiation (let ((_let_0 (even_odd_even int))) (forall ((Y $$unsorted) (X $$unsorted)) (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)))) )) 17.32/16.91 ( (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))) ) 17.32/16.91 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.91 ( 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 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(hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_118541) BOUND_VARIABLE_118542)) _let_0)))) ))))) 17.32/16.91 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.91 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.91 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.91 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.91 ) 17.32/16.91 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_118590 $$unsorted) (BOUND_VARIABLE_118591 $$unsorted)) (or (not (number_semiring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_4 _let_5 (hAPP X_a X_a (hAPP X_a _let_4 _let_5 (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_118590) _let_1)) (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_118591) _let_1))) (hAPP X_a X_a (hAPP X_a _let_4 _let_6 (hAPP X_a X_a (hAPP X_a _let_4 _let_6 (hAPP int X_a (number_number_of X_a) _let_0)) BOUND_VARIABLE_118590)) BOUND_VARIABLE_118591)) (hAPP nat X_a (hAPP X_a _let_2 _let_3 (hAPP X_a X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_118590) BOUND_VARIABLE_118591)) _let_1))) )))))))) 17.32/16.91 ( nat, (one_one nat), (one_one nat) ) 17.32/16.91 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 17.32/16.91 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 17.32/16.91 ( complex, (hAPP real complex (of_real complex) pi), ii ) 17.32/16.91 ) 17.32/16.91 (instantiation (let ((_let_0 (combc X_a X_b X_c))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (= _let_0 (ti (fun (fun X_a (fun X_b X_c)) (fun X_b (fun X_a X_c))) _let_0)) )) 17.32/16.91 ( bool, bool, bool ) 17.32/16.91 ( bool, real, bool ) 17.32/16.91 ( bool, nat, bool ) 17.32/16.91 ( bool, int, bool ) 17.32/16.91 ( bool, (product_prod int int), bool ) 17.32/16.91 ( real, real, bool ) 17.32/16.91 ( real, real, real ) 17.32/16.91 ( real, real, complex ) 17.32/16.91 ( real, real, (fun nat (product_prod real real)) ) 17.32/16.91 ( real, nat, real ) 17.32/16.91 ( real, (fun nat bool), (fun int (fun nat bool)) ) 17.32/16.91 ( real, int, real ) 17.32/16.91 ( real, (fun int bool), (fun int (fun int bool)) ) 17.32/16.91 ( real, (fun real bool), bool ) 17.32/16.91 ( real, (fun real bool), (fun bool bool) ) 17.32/16.91 ( real, (fun real real), real ) 17.32/16.91 ( real, (fun real real), (fun real bool) ) 17.32/16.91 ( real, (fun real real), (fun real real) ) 17.32/16.91 ( real, (fun real (fun real bool)), (fun (fun int real) (fun int bool)) ) 17.32/16.91 ( real, (fun real (fun real bool)), (fun (fun nat real) (fun nat bool)) ) 17.32/16.91 ( real, (fun (product_prod real real) bool), (fun real (fun nat (product_prod real real))) ) 17.32/16.91 ( real, (fun real (fun int bool)), bool ) 17.32/16.91 ( real, (fun real (fun int (fun int bool))), (fun int bool) ) 17.32/16.91 ( real, (fun real (fun int (fun int bool))), (fun int (fun int (fun bool bool))) ) 17.32/16.91 ( 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))) ) 17.32/16.91 ( real, (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 17.32/16.91 ( real, (fun int (fun int real)), (fun int (fun int bool)) ) 17.32/16.91 ( real, (fun real (fun (fun int real) (fun int bool))), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 17.32/16.91 ( real, (fun real (fun int (fun nat bool))), (fun int bool) ) 17.32/16.91 ( real, (fun real (fun int (fun nat bool))), (fun int (fun nat (fun bool bool))) ) 17.32/16.91 ( 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))) ) 17.32/16.91 ( real, (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 17.32/16.91 ( real, (fun int (fun nat real)), (fun int (fun nat bool)) ) 17.32/16.91 ( real, (fun real (fun (fun nat real) (fun nat bool))), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 17.32/16.91 ( nat, real, real ) 17.32/16.91 ( nat, real, (product_prod real real) ) 17.32/16.91 ( nat, nat, bool ) 17.32/16.91 ( nat, nat, nat ) 17.32/16.91 ( nat, nat, (fun nat bool) ) 17.32/16.91 ( nat, nat, (product_prod int int) ) 17.32/16.91 ( nat, nat, (product_prod nat nat) ) 17.32/16.91 ( nat, nat, 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(fun int (fun int bool)), (fun int bool) ) 17.32/16.91 ( int, (fun int (fun int bool)), (fun int (fun bool bool)) ) 17.32/16.91 ( int, (fun int (fun int bool)), (fun (fun int int) (fun int bool)) ) 17.32/16.91 ( int, (product_prod int int), bool ) 17.32/16.91 ( int, (product_prod int int), int ) 17.32/16.91 ( int, (fun int (fun int int)), (fun int (fun int bool)) ) 17.32/16.91 ( int, (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 17.32/16.91 ( int, (fun int (fun int (fun int bool))), (fun int (fun int bool)) ) 17.32/16.91 ( int, (fun int real), bool ) 17.32/16.91 ( int, (fun int real), real ) 17.32/16.91 ( int, (fun int real), (fun real real) ) 17.32/16.91 ( int, (fun int real), (fun int real) ) 17.32/16.91 ( int, (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 17.32/16.91 ( int, (fun int (fun int real)), (fun int bool) ) 17.32/16.91 ( int, (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 17.32/16.91 ( int, (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 17.32/16.91 ( int, (fun int (fun nat bool)), bool ) 17.32/16.91 ( int, (fun int (fun nat bool)), (fun nat (fun bool bool)) ) 17.32/16.91 ( int, (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 17.32/16.91 ( int, (fun int (fun nat real)), (fun nat bool) ) 17.32/16.91 ( (fun int bool), real, (fun int (fun int bool)) ) 17.32/16.91 ( (fun int bool), int, bool ) 17.32/16.91 ( (fun int bool), int, (fun int bool) ) 17.32/16.91 ( (fun int bool), (fun int (fun bool bool)), (fun int bool) ) 17.32/16.91 ( (fun int bool), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (fun int (fun int bool)) ) 17.32/16.91 ( (fun nat real), real, (fun nat bool) ) 17.32/16.91 ( (fun nat real), int, (fun nat real) ) 17.32/16.91 ( (fun nat real), (fun real bool), (fun nat bool) ) 17.32/16.91 ( (fun nat real), (fun real real), (fun nat real) ) 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(fun (product_prod int int) bool) ) 17.32/16.91 ( (product_prod int int), (fun (product_prod int int) int), bool ) 17.32/16.91 ( (product_prod int int), (fun (product_prod int int) int), int ) 17.32/16.91 ( (product_prod int int), (fun (product_prod int int) int), (fun int bool) ) 17.32/16.91 ( (product_prod int int), (fun (product_prod int int) int), (fun int int) ) 17.32/16.91 ( (product_prod int int), (fun (product_prod int int) int), (fun (product_prod int int) int) ) 17.32/16.91 ( (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)) ) 17.32/16.91 ( (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)) ) 17.32/16.91 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (fun (product_prod int int) bool) ) 17.32/16.91 ( (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)) ) 17.32/16.91 ( (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))) ) 17.32/16.91 ( (filter real), real, bool ) 17.32/16.91 ( (filter nat), real, bool ) 17.32/16.91 ( (product_prod nat nat), nat, bool ) 17.32/16.91 ( (product_prod nat nat), (product_prod nat nat), bool ) 17.32/16.91 ( (fun (product_prod int int) bool), (fun bool bool), (fun (product_prod int int) bool) ) 17.32/16.91 ( (fun (product_prod int int) bool), (product_prod int int), (fun (product_prod int int) bool) ) 17.32/16.91 ( code_code_numeral, code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 17.32/16.91 ( (fun (product_prod int int) int), (fun int int), (fun (product_prod int int) int) ) 17.32/16.91 ( (fun (product_prod int int) int), (product_prod int int), (fun (product_prod int int) bool) ) 17.32/16.91 ( (fun (product_prod int int) int), (product_prod int int), (fun (product_prod int int) int) ) 17.32/16.91 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)), (fun (product_prod int int) bool) ) 17.32/16.91 ( (fun int real), real, (fun int bool) ) 17.32/16.91 ( (fun int real), int, (fun int real) ) 17.32/16.91 ( (fun int real), (fun real bool), (fun int bool) ) 17.32/16.91 ( (fun int real), (fun real real), (fun int real) ) 17.32/16.91 ( (fun int (fun int real)), real, (fun int (fun int bool)) ) 17.32/16.91 ( (fun int (fun int real)), (fun (fun int real) (fun int bool)), (fun int (fun int bool)) ) 17.32/16.91 ( (fun int (fun nat real)), real, (fun int (fun nat bool)) ) 17.32/16.91 ( (fun int (fun nat real)), (fun (fun nat real) (fun nat bool)), (fun int (fun nat bool)) ) 17.32/16.91 ) 17.32/16.91 (instantiation (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (hAPP X_a (fun X_a X_a) (div_div X_a) BOUND_VARIABLE_118639))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_118638 $$unsorted) (BOUND_VARIABLE_118639 $$unsorted)) (or (not (ring_div X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_118638) BOUND_VARIABLE_118639))) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_118638)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_118638)))) ))) 17.32/16.91 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.32/16.92 ) 17.32/16.92 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of nat))) (forall ((N $$unsorted)) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) N))) (not (forall ((X_2 $$unsorted)) (not (= (hAPP nat nat (hAPP nat _let_0 (times_times nat) (hAPP int nat _let_2 (hAPP int int bit0 _let_1))) X_2) (hAPP nat nat (hAPP nat _let_0 (power_power nat) N) (hAPP int nat _let_2 _let_1)))) ))) )))) 17.32/16.92 ( (zero_zero nat) ) 17.32/16.92 ( (one_one nat) ) 17.32/16.92 ) 17.32/16.92 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_118677) BOUND_VARIABLE_118676))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_118676 $$unsorted) (BOUND_VARIABLE_118677 $$unsorted)) (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_118677))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_118677) (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_118677) _let_2)) _let_2))) )))) 17.32/16.92 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 17.32/16.92 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 17.32/16.92 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 17.32/16.92 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 17.32/16.92 ) 17.32/16.92 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118770 $$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_118770)) (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_118770))))) ) 17.32/16.92 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.32/16.92 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.92 ( real, min_1 ) 17.32/16.92 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.92 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.32/16.92 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.32/16.92 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 17.32/16.92 ( nat, pls ) 17.32/16.92 ( nat, (hAPP int int bit1 pls) ) 17.32/16.92 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.32/16.92 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.32/16.92 ( int, pls ) 17.32/16.92 ( int, (hAPP int int bit1 pls) ) 17.32/16.92 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.32/16.92 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.92 ( int, min_1 ) 17.32/16.92 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.32/16.92 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.32/16.92 ( complex, min_1 ) 17.32/16.92 ( quickcheck_code_int, (zero_zero int) ) 17.32/16.92 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 17.32/16.92 ( quickcheck_code_int, (one_one int) ) 17.32/16.92 ( code_code_numeral, pls ) 17.32/16.92 ( code_code_numeral, (hAPP int int bit1 pls) ) 17.32/16.92 ) 17.32/16.92 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118783 $$unsorted) (BOUND_VARIABLE_118784 $$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_118783) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_118784) BOUND_VARIABLE_118783)))) ) 17.32/16.92 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.92 ( 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))))) ) 17.32/16.92 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.92 ( 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)))) ) 17.32/16.92 ( 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))) ) 17.32/16.92 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.92 ( 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))) ) 17.32/16.92 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.32/16.92 ( complex, ii, ii ) 17.32/16.92 ( 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)) ) 17.32/16.92 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.92 ) 17.32/16.92 (instantiation (let ((_let_0 (hAPP int (fun nat int) (power_power int) X))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (= (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))) )) 17.32/16.92 ( s, (one_one nat), (one_one nat) ) 17.32/16.92 ( s1, (one_one nat), (one_one nat) ) 17.32/16.92 ( skv_8, (one_one nat), (one_one nat) ) 17.32/16.92 ) 17.32/16.92 (instantiation (let ((_let_0 (fun nat bool))) (forall ((X_2 $$unsorted)) (= (hAPP nat _let_0 (ord_less nat) X_2) (hAPP nat _let_0 (ord_less_eq nat) (hAPP nat nat suc X_2))) )) 17.32/16.92 ( (zero_zero nat) ) 17.32/16.92 ( (hAPP nat nat suc (zero_zero nat)) ) 17.32/16.92 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 17.32/16.92 ) 17.32/16.92 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (real_1 nat))) (forall ((R_4 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) R_4))) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP nat real _let_2 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N_2) (one_one nat)))) R_4))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) R_4) (hAPP nat real _let_2 N_2))))) ))) )))) 17.32/16.92 ( pi ) 17.32/16.92 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.92 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.92 ( skv_6 ) 17.32/16.92 ( skv_11 ) 17.32/16.92 ( skv_12 ) 17.32/16.92 ( skv_14 ) 17.32/16.92 ) 17.32/16.92 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (div_mod int))) (forall ((X $$unsorted) (M $$unsorted) (Y $$unsorted)) (or (not (= (hAPP int int (hAPP int _let_1 _let_2 Y) M) (hAPP int int (hAPP int _let_1 _let_2 X) M))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong X) Y) M))) )))) 17.32/16.92 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 17.32/16.92 ( (hAPP nat int (hAPP 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)))) ) 17.32/16.92 ( 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 ) 17.32/16.92 ( 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_3 ) 17.32/16.92 ( 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_9 ) 17.32/16.92 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 17.32/16.92 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 17.32/16.92 ) 17.32/16.92 (instantiation (let ((_let_0 (zero_zero int))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (hAPP int int _let_1 V))) (let ((_let_5 (hAPP int int _let_1 W))) (let ((_let_6 (hAPP int _let_3 posDivAlg _let_5))) (let ((_let_7 (hAPP int _let_2 _let_6 _let_4))) (let ((_let_8 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_5) _let_4)))) (forall ((W $$unsorted) (V $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_0) _let_4))) (and (or _let_8 (= _let_7 (hAPP _let_2 _let_2 (hAPP int (fun _let_2 _let_2) adjust _let_4) (hAPP int _let_2 _let_6 (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int _let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) _let_4))))) (or (not _let_8) (= _let_7 (hAPP int _let_2 (hAPP int _let_3 (product_Pair int int) _let_0) _let_5))))) )))))))))) 17.32/16.92 ( pls, pls ) 17.32/16.92 ( pls, (hAPP int int bit1 pls) ) 17.32/16.92 ) 17.32/16.92 (instantiation (let ((_let_0 (even_odd_even int))) (forall ((Y $$unsorted) (X $$unsorted)) (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))))) )) 17.32/16.92 ( (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) ) 17.32/16.92 ( (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)))) ) 17.32/16.92 ) 17.32/16.92 (instantiation (let ((_let_0 (fun int int))) (forall ((N $$unsorted) (K_4 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero 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) (ti int K_4))) )) 17.32/16.92 ( (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))) ) 17.32/16.92 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.92 ( 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))) ) 17.32/16.92 ( skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.32/16.92 ) 17.32/16.92 (instantiation (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (times_times X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_119051 $$unsorted) (BOUND_VARIABLE_119052 $$unsorted)) (or (not (linordered_idom X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_119051)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_119052)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_119051) BOUND_VARIABLE_119052)))) )))) 17.32/16.92 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.32/16.92 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.32/16.92 ( 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)))))) ) 17.32/16.92 ( 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 ) 17.32/16.92 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 17.32/16.92 ( 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))), (zero_zero int) ) 17.32/16.92 ( 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))), t ) 17.32/16.93 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_1 ) 17.32/16.93 ( complex, ii, ii ) 17.32/16.93 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 17.32/16.93 ( 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 ) 17.32/16.93 ) 17.32/16.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119100 $$unsorted)) (or (not (field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_119100)) (= (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_119100)) BOUND_VARIABLE_119100))) ) 17.32/16.93 ( bool, fFalse ) 17.32/16.93 ( bool, fTrue ) 17.32/16.93 ( real, (zero_zero real) ) 17.32/16.93 ( real, pi ) 17.32/16.93 ( (fun nat bool), (even_odd_even nat) ) 17.32/16.93 ( (fun nat bool), prime ) 17.32/16.93 ( (fun nat nat), suc ) 17.32/16.93 ( (fun nat nat), (fact_fact nat) ) 17.32/16.93 ( (fun nat nat), (size_size nat) ) 17.32/16.93 ( (fun nat nat), fact ) 17.32/16.93 ( (fun nat nat), nat_size ) 17.32/16.93 ( int, pls ) 17.32/16.93 ( int, m ) 17.32/16.93 ( int, min_1 ) 17.32/16.93 ( int, s ) 17.32/16.93 ( int, s1 ) 17.32/16.93 ( int, t ) 17.32/16.93 ( (fun int bool), zprime ) 17.32/16.93 ( (fun int bool), nat_neg ) 17.32/16.93 ( (fun int bool), zEven ) 17.32/16.93 ( (fun int bool), nat_is_nat ) 17.32/16.93 ( (fun int bool), zOdd ) 17.32/16.93 ( (fun int bool), (even_odd_even int) ) 17.32/16.93 ( (fun int bool), twoSqu1091635170sum2sq ) 17.32/16.93 ( (fun int nat), nat_1 ) 17.32/16.93 ( (fun int nat), phi ) 17.32/16.93 ( (fun real real), sqrt ) 17.32/16.93 ( (fun real real), tan ) 17.32/16.93 ( (fun real real), cos ) 17.32/16.93 ( (fun real real), arccos ) 17.32/16.93 ( (fun real real), ln ) 17.32/16.93 ( (fun real real), sin ) 17.32/16.93 ( (fun real real), arctan ) 17.32/16.93 ( (fun real real), arcsin ) 17.32/16.93 ( complex, ii ) 17.32/16.93 ( (fun complex complex), cnj ) 17.32/16.93 ( (fun complex complex), expi ) 17.32/16.93 ( (fun nat real), (real_1 nat) ) 17.32/16.93 ( (fun nat real), cos_coeff ) 17.32/16.93 ( (fun nat real), sin_coeff ) 17.32/16.93 ( (fun int int), bit0 ) 17.32/16.93 ( (fun int int), bit1 ) 17.32/16.93 ( (fun int int), pred ) 17.32/16.93 ( (fun int int), succ ) 17.32/16.93 ( (fun int int), (fact_fact int) ) 17.32/16.93 ( (fun int int), zfact ) 17.32/16.93 ( (fun bool bool), fNot ) 17.32/16.93 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.32/16.93 ( (fun bool (fun bool bool)), fconj ) 17.32/16.93 ( (fun bool (fun bool bool)), fdisj ) 17.32/16.93 ( (fun bool (fun bool bool)), fimplies ) 17.32/16.93 ( (fun int (fun int bool)), sRStar ) 17.32/16.93 ( (fun int (fun int bool)), quadRes ) 17.32/16.93 ( (fun int (fun int bool)), norRRset ) 17.32/16.93 ( (fun int (fun int bool)), d22set ) 17.32/16.93 ( (fun int (fun int bool)), sr ) 17.32/16.93 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 17.32/16.93 ( (fun nat (fun nat nat)), nat_gcd ) 17.32/16.93 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 17.32/16.93 ( (fun nat (fun nat nat)), nat_lcm ) 17.32/16.93 ( (fun nat (fun real real)), root ) 17.32/16.93 ( (fun real (fun real real)), log ) 17.32/16.93 ( (fun real (fun real real)), powr ) 17.32/16.93 ( (fun nat (fun nat bool)), coprime ) 17.32/16.93 ( (fun (fun int bool) int), (the int) ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 17.32/16.93 ( (fun nat (fun nat (product_prod int int))), bezw ) 17.32/16.93 ( (fun (fun int bool) bool), nat_nat_set ) 17.32/16.93 ( (filter nat), sequentially ) 17.32/16.93 ( (fun (product_prod nat nat) bool), pred_nat ) 17.32/16.93 ( (fun (product_prod int int) bool), frac_1 ) 17.32/16.93 ( (fun real complex), cis ) 17.32/16.93 ( (fun complex real), im ) 17.32/16.93 ( (fun complex real), re ) 17.32/16.93 ( (fun complex real), arg ) 17.32/16.93 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 17.32/16.93 ( (fun int (fun int int)), int_gcd ) 17.32/16.93 ( (fun int (fun int int)), multInv ) 17.32/16.93 ( (fun int (fun int int)), legacy_zgcd ) 17.32/16.93 ( (fun int (fun int int)), z3mod ) 17.32/16.93 ( (fun int (fun int int)), inv ) 17.32/16.93 ( (fun int (fun int int)), (gcd_gcd int) ) 17.32/16.93 ( (fun int (fun int int)), standardRes ) 17.32/16.93 ( (fun int (fun int int)), legendre ) 17.32/16.93 ( (fun int (fun int int)), nat_tsub ) 17.32/16.93 ( (fun int (fun int int)), z3div ) 17.32/16.93 ( (fun int (fun int int)), int_lcm ) 17.32/16.93 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 17.32/16.93 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 17.32/16.93 ( (fun int (fun (fun int bool) bool)), rsetR ) 17.32/16.93 ( (fun int (fun (fun int bool) bool)), resSet ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 17.32/16.93 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 17.32/16.93 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 17.32/16.93 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 17.32/16.93 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.32/16.93 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.32/16.93 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.32/16.93 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.32/16.93 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.32/16.93 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 17.32/16.93 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 17.32/16.93 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 17.32/16.93 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 17.32/16.93 ( (fun real nat), natfloor ) 17.32/16.93 ( (fun real nat), natceiling ) 17.32/16.93 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.32/16.93 ( (fun int (fun int (fun int bool))), wset ) 17.32/16.93 ( (fun int (fun int (fun int bool))), bnorRset ) 17.32/16.93 ( (fun int (fun int (fun int bool))), zcong ) 17.32/16.93 ( (fun int (fun int (fun int bool))), noXRRset ) 17.32/16.93 ( (fun int (fun int (fun int bool))), zcongm ) 17.32/16.93 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.32/16.93 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.32/16.93 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.32/16.93 ( (fun int real), (real_1 int) ) 17.32/16.93 ( (fun complex nat), (size_size complex) ) 17.32/16.93 ( (fun complex nat), complex_size ) 17.32/16.93 ( (fun int (list int)), quickc666637781d_zero ) 17.32/16.93 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.32/16.93 ( (fun (product_prod int int) rat), frct ) 17.32/16.93 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.32/16.93 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.32/16.93 ( (fun (fun nat rat) bool), vanishes ) 17.32/16.93 ( (fun int (fun int rat)), fract ) 17.32/16.93 ( (fun code_code_numeral int), code_int_of ) 17.32/16.93 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.32/16.93 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.32/16.93 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.32/16.93 ( (fun real (fun real complex)), complex_1 ) 17.32/16.93 ( (fun real (fun real complex)), rcis ) 17.32/16.93 ( (fun int (fun nat nat)), nat_aux ) 17.32/16.93 ( (fun rat real), ratreal ) 17.32/16.93 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.32/16.93 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.32/16.93 ( (fun rat (product_prod int int)), quotient_of ) 17.32/16.93 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.32/16.93 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.32/16.93 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.32/16.93 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.32/16.93 ) 17.32/16.93 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP real _let_0 (ord_less_eq real) (zero_zero real)))) (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool _let_1 Y))) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_1 X_2))) (not (= Y (hAPP real real tan X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X_2) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ))) ))) 17.32/16.93 ( pi ) 17.32/16.93 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.93 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.93 ( skv_6 ) 17.32/16.93 ( skv_11 ) 17.32/16.93 ( skv_12 ) 17.32/16.93 ( skv_14 ) 17.32/16.93 ) 17.32/16.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119147 $$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_119147) BOUND_VARIABLE_119147) (ti X_a BOUND_VARIABLE_119147))) ) 17.32/16.93 ( bool, fFalse ) 17.32/16.93 ( bool, fTrue ) 17.32/16.93 ( real, pi ) 17.32/16.93 ( (fun nat bool), (even_odd_even nat) ) 17.32/16.93 ( (fun nat bool), prime ) 17.32/16.93 ( (fun nat nat), suc ) 17.32/16.93 ( (fun nat nat), (fact_fact nat) ) 17.32/16.93 ( (fun nat nat), (size_size nat) ) 17.32/16.93 ( (fun nat nat), fact ) 17.32/16.93 ( (fun nat nat), nat_size ) 17.32/16.93 ( int, pls ) 17.32/16.93 ( int, m ) 17.32/16.93 ( int, min_1 ) 17.32/16.93 ( int, s ) 17.32/16.93 ( int, s1 ) 17.32/16.93 ( int, t ) 17.32/16.93 ( (fun int bool), zprime ) 17.32/16.93 ( (fun int bool), nat_neg ) 17.32/16.93 ( (fun int bool), zEven ) 17.32/16.93 ( (fun int bool), nat_is_nat ) 17.32/16.93 ( (fun int bool), zOdd ) 17.32/16.93 ( (fun int bool), (even_odd_even int) ) 17.32/16.93 ( (fun int bool), twoSqu1091635170sum2sq ) 17.32/16.93 ( (fun int nat), nat_1 ) 17.32/16.93 ( (fun int nat), phi ) 17.32/16.93 ( (fun real real), sqrt ) 17.32/16.93 ( (fun real real), tan ) 17.32/16.93 ( (fun real real), cos ) 17.32/16.93 ( (fun real real), arccos ) 17.32/16.93 ( (fun real real), ln ) 17.32/16.93 ( (fun real real), sin ) 17.32/16.93 ( (fun real real), arctan ) 17.32/16.93 ( (fun real real), arcsin ) 17.32/16.93 ( complex, ii ) 17.32/16.93 ( (fun complex complex), cnj ) 17.32/16.93 ( (fun complex complex), expi ) 17.32/16.93 ( (fun nat real), (real_1 nat) ) 17.32/16.93 ( (fun nat real), cos_coeff ) 17.32/16.93 ( (fun nat real), sin_coeff ) 17.32/16.93 ( (fun int int), bit0 ) 17.32/16.93 ( (fun int int), bit1 ) 17.32/16.93 ( (fun int int), pred ) 17.32/16.93 ( (fun int int), succ ) 17.32/16.93 ( (fun int int), (fact_fact int) ) 17.32/16.93 ( (fun int int), zfact ) 17.32/16.93 ( (fun bool bool), fNot ) 17.32/16.93 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.32/16.93 ( (fun bool (fun bool bool)), fconj ) 17.32/16.93 ( (fun bool (fun bool bool)), fdisj ) 17.32/16.93 ( (fun bool (fun bool bool)), fimplies ) 17.32/16.93 ( (fun int (fun int bool)), sRStar ) 17.32/16.93 ( (fun int (fun int bool)), quadRes ) 17.32/16.93 ( (fun int (fun int bool)), norRRset ) 17.32/16.93 ( (fun int (fun int bool)), d22set ) 17.32/16.93 ( (fun int (fun int bool)), sr ) 17.32/16.93 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 17.32/16.93 ( (fun nat (fun nat nat)), nat_gcd ) 17.32/16.93 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 17.32/16.93 ( (fun nat (fun nat nat)), nat_lcm ) 17.32/16.93 ( (fun nat (fun real real)), root ) 17.32/16.93 ( (fun real (fun real real)), log ) 17.32/16.93 ( (fun real (fun real real)), powr ) 17.32/16.93 ( (fun nat (fun nat bool)), coprime ) 17.32/16.93 ( (fun (fun int bool) int), (the int) ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 17.32/16.93 ( (fun nat (fun nat (product_prod int int))), bezw ) 17.32/16.93 ( (fun (fun int bool) bool), nat_nat_set ) 17.32/16.93 ( (filter nat), sequentially ) 17.32/16.93 ( (fun (product_prod nat nat) bool), pred_nat ) 17.32/16.93 ( (fun (product_prod int int) bool), frac_1 ) 17.32/16.93 ( (fun real complex), cis ) 17.32/16.93 ( (fun complex real), im ) 17.32/16.93 ( (fun complex real), re ) 17.32/16.93 ( (fun complex real), arg ) 17.32/16.93 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 17.32/16.93 ( (fun int (fun int int)), int_gcd ) 17.32/16.93 ( (fun int (fun int int)), multInv ) 17.32/16.93 ( (fun int (fun int int)), legacy_zgcd ) 17.32/16.93 ( (fun int (fun int int)), z3mod ) 17.32/16.93 ( (fun int (fun int int)), inv ) 17.32/16.93 ( (fun int (fun int int)), (gcd_gcd int) ) 17.32/16.93 ( (fun int (fun int int)), standardRes ) 17.32/16.93 ( (fun int (fun int int)), legendre ) 17.32/16.93 ( (fun int (fun int int)), nat_tsub ) 17.32/16.93 ( (fun int (fun int int)), z3div ) 17.32/16.93 ( (fun int (fun int int)), int_lcm ) 17.32/16.93 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 17.32/16.93 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 17.32/16.93 ( (fun int (fun (fun int bool) bool)), rsetR ) 17.32/16.93 ( (fun int (fun (fun int bool) bool)), resSet ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 17.32/16.93 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 17.32/16.93 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 17.32/16.93 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 17.32/16.93 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.32/16.93 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.32/16.93 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.32/16.93 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.32/16.93 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.32/16.93 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 17.32/16.93 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 17.32/16.93 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 17.32/16.93 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 17.32/16.93 ( (fun real nat), natfloor ) 17.32/16.93 ( (fun real nat), natceiling ) 17.32/16.93 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.32/16.93 ( (fun int (fun int (fun int bool))), wset ) 17.32/16.93 ( (fun int (fun int (fun int bool))), bnorRset ) 17.32/16.93 ( (fun int (fun int (fun int bool))), zcong ) 17.32/16.93 ( (fun int (fun int (fun int bool))), noXRRset ) 17.32/16.93 ( (fun int (fun int (fun int bool))), zcongm ) 17.32/16.93 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.32/16.93 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.32/16.93 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.32/16.93 ( (fun int real), (real_1 int) ) 17.32/16.93 ( (fun complex nat), (size_size complex) ) 17.32/16.93 ( (fun complex nat), complex_size ) 17.32/16.93 ( (fun int (list int)), quickc666637781d_zero ) 17.32/16.93 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.32/16.93 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.32/16.93 ( (fun (product_prod int int) rat), frct ) 17.32/16.93 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.32/16.93 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.32/16.93 ( (fun (fun nat rat) bool), vanishes ) 17.32/16.93 ( (fun int (fun int rat)), fract ) 17.32/16.93 ( (fun code_code_numeral int), code_int_of ) 17.32/16.93 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.32/16.93 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.32/16.93 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.32/16.93 ( (fun real (fun real complex)), complex_1 ) 17.32/16.93 ( (fun real (fun real complex)), rcis ) 17.32/16.93 ( (fun int (fun nat nat)), nat_aux ) 17.32/16.93 ( (fun rat real), ratreal ) 17.32/16.93 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.32/16.93 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.32/16.93 ( (fun rat (product_prod int int)), quotient_of ) 17.32/16.93 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.32/16.93 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.32/16.93 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.32/16.93 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.32/16.93 ) 17.32/16.93 (instantiation (let ((_let_0 (ord_less_eq int))) (let ((_let_1 (hAPP int (fun int bool) (ord_less int) (zero_zero int)))) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_0 (zero_zero int)) A_2))) (= (and (hBOOL (hAPP int bool (hAPP int _let_0 _let_0 B_1) A_2)) (hBOOL (hAPP int bool _let_1 B_1))) (hBOOL (hAPP int bool _let_1 (hAPP int int (hAPP int (fun int int) (div_div int) A_2) B_1)))))) ))) 17.32/16.93 ( (zero_zero int), (one_one int) ) 17.32/16.93 ( (zero_zero int), min_1 ) 17.32/16.93 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.93 ( (zero_zero int), s ) 17.32/16.93 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 17.32/16.93 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.32/16.93 ( (zero_zero int), skv_3 ) 17.32/16.93 ( (zero_zero int), skv_9 ) 17.32/16.93 ( (one_one int), t ) 17.32/16.93 ( min_1, pls ) 17.32/16.93 ( min_1, min_1 ) 17.32/16.93 ) 17.32/16.93 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (let ((_let_3 (filter X_a))) (let ((_let_4 (fun _let_3 bool))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_119196 $$unsorted) (BOUND_VARIABLE_119197 $$unsorted) (BOUND_VARIABLE_119198 $$unsorted)) (or (not (metric_space X_a)) (not (metric_space X_b)) (not (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 R_2))) (not (forall ((S_1 $$unsorted)) (or (not (forall ((X_2 $$unsorted)) (or (= (ti X_a X_2) (ti X_a BOUND_VARIABLE_119198)) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) X_2) BOUND_VARIABLE_119198)) S_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_b real (hAPP X_b (fun X_b real) (dist_dist X_b) (hAPP X_a X_b BOUND_VARIABLE_119196 X_2)) BOUND_VARIABLE_119197)) R_2))) )) (not (hBOOL (hAPP real bool _let_2 S_1)))) ))) )) (hBOOL (hAPP _let_3 bool (hAPP X_b _let_4 (hAPP (fun X_a X_b) (fun X_b _let_4) (tendsto X_a X_b) BOUND_VARIABLE_119196) BOUND_VARIABLE_119197) (hAPP X_a _let_3 (at X_a) BOUND_VARIABLE_119198)))) )))))) 17.32/16.94 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.94 ) 17.32/16.94 (instantiation (forall ((W_1 $$unsorted) (Z $$unsorted)) (= (not (forall ((N_2 $$unsorted)) (not (= (hAPP int int (hAPP int (fun int int) (plus_plus int) W_1) (hAPP nat int (semiring_1_of_nat int) (hAPP nat nat suc N_2))) (ti int Z))) )) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) W_1) Z))) ) 17.32/16.94 ( (zero_zero int), (zero_zero int) ) 17.32/16.94 ( (zero_zero int), (one_one int) ) 17.32/16.94 ( (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))) ) 17.32/16.94 ( (zero_zero int), min_1 ) 17.32/16.94 ( min_1, (zero_zero int) ) 17.32/16.94 ( min_1, min_1 ) 17.32/16.94 ( 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))) ) 17.32/16.94 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.32/16.94 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.32/16.94 ( t, (zero_zero int) ) 17.32/16.94 ( t, (one_one int) ) 17.32/16.94 ( 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))) ) 17.32/16.94 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.32/16.94 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.32/16.94 ) 17.32/16.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119285 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_119285) (hAPP int X_a (ring_1_of_int X_a) (hAPP int int (number_number_of int) BOUND_VARIABLE_119285)))) ) 17.32/16.94 ( real, pls ) 17.32/16.94 ( real, (hAPP int int bit1 pls) ) 17.32/16.94 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.32/16.94 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.94 ( real, min_1 ) 17.32/16.94 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.94 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.32/16.94 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.32/16.94 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 17.32/16.94 ( nat, pls ) 17.32/16.94 ( nat, (hAPP int int bit1 pls) ) 17.32/16.94 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.32/16.94 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.32/16.94 ( int, pls ) 17.32/16.94 ( int, (hAPP int int bit1 pls) ) 17.32/16.94 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.32/16.94 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.94 ( int, min_1 ) 17.32/16.94 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.32/16.94 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.32/16.94 ( complex, min_1 ) 17.32/16.94 ( quickcheck_code_int, (zero_zero int) ) 17.32/16.94 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 17.32/16.94 ( quickcheck_code_int, (one_one int) ) 17.32/16.94 ( code_code_numeral, pls ) 17.32/16.94 ( code_code_numeral, (hAPP int int bit1 pls) ) 17.32/16.94 ) 17.32/16.94 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_119301 $$unsorted)) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_119301) (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_119301)) BOUND_VARIABLE_119301)) _let_4)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119301) _let_4)))) )))))) 17.32/16.94 ( nat, (one_one nat) ) 17.32/16.94 ( int, (one_one int) ) 17.32/16.94 ) 17.32/16.94 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat _let_0))) (let ((_let_2 (fun (filter nat) bool))) (let ((_let_3 (fun nat X_a))) (let ((_let_4 (fun _let_0 X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_119369 $$unsorted) (BOUND_VARIABLE_119370 $$unsorted)) (or (not (topological_space X_a)) (not (comm_monoid_add X_a)) (= (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_2 (hAPP _let_3 (fun X_a _let_2) (tendsto nat X_a) (hAPP _let_1 _let_3 (hAPP _let_4 (fun _let_1 _let_3) (combb _let_0 X_a nat) (hAPP _let_3 _let_4 (big_co1399186613setsum nat X_a) BOUND_VARIABLE_119369)) (hAPP nat _let_1 (ord_atLeastLessThan nat) (zero_zero nat)))) BOUND_VARIABLE_119370) sequentially)) (hBOOL (hAPP X_a bool (hAPP _let_3 (fun X_a bool) (sums X_a) BOUND_VARIABLE_119369) BOUND_VARIABLE_119370)))) )))))) 17.32/16.94 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 17.32/16.94 ) 17.32/16.94 (instantiation (forall ((A_1 $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X))) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natfloor X)) A_1) (hAPP real nat natfloor (hAPP real real (hAPP real (fun real real) (plus_plus real) X) (hAPP nat real (real_1 nat) A_1))))) ) 17.32/16.94 ( (one_one nat), (one_one real) ) 17.32/16.94 ) 17.32/16.94 (instantiation (let ((_let_0 (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 pls)))) (forall ((X_a $$unsorted)) (or (not (field X_a)) (not (number_ring X_a)) (= _let_0 (hAPP X_a X_a (inverse_inverse X_a) _let_0))) )) 17.32/16.94 ( real ) 17.32/16.94 ( nat ) 17.32/16.94 ( int ) 17.32/16.94 ( complex ) 17.32/16.94 ( rat ) 17.32/16.94 ( quickcheck_code_int ) 17.32/16.94 ( code_code_numeral ) 17.32/16.94 ) 17.32/16.94 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (sgn_sgn X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_119525 $$unsorted) (BOUND_VARIABLE_119526 $$unsorted)) (or (not (real_n1866405975lgebra X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119525) BOUND_VARIABLE_119526)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_119525)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_119526)))) )))) 17.32/16.94 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.32/16.94 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.32/16.94 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 17.32/16.94 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 17.32/16.94 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 17.32/16.94 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 17.32/16.94 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 17.32/16.94 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1 ) 17.32/16.94 ( complex, ii, ii ) 17.32/16.94 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 17.32/16.94 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 17.32/16.94 ) 17.32/16.94 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_119548 $$unsorted) (BOUND_VARIABLE_119549 $$unsorted) (BOUND_VARIABLE_119550 $$unsorted)) (or (not (order X_a)) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a BOUND_VARIABLE_119550 N_2)) (hAPP nat X_a BOUND_VARIABLE_119550 (hAPP nat nat suc N_2)))) )) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_119548) BOUND_VARIABLE_119549))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a BOUND_VARIABLE_119550 BOUND_VARIABLE_119548)) (hAPP nat X_a BOUND_VARIABLE_119550 BOUND_VARIABLE_119549)))) ))) 17.32/16.94 ( int, (zero_zero nat), (zero_zero nat), (semiring_1_of_nat int) ) 17.32/16.94 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)), (semiring_1_of_nat int) ) 17.32/16.94 ) 17.32/16.94 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (one_one X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_119579 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (= (or (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_119579)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_119579) (zero_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_119579)) _let_2)))) )))) 17.32/16.94 ( real, (zero_zero real) ) 17.32/16.94 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.94 ( 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)))) ) 17.32/16.94 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.94 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.94 ( real, skv_14 ) 17.32/16.94 ( int, (zero_zero int) ) 17.32/16.94 ( int, (one_one int) ) 17.32/16.94 ( int, min_1 ) 17.32/16.94 ( complex, ii ) 17.32/16.94 ) 17.32/16.94 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_119607))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_119607 $$unsorted) (BOUND_VARIABLE_119608 $$unsorted) (BOUND_VARIABLE_119609 $$unsorted)) (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_119608) BOUND_VARIABLE_119609))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_119608))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_119609))) )) 17.32/16.94 ( real, (zero_zero real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.94 ( 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 ) 17.32/16.94 ( 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 real real (hAPP real (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))) ) 17.32/16.94 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.32/16.94 ( real, skv_14, (zero_zero real), pi ) 17.32/16.94 ( int, (zero_zero int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 17.32/16.94 ( int, (one_one int), (zero_zero int), s ) 17.32/16.94 ( int, min_1, (zero_zero int), min_1 ) 17.32/16.94 ) 17.32/16.94 (instantiation (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 (fun X_a X_a))) (let ((_let_5 (times_times X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_119642 $$unsorted) (BOUND_VARIABLE_119643 $$unsorted) (BOUND_VARIABLE_119644 $$unsorted) (BOUND_VARIABLE_119645 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119644) BOUND_VARIABLE_119645))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_119642) BOUND_VARIABLE_119643))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_3) BOUND_VARIABLE_119644))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_3) BOUND_VARIABLE_119642))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_119644) BOUND_VARIABLE_119642)) (hAPP X_a X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_119645) BOUND_VARIABLE_119643)))) ))))))) 17.32/16.94 ( int, skv_1, (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.32/16.94 ) 17.32/16.94 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (minus_minus nat))) (let ((_let_2 (fact_fact nat))) (let ((_let_3 (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat suc M)) N))) (forall ((N $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N) (hAPP nat nat suc M)))) (= (hAPP nat nat _let_2 _let_3) (hAPP nat nat (hAPP nat _let_0 (times_times nat) _let_3) (hAPP nat nat _let_2 (hAPP nat nat (hAPP nat _let_0 _let_1 M) N))))) ))))) 17.32/16.94 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 17.32/16.94 ) 17.32/16.94 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int _let_0 (ord_less_eq int) (zero_zero int)))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_1 X_1))) (not (hBOOL (hAPP int bool _let_1 Y_1))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (dvd_dvd nat) (hAPP int nat nat_1 X_1)) (hAPP int nat nat_1 Y_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) X_1) Y_1)))) ))) 17.32/16.94 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.32/16.95 ) 17.32/16.95 (instantiation (let ((_let_0 (product_prod X_a X_c))) (let ((_let_1 (product_prod X_a X_b))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (= (hAPP X_b _let_1 (hAPP X_a (fun X_b _let_1) (product_Pair X_a X_b) X_1) (hAPP X_c X_b F Y_1)) (hAPP _let_0 _let_1 (hAPP (fun X_c X_b) (fun _let_0 _let_1) (product_apsnd X_c X_b X_a) F) (hAPP X_c _let_0 (hAPP X_a (fun X_c _let_0) (product_Pair X_a X_c) X_1) Y_1))) ))) 17.32/16.95 ( int, int, int, (number_number_of int), (zero_zero int), (hAPP int int bit1 pls) ) 17.32/16.95 ( int, int, int, (number_number_of int), (one_one int), (hAPP int int bit1 pls) ) 17.32/16.95 ( int, int, int, (number_number_of int), s, (hAPP int int bit1 pls) ) 17.32/16.95 ) 17.32/16.95 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat real))) (let ((_let_4 (power_power real))) (let ((_let_5 (ord_less real))) (let ((_let_6 (one_one real))) (let ((_let_7 (fun nat _let_0))) (let ((_let_8 (fun nat _let_2))) (let ((_let_9 (fun _let_3 _let_3))) (let ((_let_10 (combs nat real real))) (let ((_let_11 (fun _let_0 _let_3))) (let ((_let_12 (combb nat real nat))) (let ((_let_13 (number_number_of real))) (let ((_let_14 (hAPP (fun real _let_2) (fun _let_3 _let_8) (combb real _let_2 nat) (times_times real)))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_5 (zero_zero real)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_5 X_1) (hAPP int real _let_13 (hAPP int int bit0 (hAPP int int bit1 pls)))))) (= (hAPP real real ln X_1) (hAPP _let_3 real (suminf real) (hAPP _let_3 _let_3 (hAPP _let_8 _let_9 _let_10 (hAPP _let_3 _let_8 _let_14 (hAPP _let_3 _let_3 (hAPP _let_8 _let_9 _let_10 (hAPP _let_3 _let_8 _let_14 (hAPP real _let_3 _let_4 (hAPP int real _let_13 min_1)))) (hAPP _let_3 _let_3 (hAPP _let_2 _let_9 (combb real real nat) (hAPP real _let_2 (inverse_divide real) _let_6)) (hAPP _let_0 _let_3 (hAPP _let_3 _let_11 _let_12 (real_1 nat)) (hAPP nat _let_0 (hAPP _let_7 _let_7 (combc nat nat nat) (plus_plus nat)) (one_one nat))))))) (hAPP _let_0 _let_3 (hAPP _let_3 _let_11 _let_12 (hAPP real _let_3 _let_4 (hAPP real real (hAPP real _let_2 (minus_minus real) X_1) _let_6))) suc))))) )))))))))))))))) 17.32/16.95 ( (zero_zero real) ) 17.32/16.95 ( (one_one real) ) 17.32/16.95 ( pi ) 17.32/16.95 ( (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)))) ) 17.32/16.95 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 17.32/16.95 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.95 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.95 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 17.32/16.95 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 17.32/16.95 ( skv_2 ) 17.32/16.95 ( skv_10 ) 17.32/16.95 ( skv_13 ) 17.32/16.95 ) 17.32/16.95 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int rat (ring_1_of_int rat) K_4) (hAPP int rat (hAPP int (fun int rat) fract K_4) (one_one int))) ) 17.32/16.95 ( (zero_zero int) ) 17.32/16.95 ( (one_one int) ) 17.32/16.95 ) 17.32/16.95 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (hAPP int (fun int _let_0) zcong X))) (forall ((X $$unsorted) (P_5 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (hAPP int int _let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (hAPP int int _let_1 min_1)) P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (one_one int)) P_5)))) )))) 17.32/16.95 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.32/16.95 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.32/16.95 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.32/16.95 ) 17.32/16.95 (instantiation (let ((_let_0 (fun int bool))) (forall ((Z $$unsorted) (W_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) W_1))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W_1) Z)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP int nat nat_1 W_1)) (hAPP int nat nat_1 Z))))) )) 17.32/16.95 ( (zero_zero int), (zero_zero int) ) 17.32/16.95 ( (zero_zero int), min_1 ) 17.32/16.95 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.32/16.95 ( (zero_zero int), t ) 17.32/16.95 ( (one_one int), (zero_zero int) ) 17.32/16.95 ( (one_one int), t ) 17.32/16.95 ( (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))), (zero_zero int) ) 17.32/16.95 ( (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))), s ) 17.32/16.95 ( (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))), t ) 17.32/16.95 ( (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_3 ) 17.32/16.95 ( (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_9 ) 17.32/16.95 ( min_1, (zero_zero int) ) 17.32/16.95 ( min_1, min_1 ) 17.32/16.95 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 17.32/16.95 ( (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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.32/16.95 ) 17.32/16.95 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_119758 $$unsorted) (BOUND_VARIABLE_119759 $$unsorted)) (or (not (order X_a)) (= (ti X_a BOUND_VARIABLE_119758) (ti X_a BOUND_VARIABLE_119759)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_119759) BOUND_VARIABLE_119758))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_119759) BOUND_VARIABLE_119758))) )) 17.32/16.95 ( real, (zero_zero real), pi ) 17.32/16.95 ( 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))))) ) 17.32/16.95 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.95 ( real, pi, (zero_zero real) ) 17.32/16.95 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.95 ( 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)) ) 17.32/16.95 ( 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)))) ) 17.32/16.95 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 17.32/16.95 ( 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)))), (zero_zero real) ) 17.32/16.95 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 17.32/16.95 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.32/16.95 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 17.32/16.95 ( real, skv_2, (zero_zero real) ) 17.32/16.95 ( real, skv_6, (zero_zero real) ) 17.32/16.95 ( real, skv_10, (zero_zero real) ) 17.32/16.95 ( real, skv_11, (zero_zero real) ) 17.32/16.95 ( real, skv_12, (zero_zero real) ) 17.32/16.95 ( real, skv_13, (zero_zero real) ) 17.32/16.95 ( real, skv_14, (zero_zero real) ) 17.32/16.95 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 17.32/16.95 ( int, (zero_zero int), (zero_zero int) ) 17.32/16.95 ( int, (zero_zero int), min_1 ) 17.32/16.95 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.32/16.95 ( int, (zero_zero int), t ) 17.32/16.95 ( int, pls, min_1 ) 17.32/16.95 ( int, (one_one int), (zero_zero int) ) 17.32/16.95 ( int, (one_one int), t ) 17.32/16.95 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 17.32/16.95 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 17.32/16.95 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 17.32/16.95 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_3 ) 17.32/16.95 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_9 ) 17.32/16.95 ( int, min_1, (zero_zero int) ) 17.32/16.95 ( int, min_1, min_1 ) 17.32/16.95 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 17.32/16.95 ( int, s, (zero_zero int) ) 17.32/16.95 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 17.32/16.95 ( int, t, (one_one int) ) 17.32/16.95 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 17.32/16.95 ( 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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.32/16.95 ( int, skv_3, (zero_zero int) ) 17.32/16.95 ( int, skv_9, (zero_zero int) ) 17.32/16.95 ) 17.32/16.95 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_119848 $$unsorted)) (or (not (ring_1 X_a)) (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_119848)) _let_0) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_119848) _let_0))) )))) 17.32/16.95 ( real, (one_one real) ) 17.32/16.95 ( 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)))) ) 17.32/16.95 ( 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) ) 17.32/16.95 ( int, pls ) 17.32/16.95 ( int, (one_one int) ) 17.32/16.95 ( int, min_1 ) 17.32/16.95 ( int, s ) 17.32/16.95 ( int, s1 ) 17.32/16.95 ( int, skv_8 ) 17.32/16.95 ( complex, ii ) 17.32/16.95 ( complex, (one_one complex) ) 17.32/16.95 ) 17.32/16.95 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (= (ti _let_0 A_3) (hAPP _let_1 _let_0 (complete_Sup_Sup _let_0) (hAPP _let_0 _let_1 (pow X_a) A_3))) ))) 17.32/16.95 ( bool, fNot ) 17.32/16.95 ( nat, (even_odd_even nat) ) 17.32/16.95 ( nat, prime ) 17.32/16.95 ( int, zprime ) 17.32/16.95 ( int, nat_neg ) 17.32/16.95 ( int, zEven ) 17.32/16.95 ( int, nat_is_nat ) 17.32/16.95 ( int, zOdd ) 17.32/16.95 ( int, (even_odd_even int) ) 17.32/16.95 ( int, twoSqu1091635170sum2sq ) 17.32/16.95 ( (fun int bool), nat_nat_set ) 17.32/16.95 ( (product_prod int int), frac_1 ) 17.32/16.95 ( (product_prod nat nat), pred_nat ) 17.32/16.95 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_less ) 17.32/16.95 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_leq ) 17.32/16.95 ( (fun nat rat), vanishes ) 17.32/16.95 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), ratrel ) 17.32/16.95 ) 17.32/16.95 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_119968 $$unsorted) (BOUND_VARIABLE_119977 $$unsorted)) (or (not (abs_if X_a)) (and (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119968) _let_2))) (= (hAPP X_a X_a _let_3 BOUND_VARIABLE_119968) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_119968))) (or (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119977) _let_2)) (= (hAPP X_a X_a _let_3 BOUND_VARIABLE_119977) (ti X_a BOUND_VARIABLE_119977))))) ))))) 17.32/16.95 ( real, (zero_zero real), (zero_zero real) ) 17.32/16.95 ( real, (one_one real), (one_one real) ) 17.32/16.95 ( real, pi, pi ) 17.32/16.95 ( 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 real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.95 ( 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))))), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 17.32/16.95 ( 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)))) ) 17.32/16.96 ( 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)) ) 17.32/16.96 ( nat, (zero_zero nat), (zero_zero nat) ) 17.32/16.96 ( int, (zero_zero int), (zero_zero int) ) 17.32/16.96 ( int, min_1, min_1 ) 17.32/16.96 ( int, s, s ) 17.32/16.96 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.32/16.96 ( int, t, t ) 17.32/16.96 ( int, skv_3, skv_3 ) 17.32/16.96 ( int, skv_9, skv_9 ) 17.32/16.96 ) 17.32/16.96 (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))) ) 17.32/16.96 ( (zero_zero real) ) 17.32/16.96 ( pi ) 17.32/16.96 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.96 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.96 ( skv_2 ) 17.32/16.96 ( skv_10 ) 17.32/16.96 ( skv_13 ) 17.32/16.96 ) 17.32/16.96 (instantiation (let ((_let_0 (number_number_of int))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (hAPP int int bit0 _let_1))) (let ((_let_3 (ti int P_5))) (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_5))) (= (hAPP int int _let_0 _let_2) _let_3) (= _let_3 (hAPP int int _let_0 (hAPP int int bit1 _let_1))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int _let_0 (hAPP int int bit1 _let_2))) P_5))) ))))) 17.32/16.96 ( pls ) 17.32/16.96 ( m ) 17.32/16.96 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.32/16.96 ( min_1 ) 17.32/16.96 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.96 ( s ) 17.32/16.96 ( s1 ) 17.32/16.96 ( t ) 17.32/16.96 ) 17.32/16.96 (instantiation (let ((_let_0 (one_one real))) (forall ((N $$unsorted)) (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))) )) 17.32/16.96 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.96 ) 17.32/16.96 (instantiation (forall ((N $$unsorted)) (= (hAPP real int (archim2085082626_floor real) (hAPP int real (real_1 int) N)) (ti int N)) ) 17.32/16.96 ( (zero_zero int) ) 17.32/16.96 ( pls ) 17.32/16.96 ( m ) 17.32/16.96 ( (one_one int) ) 17.32/16.96 ( min_1 ) 17.32/16.96 ( s ) 17.32/16.96 ( s1 ) 17.32/16.96 ( t ) 17.32/16.96 ) 17.32/16.96 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120140 $$unsorted)) (or (not (monoid_add X_a)) (= (ti X_a BOUND_VARIABLE_120140) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (zero_zero X_a)) BOUND_VARIABLE_120140))) ) 17.32/16.96 ( bool, fFalse ) 17.32/16.96 ( bool, fTrue ) 17.32/16.96 ( real, pi ) 17.32/16.96 ( (fun nat bool), (even_odd_even nat) ) 17.32/16.96 ( (fun nat bool), prime ) 17.32/16.96 ( (fun nat nat), suc ) 17.32/16.96 ( (fun nat nat), (fact_fact nat) ) 17.32/16.96 ( (fun nat nat), (size_size nat) ) 17.32/16.96 ( (fun nat nat), fact ) 17.32/16.96 ( (fun nat nat), nat_size ) 17.32/16.96 ( int, pls ) 17.32/16.96 ( int, m ) 17.32/16.96 ( int, min_1 ) 17.32/16.96 ( int, s ) 17.32/16.96 ( int, s1 ) 17.32/16.96 ( int, t ) 17.32/16.96 ( (fun int bool), zprime ) 17.32/16.96 ( (fun int bool), nat_neg ) 17.32/16.96 ( (fun int bool), zEven ) 17.32/16.96 ( (fun int bool), nat_is_nat ) 17.32/16.96 ( (fun int bool), zOdd ) 17.32/16.96 ( (fun int bool), (even_odd_even int) ) 17.32/16.96 ( (fun int bool), twoSqu1091635170sum2sq ) 17.32/16.96 ( (fun int nat), nat_1 ) 17.32/16.96 ( (fun int nat), phi ) 17.32/16.96 ( (fun real real), sqrt ) 17.32/16.96 ( (fun real real), tan ) 17.32/16.96 ( (fun real real), cos ) 17.32/16.96 ( (fun real real), arccos ) 17.32/16.96 ( (fun real real), ln ) 17.32/16.96 ( (fun real real), sin ) 17.32/16.96 ( (fun real real), arctan ) 17.32/16.96 ( (fun real real), arcsin ) 17.32/16.96 ( complex, ii ) 17.32/16.96 ( (fun complex complex), cnj ) 17.32/16.96 ( (fun complex complex), expi ) 17.32/16.96 ( (fun nat real), (real_1 nat) ) 17.32/16.96 ( (fun nat real), cos_coeff ) 17.32/16.96 ( (fun nat real), sin_coeff ) 17.32/16.96 ( (fun int int), bit0 ) 17.32/16.96 ( (fun int int), bit1 ) 17.32/16.96 ( (fun int int), pred ) 17.32/16.96 ( (fun int int), succ ) 17.32/16.96 ( (fun int int), (fact_fact int) ) 17.32/16.96 ( (fun int int), zfact ) 17.32/16.96 ( (fun bool bool), fNot ) 17.32/16.96 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.32/16.96 ( (fun bool (fun bool bool)), fconj ) 17.32/16.96 ( (fun bool (fun bool bool)), fdisj ) 17.32/16.96 ( (fun bool (fun bool bool)), fimplies ) 17.32/16.96 ( (fun int (fun int bool)), sRStar ) 17.32/16.96 ( (fun int (fun int bool)), quadRes ) 17.32/16.96 ( (fun int (fun int bool)), norRRset ) 17.32/16.96 ( (fun int (fun int bool)), d22set ) 17.32/16.96 ( (fun int (fun int bool)), sr ) 17.32/16.96 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 17.32/16.96 ( (fun nat (fun nat nat)), nat_gcd ) 17.32/16.96 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 17.32/16.96 ( (fun nat (fun nat nat)), nat_lcm ) 17.32/16.96 ( (fun nat (fun real real)), root ) 17.32/16.96 ( (fun real (fun real real)), log ) 17.32/16.96 ( (fun real (fun real real)), powr ) 17.32/16.96 ( (fun nat (fun nat bool)), coprime ) 17.32/16.96 ( (fun (fun int bool) int), (the int) ) 17.32/16.96 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 17.32/16.96 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 17.32/16.96 ( (fun nat (fun nat (product_prod int int))), bezw ) 17.32/16.96 ( (fun (fun int bool) bool), nat_nat_set ) 17.32/16.96 ( (filter nat), sequentially ) 17.32/16.96 ( (fun (product_prod nat nat) bool), pred_nat ) 17.32/16.96 ( (fun (product_prod int int) bool), frac_1 ) 17.32/16.96 ( (fun real complex), cis ) 17.32/16.96 ( (fun complex real), im ) 17.32/16.96 ( (fun complex real), re ) 17.32/16.96 ( (fun complex real), arg ) 17.32/16.96 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 17.32/16.96 ( (fun int (fun int int)), int_gcd ) 17.32/16.96 ( (fun int (fun int int)), multInv ) 17.32/16.96 ( (fun int (fun int int)), legacy_zgcd ) 17.32/16.96 ( (fun int (fun int int)), z3mod ) 17.32/16.96 ( (fun int (fun int int)), inv ) 17.32/16.96 ( (fun int (fun int int)), (gcd_gcd int) ) 17.32/16.96 ( (fun int (fun int int)), standardRes ) 17.32/16.96 ( (fun int (fun int int)), legendre ) 17.32/16.96 ( (fun int (fun int int)), nat_tsub ) 17.32/16.96 ( (fun int (fun int int)), z3div ) 17.32/16.96 ( (fun int (fun int int)), int_lcm ) 17.32/16.96 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 17.32/16.96 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 17.32/16.96 ( (fun int (fun (fun int bool) bool)), rsetR ) 17.32/16.96 ( (fun int (fun (fun int bool) bool)), resSet ) 17.32/16.96 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 17.32/16.96 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 17.32/16.96 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 17.32/16.96 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.32/16.96 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 17.32/16.96 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 17.32/16.96 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 17.32/16.96 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 17.32/16.96 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.32/16.96 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.32/16.96 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.32/16.96 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.32/16.96 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.32/16.96 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.32/16.96 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 17.32/16.96 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 17.32/16.96 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 17.32/16.96 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 17.32/16.96 ( (fun real nat), natfloor ) 17.32/16.96 ( (fun real nat), natceiling ) 17.32/16.96 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.32/16.96 ( (fun int (fun int (fun int bool))), wset ) 17.32/16.96 ( (fun int (fun int (fun int bool))), bnorRset ) 17.32/16.96 ( (fun int (fun int (fun int bool))), zcong ) 17.32/16.96 ( (fun int (fun int (fun int bool))), noXRRset ) 17.32/16.96 ( (fun int (fun int (fun int bool))), zcongm ) 17.32/16.96 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.32/16.96 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.32/16.96 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.32/16.96 ( (fun int real), (real_1 int) ) 17.32/16.96 ( (fun complex nat), (size_size complex) ) 17.32/16.96 ( (fun complex nat), complex_size ) 17.32/16.96 ( (fun int (list int)), quickc666637781d_zero ) 17.32/16.96 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.32/16.96 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.32/16.96 ( (fun (product_prod int int) rat), frct ) 17.32/16.96 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.32/16.96 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.32/16.96 ( (fun (fun nat rat) bool), vanishes ) 17.32/16.96 ( (fun int (fun int rat)), fract ) 17.32/16.96 ( (fun code_code_numeral int), code_int_of ) 17.32/16.96 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.32/16.96 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.32/16.96 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.32/16.96 ( (fun real (fun real complex)), complex_1 ) 17.32/16.96 ( (fun real (fun real complex)), rcis ) 17.32/16.96 ( (fun int (fun nat nat)), nat_aux ) 17.32/16.96 ( (fun rat real), ratreal ) 17.32/16.96 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.32/16.96 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.32/16.96 ( (fun rat (product_prod int int)), quotient_of ) 17.32/16.96 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.32/16.96 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.32/16.96 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.32/16.96 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.32/16.96 ) 17.32/16.96 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120154 $$unsorted)) (or (not (real_algebra_1 X_a)) (= (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) BOUND_VARIABLE_120154) (one_one X_a)) (hAPP real X_a (of_real X_a) BOUND_VARIABLE_120154))) ) 17.32/16.96 ( complex, pi ) 17.32/16.96 ( complex, (hAPP int real (number_number_of real) min_1) ) 17.32/16.96 ( complex, (hAPP real real (uminus_uminus real) (one_one real)) ) 17.32/16.96 ) 17.32/16.96 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (hAPP int int (hAPP int _let_0 (div_div int) (hAPP int int (hAPP int _let_0 (minus_minus int) P_5) (one_one int))) _let_1))) (forall ((P_5 $$unsorted)) (= (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)))) (hAPP int nat nat_1 _let_2)) (hAPP int nat nat_1 (hAPP int int (hAPP int _let_0 (times_times int) _let_1) _let_2))) )))) 17.32/16.96 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.96 ) 17.32/16.96 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((A_2 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_1))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP nat real (real_1 nat) A_2)) X_1)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) A_2) (hAPP real nat natfloor X_1))))) ))) 17.32/16.96 ( (zero_zero nat), pi ) 17.32/16.96 ( (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)))) ) 17.32/16.96 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.96 ( (zero_zero nat), skv_6 ) 17.32/16.96 ( (zero_zero nat), skv_11 ) 17.32/16.96 ( (zero_zero nat), skv_12 ) 17.32/16.96 ( (zero_zero nat), skv_14 ) 17.32/16.96 ) 17.32/16.96 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (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)) ))) 17.32/16.96 ( (zero_zero real), pi ) 17.32/16.96 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.96 ( (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.96 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.96 ( (zero_zero real), skv_6 ) 17.32/16.96 ( (zero_zero real), skv_11 ) 17.32/16.96 ( (zero_zero real), skv_12 ) 17.32/16.96 ( (zero_zero real), skv_14 ) 17.32/16.96 ( pi, (zero_zero real) ) 17.32/16.96 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.96 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.32/16.96 ( (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)))) ) 17.32/16.96 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 17.32/16.96 ( (hAPP real real (hAPP 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) ) 17.32/16.96 ( (hAPP real real (hAPP real (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))) ) 17.32/16.96 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.32/16.96 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.32/16.96 ( skv_6, (zero_zero real) ) 17.32/16.96 ( skv_11, (zero_zero real) ) 17.32/16.96 ( skv_12, (zero_zero 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int int) P_5) Q_3) (hAPP rat _let_0 quotient_of R_4))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) Q_3))) )) 17.32/16.96 ( (zero_zero rat), (zero_zero int), (one_one int) ) 17.32/16.96 ( (one_one rat), (one_one int), (one_one int) ) 17.32/16.96 ) 17.32/16.96 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_120390 $$unsorted) (BOUND_VARIABLE_120391 $$unsorted) (BOUND_VARIABLE_120392 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_120392)) (not (= (ti X_a BOUND_VARIABLE_120390) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_120391) BOUND_VARIABLE_120392))) (= (ti X_a BOUND_VARIABLE_120391) (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_120390) BOUND_VARIABLE_120392))) )) 17.32/16.96 ( 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))))), pi ) 17.32/16.96 ( int, m, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 17.32/16.96 ( int, min_1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), min_1 ) 17.32/16.96 ( int, s, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 17.32/16.96 ( complex, ii, ii, ii ) 17.32/16.96 ) 17.32/16.96 (instantiation (let ((_let_0 (tendsto X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (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))) )) 17.32/16.96 ( real, real ) 17.32/16.96 ( nat, real ) 17.32/16.96 ) 17.32/16.96 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120463 $$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_120463)) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_120463)) (ti X_a BOUND_VARIABLE_120463))) ) 17.32/16.96 ( bool, fFalse ) 17.32/16.96 ( bool, fTrue ) 17.32/16.96 ( real, (zero_zero real) ) 17.32/16.96 ( real, pi ) 17.32/16.96 ( (fun nat bool), (even_odd_even nat) ) 17.32/16.96 ( (fun nat bool), prime ) 17.32/16.96 ( (fun nat nat), suc ) 17.32/16.96 ( (fun nat nat), (fact_fact nat) ) 17.32/16.96 ( (fun nat nat), (size_size nat) ) 17.32/16.96 ( (fun nat nat), fact ) 17.32/16.97 ( (fun nat nat), nat_size ) 17.32/16.97 ( int, pls ) 17.32/16.97 ( int, m ) 17.32/16.97 ( int, min_1 ) 17.32/16.97 ( int, s ) 17.32/16.97 ( int, s1 ) 17.32/16.97 ( int, t ) 17.32/16.97 ( (fun int bool), zprime ) 17.32/16.97 ( (fun int bool), nat_neg ) 17.32/16.97 ( (fun int bool), zEven ) 17.32/16.97 ( (fun int bool), nat_is_nat ) 17.32/16.97 ( (fun int bool), zOdd ) 17.32/16.97 ( (fun int bool), (even_odd_even int) ) 17.32/16.97 ( (fun int bool), twoSqu1091635170sum2sq ) 17.32/16.97 ( (fun int nat), nat_1 ) 17.32/16.97 ( (fun int nat), phi ) 17.32/16.97 ( (fun real real), sqrt ) 17.32/16.97 ( (fun real real), tan ) 17.32/16.97 ( (fun real real), cos ) 17.32/16.97 ( (fun real real), arccos ) 17.32/16.97 ( (fun real real), ln ) 17.32/16.97 ( (fun real real), sin ) 17.32/16.97 ( (fun real real), arctan ) 17.32/16.97 ( (fun real real), arcsin ) 17.32/16.97 ( complex, ii ) 17.32/16.97 ( (fun complex complex), cnj ) 17.32/16.97 ( (fun complex complex), expi ) 17.32/16.97 ( (fun nat real), (real_1 nat) ) 17.32/16.97 ( (fun nat real), cos_coeff ) 17.32/16.97 ( (fun nat real), sin_coeff ) 17.32/16.97 ( (fun int int), bit0 ) 17.32/16.97 ( (fun int int), bit1 ) 17.32/16.97 ( (fun int int), pred ) 17.32/16.97 ( (fun int int), succ ) 17.32/16.97 ( (fun int int), (fact_fact int) ) 17.32/16.97 ( (fun int int), zfact ) 17.32/16.97 ( rat, (zero_zero rat) ) 17.32/16.97 ( (fun bool bool), fNot ) 17.32/16.97 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.32/16.97 ( (fun bool (fun bool bool)), fconj ) 17.32/16.97 ( (fun bool (fun bool bool)), fdisj ) 17.32/16.97 ( (fun bool (fun bool bool)), fimplies ) 17.32/16.97 ( (fun int (fun int bool)), sRStar ) 17.32/16.97 ( (fun int (fun int bool)), quadRes ) 17.32/16.97 ( (fun int (fun int bool)), norRRset ) 17.32/16.97 ( (fun int (fun int bool)), d22set ) 17.32/16.97 ( (fun int (fun int bool)), sr ) 17.32/16.97 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 17.32/16.97 ( (fun nat (fun nat nat)), nat_gcd ) 17.32/16.97 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 17.32/16.97 ( (fun nat (fun nat nat)), nat_lcm ) 17.32/16.97 ( (fun nat (fun real real)), root ) 17.32/16.97 ( (fun real (fun real real)), log ) 17.32/16.97 ( (fun real (fun real real)), powr ) 17.32/16.97 ( (fun nat (fun nat bool)), coprime ) 17.32/16.97 ( (fun (fun int bool) int), (the int) ) 17.32/16.97 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 17.32/16.97 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 17.32/16.97 ( (fun nat (fun nat (product_prod int int))), bezw ) 17.32/16.97 ( (fun (fun int bool) bool), nat_nat_set ) 17.32/16.97 ( (filter nat), sequentially ) 17.32/16.97 ( (fun (product_prod nat nat) bool), pred_nat ) 17.32/16.97 ( (fun (product_prod int int) bool), frac_1 ) 17.32/16.97 ( (fun real complex), cis ) 17.32/16.97 ( (fun complex real), im ) 17.32/16.97 ( (fun complex real), re ) 17.32/16.97 ( (fun complex real), arg ) 17.32/16.97 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 17.32/16.97 ( (fun int (fun int int)), int_gcd ) 17.32/16.97 ( (fun int (fun int int)), multInv ) 17.32/16.97 ( (fun int (fun int int)), legacy_zgcd ) 17.32/16.97 ( (fun int (fun int int)), z3mod ) 17.32/16.97 ( (fun int (fun int int)), inv ) 17.32/16.97 ( (fun int (fun int int)), (gcd_gcd int) ) 17.32/16.97 ( (fun int (fun int int)), standardRes ) 17.32/16.97 ( (fun int (fun int int)), legendre ) 17.32/16.97 ( (fun int (fun int int)), nat_tsub ) 17.32/16.97 ( (fun int (fun int int)), z3div ) 17.32/16.97 ( (fun int (fun int int)), int_lcm ) 17.32/16.97 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 17.32/16.97 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 17.32/16.97 ( (fun int (fun (fun int bool) bool)), rsetR ) 17.32/16.97 ( (fun int (fun (fun int bool) bool)), resSet ) 17.32/16.97 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 17.32/16.97 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 17.32/16.97 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 17.32/16.97 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.32/16.97 ( (let ((_let_0 (product_prod int 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_let_0))))), bolzano_bisect ) 17.32/16.97 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 17.32/16.97 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 17.32/16.97 ( (fun real nat), natfloor ) 17.32/16.97 ( (fun real nat), natceiling ) 17.32/16.97 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.32/16.97 ( (fun int (fun int (fun int bool))), wset ) 17.32/16.97 ( (fun int (fun int (fun int bool))), bnorRset ) 17.32/16.97 ( (fun int (fun int (fun int bool))), zcong ) 17.32/16.97 ( (fun int (fun int (fun int bool))), noXRRset ) 17.32/16.97 ( (fun int (fun int (fun int bool))), zcongm ) 17.32/16.97 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.32/16.97 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.32/16.97 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.32/16.97 ( (fun int real), (real_1 int) ) 17.32/16.97 ( (fun complex nat), (size_size 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(ord_less X_a) _let_0) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_120482) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) )) 17.32/16.97 ( bool, fFalse ) 17.32/16.97 ( bool, fTrue ) 17.32/16.97 ( real, pi ) 17.32/16.97 ( real, (hAPP int real (number_number_of real) min_1) ) 17.32/16.97 ( 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)))) ) 17.32/16.97 ( (fun nat bool), (even_odd_even nat) ) 17.32/16.97 ( (fun nat bool), prime ) 17.32/16.97 ( (fun nat nat), suc ) 17.32/16.97 ( (fun nat nat), (fact_fact nat) ) 17.32/16.97 ( (fun nat nat), (size_size nat) ) 17.32/16.97 ( (fun nat nat), fact ) 17.32/16.97 ( (fun nat nat), nat_size ) 17.32/16.97 ( int, pls ) 17.32/16.97 ( int, m ) 17.32/16.97 ( int, min_1 ) 17.32/16.97 ( int, s ) 17.32/16.97 ( int, s1 ) 17.32/16.97 ( int, t ) 17.32/16.97 ( int, skv_8 ) 17.32/16.97 ( (fun int bool), zprime ) 17.32/16.97 ( (fun int bool), nat_neg ) 17.32/16.97 ( (fun int bool), zEven ) 17.32/16.97 ( (fun int bool), nat_is_nat ) 17.32/16.97 ( (fun int bool), zOdd ) 17.32/16.97 ( (fun int bool), (even_odd_even int) ) 17.32/16.97 ( (fun int bool), twoSqu1091635170sum2sq ) 17.32/16.97 ( (fun int nat), nat_1 ) 17.32/16.97 ( (fun int nat), phi ) 17.32/16.97 ( (fun real real), sqrt ) 17.32/16.97 ( (fun real real), tan ) 17.32/16.97 ( (fun real real), cos ) 17.32/16.97 ( (fun real real), arccos ) 17.32/16.97 ( (fun real real), ln ) 17.32/16.97 ( (fun real real), sin ) 17.32/16.97 ( (fun real real), arctan ) 17.32/16.97 ( (fun real real), arcsin ) 17.32/16.97 ( complex, ii ) 17.32/16.97 ( (fun complex complex), cnj ) 17.32/16.97 ( (fun complex complex), expi ) 17.32/16.97 ( (fun nat real), (real_1 nat) ) 17.32/16.97 ( (fun nat real), cos_coeff ) 17.32/16.97 ( (fun nat real), sin_coeff ) 17.32/16.97 ( (fun int int), bit0 ) 17.32/16.97 ( (fun int int), bit1 ) 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(product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.32/16.97 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 17.32/16.97 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 17.32/16.97 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 17.32/16.97 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 17.32/16.97 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.32/16.97 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.32/16.97 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.32/16.97 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.32/16.97 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.32/16.97 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.32/16.97 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust 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code_c271388182l_size ) 17.32/16.97 ( (fun real (fun real complex)), complex_1 ) 17.32/16.97 ( (fun real (fun real complex)), rcis ) 17.32/16.97 ( (fun int (fun nat nat)), nat_aux ) 17.32/16.97 ( (fun rat real), ratreal ) 17.32/16.97 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.32/16.97 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.32/16.97 ( (fun rat (product_prod int int)), quotient_of ) 17.32/16.97 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.32/16.97 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.32/16.97 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.32/16.97 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.32/16.97 ) 17.32/16.97 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) N_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_1))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP int nat (number_number_of nat) N_1)) (hAPP real nat natfloor X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) N_1)) X_1)))) ))) 17.32/16.97 ( pi, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.32/16.97 ) 17.32/16.97 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120510 $$unsorted)) (or (not (division_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_120510) (one_one X_a)) (ti X_a BOUND_VARIABLE_120510))) ) 17.32/16.97 ( bool, fFalse ) 17.32/16.97 ( bool, fTrue ) 17.32/16.97 ( real, (one_one real) ) 17.32/16.97 ( real, pi ) 17.32/16.97 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.32/16.97 ( real, (hAPP real real sqrt 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17.32/16.97 ( (fun int nat), phi ) 17.32/16.97 ( (fun real real), sqrt ) 17.32/16.97 ( (fun real real), tan ) 17.32/16.97 ( (fun real real), cos ) 17.32/16.97 ( (fun real real), arccos ) 17.32/16.97 ( (fun real real), ln ) 17.32/16.97 ( (fun real real), sin ) 17.32/16.97 ( (fun real real), arctan ) 17.32/16.97 ( (fun real real), arcsin ) 17.32/16.97 ( complex, ii ) 17.32/16.97 ( (fun complex complex), cnj ) 17.32/16.97 ( (fun complex complex), expi ) 17.32/16.97 ( (fun nat real), (real_1 nat) ) 17.32/16.97 ( (fun nat real), cos_coeff ) 17.32/16.97 ( (fun nat real), sin_coeff ) 17.32/16.97 ( (fun int int), bit0 ) 17.32/16.97 ( (fun int int), bit1 ) 17.32/16.97 ( (fun int int), pred ) 17.32/16.97 ( (fun int int), succ ) 17.32/16.97 ( (fun int int), (fact_fact int) ) 17.32/16.97 ( (fun int int), zfact ) 17.32/16.97 ( (fun bool bool), fNot ) 17.32/16.97 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.32/16.97 ( (fun bool (fun bool bool)), fconj ) 17.32/16.97 ( (fun 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real nat), natceiling ) 17.32/16.98 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.32/16.98 ( (fun int (fun int (fun int bool))), wset ) 17.32/16.98 ( (fun int (fun int (fun int bool))), bnorRset ) 17.32/16.98 ( (fun int (fun int (fun int bool))), zcong ) 17.32/16.98 ( (fun int (fun int (fun int bool))), noXRRset ) 17.32/16.98 ( (fun int (fun int (fun int bool))), zcongm ) 17.32/16.98 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.32/16.98 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.32/16.98 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.32/16.98 ( (fun int real), (real_1 int) ) 17.32/16.98 ( (fun complex nat), (size_size complex) ) 17.32/16.98 ( (fun complex nat), complex_size ) 17.32/16.98 ( (fun int (list int)), quickc666637781d_zero ) 17.32/16.98 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.32/16.98 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.32/16.98 ( (fun (product_prod int int) rat), frct ) 17.32/16.98 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.32/16.98 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.32/16.98 ( (fun (fun nat rat) bool), vanishes ) 17.32/16.98 ( (fun int (fun int rat)), fract ) 17.32/16.98 ( (fun code_code_numeral int), code_int_of ) 17.32/16.98 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.32/16.98 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.32/16.98 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.32/16.98 ( (fun real (fun real complex)), complex_1 ) 17.32/16.98 ( (fun real (fun real complex)), rcis ) 17.32/16.98 ( (fun int (fun nat nat)), nat_aux ) 17.32/16.98 ( (fun rat real), ratreal ) 17.32/16.98 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.32/16.98 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.32/16.98 ( (fun rat (product_prod int int)), quotient_of ) 17.32/16.98 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.32/16.98 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.32/16.98 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.32/16.98 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.32/16.98 ) 17.32/16.98 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_120573 $$unsorted) (BOUND_VARIABLE_120574 $$unsorted)) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_120574)) BOUND_VARIABLE_120573)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_120573)) BOUND_VARIABLE_120574)))) )))) 17.32/16.98 ( int, pls, (one_one int) ) 17.32/16.98 ( int, pls, min_1 ) 17.32/16.98 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.98 ( int, pls, s ) 17.32/16.98 ( int, pls, (hAPP int int (number_number_of int) pls) ) 17.32/16.98 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.32/16.98 ( int, pls, skv_3 ) 17.32/16.98 ( int, pls, skv_9 ) 17.32/16.98 ( int, (one_one int), pls ) 17.32/16.98 ( int, (one_one int), min_1 ) 17.32/16.98 ( int, min_1, pls ) 17.32/16.98 ( int, min_1, (one_one int) ) 17.32/16.98 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), pls ) 17.32/16.98 ( int, s, pls ) 17.32/16.98 ( int, (hAPP int int (number_number_of int) pls), pls ) 17.32/16.98 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), pls ) 17.32/16.98 ( int, skv_3, pls ) 17.32/16.98 ( int, skv_9, pls ) 17.32/16.98 ) 17.32/16.98 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_0 X_1))) (not (hBOOL (hAPP real bool _let_0 Y_1))) (= (= (hAPP real real ln Y_1) (hAPP real real ln X_1)) (= Y_1 X_1))) )) 17.32/16.98 ( pi, pi ) 17.32/16.98 ( pi, skv_2 ) 17.32/16.98 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.98 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.98 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.98 ( skv_2, pi ) 17.32/16.98 ( skv_10, skv_10 ) 17.32/16.98 ( skv_10, skv_13 ) 17.32/16.98 ( skv_13, skv_10 ) 17.32/16.98 ) 17.32/16.98 (instantiation (forall ((X $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X))) (= X (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real (hAPP nat (fun real real) root N) X)) N))) ) 17.32/16.98 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.98 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.98 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.98 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.98 ) 17.32/16.98 (instantiation (let ((_let_0 (fun real real))) (forall ((X $$unsorted)) (= (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)) )) 17.32/16.98 ( (zero_zero real) ) 17.32/16.98 ( pi ) 17.32/16.98 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.98 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 17.32/16.98 ( (hAPP real real (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))))) ) 17.32/16.98 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 17.32/16.98 ( (hAPP real 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))))) ) 17.32/16.98 ( (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)))) ) 17.32/16.98 ) 17.32/16.98 (instantiation (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_121044))) (let ((_let_3 (hAPP int nat (number_number_of nat) BOUND_VARIABLE_121050))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_121044 $$unsorted) (BOUND_VARIABLE_121050 $$unsorted)) (or (not (power X_a)) (not (semiring_0 X_a)) (and (or (= _let_0 _let_2) (= (zero_zero X_a) (hAPP nat X_a _let_1 _let_2))) (or (not (= _let_0 _let_3)) (= (one_one X_a) (hAPP nat X_a _let_1 _let_3))))) ))))) 17.32/16.98 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.32/16.98 ( int, pls, pls ) 17.32/16.98 ( complex, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 17.32/16.98 ( quickcheck_code_int, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.32/16.98 ) 17.32/16.98 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (ti X_a BOUND_VARIABLE_121089))) (let ((_let_3 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_121088))) (let ((_let_4 (= _let_1 _let_3))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_121087 $$unsorted) (BOUND_VARIABLE_121088 $$unsorted) (BOUND_VARIABLE_121089 $$unsorted)) (or (not (field_inverse_zero X_a)) (not (number X_a)) (= (= _let_2 (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_121087) _let_3)) (and (or _let_4 (= (ti X_a BOUND_VARIABLE_121087) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_121089) _let_3))) (or (not _let_4) (= _let_1 _let_2))))) )))))) 17.32/16.98 ( real, pi, (hAPP int int bit0 (hAPP int int bit1 pls)), pi ) 17.32/16.98 ) 17.32/16.98 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP real _let_0 (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (let ((_let_2 (hAPP real _let_0 (inverse_divide real) Y_1))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (= (= X_1 (hAPP real real _let_2 (hAPP real real _let_1 Z))) (= (hAPP real real _let_2 Z) (hAPP real real _let_1 X_1))) )))) 17.32/16.98 ( pi, pi, pi ) 17.32/16.98 ( (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.32/16.98 ) 17.32/16.98 (instantiation (forall ((X $$unsorted)) (= (hAPP int nat nat_1 (hAPP real int (archimedean_ceiling real) X)) (hAPP real nat natceiling X)) ) 17.32/16.98 ( (zero_zero real) ) 17.32/16.98 ( (one_one real) ) 17.32/16.98 ) 17.32/16.98 (instantiation (let ((_let_0 (number_number_of int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (number_number_of rat))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (= (hAPP rat rat (hAPP rat (fun rat rat) (inverse_divide rat) (hAPP int rat _let_2 K_4)) (hAPP int rat _let_2 L_4)) (hAPP _let_1 rat frct (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) (hAPP int int _let_0 K_4)) (hAPP int int _let_0 L_4)))) )))) 17.32/16.98 ( pls, (hAPP int int bit1 pls) ) 17.32/16.98 ( (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 17.32/16.98 ) 17.32/16.98 (instantiation (let ((_let_0 (one_one X_a))) (forall ((X_a $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (= _let_0 (hAPP X_a X_a (sgn_sgn X_a) _let_0))) )) 17.32/16.98 ( real ) 17.32/16.98 ( nat ) 17.32/16.98 ( int ) 17.32/16.98 ( complex ) 17.32/16.98 ( rat ) 17.32/16.98 ( quickcheck_code_int ) 17.32/16.98 ( code_code_numeral ) 17.32/16.98 ) 17.32/16.98 (instantiation (let ((_let_0 (ti X_a A_1))) (let ((_let_1 (product_prod X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X $$unsorted) (Y $$unsorted) (A_1 $$unsorted)) (or (not (= _let_0 (hAPP _let_1 X_a (product_fst X_a X_b) (hAPP X_b _let_1 (hAPP X_a (fun X_b _let_1) (product_Pair X_a X_b) X) Y)))) (= (ti X_a X) _let_0)) ))) 17.32/16.98 ( int, int, (zero_zero int), (one_one int), min_1 ) 17.32/16.98 ( int, int, (one_one int), (one_one int), s ) 17.32/16.98 ( int, int, s, (one_one int), m ) 17.32/16.98 ) 17.32/16.98 (instantiation (let ((_let_0 (fun X_a (fun X_a bool)))) (forall ((X_a $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun X_a bool))) (= (hAPP _let_0 X_a (hilbert_Eps X_a) (hAPP X_a _let_0 (hAPP _let_0 _let_0 (combc X_a X_a bool) (fequal X_a)) X_1)) (ti X_a X_1))) )) 17.32/16.98 ( bool, fFalse ) 17.32/16.98 ( bool, fTrue ) 17.32/16.98 ( real, pi ) 17.32/16.98 ( nat, (zero_zero nat) ) 17.32/16.98 ( (fun nat bool), (even_odd_even nat) ) 17.32/16.98 ( (fun nat bool), prime ) 17.32/16.98 ( (fun nat nat), suc ) 17.32/16.98 ( (fun nat nat), (fact_fact nat) ) 17.32/16.98 ( (fun nat nat), (size_size nat) ) 17.32/16.98 ( (fun nat nat), fact ) 17.32/16.98 ( (fun nat nat), nat_size ) 17.32/16.98 ( int, (zero_zero int) ) 17.32/16.98 ( int, pls ) 17.32/16.98 ( int, m ) 17.32/16.98 ( int, min_1 ) 17.32/16.98 ( int, s ) 17.32/16.98 ( int, s1 ) 17.32/16.98 ( int, t ) 17.32/16.98 ( (fun int bool), zprime ) 17.32/16.98 ( (fun int bool), nat_neg ) 17.32/16.98 ( (fun int bool), zEven ) 17.32/16.98 ( (fun int bool), nat_is_nat ) 17.32/16.98 ( (fun int bool), zOdd ) 17.32/16.98 ( (fun int bool), (even_odd_even int) ) 17.32/16.98 ( (fun int bool), twoSqu1091635170sum2sq ) 17.32/16.98 ( (fun int nat), nat_1 ) 17.32/16.98 ( (fun int nat), phi ) 17.32/16.98 ( (fun real real), sqrt ) 17.32/16.98 ( (fun real real), tan ) 17.32/16.98 ( (fun real real), cos ) 17.32/16.98 ( (fun real real), arccos ) 17.32/16.98 ( (fun real real), ln ) 17.32/16.98 ( (fun real real), sin ) 17.32/16.98 ( (fun real real), arctan ) 17.32/16.98 ( (fun real real), arcsin ) 17.32/16.98 ( complex, ii ) 17.32/16.98 ( (fun complex complex), cnj ) 17.32/16.98 ( (fun complex complex), expi ) 17.32/16.98 ( (fun nat real), (real_1 nat) ) 17.32/16.98 ( (fun nat real), cos_coeff ) 17.32/16.98 ( (fun nat real), sin_coeff ) 17.32/16.98 ( (fun int int), bit0 ) 17.32/16.98 ( (fun int int), bit1 ) 17.32/16.98 ( (fun int int), pred ) 17.32/16.98 ( (fun int int), succ ) 17.32/16.98 ( (fun int int), (fact_fact int) ) 17.32/16.98 ( (fun int int), zfact ) 17.32/16.98 ( (fun bool bool), fNot ) 17.32/16.98 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.32/16.98 ( (fun bool (fun bool bool)), fconj ) 17.32/16.98 ( (fun bool (fun bool bool)), fdisj ) 17.32/16.98 ( (fun bool (fun bool bool)), fimplies ) 17.32/16.98 ( (fun int (fun int bool)), sRStar ) 17.32/16.98 ( (fun int (fun int bool)), quadRes ) 17.32/16.98 ( (fun int (fun int bool)), norRRset ) 17.32/16.98 ( (fun int (fun int bool)), d22set ) 17.32/16.98 ( (fun int (fun int bool)), sr ) 17.32/16.98 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 17.32/16.98 ( (fun nat (fun nat nat)), nat_gcd ) 17.32/16.98 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 17.32/16.98 ( (fun nat (fun nat nat)), nat_lcm ) 17.32/16.98 ( (fun nat (fun real real)), root ) 17.32/16.98 ( (fun real (fun real real)), log ) 17.32/16.98 ( (fun real (fun real real)), powr ) 17.32/16.98 ( (fun nat (fun nat bool)), coprime ) 17.32/16.98 ( (fun (fun int bool) int), (the int) ) 17.32/16.98 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 17.32/16.98 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 17.32/16.98 ( (fun nat (fun nat (product_prod int int))), bezw ) 17.32/16.98 ( (fun (fun int bool) bool), nat_nat_set ) 17.32/16.98 ( (filter nat), sequentially ) 17.32/16.98 ( (fun (product_prod nat nat) bool), pred_nat ) 17.32/16.98 ( (fun (product_prod int int) bool), frac_1 ) 17.32/16.99 ( (fun real complex), cis ) 17.32/16.99 ( (fun complex real), im ) 17.32/16.99 ( (fun complex real), re ) 17.32/16.99 ( (fun complex real), arg ) 17.32/16.99 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 17.32/16.99 ( (fun int (fun int int)), int_gcd ) 17.32/16.99 ( (fun int (fun int int)), multInv ) 17.32/16.99 ( (fun int (fun int int)), legacy_zgcd ) 17.32/16.99 ( (fun int (fun int int)), z3mod ) 17.32/16.99 ( (fun int (fun int int)), inv ) 17.32/16.99 ( (fun int (fun int int)), (gcd_gcd int) ) 17.32/16.99 ( (fun int (fun int int)), standardRes ) 17.32/16.99 ( (fun int (fun int int)), legendre ) 17.32/16.99 ( (fun int (fun int int)), nat_tsub ) 17.32/16.99 ( (fun int (fun int int)), z3div ) 17.32/16.99 ( (fun int (fun int int)), int_lcm ) 17.32/16.99 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 17.32/16.99 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 17.32/16.99 ( (fun int (fun (fun int bool) bool)), rsetR ) 17.32/16.99 ( (fun int (fun (fun int bool) bool)), resSet ) 17.32/16.99 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 17.32/16.99 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 17.32/16.99 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 17.32/16.99 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.32/16.99 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 17.32/16.99 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 17.32/16.99 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 17.32/16.99 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 17.32/16.99 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.32/16.99 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.32/16.99 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.32/16.99 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.32/16.99 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.32/16.99 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.32/16.99 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 17.32/16.99 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 17.32/16.99 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 17.32/16.99 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 17.32/16.99 ( (fun real nat), natfloor ) 17.32/16.99 ( (fun real nat), natceiling ) 17.32/16.99 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.32/16.99 ( (fun int (fun int (fun int bool))), wset ) 17.32/16.99 ( (fun int (fun int (fun int bool))), bnorRset ) 17.32/16.99 ( (fun int (fun int (fun int bool))), zcong ) 17.32/16.99 ( (fun int (fun int (fun int bool))), noXRRset ) 17.32/16.99 ( (fun int (fun int (fun int bool))), zcongm ) 17.32/16.99 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.32/16.99 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.32/16.99 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.32/16.99 ( (fun int real), (real_1 int) ) 17.32/16.99 ( (fun complex nat), (size_size complex) ) 17.32/16.99 ( (fun complex nat), complex_size ) 17.32/16.99 ( (fun int (list int)), quickc666637781d_zero ) 17.32/16.99 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.32/16.99 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.32/16.99 ( (fun (product_prod int int) rat), frct ) 17.32/16.99 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.32/16.99 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.32/16.99 ( (fun (fun nat rat) bool), vanishes ) 17.32/16.99 ( (fun int (fun int rat)), fract ) 17.32/16.99 ( (fun code_code_numeral int), code_int_of ) 17.32/16.99 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.32/16.99 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.32/16.99 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.32/16.99 ( (fun real (fun real complex)), complex_1 ) 17.32/16.99 ( (fun real (fun real complex)), rcis ) 17.32/16.99 ( (fun int (fun nat nat)), nat_aux ) 17.32/16.99 ( (fun rat real), ratreal ) 17.32/16.99 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.32/16.99 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.32/16.99 ( (fun rat (product_prod int int)), quotient_of ) 17.32/16.99 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.32/16.99 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.32/16.99 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.32/16.99 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.32/16.99 ) 17.32/16.99 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_121280 $$unsorted) (BOUND_VARIABLE_121281 $$unsorted) (BOUND_VARIABLE_121282 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_121282))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_121280) BOUND_VARIABLE_121281))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_121280) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_121282) BOUND_VARIABLE_121281)))) ))) 17.32/16.99 ( nat, (zero_zero nat), (one_one nat), (one_one nat) ) 17.32/16.99 ( int, (zero_zero int), (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 17.32/16.99 ( int, s, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 17.32/16.99 ( int, t, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 17.32/16.99 ( int, skv_3, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 17.32/16.99 ( int, skv_9, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 17.32/16.99 ) 17.32/16.99 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_121339 $$unsorted) (BOUND_VARIABLE_121340 $$unsorted)) (or (not (ord X_a)) (= (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_121339) (hAPP X_a _let_0 (ord_lessThan X_a) BOUND_VARIABLE_121340))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_121339) BOUND_VARIABLE_121340)))) )) 17.32/16.99 ( real, (zero_zero real), pi ) 17.32/16.99 ( 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)))) ) 17.32/16.99 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.99 ( real, (zero_zero real), skv_2 ) 17.32/16.99 ( real, (zero_zero real), skv_10 ) 17.32/16.99 ( real, (zero_zero real), skv_13 ) 17.32/16.99 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.99 ( real, pi, (zero_zero real) ) 17.32/16.99 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.99 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.99 ( 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) ) 17.32/16.99 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.32/16.99 ( 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 ) 17.32/16.99 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.32/16.99 ( int, (zero_zero int), (zero_zero int) ) 17.32/16.99 ( int, (zero_zero int), (one_one int) ) 17.32/16.99 ( 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))) ) 17.32/16.99 ( int, (zero_zero int), min_1 ) 17.32/16.99 ( int, min_1, (zero_zero int) ) 17.32/16.99 ( int, min_1, min_1 ) 17.32/16.99 ( 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))) ) 17.32/16.99 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.32/16.99 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.32/16.99 ( int, t, (zero_zero int) ) 17.32/16.99 ( int, t, (one_one int) ) 17.32/16.99 ( 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))) ) 17.32/16.99 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.32/16.99 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.32/16.99 ) 17.32/16.99 (instantiation (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))) (forall ((X_b $$unsorted) (X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (A_6 $$unsorted) (B_5 $$unsorted)) (or (not (= (hAPP X_b _let_0 (hAPP X_a _let_1 _let_2 A_1) B) (hAPP X_b _let_0 (hAPP X_a _let_1 _let_2 A_6) B_5))) (and (= (ti X_a A_6) (ti X_a A_1)) (= (ti X_b B_5) (ti X_b B)))) )))) 17.32/16.99 ( int, int, (zero_zero int), (one_one int), (zero_zero int), (one_one int) ) 17.32/16.99 ( int, int, (zero_zero int), (one_one int), (one_one int), (one_one int) ) 17.32/16.99 ( int, int, (one_one int), (one_one int), (zero_zero int), (one_one int) ) 17.32/16.99 ( int, int, (one_one int), (one_one int), s, (one_one int) ) 17.32/16.99 ( int, int, s, (one_one int), (zero_zero int), (one_one int) ) 17.32/16.99 ) 17.32/16.99 (instantiation (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_121400))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_121399 $$unsorted) (BOUND_VARIABLE_121400 $$unsorted) (BOUND_VARIABLE_121401 $$unsorted)) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_121401))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_121401) BOUND_VARIABLE_121399))) (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_121399))) )))) 17.32/16.99 ( 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 ) 17.32/16.99 ( 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) ) 17.32/16.99 ( 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)))) ) 17.32/16.99 ( 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)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.32/16.99 ( 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 ) 17.32/16.99 ( 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) ) 17.32/16.99 ( int, (zero_zero int), (zero_zero int), (zero_zero int) ) 17.32/16.99 ( int, (zero_zero int), min_1, min_1 ) 17.32/16.99 ( int, (one_one int), t, (zero_zero int) ) 17.32/16.99 ( 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) (hAPP nat int (hAPP 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)), (zero_zero int) ) 17.32/16.99 ( int, min_1, (zero_zero int), min_1 ) 17.32/16.99 ( int, min_1, min_1, (zero_zero int) ) 17.32/16.99 ) 17.32/16.99 (instantiation (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) Y))) (= Y (hAPP real real sqrt (hAPP nat real (hAPP real (fun nat real) (power_power real) Y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 17.32/16.99 ( pi ) 17.32/16.99 ( (hAPP int real (number_number_of real) min_1) ) 17.32/16.99 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.99 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.99 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.32/16.99 ( skv_6 ) 17.32/16.99 ( skv_11 ) 17.32/16.99 ( skv_12 ) 17.32/16.99 ( skv_14 ) 17.32/16.99 ) 17.32/16.99 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((N $$unsorted) (M $$unsorted)) (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)))) ))) 17.32/16.99 ( (zero_zero int), (zero_zero int) ) 17.32/16.99 ( (zero_zero int), min_1 ) 17.32/16.99 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.32/16.99 ( (zero_zero int), t ) 17.32/16.99 ( (one_one int), (zero_zero int) ) 17.32/16.99 ( (one_one int), t ) 17.32/16.99 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 17.32/16.99 ( (let ((_let_0 (fun int 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 (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_3 ) 17.32/16.99 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_9 ) 17.32/16.99 ( min_1, (zero_zero int) ) 17.32/16.99 ( min_1, min_1 ) 17.32/16.99 ( (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.50/17.00 ) 17.50/17.00 (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)) ) 17.50/17.00 ( (one_one real) ) 17.50/17.00 ) 17.50/17.00 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((N $$unsorted) (M $$unsorted)) (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)))) ))) 17.50/17.00 ( pls, min_1 ) 17.50/17.00 ( (one_one int), (zero_zero int) ) 17.50/17.00 ( min_1, (zero_zero int) ) 17.50/17.00 ( min_1, min_1 ) 17.50/17.00 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 17.50/17.00 ( s, (zero_zero int) ) 17.50/17.00 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 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17.50/17.00 ( real, nat ) 17.50/17.00 ( real, (fun int bool) ) 17.50/17.00 ( real, (fun real bool) ) 17.50/17.00 ( real, (fun real real) ) 17.50/17.00 ( real, complex ) 17.50/17.00 ( real, (fun nat real) ) 17.50/17.00 ( real, (fun bool bool) ) 17.50/17.00 ( real, (fun int (fun int bool)) ) 17.50/17.00 ( real, (fun (filter real) bool) ) 17.50/17.00 ( real, (fun (filter nat) bool) ) 17.50/17.00 ( real, (fun real complex) ) 17.50/17.00 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 17.50/17.00 ( real, (fun nat (product_prod real real)) ) 17.50/17.00 ( real, (fun real (fun nat (product_prod real real))) ) 17.50/17.00 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 17.50/17.00 ( real, (fun int (fun int (fun bool bool))) ) 17.50/17.00 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 17.50/17.00 ( real, (fun (fun int real) (fun int bool)) ) 17.50/17.00 ( real, (fun int (fun nat bool)) ) 17.50/17.00 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 17.50/17.00 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 17.50/17.00 ( real, (fun int (fun nat (fun bool bool))) ) 17.50/17.00 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 17.50/17.00 ( real, (fun (fun nat real) (fun nat bool)) ) 17.50/17.00 ( nat, bool ) 17.50/17.00 ( nat, real ) 17.50/17.00 ( nat, nat ) 17.50/17.00 ( nat, (fun nat bool) ) 17.50/17.00 ( nat, (fun nat nat) ) 17.50/17.00 ( nat, int ) 17.50/17.00 ( nat, (fun real real) ) 17.50/17.00 ( nat, complex ) 17.50/17.00 ( nat, (fun int int) ) 17.50/17.00 ( nat, rat ) 17.50/17.00 ( nat, (fun bool bool) ) 17.50/17.00 ( nat, (fun nat (fun nat bool)) ) 17.50/17.00 ( nat, (product_prod real real) ) 17.50/17.00 ( nat, (product_prod int int) ) 17.50/17.00 ( nat, (fun nat (product_prod int int)) ) 17.50/17.00 ( nat, (product_prod nat nat) ) 17.50/17.00 ( nat, (fun (product_prod nat nat) bool) ) 17.50/17.00 ( nat, (fun nat (fun (product_prod nat 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( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 17.50/17.00 ( int, (fun int (fun int bool)) ) 17.50/17.00 ( int, quickcheck_code_int ) 17.50/17.00 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 17.50/17.00 ( int, (product_prod int int) ) 17.50/17.00 ( int, (fun int (product_prod int int)) ) 17.50/17.00 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 17.50/17.00 ( int, (fun (fun int bool) bool) ) 17.50/17.00 ( int, (fun (product_prod int int) bool) ) 17.50/17.00 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 17.50/17.00 ( int, (product_prod int (product_prod int int)) ) 17.50/17.00 ( int, (fun int (product_prod int (product_prod int int))) ) 17.50/17.00 ( int, (fun (fun int int) (fun int bool)) ) 17.50/17.00 ( int, (fun int (fun (product_prod int int) bool)) ) 17.50/17.00 ( int, (fun int (fun (fun int bool) bool)) ) 17.50/17.00 ( int, (list int) ) 17.50/17.00 ( int, (fun nat (fun bool bool)) ) 17.50/17.00 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 17.50/17.00 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 17.50/17.00 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 17.50/17.00 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 17.50/17.00 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 17.50/17.00 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 17.50/17.00 ( int, (fun (product_prod int int) int) ) 17.50/17.00 ( int, (fun int (fun int (fun int bool))) ) 17.50/17.00 ( int, (fun int real) ) 17.50/17.00 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 17.50/17.00 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 17.50/17.00 ( (fun int bool), bool ) 17.50/17.00 ( (fun int bool), int ) 17.50/17.00 ( (fun int bool), (fun int bool) ) 17.50/17.00 ( (fun int bool), (fun int (fun bool bool)) ) 17.50/17.00 ( (fun int bool), (fun int (fun int bool)) ) 17.50/17.00 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 17.50/17.00 ( (fun int bool), (fun int (fun int int)) ) 17.50/17.00 ( (fun int bool), (fun real (fun int (fun int bool))) ) 17.50/17.00 ( (fun real bool), real ) 17.50/17.00 ( (fun real bool), (fun real bool) ) 17.50/17.00 ( (fun real bool), (fun real (fun bool bool)) ) 17.50/17.00 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 17.50/17.00 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 17.50/17.00 ( (fun real real), (fun real real) ) 17.50/17.00 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 17.50/17.00 ( (fun real real), (fun real (fun real real)) ) 17.50/17.00 ( (fun real real), (fun real (fun real bool)) ) 17.50/17.00 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 17.50/17.00 ( complex, real ) 17.50/17.00 ( complex, nat ) 17.50/17.00 ( complex, complex ) 17.50/17.00 ( (fun nat real), (fun nat bool) ) 17.50/17.00 ( (fun nat real), (fun nat real) ) 17.50/17.00 ( (fun nat real), (fun nat (fun real real)) ) 17.50/17.00 ( (fun nat real), (fun int (fun nat real)) ) 17.50/17.00 ( (fun int int), (fun int bool) ) 17.50/17.00 ( (fun int int), (fun int int) ) 17.50/17.00 ( (fun int int), (fun int (fun int bool)) ) 17.50/17.00 ( (fun int int), (fun int (fun int int)) ) 17.50/17.00 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 17.50/17.00 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 17.50/17.00 ( rat, real ) 17.50/17.00 ( rat, (product_prod int int) ) 17.50/17.00 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 17.50/17.00 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 17.50/17.00 ( (fun int (fun int bool)), (fun int bool) ) 17.50/17.00 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 17.50/17.00 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 17.50/17.00 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 17.50/17.00 ( quickcheck_code_int, nat ) 17.50/17.00 ( quickcheck_code_int, int ) 17.50/17.00 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 17.50/17.00 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 17.50/17.00 ( (product_prod real real), bool ) 17.50/17.00 ( (product_prod int int), bool ) 17.50/17.00 ( (product_prod int int), int ) 17.50/17.00 ( (product_prod int int), (fun int bool) ) 17.50/17.00 ( (product_prod int int), (fun int int) ) 17.50/17.00 ( (product_prod int int), rat ) 17.50/17.00 ( (product_prod int int), (fun bool bool) ) 17.50/17.00 ( (product_prod int int), (product_prod int int) ) 17.50/17.00 ( (product_prod int int), (fun (product_prod int int) bool) ) 17.50/17.00 ( (product_prod int int), (fun (product_prod int int) int) ) 17.50/17.00 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 17.50/17.00 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 17.50/17.00 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 17.50/17.00 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 17.51/17.00 ( (filter real), bool ) 17.51/17.00 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 17.51/17.00 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 17.51/17.00 ( (filter nat), bool ) 17.51/17.00 ( (product_prod nat nat), bool ) 17.51/17.00 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 17.51/17.00 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 17.51/17.00 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 17.51/17.00 ( code_code_numeral, nat ) 17.51/17.00 ( code_code_numeral, (fun nat nat) ) 17.51/17.00 ( code_code_numeral, int ) 17.51/17.00 ( code_code_numeral, code_code_numeral ) 17.51/17.00 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 17.51/17.00 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 17.51/17.00 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 17.51/17.00 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 17.51/17.00 ( (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))) ) 17.51/17.00 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 17.51/17.00 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 17.51/17.00 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 17.51/17.00 ( (fun nat rat), bool ) 17.51/17.00 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 17.51/17.00 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 17.51/17.00 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 17.51/17.00 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 17.51/17.00 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 17.51/17.00 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 17.51/17.00 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 17.51/17.00 ( (fun int real), (fun int bool) ) 17.51/17.00 ( (fun int real), (fun int real) ) 17.51/17.00 ( (fun int real), (fun int (fun int real)) ) 17.51/17.00 ( (fun int real), (fun int (fun real real)) ) 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17.51/17.00 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 17.51/17.00 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 17.51/17.00 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 17.51/17.00 ( (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))) ) 17.51/17.00 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 17.51/17.00 ( (fun (product_prod int int) (fun int int)), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))) ) 17.51/17.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 17.51/17.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))) ) 17.51/17.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))) ) 17.51/17.00 ( (fun int (fun nat bool)), (fun int bool) ) 17.51/17.00 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 17.51/17.00 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 17.51/17.00 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 17.51/17.00 ( (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 17.51/17.00 ( (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))) ) 17.51/17.00 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 17.51/17.00 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 17.51/17.00 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 17.51/17.00 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 17.51/17.00 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 17.51/17.00 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 17.51/17.00 ) 17.51/17.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121543 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_121543)) (= (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_121543)) BOUND_VARIABLE_121543))) ) 17.51/17.00 ( bool, fFalse ) 17.51/17.00 ( bool, fTrue ) 17.51/17.00 ( real, (zero_zero real) ) 17.51/17.00 ( real, pi ) 17.51/17.00 ( (fun nat bool), (even_odd_even nat) ) 17.51/17.00 ( (fun nat bool), prime ) 17.51/17.00 ( (fun nat nat), suc ) 17.51/17.00 ( (fun nat nat), (fact_fact nat) ) 17.51/17.00 ( (fun nat nat), (size_size nat) ) 17.51/17.00 ( (fun nat nat), fact ) 17.51/17.00 ( (fun nat nat), nat_size ) 17.51/17.00 ( int, pls ) 17.51/17.00 ( int, m ) 17.51/17.00 ( int, min_1 ) 17.51/17.00 ( int, s ) 17.51/17.00 ( int, s1 ) 17.51/17.00 ( int, t ) 17.51/17.00 ( (fun int bool), zprime ) 17.51/17.00 ( (fun int bool), nat_neg ) 17.51/17.00 ( (fun int bool), zEven ) 17.51/17.00 ( (fun int bool), nat_is_nat ) 17.51/17.00 ( (fun int bool), zOdd ) 17.51/17.00 ( (fun int bool), (even_odd_even int) ) 17.51/17.00 ( (fun int bool), twoSqu1091635170sum2sq ) 17.51/17.00 ( (fun int nat), nat_1 ) 17.51/17.00 ( (fun int nat), phi ) 17.51/17.00 ( (fun real real), sqrt ) 17.51/17.00 ( (fun real real), tan ) 17.51/17.00 ( (fun real real), cos ) 17.51/17.00 ( (fun real real), arccos ) 17.51/17.00 ( (fun real real), ln ) 17.51/17.00 ( (fun real real), sin ) 17.51/17.00 ( (fun real real), arctan ) 17.51/17.00 ( (fun real real), arcsin ) 17.51/17.00 ( complex, ii ) 17.51/17.00 ( (fun complex complex), cnj ) 17.51/17.00 ( (fun complex complex), expi ) 17.51/17.00 ( (fun nat real), (real_1 nat) ) 17.51/17.00 ( (fun nat real), cos_coeff ) 17.51/17.00 ( (fun nat real), sin_coeff ) 17.51/17.00 ( (fun int int), bit0 ) 17.51/17.00 ( (fun int int), bit1 ) 17.51/17.00 ( (fun int int), pred ) 17.51/17.00 ( (fun int int), succ ) 17.51/17.00 ( (fun int int), (fact_fact int) ) 17.51/17.00 ( (fun int int), zfact ) 17.51/17.00 ( (fun bool bool), fNot ) 17.51/17.00 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.51/17.00 ( (fun bool (fun bool bool)), fconj ) 17.51/17.00 ( (fun bool (fun bool bool)), fdisj ) 17.51/17.00 ( (fun bool (fun bool bool)), fimplies ) 17.51/17.00 ( (fun int (fun int bool)), sRStar ) 17.51/17.00 ( (fun int (fun int bool)), quadRes ) 17.51/17.00 ( (fun int (fun int bool)), norRRset ) 17.51/17.00 ( (fun int (fun int bool)), d22set ) 17.51/17.00 ( (fun int (fun int bool)), sr ) 17.51/17.00 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 17.51/17.00 ( (fun nat (fun nat nat)), nat_gcd ) 17.51/17.00 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 17.51/17.01 ( (fun nat (fun nat nat)), nat_lcm ) 17.51/17.01 ( (fun nat (fun real real)), root ) 17.51/17.01 ( (fun real (fun real real)), log ) 17.51/17.01 ( (fun real (fun real real)), powr ) 17.51/17.01 ( (fun nat (fun nat bool)), coprime ) 17.51/17.01 ( (fun (fun int bool) int), (the int) ) 17.51/17.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 17.51/17.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 17.51/17.01 ( (fun nat (fun nat (product_prod int int))), bezw ) 17.51/17.01 ( (fun (fun int bool) bool), nat_nat_set ) 17.51/17.01 ( (filter nat), sequentially ) 17.51/17.01 ( (fun (product_prod nat nat) bool), pred_nat ) 17.51/17.01 ( (fun (product_prod int int) bool), frac_1 ) 17.51/17.01 ( (fun real complex), cis ) 17.51/17.01 ( (fun complex real), im ) 17.51/17.01 ( (fun complex real), re ) 17.51/17.01 ( (fun complex real), arg ) 17.51/17.01 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 17.51/17.01 ( (fun int (fun int int)), int_gcd ) 17.51/17.01 ( (fun int (fun int int)), multInv ) 17.51/17.01 ( (fun int (fun int int)), legacy_zgcd ) 17.51/17.01 ( (fun int (fun int int)), z3mod ) 17.51/17.01 ( (fun int (fun int int)), inv ) 17.51/17.01 ( (fun int (fun int int)), (gcd_gcd int) ) 17.51/17.01 ( (fun int (fun int int)), standardRes ) 17.51/17.01 ( (fun int (fun int int)), legendre ) 17.51/17.01 ( (fun int (fun int int)), nat_tsub ) 17.51/17.01 ( (fun int (fun int int)), z3div ) 17.51/17.01 ( (fun int (fun int int)), int_lcm ) 17.51/17.01 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 17.51/17.01 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 17.51/17.01 ( (fun int (fun (fun int bool) bool)), rsetR ) 17.51/17.01 ( (fun int (fun (fun int bool) bool)), resSet ) 17.51/17.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 17.51/17.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 17.51/17.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 17.51/17.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.51/17.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 17.51/17.01 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 17.51/17.01 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 17.51/17.01 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 17.51/17.01 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.51/17.01 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.51/17.01 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.51/17.01 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.51/17.01 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.51/17.01 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.51/17.01 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 17.51/17.01 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 17.51/17.01 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 17.51/17.01 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 17.51/17.01 ( (fun real nat), natfloor ) 17.51/17.01 ( (fun real nat), natceiling ) 17.51/17.01 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.51/17.01 ( (fun int (fun int (fun int bool))), wset ) 17.51/17.01 ( (fun int (fun int (fun int bool))), bnorRset ) 17.51/17.01 ( (fun int (fun int (fun int bool))), zcong ) 17.51/17.01 ( (fun int (fun int (fun int bool))), noXRRset ) 17.51/17.01 ( (fun int (fun int (fun int bool))), zcongm ) 17.51/17.01 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.51/17.01 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.51/17.01 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.51/17.01 ( (fun int real), (real_1 int) ) 17.51/17.01 ( (fun complex nat), (size_size complex) ) 17.51/17.01 ( (fun complex nat), complex_size ) 17.51/17.01 ( (fun int (list int)), quickc666637781d_zero ) 17.51/17.01 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.51/17.01 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.51/17.01 ( (fun (product_prod int int) rat), frct ) 17.51/17.01 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.51/17.01 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.51/17.01 ( (fun (fun nat rat) bool), vanishes ) 17.51/17.01 ( (fun int (fun int rat)), fract ) 17.51/17.01 ( (fun code_code_numeral int), code_int_of ) 17.51/17.01 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.51/17.01 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.51/17.01 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.51/17.01 ( (fun real (fun real complex)), complex_1 ) 17.51/17.01 ( (fun real (fun real complex)), rcis ) 17.51/17.01 ( (fun int (fun nat nat)), nat_aux ) 17.51/17.01 ( (fun rat real), ratreal ) 17.51/17.01 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.51/17.01 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.51/17.01 ( (fun rat (product_prod int int)), quotient_of ) 17.51/17.01 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.51/17.01 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.51/17.01 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.51/17.01 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.51/17.01 ) 17.51/17.01 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_121568 $$unsorted) (BOUND_VARIABLE_121569 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_121569))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) _let_1) BOUND_VARIABLE_121568))) (hBOOL (hAPP X_a bool _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_121569) BOUND_VARIABLE_121568)))) )))) 17.51/17.01 ( nat, (one_one nat), (one_one nat) ) 17.51/17.01 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 17.51/17.01 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.01 ) 17.51/17.01 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (one_one real))) (let ((_let_3 (combc nat nat nat))) (let ((_let_4 (fun nat _let_0))) (let ((_let_5 (fun _let_1 _let_1))) (let ((_let_6 (fun (fun nat nat) _let_1))) (let ((_let_7 (combb nat real nat))) (let ((_let_8 (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) _let_3 (hAPP (fun nat nat) (fun nat (fun nat nat)) (hAPP (fun nat (fun nat nat)) (fun (fun nat nat) (fun nat (fun nat nat))) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) _let_3 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) X_1)) _let_2))) (hBOOL (hAPP _let_1 bool (monoseq real) (hAPP _let_1 _let_1 (hAPP _let_4 _let_5 (combs nat real real) (hAPP _let_1 _let_4 (hAPP (fun real _let_0) (fun _let_1 _let_4) (combb real _let_0 nat) (times_times real)) (hAPP _let_1 _let_1 (hAPP _let_0 _let_5 (combb real real nat) (hAPP real _let_0 (inverse_divide real) _let_2)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_6 _let_7 (real_1 nat)) _let_8)))) (hAPP _let_0 _let_1 (hAPP _let_1 _let_6 _let_7 (hAPP real _let_1 (power_power real) X_1)) _let_8)))))) )))))))))) 17.51/17.01 ( (hAPP int real (number_number_of real) min_1) ) 17.51/17.01 ( (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)))) ) 17.51/17.01 ) 17.51/17.01 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (zero_zero nat))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (P_1 $$unsorted)) (or (not (forall ((M_2 $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat _let_0 P_1 M_2) _let_1)) )) (not (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) _let_1) N_2))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 P_1 N_2) (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) M_2) N_2)))) (hBOOL (hAPP nat bool (hAPP nat _let_0 P_1 M_2) N_2))) )) (hBOOL (hAPP nat bool (hAPP nat _let_0 P_1 Ma) N_1))) ))) 17.51/17.01 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (ord_less nat) ) 17.51/17.01 ) 17.51/17.01 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (real_1 nat))) (forall ((N $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP nat real _let_1 N)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X) (hAPP nat real _let_1 (hAPP nat nat suc N))))) (= N (hAPP int nat nat_1 (hAPP real int (archim2085082626_floor real) X)))) ))) 17.51/17.01 ( (zero_zero nat), pi ) 17.51/17.01 ( (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)))) ) 17.51/17.01 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.01 ( (zero_zero nat), skv_6 ) 17.51/17.01 ( (zero_zero nat), skv_11 ) 17.51/17.01 ( (zero_zero nat), skv_12 ) 17.51/17.01 ( (zero_zero nat), skv_14 ) 17.51/17.01 ) 17.51/17.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121644 $$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_121644))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_121644)))) ) 17.51/17.01 ( real, pi ) 17.51/17.01 ( 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)))) ) 17.51/17.01 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.01 ( real, skv_2 ) 17.51/17.01 ( real, skv_10 ) 17.51/17.01 ( real, skv_13 ) 17.51/17.01 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.01 ( int, (zero_zero int) ) 17.51/17.01 ( int, (one_one int) ) 17.51/17.01 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.51/17.01 ( int, min_1 ) 17.51/17.01 ) 17.51/17.01 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (inverse_divide real))) (let ((_let_3 (ord_less real))) (let ((_let_4 (hAPP real real (hAPP real _let_1 _let_2 pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (let ((_let_5 (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) X))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_3 (hAPP real real (uminus_uminus real) _let_4)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_3 X) _let_4))) (= (hAPP real real (hAPP real _let_1 _let_2 (hAPP real real sin _let_5)) (hAPP real real (hAPP real _let_1 (plus_plus real) (hAPP real real cos _let_5)) (one_one real))) (hAPP real real tan X))) ))))))) 17.51/17.01 ( (zero_zero real) ) 17.51/17.01 ( (one_one real) ) 17.51/17.01 ( pi ) 17.51/17.01 ( (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)))) ) 17.51/17.01 ( (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.51/17.01 ( (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))))) ) 17.51/17.01 ( (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))))) ) 17.51/17.01 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.01 ( (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))))) ) 17.51/17.01 ( (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)))) ) 17.51/17.01 ( (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)) ) 17.51/17.01 ) 17.51/17.01 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (member int))) (let ((_let_4 (ti int Ta))) (let ((_let_5 (ti int BOUND_VARIABLE_121746))) (forall ((Ta $$unsorted) (A_3 $$unsorted) (D_2 $$unsorted) (BOUND_VARIABLE_121746 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) D_2))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_3 Ta) A_3))) (not (forall ((Xa $$unsorted) (BOUND_VARIABLE_121711 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_3 Xa) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastAtMost int) (one_one int)) D_2)))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_3 BOUND_VARIABLE_121711) A_3))) (not (= (hAPP int int (hAPP int _let_1 (minus_minus int) BOUND_VARIABLE_121711) Xa) _let_5))) )) (= _let_4 _let_5) (not (= _let_4 (hAPP int int (hAPP int _let_1 (plus_plus int) BOUND_VARIABLE_121746) D_2)))) ))))))) 17.51/17.01 ( (one_one int), zEven, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), min_1 ) 17.51/17.01 ) 17.51/17.01 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (let ((_let_3 (fun (filter nat) bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_121796 $$unsorted) (BOUND_VARIABLE_121797 $$unsorted)) (or (not (metric_space X_a)) (= (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (zero_zero real)) R_2))) (not (forall ((No $$unsorted)) (or (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) No) N_2))) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) (hAPP nat X_a BOUND_VARIABLE_121796 N_2)) BOUND_VARIABLE_121797)) R_2))) )) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) (zero_zero nat)) No)))) ))) ) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_3 (hAPP (fun nat X_a) (fun X_a _let_3) (tendsto nat X_a) BOUND_VARIABLE_121796) BOUND_VARIABLE_121797) sequentially)))) ))))) 17.51/17.01 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 17.51/17.01 ) 17.51/17.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121823 $$unsorted) (BOUND_VARIABLE_121824 $$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_121823)) BOUND_VARIABLE_121824)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_121823) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_121824))))) ) 17.51/17.01 ( real, pi, (zero_zero int) ) 17.51/17.01 ( 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 int) ) 17.51/17.01 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 17.51/17.01 ) 17.51/17.01 (instantiation (let ((_let_0 (hAPP nat real (real_1 nat) A_1))) (forall ((A_1 $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) _let_0) X))) (= (hAPP real nat natfloor (hAPP real real (hAPP real (fun real real) (minus_minus real) X) _let_0)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP real nat natfloor X)) A_1))) )) 17.51/17.02 ( (zero_zero nat), pi ) 17.51/17.02 ( (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)))) ) 17.51/17.02 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.02 ( (zero_zero nat), skv_6 ) 17.51/17.02 ( (zero_zero nat), skv_11 ) 17.51/17.02 ( (zero_zero nat), skv_12 ) 17.51/17.02 ( (zero_zero nat), skv_14 ) 17.51/17.02 ) 17.51/17.02 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (zero_zero nat))) (let ((_let_3 (hAPP nat _let_1 root N_1))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_2) N_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) _let_3) X_1) (hAPP real real (inverse_inverse real) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP nat real (real_1 nat) N_1)) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real _let_3 X_1)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N_1) (hAPP nat nat suc _let_2)))))))) ))))) 17.51/17.02 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.02 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.02 ( (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))) ) 17.51/17.02 ( (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))) ) 17.51/17.02 ) 17.51/17.02 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (forall ((J $$unsorted) (I $$unsorted) (P_1 $$unsorted) (P_4 $$unsorted)) (or (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 I_2) P_4))) (not (hBOOL (hAPP nat bool P_1 I_2))) (hBOOL (hAPP nat bool P_1 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) (hAPP nat nat suc I_2)) P_4)))) )) (not (hBOOL (hAPP nat bool P_1 I))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 I) P_4))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 J) P_4))) (hBOOL (hAPP nat bool P_1 J))) ))) 17.51/17.02 ( (zero_zero nat), (zero_zero nat), (even_odd_even nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.02 ) 17.51/17.02 (instantiation (let ((_let_0 (archimedean_ceiling X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_121909 $$unsorted) (BOUND_VARIABLE_121910 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP X_a int _let_0 BOUND_VARIABLE_121909)) (hAPP int int (number_number_of int) BOUND_VARIABLE_121910)) (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_121909) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_121910))))) )) 17.51/17.02 ( nat, (one_one nat), (hAPP int int bit1 pls) ) 17.51/17.02 ( 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 bit0 (hAPP int int bit1 pls))))) m), (hAPP int int bit1 pls) ) 17.51/17.02 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int bit1 pls) ) 17.51/17.02 ) 17.51/17.02 (instantiation (let ((_let_0 (inverse_inverse real))) (let ((_let_1 (hAPP nat (fun real real) root N))) (forall ((X $$unsorted) (N $$unsorted)) (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)))) ))) 17.51/17.02 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.02 ) 17.51/17.02 (instantiation (let ((_let_0 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_121982 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP X_a X_a (uminus_uminus X_a) (one_one X_a))) (hAPP int X_a _let_0 BOUND_VARIABLE_121982)) (hAPP int X_a _let_0 (hAPP int int pred BOUND_VARIABLE_121982)))) )) 17.51/17.02 ( real, pls ) 17.51/17.02 ( int, pls ) 17.51/17.02 ( complex, pls ) 17.51/17.02 ) 17.51/17.02 (instantiation (let ((_let_0 (fun nat nat))) (forall ((Z_1 $$unsorted)) (= (hAPP nat nat (hAPP nat _let_0 (times_times nat) Z_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) Z_1) Z_1)) )) 17.51/17.02 ( (one_one nat) ) 17.51/17.02 ) 17.51/17.02 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (collect X_a))) (forall ((X_a $$unsorted) (P_1 $$unsorted)) (= (hAPP _let_0 _let_0 _let_1 (hAPP _let_0 _let_0 (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool X_a) fNot) P_1)) (hAPP _let_0 _let_0 (uminus_uminus _let_0) (hAPP _let_0 _let_0 _let_1 P_1))) ))) 17.51/17.02 ( nat, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat))) ) 17.51/17.02 ( int, (let ((_let_0 (fun int (fun int bool)))) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))) ) 17.51/17.02 ( (product_prod int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 int))) (let ((_let_4 (fun _let_1 _let_0))) (hAPP int _let_2 (hAPP _let_4 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_3 _let_4 (hAPP (fun int _let_0) (fun _let_3 _let_4) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))) ) 17.51/17.02 ) 17.51/17.02 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_122070 $$unsorted) (BOUND_VARIABLE_122071 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_122071) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122070) _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_122071) BOUND_VARIABLE_122070)) _let_2))) )))) 17.51/17.02 ( nat, (one_one nat), (one_one nat) ) 17.51/17.02 ( 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 bit0 (hAPP int int bit1 pls))))) m) ) 17.51/17.02 ( 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)))) ) 17.51/17.02 ) 17.51/17.02 (instantiation (let ((_let_0 (semiring_1_of_nat int))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= (hAPP nat int _let_0 Y_1) (hAPP nat int _let_0 X_1)) (= X_1 Y_1)) )) 17.51/17.02 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 17.51/17.02 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 17.51/17.02 ( (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)) ) 17.51/17.02 ( (hAPP nat nat suc (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.51/17.02 ( (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))) ) 17.51/17.02 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero nat) ) 17.51/17.02 ) 17.51/17.02 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (forall ((Z_4 $$unsorted) (Z_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_0 Z_1))) (not (hBOOL (hAPP int bool _let_0 Z_4))) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat nat_1 Z_1)) (hAPP int nat nat_1 Z_4)) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) Z_1) Z_4)))) )) 17.51/17.02 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 17.51/17.02 ( (one_one int), (one_one int) ) 17.51/17.02 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.02 ) 17.51/17.02 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) X))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) (hAPP real real ln X)))) ))) 17.51/17.02 ( (one_one real) ) 17.51/17.02 ) 17.51/17.02 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_122307 $$unsorted) (BOUND_VARIABLE_122308 $$unsorted)) (or (not (preorder X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_122307) BOUND_VARIABLE_122308)) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122307) BOUND_VARIABLE_122308)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122308) BOUND_VARIABLE_122307)))))) ))) 17.51/17.02 ( real, (zero_zero real), pi ) 17.51/17.02 ( 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)))) ) 17.51/17.02 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.02 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.02 ( real, (zero_zero real), skv_2 ) 17.51/17.02 ( real, (zero_zero real), skv_6 ) 17.51/17.02 ( real, (zero_zero real), skv_10 ) 17.51/17.02 ( real, (zero_zero real), skv_11 ) 17.51/17.02 ( real, (zero_zero real), skv_12 ) 17.51/17.02 ( real, (zero_zero real), skv_13 ) 17.51/17.02 ( real, (zero_zero real), skv_14 ) 17.51/17.02 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.02 ( real, pi, (zero_zero real) ) 17.51/17.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.51/17.02 ( 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)))) ) 17.51/17.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 17.51/17.02 ( 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) ) 17.51/17.02 ( 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))) ) 17.51/17.02 ( 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) ) 17.51/17.02 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.51/17.02 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.51/17.02 ( 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 ) 17.51/17.02 ( real, skv_6, (zero_zero real) ) 17.51/17.02 ( real, skv_11, (zero_zero real) ) 17.51/17.02 ( real, skv_12, (zero_zero real) ) 17.51/17.02 ( real, skv_14, (zero_zero real) ) 17.51/17.02 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.02 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.02 ( int, (zero_zero int), (zero_zero int) ) 17.51/17.02 ( int, (zero_zero int), (one_one int) ) 17.51/17.02 ( 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))) ) 17.51/17.02 ( int, (zero_zero int), min_1 ) 17.51/17.02 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.02 ( int, (zero_zero int), s ) 17.51/17.02 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 17.51/17.02 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.51/17.02 ( int, (zero_zero int), skv_3 ) 17.51/17.02 ( int, (zero_zero int), skv_9 ) 17.51/17.02 ( int, pls, min_1 ) 17.51/17.02 ( int, (one_one int), (zero_zero int) ) 17.51/17.02 ( int, (one_one int), t ) 17.51/17.02 ( int, min_1, (zero_zero int) ) 17.51/17.02 ( int, min_1, pls ) 17.51/17.02 ( int, min_1, min_1 ) 17.51/17.02 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 17.51/17.02 ( int, s, (zero_zero int) ) 17.51/17.02 ( 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))) ) 17.51/17.02 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.51/17.02 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.51/17.02 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 17.51/17.02 ( int, t, (zero_zero int) ) 17.51/17.02 ( int, t, (one_one int) ) 17.51/17.02 ( 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))) ) 17.51/17.02 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 17.51/17.02 ( int, skv_3, (zero_zero int) ) 17.51/17.02 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.51/17.02 ( int, skv_9, (zero_zero int) ) 17.51/17.02 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.51/17.02 ) 17.51/17.02 (instantiation (let ((_let_0 (ti X_a BOUND_VARIABLE_122337))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_122336 $$unsorted) (BOUND_VARIABLE_122337 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) _let_0) (= (= _let_0 (ti X_a BOUND_VARIABLE_122336)) (= (one_one X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_122336) BOUND_VARIABLE_122337)))) )) 17.51/17.02 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.02 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 17.51/17.02 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.02 ( 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))))))))) ) 17.51/17.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 17.51/17.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.51/17.02 ( 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))) ) 17.51/17.02 ( 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))) ) 17.51/17.03 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.03 ) 17.51/17.03 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP nat _let_0 (gcd_gcd nat) M))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP nat nat _let_1 N) (hAPP nat nat _let_1 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) M) N))) ))) 17.51/17.03 ( (one_one nat), (one_one nat) ) 17.51/17.03 ) 17.51/17.03 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (times_times real))) (let ((_let_3 (norm_norm X_a))) (forall ((X_a $$unsorted)) (or (not (real_normed_vector X_a)) (not (forall ((K_2 $$unsorted)) (or (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP X_a real _let_3 (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) A_4) B_4))) (hAPP real real (hAPP real _let_1 _let_2 (hAPP real real (hAPP real _let_1 _let_2 (hAPP real real (norm_norm real) A_4)) (hAPP X_a real _let_3 B_4))) K_2))) )) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) K_2)))) ))) ))))) 17.51/17.03 ( real ) 17.51/17.03 ( complex ) 17.51/17.03 ) 17.51/17.03 (instantiation (let ((_let_0 (fun real real))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP real real (hAPP real _let_0 (dist_dist real) X) Y) (hAPP real real (abs_abs real) (hAPP real real (hAPP real _let_0 (minus_minus real) X) Y))) )) 17.51/17.03 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 17.51/17.03 ) 17.51/17.03 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (forall ((X $$unsorted)) (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))))))) )) 17.51/17.03 ( (zero_zero real) ) 17.51/17.03 ( (one_one real) ) 17.51/17.03 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.03 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.51/17.03 ) 17.51/17.03 (instantiation (let ((_let_0 (hAPP nat nat suc (zero_zero nat)))) (forall ((V_3 $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V_3)))) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) _let_0) (hAPP int nat (number_number_of nat) V_3)))) )) 17.51/17.03 ( pls ) 17.51/17.03 ( (hAPP int int bit1 pls) ) 17.51/17.03 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.51/17.03 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.03 ( min_1 ) 17.51/17.03 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.51/17.03 ) 17.51/17.03 (instantiation (let ((_let_0 (hAPP int int (number_number_of int) V_3))) (forall ((V_3 $$unsorted)) (or (hBOOL (hAPP int bool nat_neg _let_0)) (= (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) (hAPP nat nat suc (zero_zero nat))) (hAPP int nat (number_number_of nat) V_3)) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (div_mod int) (one_one int)) _let_0)))) )) 17.51/17.03 ( pls ) 17.51/17.03 ( (hAPP int int bit1 pls) ) 17.51/17.03 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.51/17.03 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.03 ( min_1 ) 17.51/17.03 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.51/17.03 ) 17.51/17.03 (instantiation (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_122419))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_122418 $$unsorted) (BOUND_VARIABLE_122419 $$unsorted)) (or (not (real_normed_vector X_b)) (not (topological_space X_a)) (= (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_122418) (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_122418)) (zero_zero real)) _let_4)))) )))))) 17.51/17.03 ( 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)))) ) 17.51/17.03 ) 17.51/17.03 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (hAPP real real (hAPP real _let_0 _let_1 Z_1) W) (hAPP real real (hAPP real _let_0 _let_1 W) Z_1)) ))) 17.51/17.03 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.03 ( 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))))) ) 17.51/17.03 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.51/17.03 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.51/17.03 ( (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)))))) ) 17.51/17.03 ( (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.03 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 17.51/17.03 ( (hAPP real real arctan (hAPP real real (hAPP 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)))) ) 17.51/17.03 ) 17.51/17.03 (instantiation (forall ((N_1 $$unsorted)) (= (= (zero_zero nat) N_1) (= (zero_zero real) (hAPP nat real (real_1 nat) N_1))) ) 17.51/17.03 ( (zero_zero nat) ) 17.51/17.03 ( (one_one nat) ) 17.51/17.03 ) 17.51/17.03 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_122442 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_122442)) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122442) _let_2)))) )))) 17.51/17.03 ( real, (zero_zero real) ) 17.51/17.03 ( complex, ii ) 17.51/17.03 ) 17.51/17.03 (instantiation (forall ((X $$unsorted) (N $$unsorted)) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) N))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X))) (= (hAPP real nat natfloor (hAPP real real (hAPP real (fun real real) (plus_plus real) X) (hAPP int real (number_number_of real) N))) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natfloor X)) (hAPP int nat (number_number_of nat) N)))) ) 17.51/17.03 ( (one_one real), (hAPP int int bit1 pls) ) 17.51/17.03 ) 17.51/17.03 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_122487 $$unsorted) (BOUND_VARIABLE_122488 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_122488))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_122487))) (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_122488) BOUND_VARIABLE_122487)))) )) 17.51/17.03 ( nat, (one_one nat), (one_one nat) ) 17.51/17.03 ( 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) ) 17.51/17.03 ( 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)))) ) 17.51/17.03 ) 17.51/17.03 (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)))) ) 17.51/17.03 ( pi, (zero_zero nat) ) 17.51/17.03 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP 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) ) 17.51/17.03 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero nat) ) 17.51/17.03 ) 17.51/17.03 (instantiation (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_122515))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_122515 $$unsorted) (BOUND_VARIABLE_122516 $$unsorted)) (or (not (monoid_mult X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_122516)) BOUND_VARIABLE_122515) (hAPP nat X_a _let_0 (hAPP nat nat suc BOUND_VARIABLE_122516)))) )) 17.51/17.03 ( int, s, (hAPP nat nat suc (zero_zero nat)) ) 17.51/17.03 ( int, s1, (hAPP nat nat suc (zero_zero nat)) ) 17.51/17.03 ( int, skv_8, (hAPP nat nat suc (zero_zero nat)) ) 17.51/17.03 ( complex, ii, (hAPP nat nat suc (zero_zero nat)) ) 17.51/17.03 ) 17.51/17.03 (instantiation (let ((_let_0 (big_co1399186613setsum X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (or (not (comm_monoid_add X_b)) (= _let_0 (ti (fun (fun X_a X_b) (fun (fun X_a bool) X_b)) _let_0))) )) 17.51/17.03 ( bool, (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 17.51/17.03 ( real, real ) 17.51/17.03 ( real, (fun real bool) ) 17.51/17.03 ( real, (fun real (fun bool bool)) ) 17.51/17.03 ( real, (fun (fun int real) (fun int bool)) ) 17.51/17.03 ( real, (fun (fun nat real) (fun nat bool)) ) 17.51/17.03 ( nat, bool ) 17.51/17.03 ( nat, (fun nat bool) ) 17.51/17.03 ( nat, (fun nat (fun bool bool)) ) 17.51/17.03 ( nat, (fun int (fun nat bool)) ) 17.51/17.03 ( nat, (fun real (fun int (fun nat bool))) ) 17.51/17.03 ( int, bool ) 17.51/17.03 ( int, int ) 17.51/17.03 ( int, (fun int bool) ) 17.51/17.03 ( int, (fun int (fun bool bool)) ) 17.51/17.03 ( int, (fun int (fun int bool)) ) 17.51/17.03 ( int, (fun (fun int int) (fun int bool)) ) 17.51/17.03 ( int, (fun int (fun int int)) ) 17.51/17.03 ( int, (fun real (fun int (fun int bool))) ) 17.51/17.03 ( (product_prod real real), (fun real (fun real (fun nat (product_prod real real)))) ) 17.51/17.03 ( (product_prod int int), (fun (product_prod int int) bool) ) 17.51/17.03 ( (product_prod int int), (fun (product_prod int int) (fun bool bool)) ) 17.51/17.03 ) 17.51/17.03 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_122540) BOUND_VARIABLE_122541))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_122540 $$unsorted) (BOUND_VARIABLE_122541 $$unsorted)) (or (not (monoid_mult X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_122540) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122540) _let_2))) )))) 17.51/17.03 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.03 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.03 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.03 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.03 ) 17.51/17.03 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (plus_plus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_122559 $$unsorted) (BOUND_VARIABLE_122560 $$unsorted) (BOUND_VARIABLE_122561 $$unsorted)) (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_122559) BOUND_VARIABLE_122560)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122561) BOUND_VARIABLE_122560)) (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_122559) BOUND_VARIABLE_122561)) BOUND_VARIABLE_122560))) )))) 17.51/17.03 ( 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 bit0 (hAPP int int bit1 pls))))) m), (zero_zero int), (one_one int) ) 17.51/17.03 ( 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 bit0 (hAPP int int bit1 pls))))) m), t, (one_one int) ) 17.51/17.03 ( 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 bit0 (hAPP int int bit1 pls))))) m), skv_1, (one_one int) ) 17.51/17.03 ) 17.51/17.03 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X_1) _let_0)) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real (hAPP nat (fun real real) root N_1) X_1)) _let_0)))) )))) 17.51/17.03 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.03 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.03 ( (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))) ) 17.51/17.03 ( (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))) ) 17.51/17.03 ) 17.51/17.03 (instantiation (let ((_let_0 (one_one int))) (let ((_let_1 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) I_1)))) (let ((_let_2 (hAPP int int (sgn_sgn int) I_1))) (forall ((I_1 $$unsorted)) (or (= (zero_zero int) (ti int I_1)) (and (or _let_1 (= _let_2 (hAPP int int (uminus_uminus int) _let_0))) (or (not _let_1) (= _let_0 _let_2)))) )))) 17.51/17.03 ( (zero_zero int) ) 17.51/17.03 ( m ) 17.51/17.03 ( (one_one int) ) 17.51/17.03 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.51/17.03 ( min_1 ) 17.51/17.03 ( s ) 17.51/17.03 ( s1 ) 17.51/17.03 ( t ) 17.51/17.03 ) 17.51/17.03 (instantiation (let ((_let_0 (zero_zero int))) (forall ((I_1 $$unsorted)) (or (not (= _let_0 (ti int I_1))) (= _let_0 (hAPP int int (sgn_sgn int) I_1))) )) 17.51/17.04 ( pls ) 17.51/17.04 ( m ) 17.51/17.04 ( min_1 ) 17.51/17.04 ( s ) 17.51/17.04 ( s1 ) 17.51/17.04 ( t ) 17.51/17.04 ) 17.51/17.04 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (ord_less real))) (let ((_let_4 (filter real))) (let ((_let_5 (fun _let_4 bool))) (forall ((F $$unsorted) (L $$unsorted) (C_1 $$unsorted)) (or (not (hBOOL (hAPP _let_4 bool (hAPP real _let_5 (hAPP _let_2 (fun real _let_5) (tendsto real real) F) L) (hAPP real _let_4 (at real) C_1)))) (= _let_0 L) (not (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_3 _let_0) R_2))) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_3 (hAPP real real (abs_abs real) (hAPP real real (hAPP real _let_2 (minus_minus real) C_1) X_2))) R_2))) (= C_1 X_2) (not (= _let_0 (hAPP real real F X_2)))) ))) ))) ))))))) 17.51/17.04 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.04 ) 17.51/17.04 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_122682 $$unsorted) (BOUND_VARIABLE_122683 $$unsorted)) (or (not (order X_a)) (= (or (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_122682) BOUND_VARIABLE_122683)) (= (ti X_a BOUND_VARIABLE_122683) (ti X_a BOUND_VARIABLE_122682))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_122682) BOUND_VARIABLE_122683)))) )) 17.51/17.04 ( real, (zero_zero real), pi ) 17.51/17.04 ( 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)))) ) 17.51/17.04 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.04 ( real, (zero_zero real), skv_2 ) 17.51/17.04 ( real, (zero_zero real), skv_6 ) 17.51/17.04 ( real, (zero_zero real), skv_10 ) 17.51/17.04 ( real, (zero_zero real), skv_11 ) 17.51/17.04 ( real, (zero_zero real), skv_12 ) 17.51/17.04 ( real, (zero_zero real), skv_13 ) 17.51/17.04 ( real, (zero_zero real), skv_14 ) 17.51/17.04 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.04 ( real, pi, (zero_zero real) ) 17.51/17.04 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.04 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.51/17.04 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.04 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 17.51/17.04 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.51/17.04 ( 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)), pi ) 17.51/17.04 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.04 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.04 ( int, (zero_zero int), (zero_zero int) ) 17.51/17.04 ( int, (zero_zero int), (one_one int) ) 17.51/17.04 ( 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))) ) 17.51/17.04 ( int, (zero_zero int), min_1 ) 17.51/17.04 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.04 ( int, (zero_zero int), s ) 17.51/17.04 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 17.51/17.04 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.51/17.04 ( int, (zero_zero int), skv_3 ) 17.51/17.04 ( int, (zero_zero int), skv_9 ) 17.51/17.04 ( int, (one_one int), t ) 17.51/17.04 ( int, min_1, (zero_zero int) ) 17.51/17.04 ( int, min_1, pls ) 17.51/17.04 ( int, min_1, min_1 ) 17.51/17.04 ( 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))) ) 17.51/17.04 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.51/17.04 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.51/17.04 ( int, t, (zero_zero int) ) 17.51/17.04 ( int, t, (one_one int) ) 17.51/17.04 ( 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))) ) 17.51/17.04 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.51/17.04 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.51/17.04 ) 17.51/17.04 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 A_2) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 B_1) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) A_2) B_1)) zEven))) )))) 17.51/17.04 ( (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) ) 17.51/17.04 ( (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)))) ) 17.51/17.04 ) 17.51/17.04 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (one_one real)))) (forall ((Y_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root N_1) Y_1))) (hBOOL (hAPP real bool _let_0 Y_1)))) )) 17.51/17.04 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.04 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.04 ( (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))) ) 17.51/17.04 ( (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))) ) 17.51/17.04 ) 17.51/17.04 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_122771 $$unsorted) (BOUND_VARIABLE_122772 $$unsorted)) (or (not (boolean_algebra X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122771) (hAPP X_a X_a _let_2 BOUND_VARIABLE_122772)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122772) (hAPP X_a X_a _let_2 BOUND_VARIABLE_122771)))) )))) 17.51/17.04 ( int, (zero_zero int), pls ) 17.51/17.04 ( int, (zero_zero int), (one_one int) ) 17.51/17.04 ( int, pls, (zero_zero int) ) 17.51/17.04 ( int, pls, min_1 ) 17.51/17.04 ( int, pls, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.51/17.04 ( int, pls, t ) 17.51/17.04 ( int, (one_one int), (zero_zero int) ) 17.51/17.04 ( int, (one_one int), min_1 ) 17.51/17.04 ( int, min_1, pls ) 17.51/17.04 ( int, min_1, (one_one int) ) 17.51/17.04 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), pls ) 17.51/17.04 ( int, t, pls ) 17.51/17.04 ) 17.51/17.04 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int _let_0 (gcd_gcd int) M))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP int int _let_1 N) (hAPP int int _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) M) N))) ))) 17.51/17.04 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 17.51/17.04 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 17.51/17.04 ) 17.51/17.04 (instantiation (forall ((X $$unsorted)) (= (ti int X) (hAPP int int succ (hAPP int int pred X))) ) 17.51/17.04 ( pls ) 17.51/17.04 ( m ) 17.51/17.04 ( min_1 ) 17.51/17.04 ( s ) 17.51/17.04 ( s1 ) 17.51/17.04 ( t ) 17.51/17.04 ) 17.51/17.04 (instantiation (let ((_let_0 (at X_a))) (forall ((X_a $$unsorted)) (or (not (topological_space X_a)) (= _let_0 (ti (fun X_a (filter X_a)) _let_0))) )) 17.51/17.04 ( real ) 17.51/17.04 ( nat ) 17.51/17.04 ( complex ) 17.51/17.04 ) 17.51/17.04 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (fun X_b X_b))) (let ((_let_3 (times_times X_b))) (let ((_let_4 (hAPP nat X_b (hAPP X_b (fun nat X_b) (power_power X_b) (hAPP int X_b (number_number_of X_b) BOUND_VARIABLE_122838)) (hAPP int nat (number_number_of nat) BOUND_VARIABLE_122839)))) (forall ((X_b $$unsorted) (BOUND_VARIABLE_122826 $$unsorted) (BOUND_VARIABLE_122827 $$unsorted) (BOUND_VARIABLE_122838 $$unsorted) (BOUND_VARIABLE_122839 $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (fun nat X_b))) (let ((_let_2 (power_power X_b))) (let ((_let_3 (hAPP int X_b (number_number_of X_b) BOUND_VARIABLE_122838))) (or (not (monoid_mult X_b)) (not (number X_b)) (and (or (hBOOL (hAPP int bool _let_0 (hAPP int int _let_1 BOUND_VARIABLE_122827))) (= (one_one X_b) (hAPP nat X_b (hAPP X_b _let_1 _let_2 (hAPP int X_b (number_number_of X_b) BOUND_VARIABLE_122826)) (hAPP int nat _let_0 (hAPP int int bit1 BOUND_VARIABLE_122827))))) (or (not (hBOOL (hAPP int bool _let_0 (hAPP int int _let_1 BOUND_VARIABLE_122839)))) (= (hAPP nat X_b (hAPP X_b _let_1 _let_2 _let_3) (hAPP int nat _let_0 (hAPP int int bit1 BOUND_VARIABLE_122839))) (hAPP X_b X_b (hAPP X_b _let_2 _let_3 (hAPP X_b X_b (hAPP X_b _let_2 _let_3 _let_3) _let_4)) _let_4))))))))) )))))) 17.51/17.04 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), min_1, (hAPP int int bit0 (hAPP int int bit1 pls)), min_1 ) 17.51/17.04 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit1 pls), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit1 pls) ) 17.51/17.04 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)), pls, (hAPP int int bit0 (hAPP int int bit1 pls)), pls ) 17.51/17.04 ( 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))) ) 17.51/17.04 ( int, min_1, (hAPP int int bit1 (hAPP int int bit1 pls)), min_1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.51/17.04 ( complex, min_1, (hAPP int int bit0 (hAPP int int bit1 pls)), min_1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.51/17.04 ) 17.51/17.04 (instantiation (let ((_let_0 (fun int bool))) (forall ((L $$unsorted) (U_1 $$unsorted)) (= (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) U_1) L)) (hAPP _let_0 nat (finite_card int) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastLessThan int) L) U_1))) )) 17.51/17.04 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.04 ) 17.51/17.04 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (let ((_let_2 (abs_abs X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_122885 $$unsorted) (BOUND_VARIABLE_122886 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_122885)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_122886))) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122885) BOUND_VARIABLE_122886))))) )))) 17.51/17.04 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 17.51/17.04 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 17.51/17.04 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 17.51/17.04 ) 17.51/17.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122959 $$unsorted)) (or (not (group_add X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) (zero_zero X_a)) BOUND_VARIABLE_122959) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_122959))) ) 17.51/17.04 ( real, (one_one real) ) 17.51/17.04 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.04 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 17.51/17.04 ( int, pls ) 17.51/17.04 ( int, (one_one int) ) 17.51/17.04 ( int, min_1 ) 17.51/17.04 ( complex, ii ) 17.51/17.04 ( complex, (one_one complex) ) 17.51/17.04 ( code_code_numeral, (one_one code_code_numeral) ) 17.51/17.04 ) 17.51/17.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122971 $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_122971)))) ) 17.51/17.04 ( real, (zero_zero nat) ) 17.51/17.04 ( real, (one_one nat) ) 17.51/17.04 ( int, (zero_zero nat) ) 17.51/17.04 ( int, (hAPP nat nat suc (zero_zero nat)) ) 17.51/17.04 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.04 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.51/17.04 ) 17.51/17.04 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_123030 $$unsorted) (BOUND_VARIABLE_123031 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_123031) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_123030) _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_123031) BOUND_VARIABLE_123030)))) )))) 17.51/17.04 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 17.51/17.04 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.51/17.04 ( 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))) ) 17.51/17.04 ( 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)))) ) 17.51/17.04 ( 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)))) ) 17.51/17.04 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 17.51/17.05 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 17.51/17.05 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 17.51/17.05 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 17.51/17.05 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 17.51/17.05 ( 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) ) 17.51/17.05 ) 17.51/17.05 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123053 $$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_123053)) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_123053)))) ) 17.51/17.05 ( real, (one_one real) ) 17.51/17.05 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.05 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 17.51/17.05 ( int, pls ) 17.51/17.05 ( int, (one_one int) ) 17.51/17.05 ( int, min_1 ) 17.51/17.05 ( complex, ii ) 17.51/17.05 ( complex, (one_one complex) ) 17.51/17.05 ) 17.51/17.05 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) pls))) (let ((_let_1 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_123081 $$unsorted) (BOUND_VARIABLE_123082 $$unsorted)) (or (not (number_semiring X_a)) (not (hBOOL (hAPP int bool _let_0 BOUND_VARIABLE_123082))) (not (hBOOL (hAPP int bool _let_0 BOUND_VARIABLE_123081))) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP int X_a _let_1 BOUND_VARIABLE_123082)) (hAPP int X_a _let_1 BOUND_VARIABLE_123081)) (hAPP int X_a _let_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_123082) BOUND_VARIABLE_123081)))) ))) 17.51/17.05 ( nat, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 17.51/17.05 ) 17.51/17.05 (instantiation (let ((_let_0 (fun nat real))) (let ((_let_1 (fun (filter nat) bool))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (norm_norm X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_123111 $$unsorted) (BOUND_VARIABLE_123112 $$unsorted)) (let ((_let_0 (filter nat))) (or (not (real_normed_vector X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 (hAPP _let_2 (fun X_a _let_1) (tendsto nat X_a) BOUND_VARIABLE_123111) BOUND_VARIABLE_123112) sequentially))) (hBOOL (hAPP _let_0 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_123111)) (hAPP X_a real _let_3 BOUND_VARIABLE_123112)) sequentially)))) ))))) 17.51/17.05 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 17.51/17.05 ) 17.51/17.05 (instantiation (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)))))) (forall ((P_4 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_4))) (= (hAPP int _let_0 (hAPP int (fun int _let_0) wset _let_1) P_4) (hAPP int _let_0 d22set _let_1))) ))) 17.51/17.05 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.51/17.05 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.05 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.05 ) 17.51/17.05 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 X_1))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (zero_zero real)) X_1))) (not (hBOOL (hAPP real bool _let_2 Y_1))) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP real (fun _let_0 bool) (member real) X_2) (field_char_0_Rats real)))) (not (hBOOL (hAPP real bool _let_2 X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) Y_1)))) ))) )))) 17.51/17.05 ( (zero_zero real), pi ) 17.51/17.05 ( (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))))) ) 17.51/17.05 ( (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.05 ( pi, (zero_zero real) ) 17.51/17.05 ( 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)) ) 17.51/17.05 ( (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)))) ) 17.51/17.05 ( (hAPP real real (hAPP 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) ) 17.51/17.05 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 17.51/17.05 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.51/17.05 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 17.51/17.05 ( skv_2, (zero_zero real) ) 17.51/17.05 ( skv_10, (zero_zero real) ) 17.51/17.05 ( skv_13, (zero_zero real) ) 17.51/17.05 ) 17.51/17.05 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (gcd_gcd int))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP int int (hAPP int _let_0 _let_1 M) N) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) M) N)) N)) ))) 17.51/17.05 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 17.51/17.05 ( (hAPP nat int (hAPP 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) ) 17.51/17.05 ) 17.51/17.05 (instantiation (let ((_let_0 (plus_plus X_a))) (forall ((X_a $$unsorted)) (or (not (ab_semigroup_add X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0))) )) 17.51/17.05 ( bool ) 17.51/17.05 ( real ) 17.51/17.05 ( nat ) 17.51/17.05 ( (fun nat bool) ) 17.51/17.05 ( int ) 17.51/17.05 ( (fun int bool) ) 17.51/17.05 ( (fun real bool) ) 17.51/17.05 ( (fun real real) ) 17.51/17.05 ( complex ) 17.51/17.05 ( (fun nat real) ) 17.51/17.05 ( (fun int int) ) 17.51/17.05 ( rat ) 17.51/17.05 ( (fun int (fun int bool)) ) 17.51/17.05 ( quickcheck_code_int ) 17.51/17.05 ( (product_prod int int) ) 17.51/17.05 ( (fun (product_prod int int) bool) ) 17.51/17.05 ( code_code_numeral ) 17.51/17.05 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 17.51/17.05 ( (fun (product_prod int int) int) ) 17.51/17.05 ( (fun int (fun int (fun int bool))) ) 17.51/17.05 ( (fun int real) ) 17.51/17.05 ) 17.51/17.05 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int _let_0 (ord_less int) (zero_zero int)))) (forall ((I $$unsorted) (K $$unsorted)) (or (not (hBOOL (hAPP int bool _let_1 K))) (= (hBOOL (hAPP int bool _let_1 (hAPP int int (hAPP int (fun int int) (div_div int) I) K))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) K) I)))) ))) 17.51/17.05 ( pls, min_1 ) 17.51/17.05 ( (one_one int), (zero_zero int) ) 17.51/17.05 ( min_1, (zero_zero int) ) 17.51/17.05 ( min_1, min_1 ) 17.51/17.05 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 17.51/17.05 ( s, (zero_zero int) ) 17.51/17.05 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 17.51/17.05 ( t, (one_one int) ) 17.51/17.05 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 17.51/17.05 ( skv_3, (zero_zero int) ) 17.51/17.05 ( skv_9, (zero_zero int) ) 17.51/17.05 ) 17.51/17.05 (instantiation (let ((_let_0 (fun nat X_a))) (forall ((X_a $$unsorted)) (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))))) )) 17.51/17.05 ( bool ) 17.51/17.05 ( real ) 17.51/17.05 ( nat ) 17.51/17.05 ( (fun nat bool) ) 17.51/17.05 ( (fun nat nat) ) 17.51/17.05 ( int ) 17.51/17.05 ( (fun real real) ) 17.51/17.05 ( complex ) 17.51/17.05 ( (fun int int) ) 17.51/17.05 ( rat ) 17.51/17.05 ( (fun bool bool) ) 17.51/17.05 ( quickcheck_code_int ) 17.51/17.05 ( (fun nat (fun nat bool)) ) 17.51/17.05 ( (product_prod real real) ) 17.51/17.05 ( (product_prod int int) ) 17.51/17.05 ( (fun nat (product_prod int int)) ) 17.51/17.05 ( (product_prod nat nat) ) 17.51/17.05 ( (fun (product_prod nat nat) bool) ) 17.51/17.05 ( (fun nat (fun (product_prod nat nat) bool)) ) 17.51/17.05 ( (fun nat (product_prod nat nat)) ) 17.51/17.05 ( code_code_numeral ) 17.51/17.05 ) 17.51/17.05 (instantiation (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (lex_prod X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (= _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)) ))) 17.51/17.05 ( nat, nat ) 17.51/17.05 ( int, int ) 17.51/17.05 ) 17.51/17.05 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (div_div nat))) (let ((_let_2 (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) X))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat suc X)) _let_2) (hAPP nat nat (hAPP nat _let_0 _let_1 X) _let_2))) )))) 17.51/17.05 ( (zero_zero nat) ) 17.51/17.05 ( (hAPP nat nat suc (zero_zero nat)) ) 17.51/17.05 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 17.51/17.05 ( (one_one nat) ) 17.51/17.05 ) 17.51/17.05 (instantiation (let ((_let_0 (fun (product_prod X_a X_a) bool))) (let ((_let_1 (mlex_prod X_a))) (forall ((X_a $$unsorted)) (= _let_1 (ti (fun (fun X_a nat) (fun _let_0 _let_0)) _let_1)) ))) 17.51/17.05 ( real ) 17.51/17.05 ( nat ) 17.51/17.05 ( int ) 17.51/17.05 ( complex ) 17.51/17.05 ( quickcheck_code_int ) 17.51/17.05 ( (product_prod int int) ) 17.51/17.05 ( (product_prod nat nat) ) 17.51/17.05 ( code_code_numeral ) 17.51/17.05 ) 17.51/17.05 (instantiation (let ((_let_0 (fact_fact nat))) (let ((_let_1 (hAPP nat nat suc X))) (forall ((X $$unsorted)) (= (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) _let_1) (hAPP nat nat _let_0 X)) (hAPP nat nat _let_0 _let_1)) ))) 17.51/17.05 ( (zero_zero nat) ) 17.51/17.05 ( (hAPP nat nat suc (zero_zero nat)) ) 17.51/17.05 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 17.51/17.05 ) 17.51/17.05 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)))) (forall ((N $$unsorted)) (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))))))) ))) 17.51/17.05 ( (one_one nat) ) 17.51/17.05 ) 17.51/17.05 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_123390 $$unsorted) (BOUND_VARIABLE_123391 $$unsorted)) (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 (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_123390) BOUND_VARIABLE_123391)) _let_2)) (or (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_123391) _let_2)) (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_123390))) (and (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_123391)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_123390) _let_2)))))) ))))) 17.51/17.05 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.51/17.05 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.51/17.05 ( 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)))))) ) 17.51/17.05 ( 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 ) 17.51/17.05 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 17.51/17.05 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 17.51/17.05 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 17.51/17.05 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_1 ) 17.51/17.05 ( complex, ii, ii ) 17.51/17.05 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 17.51/17.05 ( 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 ) 17.51/17.05 ) 17.51/17.05 (instantiation (let ((_let_0 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_123624 $$unsorted)) (or (not (number_semiring X_a)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) pls) BOUND_VARIABLE_123624))) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (one_one X_a)) (hAPP int X_a _let_0 BOUND_VARIABLE_123624)) (hAPP int X_a _let_0 (hAPP int int succ BOUND_VARIABLE_123624)))) )) 17.51/17.05 ( nat, pls ) 17.51/17.05 ( nat, (hAPP int int bit1 pls) ) 17.51/17.05 ( nat, min_1 ) 17.51/17.05 ( int, pls ) 17.51/17.05 ( int, min_1 ) 17.51/17.05 ( quickcheck_code_int, pls ) 17.51/17.05 ( quickcheck_code_int, min_1 ) 17.51/17.05 ( code_code_numeral, pls ) 17.51/17.05 ( code_code_numeral, min_1 ) 17.51/17.05 ) 17.51/17.05 (instantiation (forall ((A_1 $$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)))) ) 17.51/17.05 ( (zero_zero nat) ) 17.51/17.05 ( (hAPP nat nat suc (zero_zero nat)) ) 17.51/17.05 ( (one_one nat) ) 17.51/17.05 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.05 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.51/17.05 ) 17.51/17.05 (instantiation (let ((_let_0 (zero_zero int))) (let ((_let_1 (fun int int))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun int rat))) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted) (B_1 $$unsorted)) (or (= _let_0 (ti int B_1)) (= _let_0 (ti int D_1)) (= (= (hAPP int int (hAPP int _let_1 _let_2 C_1) B_1) (hAPP int int (hAPP int _let_1 _let_2 A_2) D_1)) (= (hAPP int rat (hAPP int _let_3 fract C_1) D_1) (hAPP int rat (hAPP int _let_3 fract A_2) B_1)))) ))))) 17.51/17.05 ( (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)))), min_1, min_1 ) 17.51/17.05 ( (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))), s, s ) 17.51/17.05 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m, m ) 17.51/17.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t, m ) 17.51/17.06 ( (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)))), min_1, min_1 ) 17.51/17.06 ) 17.51/17.06 (instantiation (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP nat bool prime P_5))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP nat nat suc (zero_zero nat))) P_5))) ) 17.51/17.06 ( (zero_zero nat) ) 17.51/17.06 ( (one_one nat) ) 17.51/17.06 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.06 ) 17.51/17.06 (instantiation (forall ((V $$unsorted)) (= (hAPP int real (real_1 int) (hAPP int int (number_number_of int) V)) (hAPP int real (number_number_of real) V)) ) 17.51/17.06 ( pls ) 17.51/17.06 ( (hAPP int int bit1 pls) ) 17.51/17.06 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.51/17.06 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.06 ( min_1 ) 17.51/17.06 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.06 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.51/17.06 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.51/17.06 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 17.51/17.06 ) 17.51/17.06 (instantiation (let ((_let_0 (ring_1_of_int rat))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (= (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))) )) 17.51/17.06 ( (zero_zero int), (one_one int) ) 17.51/17.06 ( (one_one int), (one_one int) ) 17.51/17.06 ) 17.51/17.06 (instantiation (let ((_let_0 (fun real bool))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) Y_1) X_1))) (= X_1 (hAPP _let_0 real (complete_Sup_Sup real) (hAPP real _let_0 (hAPP real (fun real _let_0) (ord_atLeastAtMost real) Y_1) X_1)))) )) 17.51/17.06 ( (zero_zero real), pi ) 17.51/17.06 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.06 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.06 ( (zero_zero real), skv_6 ) 17.51/17.06 ( (zero_zero real), skv_11 ) 17.51/17.06 ( (zero_zero real), skv_12 ) 17.51/17.06 ( (zero_zero real), skv_14 ) 17.51/17.06 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.51/17.06 ( (hAPP real real (hAPP real (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))) ) 17.51/17.06 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.51/17.06 ( skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.06 ) 17.51/17.06 (instantiation (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) _let_0))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_123928 $$unsorted) (BOUND_VARIABLE_123929 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_123929))) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_123928))) (= (and (= _let_0 (ti X_a BOUND_VARIABLE_123929)) (= _let_0 (ti X_a BOUND_VARIABLE_123928))) (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_123929) BOUND_VARIABLE_123928)))) ))) 17.51/17.06 ( nat, (one_one nat), (one_one nat) ) 17.51/17.06 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 17.51/17.06 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.06 ) 17.51/17.06 (instantiation (let ((_let_0 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_123981 $$unsorted)) (or (not (group_add X_a)) (= (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_0 BOUND_VARIABLE_123981)) (ti X_a BOUND_VARIABLE_123981))) )) 17.51/17.06 ( bool, fFalse ) 17.51/17.06 ( bool, fTrue ) 17.51/17.06 ( real, (one_one real) ) 17.51/17.06 ( real, pi ) 17.51/17.06 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.06 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 17.51/17.06 ( (fun nat bool), (even_odd_even nat) ) 17.51/17.06 ( (fun nat bool), prime ) 17.51/17.06 ( (fun nat nat), suc ) 17.51/17.06 ( (fun nat nat), (fact_fact nat) ) 17.51/17.06 ( (fun nat nat), (size_size nat) ) 17.51/17.06 ( (fun nat nat), fact ) 17.51/17.06 ( (fun nat nat), nat_size ) 17.51/17.06 ( int, pls ) 17.51/17.06 ( int, m ) 17.51/17.06 ( int, (one_one int) ) 17.51/17.06 ( int, min_1 ) 17.51/17.06 ( int, s ) 17.51/17.06 ( int, s1 ) 17.51/17.06 ( int, t ) 17.51/17.06 ( (fun int bool), zprime ) 17.51/17.06 ( (fun int bool), nat_neg ) 17.51/17.06 ( (fun int bool), zEven ) 17.51/17.06 ( (fun int bool), nat_is_nat ) 17.51/17.06 ( (fun int bool), zOdd ) 17.51/17.06 ( (fun int bool), (even_odd_even int) ) 17.51/17.06 ( (fun int bool), twoSqu1091635170sum2sq ) 17.51/17.06 ( (fun int nat), nat_1 ) 17.51/17.06 ( (fun int nat), phi ) 17.51/17.06 ( (fun real real), sqrt ) 17.51/17.06 ( (fun real real), tan ) 17.51/17.06 ( (fun real real), cos ) 17.51/17.06 ( (fun real real), arccos ) 17.51/17.06 ( (fun real real), ln ) 17.51/17.06 ( (fun real real), sin ) 17.51/17.06 ( (fun real real), arctan ) 17.51/17.06 ( (fun real real), arcsin ) 17.51/17.06 ( complex, ii ) 17.51/17.06 ( complex, (one_one complex) ) 17.51/17.06 ( (fun complex complex), cnj ) 17.51/17.06 ( (fun complex complex), expi ) 17.51/17.06 ( (fun nat real), (real_1 nat) ) 17.51/17.06 ( (fun nat real), cos_coeff ) 17.51/17.06 ( (fun nat real), sin_coeff ) 17.51/17.06 ( (fun int int), bit0 ) 17.51/17.06 ( (fun int int), bit1 ) 17.51/17.06 ( (fun int int), pred ) 17.51/17.06 ( (fun int int), succ ) 17.51/17.06 ( (fun int int), (fact_fact int) ) 17.51/17.06 ( (fun int int), zfact ) 17.51/17.06 ( (fun bool bool), fNot ) 17.51/17.06 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.51/17.06 ( (fun bool (fun bool bool)), fconj ) 17.51/17.06 ( (fun bool (fun bool bool)), fdisj ) 17.51/17.06 ( (fun bool (fun bool bool)), fimplies ) 17.51/17.06 ( (fun int (fun int bool)), sRStar ) 17.51/17.06 ( (fun int (fun int bool)), quadRes ) 17.51/17.06 ( (fun int (fun int bool)), norRRset ) 17.51/17.06 ( (fun int (fun int bool)), d22set ) 17.51/17.06 ( (fun int (fun int bool)), sr ) 17.51/17.06 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 17.51/17.06 ( (fun nat (fun nat nat)), nat_gcd ) 17.51/17.06 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 17.51/17.06 ( (fun nat (fun nat nat)), nat_lcm ) 17.51/17.06 ( (fun nat (fun real real)), root ) 17.51/17.06 ( (fun real (fun real real)), log ) 17.51/17.06 ( (fun real (fun real real)), powr ) 17.51/17.06 ( (fun nat (fun nat bool)), coprime ) 17.51/17.06 ( (fun (fun int bool) int), (the int) ) 17.51/17.06 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 17.51/17.06 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 17.51/17.06 ( (fun nat (fun nat (product_prod int int))), bezw ) 17.51/17.06 ( (fun (fun int bool) bool), nat_nat_set ) 17.51/17.06 ( (filter nat), sequentially ) 17.51/17.06 ( (fun (product_prod nat nat) bool), pred_nat ) 17.51/17.06 ( (fun (product_prod int int) bool), frac_1 ) 17.51/17.06 ( (fun real complex), cis ) 17.51/17.06 ( (fun complex real), im ) 17.51/17.06 ( (fun complex real), re ) 17.51/17.06 ( (fun complex real), arg ) 17.51/17.06 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 17.51/17.06 ( (fun int (fun int int)), int_gcd ) 17.51/17.06 ( (fun int (fun int int)), multInv ) 17.51/17.06 ( (fun int (fun int int)), legacy_zgcd ) 17.51/17.06 ( (fun int (fun int int)), z3mod ) 17.51/17.06 ( (fun int (fun int int)), inv ) 17.51/17.06 ( (fun int (fun int int)), (gcd_gcd int) ) 17.51/17.06 ( (fun int (fun int int)), standardRes ) 17.51/17.06 ( (fun int (fun int int)), legendre ) 17.51/17.06 ( (fun int (fun int int)), nat_tsub ) 17.51/17.06 ( (fun int (fun int int)), z3div ) 17.51/17.06 ( (fun int (fun int int)), int_lcm ) 17.51/17.06 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 17.51/17.06 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 17.51/17.06 ( (fun int (fun (fun int bool) bool)), rsetR ) 17.51/17.06 ( (fun int (fun (fun int bool) bool)), resSet ) 17.51/17.06 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 17.51/17.06 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 17.51/17.06 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 17.51/17.06 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.51/17.06 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 17.51/17.06 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 17.51/17.06 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 17.51/17.06 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 17.51/17.06 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.51/17.06 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.51/17.06 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.51/17.06 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.51/17.06 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.51/17.06 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.51/17.06 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 17.51/17.06 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 17.51/17.06 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 17.51/17.06 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 17.51/17.06 ( (fun real nat), natfloor ) 17.51/17.06 ( (fun real nat), natceiling ) 17.51/17.06 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.51/17.06 ( (fun int (fun int (fun int bool))), wset ) 17.51/17.06 ( (fun int (fun int (fun int bool))), bnorRset ) 17.51/17.06 ( (fun int (fun int (fun int bool))), zcong ) 17.51/17.06 ( (fun int (fun int (fun int bool))), noXRRset ) 17.51/17.06 ( (fun int (fun int (fun int bool))), zcongm ) 17.51/17.06 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.51/17.06 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.51/17.06 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.51/17.06 ( (fun int real), (real_1 int) ) 17.51/17.06 ( (fun complex nat), (size_size complex) ) 17.51/17.06 ( (fun complex nat), complex_size ) 17.51/17.06 ( (fun int (list int)), quickc666637781d_zero ) 17.51/17.06 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.51/17.06 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.51/17.06 ( (fun (product_prod int int) rat), frct ) 17.51/17.06 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.51/17.06 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.51/17.06 ( (fun (fun nat rat) bool), vanishes ) 17.51/17.06 ( (fun int (fun int rat)), fract ) 17.51/17.06 ( (fun code_code_numeral int), code_int_of ) 17.51/17.06 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.51/17.06 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.51/17.06 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.51/17.06 ( (fun real (fun real complex)), complex_1 ) 17.51/17.06 ( (fun real (fun real complex)), rcis ) 17.51/17.06 ( (fun int (fun nat nat)), nat_aux ) 17.51/17.06 ( (fun rat real), ratreal ) 17.51/17.06 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.51/17.06 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.51/17.06 ( (fun rat (product_prod int int)), quotient_of ) 17.51/17.06 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.51/17.06 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.51/17.06 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.51/17.06 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.51/17.06 ) 17.51/17.06 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (one_one real)))) (hBOOL (hAPP real bool (hAPP (fun real real) _let_0 (isCont real real) arcsin) X_1))) ))) 17.51/17.06 ( (zero_zero real) ) 17.51/17.06 ( (one_one real) ) 17.51/17.06 ( pi ) 17.51/17.06 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.06 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 17.51/17.06 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.06 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 17.51/17.06 ) 17.51/17.06 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_124007 $$unsorted)) (or (not (division_ring X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_124007)) (not (= _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_124007)))) )) 17.51/17.06 ( bool, fFalse ) 17.51/17.06 ( bool, fTrue ) 17.51/17.06 ( real, (zero_zero real) ) 17.51/17.06 ( real, pi ) 17.51/17.06 ( (fun nat bool), (even_odd_even nat) ) 17.51/17.06 ( (fun nat bool), prime ) 17.51/17.06 ( (fun nat nat), suc ) 17.51/17.06 ( (fun nat nat), (fact_fact nat) ) 17.51/17.06 ( (fun nat nat), (size_size nat) ) 17.51/17.06 ( (fun nat nat), fact ) 17.51/17.06 ( (fun nat nat), nat_size ) 17.51/17.06 ( int, pls ) 17.51/17.06 ( int, m ) 17.51/17.06 ( int, min_1 ) 17.51/17.06 ( int, s ) 17.51/17.06 ( int, s1 ) 17.51/17.06 ( int, t ) 17.51/17.06 ( (fun int bool), zprime ) 17.51/17.06 ( (fun int bool), nat_neg ) 17.51/17.06 ( (fun int bool), zEven ) 17.51/17.06 ( (fun int bool), nat_is_nat ) 17.51/17.06 ( (fun int bool), zOdd ) 17.51/17.06 ( (fun int bool), (even_odd_even int) ) 17.51/17.06 ( (fun int bool), twoSqu1091635170sum2sq ) 17.51/17.06 ( (fun int nat), nat_1 ) 17.51/17.06 ( (fun int nat), phi ) 17.51/17.06 ( (fun real real), sqrt ) 17.51/17.06 ( (fun real real), tan ) 17.51/17.06 ( (fun real real), cos ) 17.51/17.06 ( (fun real real), arccos ) 17.51/17.06 ( (fun real real), ln ) 17.51/17.06 ( (fun real real), sin ) 17.51/17.06 ( (fun real real), arctan ) 17.51/17.06 ( (fun real real), arcsin ) 17.51/17.06 ( complex, ii ) 17.51/17.06 ( (fun complex complex), cnj ) 17.51/17.06 ( (fun complex complex), expi ) 17.51/17.06 ( (fun nat real), (real_1 nat) ) 17.51/17.06 ( (fun nat real), cos_coeff ) 17.51/17.06 ( (fun nat real), sin_coeff ) 17.51/17.06 ( (fun int int), bit0 ) 17.51/17.06 ( (fun int int), bit1 ) 17.51/17.06 ( (fun int int), pred ) 17.51/17.06 ( (fun int int), succ ) 17.51/17.06 ( (fun int int), (fact_fact int) ) 17.51/17.06 ( (fun int int), zfact ) 17.51/17.06 ( (fun bool bool), fNot ) 17.51/17.06 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.51/17.06 ( (fun bool (fun bool bool)), fconj ) 17.51/17.06 ( (fun bool (fun bool bool)), fdisj ) 17.51/17.06 ( (fun bool (fun bool bool)), fimplies ) 17.51/17.06 ( (fun int (fun int bool)), sRStar ) 17.51/17.06 ( (fun int (fun int bool)), quadRes ) 17.51/17.06 ( (fun int (fun int bool)), norRRset ) 17.51/17.06 ( (fun int (fun int bool)), d22set ) 17.51/17.06 ( (fun int (fun int bool)), sr ) 17.51/17.06 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 17.51/17.06 ( (fun nat (fun nat nat)), nat_gcd ) 17.51/17.06 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 17.51/17.06 ( (fun nat (fun nat nat)), nat_lcm ) 17.51/17.06 ( (fun nat (fun real real)), root ) 17.51/17.06 ( (fun real (fun real real)), log ) 17.51/17.06 ( (fun real (fun real real)), powr ) 17.51/17.06 ( (fun nat (fun nat bool)), coprime ) 17.51/17.06 ( (fun (fun int bool) int), (the int) ) 17.51/17.06 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 17.51/17.06 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 17.51/17.06 ( (fun nat (fun nat (product_prod int int))), bezw ) 17.51/17.06 ( (fun (fun int bool) bool), nat_nat_set ) 17.51/17.06 ( (filter nat), sequentially ) 17.51/17.06 ( (fun (product_prod nat nat) bool), pred_nat ) 17.51/17.06 ( (fun (product_prod int int) bool), frac_1 ) 17.51/17.06 ( (fun real complex), cis ) 17.51/17.06 ( (fun complex real), im ) 17.51/17.06 ( (fun complex real), re ) 17.51/17.06 ( (fun complex real), arg ) 17.51/17.06 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 17.51/17.06 ( (fun int (fun int int)), int_gcd ) 17.51/17.06 ( (fun int (fun int int)), multInv ) 17.51/17.06 ( (fun int (fun int int)), legacy_zgcd ) 17.51/17.06 ( (fun int (fun int int)), z3mod ) 17.51/17.06 ( (fun int (fun int int)), inv ) 17.51/17.06 ( (fun int (fun int int)), (gcd_gcd int) ) 17.51/17.06 ( (fun int (fun int int)), standardRes ) 17.51/17.06 ( (fun int (fun int int)), legendre ) 17.51/17.06 ( (fun int (fun int int)), nat_tsub ) 17.51/17.06 ( (fun int (fun int int)), z3div ) 17.51/17.06 ( (fun int (fun int int)), int_lcm ) 17.51/17.06 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 17.51/17.06 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 17.51/17.06 ( (fun int (fun (fun int bool) bool)), rsetR ) 17.51/17.06 ( (fun int (fun (fun int bool) bool)), resSet ) 17.51/17.06 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 17.51/17.06 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 17.51/17.06 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 17.51/17.06 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.51/17.06 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 17.51/17.06 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 17.51/17.06 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 17.51/17.06 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 17.51/17.06 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.51/17.06 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.51/17.06 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.51/17.06 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.51/17.06 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.51/17.06 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.51/17.07 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 17.51/17.07 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 17.51/17.07 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 17.51/17.07 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 17.51/17.07 ( (fun real nat), natfloor ) 17.51/17.07 ( (fun real nat), natceiling ) 17.51/17.07 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.51/17.07 ( (fun int (fun int (fun int bool))), wset ) 17.51/17.07 ( (fun int (fun int (fun int bool))), bnorRset ) 17.51/17.07 ( (fun int (fun int (fun int bool))), zcong ) 17.51/17.07 ( (fun int (fun int (fun int bool))), noXRRset ) 17.51/17.07 ( (fun int (fun int (fun int bool))), zcongm ) 17.51/17.07 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.51/17.07 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.51/17.07 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.51/17.07 ( (fun int real), (real_1 int) ) 17.51/17.07 ( (fun complex nat), (size_size complex) ) 17.51/17.07 ( (fun complex nat), complex_size ) 17.51/17.07 ( (fun int (list int)), quickc666637781d_zero ) 17.51/17.07 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.51/17.07 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.51/17.07 ( (fun (product_prod int int) rat), frct ) 17.51/17.07 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.51/17.07 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.51/17.07 ( (fun (fun nat rat) bool), vanishes ) 17.51/17.07 ( (fun int (fun int rat)), fract ) 17.51/17.07 ( (fun code_code_numeral int), code_int_of ) 17.51/17.07 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.51/17.07 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.51/17.07 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.51/17.07 ( (fun real (fun real complex)), complex_1 ) 17.51/17.07 ( (fun real (fun real complex)), rcis ) 17.51/17.07 ( (fun int (fun nat nat)), nat_aux ) 17.51/17.07 ( (fun rat real), ratreal ) 17.51/17.07 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.51/17.07 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.51/17.07 ( (fun rat (product_prod int int)), quotient_of ) 17.51/17.07 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.51/17.07 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.51/17.07 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.51/17.07 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.51/17.07 ) 17.51/17.07 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (fact_fact int))) (forall ((N $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) N))) (= (hAPP int int _let_1 N) (hAPP int int (hAPP int _let_0 (times_times int) N) (hAPP int int _let_1 (hAPP int int (hAPP int _let_0 (minus_minus int) N) (one_one int)))))) ))) 17.51/17.07 ( (zero_zero int) ) 17.51/17.07 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.07 ( (one_one int) ) 17.51/17.07 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.51/17.07 ( min_1 ) 17.51/17.07 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.07 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.07 ) 17.51/17.07 (instantiation (let ((_let_0 (suminf X_a))) (forall ((X_a $$unsorted)) (or (not (topological_space X_a)) (not (comm_monoid_add X_a)) (= _let_0 (ti (fun (fun nat X_a) X_a) _let_0))) )) 17.51/17.07 ( bool ) 17.51/17.07 ( real ) 17.51/17.07 ( nat ) 17.51/17.07 ( (fun nat bool) ) 17.51/17.07 ( (fun nat nat) ) 17.51/17.07 ( int ) 17.51/17.07 ( (fun real real) ) 17.51/17.07 ( complex ) 17.51/17.07 ( (fun int int) ) 17.51/17.07 ( rat ) 17.51/17.07 ( (fun bool bool) ) 17.51/17.07 ( quickcheck_code_int ) 17.51/17.07 ( (fun nat (fun nat bool)) ) 17.51/17.07 ( (product_prod real real) ) 17.51/17.07 ( (product_prod int int) ) 17.51/17.07 ( (fun nat (product_prod int int)) ) 17.51/17.07 ( (product_prod nat nat) ) 17.51/17.07 ( (fun (product_prod nat nat) bool) ) 17.51/17.07 ( (fun nat (fun (product_prod nat nat) bool)) ) 17.51/17.07 ( (fun nat (product_prod nat nat)) ) 17.51/17.07 ( code_code_numeral ) 17.51/17.07 ) 17.51/17.07 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_124063 $$unsorted) (BOUND_VARIABLE_124064 $$unsorted)) (or (not (ab_group_add X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_124063) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_124064)) (hAPP X_a X_a (hAPP X_a _let_0 (minus_minus X_a) BOUND_VARIABLE_124063) BOUND_VARIABLE_124064))) )) 17.51/17.07 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 17.51/17.07 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 17.51/17.07 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 17.51/17.07 ) 17.51/17.07 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (hAPP nat nat suc X) (hAPP nat nat suc Y))) (= X Y)) ) 17.51/17.07 ( (zero_zero nat), (zero_zero nat) ) 17.51/17.07 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 17.51/17.07 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 17.51/17.07 ( (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 17.51/17.07 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (zero_zero nat) ) 17.51/17.07 ) 17.51/17.07 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 X_1))) (= (hBOOL (hAPP real bool _let_2 (hAPP real real ln X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) X_1)))) )))) 17.51/17.07 ( (one_one real) ) 17.51/17.07 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.07 ) 17.51/17.07 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124136 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (uminus_uminus int) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_124136)) (hAPP X_a int (archimedean_ceiling X_a) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_124136)))) ) 17.51/17.07 ( real, (one_one real) ) 17.51/17.07 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.07 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 17.51/17.07 ( int, pls ) 17.51/17.07 ( int, (one_one int) ) 17.51/17.07 ( int, min_1 ) 17.51/17.07 ( complex, ii ) 17.51/17.07 ( complex, (one_one complex) ) 17.51/17.07 ) 17.51/17.07 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124184 $$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_124184)) (zero_zero X_a))))) ) 17.51/17.07 ( real, (zero_zero nat) ) 17.51/17.07 ( real, (one_one nat) ) 17.51/17.07 ( int, (zero_zero nat) ) 17.51/17.07 ( int, (hAPP nat nat suc (zero_zero nat)) ) 17.51/17.07 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.07 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.51/17.07 ) 17.51/17.07 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP int real (real_1 int) N))) (forall ((N $$unsorted) (X $$unsorted)) (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 int int (hAPP int (fun int int) (plus_plus int) N) (one_one int)) (hAPP real int (archimedean_ceiling real) X))) ))) 17.51/17.07 ( (zero_zero int), pi ) 17.51/17.07 ( (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)))) ) 17.51/17.07 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.07 ( (zero_zero int), skv_2 ) 17.51/17.07 ( (zero_zero int), skv_10 ) 17.51/17.07 ( (zero_zero int), skv_13 ) 17.51/17.07 ( (one_one int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.07 ) 17.51/17.07 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124298 $$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_124298) (zero_zero X_a)) (ti X_a BOUND_VARIABLE_124298))) ) 17.51/17.07 ( bool, fFalse ) 17.51/17.07 ( bool, fTrue ) 17.51/17.07 ( real, pi ) 17.51/17.07 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 17.51/17.07 ( (fun nat bool), (even_odd_even nat) ) 17.51/17.07 ( (fun nat bool), prime ) 17.51/17.07 ( (fun nat nat), suc ) 17.51/17.07 ( (fun nat nat), (fact_fact nat) ) 17.51/17.07 ( (fun nat nat), (size_size nat) ) 17.51/17.07 ( (fun nat nat), fact ) 17.51/17.07 ( (fun nat nat), nat_size ) 17.51/17.07 ( int, pls ) 17.51/17.07 ( int, m ) 17.51/17.07 ( int, min_1 ) 17.51/17.07 ( int, s ) 17.51/17.07 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.07 ( int, s1 ) 17.51/17.07 ( int, t ) 17.51/17.07 ( (fun int bool), zprime ) 17.51/17.07 ( (fun int bool), nat_neg ) 17.51/17.07 ( (fun int bool), zEven ) 17.51/17.07 ( (fun int bool), nat_is_nat ) 17.51/17.07 ( (fun int bool), zOdd ) 17.51/17.07 ( (fun int bool), (even_odd_even int) ) 17.51/17.07 ( (fun int bool), twoSqu1091635170sum2sq ) 17.51/17.07 ( (fun int nat), nat_1 ) 17.51/17.07 ( (fun int nat), phi ) 17.51/17.07 ( (fun real real), sqrt ) 17.51/17.07 ( (fun real real), tan ) 17.51/17.07 ( (fun real real), cos ) 17.51/17.07 ( (fun real real), arccos ) 17.51/17.07 ( (fun real real), ln ) 17.51/17.07 ( (fun real real), sin ) 17.51/17.07 ( (fun real real), arctan ) 17.51/17.07 ( (fun real real), arcsin ) 17.51/17.07 ( complex, ii ) 17.51/17.07 ( (fun complex complex), cnj ) 17.51/17.07 ( (fun complex complex), expi ) 17.51/17.07 ( (fun nat real), (real_1 nat) ) 17.51/17.07 ( (fun nat real), cos_coeff ) 17.51/17.07 ( (fun nat real), sin_coeff ) 17.51/17.07 ( (fun int int), bit0 ) 17.51/17.07 ( (fun int int), bit1 ) 17.51/17.07 ( (fun int int), pred ) 17.51/17.07 ( (fun int int), succ ) 17.51/17.07 ( (fun int int), (fact_fact int) ) 17.51/17.07 ( (fun int int), zfact ) 17.51/17.07 ( (fun bool bool), fNot ) 17.51/17.07 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.51/17.07 ( (fun bool (fun bool bool)), fconj ) 17.51/17.07 ( (fun bool (fun bool bool)), fdisj ) 17.51/17.07 ( (fun bool (fun bool bool)), fimplies ) 17.51/17.07 ( (fun int (fun int bool)), sRStar ) 17.51/17.07 ( (fun int (fun int bool)), quadRes ) 17.51/17.07 ( (fun int (fun int bool)), norRRset ) 17.51/17.07 ( (fun int (fun int bool)), d22set ) 17.51/17.07 ( (fun int (fun int bool)), sr ) 17.51/17.07 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 17.51/17.07 ( (fun nat (fun nat nat)), nat_gcd ) 17.51/17.07 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 17.51/17.07 ( (fun nat (fun nat nat)), nat_lcm ) 17.51/17.07 ( (fun nat (fun real real)), root ) 17.51/17.07 ( (fun real (fun real real)), log ) 17.51/17.07 ( (fun real (fun real real)), powr ) 17.51/17.07 ( (fun nat (fun nat bool)), coprime ) 17.51/17.07 ( (fun (fun int bool) int), (the int) ) 17.51/17.07 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 17.51/17.07 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 17.51/17.07 ( (fun nat (fun nat (product_prod int int))), bezw ) 17.51/17.07 ( (fun (fun int bool) bool), nat_nat_set ) 17.51/17.07 ( (filter nat), sequentially ) 17.51/17.07 ( (fun (product_prod nat nat) bool), pred_nat ) 17.51/17.07 ( (fun (product_prod int int) bool), frac_1 ) 17.51/17.07 ( (fun real complex), cis ) 17.51/17.07 ( (fun complex real), im ) 17.51/17.07 ( (fun complex real), re ) 17.51/17.07 ( (fun complex real), arg ) 17.51/17.07 ( code_code_numeral, (zero_zero code_code_numeral) ) 17.51/17.07 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 17.51/17.07 ( (fun int (fun int int)), int_gcd ) 17.51/17.07 ( (fun int (fun int int)), multInv ) 17.51/17.07 ( (fun int (fun int int)), legacy_zgcd ) 17.51/17.07 ( (fun int (fun int int)), z3mod ) 17.51/17.07 ( (fun int (fun int int)), inv ) 17.51/17.07 ( (fun int (fun int int)), (gcd_gcd int) ) 17.51/17.07 ( (fun int (fun int int)), standardRes ) 17.51/17.07 ( (fun int (fun int int)), legendre ) 17.51/17.07 ( (fun int (fun int int)), nat_tsub ) 17.51/17.07 ( (fun int (fun int int)), z3div ) 17.51/17.07 ( (fun int (fun int int)), int_lcm ) 17.51/17.07 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 17.51/17.07 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 17.51/17.07 ( (fun int (fun (fun int bool) bool)), rsetR ) 17.51/17.07 ( (fun int (fun (fun int bool) bool)), resSet ) 17.51/17.07 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 17.51/17.07 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 17.51/17.07 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 17.51/17.07 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.51/17.07 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 17.51/17.07 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 17.51/17.07 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 17.51/17.07 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 17.51/17.07 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.51/17.07 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.51/17.07 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.51/17.07 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.51/17.07 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.51/17.07 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.51/17.07 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 17.51/17.07 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 17.51/17.07 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 17.51/17.07 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 17.51/17.07 ( (fun real nat), natfloor ) 17.51/17.07 ( (fun real nat), natceiling ) 17.51/17.07 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.51/17.07 ( (fun int (fun int (fun int bool))), wset ) 17.51/17.07 ( (fun int (fun int (fun int bool))), bnorRset ) 17.51/17.07 ( (fun int (fun int (fun int bool))), zcong ) 17.51/17.07 ( (fun int (fun int (fun int bool))), noXRRset ) 17.51/17.07 ( (fun int (fun int (fun int bool))), zcongm ) 17.51/17.07 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.51/17.07 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.51/17.07 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.51/17.07 ( (fun int real), (real_1 int) ) 17.51/17.07 ( (fun complex nat), (size_size complex) ) 17.51/17.07 ( (fun complex nat), complex_size ) 17.51/17.07 ( (fun int (list int)), quickc666637781d_zero ) 17.51/17.07 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.51/17.07 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.51/17.07 ( (fun (product_prod int int) rat), frct ) 17.51/17.07 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.51/17.07 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.51/17.07 ( (fun (fun nat rat) bool), vanishes ) 17.51/17.07 ( (fun int (fun int rat)), fract ) 17.51/17.07 ( (fun code_code_numeral int), code_int_of ) 17.51/17.07 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.51/17.07 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.51/17.07 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.51/17.07 ( (fun real (fun real complex)), complex_1 ) 17.51/17.07 ( (fun real (fun real complex)), rcis ) 17.51/17.07 ( (fun int (fun nat nat)), nat_aux ) 17.51/17.07 ( (fun rat real), ratreal ) 17.51/17.07 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.51/17.07 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.51/17.07 ( (fun rat (product_prod int int)), quotient_of ) 17.51/17.07 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.51/17.07 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.51/17.07 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.51/17.07 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.51/17.07 ) 17.51/17.07 (instantiation (let ((_let_0 (abs_Frac X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun (product_prod int int) X_a) _let_0)) )) 17.51/17.07 ( bool ) 17.51/17.07 ( int ) 17.51/17.07 ( (fun int bool) ) 17.51/17.07 ( (fun int int) ) 17.51/17.07 ( rat ) 17.51/17.07 ( (fun bool bool) ) 17.51/17.07 ( (product_prod int int) ) 17.51/17.07 ( (fun (product_prod int int) bool) ) 17.51/17.07 ( (fun (product_prod int int) int) ) 17.51/17.07 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 17.51/17.07 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 17.51/17.07 ( (fun (product_prod int int) (fun int bool)) ) 17.51/17.07 ( (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 17.51/17.07 ) 17.51/17.07 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124359 $$unsorted) (BOUND_VARIABLE_124360 $$unsorted)) (or (not (ab_group_add X_a)) (= (= (ti X_a BOUND_VARIABLE_124359) (ti X_a BOUND_VARIABLE_124360)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_124359) BOUND_VARIABLE_124360)))) ) 17.51/17.07 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 17.51/17.08 ( 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)))), (hAPP int int (number_number_of int) min_1) ) 17.51/17.08 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 17.51/17.08 ) 17.51/17.08 (instantiation (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))) (forall ((N $$unsorted) (M $$unsorted)) (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 M) (ti int N))) )))) 17.51/17.08 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.51/17.08 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.51/17.08 ) 17.51/17.08 (instantiation (let ((_let_0 (the X_a))) (forall ((X_a $$unsorted)) (or (not (comm_monoid_add X_a)) (not (topological_space X_a)) (= _let_0 (ti (fun (fun X_a bool) X_a) _let_0))) )) 17.51/17.08 ( bool ) 17.51/17.08 ( real ) 17.51/17.08 ( nat ) 17.51/17.08 ( (fun nat bool) ) 17.51/17.08 ( int ) 17.51/17.08 ( (fun int bool) ) 17.51/17.08 ( complex ) 17.51/17.08 ( rat ) 17.51/17.08 ( quickcheck_code_int ) 17.51/17.08 ( (product_prod real real) ) 17.51/17.08 ( (product_prod int int) ) 17.51/17.08 ( (filter real) ) 17.51/17.08 ( (filter nat) ) 17.51/17.08 ( (product_prod nat nat) ) 17.51/17.08 ( code_code_numeral ) 17.51/17.08 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 17.51/17.08 ( (fun nat rat) ) 17.51/17.08 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 17.51/17.08 ) 17.51/17.08 (instantiation (let ((_let_0 (zero_zero complex))) (forall ((Z $$unsorted)) (= (= _let_0 (hAPP complex complex cnj Z)) (= _let_0 Z)) )) 17.51/17.08 ( ii ) 17.51/17.08 ( (zero_zero complex) ) 17.51/17.08 ( (one_one complex) ) 17.51/17.08 ) 17.51/17.08 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124417 $$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_124417) (zero_zero X_a)) (ti X_a BOUND_VARIABLE_124417))) ) 17.51/17.08 ( bool, fFalse ) 17.51/17.08 ( bool, fTrue ) 17.51/17.08 ( real, pi ) 17.51/17.08 ( nat, (one_one nat) ) 17.51/17.08 ( (fun nat bool), (even_odd_even nat) ) 17.51/17.08 ( (fun nat bool), prime ) 17.51/17.08 ( (fun nat nat), suc ) 17.51/17.08 ( (fun nat nat), (fact_fact nat) ) 17.51/17.08 ( (fun nat nat), (size_size nat) ) 17.51/17.08 ( (fun nat nat), fact ) 17.51/17.08 ( (fun nat nat), nat_size ) 17.51/17.08 ( int, pls ) 17.51/17.08 ( int, m ) 17.51/17.08 ( 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) ) 17.51/17.08 ( int, min_1 ) 17.51/17.08 ( int, s ) 17.51/17.08 ( 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)))) ) 17.51/17.08 ( int, s1 ) 17.51/17.08 ( int, t ) 17.51/17.08 ( (fun int bool), zprime ) 17.51/17.08 ( (fun int bool), nat_neg ) 17.51/17.08 ( (fun int bool), zEven ) 17.51/17.08 ( (fun int bool), nat_is_nat ) 17.51/17.08 ( (fun int bool), zOdd ) 17.51/17.08 ( (fun int bool), (even_odd_even int) ) 17.51/17.08 ( (fun int bool), twoSqu1091635170sum2sq ) 17.51/17.08 ( (fun int nat), nat_1 ) 17.51/17.08 ( (fun int nat), phi ) 17.51/17.08 ( (fun real real), sqrt ) 17.51/17.08 ( (fun real real), tan ) 17.51/17.08 ( (fun real real), cos ) 17.51/17.08 ( (fun real real), arccos ) 17.51/17.08 ( (fun real real), ln ) 17.51/17.08 ( (fun real real), sin ) 17.51/17.08 ( (fun real real), arctan ) 17.51/17.08 ( (fun real real), arcsin ) 17.51/17.08 ( complex, ii ) 17.51/17.08 ( (fun complex complex), cnj ) 17.51/17.08 ( (fun complex complex), expi ) 17.51/17.08 ( (fun nat real), (real_1 nat) ) 17.51/17.08 ( (fun nat real), cos_coeff ) 17.51/17.08 ( (fun nat real), sin_coeff ) 17.51/17.08 ( (fun int int), bit0 ) 17.51/17.08 ( (fun int int), bit1 ) 17.51/17.08 ( (fun int int), pred ) 17.51/17.08 ( (fun int int), succ ) 17.51/17.08 ( (fun int int), (fact_fact int) ) 17.51/17.08 ( (fun int int), zfact ) 17.51/17.08 ( (fun bool bool), fNot ) 17.51/17.08 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.51/17.08 ( (fun bool (fun bool bool)), fconj ) 17.51/17.08 ( (fun bool (fun bool bool)), fdisj ) 17.51/17.08 ( (fun bool (fun bool bool)), fimplies ) 17.51/17.08 ( (fun int (fun int bool)), sRStar ) 17.51/17.08 ( (fun int (fun int bool)), quadRes ) 17.51/17.08 ( (fun int (fun int bool)), norRRset ) 17.51/17.08 ( (fun int (fun int bool)), d22set ) 17.51/17.08 ( (fun int (fun int bool)), sr ) 17.51/17.08 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 17.51/17.08 ( (fun nat (fun nat nat)), nat_gcd ) 17.51/17.08 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 17.51/17.08 ( (fun nat (fun nat nat)), nat_lcm ) 17.51/17.08 ( (fun nat (fun real real)), root ) 17.51/17.08 ( (fun real (fun real real)), log ) 17.51/17.08 ( (fun real (fun real real)), powr ) 17.51/17.08 ( (fun nat (fun nat bool)), coprime ) 17.51/17.08 ( (fun (fun int bool) int), (the int) ) 17.51/17.08 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 17.51/17.08 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 17.51/17.08 ( (fun nat (fun nat (product_prod int int))), bezw ) 17.51/17.08 ( (fun (fun int bool) bool), nat_nat_set ) 17.51/17.08 ( (filter nat), sequentially ) 17.51/17.08 ( (fun (product_prod nat nat) bool), pred_nat ) 17.51/17.08 ( (fun (product_prod int int) bool), frac_1 ) 17.51/17.08 ( (fun real complex), cis ) 17.51/17.08 ( (fun complex real), im ) 17.51/17.08 ( (fun complex real), re ) 17.51/17.08 ( (fun complex real), arg ) 17.51/17.08 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 17.51/17.08 ( (fun int (fun int int)), int_gcd ) 17.51/17.08 ( (fun int (fun int int)), multInv ) 17.51/17.08 ( (fun int (fun int int)), legacy_zgcd ) 17.51/17.08 ( (fun int (fun int int)), z3mod ) 17.51/17.08 ( (fun int (fun int int)), inv ) 17.51/17.08 ( (fun int (fun int int)), (gcd_gcd int) ) 17.51/17.08 ( (fun int (fun int int)), standardRes ) 17.51/17.08 ( (fun int (fun int int)), legendre ) 17.51/17.08 ( (fun int (fun int int)), nat_tsub ) 17.51/17.08 ( (fun int (fun int int)), z3div ) 17.51/17.08 ( (fun int (fun int int)), int_lcm ) 17.51/17.08 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 17.51/17.08 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 17.51/17.08 ( (fun int (fun (fun int bool) bool)), rsetR ) 17.51/17.08 ( (fun int (fun (fun int bool) bool)), resSet ) 17.51/17.08 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 17.51/17.08 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 17.51/17.08 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 17.51/17.08 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.51/17.08 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 17.51/17.08 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 17.51/17.08 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 17.51/17.08 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 17.51/17.08 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.51/17.08 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.51/17.08 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.51/17.08 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.51/17.08 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.51/17.08 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.51/17.08 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 17.51/17.08 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 17.51/17.08 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 17.51/17.08 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 17.51/17.08 ( (fun real nat), natfloor ) 17.51/17.08 ( (fun real nat), natceiling ) 17.51/17.08 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.51/17.08 ( (fun int (fun int (fun int bool))), wset ) 17.51/17.08 ( (fun int (fun int (fun int bool))), bnorRset ) 17.51/17.08 ( (fun int (fun int (fun int bool))), zcong ) 17.51/17.08 ( (fun int (fun int (fun int bool))), noXRRset ) 17.51/17.08 ( (fun int (fun int (fun int bool))), zcongm ) 17.51/17.08 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.51/17.08 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.51/17.08 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.51/17.08 ( (fun int real), (real_1 int) ) 17.51/17.08 ( (fun complex nat), (size_size complex) ) 17.51/17.08 ( (fun complex nat), complex_size ) 17.51/17.08 ( (fun int (list int)), quickc666637781d_zero ) 17.51/17.08 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.51/17.08 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.51/17.08 ( (fun (product_prod int int) rat), frct ) 17.51/17.08 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.51/17.08 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.51/17.08 ( (fun (fun nat rat) bool), vanishes ) 17.51/17.08 ( (fun int (fun int rat)), fract ) 17.51/17.08 ( (fun code_code_numeral int), code_int_of ) 17.51/17.08 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.51/17.08 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.51/17.08 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.51/17.08 ( (fun real (fun real complex)), complex_1 ) 17.51/17.08 ( (fun real (fun real complex)), rcis ) 17.51/17.08 ( (fun int (fun nat nat)), nat_aux ) 17.51/17.08 ( (fun rat real), ratreal ) 17.51/17.08 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.51/17.08 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.51/17.08 ( (fun rat (product_prod int int)), quotient_of ) 17.51/17.08 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.51/17.08 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.51/17.08 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.51/17.08 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.51/17.08 ) 17.51/17.08 (instantiation (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (inverse_inverse X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_124488 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_124488)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_124488)))) ))) 17.51/17.08 ( real, (zero_zero real) ) 17.51/17.08 ( complex, ii ) 17.51/17.08 ) 17.51/17.08 (instantiation (let ((_let_0 (one_one int))) (let ((_let_1 (ti int Z))) (forall ((Z $$unsorted)) (= (or (= (hAPP int int (number_number_of int) min_1) _let_1) (= _let_0 _let_1)) (= _let_0 (hAPP int int (abs_abs int) Z))) ))) 17.51/17.08 ( pls ) 17.51/17.08 ( m ) 17.51/17.08 ( min_1 ) 17.51/17.08 ( s ) 17.51/17.08 ( s1 ) 17.51/17.08 ( t ) 17.51/17.08 ) 17.51/17.08 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((X $$unsorted)) (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))) ))) 17.51/17.08 ( (one_one real) ) 17.51/17.08 ) 17.51/17.08 (instantiation (let ((_let_0 (fun real real))) (forall ((X $$unsorted)) (= (hAPP real real (uminus_uminus real) (hAPP real real sin X)) (hAPP real real cos (hAPP real real (hAPP real _let_0 (plus_plus real) X) (hAPP real real (hAPP real _let_0 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))) )) 17.51/17.08 ( (zero_zero real) ) 17.51/17.08 ( pi ) 17.51/17.08 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.08 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 17.51/17.08 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 17.51/17.08 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 17.51/17.08 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 17.51/17.08 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 17.51/17.08 ) 17.51/17.08 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_124576 $$unsorted) (BOUND_VARIABLE_124577 $$unsorted)) (or (not (ring_11004092258visors X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_124577)) (not (= _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_124577) BOUND_VARIABLE_124576)))) )) 17.51/17.08 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 17.51/17.08 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 17.51/17.08 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 17.51/17.08 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 17.51/17.08 ) 17.51/17.08 (instantiation (let ((_let_0 (abs_abs X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_124649 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (= (hAPP X_a X_a _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_124649)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_124649))) )) 17.51/17.08 ( real, (one_one real) ) 17.51/17.08 ( 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)))) ) 17.51/17.08 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 17.51/17.08 ( int, pls ) 17.51/17.08 ( int, (one_one int) ) 17.51/17.08 ( int, min_1 ) 17.51/17.08 ( complex, ii ) 17.51/17.08 ( complex, (one_one complex) ) 17.51/17.08 ) 17.51/17.08 (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)))) ) 17.51/17.08 ( (zero_zero int), pi ) 17.51/17.08 ( (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)))) ) 17.51/17.08 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.08 ( (zero_zero int), skv_6 ) 17.51/17.08 ( (zero_zero int), skv_11 ) 17.51/17.08 ( (zero_zero int), skv_12 ) 17.51/17.08 ( (zero_zero int), skv_14 ) 17.51/17.08 ) 17.51/17.08 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (product_prod nat nat))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun nat _let_1))) (let ((_let_4 (product_Pair nat nat))) (let ((_let_5 (hAPP (fun _let_1 _let_2) _let_2 (accp _let_1) nat_gcd_rel))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool _let_5 (hAPP nat _let_1 (hAPP nat _let_3 _let_4 A0) A1)))) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool _let_5 (hAPP nat _let_1 (hAPP nat _let_3 _let_4 X_2) Y_2)))) (and (not (= (zero_zero nat) Y_2)) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 P_1 Y_2) (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) X_2) Y_2))))) (hBOOL (hAPP nat bool (hAPP nat _let_0 P_1 X_2) Y_2))) )) (hBOOL (hAPP nat bool (hAPP nat _let_0 P_1 A0) A1))) ))))))) 17.51/17.08 ( (ord_less nat), (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.08 ) 17.51/17.08 (instantiation (forall ((Z_1 $$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)))) ) 17.51/17.08 ( (zero_zero int) ) 17.51/17.08 ( pls ) 17.51/17.08 ( m ) 17.51/17.08 ( (one_one int) ) 17.51/17.08 ( min_1 ) 17.51/17.08 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.08 ( (hAPP int int (number_number_of int) min_1) ) 17.51/17.08 ( s ) 17.51/17.08 ( (hAPP int int (number_number_of int) pls) ) 17.51/17.08 ( s1 ) 17.51/17.08 ( t ) 17.51/17.08 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.51/17.08 ) 17.51/17.08 (instantiation (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (not (= (hAPP int int bit0 L_4) (hAPP int int bit1 K_4))) ) 17.51/17.08 ( pls, (hAPP int int bit1 pls) ) 17.51/17.08 ( (hAPP int int bit1 pls), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.51/17.08 ( (hAPP int int bit1 (hAPP int int bit1 pls)), pls ) 17.51/17.08 ( (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)) ) 17.51/17.08 ( (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 pls))) ) 17.51/17.08 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))), min_1 ) 17.51/17.08 ) 17.51/17.08 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_124720 $$unsorted) (BOUND_VARIABLE_124721 $$unsorted)) (or (not (semiring_div X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_124720) BOUND_VARIABLE_124721))) (= (ti X_a BOUND_VARIABLE_124721) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) (hAPP X_a X_a (hAPP X_a _let_0 (div_div X_a) BOUND_VARIABLE_124721) BOUND_VARIABLE_124720)) BOUND_VARIABLE_124720))) )) 17.51/17.08 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.51/17.09 ) 17.51/17.09 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_124758 $$unsorted) (BOUND_VARIABLE_124759 $$unsorted)) (or (not (ord X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_124758) BOUND_VARIABLE_124759)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_124758) (hAPP X_a _let_0 (ord_atMost X_a) BOUND_VARIABLE_124759))))) )) 17.51/17.09 ( real, (zero_zero real), pi ) 17.51/17.09 ( 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)))) ) 17.51/17.09 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.09 ( real, (zero_zero real), skv_6 ) 17.51/17.09 ( real, (zero_zero real), skv_11 ) 17.51/17.09 ( real, (zero_zero real), skv_12 ) 17.51/17.09 ( real, (zero_zero real), skv_14 ) 17.51/17.09 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.51/17.09 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.09 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.51/17.09 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.09 ( int, (zero_zero int), (one_one int) ) 17.51/17.09 ( int, (zero_zero int), min_1 ) 17.51/17.09 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.09 ( int, (zero_zero int), s ) 17.51/17.09 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 17.51/17.09 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.51/17.09 ( int, (zero_zero int), skv_3 ) 17.51/17.09 ( int, (zero_zero int), skv_9 ) 17.51/17.09 ( int, (one_one int), t ) 17.51/17.09 ( int, min_1, pls ) 17.51/17.09 ( int, min_1, min_1 ) 17.51/17.09 ) 17.51/17.09 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (fun (filter nat) bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_124790 $$unsorted) (BOUND_VARIABLE_124791 $$unsorted)) (or (not (metric_space X_a)) (= (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) R_2))) (not (forall ((No $$unsorted)) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) (hAPP nat X_a BOUND_VARIABLE_124790 N_2)) BOUND_VARIABLE_124791)) R_2))) )) ))) ) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_2 (hAPP (fun nat X_a) (fun X_a _let_2) (tendsto nat X_a) BOUND_VARIABLE_124790) BOUND_VARIABLE_124791) sequentially)))) )))) 17.51/17.09 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 17.51/17.09 ) 17.51/17.09 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124848 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_124848)) (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_124848)))) ) 17.51/17.09 ( real, (zero_zero nat) ) 17.51/17.09 ( real, (one_one nat) ) 17.51/17.09 ( int, (zero_zero nat) ) 17.51/17.09 ( int, (hAPP nat nat suc (zero_zero nat)) ) 17.51/17.09 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.09 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.51/17.09 ) 17.51/17.09 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (number_number_of int) K_4) (hAPP quickcheck_code_int int quickcheck_int_of (hAPP int quickcheck_code_int (number_number_of quickcheck_code_int) K_4))) ) 17.51/17.09 ( (zero_zero int) ) 17.51/17.09 ( pls ) 17.51/17.09 ( (hAPP int int bit1 pls) ) 17.51/17.09 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.51/17.09 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.09 ( (one_one int) ) 17.51/17.09 ( min_1 ) 17.51/17.09 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.51/17.09 ) 17.51/17.09 (instantiation (let ((_let_0 (one_one int))) (let ((_let_1 (hAPP int int (number_number_of int) min_1))) (let ((_let_2 (ti int N_1))) (let ((_let_3 (ti int Ma))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (= _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) Ma) N_1)) (or (and (= _let_0 _let_2) (= _let_0 _let_3)) (and (= _let_1 _let_2) (= _let_1 _let_3)))) ))))) 17.51/17.09 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 17.51/17.09 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 17.51/17.09 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 17.51/17.09 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1 ) 17.51/17.09 ) 17.51/17.09 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_124891 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_124891)) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_124891) _let_2)))) )))) 17.51/17.09 ( real, (zero_zero real) ) 17.51/17.09 ( rat, (zero_zero rat) ) 17.51/17.09 ) 17.51/17.09 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun int bool))) (let ((_let_2 (zero_zero int))) (forall ((U_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less_eq int) _let_2) U_1))) (= (hAPP int _let_1 (hAPP int (fun int _let_1) (ord_atLeastLessThan int) _let_2) U_1) (hAPP _let_0 _let_1 (hAPP (fun nat int) (fun _let_0 _let_1) (image nat int) (semiring_1_of_nat int)) (hAPP nat _let_0 (ord_lessThan nat) (hAPP int nat nat_1 U_1))))) )))) 17.51/17.09 ( (zero_zero int) ) 17.51/17.09 ( (one_one int) ) 17.51/17.09 ( min_1 ) 17.51/17.09 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.09 ( s ) 17.51/17.09 ( (hAPP int int (number_number_of int) pls) ) 17.51/17.09 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.51/17.09 ( skv_3 ) 17.51/17.09 ( skv_9 ) 17.51/17.09 ) 17.51/17.09 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_125004 $$unsorted) (BOUND_VARIABLE_125005 $$unsorted)) (or (not (ordere453448008miring X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_125005))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_125004))) (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_125005) BOUND_VARIABLE_125004)))) )) 17.51/17.09 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.09 ( 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))))) ) 17.51/17.09 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.09 ( 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)))) ) 17.51/17.09 ( 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))) ) 17.51/17.09 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.09 ( 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))) ) 17.51/17.09 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.51/17.09 ( complex, ii, ii ) 17.51/17.09 ( 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)) ) 17.51/17.09 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.09 ) 17.51/17.09 (instantiation (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))))) (forall ((N $$unsorted)) (or (hBOOL (hAPP nat bool prime N)) (not (hBOOL (hAPP nat bool _let_2 N))) (not (forall ((M_2 $$unsorted) (K_1 $$unsorted)) (or (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))) (not (hBOOL (hAPP nat bool _let_2 M_2)))) ))) )))) 17.51/17.09 ( (zero_zero nat) ) 17.51/17.09 ( (one_one nat) ) 17.51/17.09 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.09 ) 17.51/17.09 (instantiation (let ((_let_0 (product_Pair X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (= _let_0 (ti (fun X_a (fun X_b (product_prod X_a X_b))) _let_0)) )) 17.51/17.09 ( real, real ) 17.51/17.09 ( nat, nat ) 17.51/17.09 ( int, int ) 17.51/17.09 ( int, (product_prod int int) ) 17.51/17.09 ( quickcheck_code_int, quickcheck_code_int ) 17.51/17.09 ( (product_prod int int), (product_prod int int) ) 17.51/17.09 ( (product_prod nat nat), (product_prod nat nat) ) 17.51/17.09 ( code_code_numeral, code_code_numeral ) 17.51/17.09 ) 17.51/17.09 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (dvd_dvd nat))) (let ((_let_2 (fun nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_125062 $$unsorted) (BOUND_VARIABLE_125063 $$unsorted) (BOUND_VARIABLE_125064 $$unsorted)) (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_125064))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 BOUND_VARIABLE_125062) BOUND_VARIABLE_125063))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP nat X_a BOUND_VARIABLE_125064 BOUND_VARIABLE_125062)) (hAPP nat X_a BOUND_VARIABLE_125064 BOUND_VARIABLE_125063)))) )))) 17.51/17.09 ( int, (zero_zero nat), (zero_zero nat), (semiring_1_of_nat int) ) 17.51/17.09 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)), (semiring_1_of_nat int) ) 17.51/17.09 ( 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) ) 17.51/17.09 ( 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) ) 17.51/17.09 ) 17.51/17.09 (instantiation (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (times_times X_a))) (let ((_let_3 (plus_plus X_a))) (let ((_let_4 (inverse_inverse X_a))) (let ((_let_5 (hAPP X_a X_a _let_4 BOUND_VARIABLE_125124))) (let ((_let_6 (hAPP X_a X_a _let_4 BOUND_VARIABLE_125123))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_125123 $$unsorted) (BOUND_VARIABLE_125124 $$unsorted)) (or (not (field X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_125124)) (= _let_0 (ti X_a BOUND_VARIABLE_125123)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_3 _let_5) _let_6) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a _let_1 _let_3 BOUND_VARIABLE_125124) BOUND_VARIABLE_125123)) _let_5)) _let_6))) )))))))) 17.51/17.09 ( nat, (one_one nat), (one_one nat) ) 17.51/17.09 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 17.51/17.09 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.09 ) 17.51/17.09 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (forall ((X_2 $$unsorted)) (= (hAPP real real sin X_2) (hAPP _let_1 real (suminf real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) sin_coeff)) (hAPP real _let_1 (power_power real) X_2)))) )))) 17.51/17.09 ( (zero_zero real) ) 17.51/17.09 ( pi ) 17.51/17.09 ( (hAPP int real (number_number_of real) min_1) ) 17.51/17.09 ( (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)))) ) 17.51/17.09 ( (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) ) 17.51/17.09 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.51/17.09 ( (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))))) ) 17.51/17.09 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 17.51/17.09 ( (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))))) ) 17.51/17.09 ( (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)))) ) 17.51/17.09 ) 17.51/17.09 (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))) ) 17.51/17.09 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.09 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.09 ( (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))) ) 17.51/17.09 ( (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))) ) 17.51/17.09 ) 17.51/17.09 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (product_Pair int int))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (hAPP (fun _let_1 _let_4) _let_4 (accp _let_1) upto_rel))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool _let_5 (hAPP int _let_1 (hAPP int _let_2 _let_3 A0) A1)))) (not (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool _let_5 (hAPP int _let_1 (hAPP int _let_2 _let_3 I_2) J_1)))) (and (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) I_2) J_1)) (not (hBOOL (hAPP int bool (hAPP int _let_0 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_0 P_1 I_2) J_1))) )) (hBOOL (hAPP int bool (hAPP int _let_0 P_1 A0) A1))) ))))))) 17.51/17.10 ( (ord_less_eq int), (zero_zero int), (one_one int) ) 17.51/17.10 ( (ord_less_eq int), (zero_zero int), min_1 ) 17.51/17.10 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.51/17.10 ( (ord_less_eq int), (zero_zero int), s ) 17.51/17.10 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 17.51/17.10 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.51/17.10 ( (ord_less_eq int), (zero_zero int), skv_3 ) 17.51/17.10 ( (ord_less_eq int), (zero_zero int), skv_9 ) 17.51/17.10 ( (ord_less_eq int), (one_one int), t ) 17.51/17.10 ( (ord_less_eq int), min_1, pls ) 17.51/17.10 ( (ord_less_eq int), min_1, min_1 ) 17.51/17.10 ( (ord_less int), (zero_zero int), (zero_zero int) ) 17.51/17.10 ( (ord_less int), (zero_zero int), (one_one int) ) 17.51/17.10 ( (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))) ) 17.51/17.10 ( (ord_less int), (zero_zero int), min_1 ) 17.51/17.10 ( (ord_less int), min_1, (zero_zero int) ) 17.51/17.10 ( (ord_less int), min_1, min_1 ) 17.51/17.10 ( (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))) ) 17.51/17.10 ( (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.51/17.10 ( (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.69/17.10 ( (ord_less int), t, (zero_zero int) ) 17.69/17.10 ( (ord_less int), t, (one_one int) ) 17.69/17.10 ( (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))) ) 17.69/17.10 ( (ord_less int), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.10 ( (ord_less int), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.10 ( (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.69/17.10 ( quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 17.69/17.10 ( (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))) ) 17.69/17.10 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.10 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.10 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.10 ( (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))) ) 17.69/17.10 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.10 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.10 ) 17.69/17.10 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_125217 $$unsorted)) (or (not (field_char_0 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_125217)) (field_char_0_Rats X_a)))) )) 17.69/17.10 ( real, (zero_zero nat) ) 17.69/17.10 ( real, (one_one nat) ) 17.69/17.10 ( int, (zero_zero nat) ) 17.69/17.10 ( int, (hAPP nat nat suc (zero_zero nat)) ) 17.69/17.10 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.10 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.69/17.10 ) 17.69/17.10 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_125255)))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_125255) _let_2)))) (let ((_let_6 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_125253))) (let ((_let_7 (hAPP X_a _let_0 _let_1 _let_6))) (let ((_let_8 (hAPP X_a X_a (hAPP X_a _let_3 (times_times X_a) _let_6) BOUND_VARIABLE_125255))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_125253 $$unsorted) (BOUND_VARIABLE_125254 $$unsorted) (BOUND_VARIABLE_125255 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (not (number X_a)) (= (and (or _let_4 (and (or _let_5 (hBOOL (hAPP X_a bool _let_7 _let_2))) (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_125254) _let_8))))) (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_8) BOUND_VARIABLE_125254)))) (hBOOL (hAPP X_a bool _let_7 (hAPP X_a X_a (hAPP X_a _let_3 (inverse_divide X_a) BOUND_VARIABLE_125254) BOUND_VARIABLE_125255))))) )))))))))) 17.69/17.10 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (zero_zero real), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.69/17.10 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.69/17.10 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.69/17.10 ) 17.69/17.10 (instantiation (let ((_let_0 (hAPP int (fun int bool) (dvd_dvd int) K_4))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (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))) )) 17.69/17.10 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 17.69/17.10 ) 17.69/17.10 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int int (number_number_of int) min_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_1) zOdd))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) X_1))) (= _let_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) _let_1) (hAPP int nat nat_1 X_1)))) ))) 17.69/17.10 ( (zero_zero int) ) 17.69/17.10 ( (one_one int) ) 17.69/17.10 ( min_1 ) 17.69/17.10 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.10 ( s ) 17.69/17.10 ( (hAPP int int (number_number_of int) pls) ) 17.69/17.10 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.69/17.10 ( skv_3 ) 17.69/17.10 ( skv_9 ) 17.69/17.10 ) 17.69/17.10 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_125316 $$unsorted) (BOUND_VARIABLE_125317 $$unsorted)) (or (not (linorder X_a)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_125316) BOUND_VARIABLE_125317)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_125317) BOUND_VARIABLE_125316))) )) 17.69/17.10 ( real, (zero_zero real), pi ) 17.69/17.10 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.10 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.10 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.10 ( real, (zero_zero real), skv_2 ) 17.69/17.10 ( real, (zero_zero real), skv_10 ) 17.69/17.10 ( real, (zero_zero real), skv_13 ) 17.69/17.10 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.10 ( real, pi, (zero_zero real) ) 17.69/17.10 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.10 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.10 ( 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)))) ) 17.69/17.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 17.69/17.10 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.69/17.10 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.10 ( 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) ) 17.69/17.10 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.69/17.10 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.69/17.10 ( 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 ) 17.69/17.10 ( real, skv_6, (zero_zero real) ) 17.69/17.10 ( real, skv_11, (zero_zero real) ) 17.69/17.10 ( real, skv_12, (zero_zero real) ) 17.69/17.10 ( real, skv_14, (zero_zero real) ) 17.69/17.10 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.10 ( int, (zero_zero int), (zero_zero int) ) 17.69/17.10 ( int, (zero_zero int), (one_one int) ) 17.69/17.10 ( 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))) ) 17.69/17.11 ( int, (zero_zero int), min_1 ) 17.69/17.11 ( int, pls, min_1 ) 17.69/17.11 ( int, (one_one int), (zero_zero int) ) 17.69/17.11 ( int, min_1, (zero_zero int) ) 17.69/17.11 ( int, min_1, min_1 ) 17.69/17.11 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 17.69/17.11 ( int, s, (zero_zero int) ) 17.69/17.11 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.11 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.69/17.11 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.69/17.11 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 17.69/17.11 ( int, t, (zero_zero int) ) 17.69/17.11 ( int, t, (one_one int) ) 17.69/17.11 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.11 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 17.69/17.11 ( int, skv_3, (zero_zero int) ) 17.69/17.11 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.11 ( int, skv_9, (zero_zero int) ) 17.69/17.11 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.11 ) 17.69/17.11 (instantiation (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))) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 I_1) J_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) K_4))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int _let_2 I_1)) (hAPP int int _let_2 J_2)))) )))) 17.69/17.11 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1, (zero_zero int) ) 17.69/17.11 ) 17.69/17.11 (instantiation (let ((_let_0 (fun nat bool))) (forall ((S $$unsorted)) (= (hBOOL (hAPP _let_0 bool (finite_finite_1 nat) S)) (not (forall ((K_1 $$unsorted)) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) S) (hAPP nat _let_0 (ord_atMost nat) K_1)))) ))) )) 17.69/17.11 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 17.69/17.11 ) 17.69/17.11 (instantiation (let ((_let_0 (fun int bool))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_2) B_1) (zero_zero int))) (= (ti int B_1) (ti int A_2))) )) 17.69/17.11 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 17.69/17.11 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.11 ( s1, s ) 17.69/17.11 ( s1, skv_3 ) 17.69/17.11 ( s1, skv_9 ) 17.69/17.11 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 17.69/17.11 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 17.69/17.11 ) 17.69/17.11 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (ord_less int))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (zero_zero int)) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 A_1) P_5))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP int int (hAPP int _let_1 (times_times int) A_1) (hAPP int int (hAPP int _let_1 inv P_5) A_1))) (one_one int)) P_5))) )))) 17.69/17.11 ( (zero_zero int), (zero_zero int) ) 17.69/17.11 ( (zero_zero int), (one_one int) ) 17.69/17.11 ( (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))) ) 17.69/17.11 ( (zero_zero int), min_1 ) 17.69/17.11 ( min_1, (zero_zero int) ) 17.69/17.11 ( min_1, min_1 ) 17.69/17.11 ( 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))) ) 17.69/17.11 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.69/17.11 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.69/17.11 ( t, (zero_zero int) ) 17.69/17.11 ( t, (one_one int) ) 17.69/17.11 ( 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))) ) 17.69/17.11 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.11 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.11 ) 17.69/17.11 (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))) ) 17.69/17.11 ( (one_one rat) ) 17.69/17.11 ) 17.69/17.11 (instantiation (let ((_let_0 (fun nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_125420 $$unsorted)) (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_125420)) (one_one real)))) (hBOOL (hAPP _let_0 bool (summable X_a) (hAPP X_a _let_0 (power_power X_a) BOUND_VARIABLE_125420)))) )) 17.69/17.11 ( real, (hAPP int real (number_number_of real) min_1) ) 17.69/17.11 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.11 ( int, s ) 17.69/17.11 ( int, s1 ) 17.69/17.11 ( int, skv_8 ) 17.69/17.11 ( complex, ii ) 17.69/17.11 ) 17.69/17.11 (instantiation (forall ((N $$unsorted)) (= (hAPP real real cos (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP nat real (real_1 nat) N)) pi)) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) N)) ) 17.69/17.11 ( (zero_zero nat) ) 17.69/17.11 ( (one_one nat) ) 17.69/17.11 ) 17.69/17.11 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N))) (= (zero_zero nat) (hAPP nat nat (hAPP nat (fun nat nat) (div_div nat) M) N))) ) 17.69/17.11 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.11 ) 17.69/17.11 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((N $$unsorted) (P_5 $$unsorted)) (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))) ))) 17.69/17.11 ( (zero_zero int), (zero_zero int) ) 17.69/17.11 ( (zero_zero int), (one_one int) ) 17.69/17.11 ( (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))) ) 17.69/17.11 ( (zero_zero int), min_1 ) 17.69/17.11 ( min_1, (zero_zero int) ) 17.69/17.11 ( min_1, min_1 ) 17.69/17.11 ( 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))) ) 17.69/17.11 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.69/17.11 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.69/17.11 ( t, (zero_zero int) ) 17.69/17.11 ( t, (one_one int) ) 17.69/17.11 ( 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))) ) 17.69/17.11 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.11 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.11 ) 17.69/17.11 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun X_a bool))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool (hAPP X_a (fun _let_1 bool) (member X_a) X_1) A_3))) (not (= (ti X_b B_1) (hAPP X_a X_b F X_1))) (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) B_1) (hAPP _let_1 _let_0 (hAPP (fun X_a X_b) (fun _let_1 _let_0) (image X_a X_b) F) A_3)))) ))) 17.69/17.11 ( int, int, min_1, (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int), zEven ) 17.69/17.11 ) 17.69/17.11 (instantiation (let ((_let_0 (one_one int))) (forall ((A_1 $$unsorted)) (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))) )) 17.69/17.11 ( s ) 17.69/17.11 ( s1 ) 17.69/17.11 ( skv_8 ) 17.69/17.11 ) 17.69/17.11 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (hAPP int _let_0 _let_1 _let_2))) (let ((_let_4 (fun int int))) (let ((_let_5 (ord_less int))) (let ((_let_6 (hAPP int int (hAPP int _let_4 (plus_plus int) (hAPP int int (hAPP int _let_4 (times_times int) B_5) Q_5)) R_5))) (forall ((B $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted) (B_5 $$unsorted) (Q_5 $$unsorted) (R_5 $$unsorted)) (or (not (= (hAPP int int (hAPP int _let_4 (plus_plus int) (hAPP int int (hAPP int _let_4 (times_times int) B) Q_3)) R_4) _let_6)) (not (hBOOL (hAPP int bool _let_3 _let_6))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_5 R_5) B_5))) (not (hBOOL (hAPP int bool _let_3 R_4))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_5 _let_2) B_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B_5) B))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Q_3) Q_5))) )))))))) 17.69/17.11 ( (hAPP int int (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) ) 17.69/17.11 ) 17.69/17.11 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (zero_zero nat))) (let ((_let_3 (hAPP nat _let_1 root N_1))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_2) N_1))) (not (hBOOL (hAPP nat bool (even_odd_even nat) N_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X_1) (zero_zero real)))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) _let_3) X_1) (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) N_1))) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real _let_3 X_1)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N_1) (hAPP nat nat suc _let_2)))))))) ))))) 17.69/17.11 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.11 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.11 ( (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))) ) 17.69/17.11 ( (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))) ) 17.69/17.11 ) 17.69/17.11 (instantiation (let ((_let_0 (product_prod int int))) (forall ((K_4 $$unsorted)) (= (hAPP rat rat (hAPP rat (fun rat rat) (inverse_divide rat) (one_one rat)) (hAPP int rat (number_number_of rat) K_4)) (hAPP _let_0 rat frct (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) (one_one int)) (hAPP int int (number_number_of int) K_4)))) )) 17.69/17.11 ( pls ) 17.69/17.11 ( (hAPP int int bit1 pls) ) 17.69/17.11 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.69/17.11 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.11 ( min_1 ) 17.69/17.11 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.69/17.11 ) 17.69/17.11 (instantiation (forall ((V $$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))) ) 17.69/17.12 ( pls ) 17.69/17.12 ( (hAPP int int bit1 pls) ) 17.69/17.12 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.69/17.12 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.12 ( min_1 ) 17.69/17.12 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.69/17.12 ) 17.69/17.12 (instantiation (let ((_let_0 (norm_norm X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_125673 $$unsorted) (BOUND_VARIABLE_125674 $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_125673) BOUND_VARIABLE_125674))) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP X_a real _let_0 BOUND_VARIABLE_125673)) BOUND_VARIABLE_125674)))) )) 17.69/17.12 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.12 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.12 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.12 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.12 ) 17.69/17.12 (instantiation (forall ((V $$unsorted)) (= (zero_zero real) (hAPP complex real im (hAPP int complex (number_number_of complex) V))) ) 17.69/17.12 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.69/17.12 ( min_1 ) 17.69/17.12 ) 17.69/17.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125712 $$unsorted)) (or (not (semiring_div X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_125712)) (= (one_one X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (div_div X_a) BOUND_VARIABLE_125712) BOUND_VARIABLE_125712))) ) 17.69/17.12 ( bool, fFalse ) 17.69/17.12 ( bool, fTrue ) 17.69/17.12 ( real, pi ) 17.69/17.12 ( (fun nat bool), (even_odd_even nat) ) 17.69/17.12 ( (fun nat bool), prime ) 17.69/17.12 ( (fun nat nat), suc ) 17.69/17.12 ( (fun nat nat), (fact_fact nat) ) 17.69/17.12 ( (fun nat nat), (size_size nat) ) 17.69/17.12 ( (fun nat nat), fact ) 17.69/17.12 ( (fun nat nat), nat_size ) 17.69/17.12 ( int, pls ) 17.69/17.12 ( int, m ) 17.69/17.12 ( 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code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.69/17.12 ( (fun int real), (real_1 int) ) 17.69/17.12 ( (fun complex nat), (size_size complex) ) 17.69/17.12 ( (fun complex nat), complex_size ) 17.69/17.12 ( (fun int (list int)), quickc666637781d_zero ) 17.69/17.12 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.69/17.12 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.69/17.12 ( (fun (product_prod int int) rat), frct ) 17.69/17.12 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.69/17.12 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.69/17.12 ( (fun (fun nat rat) bool), vanishes ) 17.69/17.12 ( (fun int (fun int rat)), fract ) 17.69/17.12 ( (fun code_code_numeral int), code_int_of ) 17.69/17.12 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.69/17.12 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.69/17.12 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.69/17.12 ( (fun real (fun real complex)), complex_1 ) 17.69/17.12 ( (fun real (fun real complex)), rcis ) 17.69/17.12 ( (fun int (fun nat nat)), nat_aux ) 17.69/17.12 ( (fun rat real), ratreal ) 17.69/17.12 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.69/17.12 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.69/17.12 ( (fun rat (product_prod int int)), quotient_of ) 17.69/17.12 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.69/17.12 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.69/17.12 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.69/17.12 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.69/17.12 ) 17.69/17.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125731 $$unsorted)) (or (not (field X_a)) (= (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_125731) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) (one_one X_a)) BOUND_VARIABLE_125731))) ) 17.69/17.12 ( real, (zero_zero real) ) 17.69/17.12 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.12 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 17.69/17.12 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.12 ( 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))))))))) ) 17.69/17.12 ( complex, ii ) 17.69/17.12 ) 17.69/17.12 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (fun int int))) (let ((_let_3 (hAPP int int (hAPP int _let_2 (plus_plus int) A_1) B))) (forall ((B $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_3) _let_1))) (= _let_3 (hAPP int int (hAPP int _let_2 (div_mod int) A_1) B))) ))))) 17.69/17.12 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 17.69/17.12 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.12 ) 17.69/17.12 (instantiation (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_125750 $$unsorted)) (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_125750)) BOUND_VARIABLE_125750) sequentially))) ))) 17.69/17.12 ( bool, fTrue ) 17.69/17.12 ) 17.69/17.12 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_125767 $$unsorted) (BOUND_VARIABLE_125768 $$unsorted) (BOUND_VARIABLE_125769 $$unsorted)) (or (not (order X_a)) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a BOUND_VARIABLE_125769 N_2)) (hAPP nat X_a BOUND_VARIABLE_125769 (hAPP nat nat suc N_2)))) )) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_125767) BOUND_VARIABLE_125768)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a BOUND_VARIABLE_125769 BOUND_VARIABLE_125767)) (hAPP nat X_a BOUND_VARIABLE_125769 BOUND_VARIABLE_125768))))) ))) 17.69/17.12 ( int, (zero_zero nat), (zero_zero nat), (semiring_1_of_nat int) ) 17.69/17.12 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)), (semiring_1_of_nat int) ) 17.69/17.12 ) 17.69/17.12 (instantiation (let ((_let_0 (sums X_a))) (forall ((X_a $$unsorted)) (or (not (comm_monoid_add X_a)) (not (topological_space X_a)) (= _let_0 (ti (fun (fun nat X_a) (fun X_a bool)) _let_0))) )) 17.69/17.12 ( bool ) 17.69/17.12 ( real ) 17.69/17.12 ( nat ) 17.69/17.12 ( (fun nat bool) ) 17.69/17.12 ( (fun nat nat) ) 17.69/17.12 ( int ) 17.69/17.12 ( (fun int bool) ) 17.69/17.12 ( (fun real real) ) 17.69/17.12 ( complex ) 17.69/17.12 ( (fun int int) ) 17.69/17.12 ( rat ) 17.69/17.12 ( (fun bool bool) ) 17.69/17.12 ( quickcheck_code_int ) 17.69/17.12 ( (fun nat (fun nat bool)) ) 17.69/17.12 ( (product_prod real real) ) 17.69/17.12 ( (product_prod int int) ) 17.69/17.12 ( (fun nat (product_prod int int)) ) 17.69/17.12 ( (filter real) ) 17.69/17.12 ( (filter nat) ) 17.69/17.12 ( (product_prod nat nat) ) 17.69/17.12 ( (fun (product_prod nat nat) bool) ) 17.69/17.12 ( (fun nat (fun (product_prod nat nat) bool)) ) 17.69/17.12 ( (fun nat (product_prod nat nat)) ) 17.69/17.12 ( code_code_numeral ) 17.69/17.12 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 17.69/17.12 ( (fun nat rat) ) 17.69/17.12 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 17.69/17.12 ) 17.69/17.12 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool _let_0 X))) (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt X)))) )) 17.69/17.12 ( (zero_zero real) ) 17.69/17.12 ( (one_one real) ) 17.69/17.12 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.12 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.69/17.12 ) 17.69/17.12 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (forall ((X $$unsorted)) (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)))) )))) 17.69/17.12 ( (zero_zero real) ) 17.69/17.12 ( (one_one real) ) 17.69/17.12 ( pi ) 17.69/17.12 ( (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)))) ) 17.69/17.12 ( (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) ) 17.69/17.12 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 17.69/17.12 ( (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 (hAPP int int bit1 pls))))) ) 17.69/17.12 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 17.69/17.12 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.12 ( (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 bit0 (hAPP int int bit1 pls))))) ) 17.69/17.12 ( (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)))) ) 17.69/17.12 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 17.69/17.12 ) 17.69/17.12 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_125891 $$unsorted) (BOUND_VARIABLE_125892 $$unsorted)) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_125891) (hAPP X_a X_a _let_2 BOUND_VARIABLE_125892))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_125892) (hAPP X_a X_a _let_2 BOUND_VARIABLE_125891))))) )))) 17.69/17.12 ( int, (zero_zero int), pls ) 17.69/17.12 ( int, (zero_zero int), (one_one int) ) 17.69/17.12 ( int, pls, (zero_zero int) ) 17.69/17.12 ( int, pls, min_1 ) 17.69/17.12 ( int, pls, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.69/17.12 ( int, pls, t ) 17.69/17.12 ( int, (one_one int), (zero_zero int) ) 17.69/17.12 ( int, (one_one int), min_1 ) 17.69/17.12 ( int, min_1, pls ) 17.69/17.12 ( int, min_1, (one_one int) ) 17.69/17.12 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), pls ) 17.69/17.12 ( int, t, pls ) 17.69/17.12 ) 17.69/17.12 (instantiation (let ((_let_0 (hAPP int (fun int bool) (dvd_dvd int) P_5))) (forall ((M $$unsorted) (N $$unsorted) (P_5 $$unsorted)) (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 M)) (hBOOL (hAPP int bool _let_0 N))) )) 17.69/17.12 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.12 ) 17.69/17.12 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (times_times int) Z_1) (one_one int)) (ti int Z_1)) ) 17.69/17.12 ( pls ) 17.69/17.12 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.12 ( m ) 17.69/17.12 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.12 ( min_1 ) 17.69/17.12 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.12 ( s ) 17.69/17.12 ( s1 ) 17.69/17.12 ( t ) 17.69/17.12 ) 17.69/17.12 (instantiation (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_126017 $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (norm_norm X_a) BOUND_VARIABLE_126017)) (one_one real)))) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 (fun X_a _let_0) (tendsto nat X_a) (hAPP X_a _let_1 (power_power X_a) BOUND_VARIABLE_126017)) (zero_zero X_a)) sequentially))) ))) 17.69/17.13 ( real, (hAPP int real (number_number_of real) min_1) ) 17.69/17.13 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.13 ( int, s ) 17.69/17.13 ( int, s1 ) 17.69/17.13 ( int, skv_8 ) 17.69/17.13 ( complex, ii ) 17.69/17.13 ) 17.69/17.13 (instantiation (let ((_let_0 (uminus_uminus real))) (let ((_let_1 (hAPP nat (fun real real) root N))) (forall ((X $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (hAPP real real _let_1 (hAPP real real _let_0 X)) (hAPP real real _let_0 (hAPP real real _let_1 X)))) ))) 17.69/17.13 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.13 ) 17.69/17.13 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (ring_1_Ints X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_126050 $$unsorted) (BOUND_VARIABLE_126051 $$unsorted)) (or (not (ring_1 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_126051) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_126050) _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_126051) BOUND_VARIABLE_126050)) _let_3))) ))))) 17.69/17.13 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.13 ( 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))))) ) 17.69/17.13 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.13 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.13 ( 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 (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.13 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.13 ( 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))) ) 17.69/17.13 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.13 ( complex, ii, ii ) 17.69/17.13 ( 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)) ) 17.69/17.13 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.13 ) 17.69/17.13 (instantiation (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (hAPP int nat (number_number_of nat) BOUND_VARIABLE_126117))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_126116 $$unsorted) (BOUND_VARIABLE_126117 $$unsorted)) (or (not (power X_a)) (not (mult_zero X_a)) (not (no_zero_divisors X_a)) (not (zero_neq_one X_a)) (= (and (not (= (zero_zero nat) _let_1)) (= _let_0 (ti X_a BOUND_VARIABLE_126116))) (= _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_126116) _let_1)))) ))) 17.69/17.13 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.69/17.13 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.69/17.13 ( int, skv_8, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.69/17.13 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.69/17.13 ) 17.69/17.13 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (ord_less real))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (hAPP real real (hAPP real _let_1 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_3))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_3) (fun _let_0 _let_6) (combb bool _let_3 real) fconj))) (let ((_let_10 (combc real real bool))) (forall ((Y_1 $$unsorted)) (= (hAPP real real arctan Y_1) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_2 (hAPP real real (uminus_uminus real) _let_4)))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_2) _let_4))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_1 _let_5 (hAPP _let_5 (fun _let_1 _let_5) (combb real _let_0 real) (fequal real)) tan)) Y_1))))) )))))))))))) 17.69/17.13 ( (zero_zero real) ) 17.69/17.13 ( (one_one real) ) 17.69/17.13 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 17.69/17.13 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 17.69/17.13 ) 17.69/17.13 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (uminus_uminus _let_0))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (= (hAPP _let_0 _let_0 _let_1 (hAPP _let_0 _let_0 _let_1 A_3)) (ti _let_0 A_3)) ))) 17.69/17.13 ( bool, fNot ) 17.69/17.13 ( nat, (even_odd_even nat) ) 17.69/17.13 ( nat, prime ) 17.69/17.13 ( int, zprime ) 17.69/17.13 ( int, nat_neg ) 17.69/17.13 ( int, zEven ) 17.69/17.13 ( int, nat_is_nat ) 17.69/17.13 ( int, zOdd ) 17.69/17.13 ( int, (even_odd_even int) ) 17.69/17.13 ( int, twoSqu1091635170sum2sq ) 17.69/17.13 ( (fun int bool), nat_nat_set ) 17.69/17.13 ( (product_prod int int), frac_1 ) 17.69/17.13 ( (product_prod nat nat), pred_nat ) 17.69/17.13 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_less ) 17.69/17.13 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_leq ) 17.69/17.13 ( (fun nat rat), vanishes ) 17.69/17.13 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), ratrel ) 17.69/17.13 ) 17.69/17.13 (instantiation (let ((_let_0 (of_real X_a))) (forall ((X_a $$unsorted)) (or (not (real_algebra_1 X_a)) (= _let_0 (ti (fun real X_a) _let_0))) )) 17.69/17.13 ( bool ) 17.69/17.13 ( real ) 17.69/17.13 ( nat ) 17.69/17.13 ( (fun int bool) ) 17.69/17.13 ( (fun real bool) ) 17.69/17.13 ( (fun real real) ) 17.69/17.13 ( complex ) 17.69/17.13 ( (fun nat real) ) 17.69/17.13 ( (fun bool bool) ) 17.69/17.13 ( (fun int (fun int bool)) ) 17.69/17.13 ( (fun (filter real) bool) ) 17.69/17.13 ( (fun (filter nat) bool) ) 17.69/17.13 ( (fun real complex) ) 17.69/17.13 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 17.69/17.13 ( (fun nat (product_prod real real)) ) 17.69/17.13 ( (fun real (fun nat (product_prod real real))) ) 17.69/17.13 ( (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 17.69/17.13 ( (fun int (fun int (fun bool bool))) ) 17.69/17.13 ( (fun (fun int (fun int real)) (fun int (fun int bool))) ) 17.69/17.13 ( (fun (fun int real) (fun int bool)) ) 17.69/17.13 ( (fun int (fun nat bool)) ) 17.69/17.13 ( (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 17.69/17.13 ( (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 17.69/17.13 ( (fun int (fun nat (fun bool bool))) ) 17.69/17.13 ( (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 17.69/17.13 ( (fun (fun nat real) (fun nat bool)) ) 17.69/17.13 ) 17.69/17.13 (instantiation (let ((_let_0 (fun X_b X_b))) (let ((_let_1 (plus_plus X_b))) (let ((_let_2 (times_times X_b))) (let ((_let_3 (hAPP int X_b (number_number_of X_b) BOUND_VARIABLE_126178))) (forall ((X_b $$unsorted) (BOUND_VARIABLE_126176 $$unsorted) (BOUND_VARIABLE_126177 $$unsorted) (BOUND_VARIABLE_126178 $$unsorted)) (or (not (number X_b)) (not (semiring X_b)) (= (hAPP X_b X_b (hAPP X_b _let_0 _let_2 (hAPP X_b X_b (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_126176) BOUND_VARIABLE_126177)) _let_3) (hAPP X_b X_b (hAPP X_b _let_0 _let_1 (hAPP X_b X_b (hAPP X_b _let_0 _let_2 BOUND_VARIABLE_126176) _let_3)) (hAPP X_b X_b (hAPP X_b _let_0 _let_2 BOUND_VARIABLE_126177) _let_3)))) ))))) 17.69/17.13 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), pls ) 17.69/17.13 ) 17.69/17.13 (instantiation (let ((_let_0 (one_one real))) (forall ((A_1 $$unsorted)) (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))) )) 17.69/17.13 ( pi ) 17.69/17.13 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.13 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.13 ( skv_2 ) 17.69/17.13 ( skv_10 ) 17.69/17.13 ( skv_13 ) 17.69/17.13 ) 17.69/17.13 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_2) B_1) Ma)) (not (forall ((K_1 $$unsorted)) (not (= (ti int B_1) (hAPP int int (hAPP int _let_1 (plus_plus int) A_2) (hAPP int int (hAPP int _let_1 (times_times int) Ma) K_1)))) ))) ))) 17.69/17.13 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.13 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (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))) ) 17.69/17.13 ( 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))) ) 17.69/17.13 ( s1, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.13 ( s1, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.13 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.13 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.13 ) 17.69/17.13 (instantiation (let ((_let_0 (product_prod int int))) (forall ((A_1 $$unsorted) (B $$unsorted)) (or (not (= (hAPP rat _let_0 quotient_of A_1) (hAPP rat _let_0 quotient_of B))) (= A_1 B)) )) 17.69/17.13 ( (zero_zero rat), (zero_zero rat) ) 17.69/17.13 ( (zero_zero rat), (one_one rat) ) 17.69/17.13 ( (one_one rat), (zero_zero rat) ) 17.69/17.13 ) 17.69/17.13 (instantiation (let ((_let_0 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_126267 $$unsorted) (BOUND_VARIABLE_126268 $$unsorted)) (or (not (number_ring X_a)) (not (ring_char_0 X_a)) (= (= (ti int BOUND_VARIABLE_126267) (ti int BOUND_VARIABLE_126268)) (= (hAPP int X_a _let_0 BOUND_VARIABLE_126267) (hAPP int X_a _let_0 BOUND_VARIABLE_126268)))) )) 17.69/17.13 ( real, s, min_1 ) 17.69/17.13 ( int, m, m ) 17.69/17.13 ( int, m, t ) 17.69/17.13 ( complex, min_1, min_1 ) 17.69/17.13 ( complex, min_1, s ) 17.69/17.13 ( rat, t, m ) 17.69/17.13 ) 17.69/17.13 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_126287 $$unsorted) (BOUND_VARIABLE_126288 $$unsorted)) (or (not (ordered_ab_group_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_126287) BOUND_VARIABLE_126288))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_126288)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_126287)))) )))) 17.69/17.13 ( real, (zero_zero real), pi ) 17.69/17.13 ( 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)))) ) 17.69/17.13 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.13 ( real, (zero_zero real), skv_6 ) 17.69/17.13 ( real, (zero_zero real), skv_11 ) 17.69/17.13 ( real, (zero_zero real), skv_12 ) 17.69/17.13 ( real, (zero_zero real), skv_14 ) 17.69/17.13 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.69/17.13 ( 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))) ) 17.69/17.13 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.69/17.13 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.13 ( int, (zero_zero int), (one_one int) ) 17.69/17.13 ( int, (zero_zero int), min_1 ) 17.69/17.13 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.13 ( int, (zero_zero int), s ) 17.69/17.13 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 17.69/17.13 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.69/17.13 ( int, (zero_zero int), skv_3 ) 17.69/17.13 ( int, (zero_zero int), skv_9 ) 17.69/17.13 ( int, pls, pls ) 17.69/17.13 ( int, pls, (one_one int) ) 17.69/17.13 ( int, (one_one int), pls ) 17.69/17.13 ( int, (one_one int), (one_one int) ) 17.69/17.13 ( int, (one_one int), t ) 17.69/17.13 ( int, min_1, pls ) 17.69/17.13 ( int, min_1, min_1 ) 17.69/17.13 ) 17.69/17.13 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (div_mod X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_126311 $$unsorted) (BOUND_VARIABLE_126312 $$unsorted)) (or (not (semiring_div X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_126311) BOUND_VARIABLE_126312)) BOUND_VARIABLE_126312) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_126311) BOUND_VARIABLE_126312))) ))) 17.69/17.13 ( nat, (one_one nat), (one_one nat) ) 17.69/17.13 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 17.69/17.13 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 17.69/17.14 ) 17.69/17.14 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_126339 $$unsorted) (BOUND_VARIABLE_126340 $$unsorted)) (or (not (linordered_idom X_a)) (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_126340)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_126339) BOUND_VARIABLE_126340))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_126339)))) )) 17.69/17.14 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.14 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.14 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.14 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.14 ) 17.69/17.14 (instantiation (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_126407 $$unsorted) (BOUND_VARIABLE_126408 $$unsorted)) (or (not (comm_ring_1 X_a)) (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_126408)) (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_126407)) BOUND_VARIABLE_126408) (hAPP X_a X_a _let_0 (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_126407) BOUND_VARIABLE_126408)))) )))) 17.69/17.14 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.14 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.14 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.14 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.14 ) 17.69/17.14 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_126495 $$unsorted)) (or (not (monoid_mult X_a)) (= (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_126495) (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls)))) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_126495) BOUND_VARIABLE_126495)) BOUND_VARIABLE_126495))) ))) 17.69/17.14 ( real, (hAPP int real (number_number_of real) min_1) ) 17.69/17.14 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.14 ( int, s ) 17.69/17.14 ( int, s1 ) 17.69/17.14 ( int, skv_8 ) 17.69/17.14 ( complex, ii ) 17.69/17.14 ) 17.69/17.14 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (number_number_of nat))) (let ((_let_3 (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 V_1) V_2)))) (forall ((V_1 $$unsorted) (V_2 $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP int nat _let_2 V_1)) (hAPP int nat _let_2 V_2))) (and _let_3 (or (not _let_3) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 pls) V_2))))) ))))) 17.69/17.14 ( (zero_zero int), (zero_zero int) ) 17.69/17.14 ( (zero_zero int), (one_one int) ) 17.69/17.14 ( (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))) ) 17.69/17.14 ( (zero_zero int), min_1 ) 17.69/17.14 ( pls, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.69/17.14 ( min_1, (zero_zero int) ) 17.69/17.14 ( min_1, min_1 ) 17.69/17.14 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.14 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.69/17.14 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.69/17.14 ( t, (zero_zero int) ) 17.69/17.14 ( t, (one_one int) ) 17.69/17.14 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.14 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.14 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.14 ) 17.69/17.14 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP nat int (hAPP int (fun nat int) (power_power int) X_1) N_1)) zOdd)) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_1) zOdd)))) )))) 17.69/17.14 ( s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.14 ( s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.14 ( skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.14 ) 17.69/17.14 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_126546 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_126546) BOUND_VARIABLE_126546) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_126546) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls)))))) )) 17.69/17.14 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.14 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.14 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 17.69/17.14 ( nat, (one_one nat) ) 17.69/17.14 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.14 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 17.69/17.14 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.14 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.14 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.14 ( complex, ii ) 17.69/17.14 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.14 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 17.69/17.14 ) 17.69/17.14 (instantiation (forall ((N_1 $$unsorted) (P_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool P_1 (zero_zero nat)))) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool P_1 N_2))) (hBOOL (hAPP nat bool P_1 (hAPP nat nat suc N_2)))) )) (hBOOL (hAPP nat bool P_1 N_1))) ) 17.69/17.14 ( (zero_zero nat), (even_odd_even nat) ) 17.69/17.14 ( (zero_zero nat), prime ) 17.69/17.14 ( (one_one nat), (even_odd_even nat) ) 17.69/17.14 ( (one_one nat), prime ) 17.69/17.14 ( (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)) ) 17.69/17.14 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), prime ) 17.69/17.14 ) 17.69/17.14 (instantiation (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))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted)) (or (and (not (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_1 _let_1 _let_3 Q_1)))) (not (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_1 _let_1 _let_3 P_1))))) (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_1 _let_1 _let_3 (hAPP _let_1 _let_1 (hAPP _let_4 (fun _let_1 _let_1) (combs X_a bool bool) (hAPP _let_1 _let_4 (hAPP (fun bool _let_0) (fun _let_1 _let_4) (combb bool _let_0 X_a) fconj) P_1)) Q_1))))) )))))) 17.69/17.14 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP real _let_0 (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))), (let ((_let_0 (fun real (fun real bool)))) (hAPP real (fun real bool) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 17.69/17.14 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun real _let_2))) (let ((_let_5 (combc real real bool))) (hAPP _let_0 _let_0 (hAPP _let_4 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_4 (hAPP (fun bool _let_2) (fun _let_0 _let_4) (combb bool _let_2 real) fconj) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))))))), (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 17.69/17.14 ) 17.69/17.14 (instantiation (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (inverse_divide X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_126633 $$unsorted) (BOUND_VARIABLE_126641 $$unsorted)) (or (not (divisi14063676e_zero X_a)) (and (or (not (= _let_0 (ti X_a BOUND_VARIABLE_126633))) (= _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_126633) BOUND_VARIABLE_126633))) (or (= _let_0 (ti X_a BOUND_VARIABLE_126641)) (= (one_one X_a) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_126641) BOUND_VARIABLE_126641))))) )))) 17.69/17.14 ( bool, fFalse, fFalse ) 17.69/17.14 ( bool, fTrue, fTrue ) 17.69/17.14 ( real, pi, pi ) 17.69/17.14 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat) ) 17.69/17.14 ( (fun nat bool), prime, prime ) 17.69/17.14 ( (fun nat nat), suc, suc ) 17.69/17.14 ( (fun nat nat), (fact_fact nat), (fact_fact nat) ) 17.69/17.14 ( (fun nat nat), (size_size nat), (size_size nat) ) 17.69/17.14 ( (fun nat nat), fact, fact ) 17.69/17.14 ( (fun nat nat), nat_size, nat_size ) 17.69/17.14 ( int, pls, pls ) 17.69/17.14 ( int, m, m ) 17.69/17.14 ( int, min_1, min_1 ) 17.69/17.14 ( int, s, s ) 17.69/17.14 ( int, s1, s1 ) 17.69/17.14 ( int, t, t ) 17.69/17.14 ( (fun int bool), zprime, zprime ) 17.69/17.14 ( (fun int bool), nat_neg, nat_neg ) 17.69/17.14 ( (fun int bool), zEven, zEven ) 17.69/17.14 ( (fun int bool), nat_is_nat, nat_is_nat ) 17.69/17.14 ( (fun int bool), zOdd, zOdd ) 17.69/17.14 ( (fun int bool), (even_odd_even int), (even_odd_even int) ) 17.69/17.14 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 17.69/17.14 ( (fun int nat), nat_1, nat_1 ) 17.69/17.14 ( (fun int nat), phi, phi ) 17.69/17.14 ( (fun real real), sqrt, sqrt ) 17.69/17.14 ( (fun real real), tan, tan ) 17.69/17.14 ( (fun real real), cos, cos ) 17.69/17.14 ( (fun real real), arccos, arccos ) 17.69/17.14 ( (fun real real), ln, ln ) 17.69/17.14 ( (fun real real), sin, sin ) 17.69/17.14 ( (fun real real), arctan, arctan ) 17.69/17.14 ( (fun real real), arcsin, arcsin ) 17.69/17.14 ( complex, ii, ii ) 17.69/17.14 ( (fun complex complex), cnj, cnj ) 17.69/17.14 ( (fun complex complex), expi, expi ) 17.69/17.14 ( (fun nat real), (real_1 nat), (real_1 nat) ) 17.69/17.14 ( (fun nat real), cos_coeff, cos_coeff ) 17.69/17.14 ( (fun nat real), sin_coeff, sin_coeff ) 17.69/17.14 ( (fun int int), bit0, bit0 ) 17.69/17.14 ( (fun int int), bit1, bit1 ) 17.69/17.14 ( (fun int int), pred, pred ) 17.69/17.14 ( (fun int int), succ, succ ) 17.69/17.14 ( (fun int int), (fact_fact int), (fact_fact int) ) 17.69/17.14 ( (fun int int), zfact, zfact ) 17.69/17.14 ( (fun bool bool), fNot, fNot ) 17.69/17.14 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset ) 17.69/17.14 ( (fun bool (fun bool bool)), fconj, fconj ) 17.69/17.14 ( (fun bool (fun bool bool)), fdisj, fdisj ) 17.69/17.14 ( (fun bool (fun bool bool)), fimplies, fimplies ) 17.69/17.14 ( (fun int (fun int bool)), sRStar, sRStar ) 17.69/17.14 ( (fun int (fun int bool)), quadRes, quadRes ) 17.69/17.14 ( (fun int (fun int bool)), norRRset, norRRset ) 17.69/17.14 ( (fun int (fun int bool)), d22set, d22set ) 17.69/17.14 ( (fun int (fun int bool)), sr, sr ) 17.69/17.14 ( (fun int (fun int bool)), quickc1265749348ro_rel, quickc1265749348ro_rel ) 17.69/17.14 ( (fun nat (fun nat nat)), nat_gcd, nat_gcd ) 17.69/17.14 ( (fun nat (fun nat nat)), (gcd_gcd nat), (gcd_gcd nat) ) 17.69/17.14 ( (fun nat (fun nat nat)), nat_lcm, nat_lcm ) 17.69/17.14 ( (fun nat (fun real real)), root, root ) 17.69/17.14 ( (fun real (fun real real)), log, log ) 17.69/17.14 ( (fun real (fun real real)), powr, powr ) 17.69/17.14 ( (fun nat (fun nat bool)), coprime, coprime ) 17.69/17.14 ( (fun (fun int bool) int), (the int), (the int) ) 17.69/17.14 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, normalize ) 17.69/17.14 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, negateSnd ) 17.69/17.14 ( (fun nat (fun nat (product_prod int int))), bezw, bezw ) 17.69/17.14 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set ) 17.69/17.14 ( (filter nat), sequentially, sequentially ) 17.69/17.14 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat ) 17.69/17.14 ( (fun (product_prod int int) bool), frac_1, frac_1 ) 17.69/17.14 ( (fun real complex), cis, cis ) 17.69/17.14 ( (fun complex real), im, im ) 17.69/17.14 ( (fun complex real), re, re ) 17.69/17.14 ( (fun complex real), arg, arg ) 17.69/17.14 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral ) 17.69/17.14 ( (fun int (fun int int)), int_gcd, int_gcd ) 17.69/17.14 ( (fun int (fun int int)), multInv, multInv ) 17.69/17.14 ( (fun int (fun int int)), legacy_zgcd, legacy_zgcd ) 17.69/17.14 ( (fun int (fun int int)), z3mod, z3mod ) 17.69/17.14 ( (fun int (fun int int)), inv, inv ) 17.69/17.14 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int) ) 17.69/17.14 ( (fun int (fun int int)), standardRes, standardRes ) 17.69/17.14 ( (fun int (fun int int)), legendre, legendre ) 17.69/17.14 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 17.69/17.14 ( (fun int (fun int int)), z3div, z3div ) 17.69/17.14 ( (fun int (fun int int)), int_lcm, int_lcm ) 17.69/17.14 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than2 ) 17.69/17.14 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than ) 17.69/17.14 ( (fun int (fun (fun int bool) bool)), rsetR, rsetR ) 17.69/17.14 ( (fun int (fun (fun int bool) bool)), resSet, resSet ) 17.69/17.14 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, lazy_small_lazy_rel ) 17.69/17.14 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, posDivAlg_rel ) 17.69/17.14 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, upto_rel ) 17.69/17.14 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, negDivAlg_rel ) 17.69/17.14 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, norm_frac_rel ) 17.69/17.14 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_less ) 17.69/17.14 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_leq ) 17.69/17.14 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel ) 17.69/17.14 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd ) 17.69/17.14 ( (fun int (fun int (product_prod int int))), negDivAlg, negDivAlg ) 17.69/17.14 ( (fun int (fun int (product_prod int int))), divmod_int, divmod_int ) 17.69/17.14 ( (fun int (fun int (product_prod int int))), posDivAlg, posDivAlg ) 17.69/17.14 ( (fun int (fun int (product_prod int int))), pdivmod, pdivmod ) 17.69/17.14 ( (fun int (fun int (product_prod int int))), norm_frac, norm_frac ) 17.69/17.14 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust ) 17.69/17.14 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, bolzano_bisect ) 17.69/17.14 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 17.69/17.14 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 17.69/17.14 ( (fun real nat), natfloor, natfloor ) 17.69/17.14 ( (fun real nat), natceiling, natceiling ) 17.69/17.14 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int ) 17.69/17.14 ( (fun int (fun int (fun int bool))), wset, wset ) 17.69/17.14 ( (fun int (fun int (fun int bool))), bnorRset, bnorRset ) 17.69/17.14 ( (fun int (fun int (fun int bool))), zcong, zcong ) 17.69/17.14 ( (fun int (fun int (fun int bool))), noXRRset, noXRRset ) 17.69/17.14 ( (fun int (fun int (fun int bool))), zcongm, zcongm ) 17.69/17.14 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair ) 17.69/17.14 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS ) 17.69/17.14 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral ) 17.69/17.15 ( (fun int real), (real_1 int), (real_1 int) ) 17.69/17.15 ( (fun complex nat), (size_size complex), (size_size complex) ) 17.69/17.15 ( (fun complex nat), complex_size, complex_size ) 17.69/17.15 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero ) 17.69/17.15 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel ) 17.69/17.15 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel ) 17.69/17.15 ( (fun (product_prod int int) rat), frct, frct ) 17.69/17.15 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux ) 17.69/17.15 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel ) 17.69/17.15 ( (fun (fun nat rat) bool), vanishes, vanishes ) 17.69/17.15 ( (fun int (fun int rat)), fract, fract ) 17.69/17.15 ( (fun code_code_numeral int), code_int_of, code_int_of ) 17.69/17.15 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat ) 17.69/17.15 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral) ) 17.69/17.15 ( (fun code_code_numeral nat), code_c271388182l_size, code_c271388182l_size ) 17.69/17.15 ( (fun real (fun real complex)), complex_1, complex_1 ) 17.69/17.15 ( (fun real (fun real complex)), rcis, rcis ) 17.69/17.15 ( (fun int (fun nat nat)), nat_aux, nat_aux ) 17.69/17.15 ( (fun rat real), ratreal, ratreal ) 17.69/17.15 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of ) 17.69/17.15 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int ) 17.69/17.15 ( (fun rat (product_prod int int)), quotient_of, quotient_of ) 17.69/17.15 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR ) 17.69/17.15 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 17.69/17.15 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of ) 17.69/17.15 ( (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 ) 17.69/17.15 ) 17.69/17.15 (instantiation (let ((_let_0 (fEx X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun (fun X_a bool) bool) _let_0)) )) 17.69/17.15 ( nat ) 17.69/17.15 ( int ) 17.69/17.15 ) 17.69/17.15 (instantiation (let ((_let_0 (archim2085082626_floor X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_126666 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP X_a int _let_0 BOUND_VARIABLE_126666)) (one_one int)) (hAPP X_a int _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_126666) (one_one X_a))))) )) 17.69/17.15 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 17.69/17.15 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.15 ( code_code_numeral, (zero_zero code_code_numeral) ) 17.69/17.15 ) 17.69/17.15 (instantiation (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) N_1))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (or (hBOOL (hAPP nat bool _let_0 Ma)) (= (hBOOL (hAPP nat bool _let_0 (hAPP nat nat suc Ma))) (= N_1 Ma))) )) 17.69/17.15 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 17.69/17.15 ) 17.69/17.15 (instantiation (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_126763 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_126763)) _let_0))) (= _let_0 (ti X_a BOUND_VARIABLE_126763)) (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_126763) _let_0))) )))) 17.69/17.15 ( bool, fFalse ) 17.69/17.15 ( bool, fTrue ) 17.69/17.15 ( real, (zero_zero real) ) 17.69/17.15 ( real, pi ) 17.69/17.15 ( (fun nat bool), (even_odd_even nat) ) 17.69/17.15 ( (fun nat bool), prime ) 17.69/17.15 ( (fun nat nat), suc ) 17.69/17.15 ( (fun nat nat), (fact_fact nat) ) 17.69/17.15 ( (fun nat nat), (size_size nat) ) 17.69/17.15 ( (fun nat nat), fact ) 17.69/17.15 ( (fun nat nat), nat_size ) 17.69/17.15 ( int, pls ) 17.69/17.15 ( int, m ) 17.69/17.15 ( int, min_1 ) 17.69/17.15 ( int, s ) 17.69/17.15 ( int, s1 ) 17.69/17.15 ( int, t ) 17.69/17.15 ( (fun int bool), zprime ) 17.69/17.15 ( (fun int bool), nat_neg ) 17.69/17.15 ( (fun int bool), zEven ) 17.69/17.15 ( (fun int bool), nat_is_nat ) 17.69/17.15 ( (fun int bool), zOdd ) 17.69/17.15 ( (fun int bool), (even_odd_even int) ) 17.69/17.15 ( (fun int bool), twoSqu1091635170sum2sq ) 17.69/17.15 ( (fun int nat), nat_1 ) 17.69/17.15 ( (fun int nat), phi ) 17.69/17.15 ( (fun real real), sqrt ) 17.69/17.15 ( (fun real real), tan ) 17.69/17.15 ( (fun real real), cos ) 17.69/17.15 ( (fun real real), arccos ) 17.69/17.15 ( (fun real real), ln ) 17.69/17.15 ( (fun real real), sin ) 17.69/17.15 ( (fun real real), arctan ) 17.69/17.15 ( (fun real real), arcsin ) 17.69/17.15 ( complex, ii ) 17.69/17.15 ( (fun complex complex), cnj ) 17.69/17.15 ( (fun complex complex), expi ) 17.69/17.15 ( (fun nat real), (real_1 nat) ) 17.69/17.15 ( (fun nat real), cos_coeff ) 17.69/17.15 ( (fun nat real), sin_coeff ) 17.69/17.15 ( (fun int int), bit0 ) 17.69/17.15 ( (fun int int), bit1 ) 17.69/17.15 ( (fun int int), pred ) 17.69/17.15 ( (fun int int), succ ) 17.69/17.15 ( (fun int int), (fact_fact int) ) 17.69/17.15 ( (fun int int), zfact ) 17.69/17.15 ( (fun bool bool), fNot ) 17.69/17.15 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.69/17.15 ( (fun bool (fun bool bool)), fconj ) 17.69/17.15 ( (fun bool (fun bool bool)), fdisj ) 17.69/17.15 ( (fun bool (fun bool bool)), fimplies ) 17.69/17.15 ( (fun int (fun int bool)), sRStar ) 17.69/17.15 ( (fun int (fun int bool)), quadRes ) 17.69/17.15 ( (fun int (fun int bool)), norRRset ) 17.69/17.15 ( (fun int (fun int bool)), d22set ) 17.69/17.15 ( (fun int (fun int bool)), sr ) 17.69/17.15 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 17.69/17.15 ( (fun nat (fun nat nat)), nat_gcd ) 17.69/17.15 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 17.69/17.15 ( (fun nat (fun nat nat)), nat_lcm ) 17.69/17.15 ( (fun nat (fun real real)), 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17.69/17.15 ( (fun int (fun int int)), legacy_zgcd ) 17.69/17.15 ( (fun int (fun int int)), z3mod ) 17.69/17.15 ( (fun int (fun int int)), inv ) 17.69/17.15 ( (fun int (fun int int)), (gcd_gcd int) ) 17.69/17.15 ( (fun int (fun int int)), standardRes ) 17.69/17.15 ( (fun int (fun int int)), legendre ) 17.69/17.15 ( (fun int (fun int int)), nat_tsub ) 17.69/17.15 ( (fun int (fun int int)), z3div ) 17.69/17.15 ( (fun int (fun int int)), int_lcm ) 17.69/17.15 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 17.69/17.15 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 17.69/17.15 ( (fun int (fun (fun int bool) bool)), rsetR ) 17.69/17.15 ( (fun int (fun (fun int bool) bool)), resSet ) 17.69/17.15 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 17.69/17.15 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 17.69/17.15 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 17.69/17.15 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.69/17.15 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 17.69/17.15 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 17.69/17.15 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 17.69/17.15 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 17.69/17.15 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.69/17.15 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.69/17.15 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.69/17.15 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.69/17.15 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.69/17.15 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.69/17.15 ( (let ((_let_0 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code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.69/17.15 ( (fun int real), (real_1 int) ) 17.69/17.15 ( (fun complex nat), (size_size complex) ) 17.69/17.15 ( (fun complex nat), complex_size ) 17.69/17.15 ( (fun int (list int)), quickc666637781d_zero ) 17.69/17.15 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.69/17.15 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.69/17.15 ( (fun (product_prod int int) rat), frct ) 17.69/17.15 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.69/17.15 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.69/17.15 ( (fun (fun nat rat) bool), vanishes ) 17.69/17.15 ( (fun int (fun int rat)), fract ) 17.69/17.15 ( (fun code_code_numeral int), code_int_of ) 17.69/17.15 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.69/17.15 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.69/17.15 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.69/17.15 ( (fun real (fun real complex)), complex_1 ) 17.69/17.15 ( (fun real (fun real complex)), rcis ) 17.69/17.15 ( (fun int (fun nat nat)), nat_aux ) 17.69/17.15 ( (fun rat real), ratreal ) 17.69/17.15 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.69/17.15 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.69/17.15 ( (fun rat (product_prod int int)), quotient_of ) 17.69/17.15 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.69/17.15 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.69/17.15 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.69/17.15 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.69/17.15 ) 17.69/17.15 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_4 (one_one real))) (let ((_let_5 (hAPP int real (number_number_of real) _let_3))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real _let_2 (inverse_divide real) _let_4) _let_5))) 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 (abs_abs real) (hAPP real real (hAPP real _let_2 (minus_minus real) (hAPP real real ln (hAPP real real (hAPP real _let_2 (plus_plus real) _let_4) X))) X))) (hAPP real real (hAPP real _let_2 (times_times real) _let_5) (hAPP nat real (hAPP real (fun nat real) (power_power real) X) (hAPP int nat (number_number_of nat) _let_3)))))) ))))))) 17.69/17.15 ( (hAPP int real (number_number_of real) min_1) ) 17.69/17.15 ( (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)))) ) 17.69/17.15 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.15 ) 17.69/17.15 (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)))) ) 17.69/17.15 ( (zero_zero real), pi ) 17.69/17.15 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.15 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.15 ( (zero_zero real), skv_6 ) 17.69/17.15 ( (zero_zero real), skv_11 ) 17.69/17.15 ( (zero_zero real), skv_12 ) 17.69/17.15 ( (zero_zero real), skv_14 ) 17.69/17.15 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.69/17.15 ( (hAPP real real (hAPP real (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))) ) 17.69/17.15 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.69/17.15 ( skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.15 ) 17.69/17.15 (instantiation (let ((_let_0 (fun nat bool))) (forall ((N_4 $$unsorted)) (= (hBOOL (hAPP _let_0 bool (finite_finite_1 nat) N_4)) (not (forall ((M_2 $$unsorted)) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP nat (fun _let_0 bool) (member nat) X_2) N_4))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) X_2) M_2))) )) ))) )) 17.69/17.15 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 17.69/17.15 ) 17.69/17.15 (instantiation (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) I_1))) (forall ((M $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (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)))) )) 17.69/17.15 ( (one_one nat), (zero_zero nat), (one_one nat) ) 17.69/17.15 ) 17.69/17.15 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (inverse_inverse X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_126863 $$unsorted) (BOUND_VARIABLE_126864 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_126863) BOUND_VARIABLE_126864))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_126864) (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_126864)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_126863)))) )))) 17.69/17.15 ( real, (zero_zero real), pi ) 17.69/17.15 ( 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)))) ) 17.69/17.15 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.15 ( real, (zero_zero real), skv_6 ) 17.69/17.15 ( real, (zero_zero real), skv_11 ) 17.69/17.15 ( real, (zero_zero real), skv_12 ) 17.69/17.15 ( real, (zero_zero real), skv_14 ) 17.69/17.15 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.69/17.15 ( real, (hAPP real real (hAPP real (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))) ) 17.69/17.15 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.69/17.15 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.15 ( int, (zero_zero int), (one_one int) ) 17.69/17.15 ( int, (zero_zero int), min_1 ) 17.69/17.15 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.15 ( int, (zero_zero int), s ) 17.69/17.15 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 17.69/17.15 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.69/17.15 ( int, (zero_zero int), skv_3 ) 17.69/17.15 ( int, (zero_zero int), skv_9 ) 17.69/17.15 ( int, (one_one int), t ) 17.69/17.15 ( int, min_1, pls ) 17.69/17.15 ( int, min_1, min_1 ) 17.69/17.15 ) 17.69/17.15 (instantiation (let ((_let_0 (semiring_1_of_nat X_a))) (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (= _let_0 (ti (fun nat X_a) _let_0))) )) 17.69/17.15 ( bool ) 17.69/17.15 ( real ) 17.69/17.15 ( nat ) 17.69/17.15 ( (fun nat bool) ) 17.69/17.15 ( (fun nat nat) ) 17.69/17.15 ( int ) 17.69/17.15 ( (fun real real) ) 17.69/17.15 ( complex ) 17.69/17.15 ( (fun int int) ) 17.69/17.15 ( rat ) 17.69/17.15 ( (fun bool bool) ) 17.69/17.15 ( quickcheck_code_int ) 17.69/17.15 ( (fun nat (fun nat bool)) ) 17.69/17.15 ( (product_prod real real) ) 17.69/17.15 ( (product_prod int int) ) 17.69/17.15 ( (fun nat (product_prod int int)) ) 17.69/17.15 ( (product_prod nat nat) ) 17.69/17.15 ( (fun (product_prod nat nat) bool) ) 17.69/17.15 ( (fun nat (fun (product_prod nat nat) bool)) ) 17.69/17.15 ( (fun nat (product_prod nat nat)) ) 17.69/17.15 ( code_code_numeral ) 17.69/17.15 ) 17.69/17.15 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_126937 $$unsorted) (BOUND_VARIABLE_126938 $$unsorted) (BOUND_VARIABLE_126939 $$unsorted) (BOUND_VARIABLE_126940 $$unsorted)) (or (not (ordered_ab_group_add X_a)) (not (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_126939) BOUND_VARIABLE_126940) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_126937) BOUND_VARIABLE_126938))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_126937) BOUND_VARIABLE_126938)) (hBOOL (hAPP X_a bool (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_126939) BOUND_VARIABLE_126940)))) ))))) 17.69/17.15 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 17.69/17.16 ( 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)))), (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 17.69/17.16 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral), (zero_zero code_code_numeral), (one_one code_code_numeral) ) 17.69/17.16 ) 17.69/17.16 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126966 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) BOUND_VARIABLE_126966)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_126966))))) ) 17.69/17.16 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.69/17.16 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.16 ( real, min_1 ) 17.69/17.16 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.16 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.69/17.16 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.69/17.16 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 17.69/17.16 ( nat, pls ) 17.69/17.16 ( nat, (hAPP int int bit1 pls) ) 17.69/17.16 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.69/17.16 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.69/17.16 ( int, pls ) 17.69/17.16 ( int, (hAPP int int bit1 pls) ) 17.69/17.16 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.69/17.16 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.16 ( int, min_1 ) 17.69/17.16 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.69/17.16 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.69/17.16 ( complex, min_1 ) 17.69/17.16 ( quickcheck_code_int, (zero_zero int) ) 17.69/17.16 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 17.69/17.16 ( quickcheck_code_int, (one_one int) ) 17.69/17.16 ( code_code_numeral, pls ) 17.69/17.16 ( code_code_numeral, (hAPP int int bit1 pls) ) 17.69/17.16 ) 17.69/17.16 (instantiation (let ((_let_0 (combb X_b X_c X_a))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (= _let_0 (ti (fun (fun X_b X_c) (fun (fun X_a X_b) (fun X_a X_c))) _let_0)) )) 17.69/17.16 ( bool, bool, real ) 17.69/17.16 ( bool, bool, nat ) 17.69/17.16 ( bool, bool, int ) 17.69/17.16 ( bool, bool, (product_prod int int) ) 17.69/17.16 ( bool, (fun int bool), int ) 17.69/17.16 ( bool, (fun int int), int ) 17.69/17.16 ( bool, (fun bool bool), real ) 17.69/17.16 ( bool, (fun bool bool), nat ) 17.69/17.16 ( bool, (fun bool bool), int ) 17.69/17.16 ( bool, (fun bool bool), (product_prod int int) ) 17.69/17.16 ( real, bool, nat ) 17.69/17.16 ( real, bool, int ) 17.69/17.16 ( real, real, real ) 17.69/17.16 ( real, real, nat ) 17.69/17.16 ( real, real, int ) 17.69/17.16 ( real, (fun real bool), real ) 17.69/17.16 ( real, (fun real real), real ) 17.69/17.16 ( real, (fun real real), nat ) 17.69/17.16 ( real, (fun real real), int ) 17.69/17.16 ( real, (fun int real), int ) 17.69/17.16 ( nat, real, nat ) 17.69/17.16 ( nat, (fun nat bool), nat ) 17.69/17.16 ( nat, (fun nat nat), nat ) 17.69/17.16 ( (fun nat bool), bool, int ) 17.69/17.16 ( (fun nat bool), (fun nat (fun bool bool)), int ) 17.69/17.16 ( int, bool, int ) 17.69/17.16 ( int, bool, (product_prod int int) ) 17.69/17.16 ( int, int, int ) 17.69/17.16 ( int, int, (product_prod int int) ) 17.69/17.16 ( int, (fun int bool), int ) 17.69/17.16 ( int, (fun int bool), (product_prod int int) ) 17.69/17.16 ( int, (fun int int), int ) 17.69/17.16 ( int, (fun int int), (product_prod int int) ) 17.69/17.16 ( int, (fun (product_prod int int) int), (product_prod int int) ) 17.69/17.16 ( (fun int bool), bool, real ) 17.69/17.16 ( (fun int bool), bool, int ) 17.69/17.16 ( (fun int bool), (fun int bool), int ) 17.69/17.16 ( (fun int bool), (fun int (fun bool bool)), int ) 17.69/17.16 ( (fun int bool), (fun (fun int int) (fun int bool)), int ) 17.69/17.16 ( (fun real bool), (fun (fun int real) (fun int bool)), real ) 17.69/17.16 ( (fun real bool), (fun (fun nat real) (fun nat bool)), real ) 17.69/17.16 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), int ) 17.69/17.16 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)), int ) 17.69/17.16 ( (fun nat real), (fun nat bool), int ) 17.69/17.16 ( (fun int int), (fun int (fun int bool)), int ) 17.69/17.16 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)), int ) 17.69/17.16 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)), (product_prod int int) ) 17.69/17.16 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (product_prod int int) ) 17.69/17.16 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), int ) 17.69/17.16 ( (fun int (fun int bool)), (fun int bool), real ) 17.69/17.16 ( (fun int (fun int bool)), (fun int (fun int bool)), int ) 17.69/17.16 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))), real ) 17.69/17.16 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool), (product_prod int int) ) 17.69/17.16 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), int ) 17.69/17.16 ( (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 ) 17.69/17.16 ( (fun (product_prod int int) int), (fun (product_prod int int) bool), (product_prod int int) ) 17.69/17.16 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)), (product_prod int int) ) 17.69/17.16 ( (fun int real), (fun int bool), int ) 17.69/17.16 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), real ) 17.69/17.16 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))), real ) 17.69/17.16 ( (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) ) 17.69/17.16 ( (fun int (fun nat bool)), (fun int bool), real ) 17.69/17.16 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))), real ) 17.69/17.16 ( (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 ) 17.69/17.16 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), real ) 17.69/17.16 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))), real ) 17.69/17.16 ) 17.69/17.16 (instantiation (let ((_let_0 (uminus_uminus int))) (forall ((K_4 $$unsorted)) (= (hAPP int int bit1 (hAPP int int pred (hAPP int int _let_0 K_4))) (hAPP int int _let_0 (hAPP int int bit1 K_4))) )) 17.69/17.16 ( pls ) 17.69/17.16 ( (one_one int) ) 17.69/17.16 ( min_1 ) 17.69/17.16 ) 17.69/17.16 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127008 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_127008)) (zero_zero int))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_127008) (hAPP int X_a (number_number_of X_a) min_1))))) ) 17.69/17.16 ( real, (zero_zero real) ) 17.69/17.16 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.16 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.16 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.16 ( real, skv_14 ) 17.69/17.16 ( int, (zero_zero int) ) 17.69/17.16 ( int, (one_one int) ) 17.69/17.16 ( int, min_1 ) 17.69/17.16 ) 17.69/17.16 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (hAPP int _let_0 _let_1 (zero_zero int)))) (forall ((M $$unsorted) (Y $$unsorted) (X $$unsorted)) (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))) )))) 17.69/17.16 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.16 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.16 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.16 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 17.69/17.16 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP 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)))) ) 17.69/17.16 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_3, s1 ) 17.69/17.16 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_9, s1 ) 17.69/17.16 ) 17.69/17.16 (instantiation (forall ((X_a $$unsorted)) (or (not (zero_neq_one X_a)) (not (= (zero_zero X_a) (one_one X_a)))) ) 17.69/17.16 ( real ) 17.69/17.16 ( nat ) 17.69/17.16 ( int ) 17.69/17.16 ( complex ) 17.69/17.16 ( rat ) 17.69/17.16 ( quickcheck_code_int ) 17.69/17.16 ( code_code_numeral ) 17.69/17.16 ) 17.69/17.16 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) B_1))) (= (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less_eq rat) (zero_zero rat)) (hAPP int rat (hAPP int (fun int rat) fract A_2) B_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) A_2)))) ))) 17.69/17.16 ( (zero_zero int), (one_one int) ) 17.69/17.16 ( (one_one int), (one_one int) ) 17.69/17.16 ) 17.69/17.16 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (let ((_let_4 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_127167))) (let ((_let_5 (hBOOL (hAPP X_a bool _let_3 _let_4)))) (let ((_let_6 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_127168) _let_4))) (let ((_let_7 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_4) _let_2)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_127166 $$unsorted) (BOUND_VARIABLE_127167 $$unsorted) (BOUND_VARIABLE_127168 $$unsorted)) (or (not (number X_a)) (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_127166) _let_4)) BOUND_VARIABLE_127168)) (and (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_127166) _let_6))) (or _let_5 (and (or _let_7 (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_127168))) (or (not _let_7) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_6) BOUND_VARIABLE_127166)))))))) ))))))))) 17.69/17.16 ( real, pi, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.16 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.69/17.16 ) 17.69/17.16 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (forall ((Y $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP real bool _let_1 X))) (not (hBOOL (hAPP real bool _let_1 Y))) (= (hAPP real real ln (hAPP real real (hAPP real _let_0 (inverse_divide real) X) Y)) (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real ln X)) (hAPP real real ln Y)))) ))) 17.69/17.16 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 17.69/17.16 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.69/17.16 ( (hAPP int 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))) ) 17.69/17.16 ( (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)))) ) 17.69/17.16 ( (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)))) ) 17.69/17.16 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 17.69/17.16 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 17.69/17.16 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 17.69/17.16 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 17.69/17.16 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 17.69/17.16 ( (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) ) 17.69/17.16 ) 17.69/17.16 (instantiation (let ((_let_0 (fun nat X_a))) (let ((_let_1 (power_power X_a))) (let ((_let_2 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (let ((_let_3 (hAPP nat nat suc BOUND_VARIABLE_127234))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_127233 $$unsorted) (BOUND_VARIABLE_127234 $$unsorted) (BOUND_VARIABLE_127235 $$unsorted)) (or (not (linordered_semidom X_a)) (not (= (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_127235) _let_3) (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_127233) _let_3))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_127233))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_127235))) (= (ti X_a BOUND_VARIABLE_127233) (ti X_a BOUND_VARIABLE_127235))) ))))) 17.69/17.16 ( real, (hAPP int real (number_number_of real) min_1), (hAPP nat nat suc (zero_zero nat)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.16 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat nat suc (zero_zero nat)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.17 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.17 ( int, s, (zero_zero nat), s ) 17.69/17.17 ( int, s, (hAPP nat nat suc (zero_zero nat)), s ) 17.69/17.17 ( int, s, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), s ) 17.69/17.17 ( int, s, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), s1 ) 17.69/17.17 ( int, s1, (zero_zero nat), s ) 17.69/17.17 ( complex, ii, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), ii ) 17.69/17.17 ) 17.69/17.17 (instantiation (forall ((X $$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)))) ) 17.69/17.17 ( (zero_zero int) ) 17.69/17.17 ( (one_one int) ) 17.69/17.17 ( min_1 ) 17.69/17.17 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.17 ( s ) 17.69/17.17 ( (hAPP int int (number_number_of int) pls) ) 17.69/17.17 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.69/17.17 ( skv_3 ) 17.69/17.17 ( skv_9 ) 17.69/17.17 ) 17.69/17.17 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (forall ((B $$unsorted) (A_1 $$unsorted)) (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))) ))) 17.69/17.17 ( (zero_zero int), (zero_zero int) ) 17.69/17.17 ( (zero_zero int), min_1 ) 17.69/17.17 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.69/17.17 ( (zero_zero int), t ) 17.69/17.17 ( (one_one int), (zero_zero int) ) 17.69/17.17 ( (one_one int), t ) 17.69/17.17 ( (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) ) 17.69/17.17 ( (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 ) 17.69/17.17 ( (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 ) 17.69/17.17 ( (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_3 ) 17.69/17.17 ( (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_9 ) 17.69/17.17 ( min_1, (zero_zero int) ) 17.69/17.17 ( min_1, min_1 ) 17.69/17.17 ( (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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.69/17.17 ) 17.69/17.17 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (div_div nat))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (forall ((M $$unsorted)) (= (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_1 M) _let_2)) (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat suc (hAPP nat nat suc M))) _let_2)) )))) 17.69/17.17 ( (zero_zero nat) ) 17.69/17.17 ( (hAPP nat nat suc (zero_zero nat)) ) 17.69/17.17 ) 17.69/17.17 (instantiation (forall ((X_a $$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))))) ) 17.69/17.17 ( bool ) 17.69/17.17 ( real ) 17.69/17.17 ( nat ) 17.69/17.17 ( (fun nat bool) ) 17.69/17.17 ( int ) 17.69/17.17 ( (fun int bool) ) 17.69/17.17 ( complex ) 17.69/17.17 ( rat ) 17.69/17.17 ( quickcheck_code_int ) 17.69/17.17 ( (product_prod real real) ) 17.69/17.17 ( (product_prod int int) ) 17.69/17.17 ( (filter real) ) 17.69/17.17 ( (filter nat) ) 17.69/17.17 ( (product_prod nat nat) ) 17.69/17.17 ( code_code_numeral ) 17.69/17.17 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 17.69/17.17 ( (fun nat rat) ) 17.69/17.17 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 17.69/17.17 ) 17.69/17.17 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (ord_less real))) (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 A_2) B_1))) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_2) X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) B_1))) (not (forall ((Y_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X_2) Y_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 Y_2) (zero_zero real))))) ))) )) (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP real real F B_1)) (hAPP real real F A_2)))) )))) 17.69/17.17 ( sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 17.69/17.17 ( sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 17.69/17.17 ( cos, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.17 ) 17.69/17.17 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real real))) (let ((_let_6 (fun nat real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun _let_1 real))) (let ((_let_9 (fun nat _let_5))) (let ((_let_10 (fun nat _let_1))) (let ((_let_11 (fun (filter nat) bool))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (tendsto nat real))) (let ((_let_14 (hAPP _let_6 _let_6 (hAPP _let_9 (fun _let_6 _let_6) (combs nat real real) (hAPP _let_6 _let_9 (hAPP (fun real _let_5) (fun _let_6 _let_9) (combb real _let_5 nat) (times_times real)) (hAPP real _let_6 (power_power real) (hAPP int real (number_number_of real) min_1)))) A_2))) (forall ((A_2 $$unsorted)) (let ((_let_0 (filter nat))) (or (not (hBOOL (hAPP _let_0 bool (hAPP real _let_11 (hAPP _let_6 _let_12 _let_13 A_2) _let_0) sequentially))) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_3 _let_4 _let_0) (hAPP nat real A_2 N_2))) )) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_3 _let_4 (hAPP nat real A_2 (hAPP nat nat suc N_2))) (hAPP nat real A_2 N_2))) )) (hBOOL (hAPP _let_0 bool (hAPP real _let_11 (hAPP _let_6 _let_12 _let_13 (hAPP _let_10 _let_6 (hAPP _let_8 (fun _let_10 _let_6) (combb _let_1 real nat) (hAPP _let_6 _let_8 (big_co1399186613setsum nat real) _let_14)) (hAPP _let_2 _let_10 (hAPP _let_10 (fun _let_2 _let_10) (combb nat _let_1 nat) (hAPP nat _let_10 (ord_atLeastLessThan nat) (zero_zero nat))) (hAPP nat _let_2 (hAPP _let_7 _let_7 (combc nat nat nat) (hAPP _let_2 _let_7 (hAPP _let_7 (fun _let_2 _let_7) (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_6 real (suminf real) _let_14)) sequentially)))) )))))))))))))))) 17.69/17.17 ( (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 17.69/17.17 ) 17.69/17.17 (instantiation (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP int bool (even_odd_even int) X_1)) (not (forall ((Y_2 $$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_2) (ti int X_1))) ))) ) 17.69/17.17 ( (zero_zero int) ) 17.69/17.17 ( (one_one int) ) 17.69/17.17 ) 17.69/17.17 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X))) (= (hAPP real real (uminus_uminus real) (hAPP real real ln X)) (hAPP real real ln (hAPP real real (inverse_inverse real) X)))) ) 17.69/17.17 ( (zero_zero real) ) 17.69/17.17 ( pi ) 17.69/17.17 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.17 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.17 ( skv_2 ) 17.69/17.17 ( skv_10 ) 17.69/17.17 ( skv_13 ) 17.69/17.17 ) 17.69/17.17 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_127424 $$unsorted) (BOUND_VARIABLE_127425 $$unsorted) (BOUND_VARIABLE_127426 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_127426))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_127424) BOUND_VARIABLE_127426)) BOUND_VARIABLE_127425))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_127424) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_127425) BOUND_VARIABLE_127426)))) )))) 17.69/17.17 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.17 ) 17.69/17.17 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat _let_0))) (let ((_let_2 (fun (filter nat) bool))) (let ((_let_3 (fun nat X_a))) (let ((_let_4 (fun _let_0 X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_127458 $$unsorted)) (or (not (t2_space X_a)) (not (comm_monoid_add X_a)) (not (hBOOL (hAPP _let_3 bool (summable X_a) BOUND_VARIABLE_127458))) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_2 (hAPP _let_3 (fun X_a _let_2) (tendsto nat X_a) (hAPP _let_1 _let_3 (hAPP _let_4 (fun _let_1 _let_3) (combb _let_0 X_a nat) (hAPP _let_3 _let_4 (big_co1399186613setsum nat X_a) BOUND_VARIABLE_127458)) (hAPP nat _let_1 (ord_atLeastLessThan nat) (zero_zero nat)))) (hAPP _let_3 X_a (suminf X_a) BOUND_VARIABLE_127458)) sequentially))) )))))) 17.69/17.17 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (combc nat nat nat))) (let ((_let_4 (fun nat _let_0))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun _let_1 _let_4))) (let ((_let_7 (combb real _let_0 nat))) (hAPP _let_1 _let_1 (hAPP _let_4 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_4 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 17.69/17.17 ) 17.69/17.17 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (forall ((N $$unsorted)) (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)))) ))) 17.69/17.17 ( (zero_zero int) ) 17.69/17.17 ( (one_one int) ) 17.69/17.17 ( min_1 ) 17.69/17.17 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.17 ( s ) 17.69/17.17 ( (hAPP int int (number_number_of int) pls) ) 17.69/17.17 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.69/17.17 ( skv_3 ) 17.69/17.17 ( skv_9 ) 17.69/17.17 ) 17.69/17.17 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (div_mod int))) (forall ((X_1 $$unsorted) (N_1 $$unsorted) (Y_1 $$unsorted)) (= (= (hAPP int int (hAPP int _let_0 _let_1 X_1) N_1) (hAPP int int (hAPP int _let_0 _let_1 Y_1) N_1)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) N_1) (hAPP int int (hAPP int _let_0 (minus_minus int) X_1) Y_1)))) ))) 17.69/17.17 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 17.69/17.17 ) 17.69/17.17 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_127533))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_127533 $$unsorted) (BOUND_VARIABLE_127534 $$unsorted) (BOUND_VARIABLE_127535 $$unsorted)) (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_127534) BOUND_VARIABLE_127535)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_127534)) BOUND_VARIABLE_127535))) )))) 17.69/17.17 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.69/17.17 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.69/17.17 ( 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 ) 17.69/17.17 ) 17.69/17.17 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (hAPP int _let_0 (ord_less_eq int) _let_1))) (let ((_let_3 (fun int int))) (let ((_let_4 (ord_less int))) (forall ((B_5 $$unsorted) (Q_5 $$unsorted) (R_5 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_2 (hAPP int int (hAPP int _let_3 (plus_plus int) (hAPP int int (hAPP int _let_3 (times_times int) B_5) Q_5)) R_5)))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 R_5) B_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 _let_1) B_5))) (hBOOL (hAPP int bool _let_2 Q_5))) )))))) 17.69/17.18 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, (one_one int) ) 17.69/17.18 ) 17.69/17.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127570 $$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_127570) (one_one X_a)) (ti X_a BOUND_VARIABLE_127570))) ) 17.69/17.18 ( bool, fFalse ) 17.69/17.18 ( bool, fTrue ) 17.69/17.18 ( real, pi ) 17.69/17.18 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.18 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.18 ( 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))))) ) 17.69/17.18 ( (fun nat bool), (even_odd_even nat) ) 17.69/17.18 ( (fun nat bool), prime ) 17.69/17.18 ( (fun nat nat), suc ) 17.69/17.18 ( (fun nat nat), (fact_fact nat) ) 17.69/17.18 ( (fun nat nat), (size_size nat) ) 17.69/17.18 ( (fun nat nat), fact ) 17.69/17.18 ( (fun nat nat), nat_size ) 17.69/17.18 ( int, pls ) 17.69/17.18 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.18 ( int, m ) 17.69/17.18 ( 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))) ) 17.69/17.18 ( int, min_1 ) 17.69/17.18 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.18 ( int, s ) 17.69/17.18 ( int, s1 ) 17.69/17.18 ( int, t ) 17.69/17.18 ( (fun int bool), zprime ) 17.69/17.18 ( (fun int bool), nat_neg ) 17.69/17.18 ( (fun int bool), zEven ) 17.69/17.18 ( (fun int bool), nat_is_nat ) 17.69/17.18 ( (fun int bool), zOdd ) 17.69/17.18 ( (fun int bool), (even_odd_even int) ) 17.69/17.18 ( (fun int bool), twoSqu1091635170sum2sq ) 17.69/17.18 ( (fun int nat), nat_1 ) 17.69/17.18 ( (fun int nat), phi ) 17.69/17.18 ( (fun real real), sqrt ) 17.69/17.18 ( (fun real real), tan ) 17.69/17.18 ( (fun real real), cos ) 17.69/17.18 ( (fun real real), arccos ) 17.69/17.18 ( (fun real real), ln ) 17.69/17.18 ( (fun real real), sin ) 17.69/17.18 ( (fun real real), arctan ) 17.69/17.18 ( (fun real real), arcsin ) 17.69/17.18 ( complex, ii ) 17.69/17.18 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.18 ( 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)) ) 17.69/17.18 ( (fun complex complex), cnj ) 17.69/17.18 ( (fun complex complex), expi ) 17.69/17.18 ( (fun nat real), (real_1 nat) ) 17.69/17.18 ( (fun nat real), cos_coeff ) 17.69/17.18 ( (fun nat real), sin_coeff ) 17.69/17.18 ( (fun int int), bit0 ) 17.69/17.18 ( (fun int int), bit1 ) 17.69/17.18 ( (fun int int), pred ) 17.69/17.18 ( (fun int int), succ ) 17.69/17.18 ( (fun int int), (fact_fact int) ) 17.69/17.18 ( (fun int int), zfact ) 17.69/17.18 ( (fun bool bool), fNot ) 17.69/17.18 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 17.69/17.18 ( (fun bool (fun bool bool)), fconj ) 17.69/17.18 ( (fun bool (fun bool bool)), fdisj ) 17.69/17.18 ( (fun bool (fun bool bool)), fimplies ) 17.69/17.18 ( (fun int (fun int bool)), sRStar ) 17.69/17.18 ( (fun int (fun int bool)), quadRes ) 17.69/17.18 ( (fun int (fun int bool)), norRRset ) 17.69/17.18 ( (fun int (fun int bool)), d22set ) 17.69/17.18 ( (fun int (fun int bool)), sr ) 17.69/17.18 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 17.69/17.18 ( (fun nat (fun nat nat)), nat_gcd ) 17.69/17.18 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 17.69/17.18 ( (fun nat (fun nat nat)), nat_lcm ) 17.69/17.18 ( (fun nat (fun real real)), root ) 17.69/17.18 ( (fun real (fun real real)), log ) 17.69/17.18 ( (fun real (fun real real)), powr ) 17.69/17.18 ( (fun nat (fun nat bool)), coprime ) 17.69/17.18 ( (fun (fun int bool) int), (the int) ) 17.69/17.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 17.69/17.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 17.69/17.18 ( (fun nat (fun nat (product_prod int int))), bezw ) 17.69/17.18 ( (fun (fun int bool) bool), nat_nat_set ) 17.69/17.18 ( (filter nat), sequentially ) 17.69/17.18 ( (fun (product_prod nat nat) bool), pred_nat ) 17.69/17.18 ( (fun (product_prod int int) bool), frac_1 ) 17.69/17.18 ( (fun real complex), cis ) 17.69/17.18 ( (fun complex real), im ) 17.69/17.18 ( (fun complex real), re ) 17.69/17.18 ( (fun complex real), arg ) 17.69/17.18 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 17.69/17.18 ( (fun int (fun int int)), int_gcd ) 17.69/17.18 ( (fun int (fun int int)), multInv ) 17.69/17.18 ( (fun int (fun int int)), legacy_zgcd ) 17.69/17.18 ( (fun int (fun int int)), z3mod ) 17.69/17.18 ( (fun int (fun int int)), inv ) 17.69/17.18 ( (fun int (fun int int)), (gcd_gcd int) ) 17.69/17.18 ( (fun int (fun int int)), standardRes ) 17.69/17.18 ( (fun int (fun int int)), legendre ) 17.69/17.18 ( (fun int (fun int int)), nat_tsub ) 17.69/17.18 ( (fun int (fun int int)), z3div ) 17.69/17.18 ( (fun int (fun int int)), int_lcm ) 17.69/17.18 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 17.69/17.18 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 17.69/17.18 ( (fun int (fun (fun int bool) bool)), rsetR ) 17.69/17.18 ( (fun int (fun (fun int bool) bool)), resSet ) 17.69/17.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 17.69/17.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 17.69/17.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 17.69/17.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 17.69/17.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 17.69/17.18 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 17.69/17.18 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 17.69/17.18 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 17.69/17.18 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.69/17.18 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.69/17.18 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.69/17.18 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.69/17.18 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.69/17.18 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.69/17.18 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 17.69/17.18 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 17.69/17.18 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 17.69/17.18 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 17.69/17.18 ( (fun real nat), natfloor ) 17.69/17.18 ( (fun real nat), natceiling ) 17.69/17.18 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.69/17.18 ( (fun int (fun int (fun int bool))), wset ) 17.69/17.18 ( (fun int (fun int (fun int bool))), bnorRset ) 17.69/17.18 ( (fun int (fun int (fun int bool))), zcong ) 17.69/17.18 ( (fun int (fun int (fun int bool))), noXRRset ) 17.69/17.18 ( (fun int (fun int (fun int bool))), zcongm ) 17.69/17.18 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.69/17.18 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.69/17.18 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.69/17.18 ( (fun int real), (real_1 int) ) 17.69/17.18 ( (fun complex nat), (size_size complex) ) 17.69/17.18 ( (fun complex nat), complex_size ) 17.69/17.18 ( (fun int (list int)), quickc666637781d_zero ) 17.69/17.18 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.69/17.18 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.69/17.18 ( (fun (product_prod int int) rat), frct ) 17.69/17.18 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.69/17.18 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.69/17.18 ( (fun (fun nat rat) bool), vanishes ) 17.69/17.18 ( (fun int (fun int rat)), fract ) 17.69/17.18 ( (fun code_code_numeral int), code_int_of ) 17.69/17.18 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.69/17.18 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.69/17.18 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.69/17.18 ( (fun real (fun real complex)), complex_1 ) 17.69/17.18 ( (fun real (fun real complex)), rcis ) 17.69/17.18 ( (fun int (fun nat nat)), nat_aux ) 17.69/17.18 ( (fun rat real), ratreal ) 17.69/17.18 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.69/17.18 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.69/17.18 ( (fun rat (product_prod int int)), quotient_of ) 17.69/17.18 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.69/17.18 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.69/17.18 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.69/17.18 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.69/17.18 ) 17.69/17.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127760 $$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_127760)) (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_127760))))) ) 17.69/17.18 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.69/17.18 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.18 ( real, min_1 ) 17.69/17.18 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.18 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.69/17.18 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.69/17.18 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 17.69/17.18 ( nat, pls ) 17.69/17.18 ( nat, (hAPP int int bit1 pls) ) 17.69/17.18 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.69/17.18 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.69/17.18 ( int, pls ) 17.69/17.18 ( int, (hAPP int int bit1 pls) ) 17.69/17.18 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.69/17.18 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.18 ( int, min_1 ) 17.69/17.18 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.69/17.18 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.69/17.18 ( complex, min_1 ) 17.69/17.18 ( quickcheck_code_int, (zero_zero int) ) 17.69/17.18 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 17.69/17.18 ( quickcheck_code_int, (one_one int) ) 17.69/17.18 ( code_code_numeral, pls ) 17.69/17.18 ( code_code_numeral, (hAPP int int bit1 pls) ) 17.69/17.18 ) 17.69/17.18 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_127842 $$unsorted) (BOUND_VARIABLE_127843 $$unsorted)) (or (not (linorder X_a)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_127842) BOUND_VARIABLE_127843)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_127842) BOUND_VARIABLE_127843)) (= (ti X_a BOUND_VARIABLE_127842) (ti X_a BOUND_VARIABLE_127843)))) )) 17.69/17.18 ( real, (zero_zero real), pi ) 17.69/17.18 ( 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)))) ) 17.69/17.18 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.18 ( real, (zero_zero real), skv_2 ) 17.69/17.18 ( real, (zero_zero real), skv_6 ) 17.69/17.18 ( real, (zero_zero real), skv_10 ) 17.69/17.18 ( real, (zero_zero real), skv_11 ) 17.69/17.18 ( real, (zero_zero real), skv_12 ) 17.69/17.18 ( real, (zero_zero real), skv_13 ) 17.69/17.18 ( real, (zero_zero real), skv_14 ) 17.69/17.18 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.18 ( real, pi, (zero_zero real) ) 17.69/17.18 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.69/17.18 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.69/17.18 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.18 ( 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))))), (zero_zero real) ) 17.69/17.18 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 17.69/17.18 ( 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 ) 17.69/17.18 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.18 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.18 ( int, (zero_zero int), (zero_zero int) ) 17.69/17.18 ( int, (zero_zero int), (one_one int) ) 17.69/17.18 ( 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))) ) 17.69/17.18 ( int, (zero_zero int), min_1 ) 17.69/17.18 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.69/17.18 ( int, (zero_zero int), s ) 17.69/17.18 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 17.69/17.18 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 17.69/17.18 ( int, (zero_zero int), skv_3 ) 17.69/17.18 ( int, (zero_zero int), skv_9 ) 17.69/17.18 ( int, (one_one int), t ) 17.69/17.18 ( int, min_1, (zero_zero int) ) 17.69/17.18 ( int, min_1, pls ) 17.69/17.18 ( int, min_1, min_1 ) 17.69/17.18 ( 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))) ) 17.69/17.18 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 17.69/17.18 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.83/17.27 ( int, t, (zero_zero int) ) 17.83/17.27 ( int, t, (one_one int) ) 17.83/17.27 ( 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))) ) 17.83/17.27 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.83/17.27 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.83/17.27 ) 17.83/17.27 (instantiation (let ((_let_0 (product_prod int int))) (forall ((P_5 $$unsorted)) (= (hAPP rat _let_0 quotient_of (hAPP rat rat (sgn_sgn rat) P_5)) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) (hAPP int int (sgn_sgn int) (hAPP _let_0 int (product_fst int int) (hAPP rat _let_0 quotient_of P_5)))) (one_one int))) )) 17.83/17.27 ( (zero_zero rat) ) 17.83/17.27 ) 17.83/17.27 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (one_one real))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) _let_2))) (= (hAPP real real sin (hAPP real real arccos X)) (hAPP real real sqrt (hAPP real real (hAPP real (fun real real) (minus_minus real) _let_2) (hAPP nat real (hAPP real (fun nat real) (power_power real) X) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) )))) 17.83/17.27 ( (zero_zero real) ) 17.83/17.27 ( (hAPP int real (number_number_of real) min_1) ) 17.83/17.27 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.83/17.27 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.83/17.27 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.83/17.27 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.83/17.27 ( skv_14 ) 17.83/17.27 ) 17.83/17.27 (instantiation (forall ((X_a $$unsorted) (A_2 $$unsorted) (P_1 $$unsorted) (BOUND_VARIABLE_127970 $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 A_2))) (= (hAPP (fun X_a bool) X_a (hilbert_Eps X_a) P_1) (ti X_a A_2)) (not (forall ((Y_2 $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 Y_2))) (= (ti X_a Y_2) (ti X_a BOUND_VARIABLE_127970))) )) (not (hBOOL (hAPP X_a bool P_1 BOUND_VARIABLE_127970)))) ) 17.83/17.27 ( 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) ) 17.83/17.27 ( 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) ) 17.83/17.27 ( 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) ) 17.83/17.27 ( real, (zero_zero real), (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 17.83/17.27 ( real, (one_one real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 17.83/17.27 ( real, pi, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 17.83/17.27 ( real, pi, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 17.83/17.27 ( 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 ) 17.83/17.27 ( 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 ) 17.83/17.27 ( 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))) ) 17.83/17.27 ( 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))) ) 17.83/17.27 ( 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_14), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.83/17.27 ( real, (hAPP real real (hAPP real (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)))) ) 17.83/17.27 ( real, (hAPP real real (hAPP real (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)))) ) 17.83/17.27 ( 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)))) ) 17.83/17.27 ( 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)))) ) 17.83/17.27 ( 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)))) ) 17.83/17.27 ( 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)))) ) 17.83/17.27 ( real, skv_2, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 17.83/17.27 ( real, skv_6, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_6 ) 17.83/17.27 ( real, skv_10, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_10 ) 17.83/17.27 ( real, skv_11, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 17.83/17.27 ( real, skv_12, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 17.83/17.27 ( real, skv_13, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_13 ) 17.83/17.27 ( real, skv_14, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_14 ) 17.83/17.27 ( nat, (zero_zero nat), (even_odd_even nat), (zero_zero nat) ) 17.83/17.27 ( nat, (zero_zero nat), prime, (zero_zero nat) ) 17.83/17.27 ( nat, (one_one nat), (even_odd_even nat), (one_one nat) ) 17.83/17.27 ( nat, (one_one nat), prime, (one_one nat) ) 17.83/17.27 ( 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))) ) 17.83/17.27 ( 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))) ) 17.83/17.27 ( (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)) ) 17.83/17.27 ( (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) ) 17.83/17.27 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less int) pls), (zero_zero int) ) 17.83/17.27 ( int, (zero_zero int), nat_is_nat, (zero_zero int) ) 17.83/17.27 ( int, (zero_zero int), (even_odd_even int), (zero_zero int) ) 17.83/17.27 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))), (zero_zero int) ) 17.83/17.27 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less int) min_1), (zero_zero int) ) 17.83/17.27 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less int) t), (zero_zero int) ) 17.83/17.28 ( int, pls, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 17.83/17.28 ( int, (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 17.83/17.28 ( int, (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 17.83/17.28 ( int, (one_one int), nat_neg, (one_one int) ) 17.83/17.28 ( int, (one_one int), nat_is_nat, (one_one int) ) 17.83/17.28 ( int, (one_one int), (even_odd_even int), (one_one int) ) 17.83/17.28 ( int, (one_one int), (hAPP int (fun int bool) (ord_less int) t), (one_one int) ) 17.83/17.28 ( 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))), 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))) ) 17.83/17.28 ( 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 (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))) ) 17.83/17.28 ( 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 (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))) ) 17.83/17.28 ( 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))), (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))) ) 17.83/17.28 ( 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))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.83/17.28 ( 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 (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))) ) 17.83/17.28 ( 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))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.83/17.28 ( 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))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.83/17.28 ( 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 (fun int bool) (ord_less int) skv_3), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.83/17.28 ( 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))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_3)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.83/17.28 ( 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))), (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_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.83/17.28 ( 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 (fun int bool) (ord_less int) skv_9), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.83/17.28 ( 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))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_9)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.83/17.28 ( int, min_1, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 17.83/17.28 ( int, min_1, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 17.83/17.28 ( int, min_1, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 17.83/17.28 ( int, min_1, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 17.83/17.28 ( 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))) ) 17.83/17.28 ( 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))) ) 17.83/17.28 ( 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))) ) 17.83/17.28 ( int, (hAPP int int (number_number_of int) min_1), nat_neg, (hAPP int int (number_number_of int) min_1) ) 17.83/17.28 ( int, (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 17.83/17.28 ( int, s, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 17.83/17.28 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.83/17.28 ( int, (hAPP int int (number_number_of int) pls), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 17.83/17.28 ( int, (hAPP int int (number_number_of int) pls), nat_neg, (hAPP int int (number_number_of int) pls) ) 17.83/17.28 ( int, t, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 17.83/17.28 ( 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) (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))) ) 17.83/17.28 ( 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))) ) 17.83/17.28 ( 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))) ) 17.83/17.28 ( 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) (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))) (zero_zero int)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun int bool) (ord_less 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)))), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 17.83/17.28 ( int, skv_3, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_3 ) 17.83/17.28 ( int, skv_9, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_9 ) 17.83/17.28 ( (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)) ) 17.83/17.28 ( (fun int bool), zEven, (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 17.83/17.28 ( (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))))) ) 17.83/17.28 ( (filter nat), sequentially, (trivial_limit nat), sequentially ) 17.83/17.28 ( (filter nat), sequentially, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 17.83/17.28 ) 17.83/17.28 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (forall ((Y $$unsorted) (X $$unsorted)) (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) (times_times 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) (times_times int) X) Y)))) )) 17.83/17.28 ( (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))) ) 17.83/17.28 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.83/17.28 ( 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))) ) 17.83/17.29 ( skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.83/17.29 ) 17.83/17.29 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)))) (forall ((Y_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (hBOOL (hAPP real bool _let_0 Y_1)) (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root N_1) Y_1))))) )) 17.83/17.29 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.83/17.29 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.83/17.29 ( (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))) ) 17.83/17.29 ( (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))) ) 17.83/17.29 ) 17.83/17.29 (instantiation (let ((_let_0 (fun int bool))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_1) zEven))) (= (zero_zero int) (hAPP int int (hAPP int (fun int int) (div_mod int) X_1) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) )) 17.83/17.29 ( (one_one int) ) 17.83/17.29 ) 17.83/17.29 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int (fun _let_0 bool) (member int) X_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_1 zEven))) (not (hBOOL (hAPP _let_0 bool _let_1 zOdd)))) ))) 17.83/17.29 ( (one_one int) ) 17.83/17.29 ) 17.83/17.29 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (one_one real))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) _let_2))) (= (hAPP real real sqrt (hAPP real real (hAPP real (fun real real) (minus_minus real) _let_2) (hAPP nat real (hAPP real (fun nat real) (power_power real) X) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real real cos (hAPP real real arcsin X)))) )))) 17.83/17.29 ( (zero_zero real) ) 17.83/17.29 ( (hAPP int real (number_number_of real) min_1) ) 17.83/17.29 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.83/17.29 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.83/17.29 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.83/17.29 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.83/17.29 ( skv_14 ) 17.83/17.29 ) 17.83/17.29 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (forall ((X $$unsorted)) (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)))) ))) 17.83/17.29 ( (one_one real) ) 17.83/17.29 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.83/17.29 ) 17.83/17.29 (instantiation (let ((_let_0 (ring_1_Ints X_a))) (forall ((X_a $$unsorted)) (or (not (ring_1 X_a)) (= _let_0 (ti (fun X_a bool) _let_0))) )) 17.83/17.29 ( bool ) 17.83/17.29 ( real ) 17.83/17.29 ( nat ) 17.83/17.29 ( (fun nat bool) ) 17.83/17.29 ( int ) 17.83/17.29 ( (fun int bool) ) 17.83/17.29 ( complex ) 17.83/17.29 ( rat ) 17.83/17.29 ( (product_prod real real) ) 17.83/17.29 ( (product_prod int int) ) 17.83/17.29 ( (filter real) ) 17.83/17.29 ( (filter nat) ) 17.83/17.29 ( (product_prod nat nat) ) 17.83/17.29 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 17.83/17.29 ( (fun nat rat) ) 17.83/17.29 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 17.83/17.29 ) 17.83/17.29 (instantiation (let ((_let_0 (fun X_a X_c))) (let ((_let_1 (fun X_b X_c))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP X_b X_c (hAPP X_a _let_1 P R) Q) (hAPP X_a X_c (hAPP X_b _let_0 (hAPP (fun X_a _let_1) (fun X_b _let_0) (combc X_a X_b X_c) P) Q) R)) ))) 17.83/17.29 ( 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)))) ) 17.83/17.29 ( real, bool, real, (ord_less_eq real), pi, (zero_zero real) ) 17.83/17.29 ( real, bool, real, (ord_less_eq real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.83/17.29 ( 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)))) ) 17.83/17.29 ( real, bool, real, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 17.83/17.29 ( 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) ) 17.83/17.29 ( 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) ) 17.83/17.29 ( real, bool, real, (ord_less_eq real), skv_6, (zero_zero real) ) 17.83/17.29 ( real, bool, real, (ord_less_eq real), skv_11, (zero_zero real) ) 17.83/17.29 ( real, bool, real, (ord_less_eq real), skv_12, (zero_zero real) ) 17.83/17.29 ( real, bool, real, (ord_less_eq real), skv_14, (zero_zero real) ) 17.83/17.29 ( real, bool, real, (ord_less real), (zero_zero real), pi ) 17.83/17.29 ( 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))))) ) 17.83/17.29 ( 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)))) ) 17.83/17.29 ( real, bool, real, (ord_less real), pi, (zero_zero real) ) 17.83/17.29 ( 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)) ) 17.83/17.29 ( 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)))) ) 17.83/17.29 ( 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) ) 17.83/17.29 ( 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 ) 17.83/17.29 ( 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) ) 17.83/17.29 ( 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) ) 17.83/17.29 ( real, bool, real, (ord_less real), skv_2, (zero_zero real) ) 17.83/17.29 ( real, bool, real, (ord_less real), skv_10, (zero_zero real) ) 17.83/17.29 ( real, bool, real, (ord_less real), skv_13, (zero_zero real) ) 17.83/17.29 ( 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) ) 17.83/17.29 ( real, bool, (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real (fun (filter nat) bool)) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))))), sequentially, (zero_zero real) ) 17.83/17.29 ( real, real, real, (minus_minus real), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 17.83/17.29 ( 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) ) 17.94/17.29 ( real, real, real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.94/17.29 ( 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))) ) 17.94/17.29 ( 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)))) ) 17.94/17.29 ( 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)))) ) 17.94/17.29 ( 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 ) 17.94/17.29 ( 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 ) 17.94/17.29 ( real, real, real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 17.94/17.29 ( 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) ) 17.94/17.29 ( 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) ) 17.94/17.29 ( 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) ) 17.94/17.29 ( real, real, real, (times_times real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.94/17.29 ( 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))))) ) 17.94/17.29 ( real, real, real, (times_times real), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.94/17.29 ( 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)))) ) 17.94/17.29 ( real, complex, real, complex_1, (zero_zero real), (zero_zero real) ) 17.94/17.29 ( real, complex, real, complex_1, (zero_zero real), (one_one real) ) 17.94/17.29 ( real, complex, real, complex_1, (one_one real), (zero_zero real) ) 17.94/17.29 ( 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) ) 17.94/17.29 ( nat, real, real, root, (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.94/17.29 ( nat, real, real, root, (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 17.94/17.29 ( 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))) ) 17.94/17.29 ( 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))) ) 17.94/17.29 ( nat, nat, nat, (plus_plus nat), (one_one nat), (one_one nat) ) 17.94/17.29 ( int, bool, int, (ord_less_eq int), pls, min_1 ) 17.94/17.29 ( int, bool, int, (ord_less_eq int), (one_one int), (zero_zero int) ) 17.94/17.29 ( int, bool, int, (ord_less_eq int), min_1, (zero_zero int) ) 17.94/17.29 ( int, bool, int, (ord_less_eq int), min_1, min_1 ) 17.94/17.29 ( 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) ) 17.94/17.29 ( int, bool, int, (ord_less_eq int), s, (zero_zero int) ) 17.94/17.29 ( int, bool, int, (ord_less_eq int), (hAPP int int (number_number_of int) pls), (zero_zero int) ) 17.94/17.29 ( int, bool, int, (ord_less_eq int), t, (one_one int) ) 17.94/17.29 ( 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) ) 17.94/17.29 ( int, bool, int, (ord_less_eq int), skv_3, (zero_zero int) ) 17.94/17.29 ( int, bool, int, (ord_less_eq int), skv_9, (zero_zero int) ) 17.94/17.29 ( int, bool, int, (ord_less int), (zero_zero int), (zero_zero int) ) 17.94/17.29 ( int, bool, int, (ord_less int), (zero_zero int), min_1 ) 17.94/17.29 ( int, bool, int, (ord_less int), (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.94/17.29 ( int, bool, int, (ord_less int), (zero_zero int), t ) 17.94/17.29 ( int, bool, int, (ord_less int), (one_one int), (zero_zero int) ) 17.94/17.29 ( int, bool, int, (ord_less int), (one_one int), t ) 17.94/17.29 ( 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) ) 17.94/17.29 ( 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 ) 17.94/17.29 ( 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 ) 17.94/17.29 ( 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_3 ) 17.94/17.29 ( 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_9 ) 17.94/17.29 ( int, bool, int, (ord_less int), min_1, (zero_zero int) ) 17.94/17.30 ( int, bool, int, (ord_less int), min_1, min_1 ) 17.94/17.30 ( int, bool, int, (ord_less 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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 17.97/17.30 ( int, bool, int, (dvd_dvd int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.97/17.30 ( int, bool, int, quadRes, (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.97/17.30 ( 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 ) 17.97/17.30 ( 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_3 ) 17.97/17.30 ( 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_9 ) 17.97/17.30 ( int, bool, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 17.97/17.30 ( 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)))) ) 17.97/17.30 ( int, bool, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 17.97/17.30 ( int, bool, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 17.97/17.30 ( int, bool, (fun int bool), (member int), zEven, (one_one int) ) 17.97/17.30 ( int, int, nat, (power_power int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 17.97/17.30 ( int, int, nat, (power_power int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 17.97/17.30 ( int, int, nat, (power_power int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 17.97/17.30 ( 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) ) 17.97/17.30 ( 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)))) ) 17.97/17.30 ( int, int, int, (times_times 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))) ) 17.97/17.30 ( 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)))) ) 17.97/17.30 ( 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))) ) 17.97/17.30 ( int, int, int, (times_times int), skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 17.97/17.30 ( int, int, int, (minus_minus int), (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.97/17.30 ( int, int, int, legendre, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 17.97/17.30 ( int, (fun int bool), int, zcong, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.97/17.30 ( int, (fun int bool), int, zcong, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.97/17.30 ( int, (fun int bool), int, zcong, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 17.97/17.30 ( int, (fun int bool), int, zcong, s, s1 ) 17.97/17.30 ( 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)))) ) 17.97/17.30 ( int, (fun int bool), int, zcong, skv_3, s1 ) 17.97/17.30 ( int, (fun int bool), int, zcong, skv_9, s1 ) 17.97/17.30 ( int, rat, int, fract, (one_one int), (zero_zero int) ) 17.97/17.30 ( int, rat, int, fract, (one_one int), (one_one int) ) 17.97/17.30 ( int, (product_prod int int), int, (product_Pair int int), (one_one int), (zero_zero int) ) 17.97/17.30 ( int, (product_prod int int), int, (product_Pair int int), (one_one int), (one_one int) ) 17.97/17.30 ( int, (product_prod int int), int, (product_Pair int int), (one_one int), s ) 17.97/17.30 ( (fun int nat), bool, (fun int bool), (nat_tr1645093318rphism int nat), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), nat_1 ) 17.97/17.30 ( (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) ) 17.97/17.30 ( (fun real real), (fun nat real), (fun nat real), (combb real real nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))), (inverse_inverse real) ) 17.97/17.30 ( (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))) ) 17.97/17.30 ( complex, complex, nat, (power_power 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( (filter nat), sequentially ) 17.97/17.39 ( (fun (product_prod nat nat) bool), pred_nat ) 17.97/17.39 ( (fun (product_prod int int) bool), frac_1 ) 17.97/17.39 ( (fun real complex), cis ) 17.97/17.39 ( (fun complex real), im ) 17.97/17.39 ( (fun complex real), re ) 17.97/17.39 ( (fun complex real), arg ) 17.97/17.39 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 17.97/17.39 ( (fun int (fun int int)), int_gcd ) 17.97/17.39 ( (fun int (fun int int)), multInv ) 17.97/17.39 ( (fun int (fun int int)), legacy_zgcd ) 17.97/17.39 ( (fun int (fun int int)), z3mod ) 17.97/17.39 ( (fun int (fun int int)), inv ) 17.97/17.39 ( (fun int (fun int int)), (gcd_gcd int) ) 17.97/17.39 ( (fun int (fun int int)), standardRes ) 17.97/17.39 ( (fun int (fun int int)), legendre ) 17.97/17.39 ( (fun int (fun int int)), nat_tsub ) 17.97/17.39 ( (fun int (fun int int)), z3div ) 17.97/17.39 ( (fun int (fun int int)), int_lcm ) 17.97/17.39 ( (fun int (fun (product_prod int int) bool)), 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bool))), divmod_int_rel ) 17.97/17.39 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 17.97/17.39 ( (fun int (fun int (product_prod int int))), negDivAlg ) 17.97/17.39 ( (fun int (fun int (product_prod int int))), divmod_int ) 17.97/17.39 ( (fun int (fun int (product_prod int int))), posDivAlg ) 17.97/17.39 ( (fun int (fun int (product_prod int int))), pdivmod ) 17.97/17.39 ( (fun int (fun int (product_prod int int))), norm_frac ) 17.97/17.39 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 17.97/17.39 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 17.97/17.39 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 17.97/17.39 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 17.97/17.39 ( (fun real nat), natfloor ) 17.97/17.39 ( (fun real nat), natceiling ) 17.97/17.39 ( (fun int quickcheck_code_int), quickcheck_of_int ) 17.97/17.39 ( (fun int (fun int (fun int bool))), wset ) 17.97/17.39 ( (fun int (fun int (fun int bool))), bnorRset ) 17.97/17.39 ( (fun int (fun int (fun int bool))), zcong ) 17.97/17.39 ( (fun int (fun int (fun int bool))), noXRRset ) 17.97/17.39 ( (fun int (fun int (fun int bool))), zcongm ) 17.97/17.39 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 17.97/17.39 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 17.97/17.39 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 17.97/17.39 ( (fun int real), (real_1 int) ) 17.97/17.39 ( (fun complex nat), (size_size complex) ) 17.97/17.39 ( (fun complex nat), complex_size ) 17.97/17.39 ( (fun int (list int)), quickc666637781d_zero ) 17.97/17.39 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 17.97/17.39 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 17.97/17.39 ( (fun (product_prod int int) rat), frct ) 17.97/17.39 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 17.97/17.39 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 17.97/17.39 ( (fun (fun nat rat) bool), vanishes ) 17.97/17.39 ( (fun int (fun int rat)), fract ) 17.97/17.39 ( (fun code_code_numeral int), code_int_of ) 17.97/17.39 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 17.97/17.39 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 17.97/17.39 ( (fun code_code_numeral nat), code_c271388182l_size ) 17.97/17.39 ( (fun real (fun real complex)), complex_1 ) 17.97/17.39 ( (fun real (fun real complex)), rcis ) 17.97/17.39 ( (fun int (fun nat nat)), nat_aux ) 17.97/17.39 ( (fun rat real), ratreal ) 17.97/17.39 ( (fun quickcheck_code_int int), quickcheck_int_of ) 17.97/17.39 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 17.97/17.39 ( (fun rat (product_prod int int)), quotient_of ) 17.97/17.39 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 17.97/17.39 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 17.97/17.39 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 17.97/17.39 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 17.97/17.39 ) 17.97/17.39 (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)))) ) 17.97/17.39 ( bool ) 17.97/17.39 ( real ) 17.97/17.39 ( nat ) 17.97/17.39 ( (fun nat bool) ) 17.97/17.39 ( int ) 17.97/17.39 ( (fun int bool) ) 17.97/17.39 ( (fun real bool) ) 17.97/17.39 ( (fun real real) ) 17.97/17.39 ( complex ) 17.97/17.39 ( (fun nat real) ) 17.97/17.39 ( (fun int int) ) 17.97/17.39 ( rat ) 17.97/17.39 ( (fun int (fun int bool)) ) 17.97/17.39 ( quickcheck_code_int ) 17.97/17.39 ( (product_prod real real) ) 17.97/17.39 ( (product_prod int int) ) 17.97/17.39 ( (filter real) ) 17.97/17.39 ( (filter nat) ) 17.97/17.39 ( (product_prod nat nat) ) 17.97/17.39 ( (fun (product_prod int int) bool) ) 17.97/17.39 ( code_code_numeral ) 17.97/17.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 17.97/17.39 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 17.97/17.39 ( (fun nat rat) ) 17.97/17.39 ( (fun (product_prod int int) int) ) 17.97/17.39 ( (fun int (fun int (fun int bool))) ) 17.97/17.39 ( (fun int real) ) 17.97/17.39 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 17.97/17.39 ) 17.97/17.39 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_128364 $$unsorted) (BOUND_VARIABLE_128365 $$unsorted)) (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_128364) BOUND_VARIABLE_128365)) BOUND_VARIABLE_128364))) )) 17.97/17.39 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 17.97/17.39 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 17.97/17.39 ( 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)))))) ) 17.97/17.39 ( 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 ) 17.97/17.39 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 17.97/17.39 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 17.97/17.39 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 17.97/17.39 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_1 ) 17.97/17.40 ( complex, ii, ii ) 17.97/17.40 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 17.97/17.40 ( 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 ) 17.97/17.40 ) 17.97/17.40 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (minus_minus int) K_4) min_1) (hAPP int int succ K_4)) ) 17.97/17.40 ( pls ) 17.97/17.40 ( min_1 ) 17.97/17.40 ( (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)))) ) 17.97/17.40 ) 17.97/17.40 (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 nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natceiling X)) (hAPP int nat (number_number_of nat) N)) (hAPP real nat natceiling (hAPP real real (hAPP real (fun real real) (plus_plus real) X) (hAPP int real (number_number_of real) N))))) ) 17.97/17.40 ( (one_one real), (hAPP int int bit1 pls) ) 17.97/17.40 ) 17.97/17.40 (instantiation (let ((_let_0 (even_odd_even nat))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (not (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) N_1)))) (= (hBOOL (hAPP nat bool _let_0 N_1)) (not (hBOOL (hAPP nat bool _let_0 Ma))))) )) 17.97/17.40 ( (one_one nat), (one_one nat) ) 17.97/17.40 ) 17.97/17.40 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int bit0 (hAPP int int succ K_4)) (hAPP int int succ (hAPP int int bit1 K_4))) ) 17.97/17.40 ( pls ) 17.97/17.40 ( (hAPP int int bit1 pls) ) 17.97/17.40 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 17.97/17.40 ( min_1 ) 17.97/17.40 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 17.97/17.40 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 17.97/17.40 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 17.97/17.40 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 17.97/17.40 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 17.97/17.40 ) 17.97/17.40 (instantiation (forall ((M $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) M))) (= (ti int M) (hAPP int int (hAPP int (fun int int) legacy_zgcd M) M))) ) 18.11/17.40 ( pls ) 18.11/17.40 ( m ) 18.11/17.40 ( (one_one int) ) 18.11/17.40 ( min_1 ) 18.11/17.40 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.40 ( s ) 18.11/17.40 ( (hAPP int int (number_number_of int) pls) ) 18.11/17.40 ( s1 ) 18.11/17.40 ( t ) 18.11/17.40 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.11/17.40 ( skv_3 ) 18.11/17.40 ( skv_9 ) 18.11/17.40 ) 18.11/17.40 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_128483 $$unsorted)) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_128483)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_128483)) _let_2)))) )))) 18.11/17.40 ( real, (one_one real) ) 18.11/17.40 ( real, pi ) 18.11/17.40 ( 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)))) ) 18.11/17.40 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.11/17.40 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.11/17.40 ( real, skv_6 ) 18.11/17.40 ( real, skv_11 ) 18.11/17.40 ( real, skv_12 ) 18.11/17.40 ( real, skv_14 ) 18.11/17.40 ( int, pls ) 18.11/17.40 ( int, (one_one int) ) 18.11/17.40 ( int, min_1 ) 18.11/17.40 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.40 ( int, s ) 18.11/17.40 ( int, (hAPP int int (number_number_of int) pls) ) 18.11/17.40 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.11/17.40 ( int, skv_3 ) 18.11/17.40 ( int, skv_9 ) 18.11/17.40 ( complex, ii ) 18.11/17.40 ( complex, (one_one complex) ) 18.11/17.40 ) 18.11/17.40 (instantiation (let ((_let_0 (product_prod X_b X_c))) (let ((_let_1 (fun X_c X_a))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted) (Z $$unsorted)) (or (not (hBOOL (hAPP X_a bool Q_1 (hAPP _let_0 X_a (hAPP (fun X_b _let_1) (fun _let_0 X_a) (product_prod_case X_b X_c X_a) P_1) Z)))) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (or (not (= (hAPP X_c _let_0 (hAPP X_b (fun X_c _let_0) (product_Pair X_b X_c) X_2) Y_2) (ti _let_0 Z))) (not (hBOOL (hAPP X_a bool Q_1 (hAPP X_c X_a (hAPP X_b _let_1 P_1 X_2) Y_2))))) ))) ))) 18.11/17.40 ( int, int, int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP _let_0 _let_1 (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))), (let ((_let_0 (product_prod int int))) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) s) (one_one int))) ) 18.11/17.40 ( 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_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP _let_0 _let_1 (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))), (let ((_let_0 (product_prod int int))) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) s) (one_one int))) ) 18.11/17.40 ) 18.11/17.40 (instantiation (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))) (forall ((P_5 $$unsorted) (Q_3 $$unsorted)) (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))) ))) 18.11/17.40 ( (zero_zero int), (one_one int) ) 18.11/17.40 ( (one_one int), (one_one int) ) 18.11/17.40 ( s, (one_one int) ) 18.11/17.40 ) 18.11/17.40 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (= (one_one X_a) (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 pls)))) ) 18.11/17.40 ( real ) 18.11/17.40 ( nat ) 18.11/17.40 ( int ) 18.11/17.40 ( complex ) 18.11/17.40 ( rat ) 18.11/17.40 ( quickcheck_code_int ) 18.11/17.40 ( code_code_numeral ) 18.11/17.40 ) 18.11/17.40 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (one_one real))) (let ((_let_3 (plus_plus real))) (let ((_let_4 (abs_abs real))) (forall ((Y $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP real real _let_4 X)) _let_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (hAPP real real _let_4 Y)) _let_2))) (= (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (hAPP real real (hAPP real _let_1 _let_3 X) Y)) (hAPP real real (hAPP real _let_1 (minus_minus real) _let_2) (hAPP real real (hAPP real _let_1 (times_times real) X) Y)))) (hAPP real real (hAPP real _let_1 _let_3 (hAPP real real arctan X)) (hAPP real real arctan Y)))) )))))) 18.11/17.40 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.40 ( 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))))) ) 18.11/17.40 ( (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.40 ( (hAPP real real arctan (hAPP real real (hAPP 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)))) ) 18.11/17.40 ) 18.11/17.40 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted)) (or (not (sgn_if X_a)) (= _let_0 (hAPP X_a X_a (sgn_sgn X_a) _let_0))) )) 18.11/17.40 ( real ) 18.11/17.40 ( nat ) 18.11/17.40 ( int ) 18.11/17.40 ( complex ) 18.11/17.40 ( rat ) 18.11/17.40 ( quickcheck_code_int ) 18.11/17.40 ( code_code_numeral ) 18.11/17.40 ) 18.11/17.40 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) K_4)) K_4) (hAPP int int bit1 K_4)) ))) 18.11/17.40 ( pls ) 18.11/17.40 ( (hAPP int int bit1 pls) ) 18.11/17.40 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.11/17.40 ( min_1 ) 18.11/17.40 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.11/17.40 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 18.11/17.40 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 18.11/17.40 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 18.11/17.40 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 18.11/17.40 ) 18.11/17.40 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_128573 $$unsorted) (BOUND_VARIABLE_128574 $$unsorted) (BOUND_VARIABLE_128575 $$unsorted)) (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_128575))) (= (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_128573) BOUND_VARIABLE_128575)) BOUND_VARIABLE_128574)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_128573) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_128574) BOUND_VARIABLE_128575))))) )))) 18.11/17.40 ( real, (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.11/17.40 ( 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))) ) 18.11/17.40 ( 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)), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.11/17.40 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 18.11/17.40 ) 18.11/17.40 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (dvd_dvd X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_128626 $$unsorted) (BOUND_VARIABLE_128627 $$unsorted)) (or (not (comm_ring_1 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_128626)) BOUND_VARIABLE_128627)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_128626) BOUND_VARIABLE_128627)))) ))) 18.11/17.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int 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)) ) 18.11/17.40 ) 18.11/17.40 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (ord_atLeastLessThan int))) (forall ((L $$unsorted) (U_1 $$unsorted)) (= (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (image int int) (hAPP int _let_1 (hAPP _let_3 _let_3 (combc int int int) (plus_plus int)) L)) (hAPP int _let_0 (hAPP int _let_2 _let_4 (zero_zero int)) (hAPP int int (hAPP int _let_1 (minus_minus int) U_1) L))) (hAPP int _let_0 (hAPP int _let_2 _let_4 L) U_1)) )))))) 18.11/17.40 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.11/17.40 ) 18.11/17.40 (instantiation (let ((_let_0 (number_number_of int))) (let ((_let_1 (uminus_uminus int))) (forall ((W $$unsorted)) (= (hAPP int int _let_1 (hAPP int int _let_0 W)) (hAPP int int _let_0 (hAPP int int _let_1 W))) ))) 18.11/17.40 ( pls ) 18.11/17.41 ( (hAPP int int bit1 pls) ) 18.11/17.41 ( (one_one int) ) 18.11/17.41 ( min_1 ) 18.11/17.41 ) 18.11/17.41 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_128755))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_128754 $$unsorted) (BOUND_VARIABLE_128755 $$unsorted) (BOUND_VARIABLE_128756 $$unsorted)) (or (not (ord X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_128756))) (not (= (ti X_a BOUND_VARIABLE_128756) (ti X_a BOUND_VARIABLE_128754))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_128754))) )) 18.11/17.41 ( real, pi, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.11/17.41 ( int, pls, (zero_zero int), (one_one int) ) 18.11/17.41 ( int, m, (zero_zero int), s ) 18.11/17.41 ( int, min_1, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 18.11/17.41 ( int, s, (zero_zero int), min_1 ) 18.11/17.41 ( int, s1, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.41 ( int, t, min_1, min_1 ) 18.11/17.41 ) 18.11/17.41 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) X) Y))) (= (hAPP int int (abs_abs int) X) (hAPP int int (hAPP int (fun int int) (gcd_gcd int) X) Y))) ) 18.11/17.41 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 18.11/17.41 ) 18.11/17.41 (instantiation (let ((_let_0 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_128921 $$unsorted)) (or (not (number_semiring X_a)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) pls) BOUND_VARIABLE_128921))) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_128921)) (one_one X_a)) (hAPP int X_a _let_0 (hAPP int int succ BOUND_VARIABLE_128921)))) )) 18.11/17.41 ( nat, pls ) 18.11/17.41 ( nat, (hAPP int int bit1 pls) ) 18.11/17.41 ( nat, min_1 ) 18.11/17.41 ( int, pls ) 18.11/17.41 ( int, min_1 ) 18.11/17.41 ( quickcheck_code_int, pls ) 18.11/17.41 ( quickcheck_code_int, min_1 ) 18.11/17.41 ( code_code_numeral, pls ) 18.11/17.41 ( code_code_numeral, min_1 ) 18.11/17.41 ) 18.11/17.41 (instantiation (let ((_let_0 (one_one nat))) (forall ((V $$unsorted)) (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)))) )) 18.11/17.41 ( (zero_zero int) ) 18.11/17.41 ( pls ) 18.11/17.41 ( (hAPP int int bit1 pls) ) 18.11/17.41 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.11/17.41 ( min_1 ) 18.11/17.41 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.11/17.41 ( s ) 18.11/17.41 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 18.11/17.41 ( t ) 18.11/17.41 ( skv_3 ) 18.11/17.41 ( skv_9 ) 18.11/17.41 ) 18.11/17.41 (instantiation (let ((_let_0 (number_number_of nat))) (forall ((V $$unsorted)) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V) pls)) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)) (hAPP int nat _let_0 V)) (hAPP int nat _let_0 (hAPP int int succ V)))) )) 18.11/17.41 ( (zero_zero int) ) 18.11/17.41 ( pls ) 18.11/17.41 ( (hAPP int int bit1 pls) ) 18.11/17.41 ( min_1 ) 18.11/17.41 ( s ) 18.11/17.41 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 18.11/17.41 ( t ) 18.11/17.41 ( skv_3 ) 18.11/17.41 ( skv_9 ) 18.11/17.41 ) 18.11/17.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128953 $$unsorted)) (or (not (linordered_semidom X_a)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) BOUND_VARIABLE_128953)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_128953))))) ) 18.11/17.41 ( real, (zero_zero nat) ) 18.11/17.41 ( real, (one_one nat) ) 18.11/17.41 ( int, (zero_zero nat) ) 18.11/17.41 ( int, (hAPP nat nat suc (zero_zero nat)) ) 18.11/17.41 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.41 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.11/17.41 ) 18.11/17.41 (instantiation (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_5))) (= (hAPP int nat phi P_5) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) P_5) (one_one int))))) ) 18.11/17.41 ( (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))) ) 18.11/17.41 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.41 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.11/17.41 ) 18.11/17.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129012 $$unsorted)) (or (not (comm_monoid_mult X_a)) (= (ti X_a BOUND_VARIABLE_129012) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_129012) (one_one X_a)))) ) 18.11/17.41 ( bool, fFalse ) 18.11/17.41 ( bool, fTrue ) 18.11/17.41 ( real, pi ) 18.11/17.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.11/17.41 ( 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))))) ) 18.11/17.41 ( (fun nat bool), (even_odd_even nat) ) 18.11/17.41 ( (fun nat bool), prime ) 18.11/17.41 ( (fun nat nat), suc ) 18.11/17.41 ( (fun nat nat), (fact_fact nat) ) 18.11/17.41 ( (fun nat nat), (size_size nat) ) 18.11/17.41 ( (fun nat nat), fact ) 18.11/17.41 ( (fun nat nat), nat_size ) 18.11/17.41 ( int, pls ) 18.11/17.41 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.11/17.41 ( int, m ) 18.11/17.41 ( 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))) ) 18.11/17.41 ( int, min_1 ) 18.11/17.41 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.41 ( int, s ) 18.11/17.41 ( int, s1 ) 18.11/17.41 ( int, t ) 18.11/17.41 ( (fun int bool), zprime ) 18.11/17.41 ( (fun int bool), nat_neg ) 18.11/17.41 ( (fun int bool), zEven ) 18.11/17.41 ( (fun int bool), nat_is_nat ) 18.11/17.41 ( (fun int bool), zOdd ) 18.11/17.41 ( (fun int bool), (even_odd_even int) ) 18.11/17.41 ( (fun int bool), twoSqu1091635170sum2sq ) 18.11/17.41 ( (fun int nat), nat_1 ) 18.11/17.41 ( (fun int nat), phi ) 18.11/17.41 ( (fun real real), sqrt ) 18.11/17.41 ( (fun real real), tan ) 18.11/17.41 ( (fun real real), cos ) 18.11/17.41 ( (fun real real), arccos ) 18.11/17.41 ( (fun real real), ln ) 18.11/17.41 ( (fun real real), sin ) 18.11/17.41 ( (fun real real), arctan ) 18.11/17.41 ( (fun real real), arcsin ) 18.11/17.41 ( complex, ii ) 18.11/17.41 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.41 ( 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)) ) 18.11/17.41 ( (fun complex complex), cnj ) 18.11/17.41 ( (fun complex complex), expi ) 18.11/17.41 ( (fun nat real), (real_1 nat) ) 18.11/17.41 ( (fun nat real), cos_coeff ) 18.11/17.41 ( (fun nat real), sin_coeff ) 18.11/17.41 ( (fun int int), bit0 ) 18.11/17.41 ( (fun int int), bit1 ) 18.11/17.41 ( (fun int int), pred ) 18.11/17.41 ( (fun int int), succ ) 18.11/17.41 ( (fun int int), (fact_fact int) ) 18.11/17.41 ( (fun int int), zfact ) 18.11/17.41 ( (fun bool bool), fNot ) 18.11/17.41 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 18.11/17.41 ( (fun bool (fun bool bool)), fconj ) 18.11/17.41 ( (fun bool (fun bool bool)), fdisj ) 18.11/17.41 ( (fun bool (fun bool bool)), fimplies ) 18.11/17.41 ( (fun int (fun int bool)), sRStar ) 18.11/17.41 ( (fun int (fun int bool)), quadRes ) 18.11/17.41 ( (fun int (fun int bool)), norRRset ) 18.11/17.41 ( (fun int (fun int bool)), d22set ) 18.11/17.41 ( (fun int (fun int bool)), sr ) 18.11/17.41 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 18.11/17.41 ( (fun nat (fun nat nat)), nat_gcd ) 18.11/17.41 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 18.11/17.41 ( (fun nat (fun nat nat)), nat_lcm ) 18.11/17.41 ( (fun nat (fun real real)), root ) 18.11/17.41 ( (fun real (fun real real)), log ) 18.11/17.41 ( (fun real (fun real real)), powr ) 18.11/17.41 ( (fun nat (fun nat bool)), coprime ) 18.11/17.41 ( (fun (fun int bool) int), (the int) ) 18.11/17.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 18.11/17.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 18.11/17.41 ( (fun nat (fun nat (product_prod int int))), bezw ) 18.11/17.41 ( (fun (fun int bool) bool), nat_nat_set ) 18.11/17.41 ( (filter nat), sequentially ) 18.11/17.41 ( (fun (product_prod nat nat) bool), pred_nat ) 18.11/17.41 ( (fun (product_prod int int) bool), frac_1 ) 18.11/17.41 ( (fun real complex), cis ) 18.11/17.41 ( (fun complex real), im ) 18.11/17.41 ( (fun complex real), re ) 18.11/17.41 ( (fun complex real), arg ) 18.11/17.41 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 18.11/17.41 ( (fun int (fun int int)), int_gcd ) 18.11/17.41 ( (fun int (fun int int)), multInv ) 18.11/17.41 ( (fun int (fun int int)), legacy_zgcd ) 18.11/17.41 ( (fun int (fun int int)), z3mod ) 18.11/17.41 ( (fun int (fun int int)), inv ) 18.11/17.41 ( (fun int (fun int int)), (gcd_gcd int) ) 18.11/17.41 ( (fun int (fun int int)), standardRes ) 18.11/17.41 ( (fun int (fun int int)), legendre ) 18.11/17.41 ( (fun int (fun int int)), nat_tsub ) 18.11/17.41 ( (fun int (fun int int)), z3div ) 18.11/17.41 ( (fun int (fun int int)), int_lcm ) 18.11/17.41 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 18.11/17.41 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 18.11/17.41 ( (fun int (fun (fun int bool) bool)), rsetR ) 18.11/17.41 ( (fun int (fun (fun int bool) bool)), resSet ) 18.11/17.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 18.11/17.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 18.11/17.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 18.11/17.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 18.11/17.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 18.11/17.41 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 18.11/17.41 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 18.11/17.41 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 18.11/17.41 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 18.11/17.41 ( (fun int (fun int (product_prod int int))), negDivAlg ) 18.11/17.41 ( (fun int (fun int (product_prod int int))), divmod_int ) 18.11/17.41 ( (fun int (fun int (product_prod int int))), posDivAlg ) 18.11/17.41 ( (fun int (fun int (product_prod int int))), pdivmod ) 18.11/17.41 ( (fun int (fun int (product_prod int int))), norm_frac ) 18.11/17.41 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 18.11/17.41 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 18.11/17.41 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 18.11/17.41 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 18.11/17.41 ( (fun real nat), natfloor ) 18.11/17.41 ( (fun real nat), natceiling ) 18.11/17.41 ( (fun int quickcheck_code_int), quickcheck_of_int ) 18.11/17.41 ( (fun int (fun int (fun int bool))), wset ) 18.11/17.41 ( (fun int (fun int (fun int bool))), bnorRset ) 18.11/17.41 ( (fun int (fun int (fun int bool))), zcong ) 18.11/17.41 ( (fun int (fun int (fun int bool))), noXRRset ) 18.11/17.41 ( (fun int (fun int (fun int bool))), zcongm ) 18.11/17.41 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 18.11/17.41 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 18.11/17.41 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 18.11/17.41 ( (fun int real), (real_1 int) ) 18.11/17.41 ( (fun complex nat), (size_size complex) ) 18.11/17.41 ( (fun complex nat), complex_size ) 18.11/17.41 ( (fun int (list int)), quickc666637781d_zero ) 18.11/17.41 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 18.11/17.41 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 18.11/17.41 ( (fun (product_prod int int) rat), frct ) 18.11/17.41 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 18.11/17.41 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 18.11/17.41 ( (fun (fun nat rat) bool), vanishes ) 18.11/17.41 ( (fun int (fun int rat)), fract ) 18.11/17.41 ( (fun code_code_numeral int), code_int_of ) 18.11/17.41 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 18.11/17.41 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 18.11/17.41 ( (fun code_code_numeral nat), code_c271388182l_size ) 18.11/17.41 ( (fun real (fun real complex)), complex_1 ) 18.11/17.41 ( (fun real (fun real complex)), rcis ) 18.11/17.41 ( (fun int (fun nat nat)), nat_aux ) 18.11/17.41 ( (fun rat real), ratreal ) 18.11/17.41 ( (fun quickcheck_code_int int), quickcheck_int_of ) 18.11/17.41 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 18.11/17.41 ( (fun rat (product_prod int int)), quotient_of ) 18.11/17.41 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 18.11/17.41 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 18.11/17.41 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 18.11/17.41 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 18.11/17.41 ) 18.11/17.41 (instantiation (forall ((V $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) V) pls))) (= (zero_zero nat) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat (number_number_of nat) V)) (one_one nat)))) ) 18.11/17.41 ( (zero_zero int) ) 18.11/17.41 ( pls ) 18.11/17.41 ( (hAPP int int bit1 pls) ) 18.11/17.41 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.11/17.41 ( (one_one int) ) 18.11/17.41 ( min_1 ) 18.11/17.41 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.11/17.41 ) 18.11/17.41 (instantiation (let ((_let_0 (number_number_of nat))) (forall ((V $$unsorted)) (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)))) )) 18.11/17.41 ( (zero_zero int) ) 18.11/17.41 ( pls ) 18.11/17.41 ( (one_one int) ) 18.11/17.41 ( min_1 ) 18.11/17.41 ) 18.11/17.41 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) B_1))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 A_2) B_1)) (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less rat) (hAPP int rat (hAPP int (fun int rat) fract A_2) B_1)) (one_one rat))))) ))) 18.11/17.41 ( (zero_zero int), (zero_zero int) ) 18.11/17.41 ( (zero_zero int), (one_one int) ) 18.11/17.41 ( (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))) ) 18.11/17.41 ( (zero_zero int), min_1 ) 18.11/17.41 ( (one_one int), (one_one int) ) 18.11/17.41 ( min_1, (zero_zero int) ) 18.11/17.41 ( min_1, min_1 ) 18.11/17.41 ( 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))) ) 18.11/17.41 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 18.11/17.41 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 18.11/17.41 ( t, (zero_zero int) ) 18.11/17.41 ( t, (one_one int) ) 18.11/17.41 ( 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))) ) 18.11/17.41 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.11/17.41 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.11/17.41 ) 18.11/17.41 (instantiation (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)))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) pi))) (hBOOL (hAPP real bool _let_2 (hAPP real real sin X)))) )))) 18.11/17.42 ( (zero_zero real) ) 18.11/17.42 ( pi ) 18.11/17.42 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.11/17.42 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.11/17.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 18.11/17.42 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 18.11/17.42 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.11/17.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 18.11/17.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 18.11/17.42 ( skv_14 ) 18.11/17.42 ) 18.11/17.42 (instantiation (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (= (hAPP nat X_a (semiring_1_of_nat X_a) (zero_zero nat)) (zero_zero X_a))) ) 18.11/17.42 ( real ) 18.11/17.42 ( nat ) 18.11/17.42 ( int ) 18.11/17.42 ( complex ) 18.11/17.42 ( rat ) 18.11/17.42 ( quickcheck_code_int ) 18.11/17.42 ( code_code_numeral ) 18.11/17.42 ) 18.11/17.42 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_129154 $$unsorted) (BOUND_VARIABLE_129155 $$unsorted)) (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_129154)) BOUND_VARIABLE_129155))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_129154) BOUND_VARIABLE_129155))) ))) 18.11/17.42 ( real, (zero_zero real), pi ) 18.11/17.42 ( 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)))) ) 18.11/17.42 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.11/17.42 ( real, (zero_zero real), skv_6 ) 18.11/17.42 ( real, (zero_zero real), skv_11 ) 18.11/17.42 ( real, (zero_zero real), skv_12 ) 18.11/17.42 ( real, (zero_zero real), skv_14 ) 18.11/17.42 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.11/17.42 ( real, (hAPP real real (hAPP real (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))) ) 18.11/17.42 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.11/17.42 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.42 ( int, (zero_zero int), (one_one int) ) 18.11/17.42 ( int, (zero_zero int), min_1 ) 18.11/17.42 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.42 ( int, (zero_zero int), s ) 18.11/17.42 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 18.11/17.42 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.11/17.42 ( int, (zero_zero int), skv_3 ) 18.11/17.42 ( int, (zero_zero int), skv_9 ) 18.11/17.42 ( int, (one_one int), t ) 18.11/17.42 ( int, min_1, pls ) 18.11/17.42 ( int, min_1, min_1 ) 18.11/17.42 ) 18.11/17.42 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (real_1 int))) (forall ((R_4 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) R_4))) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) R_4) (hAPP int real _let_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) N_2) (one_one int)))))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real _let_2 N_2)) R_4)))) ))) )))) 18.11/17.42 ( pi ) 18.11/17.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.11/17.42 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.11/17.42 ( skv_6 ) 18.11/17.42 ( skv_11 ) 18.11/17.42 ( skv_12 ) 18.11/17.42 ( skv_14 ) 18.11/17.42 ) 18.11/17.42 (instantiation (let ((_let_0 (zero_zero nat))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) N_1)) (and (= _let_0 Ma) (= _let_0 N_1))) )) 18.11/17.42 ( (one_one nat), (one_one nat) ) 18.11/17.42 ) 18.11/17.42 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (plus_plus nat))) (forall ((N $$unsorted) (V $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V)))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 (one_one nat)) N) (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP int nat (number_number_of nat) V)) N)))) ))) 18.11/17.42 ( (one_one nat), (hAPP int int bit1 pls) ) 18.11/17.42 ) 18.11/17.42 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (plus_plus nat))) (let ((_let_2 (number_number_of nat))) (forall ((N $$unsorted) (V $$unsorted)) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V))) (= (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP int nat _let_2 V)) N)) (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP int nat _let_2 (hAPP int int succ V))) N))) )))) 18.11/17.42 ( (one_one nat), pls ) 18.11/17.42 ( (one_one nat), (hAPP int int bit1 pls) ) 18.11/17.42 ) 18.11/17.42 (instantiation (let ((_let_0 (one_one real))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X))) (not (= (hAPP real real (hAPP real (fun real real) (minus_minus real) X) _let_0) (hAPP real real ln X))) (= _let_0 X)) )) 18.11/17.42 ( (one_one real) ) 18.11/17.42 ( pi ) 18.11/17.42 ( (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)))) ) 18.11/17.42 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.11/17.42 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 18.11/17.42 ( skv_2 ) 18.11/17.42 ( skv_10 ) 18.11/17.42 ( skv_13 ) 18.11/17.42 ) 18.11/17.42 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP int bool _let_0 X))) (hBOOL (hAPP int bool _let_0 (hAPP int int (fact_fact int) X)))) )) 18.11/17.42 ( (zero_zero int) ) 18.11/17.42 ( (one_one int) ) 18.11/17.42 ) 18.11/17.42 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (div_div nat))) (let ((_let_2 (zero_zero nat))) (let ((_let_3 (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N)))) (let ((_let_4 (hAPP nat nat (hAPP nat _let_0 _let_1 M) N))) (forall ((M $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_2) N))) (and (or (not _let_3) (= _let_2 _let_4)) (or _let_3 (= _let_4 (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) M) N)) N)))))) )))))) 18.11/17.42 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.42 ) 18.11/17.42 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (or (not (= M (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) N))) (= (zero_zero nat) N)) ) 18.11/17.42 ( (one_one nat), (one_one nat) ) 18.11/17.42 ) 18.11/17.42 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (times_times X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_129334 $$unsorted) (BOUND_VARIABLE_129335 $$unsorted) (BOUND_VARIABLE_129336 $$unsorted) (BOUND_VARIABLE_129337 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_129336) BOUND_VARIABLE_129337))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_129334) BOUND_VARIABLE_129335))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_129337))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) _let_2) BOUND_VARIABLE_129334))) (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_129336) BOUND_VARIABLE_129334)) (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_129337) BOUND_VARIABLE_129335)))) )))))) 18.11/17.42 ( int, skv_1, (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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.11/17.42 ) 18.11/17.42 (instantiation (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)))) (forall ((N_1 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool _let_0 N_1))) (= (hAPP _let_0 nat (finite_card int) (hAPP _let_0 _let_0 (collect int) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs int bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 int) fconj) _let_0)) (hAPP int _let_0 (hAPP _let_3 _let_3 (combc int int bool) (ord_less int)) N_1)))) (hAPP int nat nat_1 N_1)))) ))))) 18.11/17.42 ( (zero_zero int) ) 18.11/17.42 ( (one_one int) ) 18.11/17.42 ( min_1 ) 18.11/17.42 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.42 ( s ) 18.11/17.42 ( (hAPP int int (number_number_of int) pls) ) 18.11/17.42 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.11/17.42 ( skv_3 ) 18.11/17.42 ( skv_9 ) 18.11/17.42 ) 18.11/17.42 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_129438 $$unsorted) (BOUND_VARIABLE_129439 $$unsorted) (BOUND_VARIABLE_129440 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_129440) (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_129439) BOUND_VARIABLE_129440)) BOUND_VARIABLE_129438)) (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_129438) BOUND_VARIABLE_129440)) BOUND_VARIABLE_129439)))) )))) 18.11/17.42 ( real, (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.11/17.42 ( 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))) ) 18.11/17.42 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.11/17.42 ( 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))), skv_1 ) 18.11/17.42 ( 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))) (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))), skv_1 ) 18.11/17.42 ) 18.11/17.42 (instantiation (forall ((X $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X) (hAPP nat real (real_1 nat) A_1)))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP real nat natceiling X)) A_1))) ) 18.11/17.42 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero nat) ) 18.11/17.42 ) 18.11/17.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129496 $$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_129496) BOUND_VARIABLE_129496) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_129496) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 18.11/17.42 ( real, (hAPP int real (number_number_of real) min_1) ) 18.11/17.42 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.42 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.11/17.42 ( 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)))) ) 18.11/17.42 ( 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))))) ) 18.11/17.42 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.11/17.42 ( 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))) ) 18.11/17.42 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.42 ( int, s ) 18.11/17.42 ( int, s1 ) 18.11/17.42 ( int, skv_8 ) 18.11/17.42 ( complex, ii ) 18.11/17.42 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.42 ( 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)) ) 18.11/17.42 ) 18.11/17.42 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_129508 $$unsorted)) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_129508)) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_129508) BOUND_VARIABLE_129508))))) )) 18.11/17.43 ( nat, (one_one nat) ) 18.11/17.43 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 18.11/17.43 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.11/17.43 ) 18.11/17.43 (instantiation (forall ((N $$unsorted)) (= (hAPP int real (real_1 int) (hAPP nat int (semiring_1_of_nat int) N)) (hAPP nat real (real_1 nat) N)) ) 18.11/17.43 ( (zero_zero nat) ) 18.11/17.43 ( (hAPP nat nat suc (zero_zero nat)) ) 18.11/17.43 ( (one_one nat) ) 18.11/17.43 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.43 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.11/17.43 ) 18.11/17.43 (instantiation (let ((_let_0 (fun nat bool))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (and (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) Ma) N_1)) (not (= Ma N_1))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) Ma) N_1))) )) 18.11/17.43 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.43 ) 18.11/17.43 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (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 _let_0 X))) (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root N) X)))) )) 18.11/17.43 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.43 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.43 ( (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))) ) 18.11/17.43 ( (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))) ) 18.11/17.43 ) 18.11/17.43 (instantiation (let ((_let_0 (inverse_inverse X_a))) (forall ((X_a $$unsorted)) (or (not (division_ring X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 18.11/17.43 ( bool ) 18.11/17.43 ( real ) 18.11/17.43 ( nat ) 18.11/17.43 ( (fun nat bool) ) 18.11/17.43 ( int ) 18.11/17.43 ( (fun int bool) ) 18.11/17.43 ( (fun real bool) ) 18.11/17.43 ( (fun real real) ) 18.11/17.43 ( complex ) 18.11/17.43 ( (fun nat real) ) 18.11/17.43 ( (fun int int) ) 18.11/17.43 ( rat ) 18.11/17.43 ( (fun int (fun int bool)) ) 18.11/17.43 ( (product_prod int int) ) 18.11/17.43 ( (fun (product_prod int int) bool) ) 18.11/17.43 ( code_code_numeral ) 18.11/17.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 18.11/17.43 ( (fun (product_prod int int) int) ) 18.11/17.43 ( (fun int (fun int (fun int bool))) ) 18.11/17.43 ( (fun int real) ) 18.11/17.43 ) 18.11/17.43 (instantiation (let ((_let_0 (fun X_a X_b))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (isCont X_a X_b))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_129614 $$unsorted) (BOUND_VARIABLE_129615 $$unsorted)) (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_129614) BOUND_VARIABLE_129615))) (= (zero_zero X_b) (hAPP X_a X_b BOUND_VARIABLE_129614 BOUND_VARIABLE_129615)) (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_129614)) BOUND_VARIABLE_129615))) )))) 18.11/17.43 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 18.11/17.43 ( 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)))) ) 18.11/17.43 ( 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)))) ) 18.11/17.43 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_6 ) 18.11/17.43 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 18.11/17.43 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 18.11/17.43 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_14 ) 18.11/17.43 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 18.11/17.43 ( 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)))) ) 18.11/17.43 ( 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)))) ) 18.11/17.43 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 18.11/17.43 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_10 ) 18.11/17.43 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_13 ) 18.11/17.43 ( 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))) ) 18.11/17.43 ( 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)))) ) 18.11/17.43 ( 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) ) 18.11/17.43 ( 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) ) 18.11/17.43 ( 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) ) 18.11/17.43 ( bool, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 18.11/17.43 ( 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))) ) 18.11/17.43 ( 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 ) 18.11/17.43 ( bool, real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 18.11/17.43 ( 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)))) ) 18.11/17.43 ( 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 ) 18.11/17.43 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) skv_14), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.43 ( bool, nat, (even_odd_even nat), (zero_zero nat) ) 18.11/17.43 ( bool, nat, (even_odd_even nat), (one_one nat) ) 18.11/17.43 ( 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))) ) 18.11/17.43 ( bool, nat, prime, (zero_zero nat) ) 18.11/17.43 ( bool, nat, prime, (one_one nat) ) 18.11/17.43 ( bool, nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.43 ( bool, (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 18.11/17.43 ( 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) ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 18.11/17.43 ( 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))) ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 18.11/17.43 ( 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))) ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_3 ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_9 ) 18.11/17.43 ( 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))) ) 18.11/17.43 ( bool, int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 18.11/17.43 ( 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))) ) 18.11/17.43 ( bool, int, nat_neg, (one_one int) ) 18.11/17.43 ( bool, int, nat_neg, (hAPP int int (number_number_of int) min_1) ) 18.11/17.43 ( bool, int, nat_neg, (hAPP int int (number_number_of int) pls) ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), (zero_zero int) ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 18.11/17.43 ( bool, int, nat_is_nat, (zero_zero int) ) 18.11/17.43 ( bool, int, nat_is_nat, (one_one int) ) 18.11/17.43 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.43 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.11/17.43 ( bool, int, (even_odd_even int), (zero_zero int) ) 18.11/17.43 ( bool, int, (even_odd_even int), (one_one int) ) 18.11/17.43 ( 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))) ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))), (zero_zero int) ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less int) min_1), (zero_zero int) ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 18.11/17.43 ( bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 18.11/17.43 ( 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))) ) 18.11/17.43 ( 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))) ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 18.11/17.43 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.11/17.43 ( bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less int) t), (zero_zero int) ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less int) t), (one_one int) ) 18.11/17.43 ( 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))) ) 18.11/17.43 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.11/17.43 ( bool, int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.11/17.43 ( bool, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun int bool) (ord_less 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)))), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 18.11/17.43 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_3), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.11/17.43 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_3)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.11/17.43 ( 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_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.11/17.44 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_9), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.11/17.44 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_9)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.11/17.44 ( bool, (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 18.11/17.44 ( 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)) ) 18.11/17.44 ( 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))))) ) 18.11/17.44 ( bool, (filter nat), (trivial_limit nat), sequentially ) 18.11/17.44 ( bool, (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 18.11/17.44 ( real, real, sqrt, (zero_zero real) ) 18.11/17.44 ( real, real, sqrt, (one_one real) ) 18.11/17.44 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.44 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.11/17.44 ( real, real, (uminus_uminus real), (one_one real) ) 18.11/17.44 ( real, real, (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.11/17.44 ( real, real, (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.11/17.44 ( real, real, tan, (zero_zero real) ) 18.11/17.44 ( real, real, tan, pi ) 18.11/17.44 ( 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))))) ) 18.11/17.44 ( 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))))) ) 18.11/17.44 ( 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)))) ) 18.11/17.44 ( real, real, cos, (zero_zero real) ) 18.11/17.44 ( real, real, cos, pi ) 18.11/17.44 ( real, real, cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.44 ( 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)))) ) 18.11/17.44 ( 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) ) 18.11/17.44 ( 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))))) ) 18.11/17.44 ( real, real, cos, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 18.11/17.44 ( 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))))) ) 18.11/17.44 ( 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)))) ) 18.11/17.44 ( real, real, cos, skv_14 ) 18.11/17.44 ( real, real, ln, (one_one real) ) 18.11/17.44 ( real, real, (inverse_inverse real), (zero_zero real) ) 18.11/17.44 ( real, real, sin, (zero_zero real) ) 18.11/17.44 ( real, real, sin, pi ) 18.11/17.44 ( 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)))) ) 18.11/17.44 ( 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) ) 18.11/17.44 ( 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 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(inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.11/17.44 ( real, real, (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)))) ) 18.11/17.44 ( 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))) ) 18.11/17.44 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 18.11/17.44 ( real, real, (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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real 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int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 18.11/17.44 ( real, real, arctan, (hAPP real real (hAPP 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)))))))))) ) 18.11/17.44 ( 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)))))) ) 18.11/17.44 ( real, real, (sgn_sgn real), (zero_zero real) ) 18.11/17.44 ( 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))) ) 18.11/17.44 ( 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)))) ) 18.11/17.44 ( real, real, (hAPP 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)))) ) 18.11/17.44 ( real, real, (hAPP 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))))))))) ) 18.11/17.44 ( 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))) ) 18.11/17.44 ( 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))) ) 18.11/17.44 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), pi ) 18.11/17.44 ( 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))) ) 18.11/17.44 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1))))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 18.11/17.44 ( real, nat, (real_1 nat), (zero_zero nat) ) 18.11/17.44 ( real, nat, (real_1 nat), (one_one nat) ) 18.11/17.44 ( real, int, (real_1 int), (zero_zero int) ) 18.11/17.44 ( real, int, (real_1 int), (one_one int) ) 18.11/17.44 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.11/17.44 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.44 ( real, int, (number_number_of real), min_1 ) 18.11/17.44 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.44 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.11/17.44 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.11/17.44 ( 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)))))))) ) 18.11/17.44 ( real, (fun real bool), (the real), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0)))))))))))))) ) 18.11/17.44 ( real, complex, im, ii ) 18.11/17.44 ( real, complex, im, (zero_zero complex) ) 18.11/17.44 ( real, complex, im, (one_one complex) ) 18.11/17.44 ( real, complex, re, ii ) 18.11/17.44 ( real, complex, re, (zero_zero complex) ) 18.11/17.44 ( real, complex, re, (one_one complex) ) 18.11/17.44 ( real, (fun nat real), (suminf real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (combc nat nat nat))) (let ((_let_4 (fun nat _let_0))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun _let_1 _let_4))) (let ((_let_7 (combb real _let_0 nat))) (hAPP _let_1 _let_1 (hAPP _let_4 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_4 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 18.11/17.44 ( real, rat, ratreal, (zero_zero rat) ) 18.11/17.44 ( real, rat, ratreal, (one_one rat) ) 18.11/17.44 ( nat, real, natfloor, (zero_zero real) ) 18.11/17.44 ( nat, real, natfloor, (one_one real) ) 18.11/17.44 ( nat, real, natceiling, (zero_zero real) ) 18.11/17.44 ( nat, real, natceiling, (one_one real) ) 18.11/17.44 ( nat, nat, suc, (zero_zero nat) ) 18.11/17.44 ( nat, nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 18.11/17.44 ( nat, nat, suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 18.11/17.44 ( nat, nat, (fact_fact nat), (zero_zero nat) ) 18.11/17.44 ( nat, nat, (fact_fact nat), (hAPP nat nat suc (zero_zero nat)) ) 18.11/17.44 ( nat, nat, (size_size nat), (zero_zero nat) ) 18.11/17.44 ( nat, nat, fact, (zero_zero nat) ) 18.11/17.44 ( nat, nat, nat_size, (zero_zero nat) ) 18.11/17.44 ( nat, nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (one_one nat) ) 18.11/17.44 ( nat, int, nat_1, (zero_zero int) ) 18.11/17.44 ( nat, int, nat_1, (one_one int) ) 18.11/17.44 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.44 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.11/17.44 ( nat, int, (number_number_of nat), pls ) 18.11/17.44 ( nat, int, (number_number_of nat), (hAPP int int bit1 pls) ) 18.11/17.44 ( nat, int, (number_number_of nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.11/17.44 ( nat, int, (number_number_of nat), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.11/17.44 ( nat, code_code_numeral, (size_size code_code_numeral), (zero_zero code_code_numeral) ) 18.11/17.44 ( nat, code_code_numeral, code_c271388182l_size, (zero_zero code_code_numeral) ) 18.11/17.44 ( (fun nat bool), bool, (combk bool nat), fTrue ) 18.11/17.44 ( (fun nat bool), nat, (ord_less nat), (zero_zero nat) ) 18.11/17.44 ( (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) ) 18.11/17.44 ( (fun nat bool), (fun nat bool), (collect nat), prime ) 18.11/17.44 ( (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))) ) 18.11/17.44 ( (fun nat nat), nat, (plus_plus nat), (one_one nat) ) 18.11/17.45 ( (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))) ) 18.11/17.45 ( (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 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(fun nat int) (power_power int) skv_8), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.45 ( int, int, (number_number_of int), pls ) 18.11/17.45 ( int, int, (number_number_of int), (hAPP int int bit1 pls) ) 18.11/17.45 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.11/17.45 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.11/17.45 ( int, int, (number_number_of int), min_1 ) 18.11/17.45 ( int, int, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.11/17.45 ( int, int, bit0, pls ) 18.11/17.45 ( int, int, bit0, (hAPP int int bit1 pls) ) 18.11/17.45 ( int, int, bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.11/17.45 ( int, int, bit0, min_1 ) 18.11/17.45 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.11/17.45 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.11/17.45 ( int, int, bit1, pls ) 18.11/17.45 ( int, int, bit1, (hAPP int int bit1 pls) ) 18.11/17.45 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.11/17.45 ( int, int, bit1, min_1 ) 18.11/17.45 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.11/17.45 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 18.11/17.45 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 18.11/17.45 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 18.11/17.45 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 18.11/17.45 ( int, int, (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP 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) 18.11/17.45 ( (fun int bool), int, (ord_less_eq int), (one_one int) ) 18.11/17.45 ( (fun int bool), int, (ord_less_eq int), min_1 ) 18.11/17.45 ( (fun int bool), int, (ord_less int), (zero_zero int) ) 18.11/17.45 ( (fun int bool), int, (ord_less int), min_1 ) 18.11/17.45 ( (fun int bool), int, (ord_less int), s ) 18.11/17.45 ( (fun int bool), int, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 18.11/17.45 ( (fun int bool), int, (ord_less int), t ) 18.11/17.45 ( (fun int bool), int, (ord_less int), skv_3 ) 18.11/17.45 ( (fun int bool), int, (ord_less int), skv_9 ) 18.11/17.45 ( (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 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18.28/17.57 ( (fun (fun real (fun int (fun nat bool))) (fun real (fun int (fun nat (fun bool bool))))), (fun (fun int (fun nat bool)) (fun int (fun nat (fun bool bool)))), (combb (fun int (fun nat bool)) (fun int (fun nat (fun bool bool))) real), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 nat) fconj)))))) ) 18.28/17.57 ( (fun int (fun nat real)), (fun nat real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_4 (fun (fun nat real) (fun int (fun nat real))) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 nat) ) 18.28/17.57 ( (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (fun real (fun (fun nat real) (fun nat bool))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (fun int _let_1) (fun int _let_0)))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP (fun _let_3 _let_2) (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (combb _let_1 _let_0 int)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun nat real) (fun nat bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool nat)) (fequal real)))))) ) 18.28/17.57 ( (fun (fun int (fun nat real)) (fun real (fun int (fun nat bool)))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (combc real (fun int (fun nat real)) (fun int (fun nat bool))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun nat real)) (fun int (fun nat bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool nat)) (fequal real))))))))) ) 18.28/17.57 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun real bool)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun (fun nat real) (fun nat bool)))) (hAPP (fun _let_0 _let_1) (fun (fun real _let_0) (fun real _let_1)) (combb _let_0 _let_1 real) (combb real bool nat)))), (fequal real) ) 18.28/17.57 ( (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (fun (fun real (fun _let_1 _let_0)) 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real real) (fun _let_0 _let_0) int)), (combb real real nat) ) 18.28/17.57 ) 18.28/17.57 (instantiation (let ((_let_0 (fun nat bool))) (forall ((S $$unsorted)) (= (not (forall ((K_1 $$unsorted)) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) S) (hAPP nat _let_0 (ord_lessThan nat) K_1)))) )) (hBOOL (hAPP _let_0 bool (finite_finite_1 nat) S))) )) 18.28/17.57 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 18.28/17.57 ) 18.28/17.57 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun rat bool))) (let ((_let_3 (fun int rat))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (product_prod int int))) (let ((_let_6 (product_snd int int))) (let ((_let_7 (fun _let_5 bool))) (let ((_let_8 (product_fst int int))) (let ((_let_9 (fun _let_5 int))) (let ((_let_10 (fun _let_5 rat))) (let ((_let_11 (fun _let_5 _let_4))) (let ((_let_12 (fun _let_7 _let_7))) (let ((_let_13 (combs _let_5 bool bool))) (let ((_let_14 (hAPP (fun bool _let_4) (fun _let_7 _let_11) (combb bool _let_4 _let_5) fconj))) (let ((_let_15 (fun _let_5 _let_3))) (let ((_let_16 (fun _let_5 _let_0))) (let ((_let_17 (fun _let_5 _let_1))) (forall ((X_1 $$unsorted)) (= (hAPP rat _let_5 quotient_of X_1) (hAPP _let_7 _let_5 (the _let_5) (hAPP _let_7 _let_7 (hAPP _let_11 _let_12 _let_13 (hAPP _let_7 _let_11 _let_14 (hAPP _let_10 _let_7 (hAPP _let_2 (fun _let_10 _let_7) (combb rat bool _let_5) (hAPP rat _let_2 (fequal rat) X_1)) (hAPP _let_9 _let_10 (hAPP _let_15 (fun _let_9 _let_10) (combs _let_5 int rat) (hAPP _let_9 _let_15 (hAPP (fun int _let_3) (fun _let_9 _let_15) (combb int _let_3 _let_5) fract) _let_8)) _let_6)))) (hAPP _let_7 _let_7 (hAPP _let_11 _let_12 _let_13 (hAPP _let_7 _let_11 _let_14 (hAPP _let_9 _let_7 (hAPP _let_0 (fun _let_9 _let_7) (combb int bool _let_5) (hAPP int _let_0 (ord_less int) (zero_zero int))) _let_6))) (hAPP int _let_7 (hAPP _let_16 (fun int _let_7) (combc _let_5 int bool) (hAPP _let_9 _let_16 (hAPP (fun int _let_0) (fun _let_9 _let_16) (combb int _let_0 _let_5) (fequal int)) (hAPP _let_9 _let_9 (hAPP _let_17 (fun _let_9 _let_9) (combs _let_5 int int) (hAPP _let_9 _let_17 (hAPP (fun int _let_1) (fun _let_9 _let_17) (combb int _let_1 _let_5) (gcd_gcd int)) _let_8)) _let_6))) (one_one int)))))) ))))))))))))))))))) 18.28/17.58 ( (zero_zero rat) ) 18.28/17.58 ( (one_one rat) ) 18.28/17.58 ) 18.28/17.58 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_129696 $$unsorted) (BOUND_VARIABLE_129697 $$unsorted)) (or (not (dense_linorder X_a)) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) X_2) BOUND_VARIABLE_129697))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 X_2) BOUND_VARIABLE_129696))) )) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_129697) BOUND_VARIABLE_129696))) ))) 18.28/17.58 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.58 ( real, pi, (zero_zero real) ) 18.28/17.58 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.28/17.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 18.28/17.58 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.28/17.58 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.28/17.58 ( real, skv_6, (zero_zero real) ) 18.28/17.58 ( real, skv_11, (zero_zero real) ) 18.28/17.58 ( real, skv_12, (zero_zero real) ) 18.28/17.58 ( real, skv_14, (zero_zero real) ) 18.28/17.58 ( int, pls, min_1 ) 18.28/17.58 ( int, (one_one int), (zero_zero int) ) 18.28/17.58 ( int, min_1, (zero_zero int) ) 18.28/17.58 ( int, min_1, min_1 ) 18.28/17.58 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 18.28/17.58 ( int, s, (zero_zero int) ) 18.28/17.58 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 18.28/17.58 ( int, t, (one_one int) ) 18.28/17.58 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 18.28/17.58 ( int, skv_3, (zero_zero int) ) 18.28/17.58 ( int, skv_9, (zero_zero int) ) 18.28/17.58 ) 18.28/17.58 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat real))) (let ((_let_4 (fun _let_0 real))) (let ((_let_5 (fun nat _let_2))) (let ((_let_6 (fun nat _let_0))) (let ((_let_7 (fun (filter nat) bool))) (let ((_let_8 (fun real _let_7))) (let ((_let_9 (tendsto nat real))) (let ((_let_10 (hAPP _let_3 _let_3 (hAPP _let_5 (fun _let_3 _let_3) (combs nat real real) (hAPP _let_3 _let_5 (hAPP (fun real _let_2) (fun _let_3 _let_5) (combb real _let_2 nat) (times_times real)) (hAPP real _let_3 (power_power real) (hAPP int real (number_number_of real) min_1)))) A_2))) (forall ((A_2 $$unsorted)) (let ((_let_0 (filter nat))) (or (not (hBOOL (hAPP _let_0 bool (hAPP real _let_7 (hAPP _let_3 _let_8 _let_9 A_2) (zero_zero real)) sequentially))) (not (hBOOL (hAPP _let_3 bool (monoseq real) A_2))) (hBOOL (hAPP _let_0 bool (hAPP real _let_7 (hAPP _let_3 _let_8 _let_9 (hAPP _let_6 _let_3 (hAPP _let_4 (fun _let_6 _let_3) (combb _let_0 real nat) (hAPP _let_3 _let_4 (big_co1399186613setsum nat real) _let_10)) (hAPP _let_1 _let_6 (hAPP _let_6 (fun _let_1 _let_6) (combb nat _let_0 nat) (hAPP nat _let_6 (ord_atLeastLessThan nat) (zero_zero nat))) (hAPP nat _let_1 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (hAPP _let_3 real (suminf real) _let_10)) sequentially)))) )))))))))))) 18.28/17.58 ( (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 18.28/17.58 ) 18.28/17.58 (instantiation (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_129761 $$unsorted)) (or (not (linordered_idom X_a)) (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_129761) _let_0) (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_129761)) _let_0))) )))) 18.28/17.58 ( int, s ) 18.28/17.58 ( int, s1 ) 18.28/17.58 ( int, skv_8 ) 18.28/17.58 ( complex, ii ) 18.28/17.58 ) 18.28/17.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129774 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_129774) (zero_zero X_a))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_129774)) (one_one int))))) ) 18.28/17.58 ( real, (zero_zero real) ) 18.28/17.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.28/17.58 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.58 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.58 ( real, skv_14 ) 18.28/17.58 ( int, (zero_zero int) ) 18.28/17.58 ( int, (one_one int) ) 18.28/17.58 ( int, min_1 ) 18.28/17.58 ) 18.28/17.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129805 $$unsorted)) (or (not (linordered_idom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_129805) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 18.28/17.58 ( real, (hAPP int real (number_number_of real) min_1) ) 18.28/17.58 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.58 ( int, s ) 18.28/17.58 ( int, s1 ) 18.28/17.58 ( int, skv_8 ) 18.28/17.58 ( complex, ii ) 18.28/17.58 ) 18.28/17.58 (instantiation (forall ((X $$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))) ) 18.28/17.58 ( (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)))) ) 18.28/17.58 ) 18.28/17.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129840 $$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_129840)) (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_129840))))) ) 18.28/17.58 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.28/17.58 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.28/17.58 ( real, min_1 ) 18.28/17.58 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.28/17.58 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.28/17.58 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.28/17.58 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 18.28/17.58 ( nat, pls ) 18.28/17.58 ( nat, (hAPP int int bit1 pls) ) 18.28/17.58 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.28/17.58 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.28/17.58 ( int, pls ) 18.28/17.58 ( int, (hAPP int int bit1 pls) ) 18.28/17.58 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.28/17.58 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.28/17.58 ( int, min_1 ) 18.28/17.58 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.28/17.58 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.28/17.58 ( complex, min_1 ) 18.28/17.58 ( quickcheck_code_int, (zero_zero int) ) 18.28/17.58 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 18.28/17.58 ( quickcheck_code_int, (one_one int) ) 18.28/17.58 ( code_code_numeral, pls ) 18.28/17.58 ( code_code_numeral, (hAPP int int bit1 pls) ) 18.28/17.58 ) 18.28/17.58 (instantiation (let ((_let_0 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_129859 $$unsorted) (BOUND_VARIABLE_129860 $$unsorted)) (or (not (boolean_algebra X_a)) (= (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_129859) (hAPP X_a X_a _let_0 BOUND_VARIABLE_129860)) (= (ti X_a BOUND_VARIABLE_129860) (ti X_a BOUND_VARIABLE_129859)))) )) 18.28/17.58 ( real, (one_one real), (one_one real) ) 18.28/17.58 ( real, (one_one real), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.28/17.58 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 18.28/17.58 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), (one_one real) ) 18.28/17.58 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.58 ( int, pls, (one_one int) ) 18.28/17.58 ( int, pls, min_1 ) 18.28/17.58 ( int, (one_one int), pls ) 18.28/17.58 ( int, (one_one int), (one_one int) ) 18.28/17.58 ( int, min_1, (one_one int) ) 18.28/17.58 ( complex, ii, (one_one complex) ) 18.28/17.58 ( complex, (one_one complex), ii ) 18.28/17.58 ( complex, (one_one complex), (one_one complex) ) 18.28/17.58 ) 18.28/17.58 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (forall ((X $$unsorted)) (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))) ))) 18.28/17.58 ( (one_one real) ) 18.28/17.58 ( pi ) 18.28/17.58 ( (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)))) ) 18.28/17.58 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.58 ( skv_2 ) 18.28/17.58 ( skv_10 ) 18.28/17.58 ( skv_13 ) 18.28/17.58 ) 18.28/17.58 (instantiation (let ((_let_0 (fun int int))) (forall ((Y $$unsorted) (X $$unsorted)) (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))) )) 18.28/17.58 ( (zero_zero int), (one_one int) ) 18.28/17.58 ( (zero_zero int), min_1 ) 18.28/17.58 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.28/17.58 ( (zero_zero int), s ) 18.28/17.58 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 18.28/17.58 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.28/17.58 ( (zero_zero int), skv_3 ) 18.28/17.58 ( (zero_zero int), skv_9 ) 18.28/17.58 ( (one_one int), t ) 18.28/17.58 ( min_1, pls ) 18.28/17.58 ( min_1, min_1 ) 18.28/17.58 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.58 ) 18.28/17.58 (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))) ) 18.28/17.58 ( (zero_zero int), (one_one int) ) 18.28/17.58 ( (zero_zero int), min_1 ) 18.28/17.58 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.28/17.58 ( (zero_zero int), s ) 18.28/17.58 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 18.28/17.58 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.28/17.58 ( (zero_zero int), skv_3 ) 18.28/17.58 ( (zero_zero int), skv_9 ) 18.28/17.58 ( (one_one int), t ) 18.28/17.58 ( min_1, pls ) 18.28/17.58 ( min_1, min_1 ) 18.28/17.58 ) 18.28/17.58 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (ord_less real))) (let ((_let_4 (filter real))) (let ((_let_5 (fun _let_4 bool))) (forall ((F $$unsorted) (L $$unsorted) (C_1 $$unsorted)) (or (not (hBOOL (hAPP _let_4 bool (hAPP real _let_5 (hAPP _let_2 (fun real _let_5) (tendsto real real) F) L) (hAPP real _let_4 (at real) C_1)))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_3 L) _let_0))) (not (forall ((R_2 $$unsorted)) (or (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_3 (hAPP real real (abs_abs real) (hAPP real real (hAPP real _let_2 (minus_minus real) C_1) X_2))) R_2))) (= C_1 X_2) (hBOOL (hAPP real bool (hAPP real _let_1 _let_3 (hAPP real real F X_2)) _let_0))) )) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_3 _let_0) R_2)))) ))) ))))))) 18.28/17.58 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.58 ) 18.28/17.58 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (and (= (zero_zero real) X_1) (= (one_one real) Y_1)) (= ii (hAPP real complex (hAPP real (fun real complex) complex_1 X_1) Y_1))) ) 18.28/17.58 ( (zero_zero real), (zero_zero real) ) 18.28/17.58 ( (zero_zero real), (one_one real) ) 18.28/17.58 ( (one_one real), (zero_zero real) ) 18.28/17.58 ) 18.28/17.58 (instantiation (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (times_times X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_129943 $$unsorted) (BOUND_VARIABLE_129944 $$unsorted)) (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_129943)) BOUND_VARIABLE_129944) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_129943) BOUND_VARIABLE_129944)))) )))) 18.28/17.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.28/17.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.28/17.58 ( 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)))))) ) 18.28/17.58 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 18.28/17.58 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 18.28/17.59 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 18.28/17.59 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 18.28/17.59 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1 ) 18.28/17.59 ( complex, ii, ii ) 18.28/17.59 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 18.28/17.59 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 18.28/17.59 ) 18.28/17.59 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_b bool))) (let ((_let_3 (ord_less X_b))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_129977 $$unsorted) (BOUND_VARIABLE_129978 $$unsorted) (BOUND_VARIABLE_129979 $$unsorted) (BOUND_VARIABLE_129980 $$unsorted)) (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_129978 BOUND_VARIABLE_129979)) BOUND_VARIABLE_129980))) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_2 _let_3 BOUND_VARIABLE_129977) BOUND_VARIABLE_129979))) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (or (not (hBOOL (hAPP X_b bool (hAPP X_b _let_2 _let_3 Y_2) X_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_b X_a BOUND_VARIABLE_129978 Y_2)) (hAPP X_b X_a BOUND_VARIABLE_129978 X_2)))) )) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_b X_a BOUND_VARIABLE_129978 BOUND_VARIABLE_129977)) BOUND_VARIABLE_129980))) ))))) 18.28/17.59 ( real, 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))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.28/17.59 ( real, real, (one_one real), cos, skv_14, pi ) 18.28/17.59 ( real, real, pi, cos, skv_14, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.59 ( real, real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), cos, skv_14, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.59 ( 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, skv_14, skv_11 ) 18.28/17.59 ( real, real, (hAPP real real cos (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) ) 18.28/17.59 ( 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_14, skv_6 ) 18.28/17.59 ( nat, int, (zero_zero nat), (semiring_1_of_nat int), (zero_zero nat), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.28/17.59 ( int, real, min_1, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)), pi ) 18.28/17.59 ( int, int, (zero_zero int), (number_number_of int), pls, s ) 18.28/17.59 ( int, int, s, (number_number_of int), pls, min_1 ) 18.28/17.59 ( int, int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (number_number_of int), pls, (hAPP int int (number_number_of int) pls) ) 18.28/17.59 ( int, int, t, bit1, min_1, min_1 ) 18.28/17.59 ( int, int, skv_3, (number_number_of int), pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.28/17.59 ( int, int, skv_9, (number_number_of int), pls, (one_one int) ) 18.28/17.59 ) 18.28/17.59 (instantiation (let ((_let_0 (product_prod_rec X_b X_c X_a))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (= _let_0 (ti (fun (fun X_b (fun X_c X_a)) (fun (product_prod X_b X_c) X_a)) _let_0)) )) 18.28/17.59 ( real, real, bool ) 18.28/17.59 ( nat, nat, bool ) 18.28/17.59 ( nat, nat, (fun (product_prod nat nat) bool) ) 18.28/17.59 ( int, int, bool ) 18.28/17.59 ( int, int, int ) 18.28/17.59 ( int, int, (fun int bool) ) 18.28/17.59 ( int, int, (fun int int) ) 18.28/17.59 ( int, int, rat ) 18.28/17.59 ( int, int, (fun bool bool) ) 18.28/17.59 ( int, int, (product_prod int int) ) 18.28/17.59 ( int, int, (fun (product_prod int int) bool) ) 18.28/17.59 ( int, int, (fun (product_prod int int) int) ) 18.28/17.59 ( int, int, (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 18.28/17.59 ( int, int, (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 18.28/17.59 ( int, int, (fun (product_prod int int) (fun int bool)) ) 18.28/17.59 ( int, int, (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 18.28/17.59 ( (product_prod int int), (product_prod int int), bool ) 18.28/17.59 ( (product_prod nat nat), (product_prod nat nat), bool ) 18.28/17.59 ) 18.28/17.59 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_130046))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_130044 $$unsorted) (BOUND_VARIABLE_130045 $$unsorted) (BOUND_VARIABLE_130046 $$unsorted)) (or (not (linord581940658strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_130046) (zero_zero X_a)))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_130044)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_130045))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_130045) BOUND_VARIABLE_130044)))) )))) 18.28/17.59 ( int, skv_1, (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.28/17.59 ) 18.28/17.59 (instantiation (let ((_let_0 (fun nat (fun nat bool)))) (let ((_let_1 (fun X_a bool))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hBOOL (hAPP _let_1 bool (finite_finite_1 X_a) A_3)) (not (forall ((N_2 $$unsorted) (F_3 $$unsorted)) (not (= (hAPP _let_0 _let_1 (hAPP (fun nat X_a) (fun _let_0 _let_1) (image nat X_a) F_3) (hAPP _let_0 _let_0 (collect nat) (hAPP nat _let_0 (hAPP _let_0 _let_0 (combc nat nat bool) (ord_less nat)) N_2))) (ti _let_1 A_3))) )))) ))) 18.28/17.59 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 18.28/17.59 ) 18.28/17.59 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_130118 $$unsorted) (BOUND_VARIABLE_130119 $$unsorted) (BOUND_VARIABLE_130120 $$unsorted)) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_130119) BOUND_VARIABLE_130120))) (not (= (ti X_a BOUND_VARIABLE_130118) (ti X_a BOUND_VARIABLE_130119))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_130118) BOUND_VARIABLE_130120))) ))) 18.28/17.59 ( real, pi, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.59 ( int, pls, (zero_zero int), (one_one int) ) 18.28/17.59 ( int, m, (zero_zero int), s ) 18.28/17.59 ( int, min_1, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 18.28/17.59 ( int, s, (zero_zero int), min_1 ) 18.28/17.59 ( int, s1, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.28/17.59 ( int, t, min_1, min_1 ) 18.28/17.59 ) 18.28/17.59 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_130195 $$unsorted) (BOUND_VARIABLE_130196 $$unsorted) (BOUND_VARIABLE_130197 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_130197) (zero_zero X_a)))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_130196) BOUND_VARIABLE_130197)) BOUND_VARIABLE_130195)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_130195) BOUND_VARIABLE_130197)) BOUND_VARIABLE_130196)))) )))) 18.28/17.59 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.28/17.59 ) 18.28/17.59 (instantiation (let ((_let_0 (fun int bool))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) Ma))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) Ma) N_1)) (= (ti int Ma) (hAPP int int (hAPP int (fun int int) legacy_zgcd N_1) Ma)))) )) 18.28/17.59 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.28/17.59 ) 18.28/17.59 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (let ((_let_2 (minus_minus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_130325 $$unsorted) (BOUND_VARIABLE_130326 $$unsorted) (BOUND_VARIABLE_130327 $$unsorted)) (or (not (field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_130327)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_130325) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_130326) BOUND_VARIABLE_130327)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_130327) BOUND_VARIABLE_130325)) BOUND_VARIABLE_130326)) BOUND_VARIABLE_130327))) )))) 18.28/17.59 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.59 ) 18.28/17.59 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_130378 $$unsorted) (BOUND_VARIABLE_130379 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_130379))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_130378))) (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_130379) BOUND_VARIABLE_130378)))) )) 18.28/17.59 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.28/17.59 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 18.28/17.59 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.28/17.59 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.59 ( 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))) ) 18.28/17.59 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.59 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.28/17.59 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.28/17.59 ( complex, ii, ii ) 18.28/17.59 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 18.28/17.59 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.28/17.59 ) 18.28/17.59 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun (filter nat) bool))) (forall ((A_2 $$unsorted)) (or (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_3 (hAPP _let_1 (fun real _let_3) (tendsto nat real) A_2) (zero_zero real)) sequentially))) (not (hBOOL (hAPP _let_1 bool (monoseq real) A_2))) (hBOOL (hAPP _let_1 bool (summable real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) A_2)))) ))))) 18.28/17.59 ( (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 18.28/17.59 ) 18.28/17.59 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_130427 $$unsorted) (BOUND_VARIABLE_130428 $$unsorted)) (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_130427)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_130428))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_130428) BOUND_VARIABLE_130427)))) )))) 18.28/17.59 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.59 ( real, pi, (zero_zero real) ) 18.28/17.59 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.28/17.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 18.28/17.59 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.28/17.59 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.28/17.59 ( real, skv_6, (zero_zero real) ) 18.28/17.59 ( real, skv_11, (zero_zero real) ) 18.28/17.59 ( real, skv_12, (zero_zero real) ) 18.28/17.59 ( real, skv_14, (zero_zero real) ) 18.28/17.59 ( int, pls, pls ) 18.28/17.59 ( int, pls, (one_one int) ) 18.28/17.59 ( int, pls, min_1 ) 18.28/17.59 ( int, (one_one int), (zero_zero int) ) 18.28/17.59 ( int, (one_one int), pls ) 18.28/17.59 ( int, (one_one int), (one_one int) ) 18.28/17.59 ( int, min_1, (zero_zero int) ) 18.28/17.59 ( int, min_1, min_1 ) 18.28/17.59 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 18.28/17.59 ( int, s, (zero_zero int) ) 18.28/17.60 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 18.28/17.60 ( int, t, (one_one int) ) 18.28/17.60 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 18.28/17.60 ( int, skv_3, (zero_zero int) ) 18.28/17.60 ( int, skv_9, (zero_zero int) ) 18.28/17.60 ) 18.28/17.60 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_130451 $$unsorted) (BOUND_VARIABLE_130452 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_130452) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_130451))) (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_130452) BOUND_VARIABLE_130451)) _let_2))) )))) 18.28/17.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 18.28/17.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.28/17.60 ( 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))) ) 18.28/17.60 ( 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)))) ) 18.28/17.60 ( 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)))) ) 18.28/17.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 18.28/17.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 18.28/17.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 18.28/17.60 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 18.28/17.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 18.28/17.60 ( 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) ) 18.28/17.60 ) 18.28/17.60 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP complex complex expi Z_1) (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP real complex (of_real complex) (hAPP real real (exp real) (hAPP complex real re Z_1)))) (hAPP real complex cis (hAPP complex real im Z_1)))) ) 18.28/17.60 ( ii ) 18.28/17.60 ( (zero_zero complex) ) 18.28/17.60 ( (one_one complex) ) 18.28/17.60 ( (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))) ) 18.28/17.60 ) 18.28/17.60 (instantiation (let ((_let_0 (fun int bool))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) B_1))) (= (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less_eq rat) (hAPP int rat (hAPP int (fun int rat) fract A_2) B_1)) (one_one rat))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) A_2) B_1)))) )) 18.28/17.60 ( (zero_zero int), (one_one int) ) 18.28/17.60 ( (zero_zero int), min_1 ) 18.28/17.60 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.28/17.60 ( (zero_zero int), s ) 18.28/17.60 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 18.28/17.60 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.28/17.60 ( (zero_zero int), skv_3 ) 18.28/17.60 ( (zero_zero int), skv_9 ) 18.28/17.60 ( (one_one int), (one_one int) ) 18.28/17.60 ( (one_one int), t ) 18.28/17.60 ( min_1, pls ) 18.28/17.60 ( min_1, min_1 ) 18.28/17.60 ) 18.28/17.60 (instantiation (let ((_let_0 (fun real bool))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (or (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X_1) Y_1)) (= X_1 Y_1)) (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) X_1) Y_1))) )) 18.28/17.60 ( (zero_zero real), pi ) 18.28/17.60 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.60 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.60 ( (zero_zero real), skv_2 ) 18.28/17.60 ( (zero_zero real), skv_6 ) 18.28/17.60 ( (zero_zero real), skv_10 ) 18.28/17.60 ( (zero_zero real), skv_11 ) 18.28/17.60 ( (zero_zero real), skv_12 ) 18.28/17.60 ( (zero_zero real), skv_13 ) 18.28/17.60 ( (zero_zero real), skv_14 ) 18.28/17.60 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.60 ( pi, (zero_zero real) ) 18.28/17.60 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.28/17.60 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.28/17.60 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.28/17.60 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 18.43/17.60 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.43/17.60 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 18.43/17.60 ( skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.60 ) 18.43/17.60 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (one_one X_a))) (let ((_let_2 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_130521 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a _let_2 (hAPP int int bit0 BOUND_VARIABLE_130521)) (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_130521)))) )))) 18.43/17.60 ( real, (hAPP int int bit1 pls) ) 18.43/17.60 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.43/17.60 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.43/17.60 ( nat, pls ) 18.43/17.60 ( nat, (hAPP int int bit1 pls) ) 18.43/17.60 ( int, pls ) 18.43/17.60 ( int, (hAPP int int bit1 pls) ) 18.43/17.60 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.43/17.60 ( complex, (hAPP int int bit1 pls) ) 18.43/17.60 ( quickcheck_code_int, pls ) 18.43/17.60 ( code_code_numeral, pls ) 18.43/17.60 ) 18.43/17.60 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a (ring_1_of_int X_a) (hAPP int int (number_number_of int) min_1)) (hAPP int X_a (number_number_of X_a) min_1))) ) 18.43/17.60 ( real ) 18.43/17.60 ( nat ) 18.43/17.60 ( int ) 18.43/17.60 ( complex ) 18.43/17.60 ( rat ) 18.43/17.60 ( quickcheck_code_int ) 18.43/17.60 ( code_code_numeral ) 18.43/17.60 ) 18.43/17.60 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (hAPP real _let_0 (times_times real) R_4))) (forall ((R_4 $$unsorted) (A_1 $$unsorted)) (= (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real _let_2 A_1)) (hAPP real real _let_2 R_4)) (hAPP real real (hAPP real _let_0 _let_1 A_1) R_4)) )))) 18.43/17.60 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.43/17.60 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.43/17.60 ( (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)))))) ) 18.43/17.60 ( (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 ) 18.43/17.60 ) 18.43/17.60 (instantiation (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))))) (forall ((X $$unsorted)) (= (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))) )))) 18.43/17.60 ( (zero_zero real) ) 18.43/17.60 ( pi ) 18.43/17.60 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.60 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.60 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.43/17.60 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 18.43/17.60 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 18.43/17.60 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 18.43/17.60 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 18.43/17.60 ( skv_14 ) 18.43/17.60 ) 18.43/17.60 (instantiation (forall ((N $$unsorted)) (= (hAPP int nat (number_number_of nat) N) (hAPP real nat natceiling (hAPP int real (number_number_of real) N))) ) 18.43/17.60 ( pls ) 18.43/17.60 ( (hAPP int int bit1 pls) ) 18.43/17.60 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.43/17.60 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.60 ( min_1 ) 18.43/17.60 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.60 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.43/17.60 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.43/17.60 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 18.43/17.60 ) 18.43/17.60 (instantiation (let ((_let_0 (norm_norm complex))) (forall ((Z_1 $$unsorted)) (= (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)))) )) 18.43/17.60 ( ii ) 18.43/17.60 ( (zero_zero complex) ) 18.43/17.60 ( (one_one complex) ) 18.43/17.60 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.60 ( (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 18.43/17.60 ) 18.43/17.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130758 $$unsorted)) (or (not (ab_sem1668676832m_mult X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_130758) BOUND_VARIABLE_130758) (ti X_a BOUND_VARIABLE_130758))) ) 18.43/17.60 ( bool, fFalse ) 18.43/17.60 ( bool, fTrue ) 18.43/17.60 ( real, pi ) 18.43/17.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.60 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 18.43/17.60 ( (fun nat bool), (even_odd_even nat) ) 18.43/17.60 ( (fun nat bool), prime ) 18.43/17.60 ( (fun nat nat), suc ) 18.43/17.60 ( (fun nat nat), (fact_fact nat) ) 18.43/17.60 ( (fun nat nat), (size_size nat) ) 18.43/17.60 ( (fun nat nat), fact ) 18.43/17.60 ( (fun nat nat), nat_size ) 18.43/17.60 ( int, pls ) 18.43/17.60 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.60 ( int, m ) 18.43/17.60 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.43/17.60 ( int, min_1 ) 18.43/17.60 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.60 ( int, s ) 18.43/17.60 ( int, s1 ) 18.43/17.60 ( int, t ) 18.43/17.60 ( (fun int bool), zprime ) 18.43/17.60 ( (fun int bool), nat_neg ) 18.43/17.60 ( (fun int bool), zEven ) 18.43/17.60 ( (fun int bool), nat_is_nat ) 18.43/17.60 ( (fun int bool), zOdd ) 18.43/17.60 ( (fun int bool), (even_odd_even int) ) 18.43/17.60 ( (fun int bool), twoSqu1091635170sum2sq ) 18.43/17.60 ( (fun int nat), nat_1 ) 18.43/17.60 ( (fun int nat), phi ) 18.43/17.60 ( (fun real real), sqrt ) 18.43/17.60 ( (fun real real), tan ) 18.43/17.60 ( (fun real real), cos ) 18.43/17.60 ( (fun real real), arccos ) 18.43/17.60 ( (fun real real), ln ) 18.43/17.60 ( (fun real real), sin ) 18.43/17.60 ( (fun real real), arctan ) 18.43/17.60 ( (fun real real), arcsin ) 18.43/17.60 ( complex, ii ) 18.43/17.60 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.60 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 18.43/17.60 ( (fun complex complex), cnj ) 18.43/17.60 ( (fun complex complex), expi ) 18.43/17.60 ( (fun nat real), (real_1 nat) ) 18.43/17.60 ( (fun nat real), cos_coeff ) 18.43/17.60 ( (fun nat real), sin_coeff ) 18.43/17.60 ( (fun int int), bit0 ) 18.43/17.60 ( (fun int int), bit1 ) 18.43/17.60 ( (fun int int), pred ) 18.43/17.60 ( (fun int int), succ ) 18.43/17.60 ( (fun int int), (fact_fact int) ) 18.43/17.60 ( (fun int int), zfact ) 18.43/17.60 ( (fun bool bool), fNot ) 18.43/17.60 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 18.43/17.60 ( (fun bool (fun bool bool)), fconj ) 18.43/17.60 ( (fun bool (fun bool bool)), fdisj ) 18.43/17.60 ( (fun bool (fun bool bool)), fimplies ) 18.43/17.60 ( (fun int (fun int bool)), sRStar ) 18.43/17.60 ( (fun int (fun int bool)), quadRes ) 18.43/17.60 ( (fun int (fun int bool)), norRRset ) 18.43/17.60 ( (fun int (fun int bool)), d22set ) 18.43/17.60 ( (fun int (fun int bool)), sr ) 18.43/17.60 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 18.43/17.60 ( (fun nat (fun nat nat)), nat_gcd ) 18.43/17.60 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 18.43/17.60 ( (fun nat (fun nat nat)), nat_lcm ) 18.43/17.60 ( (fun nat (fun real real)), root ) 18.43/17.60 ( (fun real (fun real real)), log ) 18.43/17.60 ( (fun real (fun real real)), powr ) 18.43/17.60 ( (fun nat (fun nat bool)), coprime ) 18.43/17.60 ( (fun (fun int bool) int), (the int) ) 18.43/17.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 18.43/17.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 18.43/17.60 ( (fun nat (fun nat (product_prod int int))), bezw ) 18.43/17.60 ( (fun (fun int bool) bool), nat_nat_set ) 18.43/17.60 ( (filter nat), sequentially ) 18.43/17.60 ( (fun (product_prod nat nat) bool), pred_nat ) 18.43/17.60 ( (fun (product_prod int int) bool), frac_1 ) 18.43/17.60 ( (fun real complex), cis ) 18.43/17.60 ( (fun complex real), im ) 18.43/17.60 ( (fun complex real), re ) 18.43/17.60 ( (fun complex real), arg ) 18.43/17.60 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 18.43/17.60 ( (fun int (fun int int)), int_gcd ) 18.43/17.60 ( (fun int (fun int int)), multInv ) 18.43/17.60 ( (fun int (fun int int)), legacy_zgcd ) 18.43/17.60 ( (fun int (fun int int)), z3mod ) 18.43/17.60 ( (fun int (fun int int)), inv ) 18.43/17.60 ( (fun int (fun int int)), (gcd_gcd int) ) 18.43/17.60 ( (fun int (fun int int)), standardRes ) 18.43/17.60 ( (fun int (fun int int)), legendre ) 18.43/17.60 ( (fun int (fun int int)), nat_tsub ) 18.43/17.60 ( (fun int (fun int int)), z3div ) 18.43/17.60 ( (fun int (fun int int)), int_lcm ) 18.43/17.60 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 18.43/17.60 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 18.43/17.60 ( (fun int (fun (fun int bool) bool)), rsetR ) 18.43/17.60 ( (fun int (fun (fun int bool) bool)), resSet ) 18.43/17.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 18.43/17.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 18.43/17.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 18.43/17.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 18.43/17.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 18.43/17.60 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 18.43/17.61 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 18.43/17.61 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 18.43/17.61 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 18.43/17.61 ( (fun int (fun int (product_prod int int))), negDivAlg ) 18.43/17.61 ( (fun int (fun int (product_prod int int))), divmod_int ) 18.43/17.61 ( (fun int (fun int (product_prod int int))), posDivAlg ) 18.43/17.61 ( (fun int (fun int (product_prod int int))), pdivmod ) 18.43/17.61 ( (fun int (fun int (product_prod int int))), norm_frac ) 18.43/17.61 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 18.43/17.61 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 18.43/17.61 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 18.43/17.61 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 18.43/17.61 ( (fun real nat), natfloor ) 18.43/17.61 ( (fun real nat), natceiling ) 18.43/17.61 ( (fun int quickcheck_code_int), quickcheck_of_int ) 18.43/17.61 ( (fun int (fun int (fun int bool))), wset ) 18.43/17.61 ( (fun int (fun int (fun int bool))), bnorRset ) 18.43/17.61 ( (fun int (fun int (fun int bool))), zcong ) 18.43/17.61 ( (fun int (fun int (fun int bool))), noXRRset ) 18.43/17.61 ( (fun int (fun int (fun int bool))), zcongm ) 18.43/17.61 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 18.43/17.61 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 18.43/17.61 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 18.43/17.61 ( (fun int real), (real_1 int) ) 18.43/17.61 ( (fun complex nat), (size_size complex) ) 18.43/17.61 ( (fun complex nat), complex_size ) 18.43/17.61 ( (fun int (list int)), quickc666637781d_zero ) 18.43/17.61 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 18.43/17.61 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 18.43/17.61 ( (fun (product_prod int int) rat), frct ) 18.43/17.61 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 18.43/17.61 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 18.43/17.61 ( (fun (fun nat rat) bool), vanishes ) 18.43/17.61 ( (fun int (fun int rat)), fract ) 18.43/17.61 ( (fun code_code_numeral int), code_int_of ) 18.43/17.61 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 18.43/17.61 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 18.43/17.61 ( (fun code_code_numeral nat), code_c271388182l_size ) 18.43/17.61 ( (fun real (fun real complex)), complex_1 ) 18.43/17.61 ( (fun real (fun real complex)), rcis ) 18.43/17.61 ( (fun int (fun nat nat)), nat_aux ) 18.43/17.61 ( (fun rat real), ratreal ) 18.43/17.61 ( (fun quickcheck_code_int int), quickcheck_int_of ) 18.43/17.61 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 18.43/17.61 ( (fun rat (product_prod int int)), quotient_of ) 18.43/17.61 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 18.43/17.61 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 18.43/17.61 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 18.43/17.61 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 18.43/17.61 ) 18.43/17.61 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (forall ((X $$unsorted)) (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)))) )))) 18.43/17.61 ( (zero_zero real) ) 18.43/17.61 ( (one_one real) ) 18.43/17.61 ( pi ) 18.43/17.61 ( (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)))) ) 18.43/17.61 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.43/17.61 ( (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))))) ) 18.43/17.61 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 18.43/17.61 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 18.43/17.61 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.61 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 18.43/17.61 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 18.43/17.61 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 18.43/17.61 ) 18.43/17.61 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_130857 $$unsorted) (BOUND_VARIABLE_130858 $$unsorted)) (or (not (division_ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_130857) BOUND_VARIABLE_130858) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_130857) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_130858)))) )) 18.43/17.61 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.61 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 18.43/17.61 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.61 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 18.43/17.61 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.61 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.61 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 18.43/17.61 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.43/17.61 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.61 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.61 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.61 ) 18.43/17.61 (instantiation (let ((_let_0 (dvd_dvd X_a))) (forall ((X_a $$unsorted)) (or (not (dvd X_a)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0))) )) 18.43/17.61 ( bool ) 18.43/17.61 ( real ) 18.43/17.61 ( nat ) 18.43/17.61 ( (fun nat bool) ) 18.43/17.61 ( int ) 18.43/17.61 ( (fun int bool) ) 18.43/17.61 ( complex ) 18.43/17.61 ( rat ) 18.43/17.61 ( quickcheck_code_int ) 18.43/17.61 ( (product_prod real real) ) 18.43/17.61 ( (product_prod int int) ) 18.43/17.61 ( (filter real) ) 18.43/17.61 ( (filter nat) ) 18.43/17.61 ( (product_prod nat nat) ) 18.43/17.61 ( code_code_numeral ) 18.43/17.61 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 18.43/17.61 ( (fun nat rat) ) 18.43/17.61 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 18.43/17.61 ) 18.43/17.61 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_130943 $$unsorted) (BOUND_VARIABLE_130944 $$unsorted) (BOUND_VARIABLE_130945 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_130945)) (= (= (ti X_a BOUND_VARIABLE_130944) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_130943) BOUND_VARIABLE_130945)) (= (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_130944) BOUND_VARIABLE_130945) (ti X_a BOUND_VARIABLE_130943)))) )) 18.43/17.61 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi, pi ) 18.43/17.61 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), min_1, min_1 ) 18.43/17.61 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m, m ) 18.43/17.61 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), s, s ) 18.43/17.61 ( complex, ii, ii, ii ) 18.43/17.61 ) 18.43/17.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130977 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (number_number_of int) BOUND_VARIABLE_130977) (hAPP X_a int (archimedean_ceiling X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_130977)))) ) 18.43/17.61 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.43/17.61 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.61 ( real, min_1 ) 18.43/17.61 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.61 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.43/17.61 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.43/17.61 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 18.43/17.61 ( nat, pls ) 18.43/17.61 ( nat, (hAPP int int bit1 pls) ) 18.43/17.61 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.43/17.61 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.43/17.61 ( int, pls ) 18.43/17.61 ( int, (hAPP int int bit1 pls) ) 18.43/17.61 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.43/17.61 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.61 ( int, min_1 ) 18.43/17.61 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.43/17.61 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.43/17.61 ( complex, min_1 ) 18.43/17.61 ( quickcheck_code_int, (zero_zero int) ) 18.43/17.61 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 18.43/17.61 ( quickcheck_code_int, (one_one int) ) 18.43/17.61 ( code_code_numeral, pls ) 18.43/17.61 ( code_code_numeral, (hAPP int int bit1 pls) ) 18.43/17.61 ) 18.43/17.61 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_131031 $$unsorted) (BOUND_VARIABLE_131032 $$unsorted)) (or (not (linordered_idom X_a)) (= (ti X_a BOUND_VARIABLE_131032) (ti X_a BOUND_VARIABLE_131031)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_131031) BOUND_VARIABLE_131032)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_131032) BOUND_VARIABLE_131031))) ))) 18.43/17.61 ( real, (zero_zero real), pi ) 18.43/17.61 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.61 ( 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))))) ) 18.43/17.61 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.61 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.61 ( real, (zero_zero real), skv_2 ) 18.43/17.61 ( real, (zero_zero real), skv_10 ) 18.43/17.61 ( real, (zero_zero real), skv_13 ) 18.43/17.61 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.61 ( real, pi, (zero_zero real) ) 18.43/17.61 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.61 ( 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)) ) 18.43/17.61 ( 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)))) ) 18.43/17.61 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.43/17.61 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.61 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 18.43/17.61 ( 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) ) 18.43/17.61 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.43/17.61 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.43/17.61 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 18.43/17.61 ( 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 ) 18.43/17.61 ( real, skv_2, (zero_zero real) ) 18.43/17.61 ( real, skv_10, (zero_zero real) ) 18.43/17.61 ( real, skv_13, (zero_zero real) ) 18.43/17.61 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.61 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 18.43/17.61 ( int, (zero_zero int), (zero_zero int) ) 18.43/17.61 ( int, (zero_zero int), (one_one int) ) 18.43/17.61 ( 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))) ) 18.43/17.61 ( int, (zero_zero int), min_1 ) 18.43/17.61 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 18.43/17.61 ( int, (zero_zero int), t ) 18.43/17.61 ( int, (one_one int), (zero_zero int) ) 18.43/17.61 ( int, (one_one int), t ) 18.43/17.61 ( 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))), (zero_zero int) ) 18.43/17.61 ( 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))), s ) 18.43/17.61 ( 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 ) 18.43/17.61 ( 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_3 ) 18.43/17.61 ( 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_9 ) 18.43/17.61 ( int, min_1, (zero_zero int) ) 18.43/17.61 ( int, min_1, min_1 ) 18.43/17.61 ( 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))) ) 18.43/17.61 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 18.43/17.61 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 18.43/17.61 ( int, t, (zero_zero int) ) 18.43/17.61 ( int, t, (one_one int) ) 18.43/17.61 ( 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))) ) 18.43/17.61 ( 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) (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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 18.43/17.62 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.43/17.62 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.43/17.62 ) 18.43/17.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131051 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_131051))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) BOUND_VARIABLE_131051)))) ) 18.43/17.62 ( real, (zero_zero int) ) 18.43/17.62 ( real, (one_one int) ) 18.43/17.62 ) 18.43/17.62 (instantiation (let ((_let_0 (number_number_of int))) (let ((_let_1 (number_number_of rat))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (= (hAPP rat rat (hAPP rat (fun rat rat) (inverse_divide rat) (hAPP int rat _let_1 K_4)) (hAPP int rat _let_1 L_4)) (hAPP int rat (hAPP int (fun int rat) fract (hAPP int int _let_0 K_4)) (hAPP int int _let_0 L_4))) ))) 18.43/17.62 ( pls, (hAPP int int bit1 pls) ) 18.43/17.62 ( (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 18.43/17.62 ) 18.43/17.62 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a (number_number_of X_a) min_1) (hAPP X_a X_a (uminus_uminus X_a) (one_one X_a)))) ) 18.43/17.62 ( real ) 18.43/17.62 ( nat ) 18.43/17.62 ( int ) 18.43/17.62 ( complex ) 18.43/17.62 ( rat ) 18.43/17.62 ( quickcheck_code_int ) 18.43/17.62 ( code_code_numeral ) 18.43/17.62 ) 18.43/17.62 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (div_div X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_131146))) (let ((_let_4 (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_131159))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_131144 $$unsorted) (BOUND_VARIABLE_131145 $$unsorted) (BOUND_VARIABLE_131146 $$unsorted) (BOUND_VARIABLE_131157 $$unsorted) (BOUND_VARIABLE_131158 $$unsorted) (BOUND_VARIABLE_131159 $$unsorted)) (or (not (semiring_div X_a)) (and (or (not (= _let_2 (ti X_a BOUND_VARIABLE_131146))) (= _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_3 BOUND_VARIABLE_131144)) (hAPP X_a X_a _let_3 BOUND_VARIABLE_131145)))) (or (= _let_2 (ti X_a BOUND_VARIABLE_131159)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_4 BOUND_VARIABLE_131157)) (hAPP X_a X_a _let_4 BOUND_VARIABLE_131158)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_131157) BOUND_VARIABLE_131158))))) )))))) 18.43/17.62 ( 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))) ) 18.43/17.62 ( 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))))) ) 18.43/17.62 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.62 ( 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 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)))) ) 18.43/17.62 ( 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))), (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))) ) 18.43/17.62 ( 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)))) ) 18.43/17.62 ( int, t, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.43/17.62 ( int, skv_1, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.43/17.62 ( complex, ii, ii, ii, ii, ii, ii ) 18.43/17.62 ( 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)) ) 18.43/17.62 ( 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))) ) 18.43/17.62 ) 18.43/17.62 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (one_one int))) (let ((_let_2 (ti int M_2))) (forall ((P_4 $$unsorted)) (= (hBOOL (hAPP int bool zprime P_4)) (and (forall ((M_2 $$unsorted)) (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))) (= (ti int P_4) _let_2) (= _let_1 _let_2)) ) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) P_4)))) )))) 18.43/17.62 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.43/17.62 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.62 ) 18.43/17.62 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_131272 $$unsorted) (BOUND_VARIABLE_131273 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_131273))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_131273) (hAPP nat nat suc BOUND_VARIABLE_131272))))) )) 18.43/17.62 ( int, (hAPP nat nat suc (zero_zero nat)), s ) 18.43/17.62 ( int, (hAPP nat nat suc (zero_zero nat)), s1 ) 18.43/17.62 ( int, (hAPP nat nat suc (zero_zero nat)), skv_8 ) 18.43/17.62 ( complex, (hAPP nat nat suc (zero_zero nat)), ii ) 18.43/17.62 ) 18.43/17.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131295 $$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_131295) (ti X_a BOUND_VARIABLE_131295))) ) 18.43/17.62 ( bool, fFalse ) 18.43/17.62 ( bool, fTrue ) 18.43/17.62 ( real, pi ) 18.43/17.62 ( (fun nat bool), (even_odd_even nat) ) 18.43/17.62 ( (fun nat bool), prime ) 18.43/17.62 ( (fun nat nat), suc ) 18.43/17.62 ( (fun nat nat), (fact_fact nat) ) 18.43/17.62 ( (fun nat nat), (size_size nat) ) 18.43/17.62 ( (fun nat nat), fact ) 18.43/17.62 ( (fun nat nat), nat_size ) 18.43/17.62 ( int, pls ) 18.43/17.62 ( int, m ) 18.43/17.62 ( int, min_1 ) 18.43/17.62 ( int, s ) 18.43/17.62 ( int, s1 ) 18.43/17.62 ( int, t ) 18.43/17.62 ( (fun int bool), zprime ) 18.43/17.62 ( (fun int bool), nat_neg ) 18.43/17.62 ( (fun int bool), zEven ) 18.43/17.62 ( (fun int bool), nat_is_nat ) 18.43/17.62 ( (fun int bool), zOdd ) 18.43/17.62 ( (fun int bool), (even_odd_even int) ) 18.43/17.62 ( (fun int bool), twoSqu1091635170sum2sq ) 18.43/17.62 ( (fun int nat), nat_1 ) 18.43/17.62 ( (fun int nat), phi ) 18.43/17.62 ( (fun real real), sqrt ) 18.43/17.62 ( (fun real real), tan ) 18.43/17.62 ( (fun real real), cos ) 18.43/17.62 ( (fun real real), arccos ) 18.43/17.62 ( (fun real real), ln ) 18.43/17.62 ( (fun real real), sin ) 18.43/17.62 ( (fun real real), arctan ) 18.43/17.62 ( (fun real real), arcsin ) 18.43/17.62 ( complex, ii ) 18.43/17.62 ( (fun complex complex), cnj ) 18.43/17.62 ( (fun complex complex), expi ) 18.43/17.62 ( (fun nat real), (real_1 nat) ) 18.43/17.62 ( (fun nat real), cos_coeff ) 18.43/17.62 ( (fun nat real), sin_coeff ) 18.43/17.62 ( (fun int int), bit0 ) 18.43/17.62 ( (fun int int), bit1 ) 18.43/17.62 ( (fun int int), pred ) 18.43/17.62 ( (fun int int), succ ) 18.43/17.62 ( (fun int int), (fact_fact int) ) 18.43/17.62 ( (fun int int), zfact ) 18.43/17.62 ( (fun bool bool), fNot ) 18.43/17.62 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 18.43/17.62 ( (fun bool (fun bool bool)), fconj ) 18.43/17.62 ( (fun bool (fun bool bool)), fdisj ) 18.43/17.62 ( (fun bool (fun bool bool)), fimplies ) 18.43/17.62 ( (fun int (fun int bool)), sRStar ) 18.43/17.62 ( (fun int (fun int bool)), quadRes ) 18.43/17.62 ( (fun int (fun int bool)), norRRset ) 18.43/17.62 ( (fun int (fun int bool)), d22set ) 18.43/17.62 ( (fun int (fun int bool)), sr ) 18.43/17.62 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 18.43/17.62 ( (fun nat (fun nat nat)), nat_gcd ) 18.43/17.62 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 18.43/17.62 ( (fun nat (fun nat nat)), nat_lcm ) 18.43/17.62 ( (fun nat (fun real real)), root ) 18.43/17.62 ( (fun real (fun real real)), log ) 18.43/17.62 ( (fun real (fun real real)), powr ) 18.43/17.62 ( (fun nat (fun nat bool)), coprime ) 18.43/17.62 ( (fun (fun int bool) int), (the int) ) 18.43/17.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 18.43/17.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 18.43/17.62 ( (fun nat (fun nat (product_prod int int))), bezw ) 18.43/17.62 ( (fun (fun int bool) bool), nat_nat_set ) 18.43/17.62 ( (filter nat), sequentially ) 18.43/17.62 ( (fun (product_prod nat nat) bool), pred_nat ) 18.43/17.62 ( (fun (product_prod int int) bool), frac_1 ) 18.43/17.62 ( (fun real complex), cis ) 18.43/17.62 ( (fun complex real), im ) 18.43/17.62 ( (fun complex real), re ) 18.43/17.62 ( (fun complex real), arg ) 18.43/17.62 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 18.43/17.62 ( (fun int (fun int int)), int_gcd ) 18.43/17.62 ( (fun int (fun int int)), multInv ) 18.43/17.62 ( (fun int (fun int int)), legacy_zgcd ) 18.43/17.62 ( (fun int (fun int int)), z3mod ) 18.43/17.62 ( (fun int (fun int int)), inv ) 18.43/17.62 ( (fun int (fun int int)), (gcd_gcd int) ) 18.43/17.62 ( (fun int (fun int int)), standardRes ) 18.43/17.62 ( (fun int (fun int int)), legendre ) 18.43/17.62 ( (fun int (fun int int)), nat_tsub ) 18.43/17.62 ( (fun int (fun int int)), z3div ) 18.43/17.62 ( (fun int (fun int int)), int_lcm ) 18.43/17.62 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 18.43/17.62 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 18.43/17.62 ( (fun int (fun (fun int bool) bool)), rsetR ) 18.43/17.62 ( (fun int (fun (fun int bool) bool)), resSet ) 18.43/17.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 18.43/17.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 18.43/17.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 18.43/17.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 18.43/17.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 18.43/17.62 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 18.43/17.62 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 18.43/17.62 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 18.43/17.62 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 18.43/17.62 ( (fun int (fun int (product_prod int int))), negDivAlg ) 18.43/17.62 ( (fun int (fun int (product_prod int int))), divmod_int ) 18.43/17.63 ( (fun int (fun int (product_prod int int))), posDivAlg ) 18.43/17.63 ( (fun int (fun int (product_prod int int))), pdivmod ) 18.43/17.63 ( (fun int (fun int (product_prod int int))), norm_frac ) 18.43/17.63 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 18.43/17.63 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 18.43/17.63 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 18.43/17.63 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 18.43/17.63 ( (fun real nat), natfloor ) 18.43/17.63 ( (fun real nat), natceiling ) 18.43/17.63 ( (fun int quickcheck_code_int), quickcheck_of_int ) 18.43/17.63 ( (fun int (fun int (fun int bool))), wset ) 18.43/17.63 ( (fun int (fun int (fun int bool))), bnorRset ) 18.43/17.63 ( (fun int (fun int (fun int bool))), zcong ) 18.43/17.63 ( (fun int (fun int (fun int bool))), noXRRset ) 18.43/17.63 ( (fun int (fun int (fun int bool))), zcongm ) 18.43/17.63 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 18.43/17.63 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 18.43/17.63 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 18.43/17.63 ( (fun int real), (real_1 int) ) 18.43/17.63 ( (fun complex nat), (size_size complex) ) 18.43/17.63 ( (fun complex nat), complex_size ) 18.43/17.63 ( (fun int (list int)), quickc666637781d_zero ) 18.43/17.63 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 18.43/17.63 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 18.43/17.63 ( (fun (product_prod int int) rat), frct ) 18.43/17.63 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 18.43/17.63 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 18.43/17.63 ( (fun (fun nat rat) bool), vanishes ) 18.43/17.63 ( (fun int (fun int rat)), fract ) 18.43/17.63 ( (fun code_code_numeral int), code_int_of ) 18.43/17.63 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 18.43/17.63 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 18.43/17.63 ( (fun code_code_numeral nat), code_c271388182l_size ) 18.43/17.63 ( (fun real (fun real complex)), complex_1 ) 18.43/17.63 ( (fun real (fun real complex)), rcis ) 18.43/17.63 ( (fun int (fun nat nat)), nat_aux ) 18.43/17.63 ( (fun rat real), ratreal ) 18.43/17.63 ( (fun quickcheck_code_int int), quickcheck_int_of ) 18.43/17.63 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 18.43/17.63 ( (fun rat (product_prod int int)), quotient_of ) 18.43/17.63 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 18.43/17.63 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 18.43/17.63 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 18.43/17.63 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 18.43/17.63 ) 18.43/17.63 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131309 $$unsorted)) (or (not (real_algebra_1 X_a)) (= (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_131309) (hAPP real X_a (of_real X_a) (hAPP nat real (semiring_1_of_nat real) BOUND_VARIABLE_131309)))) ) 18.43/17.63 ( real, (zero_zero nat) ) 18.43/17.63 ( real, (one_one nat) ) 18.43/17.63 ( int, (zero_zero nat) ) 18.43/17.63 ( int, (hAPP nat nat suc (zero_zero nat)) ) 18.43/17.63 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.63 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.43/17.63 ) 18.43/17.63 (instantiation (let ((_let_0 (fun int bool))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) B_1))) (= (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less_eq rat) (one_one rat)) (hAPP int rat (hAPP int (fun int rat) fract A_2) B_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B_1) A_2)))) )) 18.43/17.63 ( (zero_zero int), (one_one int) ) 18.43/17.63 ( pls, min_1 ) 18.43/17.63 ( (one_one int), (zero_zero int) ) 18.43/17.63 ( (one_one int), (one_one int) ) 18.43/17.63 ( min_1, (zero_zero int) ) 18.43/17.63 ( min_1, min_1 ) 18.43/17.63 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 18.43/17.63 ( s, (zero_zero int) ) 18.43/17.63 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 18.43/17.63 ( t, (one_one int) ) 18.43/17.63 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 18.43/17.63 ( skv_3, (zero_zero int) ) 18.43/17.63 ( skv_9, (zero_zero int) ) 18.43/17.63 ) 18.43/17.63 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (div_div X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_131361 $$unsorted) (BOUND_VARIABLE_131362 $$unsorted)) (or (not (semiring_div X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_131362)) (= (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_131361) BOUND_VARIABLE_131362)) BOUND_VARIABLE_131362) (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_131361) BOUND_VARIABLE_131362)) (one_one X_a)))) )))) 18.43/17.63 ( nat, (one_one nat), (one_one nat) ) 18.43/17.63 ( 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), (one_one int) ) 18.43/17.63 ( 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)))), (one_one int) ) 18.43/17.63 ) 18.43/17.63 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (inverse_divide X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_131408 $$unsorted) (BOUND_VARIABLE_131409 $$unsorted) (BOUND_VARIABLE_131410 $$unsorted)) (or (not (field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_131410)) (= (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_131410) BOUND_VARIABLE_131408)) BOUND_VARIABLE_131409)) BOUND_VARIABLE_131410) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_131408) (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_131409) BOUND_VARIABLE_131410)))) )))) 18.43/17.63 ( 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)))) ) 18.43/17.63 ) 18.43/17.63 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_131443))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_131442 $$unsorted) (BOUND_VARIABLE_131443 $$unsorted) (BOUND_VARIABLE_131444 $$unsorted)) (or (not (comm_ring_1 X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_131444))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_131442))) (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_131444) BOUND_VARIABLE_131442)))) )) 18.43/17.63 ( int, (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.63 ) 18.43/17.63 (instantiation (let ((_let_0 (norm_norm X_a))) (let ((_let_1 (sgn_sgn X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_131481 $$unsorted) (BOUND_VARIABLE_131488 $$unsorted)) (or (not (real_normed_vector X_a)) (and (or (= _let_2 (ti X_a BOUND_VARIABLE_131481)) (= (one_one real) (hAPP X_a real _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_131481)))) (or (not (= _let_2 (ti X_a BOUND_VARIABLE_131488))) (= (zero_zero real) (hAPP X_a real _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_131488)))))) )))) 18.43/17.63 ( bool, fFalse, fFalse ) 18.43/17.63 ( bool, fTrue, fTrue ) 18.43/17.63 ( real, pi, pi ) 18.43/17.63 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat) ) 18.43/17.63 ( (fun nat bool), prime, prime ) 18.43/17.63 ( (fun nat nat), suc, suc ) 18.43/17.63 ( (fun nat nat), (fact_fact nat), (fact_fact nat) ) 18.43/17.63 ( (fun nat nat), (size_size nat), (size_size nat) ) 18.43/17.63 ( (fun nat nat), fact, fact ) 18.43/17.63 ( (fun nat nat), nat_size, nat_size ) 18.43/17.63 ( int, pls, pls ) 18.43/17.63 ( int, m, m ) 18.43/17.63 ( int, min_1, min_1 ) 18.43/17.63 ( int, s, s ) 18.43/17.63 ( int, s1, s1 ) 18.43/17.63 ( int, t, t ) 18.43/17.63 ( (fun int bool), zprime, zprime ) 18.43/17.63 ( (fun int bool), nat_neg, nat_neg ) 18.43/17.63 ( (fun int bool), zEven, zEven ) 18.43/17.63 ( (fun int bool), nat_is_nat, nat_is_nat ) 18.43/17.63 ( (fun int bool), zOdd, zOdd ) 18.43/17.63 ( (fun int bool), (even_odd_even int), (even_odd_even int) ) 18.43/17.63 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 18.43/17.63 ( (fun int nat), nat_1, nat_1 ) 18.43/17.63 ( (fun int nat), phi, phi ) 18.43/17.63 ( (fun real real), sqrt, sqrt ) 18.43/17.63 ( (fun real real), tan, tan ) 18.43/17.63 ( (fun real real), cos, cos ) 18.43/17.63 ( (fun real real), arccos, arccos ) 18.43/17.63 ( (fun real real), ln, ln ) 18.43/17.63 ( (fun real real), sin, sin ) 18.43/17.63 ( (fun real real), arctan, arctan ) 18.43/17.63 ( (fun real real), arcsin, arcsin ) 18.43/17.63 ( complex, ii, ii ) 18.43/17.63 ( (fun complex complex), cnj, cnj ) 18.43/17.63 ( (fun complex complex), expi, expi ) 18.43/17.63 ( (fun nat real), (real_1 nat), (real_1 nat) ) 18.43/17.63 ( (fun nat real), cos_coeff, cos_coeff ) 18.43/17.63 ( (fun nat real), sin_coeff, sin_coeff ) 18.43/17.63 ( (fun int int), bit0, bit0 ) 18.43/17.63 ( (fun int int), bit1, bit1 ) 18.43/17.63 ( (fun int int), pred, pred ) 18.43/17.63 ( (fun int int), succ, succ ) 18.43/17.63 ( (fun int int), (fact_fact int), (fact_fact int) ) 18.43/17.63 ( (fun int int), zfact, zfact ) 18.43/17.63 ( (fun bool bool), fNot, fNot ) 18.43/17.63 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset ) 18.43/17.63 ( (fun bool (fun bool bool)), fconj, fconj ) 18.43/17.63 ( (fun bool (fun bool bool)), fdisj, fdisj ) 18.43/17.63 ( (fun bool (fun bool bool)), fimplies, fimplies ) 18.43/17.63 ( (fun int (fun int bool)), sRStar, sRStar ) 18.43/17.63 ( (fun int (fun int bool)), quadRes, quadRes ) 18.43/17.63 ( (fun int (fun int bool)), norRRset, norRRset ) 18.43/17.63 ( (fun int (fun int bool)), d22set, d22set ) 18.43/17.63 ( (fun int (fun int bool)), sr, sr ) 18.43/17.63 ( (fun int (fun int bool)), quickc1265749348ro_rel, quickc1265749348ro_rel ) 18.43/17.63 ( (fun nat (fun nat nat)), nat_gcd, nat_gcd ) 18.43/17.63 ( (fun nat (fun nat nat)), (gcd_gcd nat), (gcd_gcd nat) ) 18.43/17.63 ( (fun nat (fun nat nat)), nat_lcm, nat_lcm ) 18.43/17.63 ( (fun nat (fun real real)), root, root ) 18.43/17.63 ( (fun real (fun real real)), log, log ) 18.43/17.63 ( (fun real (fun real real)), powr, powr ) 18.43/17.63 ( (fun nat (fun nat bool)), coprime, coprime ) 18.43/17.63 ( (fun (fun int bool) int), (the int), (the int) ) 18.43/17.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, normalize ) 18.43/17.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, negateSnd ) 18.43/17.63 ( (fun nat (fun nat (product_prod int int))), bezw, bezw ) 18.43/17.63 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set ) 18.43/17.63 ( (filter nat), sequentially, sequentially ) 18.43/17.63 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat ) 18.43/17.63 ( (fun (product_prod int int) bool), frac_1, frac_1 ) 18.43/17.63 ( (fun real complex), cis, cis ) 18.43/17.63 ( (fun complex real), im, im ) 18.43/17.63 ( (fun complex real), re, re ) 18.43/17.63 ( (fun complex real), arg, arg ) 18.43/17.63 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral ) 18.43/17.63 ( (fun int (fun int int)), int_gcd, int_gcd ) 18.43/17.63 ( (fun int (fun int int)), multInv, multInv ) 18.43/17.63 ( (fun int (fun int int)), legacy_zgcd, legacy_zgcd ) 18.43/17.63 ( (fun int (fun int int)), z3mod, z3mod ) 18.43/17.63 ( (fun int (fun int int)), inv, inv ) 18.43/17.63 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int) ) 18.43/17.63 ( (fun int (fun int int)), standardRes, standardRes ) 18.43/17.63 ( (fun int (fun int int)), legendre, legendre ) 18.43/17.63 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 18.43/17.63 ( (fun int (fun int int)), z3div, z3div ) 18.43/17.63 ( (fun int (fun int int)), int_lcm, int_lcm ) 18.43/17.63 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than2 ) 18.43/17.63 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than ) 18.43/17.63 ( (fun int (fun (fun int bool) bool)), rsetR, rsetR ) 18.43/17.63 ( (fun int (fun (fun int bool) bool)), resSet, resSet ) 18.43/17.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, lazy_small_lazy_rel ) 18.43/17.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, posDivAlg_rel ) 18.43/17.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, upto_rel ) 18.43/17.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, negDivAlg_rel ) 18.43/17.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, norm_frac_rel ) 18.43/17.63 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_less ) 18.43/17.63 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_leq ) 18.43/17.63 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel ) 18.43/17.63 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd ) 18.43/17.63 ( (fun int (fun int (product_prod int int))), negDivAlg, negDivAlg ) 18.43/17.63 ( (fun int (fun int (product_prod int int))), divmod_int, divmod_int ) 18.43/17.63 ( (fun int (fun int (product_prod int int))), posDivAlg, posDivAlg ) 18.43/17.63 ( (fun int (fun int (product_prod int int))), pdivmod, pdivmod ) 18.43/17.63 ( (fun int (fun int (product_prod int int))), norm_frac, norm_frac ) 18.43/17.63 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust ) 18.43/17.63 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, bolzano_bisect ) 18.43/17.63 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 18.43/17.63 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 18.43/17.63 ( (fun real nat), natfloor, natfloor ) 18.43/17.63 ( (fun real nat), natceiling, natceiling ) 18.43/17.63 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int ) 18.43/17.63 ( (fun int (fun int (fun int bool))), wset, wset ) 18.43/17.63 ( (fun int (fun int (fun int bool))), bnorRset, bnorRset ) 18.43/17.63 ( (fun int (fun int (fun int bool))), zcong, zcong ) 18.43/17.63 ( (fun int (fun int (fun int bool))), noXRRset, noXRRset ) 18.43/17.63 ( (fun int (fun int (fun int bool))), zcongm, zcongm ) 18.43/17.63 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair ) 18.43/17.63 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS ) 18.43/17.63 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral ) 18.43/17.63 ( (fun int real), (real_1 int), (real_1 int) ) 18.43/17.63 ( (fun complex nat), (size_size complex), (size_size complex) ) 18.43/17.63 ( (fun complex nat), complex_size, complex_size ) 18.43/17.63 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero ) 18.43/17.63 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel ) 18.43/17.63 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel ) 18.43/17.63 ( (fun (product_prod int int) rat), frct, frct ) 18.43/17.63 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux ) 18.43/17.63 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel ) 18.43/17.63 ( (fun (fun nat rat) bool), vanishes, vanishes ) 18.43/17.63 ( (fun int (fun int rat)), fract, fract ) 18.43/17.63 ( (fun code_code_numeral int), code_int_of, code_int_of ) 18.43/17.63 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat ) 18.43/17.63 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral) ) 18.43/17.63 ( (fun code_code_numeral nat), code_c271388182l_size, code_c271388182l_size ) 18.43/17.63 ( (fun real (fun real complex)), complex_1, complex_1 ) 18.43/17.63 ( (fun real (fun real complex)), rcis, rcis ) 18.43/17.63 ( (fun int (fun nat nat)), nat_aux, nat_aux ) 18.43/17.63 ( (fun rat real), ratreal, ratreal ) 18.43/17.63 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of ) 18.43/17.63 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int ) 18.43/17.63 ( (fun rat (product_prod int int)), quotient_of, quotient_of ) 18.43/17.63 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR ) 18.43/17.63 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 18.43/17.63 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of ) 18.43/17.63 ( (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 ) 18.43/17.63 ) 18.43/17.63 (instantiation (forall ((X $$unsorted)) (= (hAPP complex real re X) (hAPP complex real re (hAPP complex complex cnj X))) ) 18.43/17.63 ( ii ) 18.43/17.63 ( (zero_zero complex) ) 18.43/17.63 ( (one_one complex) ) 18.43/17.63 ) 18.43/17.63 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 A_2) zEven))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 B_1) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) A_2) B_1)) zOdd))) )))) 18.43/17.63 ( (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) ) 18.43/17.63 ( (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)))) ) 18.43/17.63 ) 18.43/17.63 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (times_times int) X_1) Y_1)) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Y_1) zEven)) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_1) zEven))) )))) 18.43/17.63 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 18.43/17.63 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 18.43/17.63 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 18.43/17.63 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_1 ) 18.43/17.63 ) 18.43/17.63 (instantiation (let ((_let_0 (hAPP int X_b (number_number_of X_b) BOUND_VARIABLE_131690))) (forall ((X_b $$unsorted) (BOUND_VARIABLE_131690 $$unsorted)) (or (not (division_ring X_b)) (not (number X_b)) (= (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (inverse_divide X_b) (one_one X_b)) _let_0) (hAPP X_b X_b (inverse_inverse X_b) _let_0))) )) 18.43/17.63 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.43/17.63 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.63 ( real, min_1 ) 18.43/17.63 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.64 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.43/17.64 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.43/17.64 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 18.43/17.64 ( nat, pls ) 18.43/17.64 ( nat, (hAPP int int bit1 pls) ) 18.43/17.64 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.43/17.64 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.43/17.64 ( int, pls ) 18.43/17.64 ( int, (hAPP int int bit1 pls) ) 18.43/17.64 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.43/17.64 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.64 ( int, min_1 ) 18.43/17.64 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.43/17.64 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.43/17.64 ( complex, min_1 ) 18.43/17.64 ( quickcheck_code_int, (zero_zero int) ) 18.43/17.64 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 18.43/17.64 ( quickcheck_code_int, (one_one int) ) 18.43/17.64 ( code_code_numeral, pls ) 18.43/17.64 ( code_code_numeral, (hAPP int int bit1 pls) ) 18.43/17.64 ) 18.43/17.64 (instantiation (let ((_let_0 (uminus_uminus int))) (forall ((Z_4 $$unsorted) (Z_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) Z_1) (zero_zero int)))) (= (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))) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (times_times int) Z_1) Z_4)))) )) 18.43/17.64 ( (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))) ) 18.43/17.64 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.64 ( 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))) ) 18.43/17.64 ( skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.43/17.64 ) 18.43/17.64 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_131720 $$unsorted) (BOUND_VARIABLE_131721 $$unsorted)) (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_131720)) (hAPP X_a X_a (hAPP X_a _let_2 _let_4 BOUND_VARIABLE_131721) BOUND_VARIABLE_131720)) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_131721)))) )))))) 18.43/17.64 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.64 ( 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))))) ) 18.43/17.64 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.64 ( 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)))) ) 18.43/17.64 ( 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))) ) 18.43/17.64 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.64 ( 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))) ) 18.43/17.64 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.43/17.64 ( complex, ii, ii ) 18.43/17.64 ( 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)) ) 18.43/17.64 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.64 ) 18.43/17.64 (instantiation (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_131760))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_131757 $$unsorted) (BOUND_VARIABLE_131758 $$unsorted) (BOUND_VARIABLE_131759 $$unsorted) (BOUND_VARIABLE_131760 $$unsorted)) (or (not (topological_space X_b)) (not (topological_space X_a)) (not (forall ((X_2 $$unsorted)) (or (= (ti X_a X_2) (ti X_a BOUND_VARIABLE_131760)) (= (hAPP X_a X_b BOUND_VARIABLE_131759 X_2) (hAPP X_a X_b BOUND_VARIABLE_131758 X_2))) )) (= (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_131758) BOUND_VARIABLE_131757) _let_5)) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_131759) BOUND_VARIABLE_131757) _let_5)))) ))))))) 18.43/17.64 ( 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)))) ) 18.43/17.64 ) 18.43/17.64 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_131798 $$unsorted) (BOUND_VARIABLE_131799 $$unsorted)) (or (not (real_normed_algebra X_a)) (not (hBOOL (hAPP _let_0 bool _let_1 BOUND_VARIABLE_131799))) (hBOOL (hAPP _let_0 bool _let_1 (hAPP X_a _let_0 (hAPP _let_3 (fun X_a _let_0) (combc nat X_a X_a) (hAPP _let_0 _let_3 (hAPP (fun X_a _let_2) (fun _let_0 _let_3) (combb X_a _let_2 nat) (times_times X_a)) BOUND_VARIABLE_131799)) BOUND_VARIABLE_131798)))) ))))) 18.43/17.64 ( real, (one_one real), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) ) 18.43/17.64 ) 18.43/17.64 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (field_char_0_Rats X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_131831 $$unsorted) (BOUND_VARIABLE_131832 $$unsorted)) (or (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_131832) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_131831) _let_3))) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_131831)) (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_131832) BOUND_VARIABLE_131831)) _let_3))) ))))) 18.43/17.64 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 18.43/17.64 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.43/17.64 ( 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))) ) 18.43/17.64 ( 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)))) ) 18.43/17.64 ( 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)))) ) 18.43/17.64 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 18.43/17.64 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 18.43/17.64 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 18.43/17.64 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 18.43/17.64 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 18.43/17.64 ( 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) ) 18.43/17.64 ) 18.43/17.64 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (fun int int))) (let ((_let_4 (product_prod int int))) (let ((_let_5 (hAPP int (fun int _let_4) negDivAlg A_1))) (forall ((A_1 $$unsorted) (B $$unsorted)) (or (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) (hAPP int int (hAPP int _let_3 (plus_plus int) A_1) B))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B) _let_2)) (= (hAPP _let_4 _let_4 (hAPP int (fun _let_4 _let_4) adjust B) (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_3 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) B))) (hAPP int _let_4 _let_5 B))) ))))))) 18.43/17.64 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 18.43/17.64 ( (hAPP nat int (hAPP 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) ) 18.43/17.64 ) 18.43/17.64 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (product_prod int int))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP int int (hAPP int (fun int int) (plus_plus int) A_1) B))) (forall ((A_1 $$unsorted) (B $$unsorted)) (or (and (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) _let_5)))) (= (hAPP int _let_3 (hAPP int _let_4 negDivAlg A_1) B) (hAPP int _let_3 (hAPP int _let_4 (product_Pair int int) (hAPP int int (number_number_of int) min_1)) _let_5))) ))))))) 18.43/17.64 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 18.43/17.64 ( (hAPP nat int (hAPP 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) ) 18.43/17.64 ) 18.43/17.64 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (hBOOL (hAPP real bool _let_2 (hAPP real real tan X)))) )))) 18.43/17.64 ( (zero_zero real) ) 18.43/17.64 ( (one_one real) ) 18.43/17.64 ( pi ) 18.43/17.64 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.64 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 18.43/17.64 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 18.43/17.64 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.64 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 18.43/17.64 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 18.43/17.64 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 18.43/17.64 ) 18.43/17.64 (instantiation (let ((_let_0 (ord_less X_a))) (forall ((X_a $$unsorted)) (or (not (ord X_a)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0))) )) 18.43/17.64 ( bool ) 18.43/17.64 ( real ) 18.43/17.64 ( nat ) 18.43/17.64 ( (fun nat bool) ) 18.43/17.64 ( int ) 18.43/17.64 ( (fun int bool) ) 18.43/17.64 ( rat ) 18.43/17.64 ( quickcheck_code_int ) 18.43/17.64 ( (product_prod real real) ) 18.43/17.64 ( (product_prod int int) ) 18.43/17.64 ( (filter real) ) 18.43/17.64 ( (filter nat) ) 18.43/17.64 ( (product_prod nat nat) ) 18.43/17.64 ( code_code_numeral ) 18.43/17.64 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 18.43/17.64 ( (fun nat rat) ) 18.43/17.64 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 18.43/17.64 ) 18.43/17.64 (instantiation (let ((_let_0 (one_one int))) (forall ((X_1 $$unsorted) (P_1 $$unsorted)) (or (not (forall ((A_4 $$unsorted)) (or (and (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_0) A_4)) (not (hBOOL (hAPP int bool P_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) A_4) _let_0))))) (hBOOL (hAPP int bool P_1 A_4))) )) (hBOOL (hAPP int bool P_1 X_1))) )) 18.43/17.64 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) pls) ) 18.43/17.64 ( (zero_zero int), nat_is_nat ) 18.43/17.64 ( (zero_zero int), (even_odd_even int) ) 18.43/17.64 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))) ) 18.43/17.64 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) min_1) ) 18.43/17.64 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) t) ) 18.43/17.64 ( pls, (hAPP int (fun int bool) (ord_less_eq int) min_1) ) 18.43/17.64 ( (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 18.43/17.64 ( (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 18.43/17.64 ( (one_one int), nat_neg ) 18.43/17.64 ( (one_one int), nat_is_nat ) 18.43/17.64 ( (one_one int), (even_odd_even int) ) 18.43/17.64 ( (one_one int), (hAPP int (fun int bool) (ord_less int) t) ) 18.43/17.64 ( (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))), zprime ) 18.43/17.64 ( (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 (fun int bool) (ord_less int) (zero_zero int)) ) 18.43/17.64 ( (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 (fun int bool) (ord_less int) s) ) 18.43/17.65 ( (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))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)) ) 18.43/17.65 ( (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))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 18.43/17.65 ( (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 (fun int bool) (ord_less int) t) ) 18.43/17.65 ( (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))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 18.43/17.65 ( (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))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))) ) 18.43/17.65 ( (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 (fun int bool) (ord_less int) skv_3) ) 18.43/17.65 ( (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))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_3)) ) 18.43/17.65 ( (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))), (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_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 18.43/17.65 ( (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 (fun int bool) (ord_less int) skv_9) ) 18.43/17.65 ( (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))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_9)) ) 18.43/17.65 ( min_1, (hAPP int (fun int bool) (ord_less int) pls) ) 18.43/17.65 ( min_1, (hAPP int (fun int bool) (ord_less_eq int) pls) ) 18.43/17.65 ( min_1, (hAPP int (fun int bool) (ord_less int) min_1) ) 18.43/17.65 ( min_1, (hAPP int (fun int bool) (ord_less_eq int) min_1) ) 18.43/17.65 ( (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)) ) 18.43/17.65 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), zprime ) 18.43/17.65 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), nat_is_nat ) 18.43/17.65 ( (hAPP int int (number_number_of int) min_1), nat_neg ) 18.43/17.65 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) ) 18.43/17.65 ( s, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 18.43/17.65 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) ) 18.43/17.65 ( (hAPP int int (number_number_of int) pls), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 18.43/17.65 ( (hAPP int int (number_number_of int) pls), nat_neg ) 18.43/17.65 ( t, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) ) 18.43/17.65 ( (let ((_let_0 (fun int int))) (let ((_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 ) 18.43/17.65 ( (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)) ) 18.43/17.65 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), nat_is_nat ) 18.43/17.65 ( (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun int bool) (ord_less 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)))) ) 18.43/17.65 ( skv_3, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 18.43/17.65 ( skv_9, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 18.43/17.65 ) 18.43/17.65 (instantiation (let ((_let_0 (norm_norm X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_132016 $$unsorted)) (or (not (real_n1866405975lgebra X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_132016)) (= (hAPP X_a real _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_132016)) (hAPP real real (inverse_inverse real) (hAPP X_a real _let_0 BOUND_VARIABLE_132016)))) )) 18.43/17.65 ( bool, fFalse ) 18.43/17.65 ( bool, fTrue ) 18.43/17.65 ( real, (zero_zero real) ) 18.43/17.65 ( real, pi ) 18.43/17.65 ( (fun nat bool), (even_odd_even nat) ) 18.43/17.65 ( (fun nat bool), prime ) 18.43/17.65 ( (fun nat nat), suc ) 18.43/17.65 ( (fun nat nat), (fact_fact nat) ) 18.43/17.65 ( (fun nat nat), (size_size nat) ) 18.43/17.65 ( (fun nat nat), fact ) 18.43/17.65 ( (fun nat nat), nat_size ) 18.43/17.65 ( int, pls ) 18.43/17.65 ( int, m ) 18.43/17.65 ( int, min_1 ) 18.43/17.65 ( int, s ) 18.43/17.65 ( int, s1 ) 18.43/17.65 ( int, t ) 18.43/17.65 ( (fun int bool), zprime ) 18.43/17.65 ( (fun int bool), nat_neg ) 18.43/17.65 ( (fun int bool), zEven ) 18.43/17.65 ( (fun int bool), nat_is_nat ) 18.43/17.65 ( (fun int bool), zOdd ) 18.43/17.65 ( (fun int bool), (even_odd_even int) ) 18.43/17.65 ( (fun int bool), twoSqu1091635170sum2sq ) 18.43/17.65 ( (fun int nat), nat_1 ) 18.43/17.65 ( (fun int nat), phi ) 18.43/17.65 ( (fun real real), sqrt ) 18.43/17.65 ( (fun real real), tan ) 18.43/17.65 ( (fun real real), cos ) 18.43/17.65 ( (fun real real), arccos ) 18.43/17.65 ( (fun real real), ln ) 18.43/17.65 ( (fun real real), sin ) 18.43/17.65 ( (fun real real), arctan ) 18.43/17.65 ( (fun real real), arcsin ) 18.43/17.65 ( complex, ii ) 18.43/17.65 ( (fun complex complex), cnj ) 18.43/17.65 ( (fun complex complex), expi ) 18.43/17.65 ( (fun nat real), (real_1 nat) ) 18.43/17.65 ( (fun nat real), cos_coeff ) 18.43/17.65 ( (fun nat real), sin_coeff ) 18.43/17.65 ( (fun int int), bit0 ) 18.43/17.65 ( (fun int int), bit1 ) 18.43/17.65 ( (fun int int), pred ) 18.43/17.65 ( (fun int int), succ ) 18.43/17.65 ( (fun int int), (fact_fact int) ) 18.43/17.65 ( (fun int int), zfact ) 18.43/17.65 ( (fun bool bool), fNot ) 18.43/17.65 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 18.43/17.65 ( (fun bool (fun bool bool)), fconj ) 18.43/17.65 ( (fun bool (fun bool bool)), fdisj ) 18.43/17.65 ( (fun bool (fun bool bool)), fimplies ) 18.43/17.65 ( (fun int (fun int bool)), sRStar ) 18.43/17.65 ( (fun int (fun int bool)), quadRes ) 18.43/17.65 ( (fun int (fun int bool)), norRRset ) 18.43/17.65 ( (fun int (fun int bool)), d22set ) 18.43/17.65 ( (fun int (fun int bool)), sr ) 18.43/17.65 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 18.43/17.65 ( (fun nat (fun nat nat)), nat_gcd ) 18.43/17.65 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 18.43/17.65 ( (fun nat (fun nat nat)), nat_lcm ) 18.43/17.65 ( (fun nat (fun real real)), root ) 18.43/17.65 ( (fun real (fun real real)), log ) 18.43/17.65 ( (fun real (fun real real)), powr ) 18.43/17.65 ( (fun nat (fun nat bool)), coprime ) 18.43/17.65 ( (fun (fun int bool) int), (the int) ) 18.43/17.65 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 18.43/17.65 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 18.43/17.65 ( (fun nat (fun nat (product_prod int int))), bezw ) 18.43/17.65 ( (fun (fun int bool) bool), nat_nat_set ) 18.43/17.65 ( (filter nat), sequentially ) 18.43/17.65 ( (fun (product_prod nat nat) bool), pred_nat ) 18.43/17.65 ( (fun (product_prod int int) bool), frac_1 ) 18.43/17.65 ( (fun real complex), cis ) 18.43/17.65 ( (fun complex real), im ) 18.43/17.65 ( (fun complex real), re ) 18.43/17.65 ( (fun complex real), arg ) 18.43/17.65 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 18.43/17.65 ( (fun int (fun int int)), int_gcd ) 18.43/17.65 ( (fun int (fun int int)), multInv ) 18.43/17.65 ( (fun int (fun int int)), legacy_zgcd ) 18.43/17.65 ( (fun int (fun int int)), z3mod ) 18.43/17.65 ( (fun int (fun int int)), inv ) 18.43/17.65 ( (fun int (fun int int)), (gcd_gcd int) ) 18.43/17.65 ( (fun int (fun int int)), standardRes ) 18.43/17.65 ( (fun int (fun int int)), legendre ) 18.43/17.65 ( (fun int (fun int int)), nat_tsub ) 18.43/17.65 ( (fun int (fun int int)), z3div ) 18.43/17.65 ( (fun int (fun int int)), int_lcm ) 18.43/17.65 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 18.43/17.65 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 18.43/17.65 ( (fun int (fun (fun int bool) bool)), rsetR ) 18.43/17.65 ( (fun int (fun (fun int bool) bool)), resSet ) 18.43/17.65 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 18.43/17.65 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 18.43/17.65 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 18.43/17.65 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 18.43/17.65 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 18.43/17.65 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 18.43/17.65 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 18.43/17.65 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 18.43/17.65 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 18.43/17.65 ( (fun int (fun int (product_prod int int))), negDivAlg ) 18.43/17.65 ( (fun int (fun int (product_prod int int))), divmod_int ) 18.43/17.65 ( (fun int (fun int (product_prod int int))), posDivAlg ) 18.43/17.65 ( (fun int (fun int (product_prod int int))), pdivmod ) 18.43/17.65 ( (fun int (fun int (product_prod int int))), norm_frac ) 18.43/17.65 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 18.43/17.65 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 18.43/17.65 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 18.43/17.65 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 18.43/17.65 ( (fun real nat), natfloor ) 18.43/17.65 ( (fun real nat), natceiling ) 18.43/17.65 ( (fun int quickcheck_code_int), quickcheck_of_int ) 18.43/17.65 ( (fun int (fun int (fun int bool))), wset ) 18.43/17.65 ( (fun int (fun int (fun int bool))), bnorRset ) 18.43/17.65 ( (fun int (fun int (fun int bool))), zcong ) 18.43/17.65 ( (fun int (fun int (fun int bool))), noXRRset ) 18.43/17.65 ( (fun int (fun int (fun int bool))), zcongm ) 18.43/17.65 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 18.43/17.65 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 18.43/17.65 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 18.43/17.65 ( (fun int real), (real_1 int) ) 18.43/17.65 ( (fun complex nat), (size_size complex) ) 18.43/17.65 ( (fun complex nat), complex_size ) 18.43/17.65 ( (fun int (list int)), quickc666637781d_zero ) 18.43/17.65 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 18.43/17.65 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 18.43/17.65 ( (fun (product_prod int int) rat), frct ) 18.43/17.65 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 18.43/17.65 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 18.43/17.65 ( (fun (fun nat rat) bool), vanishes ) 18.43/17.65 ( (fun int (fun int rat)), fract ) 18.43/17.65 ( (fun code_code_numeral int), code_int_of ) 18.43/17.65 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 18.43/17.65 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 18.43/17.65 ( (fun code_code_numeral nat), code_c271388182l_size ) 18.43/17.65 ( (fun real (fun real complex)), complex_1 ) 18.43/17.65 ( (fun real (fun real complex)), rcis ) 18.43/17.65 ( (fun int (fun nat nat)), nat_aux ) 18.43/17.65 ( (fun rat real), ratreal ) 18.43/17.65 ( (fun quickcheck_code_int int), quickcheck_int_of ) 18.43/17.65 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 18.43/17.65 ( (fun rat (product_prod int int)), quotient_of ) 18.43/17.65 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 18.43/17.65 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 18.43/17.65 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 18.43/17.65 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 18.43/17.65 ) 18.43/17.65 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (inverse_inverse X_a))) (let ((_let_3 (zero_zero X_a))) (let ((_let_4 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_132051) BOUND_VARIABLE_132052))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_132051 $$unsorted) (BOUND_VARIABLE_132052 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_132051)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_132052))) (and (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_4) _let_3))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_132051) BOUND_VARIABLE_132052))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_3) _let_4))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_132052) BOUND_VARIABLE_132051)))))) )))))) 18.43/17.65 ( real, (zero_zero real), pi ) 18.43/17.65 ( 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)))) ) 18.43/17.65 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.65 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.65 ( real, (zero_zero real), skv_6 ) 18.43/17.65 ( real, (zero_zero real), skv_11 ) 18.43/17.65 ( real, (zero_zero real), skv_12 ) 18.43/17.65 ( real, (zero_zero real), skv_14 ) 18.43/17.65 ( real, pi, (zero_zero real) ) 18.43/17.65 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.65 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.43/17.65 ( 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)))) ) 18.43/17.65 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.43/17.66 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 18.43/17.66 ( 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) ) 18.43/17.66 ( 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))) ) 18.43/17.66 ( 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)))))) ) 18.43/17.66 ( 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 ) 18.43/17.66 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.43/17.66 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.43/17.66 ( real, skv_6, (zero_zero real) ) 18.43/17.66 ( real, skv_11, (zero_zero real) ) 18.43/17.66 ( real, skv_12, (zero_zero real) ) 18.43/17.66 ( real, skv_14, (zero_zero real) ) 18.43/17.66 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.66 ( int, (zero_zero int), (one_one int) ) 18.43/17.66 ( int, (zero_zero int), min_1 ) 18.43/17.66 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.66 ( int, (zero_zero int), s ) 18.43/17.66 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 18.43/17.66 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.43/17.66 ( int, (zero_zero int), skv_3 ) 18.43/17.66 ( int, (zero_zero int), skv_9 ) 18.43/17.66 ( int, pls, min_1 ) 18.43/17.66 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 18.43/17.66 ( int, (one_one int), (zero_zero int) ) 18.43/17.66 ( int, (one_one int), t ) 18.43/17.66 ( 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))), (zero_zero int) ) 18.43/17.66 ( 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 ) 18.43/17.66 ( 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_1 ) 18.43/17.66 ( int, min_1, (zero_zero int) ) 18.43/17.66 ( int, min_1, pls ) 18.43/17.66 ( int, min_1, min_1 ) 18.43/17.66 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 18.43/17.66 ( int, s, (zero_zero int) ) 18.43/17.66 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 18.43/17.66 ( int, t, (one_one int) ) 18.43/17.66 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 18.43/17.66 ( int, skv_3, (zero_zero int) ) 18.43/17.66 ( int, skv_9, (zero_zero int) ) 18.43/17.66 ( complex, ii, ii ) 18.43/17.66 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 18.43/17.66 ( 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 ) 18.43/17.66 ) 18.43/17.66 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP complex real re (hAPP real complex cis A_1)) (hAPP real real cos A_1)) ) 18.43/17.66 ( (zero_zero real) ) 18.43/17.66 ( pi ) 18.43/17.66 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.66 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.66 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.43/17.66 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 18.43/17.66 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 18.43/17.66 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 18.43/17.66 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 18.43/17.66 ( skv_14 ) 18.43/17.66 ) 18.43/17.66 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_132210))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_132210 $$unsorted) (BOUND_VARIABLE_132211 $$unsorted) (BOUND_VARIABLE_132212 $$unsorted)) (or (not (order X_a)) (not (= (ti X_a BOUND_VARIABLE_132211) (ti X_a BOUND_VARIABLE_132212))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_132212))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_132211))) )) 18.43/17.66 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi, pi ) 18.43/17.66 ( int, (zero_zero int), m, m ) 18.43/17.66 ( int, min_1, s1, s1 ) 18.43/17.66 ( int, s, s, s ) 18.43/17.66 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), min_1, min_1 ) 18.43/17.66 ( int, t, t, t ) 18.43/17.66 ( int, skv_3, pls, pls ) 18.43/17.66 ) 18.43/17.66 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (power_power real))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_4 (hAPP complex real re X))) (forall ((X $$unsorted)) (= (hAPP complex real re (hAPP complex complex (inverse_inverse complex) X)) (hAPP real real (hAPP real _let_0 (inverse_divide real) _let_4) (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP nat real (hAPP real _let_1 _let_2 _let_4) _let_3)) (hAPP nat real (hAPP real _let_1 _let_2 (hAPP complex real im X)) _let_3)))) )))))) 18.43/17.66 ( ii ) 18.43/17.66 ( (zero_zero complex) ) 18.43/17.66 ( (one_one complex) ) 18.43/17.66 ) 18.43/17.66 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted)) (or (not (divisi14063676e_zero X_a)) (= _let_0 (hAPP X_a X_a (inverse_inverse X_a) _let_0))) )) 18.43/17.66 ( real ) 18.43/17.66 ( nat ) 18.43/17.66 ( int ) 18.43/17.66 ( complex ) 18.43/17.66 ( rat ) 18.43/17.66 ( quickcheck_code_int ) 18.43/17.66 ( code_code_numeral ) 18.43/17.66 ) 18.43/17.66 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (let ((_let_1 (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_132296)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_132295 $$unsorted) (BOUND_VARIABLE_132296 $$unsorted)) (or (not (linordered_idom X_a)) (= (or (= (zero_zero nat) BOUND_VARIABLE_132296) (and _let_1 (not (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_132295)))) (and (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_132295)) (not _let_1))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_132295) BOUND_VARIABLE_132296))))) ))) 18.43/17.66 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.66 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.66 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.66 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.66 ) 18.43/17.66 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int bit1 K_4) (hAPP int int succ (hAPP int int bit0 K_4))) ) 18.43/17.66 ( pls ) 18.43/17.66 ( (hAPP int int bit1 pls) ) 18.43/17.66 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.43/17.66 ( min_1 ) 18.43/17.66 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.43/17.66 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.43/17.66 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 18.43/17.66 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 18.43/17.66 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 18.43/17.66 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 18.43/17.66 ) 18.43/17.66 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted)) (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)))))) )) 18.43/17.66 ( bool ) 18.43/17.66 ( real ) 18.43/17.66 ( nat ) 18.43/17.66 ( (fun nat bool) ) 18.43/17.66 ( (fun nat nat) ) 18.43/17.66 ( int ) 18.43/17.66 ( (fun real real) ) 18.43/17.66 ( complex ) 18.43/17.66 ( (fun int int) ) 18.43/17.66 ( rat ) 18.43/17.66 ( (fun bool bool) ) 18.43/17.66 ( quickcheck_code_int ) 18.43/17.66 ( (fun nat (fun nat bool)) ) 18.43/17.66 ( (product_prod real real) ) 18.43/17.66 ( (product_prod int int) ) 18.43/17.66 ( (fun nat (product_prod int int)) ) 18.43/17.66 ( (product_prod nat nat) ) 18.43/17.66 ( (fun (product_prod nat nat) bool) ) 18.43/17.66 ( (fun nat (fun (product_prod nat nat) bool)) ) 18.43/17.66 ( (fun nat (product_prod nat nat)) ) 18.43/17.66 ( code_code_numeral ) 18.43/17.66 ) 18.43/17.66 (instantiation (let ((_let_0 (sgn_sgn X_a))) (let ((_let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_132590))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_132590 $$unsorted)) (or (not (linordered_idom X_a)) (= _let_1 (hAPP X_a X_a _let_0 _let_1))) ))) 18.43/17.66 ( real, (zero_zero real) ) 18.43/17.66 ( rat, (zero_zero rat) ) 18.43/17.66 ) 18.43/17.66 (instantiation (forall ((R_4 $$unsorted)) (= (hAPP real complex (hAPP real (fun real complex) complex_1 (zero_zero real)) R_4) (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP real complex (of_real complex) R_4)) ii)) ) 18.43/17.66 ( (zero_zero real) ) 18.43/17.66 ( (one_one real) ) 18.43/17.66 ( pi ) 18.43/17.66 ( (hAPP int real (number_number_of real) min_1) ) 18.43/17.66 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 18.43/17.66 ) 18.43/17.66 (instantiation (let ((_let_0 (fun int bool))) (forall ((B $$unsorted) (A_1 $$unsorted)) (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))) (= (hAPP int int (hAPP int (fun int int) (div_mod int) A_1) B) (ti int A_1))) )) 18.43/17.66 ( (zero_zero int), (zero_zero int) ) 18.43/17.66 ( (zero_zero int), (one_one int) ) 18.43/17.66 ( (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))) ) 18.43/17.66 ( (zero_zero int), min_1 ) 18.43/17.66 ( min_1, (zero_zero int) ) 18.43/17.66 ( min_1, min_1 ) 18.43/17.66 ( 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))) ) 18.43/17.66 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 18.43/17.66 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 18.43/17.66 ( t, (zero_zero int) ) 18.43/17.66 ( t, (one_one int) ) 18.43/17.66 ( 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))) ) 18.43/17.66 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.43/17.66 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.43/17.66 ) 18.43/17.66 (instantiation (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)))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_2 X_1))) (not (hBOOL (hAPP int bool _let_2 Y_1))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP int nat nat_1 X_1)) (hAPP int nat nat_1 Y_1))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 X_1) Y_1)))) )))) 18.43/17.66 ( pls, min_1 ) 18.43/17.66 ( (one_one int), (zero_zero int) ) 18.43/17.66 ( min_1, (zero_zero int) ) 18.43/17.66 ( min_1, min_1 ) 18.43/17.66 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 18.43/17.66 ( s, (zero_zero int) ) 18.43/17.66 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 18.43/17.66 ( t, (one_one int) ) 18.43/17.66 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 18.43/17.66 ( skv_3, (zero_zero int) ) 18.43/17.66 ( skv_9, (zero_zero int) ) 18.43/17.66 ) 18.43/17.66 (instantiation (forall ((V_3 $$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_3)) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (div_div int) (one_one int)) (hAPP int int (number_number_of int) V_3)))) ) 18.43/17.66 ( pls ) 18.43/17.66 ( (hAPP int int bit1 pls) ) 18.43/17.66 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.43/17.66 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.66 ( min_1 ) 18.43/17.66 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.43/17.66 ) 18.43/17.66 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_132866 $$unsorted)) (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_132866) _let_0))) )) 18.43/17.66 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.66 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.66 ( 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))))) ) 18.43/17.66 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.66 ( 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))) ) 18.43/17.66 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.66 ( complex, ii ) 18.43/17.66 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.66 ( 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)) ) 18.43/17.66 ) 18.43/17.66 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (one_one X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_132876 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_132876))) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_132876)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_132876) _let_2))))) )))) 18.43/17.66 ( real, (zero_zero real) ) 18.43/17.66 ( real, (one_one real) ) 18.43/17.66 ( real, pi ) 18.43/17.66 ( 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)))) ) 18.43/17.66 ( 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))))) ) 18.43/17.67 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.67 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.67 ( 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)) ) 18.43/17.67 ( real, skv_2 ) 18.43/17.67 ( real, skv_10 ) 18.43/17.67 ( real, skv_13 ) 18.43/17.67 ( nat, (zero_zero nat) ) 18.43/17.67 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.67 ( int, (zero_zero int) ) 18.43/17.67 ( int, (one_one int) ) 18.43/17.67 ( 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))) ) 18.43/17.67 ( int, min_1 ) 18.43/17.67 ( int, s ) 18.43/17.67 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 18.43/17.67 ( int, t ) 18.43/17.67 ( int, skv_3 ) 18.43/17.67 ( int, skv_9 ) 18.43/17.67 ( complex, ii ) 18.43/17.67 ) 18.43/17.67 (instantiation (let ((_let_0 (ti X_a BOUND_VARIABLE_132899))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_132899 $$unsorted)) (or (not (linord219039673up_add X_a)) (= (= (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_132899) _let_0) (= (zero_zero X_a) _let_0))) )) 18.43/17.67 ( bool, fFalse ) 18.43/17.67 ( bool, fTrue ) 18.43/17.67 ( real, (one_one real) ) 18.43/17.67 ( real, pi ) 18.43/17.67 ( 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)))) ) 18.43/17.67 ( 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) ) 18.43/17.67 ( (fun nat bool), (even_odd_even nat) ) 18.43/17.67 ( (fun nat bool), prime ) 18.43/17.67 ( (fun nat nat), suc ) 18.43/17.67 ( (fun nat nat), (fact_fact nat) ) 18.43/17.67 ( (fun nat nat), (size_size nat) ) 18.43/17.67 ( (fun nat nat), fact ) 18.43/17.67 ( (fun nat nat), nat_size ) 18.43/17.67 ( int, pls ) 18.43/17.67 ( int, m ) 18.43/17.67 ( int, (one_one int) ) 18.43/17.67 ( int, min_1 ) 18.43/17.67 ( int, s ) 18.43/17.67 ( int, s1 ) 18.43/17.67 ( int, t ) 18.43/17.67 ( (fun int bool), zprime ) 18.43/17.67 ( (fun int bool), nat_neg ) 18.43/17.67 ( (fun int bool), zEven ) 18.43/17.67 ( (fun int bool), nat_is_nat ) 18.43/17.67 ( (fun int bool), zOdd ) 18.43/17.67 ( (fun int bool), (even_odd_even int) ) 18.43/17.67 ( (fun int bool), twoSqu1091635170sum2sq ) 18.43/17.67 ( (fun int nat), nat_1 ) 18.43/17.67 ( (fun int nat), phi ) 18.43/17.67 ( (fun real real), sqrt ) 18.43/17.67 ( (fun real real), tan ) 18.43/17.67 ( (fun real real), cos ) 18.43/17.67 ( (fun real real), arccos ) 18.43/17.67 ( (fun real real), ln ) 18.43/17.67 ( (fun real real), sin ) 18.43/17.67 ( (fun real real), arctan ) 18.43/17.67 ( (fun real real), arcsin ) 18.43/17.67 ( complex, ii ) 18.43/17.67 ( complex, (one_one complex) ) 18.43/17.67 ( (fun complex complex), cnj ) 18.43/17.67 ( (fun complex complex), expi ) 18.43/17.67 ( (fun nat real), (real_1 nat) ) 18.43/17.67 ( (fun nat real), cos_coeff ) 18.43/17.67 ( (fun nat real), sin_coeff ) 18.43/17.67 ( (fun int int), bit0 ) 18.43/17.67 ( (fun int int), bit1 ) 18.43/17.67 ( (fun int int), pred ) 18.43/17.67 ( (fun int int), succ ) 18.43/17.67 ( (fun int int), (fact_fact int) ) 18.43/17.67 ( (fun int int), zfact ) 18.43/17.67 ( (fun bool bool), fNot ) 18.43/17.67 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 18.43/17.67 ( (fun bool (fun bool bool)), fconj ) 18.43/17.67 ( (fun bool (fun bool bool)), fdisj ) 18.43/17.67 ( (fun bool (fun bool bool)), fimplies ) 18.43/17.67 ( (fun int (fun int bool)), sRStar ) 18.43/17.67 ( (fun int (fun int bool)), quadRes ) 18.43/17.67 ( (fun int (fun int bool)), norRRset ) 18.43/17.67 ( (fun int (fun int bool)), d22set ) 18.43/17.67 ( (fun int (fun int bool)), sr ) 18.43/17.67 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 18.43/17.67 ( (fun nat (fun nat nat)), nat_gcd ) 18.43/17.67 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 18.43/17.67 ( (fun nat (fun nat nat)), nat_lcm ) 18.43/17.67 ( (fun nat (fun real real)), root ) 18.43/17.67 ( (fun real (fun real real)), log ) 18.43/17.67 ( (fun real (fun real real)), powr ) 18.43/17.67 ( (fun nat (fun nat bool)), coprime ) 18.43/17.67 ( (fun (fun int bool) int), (the int) ) 18.43/17.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 18.43/17.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 18.43/17.67 ( (fun nat (fun nat (product_prod int int))), bezw ) 18.43/17.67 ( (fun (fun int bool) bool), nat_nat_set ) 18.43/17.67 ( (filter nat), sequentially ) 18.43/17.67 ( (fun (product_prod nat nat) bool), pred_nat ) 18.43/17.67 ( (fun (product_prod int int) bool), frac_1 ) 18.43/17.67 ( (fun real complex), cis ) 18.43/17.67 ( (fun complex real), im ) 18.43/17.67 ( (fun complex real), re ) 18.43/17.67 ( (fun complex real), arg ) 18.43/17.67 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 18.43/17.67 ( (fun int (fun int int)), int_gcd ) 18.43/17.67 ( (fun int (fun int int)), multInv ) 18.43/17.67 ( (fun int (fun int int)), legacy_zgcd ) 18.43/17.67 ( (fun int (fun int int)), z3mod ) 18.43/17.67 ( (fun int (fun int int)), inv ) 18.43/17.67 ( (fun int (fun int int)), (gcd_gcd int) ) 18.43/17.67 ( (fun int (fun int int)), standardRes ) 18.43/17.67 ( (fun int (fun int int)), legendre ) 18.43/17.67 ( (fun int (fun int int)), nat_tsub ) 18.43/17.67 ( (fun int (fun int int)), z3div ) 18.43/17.67 ( (fun int (fun int int)), int_lcm ) 18.43/17.67 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 18.43/17.67 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 18.43/17.67 ( (fun int (fun (fun int bool) bool)), rsetR ) 18.43/17.67 ( (fun int (fun (fun int bool) bool)), resSet ) 18.43/17.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 18.43/17.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 18.43/17.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 18.43/17.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 18.43/17.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 18.43/17.67 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 18.43/17.67 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 18.43/17.67 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 18.43/17.67 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 18.43/17.67 ( (fun int (fun int (product_prod int int))), negDivAlg ) 18.43/17.67 ( (fun int (fun int (product_prod int int))), divmod_int ) 18.43/17.67 ( (fun int (fun int (product_prod int int))), posDivAlg ) 18.43/17.67 ( (fun int (fun int (product_prod int int))), pdivmod ) 18.43/17.67 ( (fun int (fun int (product_prod int int))), norm_frac ) 18.43/17.67 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 18.43/17.67 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 18.43/17.67 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 18.43/17.67 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 18.43/17.67 ( (fun real nat), natfloor ) 18.43/17.67 ( (fun real nat), natceiling ) 18.43/17.67 ( (fun int quickcheck_code_int), quickcheck_of_int ) 18.43/17.67 ( (fun int (fun int (fun int bool))), wset ) 18.43/17.67 ( (fun int (fun int (fun int bool))), bnorRset ) 18.43/17.67 ( (fun int (fun int (fun int bool))), zcong ) 18.43/17.67 ( (fun int (fun int (fun int bool))), noXRRset ) 18.43/17.67 ( (fun int (fun int (fun int bool))), zcongm ) 18.43/17.67 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 18.43/17.67 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 18.43/17.67 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 18.43/17.67 ( (fun int real), (real_1 int) ) 18.43/17.67 ( (fun complex nat), (size_size complex) ) 18.43/17.67 ( (fun complex nat), complex_size ) 18.43/17.67 ( (fun int (list int)), quickc666637781d_zero ) 18.43/17.67 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 18.43/17.67 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 18.43/17.67 ( (fun (product_prod int int) rat), frct ) 18.43/17.67 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 18.43/17.67 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 18.43/17.67 ( (fun (fun nat rat) bool), vanishes ) 18.43/17.67 ( (fun int (fun int rat)), fract ) 18.43/17.67 ( (fun code_code_numeral int), code_int_of ) 18.43/17.67 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 18.43/17.67 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 18.43/17.67 ( (fun code_code_numeral nat), code_c271388182l_size ) 18.43/17.67 ( (fun real (fun real complex)), complex_1 ) 18.43/17.67 ( (fun real (fun real complex)), rcis ) 18.43/17.67 ( (fun int (fun nat nat)), nat_aux ) 18.43/17.67 ( (fun rat real), ratreal ) 18.43/17.67 ( (fun quickcheck_code_int int), quickcheck_int_of ) 18.43/17.67 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 18.43/17.67 ( (fun rat (product_prod int int)), quotient_of ) 18.43/17.67 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 18.43/17.67 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 18.43/17.67 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 18.43/17.67 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 18.43/17.67 ) 18.43/17.67 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_132915 $$unsorted) (BOUND_VARIABLE_132916 $$unsorted)) (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_132915)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_132916))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_132916) BOUND_VARIABLE_132915)))) )))) 18.43/17.67 ( real, (zero_zero real), pi ) 18.43/17.67 ( 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))))) ) 18.43/17.67 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.67 ( real, pi, (zero_zero real) ) 18.43/17.67 ( 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)) ) 18.43/17.67 ( 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)))) ) 18.43/17.67 ( 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) ) 18.43/17.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 18.43/17.67 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.43/17.67 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 18.43/17.67 ( real, skv_2, (zero_zero real) ) 18.43/17.67 ( real, skv_10, (zero_zero real) ) 18.43/17.67 ( real, skv_13, (zero_zero real) ) 18.43/17.67 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 18.43/17.67 ( int, (zero_zero int), (zero_zero int) ) 18.43/17.67 ( int, (zero_zero int), min_1 ) 18.43/17.67 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 18.43/17.67 ( int, (zero_zero int), t ) 18.43/17.67 ( int, pls, pls ) 18.43/17.67 ( int, pls, (one_one int) ) 18.43/17.67 ( int, (one_one int), (zero_zero int) ) 18.43/17.67 ( int, (one_one int), pls ) 18.43/17.67 ( int, (one_one int), (one_one int) ) 18.43/17.67 ( int, (one_one int), t ) 18.43/17.67 ( 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))), (zero_zero int) ) 18.43/17.67 ( 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))), s ) 18.43/17.67 ( 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 ) 18.43/17.67 ( 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_3 ) 18.43/17.67 ( 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_9 ) 18.43/17.67 ( int, min_1, (zero_zero int) ) 18.43/17.67 ( int, min_1, min_1 ) 18.43/17.67 ( 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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 18.43/17.67 ) 18.43/17.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132949 $$unsorted)) (or (not (real_normed_vector X_a)) (= (not (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_132949))) (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_132949))))) ) 18.43/17.67 ( bool, fFalse ) 18.43/17.67 ( bool, fTrue ) 18.43/17.67 ( real, pi ) 18.43/17.67 ( (fun nat bool), (even_odd_even nat) ) 18.43/17.67 ( (fun nat bool), prime ) 18.43/17.67 ( (fun nat nat), suc ) 18.43/17.67 ( (fun nat nat), (fact_fact nat) ) 18.43/17.67 ( (fun nat nat), (size_size nat) ) 18.43/17.67 ( (fun nat nat), fact ) 18.43/17.67 ( (fun nat nat), nat_size ) 18.43/17.67 ( int, pls ) 18.43/17.67 ( int, m ) 18.43/17.67 ( int, min_1 ) 18.43/17.67 ( int, s ) 18.43/17.67 ( int, s1 ) 18.43/17.67 ( int, t ) 18.43/17.67 ( (fun int bool), zprime ) 18.43/17.67 ( (fun int bool), nat_neg ) 18.43/17.67 ( (fun int bool), zEven ) 18.43/17.67 ( (fun int bool), nat_is_nat ) 18.43/17.67 ( (fun int bool), zOdd ) 18.43/17.67 ( (fun int bool), (even_odd_even int) ) 18.43/17.67 ( (fun int bool), twoSqu1091635170sum2sq ) 18.43/17.67 ( (fun int nat), nat_1 ) 18.43/17.67 ( (fun int nat), phi ) 18.43/17.67 ( (fun real real), sqrt ) 18.43/17.67 ( (fun real real), tan ) 18.43/17.67 ( (fun real real), cos ) 18.43/17.67 ( (fun real real), arccos ) 18.43/17.67 ( (fun real real), ln ) 18.43/17.67 ( (fun real real), sin ) 18.43/17.67 ( (fun real real), arctan ) 18.43/17.67 ( (fun real real), arcsin ) 18.43/17.67 ( complex, ii ) 18.43/17.67 ( (fun complex complex), cnj ) 18.43/17.67 ( (fun complex complex), expi ) 18.43/17.67 ( (fun nat real), (real_1 nat) ) 18.43/17.67 ( (fun nat real), cos_coeff ) 18.43/17.67 ( (fun nat real), sin_coeff ) 18.43/17.67 ( (fun int int), bit0 ) 18.43/17.67 ( (fun int int), bit1 ) 18.43/17.67 ( (fun int int), pred ) 18.43/17.67 ( (fun int int), succ ) 18.43/17.67 ( (fun int int), (fact_fact int) ) 18.43/17.67 ( (fun int int), zfact ) 18.43/17.67 ( (fun bool bool), fNot ) 18.43/17.67 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 18.43/17.67 ( (fun bool (fun bool bool)), fconj ) 18.43/17.67 ( (fun bool (fun bool bool)), fdisj ) 18.43/17.67 ( (fun bool (fun bool bool)), fimplies ) 18.43/17.67 ( (fun int (fun int bool)), sRStar ) 18.43/17.67 ( (fun int (fun int bool)), quadRes ) 18.43/17.67 ( (fun int (fun int bool)), norRRset ) 18.43/17.67 ( (fun int (fun int bool)), d22set ) 18.43/17.67 ( (fun int (fun int bool)), sr ) 18.43/17.67 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 18.43/17.67 ( (fun nat (fun nat nat)), nat_gcd ) 18.43/17.67 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 18.43/17.67 ( (fun nat (fun nat nat)), nat_lcm ) 18.43/17.67 ( (fun nat (fun real real)), root ) 18.43/17.67 ( (fun real (fun real real)), log ) 18.43/17.67 ( (fun real (fun real real)), powr ) 18.43/17.67 ( (fun nat (fun nat bool)), coprime ) 18.43/17.67 ( (fun (fun int bool) int), (the int) ) 18.43/17.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 18.43/17.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 18.43/17.67 ( (fun nat (fun nat (product_prod int int))), bezw ) 18.43/17.67 ( (fun (fun int bool) bool), nat_nat_set ) 18.43/17.67 ( (filter nat), sequentially ) 18.43/17.67 ( (fun (product_prod nat nat) bool), pred_nat ) 18.43/17.67 ( (fun (product_prod int int) bool), frac_1 ) 18.43/17.67 ( (fun real complex), cis ) 18.43/17.67 ( (fun complex real), im ) 18.43/17.67 ( (fun complex real), re ) 18.43/17.67 ( (fun complex real), arg ) 18.43/17.67 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 18.43/17.67 ( (fun int (fun int int)), int_gcd ) 18.43/17.67 ( (fun int (fun int int)), multInv ) 18.43/17.67 ( (fun int (fun int int)), legacy_zgcd ) 18.43/17.67 ( (fun int (fun int int)), z3mod ) 18.43/17.67 ( (fun int (fun int int)), inv ) 18.43/17.67 ( (fun int (fun int int)), (gcd_gcd int) ) 18.43/17.67 ( (fun int (fun int int)), standardRes ) 18.43/17.67 ( (fun int (fun int int)), legendre ) 18.43/17.67 ( (fun int (fun int int)), nat_tsub ) 18.43/17.67 ( (fun int (fun int int)), z3div ) 18.43/17.67 ( (fun int (fun int int)), int_lcm ) 18.43/17.67 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 18.43/17.67 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 18.43/17.67 ( (fun int (fun (fun int bool) bool)), rsetR ) 18.43/17.67 ( (fun int (fun (fun int bool) bool)), resSet ) 18.43/17.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 18.43/17.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 18.43/17.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 18.43/17.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 18.43/17.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 18.43/17.67 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 18.43/17.67 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 18.43/17.67 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 18.43/17.67 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 18.43/17.67 ( (fun int (fun int (product_prod int int))), negDivAlg ) 18.43/17.68 ( (fun int (fun int (product_prod int int))), divmod_int ) 18.43/17.68 ( (fun int (fun int (product_prod int int))), posDivAlg ) 18.43/17.68 ( (fun int (fun int (product_prod int int))), pdivmod ) 18.43/17.68 ( (fun int (fun int (product_prod int int))), norm_frac ) 18.43/17.68 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 18.43/17.68 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 18.43/17.68 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 18.43/17.68 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 18.43/17.68 ( (fun real nat), natfloor ) 18.43/17.68 ( (fun real nat), natceiling ) 18.43/17.68 ( (fun int quickcheck_code_int), quickcheck_of_int ) 18.43/17.68 ( (fun int (fun int (fun int bool))), wset ) 18.43/17.68 ( (fun int (fun int (fun int bool))), bnorRset ) 18.43/17.68 ( (fun int (fun int (fun int bool))), zcong ) 18.43/17.68 ( (fun int (fun int (fun int bool))), noXRRset ) 18.43/17.68 ( (fun int (fun int (fun int bool))), zcongm ) 18.43/17.68 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 18.43/17.68 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 18.43/17.68 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 18.43/17.68 ( (fun int real), (real_1 int) ) 18.43/17.68 ( (fun complex nat), (size_size complex) ) 18.43/17.68 ( (fun complex nat), complex_size ) 18.43/17.68 ( (fun int (list int)), quickc666637781d_zero ) 18.43/17.68 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 18.43/17.68 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 18.43/17.68 ( (fun (product_prod int int) rat), frct ) 18.43/17.68 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 18.43/17.68 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 18.43/17.68 ( (fun (fun nat rat) bool), vanishes ) 18.43/17.68 ( (fun int (fun int rat)), fract ) 18.43/17.68 ( (fun code_code_numeral int), code_int_of ) 18.43/17.68 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 18.43/17.68 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 18.43/17.68 ( (fun code_code_numeral nat), code_c271388182l_size ) 18.43/17.68 ( (fun real (fun real complex)), complex_1 ) 18.43/17.68 ( (fun real (fun real complex)), rcis ) 18.43/17.68 ( (fun int (fun nat nat)), nat_aux ) 18.43/17.68 ( (fun rat real), ratreal ) 18.43/17.68 ( (fun quickcheck_code_int int), quickcheck_int_of ) 18.43/17.68 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 18.43/17.68 ( (fun rat (product_prod int int)), quotient_of ) 18.43/17.68 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 18.43/17.68 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 18.43/17.68 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 18.43/17.68 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 18.43/17.68 ) 18.43/17.68 (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)))))) ) 18.43/17.68 ( (hAPP int real (number_number_of real) min_1) ) 18.43/17.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.68 ) 18.43/17.68 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (plus_plus real))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun _let_1 _let_1))) (let ((_let_5 (fun (fun nat nat) _let_1))) (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)))))) (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (= (hAPP real real (exp real) X_1) (hAPP real real (hAPP real _let_0 _let_2 (hAPP real real (hAPP real _let_0 _let_2 (one_one real)) X_1)) (hAPP _let_1 real (suminf real) (hAPP _let_1 _let_1 (hAPP _let_3 _let_4 (combs nat real real) (hAPP _let_1 _let_3 (hAPP (fun real _let_0) (fun _let_1 _let_3) (combb real _let_0 nat) (times_times real)) (hAPP _let_1 _let_1 (hAPP _let_0 _let_4 (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_5 _let_6 (real_1 nat)) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb nat nat nat) (fact_fact nat)) _let_7))))) (hAPP _let_0 _let_1 (hAPP _let_1 _let_5 _let_6 (hAPP real _let_1 (power_power real) X_1)) _let_7)))))) ))))))))) 18.43/17.68 ( (hAPP int real (number_number_of real) min_1) ) 18.43/17.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.68 ) 18.43/17.68 (instantiation (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (hAPP (fun nat X_a) (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_133014))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_133013 $$unsorted) (BOUND_VARIABLE_133014 $$unsorted) (BOUND_VARIABLE_133015 $$unsorted)) (let ((_let_0 (filter nat))) (or (not (metric_space X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_133015) sequentially))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_133013) sequentially))) (= (ti X_a BOUND_VARIABLE_133013) (ti X_a BOUND_VARIABLE_133015)))) ))) 18.43/17.68 ( real, (zero_zero real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 18.43/17.68 ) 18.43/17.68 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (forall ((X $$unsorted)) (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))) )))) 18.43/17.68 ( (one_one real) ) 18.43/17.68 ( pi ) 18.43/17.68 ( (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)))) ) 18.43/17.68 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.43/17.68 ( skv_2 ) 18.43/17.68 ( skv_10 ) 18.43/17.68 ( skv_13 ) 18.43/17.68 ) 18.43/17.68 (instantiation (let ((_let_0 (fun X_a X_b))) (let ((_let_1 (fun X_a X_c))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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)) ))) 18.43/17.68 ( 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 ) 18.43/17.68 ( 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))) ) 18.43/17.68 ( 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))) ) 18.43/17.68 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.43/17.68 ( 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))) ) 18.43/17.68 ( 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))) ) 18.43/17.68 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.43/17.68 ( 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))) ) 18.43/17.68 ( 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_14 ) 18.43/17.68 ( 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_14 ) 18.43/17.68 ( 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_14 ) 18.43/17.68 ( real, bool, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.43/17.68 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.43/17.68 ( real, bool, real, (hAPP real (fun real bool) (ord_less real) pi), cos, skv_14 ) 18.43/17.68 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.43/17.68 ( real, bool, nat, (even_odd_even nat), natceiling, (zero_zero real) ) 18.43/17.68 ( real, bool, nat, (even_odd_even nat), natceiling, (one_one real) ) 18.43/17.68 ( real, bool, nat, prime, natceiling, (zero_zero real) ) 18.43/17.68 ( real, bool, nat, prime, natceiling, (one_one real) ) 18.43/17.68 ( 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)))) ) 18.43/17.68 ( real, real, real, sqrt, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.43/17.68 ( real, real, real, sqrt, cos, skv_14 ) 18.43/17.68 ( real, real, real, (uminus_uminus real), cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.43/17.68 ( 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))) ) 18.43/17.68 ( 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 ) 18.43/17.68 ( real, real, real, tan, cos, skv_14 ) 18.43/17.68 ( 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)))) ) 18.43/17.68 ( 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)))) ) 18.43/17.68 ( 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))) ) 18.43/17.68 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.43/17.68 ( real, real, real, cos, cos, skv_14 ) 18.43/17.68 ( 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))) ) 18.43/17.68 ( 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)))) ) 18.43/17.68 ( 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)))) ) 18.43/17.69 ( 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))) ) 18.43/17.69 ( 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 ) 18.43/17.69 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.43/17.69 ( real, real, real, cos, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), pi ) 18.43/17.69 ( real, real, real, ln, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.43/17.69 ( real, real, real, (inverse_inverse real), cos, skv_14 ) 18.43/17.69 ( real, real, real, sin, cos, skv_14 ) 18.43/17.69 ( 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))) ) 18.43/17.69 ( 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)))) ) 18.43/17.69 ( 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)))) ) 18.43/17.69 ( 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))) ) 18.43/17.69 ( 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 ) 18.43/17.69 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.43/17.69 ( real, real, real, sin, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), pi ) 18.43/17.69 ( 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))) ) 18.43/17.69 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.43/17.69 ( real, real, real, arctan, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.43/17.69 ( real, real, real, arctan, cos, skv_14 ) 18.43/17.69 ( 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)))) ) 18.43/17.69 ( 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))))))))) ) 18.43/17.69 ( 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))))) ) 18.43/17.69 ( real, real, real, (sgn_sgn real), cos, skv_14 ) 18.43/17.69 ( 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))) ) 18.43/17.69 ( real, real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.43/17.69 ( real, real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1))))))))), arctan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 18.43/17.69 ( real, real, nat, (real_1 nat), natceiling, (zero_zero real) ) 18.43/17.69 ( real, real, nat, (real_1 nat), natceiling, (one_one real) ) 18.43/17.69 ( real, real, complex, im, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 18.43/17.69 ( real, real, complex, im, cis, (zero_zero real) ) 18.43/17.69 ( real, real, complex, re, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 18.43/17.69 ( real, real, complex, re, cis, (zero_zero real) ) 18.43/17.69 ( real, nat, real, natfloor, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.43/17.69 ( real, nat, real, natfloor, cos, skv_14 ) 18.43/17.69 ( real, nat, real, natceiling, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.43/17.69 ( real, nat, real, natceiling, cos, skv_14 ) 18.43/17.69 ( real, nat, nat, suc, natceiling, (zero_zero real) ) 18.43/17.69 ( real, nat, nat, suc, natceiling, (one_one real) ) 18.43/17.69 ( real, nat, nat, (fact_fact nat), natceiling, (zero_zero real) ) 18.43/17.69 ( real, nat, nat, (fact_fact nat), natceiling, (one_one real) ) 18.43/17.69 ( real, nat, nat, (size_size nat), natceiling, (zero_zero real) ) 18.43/17.69 ( real, nat, nat, fact, natceiling, (zero_zero real) ) 18.43/17.69 ( real, nat, nat, nat_size, natceiling, (zero_zero real) ) 18.43/17.69 ( real, nat, nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), natceiling, (one_one real) ) 18.43/17.69 ( real, (fun nat bool), nat, (ord_less nat), natceiling, (zero_zero real) ) 18.43/17.69 ( real, (fun nat bool), nat, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))), natceiling, (zero_zero real) ) 18.43/17.69 ( real, (fun nat nat), nat, (plus_plus nat), natceiling, (one_one real) ) 18.43/17.69 ( 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) ) 18.43/17.69 ( real, int, nat, (semiring_1_of_nat int), natceiling, (zero_zero real) ) 18.43/17.69 ( real, int, nat, (semiring_1_of_nat int), natceiling, (one_one real) ) 18.43/17.69 ( 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))) ) 18.43/17.69 ( real, (fun real bool), real, (ord_less_eq real), cos, skv_14 ) 18.43/17.69 ( 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))) ) 18.43/17.69 ( 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)))) ) 18.43/17.69 ( 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) ) 18.43/17.69 ( 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))) ) 18.43/17.69 ( real, (fun real bool), real, (ord_less real), cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.43/17.69 ( real, (fun real bool), real, (ord_less real), cos, skv_14 ) 18.43/17.69 ( 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))) ) 18.43/17.69 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.43/17.69 ( real, (fun real bool), real, (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos))))), cos, skv_14 ) 18.43/17.69 ( real, (fun real bool), (fun real bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun real (fun real bool)))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 (fun (fun real bool) (fun real bool)) (combs real bool bool) (hAPP (fun real bool) _let_2 (hAPP (fun bool _let_0) (fun (fun real bool) _let_2) (combb bool _let_0 real) fconj) (hAPP real (fun real bool) (hAPP _let_1 _let_1 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos))))), (zero_zero real) ) 18.43/17.69 ( 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)))))) ) 18.43/17.69 ( 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))) ) 18.43/17.69 ( 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))) ) 18.43/17.69 ( real, (fun real real), real, (inverse_divide real), cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.43/17.69 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.43/17.69 ( 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))) ) 18.43/17.69 ( real, complex, real, (of_real complex), (uminus_uminus real), (one_one real) ) 18.43/17.69 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.43/17.70 ( real, complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.43/17.70 ( real, complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), cos, skv_14 ) 18.43/17.70 ( real, complex, real, cis, cos, skv_14 ) 18.43/17.70 ( real, complex, real, (hAPP real (fun real complex) complex_1 (one_one real)), cos, skv_14 ) 18.43/17.70 ( 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) ) 18.43/17.70 ( real, complex, complex, cnj, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 18.43/17.70 ( real, complex, complex, cnj, cis, (zero_zero real) ) 18.43/17.70 ( real, complex, complex, (uminus_uminus complex), (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 18.43/17.70 ( real, complex, complex, (uminus_uminus complex), cis, (zero_zero real) ) 18.43/17.70 ( real, complex, complex, (inverse_inverse complex), (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 18.43/17.70 ( 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 ) 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cos)) sin)))), cos, skv_14 ) 18.43/17.70 ( real, (fun (filter nat) bool), real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real (fun (filter nat) bool)) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))))), cos, skv_14 ) 18.43/17.70 ( real, (fun nat complex), complex, (power_power complex), (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 18.43/17.70 ( real, (fun real complex), real, complex_1, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.43/17.70 ( real, (fun real complex), real, complex_1, cos, skv_14 ) 18.43/17.70 ( real, (fun real (fun bool bool)), (fun real bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun real bool) (fun real _let_0)) (combb bool _let_0 real) fconj)), (ord_less_eq real), (zero_zero real) ) 18.43/17.70 ( real, (fun real (fun bool bool)), (fun real bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun real bool) (fun real _let_0)) (combb bool _let_0 real) fconj)), (let ((_let_0 (fun real (fun real bool)))) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.43/17.70 ( nat, bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), suc, (hAPP nat nat suc (zero_zero nat)) ) 18.43/17.70 ( nat, bool, nat, prime, suc, (hAPP nat nat suc (zero_zero nat)) ) 18.43/17.70 ( nat, nat, nat, suc, suc, (hAPP nat nat suc (zero_zero nat)) ) 18.43/17.70 ( 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 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bit0 (hAPP int int bit1 pls))) ) 18.43/17.70 ( nat, (fun real real), nat, root, suc, (hAPP nat nat suc (zero_zero nat)) ) 18.43/17.70 ( nat, complex, nat, (hAPP complex (fun nat complex) (power_power complex) ii), suc, (hAPP nat nat suc (zero_zero nat)) ) 18.43/17.70 ( 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) ) 18.43/17.70 ( nat, (fun int int), nat, (hAPP (fun int (fun nat int)) (fun nat (fun int int)) (combc int nat int) (power_power int)), suc, (hAPP nat nat suc (zero_zero nat)) ) 18.60/17.70 ( nat, (fun int int), int, (plus_plus int), (hAPP int (fun nat int) (power_power int) s), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.60/17.70 ( 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))) ) 18.60/17.70 ( 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))) ) 18.60/17.70 ( 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))) ) 18.60/17.70 ( nat, (fun int (fun int bool)), int, zcong, (hAPP int (fun nat int) (power_power int) skv_8), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.60/17.70 ( nat, (fun nat (fun nat nat)), (fun nat nat), (let ((_let_0 (fun 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(fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))))), (hAPP (fun int (fun nat int)) (fun nat (fun int int)) (combc int nat int) (power_power int)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.60/17.70 ( (fun nat bool), bool, (fun nat bool), (finite_finite_1 nat), (collect nat), prime ) 18.60/17.70 ( (fun nat bool), (fun real (fun int bool)), (fun real (fun int (fun nat bool))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun _let_2 _let_1))) (hAPP _let_3 (fun (fun real _let_2) (fun real _let_1)) (combb _let_2 _let_1 real) (hAPP (fun _let_0 bool) _let_3 (combb _let_0 bool int) (fEx nat))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun nat _let_2))) (let ((_let_7 (fun (fun nat bool) _let_6))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_5))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun int _let_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 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(combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_19 (hAPP _let_24 (fun (fun nat real) _let_19) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_24 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_24) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_8 _let_9 (hAPP (fun real _let_1) (fun _let_8 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))))))))))))))))))), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP (fun nat bool) (fun nat bool) (hAPP (fun bool bool) (fun (fun nat bool) (fun nat bool)) (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat)))) ) 18.60/17.70 ( (fun nat bool), (fun real (fun int (fun nat bool))), (fun nat bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat 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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 ) 18.60/17.71 ( (fun nat nat), (fun nat real), (fun nat real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (combb real _let_0 nat))) (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))))))))), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat))), (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) ) 18.60/17.71 ( (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))))) ) 18.60/17.71 ( (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 ) 18.60/17.71 ( int, bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.71 ( 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)) ) 18.60/17.71 ( int, bool, real, (hAPP real (fun real bool) (ord_less real) pi), (number_number_of real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.60/17.71 ( int, bool, real, (hAPP real (fun real bool) (ord_less_eq real) skv_14), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.71 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (number_number_of int), pls ) 18.60/17.71 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.71 ( 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)) ) 18.60/17.71 ( 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)) ) 18.60/17.71 ( int, bool, int, zprime, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.71 ( int, bool, int, zprime, (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 18.60/17.71 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.71 ( 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) ) 18.60/17.71 ( int, bool, int, nat_neg, (number_number_of int), pls ) 18.60/17.71 ( int, bool, int, nat_neg, (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.71 ( int, bool, int, nat_neg, (number_number_of int), min_1 ) 18.60/17.71 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) pls), (number_number_of int), pls ) 18.60/17.71 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) pls), bit1, min_1 ) 18.60/17.71 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), bit1, min_1 ) 18.60/17.71 ( int, bool, int, nat_is_nat, (number_number_of int), pls ) 18.60/17.71 ( int, bool, int, nat_is_nat, (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.71 ( int, bool, int, nat_is_nat, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.71 ( int, bool, int, nat_is_nat, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.60/17.71 ( int, bool, int, (even_odd_even int), (number_number_of int), pls ) 18.60/17.71 ( int, bool, int, (even_odd_even int), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.71 ( 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) ) 18.60/17.71 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))), (number_number_of int), pls ) 18.60/17.71 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) min_1), (number_number_of int), pls ) 18.60/17.71 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) min_1), bit1, min_1 ) 18.60/17.71 ( int, bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (number_number_of int), min_1 ) 18.60/17.71 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 18.60/17.71 ( int, bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 18.60/17.71 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), (number_number_of int), pls ) 18.60/17.71 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), bit1, min_1 ) 18.60/17.71 ( int, bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 18.60/17.71 ( 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) ) 18.60/17.71 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) t), (number_number_of int), pls ) 18.60/17.71 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) t), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.71 ( 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) ) 18.60/17.71 ( int, bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 18.60/17.71 ( int, bool, int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 18.60/17.71 ( int, bool, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun int bool) (ord_less 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)))), (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))))), (zero_zero int) ) 18.60/17.71 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) skv_3), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 18.60/17.71 ( int, bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_3)), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 18.60/17.71 ( 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_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 18.60/17.71 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) skv_9), (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) ) 18.60/17.71 ( int, bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_9)), (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) ) 18.60/17.71 ( int, bool, (fun int bool), (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1), (ord_less_eq int), (zero_zero int) ) 18.60/17.71 ( int, real, real, sqrt, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.71 ( int, real, real, sqrt, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.60/17.71 ( int, real, real, cos, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.71 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) pi), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.71 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) pi), (number_number_of real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.60/17.71 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) pi), (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.60/17.71 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) pi), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.60/17.71 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.71 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (number_number_of real), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.60/17.71 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 18.60/17.71 ( 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)) ) 18.60/17.71 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.71 ( 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)) ) 18.60/17.71 ( int, real, int, (real_1 int), (number_number_of int), pls ) 18.60/17.71 ( int, real, int, (real_1 int), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.71 ( int, real, int, (number_number_of real), bit0, (hAPP int int bit1 pls) ) 18.60/17.71 ( int, real, int, (number_number_of real), bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.71 ( int, real, int, (number_number_of real), bit0, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.60/17.71 ( int, real, int, (number_number_of real), bit1, (hAPP int int bit1 pls) ) 18.60/17.71 ( int, real, int, (number_number_of real), bit1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.71 ( int, real, int, (number_number_of real), bit1, min_1 ) 18.60/17.71 ( int, real, int, (number_number_of real), bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 18.60/17.71 ( int, real, rat, ratreal, (hAPP int (fun int rat) fract (zero_zero int)), (one_one int) ) 18.60/17.72 ( int, nat, int, nat_1, (number_number_of int), pls ) 18.60/17.72 ( int, nat, int, nat_1, (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.72 ( int, nat, int, nat_1, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.72 ( int, nat, int, nat_1, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.60/17.72 ( int, nat, int, (number_number_of nat), (number_number_of int), pls ) 18.60/17.72 ( int, nat, int, (number_number_of nat), bit0, (hAPP int int bit1 pls) ) 18.60/17.72 ( int, nat, int, (number_number_of nat), bit1, pls ) 18.60/17.72 ( int, nat, int, (number_number_of nat), bit1, (hAPP int int bit1 pls) ) 18.60/17.72 ( int, nat, code_code_numeral, (size_size code_code_numeral), (number_number_of code_code_numeral), pls ) 18.60/17.72 ( int, nat, code_code_numeral, code_c271388182l_size, (number_number_of code_code_numeral), pls ) 18.60/17.72 ( int, int, nat, (semiring_1_of_nat int), (number_number_of nat), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.60/17.72 ( int, int, int, (number_number_of int), (number_number_of int), pls ) 18.60/17.72 ( int, int, int, (number_number_of int), bit0, (hAPP int int bit1 pls) ) 18.60/17.72 ( int, int, int, (number_number_of int), bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.72 ( int, int, int, (number_number_of int), bit1, pls ) 18.60/17.72 ( int, int, int, (number_number_of int), bit1, (hAPP int int bit1 pls) ) 18.60/17.72 ( int, int, int, (number_number_of int), bit1, min_1 ) 18.60/17.72 ( int, int, int, bit0, (number_number_of int), pls ) 18.60/17.72 ( int, int, int, bit0, bit0, (hAPP int int bit1 pls) ) 18.60/17.72 ( int, int, int, bit0, bit1, pls ) 18.60/17.72 ( int, int, int, bit0, bit1, (hAPP int int bit1 pls) ) 18.60/17.72 ( int, int, int, bit0, bit1, min_1 ) 18.60/17.72 ( int, int, int, bit0, bit1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.60/17.72 ( int, int, int, bit1, (number_number_of int), pls ) 18.60/17.72 ( int, int, int, bit1, bit0, (hAPP int int bit1 pls) ) 18.60/17.72 ( int, int, int, bit1, bit0, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.60/17.72 ( int, int, int, bit1, bit1, pls ) 18.60/17.72 ( int, int, int, bit1, bit1, (hAPP int int bit1 pls) ) 18.60/17.72 ( int, int, int, bit1, bit1, min_1 ) 18.60/17.72 ( int, int, int, bit1, bit1, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 18.60/17.72 ( 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))))) ) 18.60/17.72 ( 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)))))) ) 18.60/17.72 ( 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))), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.72 ( int, int, int, (uminus_uminus int), (number_number_of int), pls ) 18.60/17.72 ( int, int, int, (uminus_uminus int), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.72 ( int, int, int, (uminus_uminus int), bit1, min_1 ) 18.60/17.72 ( int, int, int, pred, (number_number_of int), pls ) 18.60/17.72 ( int, int, int, pred, bit1, min_1 ) 18.60/17.72 ( int, int, int, (hAPP int (fun int int) legendre (hAPP int int (number_number_of int) min_1)), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 18.60/17.72 ( int, int, int, succ, (number_number_of int), pls ) 18.60/17.72 ( int, int, int, succ, bit1, min_1 ) 18.60/17.72 ( int, int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.72 ( 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))))), (number_number_of int), pls ) 18.60/17.72 ( int, int, int, (hAPP int (fun int int) (minus_minus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (number_number_of int), min_1 ) 18.60/17.72 ( int, int, int, (fact_fact int), (number_number_of int), pls ) 18.60/17.72 ( int, int, int, (fact_fact int), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.72 ( int, int, quickcheck_code_int, quickcheck_int_of, quickcheck_of_int, (zero_zero int) ) 18.60/17.72 ( int, int, (product_prod int int), twoSqu1094008024sum2sq, (hAPP int (fun int (product_prod int int)) (product_Pair int int) s), (one_one int) ) 18.60/17.72 ( int, int, code_code_numeral, code_int_of, (number_number_of code_code_numeral), pls ) 18.60/17.72 ( int, (fun int bool), int, (ord_less_eq int), (number_number_of int), pls ) 18.60/17.72 ( int, (fun int bool), int, (ord_less_eq int), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.72 ( int, (fun int bool), int, (ord_less_eq int), bit1, min_1 ) 18.60/17.72 ( int, (fun int bool), int, (ord_less int), (number_number_of int), pls ) 18.60/17.72 ( int, (fun int bool), int, (ord_less int), bit1, min_1 ) 18.60/17.72 ( int, (fun int bool), int, (ord_less 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) ) 18.60/17.72 ( int, (fun int bool), int, (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 18.60/17.72 ( 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) ) 18.60/17.72 ( int, (fun int bool), int, (let ((_let_0 (fun int (fun int bool)))) (hAPP _let_0 _let_0 (combc int int bool) (fequal int))), (number_number_of int), pls ) 18.60/17.72 ( int, (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (number_number_of int), min_1 ) 18.60/17.72 ( int, (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (number_number_of int), min_1 ) 18.60/17.72 ( int, (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (number_number_of int), min_1 ) 18.60/17.72 ( int, (fun int bool), (fun int bool), (let ((_let_0 (fun int bool))) (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool int) fNot)), (let ((_let_0 (fun int (fun int bool)))) (hAPP _let_0 _let_0 (combc int int bool) (fequal int))), (zero_zero int) ) 18.60/17.72 ( int, (fun real bool), real, (ord_less_eq real), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.72 ( int, (fun real bool), real, (let ((_let_0 (fun real (fun real bool)))) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real))), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.72 ( int, (fun real real), real, (inverse_divide real), (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.60/17.72 ( int, (fun real real), real, (times_times real), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.72 ( int, (fun real real), real, (times_times real), (number_number_of real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.60/17.72 ( int, complex, real, (of_real complex), (number_number_of real), min_1 ) 18.60/17.72 ( int, complex, int, (number_number_of complex), bit0, (hAPP int int bit1 pls) ) 18.60/17.72 ( int, complex, int, (number_number_of complex), bit1, min_1 ) 18.60/17.72 ( int, (fun complex complex), complex, (times_times complex), (number_number_of complex), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.72 ( int, (fun nat real), real, (power_power real), (number_number_of real), min_1 ) 18.60/17.72 ( int, (fun int int), int, (plus_plus int), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), m ) 18.60/17.72 ( int, (fun int int), int, (times_times int), (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.60/17.72 ( int, (fun int int), int, (times_times int), (number_number_of int), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.60/17.72 ( int, (fun int int), int, (times_times int), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 18.60/17.72 ( int, (fun int int), int, legendre, (number_number_of int), min_1 ) 18.60/17.72 ( 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)))))))), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.72 ( int, rat, int, (hAPP int (fun int rat) fract (one_one int)), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.72 ( int, rat, int, (hAPP int (fun int rat) fract (zero_zero int)), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.72 ( int, rat, rat, (sgn_sgn rat), (hAPP int (fun int rat) fract (zero_zero int)), (one_one int) ) 18.60/17.72 ( 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) ) 18.60/17.72 ( int, (fun int rat), int, fract, (number_number_of int), pls ) 18.60/17.72 ( int, (fun int rat), int, fract, (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.72 ( int, (fun int (fun bool bool)), (fun int bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun int bool) (fun int _let_0)) (combb bool _let_0 int) fconj)), (ord_less int), (zero_zero int) ) 18.60/17.76 ( int, (fun int (fun int bool)), int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun int _let_2))) (hAPP _let_5 _let_5 (combc int int _let_0) (hAPP _let_5 _let_5 (hAPP (fun _let_2 _let_2) (fun _let_5 _let_5) (combb _let_2 _let_2 int) (combc int int bool)) (hAPP _let_4 _let_5 (hAPP _let_3 (fun _let_4 _let_5) (combb _let_1 _let_2 int) (hAPP _let_2 _let_3 (combb int _let_0 int) (fequal int))) int_gcd))))))))), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.76 ( 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))) ) 18.60/17.76 ( 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) ) 18.60/17.76 ( 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 bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun int _let_2))) (hAPP _let_5 _let_5 (combc int int _let_0) (hAPP _let_5 _let_5 (hAPP (fun _let_2 _let_2) (fun _let_5 _let_5) (combb _let_2 _let_2 int) (combc int int bool)) (hAPP _let_4 _let_5 (hAPP _let_3 (fun _let_4 _let_5) (combb _let_1 _let_2 int) (hAPP _let_2 _let_3 (combb int _let_0 int) (fequal int))) int_gcd))))))))), (one_one int) ) 18.60/17.77 ( int, quickcheck_code_int, int, quickcheck_of_int, (number_number_of int), pls ) 18.60/17.77 ( int, quickcheck_code_int, int, quickcheck_of_int, (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.77 ( int, quickcheck_code_int, int, (number_number_of quickcheck_code_int), bit1, pls ) 18.60/17.77 ( int, (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) (one_one int)), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.77 ( int, (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) (zero_zero int)), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.77 ( int, (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) s), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.77 ( int, (product_prod int int), rat, quotient_of, (hAPP int (fun int rat) fract (zero_zero int)), (one_one int) ) 18.60/17.77 ( int, (fun int (product_prod int int)), int, (product_Pair int int), (number_number_of int), pls ) 18.60/17.77 ( int, (fun int (product_prod int int)), int, (product_Pair int int), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.77 ( int, (fun (fun int bool) bool), int, (member int), (number_number_of int), (hAPP int int bit1 pls) ) 18.60/17.77 ( 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) (fun _let_2 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))))))), (number_number_of int), pls ) 18.60/17.77 ( int, (fun (product_prod int int) bool), (fun (product_prod int int) bool), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (hAPP (fun bool bool) (fun _let_1 _let_1) (combb bool bool _let_0) fNot))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 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) ) 18.60/17.77 ( int, code_code_numeral, int, (number_number_of code_code_numeral), (number_number_of int), pls ) 18.60/17.77 ( int, code_code_numeral, int, (number_number_of code_code_numeral), bit1, pls ) 18.60/17.77 ( int, code_code_numeral, code_code_numeral, (hAPP code_code_numeral (fun code_code_numeral code_code_numeral) (minus_minus code_code_numeral) (zero_zero code_code_numeral)), (number_number_of code_code_numeral), (hAPP int int bit1 pls) ) 18.60/17.77 ( int, (fun code_code_numeral code_code_numeral), code_code_numeral, (minus_minus code_code_numeral), (number_number_of code_code_numeral), pls ) 18.60/17.77 ( 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))) ) 18.60/17.77 ( (fun int bool), bool, (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), (collect int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_2 _let_0 (hAPP (fun _let_0 bool) (fun _let_2 _let_0) (combb _let_0 bool int) (fEx int)) (hAPP _let_1 _let_2 (hAPP _let_4 (fun _let_1 _let_2) (combc int _let_1 _let_0) (hAPP _let_2 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_2 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))) ) 18.60/17.77 ( (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)) ) 18.60/17.77 ( (fun int bool), (fun real (fun int bool)), (fun real (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_1 _let_0))) (hAPP _let_2 (fun (fun real _let_1) (fun real _let_0)) (combb _let_1 _let_0 real) (hAPP (fun _let_0 bool) _let_2 (combb _let_0 bool int) (fEx int)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (fun (fun int bool) (fun int bool)))) (let ((_let_6 (fun (fun int bool) _let_4))) (let ((_let_7 (fun real _let_0))) (let ((_let_8 (fun int _let_5))) (let ((_let_9 (fun int real))) (let ((_let_10 (fun real (fun int (fun int bool))))) (let ((_let_11 (fun (fun int bool) (fun int (fun int bool))))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun real _let_8))) (let ((_let_14 (fun int _let_4))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun _let_14 _let_8))) (let ((_let_17 (fun (fun int (fun int bool)) _let_14))) (let ((_let_18 (fun int _let_9))) (let ((_let_19 (fun _let_18 (fun int (fun int bool))))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_9 (fun int bool)))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun _let_9 _let_9))) (let ((_let_24 (fun int _let_23))) (let ((_let_25 (fun int _let_1))) (hAPP _let_12 (fun (fun int bool) _let_10) (combc real (fun int bool) (fun int (fun int bool))) (hAPP _let_13 _let_12 (hAPP (fun _let_8 _let_11) (fun _let_13 _let_12) (combb _let_8 _let_11 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_15 _let_13 (hAPP _let_16 (fun _let_15 _let_13) (combb _let_14 _let_8 real) (hAPP (fun _let_4 _let_5) _let_16 (combb _let_4 _let_5 int) (combs int bool bool))) (hAPP _let_10 _let_15 (hAPP _let_17 (fun _let_10 _let_15) (combb (fun int (fun int bool)) _let_14 real) (hAPP _let_6 _let_17 (combb (fun int bool) _let_4 int) (hAPP (fun bool _let_3) _let_6 (combb bool _let_3 int) fconj))) (hAPP _let_18 _let_10 (hAPP _let_20 (fun _let_18 _let_10) (combc real _let_18 (fun int (fun int bool))) (hAPP _let_22 _let_20 (hAPP (fun _let_21 _let_19) (fun _let_22 _let_20) (combb _let_21 _let_19 real) (combb _let_9 (fun int bool) int)) (hAPP _let_7 _let_22 (hAPP (fun _let_0 _let_21) (fun _let_7 _let_22) (combb _let_0 _let_21 real) (combb real bool int)) (fequal real)))) (hAPP _let_9 _let_18 (hAPP _let_24 (fun _let_9 _let_18) (combc int _let_9 _let_9) (hAPP _let_25 _let_24 (hAPP (fun _let_1 _let_23) (fun _let_25 _let_24) (combb _let_1 _let_23 int) (combb real real int)) (hAPP _let_9 _let_25 (hAPP (fun real _let_1) (fun _let_9 _let_25) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))))))))))))))))))), (let ((_let_0 (fun int (fun int bool)))) (hAPP (fun int bool) (fun int bool) (hAPP (fun bool bool) (fun (fun int bool) (fun int bool)) (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))) ) 18.60/17.77 ( (fun int bool), (fun real (fun int (fun int bool))), (fun int bool), (let ((_let_0 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(fequal real)))) (hAPP _let_9 _let_18 (hAPP _let_24 (fun _let_9 _let_18) (combc int _let_9 _let_9) (hAPP _let_25 _let_24 (hAPP (fun _let_1 _let_23) (fun _let_25 _let_24) (combb _let_1 _let_23 int) (combb real real int)) (hAPP _let_9 _let_25 (hAPP (fun real _let_1) (fun _let_9 _let_25) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))))))))))))))))))), (let ((_let_0 (fun int bool))) (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool int) fNot)), (let ((_let_0 (fun int (fun int bool)))) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))) ) 18.60/17.77 ( (fun real bool), real, (fun real bool), (the real), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_2 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 real) fconj) (hAPP real _let_0 (ord_less_eq real) (zero_zero 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cos)))), sin ) 18.60/17.77 ( (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 ) 18.60/17.77 ( (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 ) 18.60/17.77 ( complex, real, complex, im, cnj, (zero_zero complex) ) 18.60/17.77 ( complex, real, complex, re, cnj, (zero_zero complex) ) 18.60/17.77 ( complex, complex, complex, cnj, cnj, (zero_zero complex) ) 18.60/17.77 ( complex, complex, complex, expi, cnj, (zero_zero complex) ) 18.60/17.77 ( complex, complex, complex, expi, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex 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((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real))))) ) 18.60/17.77 ( (fun nat real), (fun real (fun (filter nat) bool)), (fun nat real), (tendsto nat real), (let ((_let_0 (fun nat real))) (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real))), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) ) 18.60/17.78 ( (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) 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_let_7 _let_8 (combs _let_3 bool bool) _let_17)) (hAPP _let_18 _let_5 (hAPP _let_19 (fun _let_18 _let_5) (combs _let_3 _let_6 (fun _let_3 bool)) (hAPP _let_20 _let_19 (hAPP (fun _let_10 _let_9) (fun _let_20 _let_19) (combb _let_10 _let_9 _let_3) (combs _let_3 int bool)) (hAPP _let_18 _let_20 (hAPP _let_11 (fun _let_18 _let_20) (combb _let_6 _let_10 _let_3) _let_12) (hAPP _let_6 _let_18 (hAPP _let_21 _let_22 (combc _let_3 _let_6 _let_6) (hAPP _let_13 _let_21 (hAPP (fun _let_1 _let_14) (fun _let_13 _let_21) (combb _let_1 _let_14 _let_3) (combb int int _let_3)) _let_23)) _let_4)))) (hAPP _let_6 _let_18 (hAPP _let_24 _let_22 (combb int _let_6 _let_3) (hAPP _let_13 _let_24 (combc _let_3 int int) _let_23)) _let_4))))))))))))))))))))))))))))), ratrel ) 18.74/17.83 ) 18.74/17.83 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) A_2) B_1)) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 A_2) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 B_1) zEven))) )))) 18.74/17.83 ( (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) ) 18.74/17.83 ( (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) ) 18.74/17.83 ) 18.74/17.83 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_133103 $$unsorted)) (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_133103))) (= _let_0 (ti X_a BOUND_VARIABLE_133103))) )) 18.74/17.83 ( bool, fFalse ) 18.74/17.83 ( bool, fTrue ) 18.74/17.83 ( real, pi ) 18.74/17.83 ( (fun nat bool), (even_odd_even nat) ) 18.74/17.83 ( (fun nat bool), prime ) 18.74/17.83 ( (fun nat nat), suc ) 18.74/17.83 ( (fun nat nat), (fact_fact nat) ) 18.74/17.83 ( (fun nat nat), (size_size nat) ) 18.74/17.83 ( (fun nat nat), fact ) 18.74/17.83 ( (fun nat nat), nat_size ) 18.74/17.83 ( int, pls ) 18.74/17.83 ( int, m ) 18.74/17.83 ( int, min_1 ) 18.74/17.83 ( int, s ) 18.74/17.83 ( int, s1 ) 18.74/17.83 ( int, t ) 18.74/17.83 ( (fun int bool), zprime ) 18.74/17.83 ( (fun int bool), nat_neg ) 18.74/17.83 ( (fun int bool), zEven ) 18.74/17.83 ( (fun int bool), nat_is_nat ) 18.74/17.83 ( (fun int bool), zOdd ) 18.74/17.83 ( (fun int bool), (even_odd_even int) ) 18.74/17.83 ( (fun int bool), twoSqu1091635170sum2sq ) 18.74/17.83 ( (fun int nat), nat_1 ) 18.74/17.83 ( (fun int nat), phi ) 18.74/17.83 ( (fun real real), sqrt ) 18.74/17.83 ( (fun real real), tan ) 18.74/17.83 ( (fun real real), cos ) 18.74/17.83 ( (fun real real), arccos ) 18.74/17.83 ( (fun real real), ln ) 18.74/17.83 ( (fun real real), sin ) 18.74/17.83 ( (fun real real), arctan ) 18.74/17.83 ( (fun real real), arcsin ) 18.74/17.83 ( complex, ii ) 18.74/17.83 ( (fun complex complex), cnj ) 18.74/17.83 ( (fun complex complex), expi ) 18.74/17.83 ( (fun nat real), (real_1 nat) ) 18.74/17.83 ( (fun nat real), cos_coeff ) 18.74/17.83 ( (fun nat real), sin_coeff ) 18.74/17.83 ( (fun int int), bit0 ) 18.74/17.83 ( (fun int int), bit1 ) 18.74/17.83 ( (fun int int), pred ) 18.74/17.83 ( (fun int int), succ ) 18.74/17.83 ( (fun int int), (fact_fact int) ) 18.74/17.83 ( (fun int int), zfact ) 18.74/17.83 ( (fun bool bool), fNot ) 18.74/17.83 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 18.74/17.83 ( (fun bool (fun bool bool)), fconj ) 18.74/17.83 ( (fun bool (fun bool bool)), fdisj ) 18.74/17.83 ( (fun bool (fun bool bool)), fimplies ) 18.74/17.83 ( (fun int (fun int bool)), sRStar ) 18.74/17.83 ( (fun int (fun int bool)), quadRes ) 18.74/17.83 ( (fun int (fun int bool)), norRRset ) 18.74/17.83 ( (fun int (fun int bool)), d22set ) 18.74/17.83 ( (fun int (fun int bool)), sr ) 18.74/17.83 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 18.74/17.83 ( (fun nat (fun nat nat)), nat_gcd ) 18.74/17.83 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 18.74/17.83 ( (fun nat (fun nat nat)), nat_lcm ) 18.74/17.83 ( (fun nat (fun real real)), root ) 18.74/17.83 ( (fun real (fun real real)), log ) 18.74/17.83 ( (fun real (fun real real)), powr ) 18.74/17.83 ( (fun nat (fun nat bool)), coprime ) 18.74/17.83 ( (fun (fun int bool) int), (the int) ) 18.74/17.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 18.74/17.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 18.74/17.83 ( (fun nat (fun nat (product_prod int int))), bezw ) 18.74/17.83 ( (fun (fun int bool) bool), nat_nat_set ) 18.74/17.83 ( (filter nat), sequentially ) 18.74/17.83 ( (fun (product_prod nat nat) bool), pred_nat ) 18.74/17.83 ( (fun (product_prod int int) bool), frac_1 ) 18.74/17.83 ( (fun real complex), cis ) 18.74/17.83 ( (fun complex real), im ) 18.74/17.83 ( (fun complex real), re ) 18.74/17.83 ( (fun complex real), arg ) 18.74/17.83 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 18.74/17.83 ( (fun int (fun int int)), int_gcd ) 18.74/17.83 ( (fun int (fun int int)), multInv ) 18.74/17.83 ( (fun int (fun int int)), legacy_zgcd ) 18.74/17.83 ( (fun int (fun int int)), z3mod ) 18.74/17.83 ( (fun int (fun int int)), inv ) 18.74/17.83 ( (fun int (fun int int)), (gcd_gcd int) ) 18.74/17.83 ( (fun int (fun int int)), standardRes ) 18.74/17.83 ( (fun int (fun int int)), legendre ) 18.74/17.83 ( (fun int (fun int int)), nat_tsub ) 18.74/17.83 ( (fun int (fun int int)), z3div ) 18.74/17.83 ( (fun int (fun int int)), int_lcm ) 18.74/17.83 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 18.74/17.83 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 18.74/17.83 ( (fun int (fun (fun int bool) bool)), rsetR ) 18.74/17.83 ( (fun int (fun (fun int bool) bool)), resSet ) 18.74/17.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 18.74/17.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 18.74/17.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 18.74/17.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 18.74/17.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 18.74/17.83 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 18.74/17.83 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 18.74/17.83 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 18.74/17.83 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 18.74/17.83 ( (fun int (fun int (product_prod int int))), negDivAlg ) 18.74/17.83 ( (fun int (fun int (product_prod int int))), divmod_int ) 18.74/17.83 ( (fun int (fun int (product_prod int int))), posDivAlg ) 18.74/17.83 ( (fun int (fun int (product_prod int int))), pdivmod ) 18.74/17.83 ( (fun int (fun int (product_prod int int))), norm_frac ) 18.74/17.83 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 18.74/17.83 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 18.74/17.83 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 18.74/17.83 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 18.74/17.83 ( (fun real nat), natfloor ) 18.74/17.83 ( (fun real nat), natceiling ) 18.74/17.83 ( (fun int quickcheck_code_int), quickcheck_of_int ) 18.74/17.83 ( (fun int (fun int (fun int bool))), wset ) 18.74/17.83 ( (fun int (fun int (fun int bool))), bnorRset ) 18.74/17.83 ( (fun int (fun int (fun int bool))), zcong ) 18.74/17.83 ( (fun int (fun int (fun int bool))), noXRRset ) 18.74/17.83 ( (fun int (fun int (fun int bool))), zcongm ) 18.74/17.83 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 18.74/17.83 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 18.74/17.83 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 18.74/17.83 ( (fun int real), (real_1 int) ) 18.74/17.83 ( (fun complex nat), (size_size complex) ) 18.74/17.83 ( (fun complex nat), complex_size ) 18.74/17.83 ( (fun int (list int)), quickc666637781d_zero ) 18.74/17.83 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 18.74/17.83 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 18.74/17.83 ( (fun (product_prod int int) rat), frct ) 18.74/17.83 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 18.74/17.83 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 18.74/17.83 ( (fun (fun nat rat) bool), vanishes ) 18.74/17.83 ( (fun int (fun int rat)), fract ) 18.74/17.83 ( (fun code_code_numeral int), code_int_of ) 18.74/17.83 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 18.74/17.83 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 18.74/17.83 ( (fun code_code_numeral nat), code_c271388182l_size ) 18.74/17.83 ( (fun real (fun real complex)), complex_1 ) 18.74/17.83 ( (fun real (fun real complex)), rcis ) 18.74/17.83 ( (fun int (fun nat nat)), nat_aux ) 18.74/17.83 ( (fun rat real), ratreal ) 18.74/17.83 ( (fun quickcheck_code_int int), quickcheck_int_of ) 18.74/17.83 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 18.74/17.83 ( (fun rat (product_prod int int)), quotient_of ) 18.74/17.83 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 18.74/17.83 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 18.74/17.83 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 18.74/17.83 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 18.74/17.83 ) 18.74/17.83 (instantiation (forall ((N_1 $$unsorted)) (= (= (zero_zero int) (hAPP nat int (semiring_1_of_nat int) N_1)) (= (zero_zero nat) N_1)) ) 18.74/17.83 ( (zero_zero nat) ) 18.74/17.83 ( (hAPP nat nat suc (zero_zero nat)) ) 18.74/17.83 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.83 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.74/17.83 ) 18.74/17.83 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_133139 $$unsorted) (BOUND_VARIABLE_133140 $$unsorted)) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_133139) BOUND_VARIABLE_133140))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_133139) BOUND_VARIABLE_133140))) )) 18.74/17.83 ( real, (zero_zero real), pi ) 18.74/17.83 ( 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)))) ) 18.74/17.83 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.74/17.83 ( real, (zero_zero real), skv_2 ) 18.74/17.83 ( real, (zero_zero real), skv_6 ) 18.74/17.83 ( real, (zero_zero real), skv_10 ) 18.74/17.83 ( real, (zero_zero real), skv_11 ) 18.74/17.83 ( real, (zero_zero real), skv_12 ) 18.74/17.83 ( real, (zero_zero real), skv_13 ) 18.74/17.83 ( real, (zero_zero real), skv_14 ) 18.74/17.83 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.74/17.83 ( real, pi, (zero_zero real) ) 18.74/17.83 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.74/17.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.74/17.84 ( 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))) ) 18.74/17.84 ( 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) ) 18.74/17.84 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.74/17.84 ( 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 ) 18.74/17.84 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.84 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.84 ( int, (zero_zero int), (zero_zero int) ) 18.74/17.84 ( int, (zero_zero int), (one_one int) ) 18.74/17.84 ( 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))) ) 18.74/17.84 ( int, (zero_zero int), min_1 ) 18.74/17.84 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.84 ( int, (zero_zero int), s ) 18.74/17.84 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 18.74/17.84 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.74/17.84 ( int, (zero_zero int), skv_3 ) 18.74/17.84 ( int, (zero_zero int), skv_9 ) 18.74/17.84 ( int, (one_one int), t ) 18.74/17.84 ( int, min_1, (zero_zero int) ) 18.74/17.84 ( int, min_1, pls ) 18.74/17.84 ( int, min_1, min_1 ) 18.74/17.84 ( 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))) ) 18.74/17.84 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 18.74/17.84 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 18.74/17.84 ( int, t, (zero_zero int) ) 18.74/17.84 ( int, t, (one_one int) ) 18.74/17.84 ( 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))) ) 18.74/17.84 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.74/17.84 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.74/17.84 ) 18.74/17.84 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (forall ((Y $$unsorted) (X $$unsorted)) (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)))) ))) 18.74/17.84 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.84 ( 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))))) ) 18.74/17.84 ( (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.84 ( (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)))) ) 18.74/17.84 ) 18.74/17.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133179 $$unsorted) (BOUND_VARIABLE_133180 $$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_133179) BOUND_VARIABLE_133180))) (= (ti X_a BOUND_VARIABLE_133180) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_max X_a) BOUND_VARIABLE_133180) BOUND_VARIABLE_133179))) ) 18.74/17.84 ( real, (zero_zero real), pi ) 18.74/17.84 ( 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)))) ) 18.74/17.84 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.74/17.84 ( real, (zero_zero real), skv_6 ) 18.74/17.84 ( real, (zero_zero real), skv_11 ) 18.74/17.84 ( real, (zero_zero real), skv_12 ) 18.74/17.84 ( real, (zero_zero real), skv_14 ) 18.74/17.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.74/17.84 ( 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))) ) 18.74/17.84 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.74/17.84 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.84 ( int, (zero_zero int), (one_one int) ) 18.74/17.84 ( int, (zero_zero int), min_1 ) 18.74/17.84 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.84 ( int, (zero_zero int), s ) 18.74/17.84 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 18.74/17.84 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.74/17.84 ( int, (zero_zero int), skv_3 ) 18.74/17.84 ( int, (zero_zero int), skv_9 ) 18.74/17.84 ( int, (one_one int), t ) 18.74/17.84 ( int, min_1, pls ) 18.74/17.84 ( int, min_1, min_1 ) 18.74/17.84 ) 18.74/17.84 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Z_1) W))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 W) Z_1))) (= (ti int W) (ti int Z_1))) ))) 18.74/17.84 ( (zero_zero int), (one_one int) ) 18.74/17.84 ( (zero_zero int), min_1 ) 18.74/17.84 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.84 ( (zero_zero int), s ) 18.74/17.84 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 18.74/17.84 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.74/17.84 ( (zero_zero int), skv_3 ) 18.74/17.84 ( (zero_zero int), skv_9 ) 18.74/17.84 ( pls, min_1 ) 18.74/17.84 ( (one_one int), (zero_zero int) ) 18.74/17.84 ( (one_one int), t ) 18.74/17.84 ( min_1, (zero_zero int) ) 18.74/17.84 ( min_1, pls ) 18.74/17.84 ( min_1, min_1 ) 18.74/17.84 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 18.74/17.84 ( s, (zero_zero int) ) 18.74/17.84 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 18.74/17.84 ( t, (one_one int) ) 18.74/17.84 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 18.74/17.84 ( skv_3, (zero_zero int) ) 18.74/17.84 ( skv_9, (zero_zero int) ) 18.74/17.84 ) 18.74/17.84 (instantiation (let ((_let_0 (times_times X_a))) (forall ((X_a $$unsorted)) (or (not (mult_zero X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0))) )) 18.74/17.84 ( bool ) 18.74/17.84 ( real ) 18.74/17.84 ( nat ) 18.74/17.84 ( (fun nat bool) ) 18.74/17.84 ( int ) 18.74/17.84 ( (fun int bool) ) 18.74/17.84 ( (fun real bool) ) 18.74/17.84 ( (fun real real) ) 18.74/17.84 ( complex ) 18.74/17.84 ( (fun nat real) ) 18.74/17.84 ( (fun int int) ) 18.74/17.84 ( rat ) 18.74/17.84 ( (fun int (fun int bool)) ) 18.74/17.84 ( quickcheck_code_int ) 18.74/17.84 ( (product_prod int int) ) 18.74/17.84 ( (fun (product_prod int int) bool) ) 18.74/17.84 ( code_code_numeral ) 18.74/17.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 18.74/17.84 ( (fun (product_prod int int) int) ) 18.74/17.84 ( (fun int (fun int (fun int bool))) ) 18.74/17.84 ( (fun int real) ) 18.74/17.84 ) 18.74/17.84 (instantiation (let ((_let_0 (complete_Sup_Sup X_a))) (forall ((X_a $$unsorted)) (or (not (comple44059174attice X_a)) (= _let_0 (ti (fun (fun X_a bool) X_a) _let_0))) )) 18.74/17.84 ( bool ) 18.74/17.84 ( real ) 18.74/17.84 ( nat ) 18.74/17.84 ( (fun nat bool) ) 18.74/17.84 ( int ) 18.74/17.84 ( (fun int bool) ) 18.74/17.84 ( (product_prod real real) ) 18.74/17.84 ( (product_prod int int) ) 18.74/17.84 ( (filter real) ) 18.74/17.84 ( (filter nat) ) 18.74/17.84 ( (product_prod nat nat) ) 18.74/17.84 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 18.74/17.84 ( (fun nat rat) ) 18.74/17.84 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 18.74/17.84 ) 18.74/17.84 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (and (= (zero_zero real) B_1) (= (one_one real) A_2)) (= (one_one complex) (hAPP real complex (hAPP real (fun real complex) complex_1 A_2) B_1))) ) 18.74/17.84 ( (zero_zero real), (zero_zero real) ) 18.74/17.84 ( (zero_zero real), (one_one real) ) 18.74/17.84 ( (one_one real), (zero_zero real) ) 18.74/17.84 ) 18.74/17.84 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (times_times real))) (let ((_let_4 (norm_norm X_a))) (forall ((X_a $$unsorted)) (or (not (real_normed_algebra X_a)) (not (forall ((K_2 $$unsorted)) (or (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real _let_4 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) A_4) B_4))) (hAPP real real (hAPP real _let_2 _let_3 (hAPP real real (hAPP real _let_2 _let_3 (hAPP X_a real _let_4 A_4)) (hAPP X_a real _let_4 B_4))) K_2))) )) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) K_2)))) ))) )))))) 18.74/17.84 ( real ) 18.74/17.84 ( complex ) 18.74/17.84 ) 18.74/17.84 (instantiation (let ((_let_0 (of_real X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_133345 $$unsorted)) (or (not (real_normed_vector X_a)) (not (real_algebra_1 X_a)) (= (hAPP X_a X_a (uminus_uminus X_a) (hAPP real X_a _let_0 BOUND_VARIABLE_133345)) (hAPP real X_a _let_0 (hAPP real real (uminus_uminus real) BOUND_VARIABLE_133345)))) )) 18.74/17.84 ( complex, (one_one real) ) 18.74/17.84 ) 18.74/17.84 (instantiation (let ((_let_0 (one_one int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (hAPP int int (number_number_of int) W))) (forall ((W $$unsorted)) (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_fst 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_div int) _let_0) _let_2))) )))) 18.74/17.84 ( pls ) 18.74/17.84 ( (hAPP int int bit1 pls) ) 18.74/17.84 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.74/17.84 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.84 ( min_1 ) 18.74/17.84 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.74/17.84 ) 18.74/17.84 (instantiation (forall ((L $$unsorted)) (= (= pls (ti int L)) (= pls (hAPP int int bit0 L))) ) 18.74/17.84 ( pls ) 18.74/17.84 ( (hAPP int int bit1 pls) ) 18.74/17.84 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.74/17.84 ( m ) 18.74/17.84 ( min_1 ) 18.74/17.84 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.74/17.84 ( s ) 18.74/17.84 ( s1 ) 18.74/17.84 ( t ) 18.74/17.84 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.74/17.84 ) 18.74/17.84 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (fun real complex))) (let ((_let_3 (hAPP real _let_0 _let_1 A_1))) (let ((_let_4 (hAPP real _let_0 _let_1 B))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP real complex (hAPP real _let_2 complex_1 A_1) B)) (hAPP real complex (hAPP real _let_2 complex_1 C) D)) (hAPP real complex (hAPP real _let_2 complex_1 (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real _let_3 C)) (hAPP real real _let_4 D))) (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP real real _let_3 D)) (hAPP real real _let_4 C)))) )))))) 18.74/17.84 ( (zero_zero real), (one_one real), (zero_zero real), (one_one real) ) 18.74/17.84 ) 18.74/17.84 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less int) (zero_zero int)))) (forall ((B $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_0 A_1))) (not (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) A_1) B)))) (hBOOL (hAPP int bool _let_0 B))) )) 18.74/17.84 ( (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.74/17.84 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.74/17.84 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.74/17.84 ( skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.74/17.84 ) 18.74/17.84 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (product_prod nat nat))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun nat _let_2))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (or (= (zero_zero nat) N_1) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Ma) N_1)) (= (hAPP _let_1 _let_1 (hAPP _let_3 (fun _let_1 _let_1) (product_prod_case nat nat _let_1) (hAPP _let_0 _let_3 (hAPP _let_3 (fun _let_0 _let_3) (combb nat _let_2 nat) (product_Pair nat nat)) suc)) (hAPP nat _let_1 (hAPP nat _let_2 divmod_nat (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) Ma) N_1)) N_1)) (hAPP nat _let_1 (hAPP nat _let_2 divmod_nat Ma) N_1))) ))))) 18.74/17.84 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.84 ) 18.74/17.84 (instantiation (let ((_let_0 (zero_zero nat))) (let ((_let_1 (product_prod nat nat))) (let ((_let_2 (fun nat _let_1))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (or (and (not (= _let_0 N_1)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Ma) N_1)))) (= (hAPP nat _let_1 (hAPP nat _let_2 divmod_nat Ma) N_1) (hAPP nat _let_1 (hAPP nat _let_2 (product_Pair nat nat) _let_0) Ma))) )))) 18.74/17.84 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.84 ) 18.74/17.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133801 $$unsorted) (BOUND_VARIABLE_133802 $$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_133801) BOUND_VARIABLE_133802))) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (div_mod X_a) BOUND_VARIABLE_133802) BOUND_VARIABLE_133801))) ) 18.74/17.84 ( 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) (hAPP nat int (hAPP 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)) ) 18.74/17.85 ) 18.74/17.85 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (hAPP real _let_0 _let_1 Z1))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (= (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))) )))) 18.74/17.85 ( (hAPP int real (number_number_of real) (hAPP 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.74/17.85 ( (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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.74/17.85 ) 18.74/17.85 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_133840))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_133839 $$unsorted) (BOUND_VARIABLE_133840 $$unsorted) (BOUND_VARIABLE_133841 $$unsorted)) (or (not (ord X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_133841))) (not (= (ti X_a BOUND_VARIABLE_133839) (ti X_a BOUND_VARIABLE_133841))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_133839))) )) 18.74/17.85 ( real, pi, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.85 ( int, pls, (zero_zero int), (zero_zero int) ) 18.74/17.85 ( int, m, (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.74/17.85 ( int, min_1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 18.74/17.85 ( int, s, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.74/17.85 ( int, s1, t, (zero_zero int) ) 18.74/17.85 ( int, t, (zero_zero int), (one_one int) ) 18.74/17.85 ) 18.74/17.85 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)))) (forall ((X $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (not (hBOOL (hAPP real bool _let_0 X))) (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root N) X)))) )) 18.74/17.85 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.85 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.85 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.85 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.85 ) 18.74/17.85 (instantiation (let ((_let_0 (one_one int))) (let ((_let_1 (abs_abs int))) (forall ((M $$unsorted) (N $$unsorted)) (or (not (= _let_0 (hAPP int int _let_1 (hAPP int int (hAPP int (fun int int) (times_times int) M) N)))) (= _let_0 (hAPP int int _let_1 M))) ))) 18.74/17.85 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 18.74/17.85 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 18.74/17.85 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 18.74/17.85 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1 ) 18.74/17.85 ) 18.74/17.85 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP real complex cis (hAPP real real (uminus_uminus real) A_1)) (hAPP complex complex (inverse_inverse complex) (hAPP real complex cis A_1))) ) 18.74/17.85 ( (one_one real) ) 18.74/17.85 ( (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)))) ) 18.74/17.85 ( (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) ) 18.74/17.85 ) 18.74/17.85 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (zero_zero int))) (forall ((Z $$unsorted) (W_1 $$unsorted)) (or (and (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) Z))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_2) W_1)))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 W_1) Z)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP int nat nat_1 W_1)) (hAPP int nat nat_1 Z))))) )))) 18.74/17.85 ( pls, min_1 ) 18.74/17.85 ( (one_one int), (zero_zero int) ) 18.74/17.85 ( min_1, (zero_zero int) ) 18.74/17.85 ( min_1, min_1 ) 18.74/17.85 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 18.74/17.85 ( s, (zero_zero int) ) 18.74/17.85 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 18.74/17.85 ( t, (one_one int) ) 18.74/17.85 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 18.74/17.85 ( skv_3, (zero_zero int) ) 18.74/17.85 ( skv_9, (zero_zero int) ) 18.74/17.85 ) 18.74/17.85 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted)) (or (not (zero X_a)) (= _let_0 (ti X_a _let_0))) )) 18.74/17.85 ( real ) 18.74/17.85 ( nat ) 18.74/17.85 ( int ) 18.74/17.85 ( complex ) 18.74/17.85 ( rat ) 18.74/17.85 ( quickcheck_code_int ) 18.74/17.85 ( code_code_numeral ) 18.74/17.85 ) 18.74/17.85 (instantiation (let ((_let_0 (fun nat (fun nat bool)))) (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hAPP nat nat suc X_1) (hAPP _let_0 nat (finite_card nat) (hAPP _let_0 _let_0 (collect nat) (hAPP nat _let_0 (hAPP _let_0 _let_0 (combc nat nat bool) (ord_less_eq nat)) X_1))))) )) 18.74/17.85 ( (zero_zero nat) ) 18.74/17.85 ( (hAPP nat nat suc (zero_zero nat)) ) 18.74/17.85 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 18.74/17.85 ) 18.74/17.85 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (one_one real))) (let ((_let_3 (combc nat nat nat))) (let ((_let_4 (fun nat _let_0))) (let ((_let_5 (fun _let_1 _let_1))) (let ((_let_6 (fun (fun nat nat) _let_1))) (let ((_let_7 (combb nat real nat))) (let ((_let_8 (fun (filter nat) bool))) (let ((_let_9 (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) _let_3 (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_3 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) X_1)) _let_2))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_8 (hAPP _let_1 (fun real _let_8) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP _let_4 _let_5 (combs nat real real) (hAPP _let_1 _let_4 (hAPP (fun real _let_0) (fun _let_1 _let_4) (combb real _let_0 nat) (times_times real)) (hAPP _let_1 _let_1 (hAPP _let_0 _let_5 (combb real real nat) (hAPP real _let_0 (inverse_divide real) _let_2)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_6 _let_7 (real_1 nat)) _let_9)))) (hAPP _let_0 _let_1 (hAPP _let_1 _let_6 _let_7 (hAPP real _let_1 (power_power real) X_1)) _let_9))) (zero_zero real)) sequentially)))) ))))))))))) 18.74/17.85 ( (hAPP int real (number_number_of real) min_1) ) 18.74/17.85 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.74/17.85 ) 18.74/17.85 (instantiation (let ((_let_0 (fequal X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0)) )) 18.74/17.85 ( bool ) 18.74/17.85 ( real ) 18.74/17.85 ( nat ) 18.74/17.85 ( (fun nat bool) ) 18.74/17.85 ( int ) 18.74/17.85 ( (fun int bool) ) 18.74/17.85 ( (product_prod real real) ) 18.74/17.85 ( (product_prod int int) ) 18.74/17.85 ( (filter real) ) 18.74/17.85 ( (filter nat) ) 18.74/17.85 ( (product_prod nat nat) ) 18.74/17.85 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 18.74/17.85 ( (fun nat rat) ) 18.74/17.85 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 18.74/17.85 ) 18.74/17.85 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_133995 $$unsorted) (BOUND_VARIABLE_133996 $$unsorted)) (or (not (real_normed_algebra X_a)) (not (hBOOL (hAPP _let_0 bool _let_1 BOUND_VARIABLE_133996))) (hBOOL (hAPP _let_0 bool _let_1 (hAPP X_a _let_0 (hAPP _let_3 (fun X_a _let_0) (combc nat X_a X_a) (hAPP _let_0 _let_3 (hAPP (fun X_a _let_2) (fun _let_0 _let_3) (combb X_a _let_2 nat) (times_times X_a)) BOUND_VARIABLE_133996)) BOUND_VARIABLE_133995)))) ))))) 18.74/17.85 ( real, (one_one real), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) ) 18.74/17.85 ) 18.74/17.85 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_1) zEven))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Y_1) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) X_1) Y_1)) zOdd))) )))) 18.74/17.85 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.74/17.85 ) 18.74/17.85 (instantiation (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (plus_plus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_134059 $$unsorted) (BOUND_VARIABLE_134060 $$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 _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_134059) BOUND_VARIABLE_134060))) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_134059)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_134060))))) )))) 18.74/17.85 ( nat, (one_one nat), (one_one nat) ) 18.74/17.85 ( 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) ) 18.74/17.85 ( 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) ) 18.74/17.85 ) 18.74/17.85 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((P_1 $$unsorted) (I $$unsorted) (K $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 I) K))) (not (hBOOL (hAPP int bool P_1 K))) (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 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))) ))) 18.74/17.85 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), s ) 18.74/17.85 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.74/17.85 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), skv_3 ) 18.74/17.85 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), skv_9 ) 18.74/17.85 ( zprime, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.85 ( (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (zero_zero int), (one_one int) ) 18.74/17.85 ( nat_neg, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 18.74/17.85 ( (hAPP int (fun int bool) (ord_less_eq int) pls), (zero_zero int), min_1 ) 18.74/17.85 ( (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))), min_1, pls ) 18.74/17.85 ( (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1, min_1 ) 18.74/17.85 ( (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), (one_one int), t ) 18.74/17.85 ) 18.74/17.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134106 $$unsorted) (BOUND_VARIABLE_134107 $$unsorted)) (or (not (semiring_div X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_134106) BOUND_VARIABLE_134107)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (div_mod X_a) BOUND_VARIABLE_134107) BOUND_VARIABLE_134106)))) ) 18.74/17.85 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 18.74/17.85 ) 18.74/17.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134129 $$unsorted) (BOUND_VARIABLE_134130 $$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_134129) BOUND_VARIABLE_134130))) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_max X_a) BOUND_VARIABLE_134129) BOUND_VARIABLE_134130) (ti X_a BOUND_VARIABLE_134130))) ) 18.74/17.86 ( real, (zero_zero real), pi ) 18.74/17.86 ( 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)))) ) 18.74/17.86 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.74/17.86 ( real, (zero_zero real), skv_6 ) 18.74/17.86 ( real, (zero_zero real), skv_11 ) 18.74/17.86 ( real, (zero_zero real), skv_12 ) 18.74/17.86 ( real, (zero_zero real), skv_14 ) 18.74/17.86 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.74/17.86 ( 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))) ) 18.74/17.86 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.74/17.86 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.86 ( int, (zero_zero int), (one_one int) ) 18.74/17.86 ( int, (zero_zero int), min_1 ) 18.74/17.86 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.86 ( int, (zero_zero int), s ) 18.74/17.86 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 18.74/17.86 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.74/17.86 ( int, (zero_zero int), skv_3 ) 18.74/17.86 ( int, (zero_zero int), skv_9 ) 18.74/17.86 ( int, (one_one int), t ) 18.74/17.86 ( int, min_1, pls ) 18.74/17.86 ( int, min_1, min_1 ) 18.74/17.86 ) 18.74/17.86 (instantiation (let ((_let_0 (fun nat real))) (let ((_let_1 (fun (filter nat) bool))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (one_one real)) X_1))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (tendsto nat real) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP real _let_0 (power_power real) X_1))) (zero_zero real)) sequentially))) ))) 18.74/17.86 ( (hAPP int real (number_number_of real) min_1) ) 18.74/17.86 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.74/17.86 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.74/17.86 ) 18.74/17.86 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less_eq X_b))) (let ((_let_2 (number_number_of X_b))) (let ((_let_3 (fun X_b X_b))) (let ((_let_4 (ord_max X_b))) (let ((_let_5 (hAPP int X_b _let_2 BOUND_VARIABLE_134255))) (let ((_let_6 (hAPP int X_b _let_2 BOUND_VARIABLE_134256))) (let ((_let_7 (hAPP int X_b _let_2 BOUND_VARIABLE_134267))) (let ((_let_8 (hAPP int X_b _let_2 BOUND_VARIABLE_134268))) (forall ((X_b $$unsorted) (BOUND_VARIABLE_134255 $$unsorted) (BOUND_VARIABLE_134256 $$unsorted) (BOUND_VARIABLE_134267 $$unsorted) (BOUND_VARIABLE_134268 $$unsorted)) (or (not (number X_b)) (not (ord X_b)) (and (or (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 _let_5) _let_6))) (= _let_6 (hAPP X_b X_b (hAPP X_b _let_3 _let_4 _let_5) _let_6))) (or (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 _let_7) _let_8)) (= _let_7 (hAPP X_b X_b (hAPP X_b _let_3 _let_4 _let_7) _let_8))))) )))))))))) 18.74/17.86 ( 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)) ) 18.74/17.86 ( 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))), (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))) ) 18.74/17.86 ( real, min_1, min_1, min_1, min_1 ) 18.74/17.86 ( 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))) ) 18.74/17.86 ( 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)) ) 18.74/17.86 ( 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))) ) 18.74/17.86 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP 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)))))))) ) 18.74/17.86 ( nat, pls, pls, pls, pls ) 18.74/17.86 ( nat, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 18.74/17.86 ( 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)) ) 18.74/17.86 ( 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)) ) 18.74/17.86 ( int, pls, pls, pls, pls ) 18.74/17.86 ( int, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 18.74/17.86 ( 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)) ) 18.74/17.86 ( 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))) ) 18.74/17.86 ( int, min_1, min_1, min_1, min_1 ) 18.74/17.86 ( 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)) ) 18.74/17.86 ( 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)) ) 18.74/17.86 ( complex, min_1, min_1, min_1, min_1 ) 18.74/17.86 ( quickcheck_code_int, (zero_zero int), (zero_zero int), (zero_zero int), (zero_zero int) ) 18.74/17.86 ( quickcheck_code_int, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 18.74/17.86 ( quickcheck_code_int, (one_one int), (one_one int), (one_one int), (one_one int) ) 18.74/17.86 ( code_code_numeral, pls, pls, pls, pls ) 18.74/17.86 ( code_code_numeral, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 18.74/17.86 ) 18.74/17.86 (instantiation (let ((_let_0 (fun nat X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (one_one X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_134291 $$unsorted)) (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_134291)) (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_134291)) (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_134291))))) )))) 18.74/17.86 ( real, (hAPP int real (number_number_of real) min_1) ) 18.74/17.86 ( 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)))) ) 18.74/17.86 ( int, s ) 18.74/17.86 ( int, s1 ) 18.74/17.86 ( int, skv_8 ) 18.74/17.86 ( complex, ii ) 18.74/17.86 ) 18.74/17.86 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (one_one X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_134316 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_134316) BOUND_VARIABLE_134316) (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_134316))) )))) 18.74/17.86 ( nat, (one_one nat) ) 18.74/17.86 ( 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) ) 18.74/17.86 ( 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)))) ) 18.74/17.86 ) 18.74/17.86 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (= Y (hAPP complex real im (hAPP real complex (hAPP real (fun real complex) complex_1 X) Y))) ) 18.74/17.86 ( (zero_zero real), (zero_zero real) ) 18.74/17.86 ( (zero_zero real), (one_one real) ) 18.74/17.86 ( (one_one real), (zero_zero real) ) 18.74/17.86 ) 18.74/17.86 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_134334 $$unsorted) (BOUND_VARIABLE_134335 $$unsorted)) (or (not (linorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_134334) BOUND_VARIABLE_134335))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_134335) BOUND_VARIABLE_134334)))) )) 18.74/17.86 ( real, (zero_zero real), pi ) 18.74/17.86 ( 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)))) ) 18.74/17.86 ( 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))))) ) 18.74/17.86 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.74/17.86 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.74/17.86 ( real, (zero_zero real), skv_6 ) 18.74/17.86 ( real, (zero_zero real), skv_11 ) 18.74/17.86 ( real, (zero_zero real), skv_12 ) 18.74/17.86 ( real, (zero_zero real), skv_14 ) 18.74/17.86 ( real, pi, (zero_zero real) ) 18.74/17.86 ( 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)) ) 18.74/17.86 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.74/17.86 ( 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)))) ) 18.74/17.86 ( 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) ) 18.74/17.86 ( 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))) ) 18.74/17.86 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 18.74/17.86 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.74/17.86 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.74/17.86 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 18.74/17.86 ( real, skv_2, (zero_zero real) ) 18.74/17.86 ( real, skv_10, (zero_zero real) ) 18.74/17.86 ( real, skv_13, (zero_zero real) ) 18.74/17.86 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.86 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 18.74/17.86 ( int, (zero_zero int), (zero_zero int) ) 18.74/17.86 ( int, (zero_zero int), (one_one int) ) 18.74/17.86 ( int, (zero_zero int), min_1 ) 18.74/17.86 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.86 ( int, (zero_zero int), s ) 18.74/17.86 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 18.74/17.86 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 18.74/17.86 ( int, (zero_zero int), t ) 18.74/17.86 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.74/17.86 ( int, (zero_zero int), skv_3 ) 18.74/17.86 ( int, (zero_zero int), skv_9 ) 18.74/17.86 ( int, (one_one int), (zero_zero int) ) 18.74/17.86 ( int, (one_one int), t ) 18.74/17.86 ( 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) ) 18.74/17.86 ( 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 ) 18.74/17.86 ( 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 ) 18.74/17.86 ( 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_3 ) 18.74/17.86 ( 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_9 ) 18.74/17.86 ( int, min_1, (zero_zero int) ) 18.74/17.86 ( int, min_1, pls ) 18.74/17.86 ( int, min_1, min_1 ) 18.74/17.86 ( 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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 18.74/17.86 ) 18.74/17.86 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (forall ((Y $$unsorted)) (= (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))) ))) 18.74/17.86 ( (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)))) ) 18.74/17.86 ) 18.74/17.86 (instantiation (let ((_let_0 (even_odd_even nat))) (let ((_let_1 (hAPP X_a X_a (uminus_uminus X_a) (one_one X_a)))) (let ((_let_2 (hAPP X_a (fun nat X_a) (power_power X_a) _let_1))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_134390 $$unsorted) (BOUND_VARIABLE_134397 $$unsorted)) (or (not (comm_ring_1 X_a)) (and (or (not (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_134390))) (= (one_one X_a) (hAPP nat X_a _let_2 BOUND_VARIABLE_134390))) (or (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_134397)) (= _let_1 (hAPP nat X_a _let_2 BOUND_VARIABLE_134397))))) )))) 18.74/17.86 ( complex, (zero_zero nat), (zero_zero nat) ) 18.74/17.86 ( rat, (one_one nat), (one_one nat) ) 18.74/17.86 ) 18.74/17.86 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((N $$unsorted)) (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)))) ))) 18.74/17.86 ( (zero_zero int) ) 18.74/17.86 ( (one_one int) ) 18.74/17.86 ( min_1 ) 18.74/17.86 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.86 ( s ) 18.74/17.86 ( (hAPP int int (number_number_of int) pls) ) 18.74/17.86 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.74/17.86 ( skv_3 ) 18.74/17.86 ( skv_9 ) 18.74/17.86 ) 18.74/17.86 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_134417 $$unsorted) (BOUND_VARIABLE_134418 $$unsorted)) (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_134417) BOUND_VARIABLE_134418)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_134418) BOUND_VARIABLE_134417))) ))) 18.74/17.86 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.86 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 18.74/17.86 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.74/17.87 ( 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))))))))) ) 18.74/17.87 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.87 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.74/17.87 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 18.74/17.87 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.74/17.87 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 18.74/17.87 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.74/17.87 ( 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))) ) 18.74/17.87 ( 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)))) ) 18.74/17.87 ( 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)))) ) 18.74/17.87 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 18.74/17.87 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 18.74/17.87 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 18.74/17.87 ( 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))) ) 18.74/17.87 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 18.74/17.87 ( 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))) ) 18.74/17.87 ( 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))) ) 18.74/17.87 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 18.74/17.87 ( 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) ) 18.74/17.87 ) 18.74/17.87 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (fact_fact int))) (forall ((M $$unsorted) (K_4 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) K_4))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int _let_2 M)) (hAPP int int _let_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) M) K_4))))) )))) 18.74/17.87 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 18.74/17.87 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 18.74/17.87 ) 18.74/17.87 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134451 $$unsorted)) (or (not (monoid_add X_a)) (= (ti X_a BOUND_VARIABLE_134451) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_134451) (zero_zero X_a)))) ) 18.74/17.87 ( bool, fFalse ) 18.74/17.87 ( bool, fTrue ) 18.74/17.87 ( real, pi ) 18.74/17.87 ( nat, (one_one nat) ) 18.74/17.87 ( (fun nat bool), (even_odd_even nat) ) 18.74/17.87 ( (fun nat bool), prime ) 18.74/17.87 ( (fun nat nat), suc ) 18.74/17.87 ( (fun nat nat), (fact_fact nat) ) 18.74/17.87 ( (fun nat nat), (size_size nat) ) 18.74/17.87 ( (fun nat nat), fact ) 18.74/17.87 ( (fun nat nat), nat_size ) 18.74/17.87 ( int, pls ) 18.74/17.87 ( int, m ) 18.74/17.87 ( 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) ) 18.74/17.87 ( int, min_1 ) 18.74/17.87 ( int, s ) 18.74/17.87 ( 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)))) ) 18.74/17.87 ( int, s1 ) 18.74/17.87 ( int, t ) 18.74/17.87 ( (fun int bool), zprime ) 18.74/17.87 ( (fun int bool), nat_neg ) 18.74/17.87 ( (fun int bool), zEven ) 18.74/17.87 ( (fun int bool), nat_is_nat ) 18.74/17.87 ( (fun int bool), zOdd ) 18.74/17.87 ( (fun int bool), (even_odd_even int) ) 18.74/17.87 ( (fun int bool), twoSqu1091635170sum2sq ) 18.74/17.87 ( (fun int nat), nat_1 ) 18.74/17.87 ( (fun int nat), phi ) 18.74/17.87 ( (fun real real), sqrt ) 18.74/17.87 ( (fun real real), tan ) 18.74/17.87 ( (fun real real), cos ) 18.74/17.87 ( (fun real real), arccos ) 18.74/17.87 ( (fun real real), ln ) 18.74/17.87 ( (fun real real), sin ) 18.74/17.87 ( (fun real real), arctan ) 18.74/17.87 ( (fun real real), arcsin ) 18.74/17.87 ( complex, ii ) 18.74/17.87 ( (fun complex complex), cnj ) 18.74/17.87 ( (fun complex complex), expi ) 18.74/17.87 ( (fun nat real), (real_1 nat) ) 18.74/17.87 ( (fun nat real), cos_coeff ) 18.74/17.87 ( (fun nat real), sin_coeff ) 18.74/17.87 ( (fun int int), bit0 ) 18.74/17.87 ( (fun int int), bit1 ) 18.74/17.87 ( (fun int int), pred ) 18.74/17.87 ( (fun int int), succ ) 18.74/17.87 ( (fun int int), (fact_fact int) ) 18.74/17.87 ( (fun int int), zfact ) 18.74/17.87 ( (fun bool bool), fNot ) 18.74/17.87 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 18.74/17.87 ( (fun bool (fun bool bool)), fconj ) 18.74/17.87 ( (fun bool (fun bool bool)), fdisj ) 18.74/17.87 ( (fun bool (fun bool bool)), fimplies ) 18.74/17.87 ( (fun int (fun int bool)), sRStar ) 18.74/17.87 ( (fun int (fun int bool)), quadRes ) 18.74/17.87 ( (fun int (fun int bool)), norRRset ) 18.74/17.87 ( (fun int (fun int bool)), d22set ) 18.74/17.87 ( (fun int (fun int bool)), sr ) 18.74/17.87 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 18.74/17.87 ( (fun nat (fun nat nat)), nat_gcd ) 18.74/17.87 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 18.74/17.87 ( (fun nat (fun nat nat)), nat_lcm ) 18.74/17.87 ( (fun nat (fun real real)), root ) 18.74/17.87 ( (fun real (fun real real)), log ) 18.74/17.87 ( (fun real (fun real real)), powr ) 18.74/17.87 ( (fun nat (fun nat bool)), coprime ) 18.74/17.87 ( (fun (fun int bool) int), (the int) ) 18.74/17.87 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 18.74/17.87 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 18.74/17.87 ( (fun nat (fun nat (product_prod int int))), bezw ) 18.74/17.87 ( (fun (fun int bool) bool), nat_nat_set ) 18.74/17.87 ( (filter nat), sequentially ) 18.74/17.87 ( (fun (product_prod nat nat) bool), pred_nat ) 18.74/17.87 ( (fun (product_prod int int) bool), frac_1 ) 18.74/17.87 ( (fun real complex), cis ) 18.74/17.87 ( (fun complex real), im ) 18.74/17.87 ( (fun complex real), re ) 18.74/17.87 ( (fun complex real), arg ) 18.74/17.87 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 18.74/17.87 ( (fun int (fun int int)), int_gcd ) 18.74/17.87 ( (fun int (fun int int)), multInv ) 18.74/17.87 ( (fun int (fun int int)), legacy_zgcd ) 18.74/17.87 ( (fun int (fun int int)), z3mod ) 18.74/17.87 ( (fun int (fun int int)), inv ) 18.74/17.87 ( (fun int (fun int int)), (gcd_gcd int) ) 18.74/17.87 ( (fun int (fun int int)), standardRes ) 18.74/17.87 ( (fun int (fun int int)), legendre ) 18.74/17.87 ( (fun int (fun int int)), nat_tsub ) 18.74/17.87 ( (fun int (fun int int)), z3div ) 18.74/17.87 ( (fun int (fun int int)), int_lcm ) 18.74/17.87 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 18.74/17.87 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 18.74/17.87 ( (fun int (fun (fun int bool) bool)), rsetR ) 18.74/17.87 ( (fun int (fun (fun int bool) bool)), resSet ) 18.74/17.87 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 18.74/17.87 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 18.74/17.87 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 18.74/17.87 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 18.74/17.87 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 18.74/17.87 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 18.74/17.87 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 18.74/17.87 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 18.74/17.87 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 18.74/17.87 ( (fun int (fun int (product_prod int int))), negDivAlg ) 18.74/17.87 ( (fun int (fun int (product_prod int int))), divmod_int ) 18.74/17.87 ( (fun int (fun int (product_prod int int))), posDivAlg ) 18.74/17.87 ( (fun int (fun int (product_prod int int))), pdivmod ) 18.74/17.87 ( (fun int (fun int (product_prod int int))), norm_frac ) 18.74/17.87 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 18.74/17.87 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 18.74/17.87 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 18.74/17.87 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 18.74/17.87 ( (fun real nat), natfloor ) 18.74/17.87 ( (fun real nat), natceiling ) 18.74/17.87 ( (fun int quickcheck_code_int), quickcheck_of_int ) 18.74/17.87 ( (fun int (fun int (fun int bool))), wset ) 18.74/17.87 ( (fun int (fun int (fun int bool))), bnorRset ) 18.74/17.87 ( (fun int (fun int (fun int bool))), zcong ) 18.74/17.87 ( (fun int (fun int (fun int bool))), noXRRset ) 18.74/17.87 ( (fun int (fun int (fun int bool))), zcongm ) 18.74/17.87 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 18.74/17.87 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 18.74/17.87 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 18.74/17.87 ( (fun int real), (real_1 int) ) 18.74/17.87 ( (fun complex nat), (size_size complex) ) 18.74/17.87 ( (fun complex nat), complex_size ) 18.74/17.87 ( (fun int (list int)), quickc666637781d_zero ) 18.74/17.87 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 18.74/17.87 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 18.74/17.87 ( (fun (product_prod int int) rat), frct ) 18.74/17.87 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 18.74/17.87 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 18.74/17.87 ( (fun (fun nat rat) bool), vanishes ) 18.74/17.87 ( (fun int (fun int rat)), fract ) 18.74/17.87 ( (fun code_code_numeral int), code_int_of ) 18.74/17.87 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 18.74/17.87 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 18.74/17.87 ( (fun code_code_numeral nat), code_c271388182l_size ) 18.74/17.87 ( (fun real (fun real complex)), complex_1 ) 18.74/17.87 ( (fun real (fun real complex)), rcis ) 18.74/17.87 ( (fun int (fun nat nat)), nat_aux ) 18.74/17.87 ( (fun rat real), ratreal ) 18.74/17.87 ( (fun quickcheck_code_int int), quickcheck_int_of ) 18.74/17.87 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 18.74/17.87 ( (fun rat (product_prod int int)), quotient_of ) 18.74/17.87 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 18.74/17.87 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 18.74/17.87 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 18.74/17.87 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 18.74/17.87 ) 18.74/17.87 (instantiation (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (times_times X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_134502 $$unsorted) (BOUND_VARIABLE_134503 $$unsorted)) (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_134502)) BOUND_VARIABLE_134503) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_134502) BOUND_VARIABLE_134503)))) )))) 18.74/17.87 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.74/17.87 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.74/17.87 ( 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)))))) ) 18.74/17.87 ( 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 ) 18.74/17.87 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 18.74/17.87 ( 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))), (zero_zero int) ) 18.74/17.87 ( 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))), t ) 18.74/17.87 ( 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_1 ) 18.74/17.87 ( complex, ii, ii ) 18.74/17.87 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 18.74/17.87 ( 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 ) 18.74/17.87 ) 18.74/17.87 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_134517 $$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 (abs_abs X_a) BOUND_VARIABLE_134517)) _let_0)) (= _let_0 (ti X_a BOUND_VARIABLE_134517)))) )) 18.74/17.87 ( bool, fFalse ) 18.74/17.87 ( bool, fTrue ) 18.74/17.87 ( real, pi ) 18.74/17.87 ( (fun nat bool), (even_odd_even nat) ) 18.74/17.87 ( (fun nat bool), prime ) 18.74/17.87 ( (fun nat nat), suc ) 18.74/17.87 ( (fun nat nat), (fact_fact nat) ) 18.74/17.87 ( (fun nat nat), (size_size nat) ) 18.74/17.87 ( (fun nat nat), fact ) 18.74/17.87 ( (fun nat nat), nat_size ) 18.74/17.87 ( int, pls ) 18.74/17.87 ( int, m ) 18.74/17.87 ( int, min_1 ) 18.74/17.87 ( int, s ) 18.74/17.87 ( int, s1 ) 18.74/17.87 ( int, t ) 18.74/17.87 ( (fun int bool), zprime ) 18.74/17.87 ( (fun int bool), nat_neg ) 18.74/17.87 ( (fun int bool), zEven ) 18.74/17.87 ( (fun int bool), nat_is_nat ) 18.74/17.87 ( (fun int bool), zOdd ) 18.74/17.87 ( (fun int bool), (even_odd_even int) ) 18.74/17.87 ( (fun int bool), twoSqu1091635170sum2sq ) 18.74/17.87 ( (fun int nat), nat_1 ) 18.74/17.87 ( (fun int nat), phi ) 18.74/17.87 ( (fun real real), sqrt ) 18.74/17.87 ( (fun real real), tan ) 18.74/17.87 ( (fun real real), cos ) 18.74/17.87 ( (fun real real), arccos ) 18.74/17.87 ( (fun real real), ln ) 18.74/17.87 ( (fun real real), sin ) 18.74/17.87 ( (fun real real), arctan ) 18.74/17.87 ( (fun real real), arcsin ) 18.74/17.87 ( complex, ii ) 18.74/17.87 ( (fun complex complex), cnj ) 18.74/17.87 ( (fun complex complex), expi ) 18.74/17.87 ( (fun nat real), (real_1 nat) ) 18.74/17.87 ( (fun nat real), cos_coeff ) 18.74/17.87 ( (fun nat real), sin_coeff ) 18.74/17.87 ( (fun int int), bit0 ) 18.74/17.87 ( (fun int int), bit1 ) 18.74/17.87 ( (fun int int), pred ) 18.74/17.87 ( (fun int int), succ ) 18.74/17.87 ( (fun int int), (fact_fact int) ) 18.74/17.87 ( (fun int int), zfact ) 18.74/17.87 ( (fun bool bool), fNot ) 18.74/17.87 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 18.74/17.87 ( (fun bool (fun bool bool)), fconj ) 18.74/17.87 ( (fun bool (fun bool bool)), fdisj ) 18.74/17.87 ( (fun bool (fun bool bool)), fimplies ) 18.74/17.87 ( (fun int (fun int bool)), sRStar ) 18.74/17.87 ( (fun int (fun int bool)), quadRes ) 18.74/17.87 ( (fun int (fun int bool)), norRRset ) 18.74/17.87 ( (fun int (fun int bool)), d22set ) 18.74/17.87 ( (fun int (fun int bool)), sr ) 18.74/17.87 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 18.74/17.87 ( (fun nat (fun nat nat)), nat_gcd ) 18.74/17.87 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 18.74/17.87 ( (fun nat (fun nat nat)), nat_lcm ) 18.74/17.87 ( (fun nat (fun real real)), root ) 18.74/17.87 ( (fun real (fun real real)), log ) 18.74/17.87 ( (fun real (fun real real)), powr ) 18.74/17.87 ( (fun nat (fun nat bool)), coprime ) 18.74/17.87 ( (fun (fun int bool) int), (the int) ) 18.74/17.87 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 18.74/17.87 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 18.74/17.87 ( (fun nat (fun nat (product_prod int int))), bezw ) 18.74/17.87 ( (fun (fun int bool) bool), nat_nat_set ) 18.74/17.87 ( (filter nat), sequentially ) 18.74/17.87 ( (fun (product_prod nat nat) bool), pred_nat ) 18.74/17.87 ( (fun (product_prod int int) bool), frac_1 ) 18.74/17.87 ( (fun real complex), cis ) 18.74/17.87 ( (fun complex real), im ) 18.74/17.87 ( (fun complex real), re ) 18.74/17.87 ( (fun complex real), arg ) 18.74/17.87 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 18.74/17.87 ( (fun int (fun int int)), int_gcd ) 18.74/17.87 ( (fun int (fun int int)), multInv ) 18.74/17.87 ( (fun int (fun int int)), legacy_zgcd ) 18.74/17.87 ( (fun int (fun int int)), z3mod ) 18.74/17.88 ( (fun int (fun int int)), inv ) 18.74/17.88 ( (fun int (fun int int)), (gcd_gcd int) ) 18.74/17.88 ( (fun int (fun int int)), standardRes ) 18.74/17.88 ( (fun int (fun int int)), legendre ) 18.74/17.88 ( (fun int (fun int int)), nat_tsub ) 18.74/17.88 ( (fun int (fun int int)), z3div ) 18.74/17.88 ( (fun int (fun int int)), int_lcm ) 18.74/17.88 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 18.74/17.88 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 18.74/17.88 ( (fun int (fun (fun int bool) bool)), rsetR ) 18.74/17.88 ( (fun int (fun (fun int bool) bool)), resSet ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 18.74/17.88 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 18.74/17.88 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 18.74/17.88 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 18.74/17.88 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 18.74/17.88 ( (fun int (fun int (product_prod int int))), negDivAlg ) 18.74/17.88 ( (fun int (fun int (product_prod int int))), divmod_int ) 18.74/17.88 ( (fun int (fun int (product_prod int int))), posDivAlg ) 18.74/17.88 ( (fun int (fun int (product_prod int int))), pdivmod ) 18.74/17.88 ( (fun int (fun int (product_prod int int))), norm_frac ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 18.74/17.88 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 18.74/17.88 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 18.74/17.88 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 18.74/17.88 ( (fun real nat), natfloor ) 18.74/17.88 ( (fun real nat), natceiling ) 18.74/17.88 ( (fun int quickcheck_code_int), quickcheck_of_int ) 18.74/17.88 ( (fun int (fun int (fun int bool))), wset ) 18.74/17.88 ( (fun int (fun int (fun int bool))), bnorRset ) 18.74/17.88 ( (fun int (fun int (fun int bool))), zcong ) 18.74/17.88 ( (fun int (fun int (fun int bool))), noXRRset ) 18.74/17.88 ( (fun int (fun int (fun int bool))), zcongm ) 18.74/17.88 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 18.74/17.88 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 18.74/17.88 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 18.74/17.88 ( (fun int real), (real_1 int) ) 18.74/17.88 ( (fun complex nat), (size_size complex) ) 18.74/17.88 ( (fun complex nat), complex_size ) 18.74/17.88 ( (fun int (list int)), quickc666637781d_zero ) 18.74/17.88 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 18.74/17.88 ( (fun (product_prod int int) rat), frct ) 18.74/17.88 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 18.74/17.88 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 18.74/17.88 ( (fun (fun nat rat) bool), vanishes ) 18.74/17.88 ( (fun int (fun int rat)), fract ) 18.74/17.88 ( (fun code_code_numeral int), code_int_of ) 18.74/17.88 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 18.74/17.88 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 18.74/17.88 ( (fun code_code_numeral nat), code_c271388182l_size ) 18.74/17.88 ( (fun real (fun real complex)), complex_1 ) 18.74/17.88 ( (fun real (fun real complex)), rcis ) 18.74/17.88 ( (fun int (fun nat nat)), nat_aux ) 18.74/17.88 ( (fun rat real), ratreal ) 18.74/17.88 ( (fun quickcheck_code_int int), quickcheck_int_of ) 18.74/17.88 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 18.74/17.88 ( (fun rat (product_prod int int)), quotient_of ) 18.74/17.88 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 18.74/17.88 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 18.74/17.88 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 18.74/17.88 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 18.74/17.88 ) 18.74/17.88 (instantiation (let ((_let_0 (even_odd_even int))) (forall ((X $$unsorted) (Y $$unsorted)) (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)))) )) 18.74/17.88 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 18.74/17.88 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 18.74/17.88 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 18.74/17.88 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_1 ) 18.74/17.88 ) 18.74/17.88 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134539 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (ti X_a BOUND_VARIABLE_134539) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (zero_zero X_a)) BOUND_VARIABLE_134539))) ) 18.74/17.88 ( bool, fFalse ) 18.74/17.88 ( bool, fTrue ) 18.74/17.88 ( real, pi ) 18.74/17.88 ( (fun nat bool), (even_odd_even nat) ) 18.74/17.88 ( (fun nat bool), prime ) 18.74/17.88 ( (fun nat nat), suc ) 18.74/17.88 ( (fun nat nat), (fact_fact nat) ) 18.74/17.88 ( (fun nat nat), (size_size nat) ) 18.74/17.88 ( (fun nat nat), fact ) 18.74/17.88 ( (fun nat nat), nat_size ) 18.74/17.88 ( int, pls ) 18.74/17.88 ( int, m ) 18.74/17.88 ( int, min_1 ) 18.74/17.88 ( int, s ) 18.74/17.88 ( int, s1 ) 18.74/17.88 ( int, t ) 18.74/17.88 ( (fun int bool), zprime ) 18.74/17.88 ( (fun int bool), nat_neg ) 18.74/17.88 ( (fun int bool), zEven ) 18.74/17.88 ( (fun int bool), nat_is_nat ) 18.74/17.88 ( (fun int bool), zOdd ) 18.74/17.88 ( (fun int bool), (even_odd_even int) ) 18.74/17.88 ( (fun int bool), twoSqu1091635170sum2sq ) 18.74/17.88 ( (fun int nat), nat_1 ) 18.74/17.88 ( (fun int nat), phi ) 18.74/17.88 ( (fun real real), sqrt ) 18.74/17.88 ( (fun real real), tan ) 18.74/17.88 ( (fun real real), cos ) 18.74/17.88 ( (fun real real), arccos ) 18.74/17.88 ( (fun real real), ln ) 18.74/17.88 ( (fun real real), sin ) 18.74/17.88 ( (fun real real), arctan ) 18.74/17.88 ( (fun real real), arcsin ) 18.74/17.88 ( complex, ii ) 18.74/17.88 ( (fun complex complex), cnj ) 18.74/17.88 ( (fun complex complex), expi ) 18.74/17.88 ( (fun nat real), (real_1 nat) ) 18.74/17.88 ( (fun nat real), cos_coeff ) 18.74/17.88 ( (fun nat real), sin_coeff ) 18.74/17.88 ( (fun int int), bit0 ) 18.74/17.88 ( (fun int int), bit1 ) 18.74/17.88 ( (fun int int), pred ) 18.74/17.88 ( (fun int int), succ ) 18.74/17.88 ( (fun int int), (fact_fact int) ) 18.74/17.88 ( (fun int int), zfact ) 18.74/17.88 ( (fun bool bool), fNot ) 18.74/17.88 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 18.74/17.88 ( (fun bool (fun bool bool)), fconj ) 18.74/17.88 ( (fun bool (fun bool bool)), fdisj ) 18.74/17.88 ( (fun bool (fun bool bool)), fimplies ) 18.74/17.88 ( (fun int (fun int bool)), sRStar ) 18.74/17.88 ( (fun int (fun int bool)), quadRes ) 18.74/17.88 ( (fun int (fun int bool)), norRRset ) 18.74/17.88 ( (fun int (fun int bool)), d22set ) 18.74/17.88 ( (fun int (fun int bool)), sr ) 18.74/17.88 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 18.74/17.88 ( (fun nat (fun nat nat)), nat_gcd ) 18.74/17.88 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 18.74/17.88 ( (fun nat (fun nat nat)), nat_lcm ) 18.74/17.88 ( (fun nat (fun real real)), root ) 18.74/17.88 ( (fun real (fun real real)), log ) 18.74/17.88 ( (fun real (fun real real)), powr ) 18.74/17.88 ( (fun nat (fun nat bool)), coprime ) 18.74/17.88 ( (fun (fun int bool) int), (the int) ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 18.74/17.88 ( (fun nat (fun nat (product_prod int int))), bezw ) 18.74/17.88 ( (fun (fun int bool) bool), nat_nat_set ) 18.74/17.88 ( (filter nat), sequentially ) 18.74/17.88 ( (fun (product_prod nat nat) bool), pred_nat ) 18.74/17.88 ( (fun (product_prod int int) bool), frac_1 ) 18.74/17.88 ( (fun real complex), cis ) 18.74/17.88 ( (fun complex real), im ) 18.74/17.88 ( (fun complex real), re ) 18.74/17.88 ( (fun complex real), arg ) 18.74/17.88 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 18.74/17.88 ( (fun int (fun int int)), int_gcd ) 18.74/17.88 ( (fun int (fun int int)), multInv ) 18.74/17.88 ( (fun int (fun int int)), legacy_zgcd ) 18.74/17.88 ( (fun int (fun int int)), z3mod ) 18.74/17.88 ( (fun int (fun int int)), inv ) 18.74/17.88 ( (fun int (fun int int)), (gcd_gcd int) ) 18.74/17.88 ( (fun int (fun int int)), standardRes ) 18.74/17.88 ( (fun int (fun int int)), legendre ) 18.74/17.88 ( (fun int (fun int int)), nat_tsub ) 18.74/17.88 ( (fun int (fun int int)), z3div ) 18.74/17.88 ( (fun int (fun int int)), int_lcm ) 18.74/17.88 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 18.74/17.88 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 18.74/17.88 ( (fun int (fun (fun int bool) bool)), rsetR ) 18.74/17.88 ( (fun int (fun (fun int bool) bool)), resSet ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 18.74/17.88 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 18.74/17.88 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 18.74/17.88 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 18.74/17.88 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 18.74/17.88 ( (fun int (fun int (product_prod int int))), negDivAlg ) 18.74/17.88 ( (fun int (fun int (product_prod int int))), divmod_int ) 18.74/17.88 ( (fun int (fun int (product_prod int int))), posDivAlg ) 18.74/17.88 ( (fun int (fun int (product_prod int int))), pdivmod ) 18.74/17.88 ( (fun int (fun int (product_prod int int))), norm_frac ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 18.74/17.88 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 18.74/17.88 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 18.74/17.88 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 18.74/17.88 ( (fun real nat), natfloor ) 18.74/17.88 ( (fun real nat), natceiling ) 18.74/17.88 ( (fun int quickcheck_code_int), quickcheck_of_int ) 18.74/17.88 ( (fun int (fun int (fun int bool))), wset ) 18.74/17.88 ( (fun int (fun int (fun int bool))), bnorRset ) 18.74/17.88 ( (fun int (fun int (fun int bool))), zcong ) 18.74/17.88 ( (fun int (fun int (fun int bool))), noXRRset ) 18.74/17.88 ( (fun int (fun int (fun int bool))), zcongm ) 18.74/17.88 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 18.74/17.88 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 18.74/17.88 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 18.74/17.88 ( (fun int real), (real_1 int) ) 18.74/17.88 ( (fun complex nat), (size_size complex) ) 18.74/17.88 ( (fun complex nat), complex_size ) 18.74/17.88 ( (fun int (list int)), quickc666637781d_zero ) 18.74/17.88 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 18.74/17.88 ( (fun (product_prod int int) rat), frct ) 18.74/17.88 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 18.74/17.88 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 18.74/17.88 ( (fun (fun nat rat) bool), vanishes ) 18.74/17.88 ( (fun int (fun int rat)), fract ) 18.74/17.88 ( (fun code_code_numeral int), code_int_of ) 18.74/17.88 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 18.74/17.88 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 18.74/17.88 ( (fun code_code_numeral nat), code_c271388182l_size ) 18.74/17.88 ( (fun real (fun real complex)), complex_1 ) 18.74/17.88 ( (fun real (fun real complex)), rcis ) 18.74/17.88 ( (fun int (fun nat nat)), nat_aux ) 18.74/17.88 ( (fun rat real), ratreal ) 18.74/17.88 ( (fun quickcheck_code_int int), quickcheck_int_of ) 18.74/17.88 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 18.74/17.88 ( (fun rat (product_prod int int)), quotient_of ) 18.74/17.88 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 18.74/17.88 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 18.74/17.88 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 18.74/17.88 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 18.74/17.88 ) 18.74/17.88 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_134684))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_134684 $$unsorted) (BOUND_VARIABLE_134685 $$unsorted) (BOUND_VARIABLE_134686 $$unsorted)) (or (not (comple44059174attice X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_134685) BOUND_VARIABLE_134686))) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_134685))) (hBOOL (hAPP X_a bool _let_1 (hAPP _let_0 X_a (complete_Sup_Sup X_a) BOUND_VARIABLE_134686)))) ))) 18.74/17.88 ( int, (zero_zero int), (one_one int), zEven ) 18.74/17.88 ) 18.74/17.88 (instantiation (let ((_let_0 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_134711 $$unsorted)) (or (not (boolean_algebra X_a)) (= (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_0 BOUND_VARIABLE_134711)) (ti X_a BOUND_VARIABLE_134711))) )) 18.74/17.88 ( bool, fFalse ) 18.74/17.88 ( bool, fTrue ) 18.74/17.88 ( real, (one_one real) ) 18.74/17.88 ( real, pi ) 18.74/17.88 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.74/17.88 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.74/17.88 ( (fun nat bool), (even_odd_even nat) ) 18.74/17.88 ( (fun nat bool), prime ) 18.74/17.88 ( (fun nat nat), suc ) 18.74/17.88 ( (fun nat nat), (fact_fact nat) ) 18.74/17.88 ( (fun nat nat), (size_size nat) ) 18.74/17.88 ( (fun nat nat), fact ) 18.74/17.88 ( (fun nat nat), nat_size ) 18.74/17.88 ( int, pls ) 18.74/17.88 ( int, m ) 18.74/17.88 ( int, (one_one int) ) 18.74/17.88 ( int, min_1 ) 18.74/17.88 ( int, s ) 18.74/17.88 ( int, s1 ) 18.74/17.88 ( int, t ) 18.74/17.88 ( (fun int bool), zprime ) 18.74/17.88 ( (fun int bool), nat_neg ) 18.74/17.88 ( (fun int bool), zEven ) 18.74/17.88 ( (fun int bool), nat_is_nat ) 18.74/17.88 ( (fun int bool), zOdd ) 18.74/17.88 ( (fun int bool), (even_odd_even int) ) 18.74/17.88 ( (fun int bool), twoSqu1091635170sum2sq ) 18.74/17.88 ( (fun int nat), nat_1 ) 18.74/17.88 ( (fun int nat), phi ) 18.74/17.88 ( (fun real real), sqrt ) 18.74/17.88 ( (fun real real), tan ) 18.74/17.88 ( (fun real real), cos ) 18.74/17.88 ( (fun real real), arccos ) 18.74/17.88 ( (fun real real), ln ) 18.74/17.88 ( (fun real real), sin ) 18.74/17.88 ( (fun real real), arctan ) 18.74/17.88 ( (fun real real), arcsin ) 18.74/17.88 ( complex, ii ) 18.74/17.88 ( complex, (one_one complex) ) 18.74/17.88 ( (fun complex complex), cnj ) 18.74/17.88 ( (fun complex complex), expi ) 18.74/17.88 ( (fun nat real), (real_1 nat) ) 18.74/17.88 ( (fun nat real), cos_coeff ) 18.74/17.88 ( (fun nat real), sin_coeff ) 18.74/17.88 ( (fun int int), bit0 ) 18.74/17.88 ( (fun int int), bit1 ) 18.74/17.88 ( (fun int int), pred ) 18.74/17.88 ( (fun int int), succ ) 18.74/17.88 ( (fun int int), (fact_fact int) ) 18.74/17.88 ( (fun int int), zfact ) 18.74/17.88 ( (fun bool bool), fNot ) 18.74/17.88 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 18.74/17.88 ( (fun bool (fun bool bool)), fconj ) 18.74/17.88 ( (fun bool (fun bool bool)), fdisj ) 18.74/17.88 ( (fun bool (fun bool bool)), fimplies ) 18.74/17.88 ( (fun int (fun int bool)), sRStar ) 18.74/17.88 ( (fun int (fun int bool)), quadRes ) 18.74/17.88 ( (fun int (fun int bool)), norRRset ) 18.74/17.88 ( (fun int (fun int bool)), d22set ) 18.74/17.88 ( (fun int (fun int bool)), sr ) 18.74/17.88 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 18.74/17.88 ( (fun nat (fun nat nat)), nat_gcd ) 18.74/17.88 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 18.74/17.88 ( (fun nat (fun nat nat)), nat_lcm ) 18.74/17.88 ( (fun nat (fun real real)), root ) 18.74/17.88 ( (fun real (fun real real)), log ) 18.74/17.88 ( (fun real (fun real real)), powr ) 18.74/17.88 ( (fun nat (fun nat bool)), coprime ) 18.74/17.88 ( (fun (fun int bool) int), (the int) ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 18.74/17.88 ( (fun nat (fun nat (product_prod int int))), bezw ) 18.74/17.88 ( (fun (fun int bool) bool), nat_nat_set ) 18.74/17.88 ( (filter nat), sequentially ) 18.74/17.88 ( (fun (product_prod nat nat) bool), pred_nat ) 18.74/17.88 ( (fun (product_prod int int) bool), frac_1 ) 18.74/17.88 ( (fun real complex), cis ) 18.74/17.88 ( (fun complex real), im ) 18.74/17.88 ( (fun complex real), re ) 18.74/17.88 ( (fun complex real), arg ) 18.74/17.88 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 18.74/17.88 ( (fun int (fun int int)), int_gcd ) 18.74/17.88 ( (fun int (fun int int)), multInv ) 18.74/17.88 ( (fun int (fun int int)), legacy_zgcd ) 18.74/17.88 ( (fun int (fun int int)), z3mod ) 18.74/17.88 ( (fun int (fun int int)), inv ) 18.74/17.88 ( (fun int (fun int int)), (gcd_gcd int) ) 18.74/17.88 ( (fun int (fun int int)), standardRes ) 18.74/17.88 ( (fun int (fun int int)), legendre ) 18.74/17.88 ( (fun int (fun int int)), nat_tsub ) 18.74/17.88 ( (fun int (fun int int)), z3div ) 18.74/17.88 ( (fun int (fun int int)), int_lcm ) 18.74/17.88 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 18.74/17.88 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 18.74/17.88 ( (fun int (fun (fun int bool) bool)), rsetR ) 18.74/17.88 ( (fun int (fun (fun int bool) bool)), resSet ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 18.74/17.88 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 18.74/17.88 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 18.74/17.88 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 18.74/17.88 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 18.74/17.88 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 18.74/17.88 ( (fun int (fun int (product_prod int int))), negDivAlg ) 18.74/17.89 ( (fun int (fun int (product_prod int int))), divmod_int ) 18.74/17.89 ( (fun int (fun int (product_prod int int))), posDivAlg ) 18.74/17.89 ( (fun int (fun int (product_prod int int))), pdivmod ) 18.74/17.89 ( (fun int (fun int (product_prod int int))), norm_frac ) 18.74/17.89 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 18.74/17.89 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 18.74/17.89 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 18.74/17.89 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 18.74/17.89 ( (fun real nat), natfloor ) 18.74/17.89 ( (fun real nat), natceiling ) 18.74/17.89 ( (fun int quickcheck_code_int), quickcheck_of_int ) 18.74/17.89 ( (fun int (fun int (fun int bool))), wset ) 18.74/17.89 ( (fun int (fun int (fun int bool))), bnorRset ) 18.74/17.89 ( (fun int (fun int (fun int bool))), zcong ) 18.74/17.89 ( (fun int (fun int (fun int bool))), noXRRset ) 18.74/17.89 ( (fun int (fun int (fun int bool))), zcongm ) 18.74/17.89 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 18.74/17.89 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 18.74/17.89 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 18.74/17.89 ( (fun int real), (real_1 int) ) 18.74/17.89 ( (fun complex nat), (size_size complex) ) 18.74/17.89 ( (fun complex nat), complex_size ) 18.74/17.89 ( (fun int (list int)), quickc666637781d_zero ) 18.74/17.89 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 18.74/17.89 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 18.74/17.89 ( (fun (product_prod int int) rat), frct ) 18.74/17.89 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 18.74/17.89 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 18.74/17.89 ( (fun (fun nat rat) bool), vanishes ) 18.74/17.89 ( (fun int (fun int rat)), fract ) 18.74/17.89 ( (fun code_code_numeral int), code_int_of ) 18.74/17.89 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 18.74/17.89 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 18.74/17.89 ( (fun code_code_numeral nat), code_c271388182l_size ) 18.74/17.89 ( (fun real (fun real complex)), complex_1 ) 18.74/17.89 ( (fun real (fun real complex)), rcis ) 18.74/17.89 ( (fun int (fun nat nat)), nat_aux ) 18.74/17.89 ( (fun rat real), ratreal ) 18.74/17.89 ( (fun quickcheck_code_int int), quickcheck_int_of ) 18.74/17.89 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 18.74/17.89 ( (fun rat (product_prod int int)), quotient_of ) 18.74/17.89 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 18.74/17.89 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 18.74/17.89 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 18.74/17.89 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 18.74/17.89 ) 18.74/17.89 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP complex complex cnj Z_1) (hAPP real complex (hAPP real (fun real complex) complex_1 (hAPP complex real re Z_1)) (hAPP real real (uminus_uminus real) (hAPP complex real im Z_1)))) ) 18.74/17.89 ( ii ) 18.74/17.89 ( (zero_zero complex) ) 18.74/17.89 ( (one_one complex) ) 18.74/17.89 ) 18.74/17.89 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134879 $$unsorted)) (or (not (linordered_idom X_a)) (not (number_ring X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_134879) pls)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_134879)) (zero_zero X_a))))) ) 18.74/17.89 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.74/17.89 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.89 ( real, min_1 ) 18.74/17.89 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.89 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.74/17.89 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.74/17.89 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 18.74/17.89 ( nat, pls ) 18.74/17.89 ( nat, (hAPP int int bit1 pls) ) 18.74/17.89 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.74/17.89 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.74/17.89 ( int, pls ) 18.74/17.89 ( int, (hAPP int int bit1 pls) ) 18.74/17.89 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.74/17.89 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.74/17.89 ( int, min_1 ) 18.74/17.89 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.74/17.89 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.74/17.89 ( complex, min_1 ) 18.74/17.89 ( quickcheck_code_int, (zero_zero int) ) 18.74/17.89 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 18.74/17.89 ( quickcheck_code_int, (one_one int) ) 18.74/17.89 ( code_code_numeral, pls ) 18.74/17.89 ( code_code_numeral, (hAPP int int bit1 pls) ) 18.74/17.89 ) 18.74/17.89 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134900 $$unsorted) (BOUND_VARIABLE_134901 $$unsorted)) (or (not (semiri456707255roduct X_a)) (= (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_134901)) (= (ti X_a BOUND_VARIABLE_134900) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_134900) BOUND_VARIABLE_134901)))) ) 18.74/17.89 ( nat, (one_one nat), (one_one nat) ) 18.74/17.89 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 18.74/17.89 ( int, (hAPP nat int (hAPP 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) ) 18.74/17.89 ) 18.74/17.89 (instantiation (forall ((K_4 $$unsorted)) (= (ti int K_4) (hAPP int int (hAPP int (fun int int) (plus_plus int) pls) K_4)) ) 18.74/17.89 ( pls ) 18.74/17.89 ( m ) 18.74/17.89 ( min_1 ) 18.74/17.89 ( s ) 18.74/17.89 ( s1 ) 18.74/17.89 ( t ) 18.74/17.89 ) 18.74/17.89 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (fun nat _let_3))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_134961 $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (not (banach X_a)) (hBOOL (hAPP _let_2 bool (summable X_a) (hAPP _let_2 _let_2 (hAPP _let_4 (fun _let_2 _let_2) (combs nat X_a X_a) (hAPP _let_1 _let_4 (hAPP (fun real _let_3) (fun _let_1 _let_4) (combb real _let_3 nat) (scaleR_scaleR X_a)) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) (fact_fact nat))))) (hAPP X_a _let_2 (power_power X_a) BOUND_VARIABLE_134961))))) )))))) 18.74/17.89 ( real, (hAPP int real (number_number_of real) min_1) ) 18.74/17.89 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.74/17.89 ( int, s ) 18.74/17.89 ( int, s1 ) 18.74/17.89 ( int, skv_8 ) 18.74/17.89 ( complex, ii ) 18.74/17.89 ) 18.74/17.89 (instantiation (let ((_let_0 (even_odd_even int))) (forall ((Y $$unsorted) (X $$unsorted)) (or (hBOOL (hAPP int bool _let_0 X)) (hBOOL (hAPP int bool _let_0 Y)) (not (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) X) Y))))) )) 18.74/17.89 ( (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.74/17.89 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.89/17.89 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.89/17.89 ( skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.89/17.89 ) 18.89/17.89 (instantiation (let ((_let_0 (fun nat bool))) (forall ((K $$unsorted)) (= (hAPP nat _let_0 (ord_atMost nat) K) (hAPP nat _let_0 (ord_lessThan nat) (hAPP nat nat suc K))) )) 18.89/17.89 ( (zero_zero nat) ) 18.89/17.89 ( (hAPP nat nat suc (zero_zero nat)) ) 18.89/17.89 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 18.89/17.89 ) 18.89/17.89 (instantiation (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_135017))) (let ((_let_3 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_135018))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_135017 $$unsorted) (BOUND_VARIABLE_135018 $$unsorted) (BOUND_VARIABLE_135019 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a _let_3 BOUND_VARIABLE_135019)) (hAPP X_a X_a _let_3 (hAPP X_a X_a _let_2 BOUND_VARIABLE_135019)))) ))))) 18.89/17.89 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.89/17.89 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.90/17.89 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.92/17.93 ) 18.92/17.93 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_135033 $$unsorted) (BOUND_VARIABLE_135034 $$unsorted)) (or (not (boolean_algebra X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_135034) BOUND_VARIABLE_135033)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_135033)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_135034))))) )))) 18.92/17.93 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.93 ( real, pi, (zero_zero real) ) 18.92/17.93 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.93 ( 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)))) ) 18.92/17.93 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 18.92/17.93 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.92/17.93 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.92/17.93 ( real, skv_6, (zero_zero real) ) 18.92/17.93 ( real, skv_11, (zero_zero real) ) 18.92/17.93 ( real, skv_12, (zero_zero real) ) 18.92/17.93 ( real, skv_14, (zero_zero real) ) 18.92/17.93 ( int, pls, pls ) 18.92/17.93 ( int, pls, (one_one int) ) 18.92/17.93 ( int, pls, min_1 ) 18.92/17.93 ( int, (one_one int), (zero_zero int) ) 18.92/17.93 ( int, (one_one int), pls ) 18.92/17.93 ( int, (one_one int), (one_one int) ) 18.92/17.93 ( int, min_1, (zero_zero int) ) 18.92/17.93 ( int, min_1, min_1 ) 18.92/17.93 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 18.92/17.93 ( int, s, (zero_zero int) ) 18.92/17.93 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 18.92/17.93 ( int, t, (one_one int) ) 18.92/17.93 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 18.92/17.93 ( int, skv_3, (zero_zero int) ) 18.92/17.93 ( int, skv_9, (zero_zero int) ) 18.92/17.93 ) 18.92/17.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135063 $$unsorted)) (or (not (number_ring X_a)) (not (ring_char_0 X_a)) (not (hBOOL (hAPP X_a bool (iszero X_a) (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 BOUND_VARIABLE_135063)))))) ) 18.92/17.93 ( real, (hAPP int int bit1 pls) ) 18.92/17.93 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.92/17.94 ( real, min_1 ) 18.92/17.94 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 18.92/17.94 ( nat, pls ) 18.92/17.94 ( nat, (hAPP int int bit1 pls) ) 18.92/17.94 ( int, pls ) 18.92/17.94 ( int, (hAPP int int bit1 pls) ) 18.92/17.94 ( int, min_1 ) 18.92/17.94 ( complex, min_1 ) 18.92/17.94 ( quickcheck_code_int, pls ) 18.92/17.94 ( code_code_numeral, pls ) 18.92/17.94 ) 18.92/17.94 (instantiation (forall ((N $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP int bool nat_is_nat X))) (hBOOL (hAPP int bool nat_is_nat (hAPP nat int (hAPP int (fun nat int) (power_power int) X) N)))) ) 18.92/17.94 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 18.92/17.94 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 18.92/17.94 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 18.92/17.94 ) 18.92/17.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135078 $$unsorted)) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_135078) BOUND_VARIABLE_135078)))) ) 18.92/17.94 ( real, (zero_zero real) ) 18.92/17.94 ( real, (one_one real) ) 18.92/17.94 ( real, pi ) 18.92/17.94 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.94 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 18.92/17.94 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.94 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 18.92/17.94 ( nat, (zero_zero nat) ) 18.92/17.94 ( int, (zero_zero int) ) 18.92/17.94 ( int, min_1 ) 18.92/17.94 ( int, s ) 18.92/17.94 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 18.92/17.94 ( int, t ) 18.92/17.94 ( int, skv_3 ) 18.92/17.94 ( int, skv_9 ) 18.92/17.94 ) 18.92/17.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135125 $$unsorted) (BOUND_VARIABLE_135126 $$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_135125) BOUND_VARIABLE_135126)) (= (ti X_a BOUND_VARIABLE_135126) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_135125)))) ) 18.92/17.94 ( nat, (one_one nat), (one_one nat) ) 18.92/17.94 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 18.92/17.94 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 18.92/17.94 ) 18.92/17.94 (instantiation (forall ((X_a $$unsorted)) (or (not (real_normed_vector X_a)) (not (real_algebra_1 X_a)) (= (zero_zero X_a) (hAPP real X_a (of_real X_a) (zero_zero real)))) ) 18.92/17.94 ( real ) 18.92/17.94 ( nat ) 18.92/17.94 ( int ) 18.92/17.94 ( complex ) 18.92/17.94 ( rat ) 18.92/17.94 ( quickcheck_code_int ) 18.92/17.94 ( code_code_numeral ) 18.92/17.94 ) 18.92/17.94 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (one_one int))) (let ((_let_3 (ord_less int))) (let ((_let_4 (ti int A_1))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 (zero_zero int)) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 A_1) P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP int int (hAPP int _let_1 (times_times int) A_1) A_1)) _let_2) P_5))) (= (hAPP int int (hAPP int _let_1 (minus_minus int) P_5) _let_2) _let_4) (= _let_2 _let_4)) )))))) 18.92/17.94 ( (zero_zero int), (zero_zero int) ) 18.92/17.94 ( (zero_zero int), (one_one int) ) 18.92/17.94 ( (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))) ) 18.92/17.94 ( (zero_zero int), min_1 ) 18.92/17.94 ( min_1, (zero_zero int) ) 18.92/17.94 ( min_1, min_1 ) 18.92/17.94 ( 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))) ) 18.92/17.94 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 18.92/17.94 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 18.92/17.94 ( t, (zero_zero int) ) 18.92/17.94 ( t, (one_one int) ) 18.92/17.94 ( 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))) ) 18.92/17.94 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/17.94 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/17.94 ) 18.92/17.94 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (real_1 nat))) (forall ((N $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP nat real _let_2 N)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) (hAPP nat real _let_2 (hAPP nat nat suc N))))) (= N (hAPP int nat nat_1 (hAPP real int (archim2085082626_floor real) X)))) )))) 18.92/17.94 ( (zero_zero nat), pi ) 18.92/17.94 ( (zero_zero nat), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.94 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.94 ( (zero_zero nat), skv_2 ) 18.92/17.94 ( (zero_zero nat), skv_10 ) 18.92/17.94 ( (zero_zero nat), skv_13 ) 18.92/17.94 ( (one_one nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.94 ) 18.92/17.94 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_135224))) (let ((_let_3 (ti X_a BOUND_VARIABLE_135222))) (let ((_let_4 (= _let_1 _let_2))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_135222 $$unsorted) (BOUND_VARIABLE_135223 $$unsorted) (BOUND_VARIABLE_135224 $$unsorted)) (or (not (number X_a)) (not (field_inverse_zero X_a)) (= (and (or _let_4 (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_135222) _let_2) (ti X_a BOUND_VARIABLE_135223))) (or (not _let_4) (= _let_1 _let_3))) (= _let_3 (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_135223) _let_2)))) )))))) 18.92/17.94 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.92/17.94 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), min_1, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.94 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m, min_1 ) 18.92/17.94 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.92/17.94 ( complex, ii, ii, min_1 ) 18.92/17.94 ) 18.92/17.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135270 $$unsorted) (BOUND_VARIABLE_135271 $$unsorted)) (or (not (comm_semiring_1 X_a)) (and (not (= (one_one X_a) (ti X_a BOUND_VARIABLE_135270))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) BOUND_VARIABLE_135271)))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_135270) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_135270) BOUND_VARIABLE_135271)))) ) 18.92/17.94 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.94 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.94 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.94 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.94 ) 18.92/17.94 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_135358 $$unsorted) (BOUND_VARIABLE_135359 $$unsorted)) (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_135359)) BOUND_VARIABLE_135358)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_135358)) BOUND_VARIABLE_135359)))) )))) 18.92/17.94 ( 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)))) ) 18.92/17.94 ( 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) ) 18.92/17.94 ( 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)))), (zero_zero real) ) 18.92/17.94 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), pi ) 18.92/17.94 ( int, (zero_zero int), pls ) 18.92/17.94 ( int, (zero_zero int), (one_one int) ) 18.92/17.94 ( int, pls, (zero_zero int) ) 18.92/17.94 ( int, pls, (one_one int) ) 18.92/17.94 ( 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))) ) 18.92/17.94 ( int, pls, min_1 ) 18.92/17.94 ( int, (one_one int), (zero_zero int) ) 18.92/17.94 ( int, (one_one int), pls ) 18.92/17.94 ( int, (one_one int), min_1 ) 18.92/17.94 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 18.92/17.94 ( int, min_1, pls ) 18.92/17.94 ( int, min_1, (one_one int) ) 18.92/17.94 ) 18.92/17.94 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_135479 $$unsorted) (BOUND_VARIABLE_135480 $$unsorted) (BOUND_VARIABLE_135481 $$unsorted)) (or (not (linordered_semidom X_a)) (not (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_135479) BOUND_VARIABLE_135480) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_135481) BOUND_VARIABLE_135480))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_135479))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_135481))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) BOUND_VARIABLE_135480))) (= (ti X_a BOUND_VARIABLE_135481) (ti X_a BOUND_VARIABLE_135479))) )))) 18.92/17.94 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 18.92/17.94 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 18.92/17.94 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 18.92/17.94 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 18.92/17.94 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 18.92/17.94 ) 18.92/17.94 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun (filter nat) bool))) (forall ((L $$unsorted) (F $$unsorted)) (or (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP nat real F N_2)) (hAPP nat real F (hAPP nat nat suc N_2)))) )) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP nat real F N_2)) L)) )) (not (forall ((E $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) E))) (not (forall ((N_2 $$unsorted)) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 L) (hAPP real real (hAPP real (fun real 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code_code_numeral, code_code_numeral ) 18.92/17.94 ) 18.92/17.94 (instantiation (let ((_let_0 (times_times X_a))) (forall ((X_a $$unsorted)) (or (not (ab_semigroup_mult X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0))) )) 18.92/17.94 ( bool ) 18.92/17.94 ( real ) 18.92/17.94 ( nat ) 18.92/17.94 ( (fun nat bool) ) 18.92/17.94 ( int ) 18.92/17.94 ( (fun int bool) ) 18.92/17.94 ( (fun real bool) ) 18.92/17.94 ( (fun real real) ) 18.92/17.94 ( complex ) 18.92/17.94 ( (fun nat real) ) 18.92/17.94 ( (fun int int) ) 18.92/17.94 ( rat ) 18.92/17.94 ( (fun int (fun int bool)) ) 18.92/17.94 ( quickcheck_code_int ) 18.92/17.94 ( (product_prod int int) ) 18.92/17.94 ( (fun (product_prod int int) bool) ) 18.92/17.94 ( code_code_numeral ) 18.92/17.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 18.92/17.94 ( (fun (product_prod int int) int) ) 18.92/17.94 ( (fun int (fun int (fun int bool))) ) 18.92/17.94 ( (fun int real) ) 18.92/17.94 ) 18.92/17.94 (instantiation (let ((_let_0 (zero_zero nat))) (forall ((N_1 $$unsorted)) (= (not (= _let_0 N_1)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) N_1))) )) 18.92/17.94 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.94 ) 18.92/17.94 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (one_one real))) (forall ((X $$unsorted)) (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) _let_3))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (abs_abs real) (hAPP real real (hAPP real _let_2 (minus_minus real) (hAPP real real ln (hAPP real real (hAPP real _let_2 (plus_plus real) _let_3) 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))))))) ))))) 18.92/17.94 ( pi ) 18.92/17.94 ( (hAPP int real (number_number_of real) min_1) ) 18.92/17.94 ( (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)))) ) 18.92/17.94 ( (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)))) ) 18.92/17.94 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.94 ( skv_6 ) 18.92/17.94 ( skv_11 ) 18.92/17.94 ( skv_12 ) 18.92/17.94 ( skv_14 ) 18.92/17.94 ) 18.92/17.94 (instantiation (let ((_let_0 (even_odd_even int))) (forall ((Y $$unsorted) (X $$unsorted)) (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))))) )) 18.92/17.95 ( (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) ) 18.92/17.95 ( (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)))) ) 18.92/17.95 ) 18.92/17.95 (instantiation (let ((_let_0 (fun real bool))) (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_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP X_a real (norm_norm X_a) (hAPP real X_a (of_real X_a) X_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real (norm_norm real) X_2)) K_2))) )) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) K_2)))) ))) )) 18.92/17.95 ( real ) 18.92/17.95 ( complex ) 18.92/17.95 ) 18.92/17.95 (instantiation (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP nat bool prime 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18.92/17.95 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 18.92/17.95 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 18.92/17.95 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 18.92/17.95 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 18.92/17.95 ) 18.92/17.95 (instantiation (forall ((N $$unsorted)) (= (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) N)) (hAPP real int (archim2085082626_floor real) (hAPP real real (uminus_uminus real) (hAPP nat real (real_1 nat) N)))) ) 18.92/17.95 ( (zero_zero nat) ) 18.92/17.95 ( (hAPP nat nat suc (zero_zero nat)) ) 18.92/17.95 ( (one_one nat) ) 18.92/17.95 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.95 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.92/17.95 ) 18.92/17.95 (instantiation (let ((_let_0 (fun nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_135841 $$unsorted) (BOUND_VARIABLE_135842 $$unsorted)) (or (not (comm_monoid_add X_a)) (not (t2_space X_a)) (not (hBOOL (hAPP X_a bool (hAPP _let_0 (fun X_a bool) (sums X_a) BOUND_VARIABLE_135841) BOUND_VARIABLE_135842))) (= (hAPP _let_0 X_a (suminf X_a) BOUND_VARIABLE_135841) (ti X_a BOUND_VARIABLE_135842))) )) 18.92/17.95 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 18.92/17.95 ) 18.92/17.95 (instantiation (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun X_b bool))) (let ((_let_2 (finite_finite_1 X_b))) (let ((_let_3 (collect X_b))) (let ((_let_4 (fun X_a bool))) (let ((_let_5 (fun X_b _let_4))) (let ((_let_6 (fun _let_4 _let_4))) (let ((_let_7 (fun X_a _let_0))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted)) (or (not (hBOOL (hAPP _let_4 bool (finite_finite_1 X_a) (hAPP _let_4 _let_4 (collect X_a) P_1)))) (= (forall ((Y_2 $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 Y_2))) (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_1 _let_1 _let_3 (hAPP X_a _let_1 (hAPP _let_5 (fun X_a _let_1) (combc X_b X_a bool) Q_1) Y_2))))) ) (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_1 _let_1 _let_3 (hAPP _let_5 _let_1 (hAPP (fun _let_4 bool) (fun _let_5 _let_1) (combb _let_4 bool X_b) (fEx X_a)) (hAPP _let_5 _let_5 (hAPP _let_6 (fun _let_5 _let_5) (combb _let_4 _let_4 X_b) (hAPP _let_7 _let_6 (combs X_a bool bool) (hAPP _let_4 _let_7 (hAPP (fun bool _let_0) (fun _let_4 _let_7) (combb bool _let_0 X_a) fconj) P_1))) Q_1))))))) ))))))))) 18.92/17.95 ( int, int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun int _let_2))) (hAPP int _let_2 (hAPP _let_5 _let_5 (combc int int _let_0) (hAPP _let_5 _let_5 (hAPP (fun _let_2 _let_2) (fun _let_5 _let_5) (combb _let_2 _let_2 int) (combc int int bool)) (hAPP _let_4 _let_5 (hAPP _let_3 (fun _let_4 _let_5) (combb _let_1 _let_2 int) (hAPP _let_2 _let_3 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int)))))))), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 18.92/17.95 ( (product_prod int int), (product_prod int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (product_snd int int))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun _let_2 int))) (let ((_let_6 (fun _let_5 (fun _let_2 bool)))) (let ((_let_7 (fun _let_2 _let_0))) (let ((_let_8 (fun _let_5 _let_7))) (let ((_let_9 (fun _let_2 _let_1))) (let ((_let_10 (fun _let_5 _let_5))) (let ((_let_11 (fun _let_2 _let_5))) (let ((_let_12 (fun _let_2 _let_6))) (let ((_let_13 (fun _let_2 _let_7))) (let ((_let_14 (fun _let_2 _let_10))) (let ((_let_15 (fun _let_5 _let_11))) (let ((_let_16 (hAPP _let_5 _let_9 (hAPP (fun int _let_1) (fun _let_5 _let_9) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_17 (fun int _let_5))) (hAPP _let_11 _let_4 (hAPP _let_12 (fun _let_11 _let_4) (combs _let_2 _let_5 (fun _let_2 bool)) (hAPP _let_13 _let_12 (hAPP (fun _let_7 _let_6) (fun _let_13 _let_12) (combb _let_7 _let_6 _let_2) (combs _let_2 int bool)) (hAPP _let_11 _let_13 (hAPP _let_8 (fun _let_11 _let_13) (combb _let_5 _let_7 _let_2) (hAPP (fun int _let_0) _let_8 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_5 _let_11 (hAPP _let_14 _let_15 (combc _let_2 _let_5 _let_5) (hAPP _let_9 _let_14 (hAPP (fun _let_1 _let_10) (fun _let_9 _let_14) (combb _let_1 _let_10 _let_2) (combb int int _let_2)) _let_16)) _let_3)))) (hAPP _let_5 _let_11 (hAPP _let_17 _let_15 (combb int _let_5 _let_2) (hAPP _let_9 _let_17 (combc _let_2 int int) _let_16)) _let_3)))))))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 int))) (let ((_let_4 (fun _let_1 _let_0))) (hAPP _let_2 _let_2 (hAPP (fun bool bool) (fun _let_2 _let_2) (combb bool bool _let_1) fNot) (hAPP int _let_2 (hAPP _let_4 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_3 _let_4 (hAPP (fun int _let_0) (fun _let_3 _let_4) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int)))))))) ) 18.92/17.95 ) 18.92/17.95 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (ord_less int))) (let ((_let_3 (fun _let_0 bool))) (let ((_let_4 (member int))) (forall ((Ta $$unsorted) (A_3 $$unsorted) (D_2 $$unsorted) (BOUND_VARIABLE_136098 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (zero_zero int)) D_2))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_3 _let_4 Ta) A_3))) (not (forall ((Xa $$unsorted) (BOUND_VARIABLE_136065 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_3 _let_4 Xa) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastAtMost int) (one_one int)) D_2)))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_3 _let_4 BOUND_VARIABLE_136065) A_3))) (not (= (hAPP int int (hAPP int _let_1 (minus_minus int) BOUND_VARIABLE_136065) Xa) (ti int BOUND_VARIABLE_136098)))) )) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 BOUND_VARIABLE_136098) Ta))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_1 (plus_plus int) BOUND_VARIABLE_136098) D_2)) Ta))) )))))) 18.92/17.95 ( (one_one int), zEven, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 18.92/17.95 ) 18.92/17.95 (instantiation (let ((_let_0 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_136132 $$unsorted) (BOUND_VARIABLE_136133 $$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) BOUND_VARIABLE_136132) BOUND_VARIABLE_136133)) (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_136132)) (hAPP int X_a _let_0 BOUND_VARIABLE_136133))))) )) 18.92/17.95 ( int, pls, pls ) 18.92/17.95 ( int, pls, (hAPP int int bit1 pls) ) 18.92/17.95 ( int, pls, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.92/17.95 ( int, pls, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.92/17.95 ) 18.92/17.95 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_1) zEven))) (= (hAPP int int (hAPP int _let_1 (times_times int) _let_2) (hAPP int int (hAPP int _let_1 (div_div int) X_1) _let_2)) (ti int X_1))) )))) 18.92/17.95 ( pls ) 18.92/17.95 ( m ) 18.92/17.95 ( (one_one int) ) 18.92/17.95 ( min_1 ) 18.92/17.95 ( s ) 18.92/17.95 ( s1 ) 18.92/17.95 ( t ) 18.92/17.95 ) 18.92/17.95 (instantiation (let ((_let_0 (product_prod int int))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP int bool twoSqu1091635170sum2sq X_1)) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (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 X_1))) ))) )) 18.92/17.96 ( (let ((_let_0 (fun int int))) (let ((_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))) ) 18.92/17.96 ) 18.92/17.96 (instantiation (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_136184))) (let ((_let_3 (= _let_1 (ti X_a BOUND_VARIABLE_136186)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_136184 $$unsorted) (BOUND_VARIABLE_136185 $$unsorted) (BOUND_VARIABLE_136186 $$unsorted)) (or (not (number X_a)) (not (field_inverse_zero X_a)) (= (= _let_2 (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_136185) BOUND_VARIABLE_136186)) (and (or (not _let_3) (= _let_1 _let_2)) (or _let_3 (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) _let_2) BOUND_VARIABLE_136186) (ti X_a BOUND_VARIABLE_136185)))))) ))))) 18.92/17.96 ( 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))) ) 18.92/17.96 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.96 ( real, min_1, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.96 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.96 ( 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 int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.96 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 18.92/17.96 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP 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 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))) ) 18.92/17.96 ) 18.92/17.96 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_136281 $$unsorted) (BOUND_VARIABLE_136282 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_136282))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_136281) _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_136282) BOUND_VARIABLE_136281)) _let_2))) )))) 18.92/17.96 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 18.92/17.96 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.92/17.96 ( 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))) ) 18.92/17.96 ( 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)))) ) 18.92/17.96 ( 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)))) ) 18.92/17.96 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 18.92/17.96 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 18.92/17.96 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 18.92/17.96 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 18.92/17.96 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 18.92/17.96 ( 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) ) 18.92/17.96 ) 18.92/17.96 (instantiation (let ((_let_0 (archimedean_ceiling X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_136309 $$unsorted) (BOUND_VARIABLE_136310 $$unsorted)) (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_136309) BOUND_VARIABLE_136310))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int _let_0 BOUND_VARIABLE_136309)) (hAPP X_a int _let_0 BOUND_VARIABLE_136310)))) )) 18.92/17.96 ( real, (zero_zero real), pi ) 18.92/17.96 ( 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)))) ) 18.92/17.96 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.96 ( real, (zero_zero real), skv_6 ) 18.92/17.96 ( real, (zero_zero real), skv_11 ) 18.92/17.96 ( real, (zero_zero real), skv_12 ) 18.92/17.96 ( real, (zero_zero real), skv_14 ) 18.92/17.96 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.92/17.96 ( real, (hAPP real real (hAPP real (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))) ) 18.92/17.96 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.92/17.96 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.96 ( int, (zero_zero int), (one_one int) ) 18.92/17.96 ( int, (zero_zero int), min_1 ) 18.92/17.96 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.96 ( int, (zero_zero int), s ) 18.92/17.96 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 18.92/17.96 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.92/17.96 ( int, (zero_zero int), skv_3 ) 18.92/17.96 ( int, (zero_zero int), skv_9 ) 18.92/17.96 ( int, (one_one int), t ) 18.92/17.96 ( int, min_1, pls ) 18.92/17.96 ( int, min_1, min_1 ) 18.92/17.96 ) 18.92/17.96 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (hAPP (fun int _let_0) _let_0 (accp int) quickc1265749348ro_rel))) (forall ((P_1 $$unsorted) (A0 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_2 A0))) (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_2 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))) )))) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 18.92/17.96 ( (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))) ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 18.92/17.96 ( (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))) ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_3 ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_9 ) 18.92/17.96 ( 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))) ) 18.92/17.96 ( zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 18.92/17.96 ( (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))) ) 18.92/17.96 ( nat_neg, (one_one int) ) 18.92/17.96 ( nat_neg, (hAPP int int (number_number_of int) min_1) ) 18.92/17.96 ( nat_neg, (hAPP int int (number_number_of int) pls) ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less int) pls), (zero_zero int) ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 18.92/17.96 ( nat_is_nat, (zero_zero int) ) 18.92/17.96 ( nat_is_nat, (one_one int) ) 18.92/17.96 ( nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.96 ( nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.92/17.96 ( (even_odd_even int), (zero_zero int) ) 18.92/17.96 ( (even_odd_even int), (one_one int) ) 18.92/17.96 ( 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))) ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))), (zero_zero int) ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less int) min_1), (zero_zero int) ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 18.92/17.96 ( (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 18.92/17.96 ( (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))) ) 18.92/17.96 ( (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))) ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 18.92/17.96 ( (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/17.96 ( (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less int) t), (zero_zero int) ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less int) t), (one_one int) ) 18.92/17.96 ( (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))) ) 18.92/17.96 ( (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/17.96 ( (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/17.96 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun int bool) (ord_less 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)))), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less int) skv_3), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/17.96 ( (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_3)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/17.96 ( (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_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/17.96 ( (hAPP int (fun int bool) (ord_less int) skv_9), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/17.96 ( (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_9)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/17.97 ) 18.92/17.97 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_136457 $$unsorted) (BOUND_VARIABLE_136458 $$unsorted)) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_136457) BOUND_VARIABLE_136458))) (= (= (ti X_a BOUND_VARIABLE_136457) (ti X_a BOUND_VARIABLE_136458)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_136458) BOUND_VARIABLE_136457)))) ))) 18.92/17.97 ( real, (zero_zero real), pi ) 18.92/17.97 ( 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)))) ) 18.92/17.97 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.97 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.97 ( real, (zero_zero real), skv_6 ) 18.92/17.97 ( real, (zero_zero real), skv_11 ) 18.92/17.97 ( real, (zero_zero real), skv_12 ) 18.92/17.97 ( real, (zero_zero real), skv_14 ) 18.92/17.97 ( real, pi, (zero_zero real) ) 18.92/17.97 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.97 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.92/17.97 ( 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)))) ) 18.92/17.97 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 18.92/17.97 ( real, (hAPP real real (hAPP 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) ) 18.92/17.97 ( real, (hAPP real real (hAPP real (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))) ) 18.92/17.97 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.92/17.97 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.92/17.97 ( real, skv_6, (zero_zero real) ) 18.92/17.97 ( real, skv_11, (zero_zero real) ) 18.92/17.97 ( real, skv_12, (zero_zero real) ) 18.92/17.97 ( real, skv_14, (zero_zero real) ) 18.92/17.97 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.97 ( int, (zero_zero int), (one_one int) ) 18.92/17.97 ( int, (zero_zero int), min_1 ) 18.92/17.97 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.97 ( int, (zero_zero int), s ) 18.92/17.97 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 18.92/17.97 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.92/17.97 ( int, (zero_zero int), skv_3 ) 18.92/17.97 ( int, (zero_zero int), skv_9 ) 18.92/17.97 ( int, pls, min_1 ) 18.92/17.97 ( int, (one_one int), (zero_zero int) ) 18.92/17.97 ( int, (one_one int), t ) 18.92/17.97 ( int, min_1, (zero_zero int) ) 18.92/17.97 ( int, min_1, pls ) 18.92/17.97 ( int, min_1, min_1 ) 18.92/17.97 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 18.92/17.97 ( int, s, (zero_zero int) ) 18.92/17.97 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 18.92/17.97 ( int, t, (one_one int) ) 18.92/17.97 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 18.92/17.97 ( int, skv_3, (zero_zero int) ) 18.92/17.97 ( int, skv_9, (zero_zero int) ) 18.92/17.97 ) 18.92/17.97 (instantiation (let ((_let_0 (one_one int))) (let ((_let_1 (uminus_uminus int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (hAPP int int (number_number_of int) W))) (forall ((W $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_3) (zero_zero int)))) (= (hAPP _let_2 int (product_snd int int) (hAPP _let_2 _let_2 negateSnd (hAPP int _let_2 (hAPP int (fun int _let_2) negDivAlg (hAPP int int _let_1 _let_0)) (hAPP int int _let_1 _let_3)))) (hAPP int int (hAPP int (fun int int) (div_mod int) _let_0) _let_3))) ))))) 18.92/17.97 ( pls ) 18.92/17.97 ( (hAPP int int bit1 pls) ) 18.92/17.97 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.92/17.97 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.97 ( min_1 ) 18.92/17.97 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.92/17.97 ) 18.92/17.97 (instantiation (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V_3) pls)))) (let ((_let_2 (hAPP int nat _let_0 V))) (let ((_let_3 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) _let_2) (hAPP int nat _let_0 V_3)))) (forall ((V_3 $$unsorted) (V $$unsorted)) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V) pls)) (and (or _let_1 (= _let_3 (hAPP int nat _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) V) V_3)))) (or (not _let_1) (= _let_2 _let_3)))) ))))) 18.92/17.97 ( (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 18.92/17.97 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 18.92/17.97 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.97 ) 18.92/17.97 (instantiation (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP int nat _let_0 V_3))) (forall ((V_3 $$unsorted) (V $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V) pls))) (= _let_1 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat _let_0 V)) _let_1))) ))) 18.92/17.97 ( (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 18.92/17.97 ) 18.92/17.97 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP real _let_0 log (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X))) (= (hAPP real real _let_1 X) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real _let_1 (hAPP real real (exp real) (one_one real)))) (hAPP real real ln X)))) ))) 18.92/17.97 ( (one_one real) ) 18.92/17.97 ( pi ) 18.92/17.97 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.97 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.97 ( skv_2 ) 18.92/17.97 ( skv_10 ) 18.92/17.97 ( skv_13 ) 18.92/17.97 ) 18.92/17.97 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_136524 $$unsorted) (BOUND_VARIABLE_136525 $$unsorted)) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_136524) BOUND_VARIABLE_136525))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_136525) BOUND_VARIABLE_136524)))) ))) 18.92/17.97 ( real, (zero_zero real), pi ) 18.92/17.97 ( 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)))) ) 18.92/17.97 ( 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))))) ) 18.92/17.97 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.97 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.97 ( real, (zero_zero real), skv_2 ) 18.92/17.97 ( real, (zero_zero real), skv_10 ) 18.92/17.97 ( real, (zero_zero real), skv_13 ) 18.92/17.97 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.97 ( real, pi, (zero_zero real) ) 18.92/17.97 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.97 ( 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)) ) 18.92/17.97 ( 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)))) ) 18.92/17.97 ( real, (hAPP real real (hAPP 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) ) 18.92/17.97 ( real, (hAPP real real (hAPP real (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))) ) 18.92/17.97 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 18.92/17.97 ( 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) ) 18.92/17.97 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.92/17.97 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.92/17.97 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 18.92/17.97 ( 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 ) 18.92/17.97 ( real, skv_2, (zero_zero real) ) 18.92/17.97 ( real, skv_10, (zero_zero real) ) 18.92/17.97 ( real, skv_13, (zero_zero real) ) 18.92/17.97 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.97 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 18.92/17.97 ( int, (zero_zero int), (zero_zero int) ) 18.92/17.97 ( int, (zero_zero int), (one_one int) ) 18.92/17.97 ( 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))) ) 18.92/17.97 ( int, (zero_zero int), min_1 ) 18.92/17.97 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 18.92/17.97 ( int, (zero_zero int), t ) 18.92/17.97 ( int, (one_one int), (zero_zero int) ) 18.92/17.97 ( int, (one_one int), t ) 18.92/17.97 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 18.92/17.97 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 18.92/17.97 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 18.92/17.97 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_3 ) 18.92/17.97 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_9 ) 18.92/17.97 ( int, min_1, (zero_zero int) ) 18.92/17.97 ( int, min_1, min_1 ) 18.92/17.97 ( 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))) ) 18.92/17.97 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 18.92/17.97 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 18.92/17.97 ( int, t, (zero_zero int) ) 18.92/17.97 ( int, t, (one_one int) ) 18.92/17.97 ( 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))) ) 18.92/17.97 ( 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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 18.92/17.97 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/17.97 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/17.97 ) 18.92/17.97 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_136550 $$unsorted) (BOUND_VARIABLE_136551 $$unsorted)) (or (not (order X_a)) (= (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_136550) BOUND_VARIABLE_136551)) (not (= (ti X_a BOUND_VARIABLE_136551) (ti X_a BOUND_VARIABLE_136550)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_136550) BOUND_VARIABLE_136551)))) )) 18.92/17.97 ( real, (zero_zero real), pi ) 18.92/17.97 ( 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)))) ) 18.92/17.97 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.97 ( real, (zero_zero real), skv_2 ) 18.92/17.97 ( real, (zero_zero real), skv_6 ) 18.92/17.97 ( real, (zero_zero real), skv_10 ) 18.92/17.97 ( real, (zero_zero real), skv_11 ) 18.92/17.97 ( real, (zero_zero real), skv_12 ) 18.92/17.97 ( real, (zero_zero real), skv_13 ) 18.92/17.97 ( real, (zero_zero real), skv_14 ) 18.92/17.97 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.97 ( real, pi, (zero_zero real) ) 18.92/17.97 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.97 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.92/17.97 ( real, (hAPP real real (hAPP real (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))) ) 18.92/17.97 ( 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) ) 18.92/17.97 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.92/17.97 ( 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 ) 18.92/17.97 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.97 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.97 ( int, (zero_zero int), (zero_zero int) ) 18.92/17.98 ( int, (zero_zero int), (one_one int) ) 18.92/17.98 ( 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))) ) 18.92/17.98 ( int, (zero_zero int), min_1 ) 18.92/17.98 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.98 ( int, (zero_zero int), s ) 18.92/17.98 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 18.92/17.98 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.92/17.98 ( int, (zero_zero int), skv_3 ) 18.92/17.98 ( int, (zero_zero int), skv_9 ) 18.92/17.98 ( int, (one_one int), t ) 18.92/17.98 ( int, min_1, (zero_zero int) ) 18.92/17.98 ( int, min_1, pls ) 18.92/17.98 ( int, min_1, min_1 ) 18.92/17.98 ( 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))) ) 18.92/17.98 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 18.92/17.98 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 18.92/17.98 ( int, t, (zero_zero int) ) 18.92/17.98 ( int, t, (one_one int) ) 18.92/17.98 ( 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))) ) 18.92/17.98 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/17.98 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/17.98 ) 18.92/17.98 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((X $$unsorted)) (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)))) ))) 18.92/17.98 ( (zero_zero real) ) 18.92/17.98 ( pi ) 18.92/17.98 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.98 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.98 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.92/17.98 ( (hAPP real real (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))))) ) 18.92/17.98 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 18.92/17.98 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.98 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.98 ( (hAPP real 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))))) ) 18.92/17.98 ( (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)))) ) 18.92/17.98 ( skv_6 ) 18.92/17.98 ( skv_11 ) 18.92/17.98 ( skv_12 ) 18.92/17.98 ( skv_14 ) 18.92/17.98 ) 18.92/17.98 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_136636))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_136636 $$unsorted) (BOUND_VARIABLE_136637 $$unsorted) (BOUND_VARIABLE_136638 $$unsorted)) (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_136638))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_136637))) (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_136638) BOUND_VARIABLE_136637)))) )) 18.92/17.98 ( nat, (zero_zero nat), (one_one nat), (one_one nat) ) 18.92/17.98 ( 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) ) 18.92/17.98 ( 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) ) 18.92/17.98 ( 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) ) 18.92/17.98 ( int, skv_3, (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) ) 18.92/17.98 ( int, skv_9, (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) ) 18.92/17.98 ) 18.92/17.98 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (power_power real))) (let ((_let_3 (one_one real))) (let ((_let_4 (combc nat nat nat))) (let ((_let_5 (fun nat _let_0))) (let ((_let_6 (fun _let_1 _let_1))) (let ((_let_7 (combs nat real real))) (let ((_let_8 (fun (fun nat nat) _let_1))) (let ((_let_9 (combb nat real nat))) (let ((_let_10 (hAPP (fun real _let_0) (fun _let_1 _let_5) (combb real _let_0 nat) (times_times real)))) (let ((_let_11 (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) _let_4 (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_4 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) X_1)) _let_3))) (= (hAPP _let_1 real (suminf real) (hAPP _let_1 _let_1 (hAPP _let_5 _let_6 _let_7 (hAPP _let_1 _let_5 _let_10 (hAPP real _let_1 _let_2 (hAPP int real (number_number_of real) min_1)))) (hAPP _let_1 _let_1 (hAPP _let_5 _let_6 _let_7 (hAPP _let_1 _let_5 _let_10 (hAPP _let_1 _let_1 (hAPP _let_0 _let_6 (combb real real nat) (hAPP real _let_0 (inverse_divide real) _let_3)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_8 _let_9 (real_1 nat)) _let_11)))) (hAPP _let_0 _let_1 (hAPP _let_1 _let_8 _let_9 (hAPP real _let_1 _let_2 X_1)) _let_11)))) (hAPP real real arctan X_1)))) ))))))))))))) 18.92/17.98 ( (zero_zero real) ) 18.92/17.98 ( (one_one real) ) 18.92/17.98 ( (hAPP int real (number_number_of real) min_1) ) 18.92/17.98 ( (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)))) ) 18.92/17.98 ( (hAPP real real (hAPP 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))))) ) 18.92/17.98 ( (hAPP real real (hAPP 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)))))))))) ) 18.92/17.98 ) 18.92/17.98 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_136665 $$unsorted)) (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_136665) _let_0))) )) 18.92/17.98 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.98 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.98 ( 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))))) ) 18.92/17.98 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.98 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/17.98 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.98 ( complex, ii ) 18.92/17.98 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.98 ( 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)) ) 18.92/17.98 ) 18.92/17.98 (instantiation (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (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 _let_2 A_1))) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 X_2))) (not (= A_1 (hAPP nat real (hAPP real _let_0 _let_1 X_2) N))) (not (forall ((Y_2 $$unsorted)) (or (not (= A_1 (hAPP nat real (hAPP real _let_0 _let_1 Y_2) N))) (not (hBOOL (hAPP real bool _let_2 Y_2))) (= X_2 Y_2)) ))) ))) )))) 18.92/17.98 ( (hAPP real real (hAPP real (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))) ) 18.92/17.98 ) 18.92/17.98 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (let ((_let_3 (filter X_a))) (let ((_let_4 (fun _let_3 bool))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_136877 $$unsorted) (BOUND_VARIABLE_136878 $$unsorted) (BOUND_VARIABLE_136879 $$unsorted)) (or (not (metric_space X_a)) (not (metric_space X_b)) (= (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 R_2))) (not (forall ((S_1 $$unsorted)) (or (not (forall ((X_2 $$unsorted)) (or (= (ti X_a X_2) (ti X_a BOUND_VARIABLE_136879)) (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_2) BOUND_VARIABLE_136879)) S_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_b real (hAPP X_b (fun X_b real) (dist_dist X_b) (hAPP X_a X_b BOUND_VARIABLE_136877 X_2)) BOUND_VARIABLE_136878)) R_2))) )) (not (hBOOL (hAPP real bool _let_2 S_1)))) ))) ) (hBOOL (hAPP _let_3 bool (hAPP X_b _let_4 (hAPP (fun X_a X_b) (fun X_b _let_4) (tendsto X_a X_b) BOUND_VARIABLE_136877) BOUND_VARIABLE_136878) (hAPP X_a _let_3 (at X_a) BOUND_VARIABLE_136879))))) )))))) 18.92/17.98 ( 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)))) ) 18.92/17.98 ) 18.92/17.98 (instantiation (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))))) (forall ((Z_1 $$unsorted)) (= (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) Z_1) (hAPP complex complex cnj Z_1)) (hAPP real complex (of_real complex) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP complex real re Z_1)) _let_2)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP complex real im Z_1)) _let_2)))) )))) 18.92/17.98 ( ii ) 18.92/17.98 ( (zero_zero complex) ) 18.92/17.98 ( (one_one complex) ) 18.92/17.98 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.98 ( (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 18.92/17.98 ) 18.92/17.98 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X) Y))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP real nat natceiling X)) (hAPP real nat natceiling Y)))) ) 18.92/17.98 ( (zero_zero real), pi ) 18.92/17.98 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.98 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.98 ( (zero_zero real), skv_6 ) 18.92/17.98 ( (zero_zero real), skv_11 ) 18.92/17.98 ( (zero_zero real), skv_12 ) 18.92/17.98 ( (zero_zero real), skv_14 ) 18.92/17.98 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.92/17.98 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.98 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.92/17.98 ( skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.98 ) 18.92/17.98 (instantiation (let ((_let_0 (fun int bool))) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) B_1) (hAPP int _let_0 d22set A_2)))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B_1) A_2))) )) 18.92/17.98 ( (zero_zero int), (one_one int) ) 18.92/17.98 ( (zero_zero int), min_1 ) 18.92/17.98 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.98 ( (zero_zero int), s ) 18.92/17.98 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 18.92/17.98 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.92/17.98 ( (zero_zero int), skv_3 ) 18.92/17.98 ( (zero_zero int), skv_9 ) 18.92/17.98 ( (one_one int), t ) 18.92/17.98 ( min_1, pls ) 18.92/17.98 ( min_1, min_1 ) 18.92/17.98 ) 18.92/17.98 (instantiation (forall ((X $$unsorted)) (= (hAPP real real cos X) (hAPP real real cos (hAPP real real (uminus_uminus real) X))) ) 18.92/17.98 ( (one_one real) ) 18.92/17.98 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.98 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 18.92/17.98 ) 18.92/17.98 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_136993 $$unsorted)) (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_136993) _let_0))) )) 18.92/17.98 ( real, (one_one real) ) 18.92/17.98 ( real, pi ) 18.92/17.98 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.92/17.98 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 18.92/17.98 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.99 ) 18.92/17.99 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_137012 $$unsorted) (BOUND_VARIABLE_137013 $$unsorted)) (or (not (ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_137012) (hAPP X_a X_a _let_2 BOUND_VARIABLE_137013)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_137012)) BOUND_VARIABLE_137013))) )))) 18.92/17.99 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 18.92/17.99 ) 18.92/17.99 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (fun (fun int bool) bool))) (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool zprime P_4))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) P_4))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_2) (zero_zero int)) P_4)) (hBOOL (hAPP int bool (hAPP int _let_0 quadRes P_4) A_2)) (= (hAPP int int (hAPP int _let_0 (div_div int) (hAPP int int (hAPP int _let_0 (minus_minus int) P_4) (one_one int))) _let_1) (hAPP nat int (semiring_1_of_nat int) (hAPP _let_2 nat (finite_card _let_0) (hAPP int _let_2 (hAPP int (fun int _let_2) setS A_2) P_4)))))) )))) 18.92/17.99 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/17.99 ) 18.92/17.99 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (field_char_0_Rats X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_137056 $$unsorted)) (or (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_137056) _let_3))) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_137056)) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_137056)) _let_3))) ))))) 18.92/17.99 ( bool, fFalse ) 18.92/17.99 ( bool, fTrue ) 18.92/17.99 ( real, (zero_zero real) ) 18.92/17.99 ( real, pi ) 18.92/17.99 ( (fun nat bool), (even_odd_even nat) ) 18.92/17.99 ( (fun nat bool), prime ) 18.92/17.99 ( (fun nat nat), suc ) 18.92/17.99 ( (fun nat nat), (fact_fact nat) ) 18.92/17.99 ( (fun nat nat), (size_size nat) ) 18.92/17.99 ( (fun nat nat), fact ) 18.92/17.99 ( (fun nat nat), nat_size ) 18.92/17.99 ( int, pls ) 18.92/17.99 ( int, m ) 18.92/17.99 ( int, min_1 ) 18.92/17.99 ( int, s ) 18.92/17.99 ( int, s1 ) 18.92/17.99 ( int, t ) 18.92/17.99 ( (fun int bool), zprime ) 18.92/17.99 ( (fun int bool), nat_neg ) 18.92/17.99 ( (fun int bool), zEven ) 18.92/17.99 ( (fun int bool), nat_is_nat ) 18.92/17.99 ( (fun int bool), zOdd ) 18.92/17.99 ( (fun int bool), (even_odd_even int) ) 18.92/17.99 ( (fun int bool), twoSqu1091635170sum2sq ) 18.92/17.99 ( (fun int nat), nat_1 ) 18.92/17.99 ( (fun int nat), phi ) 18.92/17.99 ( (fun real real), sqrt ) 18.92/17.99 ( (fun real real), tan ) 18.92/17.99 ( (fun real real), cos ) 18.92/17.99 ( (fun real real), arccos ) 18.92/17.99 ( (fun real real), ln ) 18.92/17.99 ( (fun real real), sin ) 18.92/17.99 ( (fun real real), arctan ) 18.92/17.99 ( (fun real real), arcsin ) 18.92/17.99 ( complex, ii ) 18.92/17.99 ( (fun complex complex), cnj ) 18.92/17.99 ( (fun complex complex), expi ) 18.92/17.99 ( (fun nat real), (real_1 nat) ) 18.92/17.99 ( (fun nat real), cos_coeff ) 18.92/17.99 ( (fun nat real), sin_coeff ) 18.92/17.99 ( (fun int int), bit0 ) 18.92/17.99 ( (fun int int), bit1 ) 18.92/17.99 ( (fun int int), pred ) 18.92/17.99 ( (fun int int), succ ) 18.92/17.99 ( (fun int int), (fact_fact int) ) 18.92/17.99 ( (fun int int), zfact ) 18.92/17.99 ( (fun bool bool), fNot ) 18.92/17.99 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 18.92/17.99 ( (fun bool (fun bool bool)), fconj ) 18.92/17.99 ( (fun bool (fun bool bool)), fdisj ) 18.92/17.99 ( (fun bool (fun bool bool)), fimplies ) 18.92/17.99 ( (fun int (fun int bool)), sRStar ) 18.92/17.99 ( (fun int (fun int bool)), quadRes ) 18.92/17.99 ( (fun int (fun int bool)), norRRset ) 18.92/17.99 ( (fun int (fun int bool)), d22set ) 18.92/17.99 ( (fun int (fun int bool)), sr ) 18.92/17.99 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 18.92/17.99 ( (fun nat (fun nat nat)), nat_gcd ) 18.92/17.99 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 18.92/17.99 ( (fun nat (fun nat nat)), nat_lcm ) 18.92/17.99 ( (fun nat (fun real real)), root ) 18.92/17.99 ( (fun real (fun real real)), log ) 18.92/17.99 ( (fun real (fun real real)), powr ) 18.92/17.99 ( (fun nat (fun nat bool)), coprime ) 18.92/17.99 ( (fun (fun int bool) int), (the int) ) 18.92/17.99 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 18.92/17.99 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 18.92/17.99 ( (fun nat (fun nat (product_prod int int))), bezw ) 18.92/17.99 ( (fun (fun int bool) bool), nat_nat_set ) 18.92/17.99 ( (filter nat), sequentially ) 18.92/17.99 ( (fun (product_prod nat nat) bool), pred_nat ) 18.92/17.99 ( (fun (product_prod int int) bool), frac_1 ) 18.92/17.99 ( (fun real complex), cis ) 18.92/17.99 ( (fun complex real), im ) 18.92/17.99 ( (fun complex real), re ) 18.92/17.99 ( (fun complex real), arg ) 18.92/17.99 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 18.92/17.99 ( (fun int (fun int int)), int_gcd ) 18.92/17.99 ( (fun int (fun int int)), multInv ) 18.92/17.99 ( (fun int (fun int int)), legacy_zgcd ) 18.92/17.99 ( (fun int (fun int int)), z3mod ) 18.92/17.99 ( (fun int (fun int int)), inv ) 18.92/17.99 ( (fun int (fun int int)), (gcd_gcd int) ) 18.92/17.99 ( (fun int (fun int int)), standardRes ) 18.92/17.99 ( (fun int (fun int int)), legendre ) 18.92/17.99 ( (fun int (fun int int)), nat_tsub ) 18.92/17.99 ( (fun int (fun int int)), z3div ) 18.92/17.99 ( (fun int (fun int int)), int_lcm ) 18.92/17.99 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 18.92/17.99 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 18.92/17.99 ( (fun int (fun (fun int bool) bool)), rsetR ) 18.92/17.99 ( (fun int (fun (fun int bool) bool)), resSet ) 18.92/17.99 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 18.92/17.99 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 18.92/17.99 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 18.92/17.99 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 18.92/17.99 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 18.92/17.99 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 18.92/17.99 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 18.92/17.99 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 18.92/17.99 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 18.92/17.99 ( (fun int (fun int (product_prod int int))), negDivAlg ) 18.92/17.99 ( (fun int (fun int (product_prod int int))), divmod_int ) 18.92/17.99 ( (fun int (fun int (product_prod int int))), posDivAlg ) 18.92/17.99 ( (fun int (fun int (product_prod int int))), pdivmod ) 18.92/17.99 ( (fun int (fun int (product_prod int int))), norm_frac ) 18.92/17.99 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 18.92/17.99 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 18.92/17.99 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 18.92/17.99 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 18.92/17.99 ( (fun real nat), natfloor ) 18.92/17.99 ( (fun real nat), natceiling ) 18.92/17.99 ( (fun int quickcheck_code_int), quickcheck_of_int ) 18.92/17.99 ( (fun int (fun int (fun int bool))), wset ) 18.92/17.99 ( (fun int (fun int (fun int bool))), bnorRset ) 18.92/17.99 ( (fun int (fun int (fun int bool))), zcong ) 18.92/17.99 ( (fun int (fun int (fun int bool))), noXRRset ) 18.92/17.99 ( (fun int (fun int (fun int bool))), zcongm ) 18.92/17.99 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 18.92/17.99 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 18.92/17.99 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 18.92/17.99 ( (fun int real), (real_1 int) ) 18.92/17.99 ( (fun complex nat), (size_size complex) ) 18.92/17.99 ( (fun complex nat), complex_size ) 18.92/17.99 ( (fun int (list int)), quickc666637781d_zero ) 18.92/17.99 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 18.92/17.99 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 18.92/17.99 ( (fun (product_prod int int) rat), frct ) 18.92/17.99 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 18.92/17.99 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 18.92/17.99 ( (fun (fun nat rat) bool), vanishes ) 18.92/17.99 ( (fun int (fun int rat)), fract ) 18.92/17.99 ( (fun code_code_numeral int), code_int_of ) 18.92/17.99 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 18.92/17.99 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 18.92/17.99 ( (fun code_code_numeral nat), code_c271388182l_size ) 18.92/17.99 ( (fun real (fun real complex)), complex_1 ) 18.92/17.99 ( (fun real (fun real complex)), rcis ) 18.92/17.99 ( (fun int (fun nat nat)), nat_aux ) 18.92/17.99 ( (fun rat real), ratreal ) 18.92/17.99 ( (fun quickcheck_code_int int), quickcheck_int_of ) 18.92/17.99 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 18.92/17.99 ( (fun rat (product_prod int int)), quotient_of ) 18.92/17.99 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 18.92/17.99 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 18.92/17.99 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 18.92/17.99 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 18.92/17.99 ) 18.92/17.99 (instantiation (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)))) (forall ((N_1 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool _let_1 N_1))) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat nat_1 N_1)) (one_one nat)) (hAPP _let_0 nat (finite_card int) (hAPP _let_0 _let_0 (collect 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) _let_1)) (hAPP int _let_0 (hAPP _let_4 _let_4 (combc int int bool) _let_0) N_1))))))) )))))) 18.92/17.99 ( (zero_zero int) ) 18.92/17.99 ( (one_one int) ) 18.92/17.99 ( min_1 ) 18.92/17.99 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.99 ( s ) 18.92/17.99 ( (hAPP int int (number_number_of int) pls) ) 18.92/17.99 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.92/17.99 ( skv_3 ) 18.92/17.99 ( skv_9 ) 18.92/17.99 ) 18.92/17.99 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (number_number_of int) K_4) (ti int K_4)) ) 18.92/17.99 ( pls ) 18.92/17.99 ( (hAPP int int bit1 pls) ) 18.92/17.99 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.92/17.99 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.99 ( m ) 18.92/17.99 ( min_1 ) 18.92/17.99 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.92/17.99 ( s ) 18.92/17.99 ( s1 ) 18.92/17.99 ( t ) 18.92/17.99 ) 18.92/17.99 (instantiation (forall ((V $$unsorted)) (= (hAPP int real (number_number_of real) V) (hAPP complex real re (hAPP int complex (number_number_of complex) V))) ) 18.92/17.99 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 18.92/17.99 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.99 ( min_1 ) 18.92/17.99 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.99 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 18.92/17.99 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.92/17.99 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 18.92/17.99 ) 18.92/17.99 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real ln (hAPP real real (hAPP real (fun real real) (plus_plus real) (one_one real)) X))) X))) ))) 18.92/17.99 ( pi ) 18.92/17.99 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.99 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/17.99 ( skv_6 ) 18.92/17.99 ( skv_11 ) 18.92/17.99 ( skv_12 ) 18.92/17.99 ( skv_14 ) 18.92/17.99 ) 18.92/17.99 (instantiation (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_137233))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_137233 $$unsorted) (BOUND_VARIABLE_137234 $$unsorted)) (or (not (real_normed_algebra X_a)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_137234)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_137234)))) ))) 18.92/17.99 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 18.92/17.99 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 18.92/17.99 ( 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)))))) ) 18.92/17.99 ( 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 ) 18.92/17.99 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 18.92/17.99 ( 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) ) 18.92/17.99 ( 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))), pls ) 18.92/17.99 ( 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 ) 18.92/17.99 ( 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_1 ) 18.92/17.99 ( complex, ii, ii ) 18.92/17.99 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 18.92/17.99 ( 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 ) 18.92/17.99 ) 18.92/17.99 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137255 $$unsorted) (BOUND_VARIABLE_137256 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_137255)) BOUND_VARIABLE_137256)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (number_number_of int) BOUND_VARIABLE_137255)) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_137256))))) ) 18.92/17.99 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), pi ) 18.92/17.99 ( int, pls, (one_one int) ) 18.92/17.99 ( int, pls, min_1 ) 18.92/17.99 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/17.99 ( int, pls, s ) 18.92/17.99 ( int, pls, (hAPP int int (number_number_of int) pls) ) 18.92/17.99 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.92/17.99 ( int, pls, skv_3 ) 18.92/17.99 ( int, pls, skv_9 ) 18.92/17.99 ( int, (hAPP int int bit1 pls), t ) 18.92/17.99 ) 18.92/17.99 (instantiation (let ((_let_0 (uminus_uminus real))) (forall ((X $$unsorted)) (= (hAPP real real sqrt (hAPP real real _let_0 X)) (hAPP real real _let_0 (hAPP real real sqrt X))) )) 18.92/17.99 ( (one_one real) ) 18.92/17.99 ) 18.92/17.99 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (ring_1_of_int real))) (let ((_let_5 (fun int (fun int int)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun int _let_1))) (forall ((X_1 $$unsorted)) (let ((_let_0 (fun int int))) (= (hAPP _let_0 int (the int) (hAPP _let_0 _let_0 (hAPP _let_3 (fun _let_0 _let_0) (combs int bool bool) (hAPP _let_0 _let_3 (hAPP (fun bool _let_2) (fun _let_0 _let_3) (combb bool _let_2 int) fconj) (hAPP real _let_0 (hAPP _let_7 (fun real _let_0) (combc int real bool) (hAPP _let_6 _let_7 (hAPP (fun real _let_1) (fun _let_6 _let_7) (combb real _let_1 int) (ord_less_eq real)) _let_4)) X_1))) (hAPP _let_6 _let_0 (hAPP _let_1 (fun _let_6 _let_0) (combb real bool int) (hAPP real _let_1 (ord_less real) X_1)) (hAPP _let_0 _let_6 (hAPP _let_6 (fun _let_0 _let_6) (combb int real int) _let_4) (hAPP int _let_0 (hAPP _let_5 _let_5 (combc int int int) (plus_plus int)) (one_one int)))))) (hAPP real int (archim2085082626_floor real) X_1))) ))))))))) 18.92/18.00 ( (zero_zero real) ) 18.92/18.00 ( (one_one real) ) 18.92/18.00 ( pi ) 18.92/18.00 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/18.00 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 18.92/18.00 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/18.00 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 18.92/18.00 ) 18.92/18.00 (instantiation (let ((_let_0 (uminus_uminus real))) (forall ((X $$unsorted)) (= (hAPP real real sin (hAPP real real _let_0 X)) (hAPP real real _let_0 (hAPP real real sin X))) )) 18.92/18.00 ( (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)))) ) 18.92/18.00 ) 18.92/18.00 (instantiation (let ((_let_0 (one_one X_a))) (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (= _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) _let_0) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) )) 18.92/18.00 ( bool ) 18.92/18.00 ( real ) 18.92/18.00 ( nat ) 18.92/18.00 ( (fun nat bool) ) 18.92/18.00 ( (fun nat nat) ) 18.92/18.00 ( int ) 18.92/18.00 ( (fun real real) ) 18.92/18.00 ( complex ) 18.92/18.00 ( (fun int int) ) 18.92/18.00 ( rat ) 18.92/18.00 ( (fun bool bool) ) 18.92/18.00 ( quickcheck_code_int ) 18.92/18.00 ( (fun nat (fun nat bool)) ) 18.92/18.00 ( (product_prod real real) ) 18.92/18.00 ( (product_prod int int) ) 18.92/18.00 ( (fun nat (product_prod int int)) ) 18.92/18.00 ( (product_prod nat nat) ) 18.92/18.00 ( (fun (product_prod nat nat) bool) ) 18.92/18.00 ( (fun nat (fun (product_prod nat nat) bool)) ) 18.92/18.00 ( (fun nat (product_prod nat nat)) ) 18.92/18.00 ( code_code_numeral ) 18.92/18.00 ) 18.92/18.00 (instantiation (let ((_let_0 (ord_less_eq int))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int (fun int bool)))) (forall ((N_1 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_0 _let_1) N_1))) (= (hAPP _let_0 nat (finite_card int) (hAPP _let_0 _let_0 (collect 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 int _let_0 (ord_less int) _let_1))) (hAPP int _let_0 (hAPP _let_4 _let_4 (combc int int bool) _let_0) N_1)))) (hAPP int nat nat_1 N_1)))) )))))) 18.92/18.00 ( (zero_zero int) ) 18.92/18.00 ( (one_one int) ) 18.92/18.00 ( min_1 ) 18.92/18.00 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/18.00 ( s ) 18.92/18.00 ( (hAPP int int (number_number_of int) pls) ) 18.92/18.00 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 18.92/18.00 ( skv_3 ) 18.92/18.00 ( skv_9 ) 18.92/18.00 ) 18.92/18.00 (instantiation (let ((_let_0 (semiring_1_of_nat int))) (forall ((X $$unsorted)) (= (hAPP int int (fact_fact int) (hAPP nat int _let_0 X)) (hAPP nat int _let_0 (hAPP nat nat (fact_fact nat) X))) )) 18.92/18.00 ( (zero_zero nat) ) 18.92/18.00 ( (hAPP nat nat suc (zero_zero nat)) ) 18.92/18.00 ) 18.92/18.00 (instantiation (let ((_let_0 (archim2085082626_floor X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_137567 $$unsorted) (BOUND_VARIABLE_137568 $$unsorted)) (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_137567)) (hAPP X_a int _let_0 BOUND_VARIABLE_137568)))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_137567) BOUND_VARIABLE_137568))) )) 18.92/18.00 ( real, (zero_zero real), pi ) 18.92/18.00 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/18.00 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/18.00 ( real, (zero_zero real), skv_2 ) 18.92/18.00 ( real, (zero_zero real), skv_10 ) 18.92/18.00 ( real, (zero_zero real), skv_13 ) 18.92/18.00 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/18.00 ( real, pi, (zero_zero real) ) 18.92/18.00 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 18.92/18.00 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/18.00 ( 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) ) 18.92/18.00 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 18.92/18.00 ( 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 ) 18.92/18.00 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 18.92/18.00 ( int, (zero_zero int), (zero_zero int) ) 18.92/18.00 ( int, (zero_zero int), (one_one int) ) 18.92/18.00 ( 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))) ) 18.92/18.00 ( int, (zero_zero int), min_1 ) 18.92/18.00 ( int, min_1, (zero_zero int) ) 18.92/18.00 ( int, min_1, min_1 ) 18.92/18.00 ( 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))) ) 18.92/18.00 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 18.92/18.00 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 18.92/18.00 ( int, t, (zero_zero int) ) 18.92/18.00 ( int, t, (one_one int) ) 18.92/18.00 ( 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))) ) 18.92/18.00 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/18.00 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 18.92/18.00 ) 18.92/18.00 (instantiation (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) M))) (forall ((M $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool _let_0 N))) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat suc N)))) )) 18.92/18.00 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 19.06/18.00 ) 19.06/18.00 (instantiation (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (= (one_one X_a) (hAPP nat X_a (semiring_1_of_nat X_a) (one_one nat)))) ) 19.06/18.00 ( real ) 19.06/18.00 ( nat ) 19.06/18.00 ( int ) 19.06/18.00 ( complex ) 19.06/18.00 ( rat ) 19.06/18.00 ( quickcheck_code_int ) 19.06/18.00 ( code_code_numeral ) 19.06/18.00 ) 19.06/18.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137627 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_137627))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) BOUND_VARIABLE_137627)))) ) 19.06/18.00 ( real, (zero_zero int) ) 19.06/18.00 ( real, (one_one int) ) 19.06/18.00 ) 19.06/18.00 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of nat))) (forall ((N $$unsorted)) (or (hBOOL (hAPP nat bool (even_odd_even nat) N)) (not (forall ((X_2 $$unsorted)) (not (= (hAPP nat nat (hAPP nat _let_0 (power_power nat) N) (hAPP int nat _let_2 _let_1)) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) (hAPP nat nat (hAPP nat _let_0 (times_times nat) (hAPP int nat _let_2 (hAPP int int bit0 _let_1))) X_2)) (one_one nat)))) ))) )))) 19.06/18.00 ( (zero_zero nat) ) 19.06/18.00 ( (one_one nat) ) 19.06/18.00 ) 19.06/18.00 (instantiation (let ((_let_0 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_137659 $$unsorted) (BOUND_VARIABLE_137660 $$unsorted)) (or (not (group_add X_a)) (= (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_137659) (hAPP X_a X_a _let_0 BOUND_VARIABLE_137660)) (= (ti X_a BOUND_VARIABLE_137659) (ti X_a BOUND_VARIABLE_137660)))) )) 19.06/18.00 ( real, (one_one real), (one_one real) ) 19.06/18.00 ( real, (one_one real), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 19.06/18.00 ( 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)))), (one_one real) ) 19.06/18.00 ( 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), (one_one real) ) 19.06/18.00 ( 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), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.00 ( int, pls, (one_one int) ) 19.06/18.00 ( int, pls, min_1 ) 19.06/18.00 ( int, (one_one int), pls ) 19.06/18.00 ( int, (one_one int), (one_one int) ) 19.06/18.00 ( int, min_1, (one_one int) ) 19.06/18.00 ( complex, ii, (one_one complex) ) 19.06/18.00 ( complex, (one_one complex), ii ) 19.06/18.00 ( complex, (one_one complex), (one_one complex) ) 19.06/18.00 ) 19.06/18.00 (instantiation (let ((_let_0 (semiring_1_of_nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_137728 $$unsorted) (BOUND_VARIABLE_137729 $$unsorted)) (or (not (linordered_semidom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_137728)) (hAPP nat X_a _let_0 BOUND_VARIABLE_137729))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) BOUND_VARIABLE_137728) BOUND_VARIABLE_137729)))) )) 19.06/18.00 ( int, (zero_zero nat), (zero_zero nat) ) 19.06/18.00 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 19.06/18.00 ( int, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.00 ( int, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.06/18.00 ) 19.06/18.00 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_137755 $$unsorted) (BOUND_VARIABLE_137756 $$unsorted)) (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_137755)) BOUND_VARIABLE_137756))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_137756)) BOUND_VARIABLE_137755))) )))) 19.06/18.00 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.00 ( 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) ) 19.06/18.00 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.06/18.00 ( 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), pi ) 19.06/18.00 ( int, (zero_zero int), pls ) 19.06/18.00 ( int, (zero_zero int), (one_one int) ) 19.06/18.00 ( int, pls, (zero_zero int) ) 19.06/18.00 ( int, pls, (one_one int) ) 19.06/18.00 ( 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))) ) 19.06/18.00 ( int, pls, min_1 ) 19.06/18.00 ( int, (one_one int), (zero_zero int) ) 19.06/18.00 ( int, (one_one int), pls ) 19.06/18.00 ( int, (one_one int), min_1 ) 19.06/18.00 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 19.06/18.00 ( int, min_1, pls ) 19.06/18.00 ( int, min_1, (one_one int) ) 19.06/18.00 ) 19.06/18.00 (instantiation (let ((_let_0 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_137813 $$unsorted) (BOUND_VARIABLE_137814 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_137813)) (hAPP int X_a _let_0 BOUND_VARIABLE_137814)) (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_137813) (hAPP int int (uminus_uminus int) BOUND_VARIABLE_137814))))) )) 19.06/18.00 ( code_code_numeral, pls, (hAPP int int bit1 pls) ) 19.06/18.00 ) 19.06/18.00 (instantiation (forall ((N $$unsorted)) (= (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) N) (hAPP real real cos (hAPP real real (hAPP real (fun real real) (times_times real) pi) (hAPP nat real (real_1 nat) N)))) ) 19.06/18.00 ( (zero_zero nat) ) 19.06/18.00 ( (one_one nat) ) 19.06/18.00 ) 19.06/18.00 (instantiation (let ((_let_0 (archimedean_ceiling X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_137863 $$unsorted) (BOUND_VARIABLE_137864 $$unsorted)) (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_137863)) (hAPP X_a int _let_0 BOUND_VARIABLE_137864)))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_137863) BOUND_VARIABLE_137864))) )) 19.06/18.00 ( real, (zero_zero real), pi ) 19.06/18.00 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.00 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.00 ( real, (zero_zero real), skv_2 ) 19.06/18.00 ( real, (zero_zero real), skv_10 ) 19.06/18.00 ( real, (zero_zero real), skv_13 ) 19.06/18.00 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.00 ( real, pi, (zero_zero real) ) 19.06/18.00 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.00 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.00 ( 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) ) 19.06/18.00 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.06/18.00 ( 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 ) 19.06/18.00 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.01 ( int, (zero_zero int), (zero_zero int) ) 19.06/18.01 ( int, (zero_zero int), (one_one int) ) 19.06/18.01 ( 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))) ) 19.06/18.01 ( int, (zero_zero int), min_1 ) 19.06/18.01 ( int, min_1, (zero_zero int) ) 19.06/18.01 ( int, min_1, min_1 ) 19.06/18.01 ( 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))) ) 19.06/18.01 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 19.06/18.01 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 19.06/18.01 ( int, t, (zero_zero int) ) 19.06/18.01 ( int, t, (one_one int) ) 19.06/18.01 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.06/18.01 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.06/18.01 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.06/18.01 ) 19.06/18.01 (instantiation (let ((_let_0 (fun X_b X_c))) (let ((_let_1 (fun X_a _let_0))) (let ((_let_2 (product_prod X_a X_b))) (let ((_let_3 (fun _let_2 X_c))) (let ((_let_4 (fun X_b _let_2))) (let ((_let_5 (fun X_a _let_4))) (let ((_let_6 (fun _let_4 _let_0))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (F $$unsorted)) (= (ti _let_3 F) (hAPP _let_1 _let_3 (product_prod_case X_a X_b X_c) (hAPP _let_5 _let_1 (hAPP _let_6 (fun _let_5 _let_1) (combb _let_4 _let_0 X_a) (hAPP _let_3 _let_6 (combb _let_2 X_c X_b) F)) (product_Pair X_a X_b)))) )))))))) 19.06/18.01 ( nat, nat, bool, pred_nat ) 19.06/18.01 ( nat, nat, (fun (product_prod nat nat) bool), nat_gcd_rel ) 19.06/18.01 ( int, int, bool, frac_1 ) 19.06/18.01 ( int, int, int, twoSqu1094008024sum2sq ) 19.06/18.01 ( int, int, rat, frct ) 19.06/18.01 ( int, int, (product_prod int int), normalize ) 19.06/18.01 ( int, int, (product_prod int int), negateSnd ) 19.06/18.01 ( int, int, (fun (product_prod int int) bool), lazy_small_lazy_rel ) 19.06/18.01 ( int, int, (fun (product_prod int int) bool), posDivAlg_rel ) 19.06/18.01 ( int, int, (fun (product_prod int int) bool), upto_rel ) 19.06/18.01 ( int, int, (fun (product_prod int int) bool), negDivAlg_rel ) 19.06/18.01 ( int, int, (fun (product_prod int int) bool), norm_frac_rel ) 19.06/18.01 ( (product_prod int int), (product_prod int int), bool, ratrel ) 19.06/18.01 ( (product_prod nat nat), (product_prod nat nat), bool, pair_less ) 19.06/18.01 ( (product_prod nat nat), (product_prod nat nat), bool, pair_leq ) 19.06/18.01 ) 19.06/18.01 (instantiation (let ((_let_0 (fun complex complex))) (forall ((Z_1 $$unsorted)) (= (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))) )) 19.06/18.01 ( ii ) 19.06/18.01 ( (zero_zero complex) ) 19.06/18.01 ( (one_one complex) ) 19.06/18.01 ) 19.06/18.01 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (fun int int))) (let ((_let_4 (plus_plus int))) (let ((_let_5 (times_times int))) (let ((_let_6 (ord_less int))) (let ((_let_7 (hAPP int int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_3 _let_5 B_5) Q_5)) R_5))) (forall ((B $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted) (B_5 $$unsorted) (Q_5 $$unsorted) (R_5 $$unsorted)) (or (not (= _let_7 (hAPP int int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_3 _let_5 B) Q_3)) R_4))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_6 _let_7) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_6 R_4) B))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) R_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_6 _let_2) B_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B_5) B))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Q_5) Q_3))) ))))))))) 19.06/18.01 ( (hAPP int int (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) ) 19.06/18.01 ) 19.06/18.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137959 $$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_137959))) (= (ti X_a BOUND_VARIABLE_137959) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_137959))) ) 19.06/18.01 ( bool, fFalse ) 19.06/18.01 ( bool, fTrue ) 19.06/18.01 ( real, pi ) 19.06/18.01 ( 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)))) ) 19.06/18.01 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.01 ( real, skv_6 ) 19.06/18.01 ( real, skv_11 ) 19.06/18.01 ( real, skv_12 ) 19.06/18.01 ( real, skv_14 ) 19.06/18.01 ( (fun nat bool), (even_odd_even nat) ) 19.06/18.01 ( (fun nat bool), prime ) 19.06/18.01 ( (fun nat nat), suc ) 19.06/18.01 ( (fun nat nat), (fact_fact nat) ) 19.06/18.01 ( (fun nat nat), (size_size nat) ) 19.06/18.01 ( (fun nat nat), fact ) 19.06/18.01 ( (fun nat nat), nat_size ) 19.06/18.01 ( int, pls ) 19.06/18.01 ( int, m ) 19.06/18.01 ( int, (one_one int) ) 19.06/18.01 ( int, min_1 ) 19.06/18.01 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.01 ( int, s ) 19.06/18.01 ( int, (hAPP int int (number_number_of int) pls) ) 19.06/18.01 ( int, s1 ) 19.06/18.01 ( int, t ) 19.06/18.01 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.06/18.01 ( int, skv_3 ) 19.06/18.01 ( int, skv_9 ) 19.06/18.01 ( (fun int bool), zprime ) 19.06/18.01 ( (fun int bool), nat_neg ) 19.06/18.01 ( (fun int bool), zEven ) 19.06/18.01 ( (fun int bool), nat_is_nat ) 19.06/18.01 ( (fun int bool), zOdd ) 19.06/18.01 ( (fun int bool), (even_odd_even int) ) 19.06/18.01 ( (fun int bool), twoSqu1091635170sum2sq ) 19.06/18.01 ( (fun int nat), nat_1 ) 19.06/18.01 ( (fun int nat), phi ) 19.06/18.01 ( (fun real real), sqrt ) 19.06/18.01 ( (fun real real), tan ) 19.06/18.01 ( (fun real real), cos ) 19.06/18.01 ( (fun real real), arccos ) 19.06/18.01 ( (fun real real), ln ) 19.06/18.01 ( (fun real real), sin ) 19.06/18.01 ( (fun real real), arctan ) 19.06/18.01 ( (fun real real), arcsin ) 19.06/18.01 ( complex, ii ) 19.06/18.01 ( (fun complex complex), cnj ) 19.06/18.01 ( (fun complex complex), expi ) 19.06/18.01 ( (fun nat real), (real_1 nat) ) 19.06/18.01 ( (fun nat real), cos_coeff ) 19.06/18.01 ( (fun nat real), sin_coeff ) 19.06/18.01 ( (fun int int), bit0 ) 19.06/18.01 ( (fun int int), bit1 ) 19.06/18.01 ( (fun int int), pred ) 19.06/18.01 ( (fun int int), succ ) 19.06/18.01 ( (fun int int), (fact_fact int) ) 19.06/18.01 ( (fun int int), zfact ) 19.06/18.01 ( (fun bool bool), fNot ) 19.06/18.01 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 19.06/18.01 ( (fun bool (fun bool bool)), fconj ) 19.06/18.01 ( (fun bool (fun bool bool)), fdisj ) 19.06/18.01 ( (fun bool (fun bool bool)), fimplies ) 19.06/18.01 ( (fun int (fun int bool)), sRStar ) 19.06/18.01 ( (fun int (fun int bool)), quadRes ) 19.06/18.01 ( (fun int (fun int bool)), norRRset ) 19.06/18.01 ( (fun int (fun int bool)), d22set ) 19.06/18.01 ( (fun int (fun int bool)), sr ) 19.06/18.01 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 19.06/18.01 ( (fun nat (fun nat nat)), nat_gcd ) 19.06/18.01 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 19.06/18.01 ( (fun nat (fun nat nat)), nat_lcm ) 19.06/18.01 ( (fun nat (fun real real)), root ) 19.06/18.01 ( (fun real (fun real real)), log ) 19.06/18.01 ( (fun real (fun real real)), powr ) 19.06/18.01 ( (fun nat (fun nat bool)), coprime ) 19.06/18.01 ( (fun (fun int bool) int), (the int) ) 19.06/18.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 19.06/18.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 19.06/18.01 ( (fun nat (fun nat (product_prod int int))), bezw ) 19.06/18.01 ( (fun (fun int bool) bool), nat_nat_set ) 19.06/18.01 ( (filter nat), sequentially ) 19.06/18.01 ( (fun (product_prod nat nat) bool), pred_nat ) 19.06/18.01 ( (fun (product_prod int int) bool), frac_1 ) 19.06/18.01 ( (fun real complex), cis ) 19.06/18.01 ( (fun complex real), im ) 19.06/18.01 ( (fun complex real), re ) 19.06/18.01 ( (fun complex real), arg ) 19.06/18.01 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 19.06/18.01 ( (fun int (fun int int)), int_gcd ) 19.06/18.01 ( (fun int (fun int int)), multInv ) 19.06/18.01 ( (fun int (fun int int)), legacy_zgcd ) 19.06/18.01 ( (fun int (fun int int)), z3mod ) 19.06/18.01 ( (fun int (fun int int)), inv ) 19.06/18.01 ( (fun int (fun int int)), (gcd_gcd int) ) 19.06/18.01 ( (fun int (fun int int)), standardRes ) 19.06/18.01 ( (fun int (fun int int)), legendre ) 19.06/18.01 ( (fun int (fun int int)), nat_tsub ) 19.06/18.01 ( (fun int (fun int int)), z3div ) 19.06/18.01 ( (fun int (fun int int)), int_lcm ) 19.06/18.01 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 19.06/18.01 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 19.06/18.01 ( (fun int (fun (fun int bool) bool)), rsetR ) 19.06/18.01 ( (fun int (fun (fun int bool) bool)), resSet ) 19.06/18.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 19.06/18.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 19.06/18.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 19.06/18.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 19.06/18.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 19.06/18.01 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 19.06/18.01 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 19.06/18.01 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 19.06/18.01 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 19.06/18.01 ( (fun int (fun int (product_prod int int))), negDivAlg ) 19.06/18.01 ( (fun int (fun int (product_prod int int))), divmod_int ) 19.06/18.01 ( (fun int (fun int (product_prod int int))), posDivAlg ) 19.06/18.01 ( (fun int (fun int (product_prod int int))), pdivmod ) 19.06/18.01 ( (fun int (fun int (product_prod int int))), norm_frac ) 19.06/18.01 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 19.06/18.01 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 19.06/18.01 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 19.06/18.01 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 19.06/18.01 ( (fun real nat), natfloor ) 19.06/18.01 ( (fun real nat), natceiling ) 19.06/18.01 ( (fun int quickcheck_code_int), quickcheck_of_int ) 19.06/18.01 ( (fun int (fun int (fun int bool))), wset ) 19.06/18.01 ( (fun int (fun int (fun int bool))), bnorRset ) 19.06/18.01 ( (fun int (fun int (fun int bool))), zcong ) 19.06/18.01 ( (fun int (fun int (fun int bool))), noXRRset ) 19.06/18.01 ( (fun int (fun int (fun int bool))), zcongm ) 19.06/18.01 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 19.06/18.01 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 19.06/18.01 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 19.06/18.01 ( (fun int real), (real_1 int) ) 19.06/18.01 ( (fun complex nat), (size_size complex) ) 19.06/18.01 ( (fun complex nat), complex_size ) 19.06/18.01 ( (fun int (list int)), quickc666637781d_zero ) 19.06/18.01 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 19.06/18.01 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 19.06/18.01 ( (fun (product_prod int int) rat), frct ) 19.06/18.01 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 19.06/18.01 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 19.06/18.01 ( (fun (fun nat rat) bool), vanishes ) 19.06/18.01 ( (fun int (fun int rat)), fract ) 19.06/18.01 ( (fun code_code_numeral int), code_int_of ) 19.06/18.01 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 19.06/18.01 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 19.06/18.01 ( (fun code_code_numeral nat), code_c271388182l_size ) 19.06/18.01 ( (fun real (fun real complex)), complex_1 ) 19.06/18.01 ( (fun real (fun real complex)), rcis ) 19.06/18.01 ( (fun int (fun nat nat)), nat_aux ) 19.06/18.01 ( (fun rat real), ratreal ) 19.06/18.01 ( (fun quickcheck_code_int int), quickcheck_int_of ) 19.06/18.01 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 19.06/18.01 ( (fun rat (product_prod int int)), quotient_of ) 19.06/18.01 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 19.06/18.01 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 19.06/18.01 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 19.06/18.01 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 19.06/18.01 ) 19.06/18.01 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_137980 $$unsorted) (BOUND_VARIABLE_137981 $$unsorted)) (or (not (boolean_algebra X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_137980) BOUND_VARIABLE_137981))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_137981)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_137980)))) )))) 19.06/18.01 ( real, (zero_zero real), pi ) 19.06/18.01 ( 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)))) ) 19.06/18.01 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.01 ( real, (zero_zero real), skv_6 ) 19.06/18.01 ( real, (zero_zero real), skv_11 ) 19.06/18.01 ( real, (zero_zero real), skv_12 ) 19.06/18.01 ( real, (zero_zero real), skv_14 ) 19.06/18.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.06/18.01 ( 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))) ) 19.06/18.01 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.06/18.01 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.01 ( int, (zero_zero int), (one_one int) ) 19.06/18.01 ( int, (zero_zero int), min_1 ) 19.06/18.01 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.01 ( int, (zero_zero int), s ) 19.06/18.01 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 19.06/18.01 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.06/18.01 ( int, (zero_zero int), skv_3 ) 19.06/18.01 ( int, (zero_zero int), skv_9 ) 19.06/18.01 ( int, pls, pls ) 19.06/18.01 ( int, pls, (one_one int) ) 19.06/18.01 ( int, (one_one int), pls ) 19.06/18.01 ( int, (one_one int), (one_one int) ) 19.06/18.01 ( int, (one_one int), t ) 19.06/18.01 ( int, min_1, pls ) 19.06/18.01 ( int, min_1, min_1 ) 19.06/18.01 ) 19.06/18.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138058 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_138058) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_138058))) ) 19.06/18.01 ( real, (zero_zero int) ) 19.06/18.01 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.06/18.01 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.01 ( real, (one_one int) ) 19.06/18.01 ( real, min_1 ) 19.06/18.01 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.01 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.06/18.01 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.06/18.01 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 19.06/18.01 ( nat, pls ) 19.06/18.01 ( nat, (hAPP int int bit1 pls) ) 19.06/18.01 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.06/18.01 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.06/18.01 ( int, pls ) 19.06/18.01 ( int, (hAPP int int bit1 pls) ) 19.06/18.01 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.06/18.01 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.01 ( int, min_1 ) 19.06/18.01 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.06/18.01 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.06/18.01 ( complex, min_1 ) 19.06/18.01 ( quickcheck_code_int, (zero_zero int) ) 19.06/18.01 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 19.06/18.01 ( quickcheck_code_int, (one_one int) ) 19.06/18.01 ( code_code_numeral, pls ) 19.06/18.01 ( code_code_numeral, (hAPP int int bit1 pls) ) 19.06/18.01 ) 19.06/18.01 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less X_b))) (let ((_let_2 (fun X_a bool))) (let ((_let_3 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_138087 $$unsorted) (BOUND_VARIABLE_138088 $$unsorted) (BOUND_VARIABLE_138089 $$unsorted) (BOUND_VARIABLE_138090 $$unsorted)) (or (not (order X_b)) (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_138089) BOUND_VARIABLE_138090))) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP X_a X_b BOUND_VARIABLE_138087 BOUND_VARIABLE_138090)) BOUND_VARIABLE_138088))) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_2 _let_3 X_2) Y_2))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less_eq X_b) (hAPP X_a X_b BOUND_VARIABLE_138087 X_2)) (hAPP X_a X_b BOUND_VARIABLE_138087 Y_2)))) )) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP X_a X_b BOUND_VARIABLE_138087 BOUND_VARIABLE_138089)) BOUND_VARIABLE_138088))) ))))) 19.06/18.02 ( real, real, tan, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.06/18.02 ( real, real, tan, skv_2, (zero_zero real), pi ) 19.06/18.02 ( real, real, cos, (zero_zero real), skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.02 ( 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), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.02 ( real, real, cos, skv_10, (zero_zero real), skv_14 ) 19.06/18.02 ( real, real, (hAPP real (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))) ) 19.06/18.02 ( real, nat, natceiling, (hAPP int nat (number_number_of nat) (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) ) 19.06/18.02 ( int, real, (real_1 int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 19.06/18.02 ( int, int, (number_number_of int), (zero_zero int), min_1, pls ) 19.06/18.02 ( int, int, succ, (one_one int), min_1, min_1 ) 19.06/18.02 ( int, int, succ, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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), min_1 ) 19.06/18.02 ( 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))))), (zero_zero int), (zero_zero int), (one_one int) ) 19.06/18.02 ( 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))))), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))), (one_one int), t ) 19.06/18.02 ) 19.06/18.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138125 $$unsorted)) (or (not (division_ring X_a)) (= (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_138125) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) (one_one X_a)) BOUND_VARIABLE_138125))) ) 19.06/18.02 ( real, (zero_zero real) ) 19.06/18.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.02 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 19.06/18.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 19.06/18.02 ( complex, ii ) 19.06/18.02 ) 19.06/18.02 (instantiation (forall ((N $$unsorted)) (= (hAPP nat int (semiring_1_of_nat int) N) (hAPP real int (archim2085082626_floor real) (hAPP nat real (real_1 nat) N))) ) 19.06/18.02 ( (zero_zero nat) ) 19.06/18.02 ( (hAPP nat nat suc (zero_zero nat)) ) 19.06/18.02 ( (one_one nat) ) 19.06/18.02 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.02 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.06/18.02 ) 19.06/18.02 (instantiation (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))) (forall ((X $$unsorted) (N $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP nat bool _let_1 M))) (not (hBOOL (hAPP nat bool _let_1 N))) (= (hAPP real real _let_3 (hAPP real real _let_2 X)) (hAPP real real _let_2 (hAPP real real _let_3 X)))) ))))) 19.06/18.02 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.02 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.02 ) 19.06/18.02 (instantiation (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_138330))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_138330 $$unsorted) (BOUND_VARIABLE_138331 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_138331)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_138331)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_138331)))) ))) 19.06/18.02 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.02 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 19.06/18.02 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.02 ( 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))))))))) ) 19.06/18.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 19.06/18.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.06/18.02 ( 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))) ) 19.06/18.02 ( 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))) ) 19.06/18.02 ( 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))) ) 19.06/18.02 ) 19.06/18.02 (instantiation (let ((_let_0 (semiring_1_of_nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_138375 $$unsorted) (BOUND_VARIABLE_138376 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_138375) BOUND_VARIABLE_138376))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_138375)) (hAPP nat X_a _let_0 BOUND_VARIABLE_138376)))) )) 19.06/18.02 ( int, (zero_zero nat), (zero_zero nat) ) 19.06/18.02 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 19.06/18.02 ) 19.06/18.02 (instantiation (forall ((X_a $$unsorted)) (or (not (banach X_a)) (not (real_normed_field X_a)) (= (one_one X_a) (hAPP X_a X_a (exp X_a) (zero_zero X_a)))) ) 19.06/18.02 ( real ) 19.06/18.02 ( nat ) 19.06/18.02 ( int ) 19.06/18.02 ( complex ) 19.06/18.02 ( rat ) 19.06/18.02 ( quickcheck_code_int ) 19.06/18.02 ( code_code_numeral ) 19.06/18.02 ) 19.06/18.02 (instantiation (let ((_let_0 (one_one X_a))) (forall ((X_a $$unsorted)) (or (not (number_semiring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) _let_0) _let_0) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls))))) )) 19.06/18.02 ( bool ) 19.06/18.02 ( real ) 19.06/18.02 ( nat ) 19.06/18.02 ( (fun nat bool) ) 19.06/18.02 ( int ) 19.06/18.02 ( (fun int bool) ) 19.06/18.02 ( (fun real bool) ) 19.06/18.02 ( (fun real real) ) 19.06/18.02 ( complex ) 19.06/18.02 ( (fun nat real) ) 19.06/18.02 ( (fun int int) ) 19.06/18.02 ( rat ) 19.06/18.02 ( (fun int (fun int bool)) ) 19.06/18.02 ( quickcheck_code_int ) 19.06/18.02 ( (product_prod int int) ) 19.06/18.02 ( (fun (product_prod int int) bool) ) 19.06/18.02 ( code_code_numeral ) 19.06/18.02 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 19.06/18.02 ( (fun (product_prod int int) int) ) 19.06/18.02 ( (fun int (fun int (fun int bool))) ) 19.06/18.02 ( (fun int real) ) 19.06/18.02 ) 19.06/18.02 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (let ((_let_2 (abs_abs X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_138524 $$unsorted) (BOUND_VARIABLE_138525 $$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 (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_138524)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_138525))) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_138525) BOUND_VARIABLE_138524))))) )))) 19.06/18.02 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 19.06/18.02 ( int, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.02 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 19.06/18.02 ) 19.06/18.02 (instantiation (let ((_let_0 (zero_zero nat))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) X))) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) X) (hAPP nat nat suc (hAPP nat nat suc _let_0))))) )) 19.06/18.02 ( (zero_zero nat) ) 19.06/18.02 ( (one_one nat) ) 19.06/18.02 ) 19.06/18.02 (instantiation (let ((_let_0 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_138563 $$unsorted) (BOUND_VARIABLE_138564 $$unsorted)) (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_138563)) (hAPP int X_a _let_0 BOUND_VARIABLE_138564)) (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (minus_minus int) BOUND_VARIABLE_138563) BOUND_VARIABLE_138564)))) )) 19.06/18.02 ( code_code_numeral, pls, (hAPP int int bit1 pls) ) 19.06/18.02 ) 19.06/18.02 (instantiation (let ((_let_0 (fun int bool))) (forall ((P_4 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) P_4))) (= (hAPP int int (hAPP int (fun int int) (minus_minus int) P_4) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (hAPP _let_0 nat (finite_card int) (hAPP int _let_0 sRStar P_4))))) )) 19.06/18.02 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.02 ) 19.06/18.02 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) _let_2)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) _let_2))) (= X (hAPP real real arctan (hAPP real real tan X)))) )))) 19.06/18.02 ( (zero_zero real) ) 19.06/18.02 ( (one_one real) ) 19.06/18.02 ( pi ) 19.06/18.02 ( (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)))) ) 19.06/18.02 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 19.06/18.02 ( (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))))) ) 19.06/18.02 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.02 ( (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))))) ) 19.06/18.02 ( (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)))) ) 19.06/18.02 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 19.06/18.02 ) 19.06/18.02 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_138699 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_138699))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_138699)))) )) 19.06/18.02 ( real, (zero_zero real) ) 19.06/18.02 ( complex, ii ) 19.06/18.02 ) 19.06/18.02 (instantiation (let ((_let_0 (exp X_a))) (let ((_let_1 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_138727 $$unsorted) (BOUND_VARIABLE_138728 $$unsorted)) (or (not (real_normed_field X_a)) (not (banach X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 (times_times X_a) (hAPP X_a X_a _let_0 BOUND_VARIABLE_138727)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_138728)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 (plus_plus X_a) BOUND_VARIABLE_138727) BOUND_VARIABLE_138728)))) ))) 19.06/18.02 ( nat, (one_one nat), (one_one nat) ) 19.06/18.02 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 19.06/18.02 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 19.06/18.02 ) 19.06/18.02 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (field_char_0_Rats X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_138753 $$unsorted) (BOUND_VARIABLE_138754 $$unsorted)) (or (not (field_inverse_zero X_a)) (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_138754) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_138753) _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_138754) BOUND_VARIABLE_138753)) _let_3))) ))))) 19.06/18.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 19.06/18.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.06/18.02 ( 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))) ) 19.06/18.02 ( 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)))) ) 19.06/18.02 ( 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)))) ) 19.06/18.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 19.06/18.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 19.06/18.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 19.06/18.02 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 19.06/18.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 19.06/18.02 ( 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) ) 19.06/18.02 ) 19.06/18.02 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (times_times real))) (let ((_let_4 (norm_norm X_a))) (forall ((X_a $$unsorted)) (or (not (real_normed_vector X_a)) (not (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) K_2))) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real _let_4 (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_2 _let_3 (hAPP real real (hAPP real _let_2 _let_3 (hAPP real real (norm_norm real) A_4)) (hAPP X_a real _let_4 B_4))) K_2))) ))) ))) )))))) 19.06/18.03 ( real ) 19.06/18.03 ( complex ) 19.06/18.03 ) 19.06/18.03 (instantiation (let ((_let_0 (hAPP int int (number_number_of int) V))) (forall ((V $$unsorted)) (or (hBOOL (hAPP int bool nat_neg _let_0)) (= _let_0 (hAPP nat int (semiring_1_of_nat int) (hAPP int nat (number_number_of nat) V)))) )) 19.06/18.03 ( pls ) 19.06/18.03 ( (hAPP int int bit1 pls) ) 19.06/18.03 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.06/18.03 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.03 ( min_1 ) 19.06/18.03 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.06/18.03 ) 19.06/18.03 (instantiation (forall ((V $$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)))) ) 19.06/18.03 ( pls ) 19.06/18.03 ( (hAPP int int bit1 pls) ) 19.06/18.03 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.06/18.03 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.03 ( min_1 ) 19.06/18.03 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.06/18.03 ) 19.06/18.03 (instantiation (let ((_let_0 (dist_dist X_a))) (forall ((X_a $$unsorted)) (or (not (metric_space X_a)) (= _let_0 (ti (fun X_a (fun X_a real)) _let_0))) )) 19.06/18.03 ( real ) 19.06/18.03 ( nat ) 19.06/18.03 ( int ) 19.06/18.03 ( (fun real bool) ) 19.06/18.03 ( complex ) 19.06/18.03 ( rat ) 19.06/18.03 ) 19.06/18.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138865 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_138865)) (one_one X_a))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_138865) (hAPP int int bit1 pls))))) ) 19.06/18.03 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.06/18.03 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.03 ( real, min_1 ) 19.06/18.03 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.03 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.06/18.03 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.06/18.03 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 19.06/18.03 ( nat, pls ) 19.06/18.03 ( nat, (hAPP int int bit1 pls) ) 19.06/18.03 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.06/18.03 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.06/18.03 ( int, pls ) 19.06/18.03 ( int, (hAPP int int bit1 pls) ) 19.06/18.03 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.06/18.03 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.03 ( int, min_1 ) 19.06/18.03 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.06/18.03 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.06/18.03 ( complex, min_1 ) 19.06/18.03 ( quickcheck_code_int, (zero_zero int) ) 19.06/18.03 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 19.06/18.03 ( quickcheck_code_int, (one_one int) ) 19.06/18.03 ( code_code_numeral, pls ) 19.06/18.03 ( code_code_numeral, (hAPP int int bit1 pls) ) 19.06/18.03 ) 19.06/18.03 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) _let_0) X_1))) (= (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 _let_0) (hAPP real real ln X_1))) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (one_one real)) X_1)))) )))) 19.06/18.03 ( (one_one real) ) 19.06/18.03 ( pi ) 19.06/18.03 ( (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)))) ) 19.06/18.03 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.03 ( skv_2 ) 19.06/18.03 ( skv_10 ) 19.06/18.03 ( skv_13 ) 19.06/18.03 ) 19.06/18.03 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_138886 $$unsorted)) (or (not (number_ring X_a)) (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_138886)) (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_138886) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) )) 19.06/18.03 ( real, (one_one real) ) 19.06/18.03 ( real, pi ) 19.06/18.03 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.06/18.03 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 19.06/18.03 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.03 ) 19.06/18.03 (instantiation (let ((_let_0 (fun int bool))) (forall ((W $$unsorted) (Z_1 $$unsorted)) (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))) )) 19.06/18.03 ( (zero_zero int), (zero_zero int) ) 19.06/18.03 ( (zero_zero int), (one_one int) ) 19.06/18.03 ( (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))) ) 19.06/18.03 ( (zero_zero int), min_1 ) 19.06/18.03 ( min_1, (zero_zero int) ) 19.06/18.03 ( min_1, min_1 ) 19.06/18.03 ( 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))) ) 19.06/18.03 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 19.06/18.03 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 19.06/18.03 ( t, (zero_zero int) ) 19.06/18.03 ( t, (one_one int) ) 19.06/18.03 ( 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))) ) 19.06/18.03 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.06/18.03 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.06/18.03 ) 19.06/18.03 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (inverse_inverse X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_138968 $$unsorted) (BOUND_VARIABLE_138969 $$unsorted)) (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_138968) BOUND_VARIABLE_138969)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_138968)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_138969)))) )))) 19.06/18.03 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.06/18.03 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.06/18.03 ( 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)))))) ) 19.06/18.03 ( 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 ) 19.06/18.03 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 19.06/18.03 ( 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))), (zero_zero int) ) 19.06/18.03 ( 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))), t ) 19.06/18.03 ( 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))), skv_1 ) 19.06/18.03 ( complex, ii, ii ) 19.06/18.03 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 19.06/18.03 ( 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 ) 19.06/18.03 ) 19.06/18.03 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (one_one X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (minus_minus X_a))) (let ((_let_4 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_138994))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_138993 $$unsorted) (BOUND_VARIABLE_138994 $$unsorted)) (or (not (field X_a)) (= _let_1 (ti X_a BOUND_VARIABLE_138994)) (= (hAPP _let_0 X_a (hAPP (fun nat X_a) (fun _let_0 X_a) (big_co1399186613setsum nat X_a) _let_4) (hAPP nat _let_0 (hAPP nat (fun nat _let_0) (ord_atLeastLessThan nat) (zero_zero nat)) BOUND_VARIABLE_138993)) (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_4 BOUND_VARIABLE_138993)) _let_1)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_138994) _let_1)))) )))))) 19.06/18.03 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 19.06/18.03 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 19.06/18.03 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 19.06/18.03 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 19.06/18.03 ) 19.06/18.03 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (ti int X))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) X))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) X) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (= (one_one int) _let_2) (= _let_1 _let_2)) )))) 19.06/18.03 ( (zero_zero int) ) 19.06/18.03 ( pls ) 19.06/18.03 ( m ) 19.06/18.03 ( (one_one int) ) 19.06/18.03 ( min_1 ) 19.06/18.03 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.03 ( s ) 19.06/18.03 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 19.06/18.03 ( (hAPP int int (number_number_of int) pls) ) 19.06/18.03 ( s1 ) 19.06/18.03 ( t ) 19.06/18.03 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.06/18.03 ( skv_3 ) 19.06/18.03 ( skv_9 ) 19.06/18.03 ) 19.06/18.03 (instantiation (forall ((X $$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))) ) 19.06/18.03 ( (zero_zero real) ) 19.06/18.03 ( (one_one real) ) 19.06/18.03 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.03 ( (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)))) ) 19.06/18.03 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.03 ( skv_14 ) 19.06/18.03 ) 19.06/18.03 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((X $$unsorted) (Y $$unsorted)) (or (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Y) X)) (= (ti int Y) (ti int X)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 X) Y))) ))) 19.06/18.03 ( (zero_zero int), (zero_zero int) ) 19.06/18.03 ( (zero_zero int), (one_one int) ) 19.06/18.03 ( (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))) ) 19.06/18.03 ( (zero_zero int), min_1 ) 19.06/18.03 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 19.06/18.03 ( (zero_zero int), t ) 19.06/18.03 ( (one_one int), (zero_zero int) ) 19.06/18.03 ( (one_one int), t ) 19.06/18.03 ( (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))), (zero_zero int) ) 19.06/18.03 ( (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))), s ) 19.06/18.03 ( (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))), t ) 19.06/18.03 ( (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))), skv_3 ) 19.06/18.03 ( (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))), skv_9 ) 19.06/18.03 ( min_1, (zero_zero int) ) 19.06/18.03 ( min_1, min_1 ) 19.06/18.03 ( 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))) ) 19.06/18.03 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 19.06/18.03 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 19.06/18.03 ( t, (zero_zero int) ) 19.06/18.03 ( t, (one_one int) ) 19.06/18.04 ( 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))) ) 19.06/18.04 ( (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 19.06/18.04 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.06/18.04 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.06/18.04 ) 19.06/18.04 (instantiation (let ((_let_0 (fun nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_139095 $$unsorted) (BOUND_VARIABLE_139096 $$unsorted)) (or (not (comm_monoid_add X_a)) (not (topological_space X_a)) (not (hBOOL (hAPP X_a bool (hAPP _let_0 (fun X_a bool) (sums X_a) BOUND_VARIABLE_139095) BOUND_VARIABLE_139096))) (hBOOL (hAPP _let_0 bool (summable X_a) BOUND_VARIABLE_139095))) )) 19.06/18.04 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 19.06/18.04 ) 19.06/18.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139112 $$unsorted)) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_139112) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (zero_zero X_a))))) ) 19.06/18.04 ( real, (hAPP int real (number_number_of real) min_1) ) 19.06/18.04 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.04 ( int, s ) 19.06/18.04 ( int, s1 ) 19.06/18.04 ( int, skv_8 ) 19.06/18.04 ( complex, ii ) 19.06/18.04 ) 19.06/18.04 (instantiation (forall ((M $$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)))) ))) ) 19.06/18.04 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.04 ) 19.06/18.04 (instantiation (let ((_let_0 (bseq X_a))) (forall ((X_a $$unsorted)) (or (not (real_normed_vector X_a)) (= _let_0 (ti (fun (fun nat X_a) bool) _let_0))) )) 19.06/18.04 ( bool ) 19.06/18.04 ( real ) 19.06/18.04 ( nat ) 19.06/18.04 ( (fun nat bool) ) 19.06/18.04 ( (fun nat nat) ) 19.06/18.04 ( int ) 19.06/18.04 ( (fun real real) ) 19.06/18.04 ( complex ) 19.06/18.04 ( (fun int int) ) 19.06/18.04 ( rat ) 19.06/18.04 ( (fun bool bool) ) 19.06/18.04 ( (fun nat (fun nat bool)) ) 19.06/18.04 ( (product_prod real real) ) 19.06/18.04 ( (product_prod int int) ) 19.06/18.04 ( (fun nat (product_prod int int)) ) 19.06/18.04 ( (product_prod nat nat) ) 19.06/18.04 ( (fun (product_prod nat nat) bool) ) 19.06/18.04 ( (fun nat (fun (product_prod nat nat) bool)) ) 19.06/18.04 ( (fun nat (product_prod nat nat)) ) 19.06/18.04 ) 19.06/18.04 (instantiation (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (forall ((Z_1 $$unsorted)) (= (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)))) )))) 19.06/18.04 ( ii ) 19.06/18.04 ( (zero_zero complex) ) 19.06/18.04 ( (one_one complex) ) 19.06/18.04 ) 19.06/18.04 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (one_one real)))) (forall ((Y_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root N_1) Y_1))) (hBOOL (hAPP real bool _let_0 Y_1)))) )) 19.06/18.04 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.04 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.04 ( (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))) ) 19.06/18.04 ( (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))) ) 19.06/18.04 ) 19.06/18.04 (instantiation (let ((_let_0 (fun nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_139170 $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (not (banach 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_139170)) (one_one real)))) (hBOOL (hAPP _let_0 bool (summable X_a) (hAPP X_a _let_0 (power_power X_a) BOUND_VARIABLE_139170)))) )) 19.06/18.04 ( real, (hAPP int real (number_number_of real) min_1) ) 19.06/18.04 ( 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)))) ) 19.06/18.04 ( int, s ) 19.06/18.04 ( int, s1 ) 19.06/18.04 ( int, skv_8 ) 19.06/18.04 ( complex, ii ) 19.06/18.04 ) 19.06/18.04 (instantiation (forall ((N $$unsorted)) (= (ti int N) (hAPP real int (archimedean_ceiling real) (hAPP int real (real_1 int) N))) ) 19.06/18.04 ( (zero_zero int) ) 19.06/18.04 ( pls ) 19.06/18.04 ( m ) 19.06/18.04 ( (one_one int) ) 19.06/18.04 ( min_1 ) 19.06/18.04 ( s ) 19.06/18.04 ( s1 ) 19.06/18.04 ( t ) 19.06/18.04 ) 19.06/18.04 (instantiation (let ((_let_0 (uminus_uminus real))) (let ((_let_1 (fun real complex))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (hAPP complex complex (uminus_uminus complex) (hAPP real complex (hAPP real _let_1 complex_1 A_1) B)) (hAPP real complex (hAPP real _let_1 complex_1 (hAPP real real _let_0 A_1)) (hAPP real real _let_0 B))) ))) 19.06/18.04 ( (zero_zero real), (one_one real) ) 19.06/18.04 ( (one_one real), (zero_zero real) ) 19.06/18.04 ) 19.06/18.04 (instantiation (let ((_let_0 (number_number_of real))) (let ((_let_1 (number_number_of rat))) (forall ((R_4 $$unsorted) (S_3 $$unsorted)) (= (hAPP rat real ratreal (hAPP rat rat (hAPP rat (fun rat rat) (inverse_divide rat) (hAPP int rat _let_1 R_4)) (hAPP int rat _let_1 S_3))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_0 R_4)) (hAPP int real _let_0 S_3))) ))) 19.06/18.04 ( (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.06/18.04 ) 19.06/18.04 (instantiation (let ((_let_0 (fun nat X_a))) (let ((_let_1 (nat_case X_a))) (forall ((X_a $$unsorted)) (= _let_1 (ti (fun X_a (fun _let_0 _let_0)) _let_1)) ))) 19.06/18.04 ( bool ) 19.06/18.04 ( real ) 19.06/18.04 ( nat ) 19.06/18.04 ( (fun nat bool) ) 19.06/18.04 ( (fun nat nat) ) 19.06/18.04 ( int ) 19.06/18.04 ( (fun real real) ) 19.06/18.04 ( complex ) 19.06/18.04 ( (fun int int) ) 19.06/18.04 ( rat ) 19.06/18.04 ( (fun bool bool) ) 19.06/18.04 ( (fun nat (fun nat bool)) ) 19.06/18.04 ( (product_prod real real) ) 19.06/18.04 ( (product_prod int int) ) 19.06/18.04 ( (fun nat (product_prod int int)) ) 19.06/18.04 ( (product_prod nat nat) ) 19.06/18.04 ( (fun (product_prod nat nat) bool) ) 19.06/18.04 ( (fun nat (fun (product_prod nat nat) bool)) ) 19.06/18.04 ( (fun nat (product_prod nat nat)) ) 19.06/18.04 ) 19.06/18.04 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_b bool))) (let ((_let_3 (ord_less X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_139268 $$unsorted) (BOUND_VARIABLE_139269 $$unsorted) (BOUND_VARIABLE_139270 $$unsorted) (BOUND_VARIABLE_139271 $$unsorted)) (or (not (order X_b)) (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_139270) BOUND_VARIABLE_139271))) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_2 (ord_less_eq X_b) (hAPP X_a X_b BOUND_VARIABLE_139268 BOUND_VARIABLE_139271)) BOUND_VARIABLE_139269))) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 X_2) Y_2))) (hBOOL (hAPP X_b bool (hAPP X_b _let_2 _let_3 (hAPP X_a X_b BOUND_VARIABLE_139268 X_2)) (hAPP X_a X_b BOUND_VARIABLE_139268 Y_2)))) )) (hBOOL (hAPP X_b bool (hAPP X_b _let_2 _let_3 (hAPP X_a X_b BOUND_VARIABLE_139268 BOUND_VARIABLE_139270)) BOUND_VARIABLE_139269))) ))))) 19.06/18.04 ( real, real, tan, skv_6, (zero_zero real), pi ) 19.06/18.04 ( real, real, tan, skv_12, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 19.06/18.04 ( real, real, cos, (zero_zero real), (hAPP real real (hAPP real (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))) ) 19.06/18.04 ( real, real, cos, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.04 ( real, real, (inverse_inverse 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) ) 19.06/18.04 ( real, real, (inverse_inverse real), skv_11, pi, (zero_zero real) ) 19.06/18.04 ( real, real, (inverse_inverse real), skv_14, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 19.06/18.04 ( int, real, (real_1 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)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 19.06/18.04 ( int, int, (number_number_of int), min_1, (zero_zero int), (zero_zero int) ) 19.06/18.04 ( int, int, (number_number_of int), s, min_1, (zero_zero int) ) 19.06/18.04 ( int, int, (number_number_of int), (hAPP int int (number_number_of int) pls), t, (zero_zero int) ) 19.06/18.04 ( int, int, (uminus_uminus int), pls, t, (one_one int) ) 19.06/18.04 ( int, int, (uminus_uminus int), min_1, (zero_zero int), (one_one int) ) 19.06/18.04 ( int, int, (hAPP int (fun int int) legendre (hAPP int int (number_number_of int) min_1)), t, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.06/18.04 ( int, int, succ, (one_one int), (zero_zero int), min_1 ) 19.06/18.04 ( int, int, succ, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), min_1, min_1 ) 19.06/18.04 ) 19.06/18.04 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_139307 $$unsorted) (BOUND_VARIABLE_139308 $$unsorted)) (or (not (boolean_algebra X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_139307) (hAPP X_a X_a _let_2 BOUND_VARIABLE_139308)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_139308) (hAPP X_a X_a _let_2 BOUND_VARIABLE_139307)))) )))) 19.06/18.04 ( int, (zero_zero int), pls ) 19.06/18.04 ( int, (zero_zero int), (one_one int) ) 19.06/18.04 ( int, pls, (zero_zero int) ) 19.06/18.04 ( int, pls, min_1 ) 19.06/18.04 ( int, (one_one int), (zero_zero int) ) 19.06/18.04 ( int, (one_one int), min_1 ) 19.06/18.04 ( int, min_1, pls ) 19.06/18.04 ( int, min_1, (one_one int) ) 19.06/18.04 ) 19.06/18.04 (instantiation (let ((_let_0 (zero_zero int))) (forall ((M $$unsorted)) (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))) )) 19.06/18.04 ( (zero_zero int) ) 19.06/18.04 ( (one_one int) ) 19.06/18.04 ( min_1 ) 19.06/18.04 ( s ) 19.06/18.04 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 19.06/18.04 ( t ) 19.06/18.04 ( skv_3 ) 19.06/18.04 ( skv_9 ) 19.06/18.04 ) 19.06/18.04 (instantiation (let ((_let_0 (even_odd_even int))) (forall ((Y $$unsorted) (X $$unsorted)) (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)))) )) 19.06/18.04 ( (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) ) 19.06/18.04 ( (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)))) ) 19.06/18.04 ) 19.06/18.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139342 $$unsorted) (BOUND_VARIABLE_139343 $$unsorted)) (or (not (dist_norm X_a)) (= (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) BOUND_VARIABLE_139342) BOUND_VARIABLE_139343) (hAPP X_a real (norm_norm X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_139342) BOUND_VARIABLE_139343)))) ) 19.06/18.04 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 19.06/18.04 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 19.06/18.04 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 19.06/18.04 ) 19.06/18.04 (instantiation (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a X_b))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_139359 $$unsorted) (BOUND_VARIABLE_139360 $$unsorted)) (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_139359) (hAPP X_a X_b BOUND_VARIABLE_139359 BOUND_VARIABLE_139360)) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_139360))) (hBOOL (hAPP X_a bool (hAPP _let_2 (fun X_a bool) (isCont X_a X_b) BOUND_VARIABLE_139359) BOUND_VARIABLE_139360)))) )))) 19.06/18.04 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 19.06/18.04 ( 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)))) ) 19.06/18.04 ( 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)))) ) 19.06/18.04 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_6 ) 19.06/18.04 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 19.06/18.04 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 19.06/18.04 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_14 ) 19.06/18.04 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 19.06/18.04 ( 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)))) ) 19.06/18.04 ( 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)))) ) 19.06/18.04 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 19.06/18.04 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_10 ) 19.06/18.04 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_13 ) 19.06/18.04 ( 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))) ) 19.06/18.04 ( 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)))) ) 19.06/18.04 ( 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) ) 19.06/18.05 ( 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) ) 19.06/18.05 ( 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) ) 19.06/18.05 ( bool, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 19.06/18.05 ( 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))) ) 19.06/18.05 ( 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 ) 19.06/18.05 ( bool, real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 19.06/18.05 ( 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)))) ) 19.06/18.05 ( 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 ) 19.06/18.05 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) skv_14), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.05 ( bool, nat, (even_odd_even nat), (zero_zero nat) ) 19.06/18.05 ( bool, nat, (even_odd_even nat), (one_one nat) ) 19.06/18.05 ( 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))) ) 19.06/18.05 ( bool, nat, prime, (zero_zero nat) ) 19.06/18.05 ( bool, nat, prime, (one_one nat) ) 19.06/18.05 ( bool, nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.05 ( bool, (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 19.06/18.05 ( 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) ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 19.06/18.05 ( 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))) ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 19.06/18.05 ( 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))) ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_3 ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_9 ) 19.06/18.05 ( 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))) ) 19.06/18.05 ( bool, int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 19.06/18.05 ( 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))) ) 19.06/18.05 ( bool, int, nat_neg, (one_one int) ) 19.06/18.05 ( bool, int, nat_neg, (hAPP int int (number_number_of int) min_1) ) 19.06/18.05 ( bool, int, nat_neg, (hAPP int int (number_number_of int) pls) ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), (zero_zero int) ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 19.06/18.05 ( bool, int, nat_is_nat, (zero_zero int) ) 19.06/18.05 ( bool, int, nat_is_nat, (one_one int) ) 19.06/18.05 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.05 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.06/18.05 ( bool, int, (even_odd_even int), (zero_zero int) ) 19.06/18.05 ( bool, int, (even_odd_even int), (one_one int) ) 19.06/18.05 ( 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))) ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))), (zero_zero int) ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less int) min_1), (zero_zero int) ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 19.06/18.05 ( bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 19.06/18.05 ( 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))) ) 19.06/18.05 ( 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))) ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 19.06/18.05 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.06/18.05 ( bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less int) t), (zero_zero int) ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less int) t), (one_one int) ) 19.06/18.05 ( 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))) ) 19.06/18.05 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.06/18.05 ( bool, int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.06/18.05 ( bool, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun int bool) (ord_less 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)))), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_3), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.06/18.05 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_3)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.06/18.05 ( 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_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.06/18.05 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_9), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.06/18.05 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_9)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.06/18.05 ( bool, (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 19.06/18.05 ( 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)) ) 19.06/18.05 ( 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))))) ) 19.06/18.05 ( bool, (filter nat), (trivial_limit nat), sequentially ) 19.06/18.05 ( bool, (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 19.06/18.05 ( real, real, sqrt, (zero_zero real) ) 19.06/18.05 ( real, real, sqrt, (one_one real) ) 19.06/18.05 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.05 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.06/18.05 ( real, real, (uminus_uminus real), (one_one real) ) 19.06/18.05 ( real, real, (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.05 ( real, real, (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 19.06/18.05 ( real, real, tan, (zero_zero real) ) 19.06/18.05 ( real, real, tan, pi ) 19.06/18.05 ( 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))))) ) 19.06/18.05 ( 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))))) ) 19.06/18.05 ( 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)))) ) 19.06/18.05 ( real, real, cos, (zero_zero real) ) 19.06/18.05 ( real, real, cos, pi ) 19.06/18.05 ( real, real, cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.05 ( 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)))) ) 19.06/18.05 ( 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) ) 19.06/18.05 ( 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))))) ) 19.06/18.05 ( real, real, cos, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 19.06/18.05 ( 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))))) ) 19.06/18.05 ( 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)))) ) 19.06/18.05 ( real, real, cos, skv_14 ) 19.06/18.05 ( real, real, ln, (one_one real) ) 19.06/18.05 ( real, real, (inverse_inverse real), (zero_zero real) ) 19.06/18.05 ( real, real, sin, (zero_zero real) ) 19.06/18.06 ( real, real, sin, pi ) 19.06/18.06 ( 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)))) ) 19.06/18.06 ( 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) ) 19.06/18.06 ( 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))))) ) 19.06/18.06 ( real, real, sin, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 19.06/18.06 ( 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))))) ) 19.06/18.06 ( 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)))) ) 19.06/18.06 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.06 ( real, 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)))) ) 19.06/18.06 ( real, real, (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)))) ) 19.06/18.06 ( 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))) ) 19.06/18.06 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 19.06/18.06 ( real, real, (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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.06/18.06 ( real, real, arctan, (zero_zero real) ) 19.06/18.06 ( real, real, arctan, (one_one real) ) 19.06/18.06 ( real, real, arctan, (hAPP real real (hAPP 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))))) ) 19.06/18.06 ( real, real, arctan, (hAPP real real (hAPP 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)))))))))) ) 19.06/18.06 ( 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)))))) ) 19.06/18.06 ( real, real, (sgn_sgn real), (zero_zero real) ) 19.06/18.06 ( 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))) ) 19.06/18.06 ( 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)))) ) 19.06/18.06 ( real, real, (hAPP 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)))) ) 19.06/18.06 ( real, real, (hAPP 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))))))))) ) 19.06/18.06 ( 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))) ) 19.06/18.06 ( 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))) ) 19.06/18.06 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), pi ) 19.06/18.06 ( 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))) ) 19.06/18.06 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1))))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 19.06/18.06 ( real, nat, (real_1 nat), (zero_zero nat) ) 19.06/18.06 ( real, nat, (real_1 nat), (one_one nat) ) 19.06/18.06 ( real, int, (real_1 int), (zero_zero int) ) 19.06/18.06 ( real, int, (real_1 int), (one_one int) ) 19.06/18.06 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.06/18.06 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.06 ( real, int, (number_number_of real), min_1 ) 19.06/18.06 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.06 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.06/18.06 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.06/18.06 ( 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)))))))) ) 19.06/18.06 ( real, (fun real bool), (the real), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0)))))))))))))) ) 19.06/18.06 ( real, complex, im, ii ) 19.06/18.06 ( real, complex, im, (zero_zero complex) ) 19.06/18.06 ( real, complex, im, (one_one complex) ) 19.06/18.06 ( real, complex, re, ii ) 19.06/18.06 ( real, complex, re, (zero_zero complex) ) 19.06/18.06 ( real, complex, re, (one_one complex) ) 19.06/18.06 ( real, (fun nat real), (suminf real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (combc nat nat nat))) (let ((_let_4 (fun nat _let_0))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun _let_1 _let_4))) (let ((_let_7 (combb real _let_0 nat))) (hAPP _let_1 _let_1 (hAPP _let_4 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_4 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 19.06/18.06 ( real, rat, ratreal, (zero_zero rat) ) 19.06/18.06 ( real, rat, ratreal, (one_one rat) ) 19.06/18.06 ( nat, real, natfloor, (zero_zero real) ) 19.06/18.06 ( nat, real, natfloor, (one_one real) ) 19.06/18.06 ( nat, real, natceiling, (zero_zero real) ) 19.06/18.06 ( nat, real, natceiling, (one_one real) ) 19.06/18.06 ( nat, nat, suc, (zero_zero nat) ) 19.06/18.06 ( nat, nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 19.06/18.06 ( nat, nat, suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 19.06/18.06 ( nat, nat, (fact_fact nat), (zero_zero nat) ) 19.06/18.06 ( nat, nat, (fact_fact nat), (hAPP nat nat suc (zero_zero nat)) ) 19.06/18.06 ( nat, nat, (size_size nat), (zero_zero nat) ) 19.06/18.06 ( nat, nat, fact, (zero_zero nat) ) 19.06/18.06 ( nat, nat, nat_size, (zero_zero nat) ) 19.06/18.06 ( nat, nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (one_one nat) ) 19.06/18.06 ( nat, int, nat_1, (zero_zero int) ) 19.06/18.06 ( nat, int, nat_1, (one_one int) ) 19.06/18.06 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.06 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.06/18.06 ( nat, int, (number_number_of nat), pls ) 19.06/18.06 ( nat, int, (number_number_of nat), (hAPP int int bit1 pls) ) 19.06/18.06 ( nat, int, (number_number_of nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.06/18.06 ( nat, int, (number_number_of nat), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.06/18.06 ( nat, code_code_numeral, (size_size code_code_numeral), (zero_zero code_code_numeral) ) 19.06/18.06 ( nat, code_code_numeral, code_c271388182l_size, (zero_zero code_code_numeral) ) 19.06/18.06 ( (fun nat bool), bool, (combk bool nat), fTrue ) 19.06/18.06 ( (fun nat bool), nat, (ord_less nat), (zero_zero nat) ) 19.06/18.06 ( (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) ) 19.06/18.06 ( (fun nat bool), (fun nat bool), (collect nat), prime ) 19.06/18.06 ( (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))) ) 19.06/18.06 ( (fun nat nat), nat, (plus_plus nat), (one_one nat) ) 19.06/18.06 ( (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))) ) 19.06/18.06 ( (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) ) 19.06/18.06 ( int, nat, (semiring_1_of_nat int), (zero_zero nat) ) 19.06/18.06 ( int, nat, (semiring_1_of_nat int), (hAPP nat nat suc (zero_zero nat)) ) 19.06/18.06 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.06 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.06/18.06 ( 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))) ) 19.06/18.06 ( 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))) ) 19.06/18.06 ( int, nat, (hAPP int (fun nat int) (power_power int) skv_8), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.06 ( int, int, (number_number_of int), pls ) 19.06/18.06 ( int, int, (number_number_of int), (hAPP int int bit1 pls) ) 19.06/18.06 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.06/18.06 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.06 ( int, int, (number_number_of int), min_1 ) 19.06/18.06 ( int, int, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.06/18.06 ( int, int, bit0, pls ) 19.06/18.06 ( int, int, bit0, (hAPP int int bit1 pls) ) 19.06/18.06 ( int, int, bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.06/18.06 ( int, int, bit0, min_1 ) 19.06/18.06 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.06/18.06 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.06/18.06 ( int, int, bit1, pls ) 19.06/18.06 ( int, int, bit1, (hAPP int int bit1 pls) ) 19.06/18.06 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.06/18.06 ( int, int, bit1, min_1 ) 19.06/18.06 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.06/18.06 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 19.06/18.06 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 19.06/18.06 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 19.06/18.06 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 19.06/18.06 ( int, int, (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), m ) 19.06/18.06 ( 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) ) 19.06/18.06 ( int, int, (uminus_uminus int), pls ) 19.06/18.06 ( int, int, (uminus_uminus int), (one_one int) ) 19.06/18.06 ( int, int, (uminus_uminus int), min_1 ) 19.06/18.06 ( int, int, pred, pls ) 19.06/18.06 ( int, int, pred, min_1 ) 19.06/18.06 ( int, int, (hAPP int (fun int int) legendre (hAPP int int (number_number_of int) min_1)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.06/18.06 ( int, int, succ, pls ) 19.06/18.06 ( int, int, succ, min_1 ) 19.06/18.06 ( 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) ) 19.06/18.06 ( 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))))), (zero_zero int) ) 19.06/18.06 ( 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 ) 19.06/18.06 ( 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_1 ) 19.06/18.06 ( int, int, (hAPP int (fun int int) (minus_minus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 19.06/18.07 ( int, int, (fact_fact int), (zero_zero int) ) 19.06/18.07 ( int, int, (fact_fact int), (one_one int) ) 19.06/18.07 ( int, quickcheck_code_int, quickcheck_int_of, (zero_zero quickcheck_code_int) ) 19.06/18.07 ( 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))) ) 19.06/18.07 ( int, code_code_numeral, code_int_of, (zero_zero code_code_numeral) ) 19.06/18.07 ( (fun int bool), int, (ord_less_eq int), (zero_zero int) ) 19.06/18.07 ( (fun int bool), int, (ord_less_eq int), (one_one int) ) 19.06/18.07 ( (fun int bool), int, (ord_less_eq int), min_1 ) 19.06/18.07 ( (fun int bool), int, (ord_less int), (zero_zero int) ) 19.06/18.07 ( (fun int bool), int, (ord_less int), min_1 ) 19.06/18.07 ( (fun int bool), int, (ord_less int), s ) 19.06/18.07 ( (fun int bool), int, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 19.06/18.07 ( (fun int bool), int, (ord_less int), t ) 19.06/18.07 ( (fun int bool), int, (ord_less int), skv_3 ) 19.06/18.07 ( (fun int bool), int, (ord_less int), skv_9 ) 19.06/18.07 ( (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))) ) 19.06/18.07 ( (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))) ) 19.06/18.07 ( (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) ) 19.06/18.07 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), s ) 19.06/18.07 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), skv_3 ) 19.06/18.07 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), skv_9 ) 19.06/18.07 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 19.06/18.07 ( (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)))) ) 19.06/18.07 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 19.06/18.07 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 19.06/18.07 ( (fun int bool), (fun int bool), (collect int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (fun int _let_1))) (hAPP _let_2 _let_0 (hAPP (fun _let_0 bool) (fun _let_2 _let_0) (combb _let_0 bool int) (fEx int)) (hAPP _let_1 _let_2 (hAPP _let_4 (fun _let_1 _let_2) (combc int _let_1 _let_0) (hAPP _let_2 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_2 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_1 (hAPP _let_5 _let_5 (combc int int int) (hAPP _let_1 _let_5 (hAPP _let_5 (fun _let_1 _let_5) (combb int _let_1 int) (plus_plus int)) (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int)))))))))) ) 19.06/18.07 ( (fun int bool), (fun int bool), (collect int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_2 _let_0 (hAPP (fun _let_0 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((_let_4 (fun int _let_3))) (let ((_let_5 (fun int _let_1))) (hAPP _let_1 _let_2 (hAPP _let_4 (fun _let_1 _let_2) (combc int _let_1 _let_0) (hAPP _let_2 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_2 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_1 (hAPP _let_5 _let_5 (combc int int int) (hAPP _let_1 _let_5 (hAPP _let_5 (fun _let_1 _let_5) (combb int _let_1 int) (plus_plus int)) (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int))))))))) ) 19.06/18.07 ( (fun int bool), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_1 _let_2 (hAPP _let_4 (fun _let_1 _let_2) (combc int _let_1 _let_0) (hAPP _let_2 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_2 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))) ) 19.06/18.07 ( (fun nat int), int, (power_power int), s ) 19.06/18.07 ( (fun nat int), int, (power_power int), s1 ) 19.06/18.07 ( (fun nat int), int, (power_power int), skv_8 ) 19.06/18.07 ( (fun real bool), real, (ord_less_eq real), (zero_zero real) ) 19.06/18.07 ( (fun real bool), real, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.07 ( (fun real bool), real, (ord_less_eq real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.07 ( (fun real bool), real, (ord_less_eq real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.07 ( (fun real bool), real, (ord_less_eq real), skv_14 ) 19.06/18.07 ( (fun real bool), real, (ord_less real), (zero_zero real) ) 19.06/18.07 ( (fun real bool), real, (ord_less real), (one_one real) ) 19.06/18.07 ( (fun real bool), real, (ord_less real), pi ) 19.06/18.07 ( (fun real bool), real, (ord_less real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.07 ( (fun real bool), real, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 19.06/18.07 ( (fun real bool), real, (ord_less real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.06/18.07 ( (fun real bool), real, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 19.06/18.07 ( (fun real bool), real, (let ((_let_0 (fun real (fun real bool)))) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.06/18.07 ( (fun real bool), real, (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos))))), (zero_zero real) ) 19.06/18.07 ( (fun real bool), (fun real bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_2 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 real) fconj) (hAPP real _let_0 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(hAPP (fun bool _let_0) (fun (fun real bool) _let_2) (combb bool _let_0 real) fconj) (hAPP real (fun real bool) (hAPP _let_1 _let_1 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP real _let_0 (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))) ) 19.06/18.07 ( (fun real bool), (fun real bool), (collect real), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (fun (fun int bool) (fun int bool)))) (let ((_let_6 (fun (fun int bool) _let_4))) (let ((_let_7 (fun int (fun int bool)))) (let ((_let_8 (fun (fun int bool) bool))) (let ((_let_9 (fun real _let_0))) (let ((_let_10 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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))) ) 19.06/18.08 ( (fun real bool), (fun real (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun real _let_0) (fun real bool)) (combb _let_0 bool real) (fEx int))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (fun (fun int bool) (fun int bool)))) (let ((_let_6 (fun (fun int bool) _let_4))) (let ((_let_7 (fun int (fun int bool)))) (let ((_let_8 (fun real _let_0))) (let ((_let_9 (fun _let_7 (fun int bool)))) (let ((_let_10 (fun int _let_5))) (let ((_let_11 (fun int real))) (let ((_let_12 (fun real (fun int bool)))) (let ((_let_13 (fun real _let_7))) (let ((_let_14 (fun (fun int bool) _let_7))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun real _let_10))) (let ((_let_17 (fun int _let_4))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun _let_17 _let_10))) (let ((_let_20 (fun _let_7 _let_17))) (let ((_let_21 (fun int _let_11))) (let ((_let_22 (fun _let_21 _let_7))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_11 (fun int bool)))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun _let_11 _let_11))) (let ((_let_27 (fun int _let_26))) (let ((_let_28 (fun int _let_1))) (hAPP _let_13 _let_12 (hAPP _let_9 (fun _let_13 _let_12) (combb _let_7 (fun int bool) real) (hAPP (fun (fun int bool) bool) _let_9 (combb (fun int bool) bool int) (fEx int))) (hAPP (fun int bool) _let_13 (hAPP _let_15 (fun (fun int bool) _let_13) (combc real (fun int bool) _let_7) (hAPP _let_16 _let_15 (hAPP (fun _let_10 _let_14) (fun _let_16 _let_15) (combb _let_10 _let_14 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_18 _let_16 (hAPP _let_19 (fun _let_18 _let_16) (combb _let_17 _let_10 real) (hAPP (fun _let_4 _let_5) _let_19 (combb 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) 19.06/18.08 ( complex, real, (hAPP real (fun real complex) complex_1 (one_one real)), (zero_zero real) ) 19.06/18.08 ( 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))) ) 19.06/18.08 ( complex, int, (number_number_of complex), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.06/18.08 ( complex, int, (number_number_of complex), min_1 ) 19.06/18.08 ( complex, complex, (hAPP complex (fun complex complex) (times_times complex) ii), ii ) 19.06/18.08 ( complex, complex, cnj, ii ) 19.06/18.08 ( complex, complex, cnj, (zero_zero complex) ) 19.06/18.08 ( complex, complex, cnj, (one_one complex) ) 19.06/18.08 ( complex, complex, (uminus_uminus complex), ii ) 19.06/18.08 ( complex, complex, (uminus_uminus complex), (one_one complex) ) 19.06/18.08 ( complex, complex, (inverse_inverse complex), ii ) 19.06/18.08 ( complex, complex, expi, (zero_zero complex) ) 19.06/18.08 ( complex, complex, 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(fun real (fun int (fun nat bool))) (fun real (fun int (fun nat (fun bool bool))))), (fun (fun int (fun nat bool)) (fun int (fun nat (fun bool bool)))), (combb (fun int (fun nat bool)) (fun int (fun nat (fun bool bool))) real), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 nat) fconj)))))) ) 19.22/18.19 ( (fun int (fun nat real)), (fun nat real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_4 (fun (fun nat real) (fun int (fun nat real))) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 nat) ) 19.22/18.19 ( (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (fun real (fun (fun nat real) (fun nat bool))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (fun int _let_1) (fun int _let_0)))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP (fun _let_3 _let_2) (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (combb _let_1 _let_0 int)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun nat real) (fun nat bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool nat)) (fequal real)))))) ) 19.22/18.19 ( (fun (fun int (fun nat real)) (fun real (fun int (fun nat bool)))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (combc real (fun int (fun nat real)) (fun int (fun nat bool))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun nat real)) (fun int (fun nat bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool nat)) (fequal real))))))))) ) 19.22/18.19 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun real bool)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun (fun nat real) (fun nat bool)))) (hAPP (fun _let_0 _let_1) (fun (fun real _let_0) (fun real _let_1)) (combb _let_0 _let_1 real) (combb real bool nat)))), (fequal real) ) 19.22/18.19 ( (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (fun (fun real (fun _let_1 _let_0)) (fun real (fun 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(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))))) ) 19.22/18.19 ( (let ((_let_0 (fun nat real))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))) ) 19.22/18.19 ( (let ((_let_0 (fun nat real))) (fun (fun int (fun real real)) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat real))) (fun (fun real real) (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (combb (fun real real) (fun _let_0 _let_0) int)), (combb real real nat) ) 19.22/18.19 ) 19.22/18.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139389 $$unsorted)) (or (not (group_add X_a)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_139389)) BOUND_VARIABLE_139389))) ) 19.22/18.19 ( real, (one_one real) ) 19.22/18.19 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.22/18.19 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 19.22/18.19 ( int, pls ) 19.22/18.19 ( int, (one_one int) ) 19.22/18.19 ( int, min_1 ) 19.22/18.19 ( complex, ii ) 19.22/18.19 ( complex, (one_one complex) ) 19.22/18.19 ) 19.22/18.19 (instantiation (let ((_let_0 (fun (filter X_a) bool))) (let ((_let_1 (fun X_a real))) (let ((_let_2 (fun X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_139450 $$unsorted) (BOUND_VARIABLE_139451 $$unsorted)) (let ((_let_0 (filter X_a))) (or (not (real_normed_vector X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_0 (hAPP _let_2 (fun X_b _let_0) (tendsto X_a X_b) BOUND_VARIABLE_139450) (zero_zero X_b)) BOUND_VARIABLE_139451))) (hBOOL (hAPP _let_0 bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (tendsto X_a real) (hAPP _let_2 _let_1 (hAPP (fun X_b real) (fun _let_2 _let_1) (combb X_b real X_a) (norm_norm X_b)) BOUND_VARIABLE_139450)) (zero_zero real)) BOUND_VARIABLE_139451)))) )))) 19.22/18.19 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 19.22/18.19 ( nat, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), sequentially ) 19.22/18.19 ) 19.22/18.19 (instantiation (let ((_let_0 (product_prod X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (ti X_a A_1) (hAPP _let_0 X_a (product_fst X_a X_b) (hAPP X_b _let_0 (hAPP X_a (fun X_b _let_0) (product_Pair X_a X_b) A_1) B))) )) 19.22/18.19 ( int, int, (zero_zero int), (one_one int) ) 19.22/18.19 ( int, int, (one_one int), (one_one int) ) 19.22/18.19 ( int, int, s, (one_one int) ) 19.22/18.19 ) 19.22/18.19 (instantiation (let ((_let_0 (product_prod int int))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (= A_2 B_1) (= (hAPP rat _let_0 quotient_of A_2) (hAPP rat _let_0 quotient_of B_1))) )) 19.22/18.19 ( (zero_zero rat), (zero_zero rat) ) 19.22/18.19 ( (zero_zero rat), (one_one rat) ) 19.22/18.19 ( (one_one rat), (zero_zero rat) ) 19.22/18.19 ) 19.22/18.19 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (hAPP real _let_0 _let_1 (hAPP complex real re X)))) (let ((_let_3 (hAPP complex real re Y))) (let ((_let_4 (hAPP real _let_0 _let_1 (hAPP complex real im X)))) (let ((_let_5 (hAPP complex real im Y))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP real complex (hAPP real (fun real complex) complex_1 (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real _let_2 _let_3)) (hAPP real real _let_4 _let_5))) (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP real real _let_2 _let_5)) (hAPP real real _let_4 _let_3))) (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) X) Y)) ))))))) 19.22/18.19 ( ii, ii ) 19.22/18.19 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 19.22/18.19 ( (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 19.22/18.19 ) 19.22/18.19 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (= (zero_zero X_a) (hAPP int X_a (number_number_of X_a) pls))) ) 19.22/18.19 ( real ) 19.22/18.19 ( nat ) 19.22/18.19 ( int ) 19.22/18.19 ( complex ) 19.22/18.19 ( rat ) 19.22/18.19 ( quickcheck_code_int ) 19.22/18.19 ( code_code_numeral ) 19.22/18.19 ) 19.22/18.19 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_1) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Y_1) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) X_1) Y_1)) zOdd))) )))) 19.22/18.19 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.22/18.19 ) 19.22/18.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139538 $$unsorted)) (or (not (linordered_idom X_a)) (= (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_139538) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_139538) (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_139538)))) ) 19.22/18.19 ( real, (zero_zero real) ) 19.22/18.19 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.22/18.19 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.22/18.19 ( 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))))) ) 19.22/18.19 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.22/18.19 ( 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))) ) 19.22/18.19 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.22/18.19 ( complex, ii ) 19.22/18.19 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.22/18.19 ( 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)) ) 19.22/18.19 ( rat, (zero_zero rat) ) 19.22/18.19 ) 19.22/18.19 (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)))) ) 19.22/18.20 ( (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))) ) 19.22/18.20 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.22/18.20 ( 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))) ) 19.22/18.20 ( skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.22/18.20 ) 19.22/18.20 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int _let_0 (ord_less_eq int) (zero_zero int)))) (let ((_let_2 (ord_less int))) (forall ((B $$unsorted) (M $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_1 A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 A_1) M))) (not (hBOOL (hAPP int bool _let_1 B))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 B) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_1) B) M))) (= (ti int B) (ti int A_1))) )))) 19.22/18.20 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.22/18.20 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.22/18.20 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.37/18.20 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s1 ) 19.37/18.20 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.37/18.20 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s1 ) 19.37/18.20 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 19.37/18.20 ) 19.37/18.20 (instantiation (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 (times_times X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_139595 $$unsorted) (BOUND_VARIABLE_139596 $$unsorted) (BOUND_VARIABLE_139597 $$unsorted) (BOUND_VARIABLE_139598 $$unsorted)) (or (not (field X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_139598)) (= _let_0 (ti X_a BOUND_VARIABLE_139597)) (= (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_139596) BOUND_VARIABLE_139597) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_139595) BOUND_VARIABLE_139598)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_3 BOUND_VARIABLE_139596) BOUND_VARIABLE_139598) (hAPP X_a X_a (hAPP X_a _let_1 _let_3 BOUND_VARIABLE_139595) BOUND_VARIABLE_139597)))) ))))) 19.37/18.20 ( real, pi, pi, pi, pi ) 19.37/18.20 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), pi, pi, pi ) 19.37/18.20 ) 19.37/18.20 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_139629 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls)))) BOUND_VARIABLE_139629) (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_139629) BOUND_VARIABLE_139629))) )) 19.37/18.20 ( real, pi ) 19.37/18.20 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.37/18.20 ( nat, (one_one nat) ) 19.37/18.20 ( 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) ) 19.37/18.20 ( 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)))) ) 19.37/18.20 ( complex, (hAPP real complex (of_real complex) pi) ) 19.37/18.20 ) 19.37/18.20 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (real_1 int))) (let ((_let_2 (hAPP real _let_0 (ord_less real) R_4))) (forall ((R_4 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 (zero_zero real)))) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP int real _let_1 N_2)) R_4))) (not (hBOOL (hAPP real bool _let_2 (hAPP int real _let_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) N_2) (one_one int))))))) ))) )))) 19.37/18.20 ( (zero_zero real) ) 19.37/18.20 ( (one_one real) ) 19.37/18.20 ( pi ) 19.37/18.20 ( (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)))) ) 19.37/18.20 ( (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))))) ) 19.37/18.20 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.37/18.20 ( (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)) ) 19.37/18.20 ) 19.37/18.20 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (number_number_of real))) (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real _let_2 min_1)) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) (one_one real)))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real _let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real real arcsin Y)))) )))) 19.37/18.20 ( (zero_zero real) ) 19.37/18.20 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.37/18.20 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.37/18.20 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.37/18.20 ( skv_14 ) 19.37/18.20 ) 19.37/18.20 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun int bool))) (forall ((A_3 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool nat_is_nat X_1))) (not (hBOOL (hAPP _let_1 bool nat_nat_set A_3))) (= (hBOOL (hAPP _let_0 bool (hAPP nat (fun _let_0 bool) (member nat) (hAPP int nat nat_1 X_1)) (hAPP _let_1 _let_0 (hAPP (fun int nat) (fun _let_1 _let_0) (image int nat) nat_1) A_3))) (hBOOL (hAPP _let_1 bool (hAPP int (fun _let_1 bool) (member int) X_1) A_3)))) ))) 19.37/18.20 ( zEven, (one_one int) ) 19.37/18.20 ) 19.37/18.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139882 $$unsorted)) (or (not (group_add X_a)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_139882) BOUND_VARIABLE_139882))) ) 19.37/18.20 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 19.37/18.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.37/18.20 ( code_code_numeral, (zero_zero code_code_numeral) ) 19.37/18.20 ) 19.37/18.20 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (= _let_0 (hAPP X_a X_a (abs_abs X_a) _let_0))) )) 19.37/18.20 ( real ) 19.37/18.20 ( nat ) 19.37/18.20 ( int ) 19.37/18.20 ( complex ) 19.37/18.20 ( rat ) 19.37/18.20 ( quickcheck_code_int ) 19.37/18.20 ( code_code_numeral ) 19.37/18.20 ) 19.37/18.20 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted)) (or (not (real_normed_vector X_a)) (= _let_0 (hAPP X_a X_a (sgn_sgn X_a) _let_0))) )) 19.37/18.20 ( real ) 19.37/18.20 ( nat ) 19.37/18.20 ( int ) 19.37/18.20 ( complex ) 19.37/18.20 ( rat ) 19.37/18.20 ( quickcheck_code_int ) 19.37/18.20 ( code_code_numeral ) 19.37/18.20 ) 19.37/18.20 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (fun int int))) (let ((_let_4 (product_prod int int))) (let ((_let_5 (fun int _let_4))) (let ((_let_6 (product_Pair int int))) (let ((_let_7 (fun _let_4 bool))) (let ((_let_8 (hAPP (fun _let_4 _let_7) _let_7 (accp _let_4) negDivAlg_rel))) (let ((_let_9 (hAPP int _let_0 P_1 A_4))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (or (not (hBOOL (hAPP _let_4 bool _let_8 (hAPP int _let_4 (hAPP int _let_5 _let_6 A0) A1)))) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (or (not (hBOOL (hAPP _let_4 bool _let_8 (hAPP int _let_4 (hAPP int _let_5 _let_6 A_4) B_4)))) (and (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) (hAPP int int (hAPP int _let_3 (plus_plus int) A_4) B_4)))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B_4) _let_2))) (not (hBOOL (hAPP int bool _let_9 (hAPP int int (hAPP int _let_3 (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_9 B_4))) )) (hBOOL (hAPP int bool (hAPP int _let_0 P_1 A0) A1))) ))))))))))) 19.37/18.20 ( (ord_less_eq int), (zero_zero int), (one_one int) ) 19.37/18.20 ( (ord_less_eq int), (zero_zero int), min_1 ) 19.37/18.20 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.37/18.20 ( (ord_less_eq int), (zero_zero int), s ) 19.37/18.20 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 19.37/18.20 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.37/18.20 ( (ord_less_eq int), (zero_zero int), skv_3 ) 19.37/18.20 ( (ord_less_eq int), (zero_zero int), skv_9 ) 19.37/18.20 ( (ord_less_eq int), (one_one int), t ) 19.37/18.20 ( (ord_less_eq int), min_1, pls ) 19.37/18.20 ( (ord_less_eq int), min_1, min_1 ) 19.37/18.20 ( (ord_less int), (zero_zero int), (zero_zero int) ) 19.37/18.20 ( (ord_less int), (zero_zero int), (one_one int) ) 19.37/18.20 ( (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))) ) 19.37/18.20 ( (ord_less int), (zero_zero int), min_1 ) 19.37/18.20 ( (ord_less int), min_1, (zero_zero int) ) 19.37/18.20 ( (ord_less int), min_1, min_1 ) 19.37/18.20 ( (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))) ) 19.37/18.20 ( (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 19.37/18.20 ( (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 19.37/18.20 ( (ord_less int), t, (zero_zero int) ) 19.37/18.20 ( (ord_less int), t, (one_one int) ) 19.37/18.20 ( (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))) ) 19.37/18.20 ( (ord_less int), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.37/18.20 ( (ord_less int), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.37/18.20 ( (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 19.37/18.20 ( quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 19.37/18.20 ( (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))) ) 19.37/18.21 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.37/18.21 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.39/18.21 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.39/18.21 ( (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))) ) 19.39/18.21 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.39/18.21 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.39/18.21 ) 19.39/18.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139926 $$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_139926) (zero_zero X_a)) (ti X_a BOUND_VARIABLE_139926))) ) 19.39/18.21 ( bool, fFalse ) 19.39/18.21 ( bool, fTrue ) 19.39/18.21 ( real, pi ) 19.39/18.21 ( nat, (one_one nat) ) 19.39/18.21 ( (fun nat bool), (even_odd_even nat) ) 19.39/18.21 ( (fun nat bool), prime ) 19.39/18.21 ( (fun nat nat), suc ) 19.39/18.21 ( (fun nat nat), (fact_fact nat) ) 19.39/18.21 ( (fun nat nat), (size_size nat) ) 19.39/18.21 ( (fun nat nat), fact ) 19.39/18.21 ( (fun nat nat), nat_size ) 19.39/18.21 ( int, pls ) 19.39/18.21 ( int, m ) 19.39/18.21 ( 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) ) 19.39/18.21 ( int, min_1 ) 19.39/18.21 ( int, s ) 19.39/18.21 ( 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)))) ) 19.39/18.21 ( int, s1 ) 19.39/18.21 ( int, t ) 19.39/18.21 ( (fun int bool), zprime ) 19.39/18.21 ( (fun int bool), nat_neg ) 19.39/18.21 ( (fun int bool), zEven ) 19.39/18.21 ( (fun int bool), nat_is_nat ) 19.39/18.21 ( (fun int bool), zOdd ) 19.39/18.21 ( (fun int bool), (even_odd_even int) ) 19.39/18.21 ( (fun int bool), twoSqu1091635170sum2sq ) 19.39/18.21 ( (fun int nat), nat_1 ) 19.39/18.21 ( (fun int nat), phi ) 19.39/18.21 ( (fun real real), sqrt ) 19.39/18.21 ( (fun real real), tan ) 19.39/18.21 ( (fun real real), cos ) 19.39/18.21 ( (fun real real), arccos ) 19.39/18.21 ( (fun real real), ln ) 19.39/18.21 ( (fun real real), sin ) 19.39/18.21 ( (fun real real), arctan ) 19.39/18.21 ( (fun real real), arcsin ) 19.39/18.21 ( complex, ii ) 19.39/18.21 ( (fun complex complex), cnj ) 19.39/18.21 ( (fun complex complex), expi ) 19.39/18.21 ( (fun nat real), (real_1 nat) ) 19.39/18.21 ( (fun nat real), cos_coeff ) 19.39/18.21 ( (fun nat real), sin_coeff ) 19.39/18.21 ( (fun int int), bit0 ) 19.39/18.21 ( (fun int int), bit1 ) 19.39/18.21 ( (fun int int), pred ) 19.39/18.21 ( (fun int int), succ ) 19.39/18.21 ( (fun int int), (fact_fact int) ) 19.39/18.21 ( (fun int int), zfact ) 19.39/18.21 ( (fun bool bool), fNot ) 19.39/18.21 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 19.39/18.21 ( (fun bool (fun bool bool)), fconj ) 19.39/18.21 ( (fun bool (fun bool bool)), fdisj ) 19.39/18.21 ( (fun bool (fun bool bool)), fimplies ) 19.39/18.21 ( (fun int (fun int bool)), sRStar ) 19.39/18.21 ( (fun int (fun int bool)), quadRes ) 19.39/18.21 ( (fun int (fun int bool)), norRRset ) 19.39/18.21 ( (fun int (fun int bool)), d22set ) 19.39/18.21 ( (fun int (fun int bool)), sr ) 19.39/18.21 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 19.39/18.21 ( (fun nat (fun nat nat)), nat_gcd ) 19.39/18.21 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 19.39/18.21 ( (fun nat (fun nat nat)), nat_lcm ) 19.39/18.21 ( (fun nat (fun real real)), root ) 19.39/18.21 ( (fun real (fun real real)), log ) 19.39/18.21 ( (fun real (fun real real)), powr ) 19.39/18.21 ( (fun nat (fun nat bool)), coprime ) 19.39/18.21 ( (fun (fun int bool) int), (the int) ) 19.39/18.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 19.39/18.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 19.39/18.21 ( (fun nat (fun nat (product_prod int int))), bezw ) 19.39/18.21 ( (fun (fun int bool) bool), nat_nat_set ) 19.39/18.21 ( (filter nat), sequentially ) 19.39/18.21 ( (fun (product_prod nat nat) bool), pred_nat ) 19.39/18.21 ( (fun (product_prod int int) bool), frac_1 ) 19.39/18.21 ( (fun real complex), cis ) 19.39/18.21 ( (fun complex real), im ) 19.39/18.21 ( (fun complex real), re ) 19.39/18.21 ( (fun complex real), arg ) 19.39/18.21 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 19.39/18.21 ( (fun int (fun int int)), int_gcd ) 19.39/18.21 ( (fun int (fun int int)), multInv ) 19.39/18.21 ( (fun int (fun int int)), legacy_zgcd ) 19.39/18.21 ( (fun int (fun int int)), z3mod ) 19.39/18.21 ( (fun int (fun int int)), inv ) 19.39/18.21 ( (fun int (fun int int)), (gcd_gcd int) ) 19.39/18.21 ( (fun int (fun int int)), standardRes ) 19.39/18.21 ( (fun int (fun int int)), legendre ) 19.39/18.21 ( (fun int (fun int int)), nat_tsub ) 19.39/18.21 ( (fun int (fun int int)), z3div ) 19.39/18.21 ( (fun int (fun int int)), int_lcm ) 19.39/18.21 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 19.39/18.21 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 19.39/18.21 ( (fun int (fun (fun int bool) bool)), rsetR ) 19.39/18.21 ( (fun int (fun (fun int bool) bool)), resSet ) 19.39/18.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 19.39/18.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 19.39/18.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 19.39/18.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 19.39/18.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 19.39/18.21 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 19.39/18.21 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 19.39/18.21 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 19.39/18.21 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 19.39/18.21 ( (fun int (fun int (product_prod int int))), negDivAlg ) 19.39/18.21 ( (fun int (fun int (product_prod int int))), divmod_int ) 19.39/18.21 ( (fun int (fun int (product_prod int int))), posDivAlg ) 19.39/18.21 ( (fun int (fun int (product_prod int int))), pdivmod ) 19.39/18.21 ( (fun int (fun int (product_prod int int))), norm_frac ) 19.39/18.21 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 19.39/18.21 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 19.39/18.21 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 19.39/18.21 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 19.39/18.21 ( (fun real nat), natfloor ) 19.39/18.21 ( (fun real nat), natceiling ) 19.39/18.21 ( (fun int quickcheck_code_int), quickcheck_of_int ) 19.39/18.21 ( (fun int (fun int (fun int bool))), wset ) 19.39/18.21 ( (fun int (fun int (fun int bool))), bnorRset ) 19.39/18.21 ( (fun int (fun int (fun int bool))), zcong ) 19.39/18.21 ( (fun int (fun int (fun int bool))), noXRRset ) 19.39/18.21 ( (fun int (fun int (fun int bool))), zcongm ) 19.39/18.21 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 19.39/18.21 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 19.39/18.21 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 19.39/18.21 ( (fun int real), (real_1 int) ) 19.39/18.21 ( (fun complex nat), (size_size complex) ) 19.39/18.21 ( (fun complex nat), complex_size ) 19.39/18.21 ( (fun int (list int)), quickc666637781d_zero ) 19.39/18.21 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 19.39/18.21 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 19.39/18.21 ( (fun (product_prod int int) rat), frct ) 19.39/18.21 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 19.39/18.21 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 19.39/18.21 ( (fun (fun nat rat) bool), vanishes ) 19.39/18.21 ( (fun int (fun int rat)), fract ) 19.39/18.21 ( (fun code_code_numeral int), code_int_of ) 19.39/18.21 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 19.39/18.21 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 19.39/18.21 ( (fun code_code_numeral nat), code_c271388182l_size ) 19.39/18.21 ( (fun real (fun real complex)), complex_1 ) 19.39/18.21 ( (fun real (fun real complex)), rcis ) 19.39/18.21 ( (fun int (fun nat nat)), nat_aux ) 19.39/18.21 ( (fun rat real), ratreal ) 19.39/18.21 ( (fun quickcheck_code_int int), quickcheck_int_of ) 19.39/18.21 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 19.39/18.21 ( (fun rat (product_prod int int)), quotient_of ) 19.39/18.21 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 19.39/18.21 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 19.39/18.21 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 19.39/18.21 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 19.39/18.21 ) 19.39/18.21 (instantiation (forall ((X $$unsorted)) (= (hAPP real real (uminus_uminus real) (hAPP complex real im X)) (hAPP complex real im (hAPP complex complex (uminus_uminus complex) X))) ) 19.39/18.21 ( ii ) 19.39/18.21 ( (one_one complex) ) 19.39/18.21 ) 19.39/18.21 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_1) zEven))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Y_1) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) X_1) Y_1)) zEven))) )))) 19.39/18.21 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 19.39/18.21 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.21 ) 19.39/18.21 (instantiation (let ((_let_0 (exp X_a))) (let ((_let_1 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_139999 $$unsorted) (BOUND_VARIABLE_140000 $$unsorted)) (or (not (real_normed_field X_a)) (not (banach 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_139999)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_140000)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 (minus_minus X_a) BOUND_VARIABLE_139999) BOUND_VARIABLE_140000)))) ))) 19.39/18.21 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 19.39/18.21 ( 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)))), (hAPP int int (number_number_of int) min_1) ) 19.39/18.21 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 19.39/18.21 ) 19.39/18.21 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (fun int int))) (let ((_let_3 (power_power int))) (let ((_let_4 (hAPP int nat nat_1 X_1))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (X_1 $$unsorted)) (or (not (= (hAPP int int (hAPP int _let_2 (times_times int) A_2) B_1) (hAPP nat int (hAPP int _let_1 _let_3 C_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_0 bool (hAPP int (fun _let_0 bool) (member int) X_1) zOdd))) (not (= (one_one int) (hAPP int int (hAPP int _let_2 legacy_zgcd A_2) B_1))) (not (forall ((K_1 $$unsorted)) (not (= (hAPP nat int (hAPP int _let_1 _let_3 K_1) _let_4) (ti int A_2))) ))) )))))) 19.39/18.21 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, s, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.39/18.21 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int), skv_8, (one_one int) ) 19.39/18.21 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t, s1, (zero_zero int) ) 19.39/18.21 ) 19.39/18.21 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_140062 $$unsorted) (BOUND_VARIABLE_140063 $$unsorted)) (or (not (group_add X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_140062) BOUND_VARIABLE_140063) (hAPP X_a X_a (hAPP X_a _let_0 (minus_minus X_a) BOUND_VARIABLE_140062) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_140063)))) )) 19.39/18.21 ( nat, (one_one nat), (one_one nat) ) 19.39/18.21 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 19.39/18.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 19.39/18.21 ) 19.39/18.21 (instantiation (let ((_let_0 (inverse_divide X_a))) (forall ((X_a $$unsorted)) (or (not (division_ring X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0))) )) 19.39/18.21 ( bool ) 19.39/18.21 ( real ) 19.39/18.21 ( nat ) 19.39/18.21 ( (fun nat bool) ) 19.39/18.21 ( int ) 19.39/18.21 ( (fun int bool) ) 19.39/18.21 ( (fun real bool) ) 19.39/18.21 ( (fun real real) ) 19.39/18.21 ( complex ) 19.39/18.21 ( (fun nat real) ) 19.39/18.21 ( (fun int int) ) 19.39/18.21 ( rat ) 19.39/18.21 ( (fun int (fun int bool)) ) 19.39/18.21 ( (product_prod int int) ) 19.39/18.21 ( (fun (product_prod int int) bool) ) 19.39/18.21 ( code_code_numeral ) 19.39/18.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 19.39/18.21 ( (fun (product_prod int int) int) ) 19.39/18.21 ( (fun int (fun int (fun int bool))) ) 19.39/18.21 ( (fun int real) ) 19.39/18.21 ) 19.39/18.21 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (hAPP real _let_0 (ord_less real) (zero_zero real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun real _let_2))) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_3 X_1))) (= (hAPP real real (hAPP nat _let_1 root N_1) X_1) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_5 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_5 (hAPP (fun bool _let_2) (fun _let_0 _let_5) (combb bool _let_2 real) fconj) _let_3)) (hAPP real _let_0 (hAPP _let_4 _let_4 (combc real real bool) (hAPP _let_1 _let_4 (hAPP _let_4 (fun _let_1 _let_4) (combb real _let_0 real) (fequal real)) (hAPP nat _let_1 (hAPP (fun real (fun nat real)) (fun nat _let_1) (combc real nat real) (power_power real)) N_1))) X_1))))) ))))))) 19.39/18.21 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 19.39/18.21 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 19.39/18.21 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.22 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.39/18.22 ) 19.39/18.22 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (ord_less real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (uminus_uminus real))) (let ((_let_6 (hAPP real _let_1 _let_3 _let_0))) (let ((_let_7 (fun real _let_1))) (let ((_let_8 (fun real _let_4))) (let ((_let_9 (hAPP real real (hAPP nat _let_2 root N_1) X_1))) (let ((_let_10 (hBOOL (hAPP real bool (hAPP real _let_1 _let_3 X_1) _let_0)))) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (or (hBOOL (hAPP real bool _let_6 X_1)) (and (or (not _let_10) (= _let_9 (hAPP real real _let_5 (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_8 (fun _let_1 _let_1) (combs real bool bool) (hAPP _let_1 _let_8 (hAPP (fun bool _let_4) (fun _let_1 _let_8) (combb bool _let_4 real) fconj) _let_6)) (hAPP real _let_1 (hAPP _let_7 _let_7 (combc real real bool) (hAPP _let_2 _let_7 (hAPP _let_7 (fun _let_2 _let_7) (combb real _let_1 real) (fequal real)) (hAPP nat _let_2 (hAPP (fun real (fun nat real)) (fun nat _let_2) (combc real nat real) (power_power real)) N_1))) (hAPP real real _let_5 X_1))))))) (or _let_10 (= _let_0 _let_9)))) )))))))))))) 19.39/18.22 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 19.39/18.22 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 19.39/18.22 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.22 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.39/18.22 ) 19.39/18.22 (instantiation (let ((_let_0 (even_odd_even nat))) (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (hBOOL (hAPP nat bool _let_0 N_1)) (not (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N_1) (one_one nat))))))) )) 19.39/18.22 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.22 ) 19.39/18.22 (instantiation (let ((_let_0 (fact_fact int))) (let ((_let_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) N) (one_one int)))) (forall ((N $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) N))) (= (hAPP int int (hAPP int (fun int int) (times_times int) _let_1) (hAPP int int _let_0 N)) (hAPP int int _let_0 _let_1))) ))) 19.39/18.22 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 19.39/18.22 ( (one_one int) ) 19.39/18.22 ( min_1 ) 19.39/18.22 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.22 ( s ) 19.39/18.22 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.22 ( (hAPP int int (number_number_of int) pls) ) 19.39/18.22 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.39/18.22 ( skv_3 ) 19.39/18.22 ( skv_9 ) 19.39/18.22 ) 19.39/18.22 (instantiation (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (div_div X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_140326 $$unsorted) (BOUND_VARIABLE_140327 $$unsorted)) (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_140326) BOUND_VARIABLE_140327))) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_140327)) BOUND_VARIABLE_140326) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_140327) BOUND_VARIABLE_140326)))) )))) 19.39/18.22 ( 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) (hAPP nat int (hAPP 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)) ) 19.39/18.22 ) 19.39/18.22 (instantiation (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (inverse_inverse X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_140427 $$unsorted)) (or (not (real_n1866405975lgebra X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_140427)) (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_140427)) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_140427)))) )))) 19.39/18.22 ( bool, fFalse ) 19.39/18.22 ( bool, fTrue ) 19.39/18.22 ( real, (zero_zero real) ) 19.39/18.22 ( real, pi ) 19.39/18.22 ( 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)))) ) 19.39/18.22 ( (fun nat bool), (even_odd_even nat) ) 19.39/18.22 ( (fun nat bool), prime ) 19.39/18.22 ( (fun nat nat), suc ) 19.39/18.22 ( (fun nat nat), (fact_fact nat) ) 19.39/18.22 ( (fun nat nat), (size_size nat) ) 19.39/18.22 ( (fun nat nat), fact ) 19.39/18.22 ( (fun nat nat), nat_size ) 19.39/18.22 ( int, pls ) 19.39/18.22 ( int, m ) 19.39/18.22 ( int, min_1 ) 19.39/18.22 ( int, s ) 19.39/18.22 ( int, s1 ) 19.39/18.22 ( int, t ) 19.39/18.22 ( (fun int bool), zprime ) 19.39/18.22 ( (fun int bool), nat_neg ) 19.39/18.22 ( (fun int bool), zEven ) 19.39/18.22 ( (fun int bool), nat_is_nat ) 19.39/18.22 ( (fun int bool), zOdd ) 19.39/18.22 ( (fun int bool), (even_odd_even int) ) 19.39/18.22 ( (fun int bool), twoSqu1091635170sum2sq ) 19.39/18.22 ( (fun int nat), nat_1 ) 19.39/18.22 ( (fun int nat), phi ) 19.39/18.22 ( (fun real real), sqrt ) 19.39/18.22 ( (fun real real), tan ) 19.39/18.22 ( (fun real real), cos ) 19.39/18.22 ( (fun real real), arccos ) 19.39/18.22 ( (fun real real), ln ) 19.39/18.22 ( (fun real real), sin ) 19.39/18.22 ( (fun real real), arctan ) 19.39/18.22 ( (fun real real), arcsin ) 19.39/18.22 ( complex, ii ) 19.39/18.22 ( (fun complex complex), cnj ) 19.39/18.22 ( (fun complex complex), expi ) 19.39/18.22 ( (fun nat real), (real_1 nat) ) 19.39/18.22 ( (fun nat real), cos_coeff ) 19.39/18.22 ( (fun nat real), sin_coeff ) 19.39/18.22 ( (fun int int), bit0 ) 19.39/18.22 ( (fun int int), bit1 ) 19.39/18.22 ( (fun int int), pred ) 19.39/18.22 ( (fun int int), succ ) 19.39/18.22 ( (fun int int), (fact_fact int) ) 19.39/18.22 ( (fun int int), zfact ) 19.39/18.22 ( (fun bool bool), fNot ) 19.39/18.22 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 19.39/18.22 ( (fun bool (fun bool bool)), fconj ) 19.39/18.22 ( (fun bool (fun bool bool)), fdisj ) 19.39/18.22 ( (fun bool (fun bool bool)), fimplies ) 19.39/18.22 ( (fun int (fun int bool)), sRStar ) 19.39/18.22 ( (fun int (fun int bool)), quadRes ) 19.39/18.22 ( (fun int (fun int bool)), norRRset ) 19.39/18.22 ( (fun int (fun int bool)), d22set ) 19.39/18.22 ( (fun int (fun int bool)), sr ) 19.39/18.22 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 19.39/18.22 ( (fun nat (fun nat nat)), nat_gcd ) 19.39/18.22 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 19.39/18.22 ( (fun nat (fun nat nat)), nat_lcm ) 19.39/18.22 ( (fun nat (fun real real)), root ) 19.39/18.22 ( (fun real (fun real real)), log ) 19.39/18.22 ( (fun real (fun real real)), powr ) 19.39/18.22 ( (fun nat (fun nat bool)), coprime ) 19.39/18.22 ( (fun (fun int bool) int), (the int) ) 19.39/18.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 19.39/18.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 19.39/18.22 ( (fun nat (fun nat (product_prod int int))), bezw ) 19.39/18.22 ( (fun (fun int bool) bool), nat_nat_set ) 19.39/18.22 ( (filter nat), sequentially ) 19.39/18.22 ( (fun (product_prod nat nat) bool), pred_nat ) 19.39/18.22 ( (fun (product_prod int int) bool), frac_1 ) 19.39/18.22 ( (fun real complex), cis ) 19.39/18.22 ( (fun complex real), im ) 19.39/18.22 ( (fun complex real), re ) 19.39/18.22 ( (fun complex real), arg ) 19.39/18.22 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 19.39/18.22 ( (fun int (fun int int)), int_gcd ) 19.39/18.22 ( (fun int (fun int int)), multInv ) 19.39/18.22 ( (fun int (fun int int)), legacy_zgcd ) 19.39/18.22 ( (fun int (fun int int)), z3mod ) 19.39/18.22 ( (fun int (fun int int)), inv ) 19.39/18.22 ( (fun int (fun int int)), (gcd_gcd int) ) 19.39/18.22 ( (fun int (fun int int)), standardRes ) 19.39/18.22 ( (fun int (fun int int)), legendre ) 19.39/18.22 ( (fun int (fun int int)), nat_tsub ) 19.39/18.22 ( (fun int (fun int int)), z3div ) 19.39/18.22 ( (fun int (fun int int)), int_lcm ) 19.39/18.22 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 19.39/18.22 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 19.39/18.22 ( (fun int (fun (fun int bool) bool)), rsetR ) 19.39/18.22 ( (fun int (fun (fun int bool) bool)), resSet ) 19.39/18.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 19.39/18.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 19.39/18.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 19.39/18.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 19.39/18.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 19.39/18.22 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 19.39/18.22 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 19.39/18.22 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 19.39/18.22 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 19.39/18.22 ( (fun int (fun int (product_prod int int))), negDivAlg ) 19.39/18.22 ( (fun int (fun int (product_prod int int))), divmod_int ) 19.39/18.22 ( (fun int (fun int (product_prod int int))), posDivAlg ) 19.39/18.22 ( (fun int (fun int (product_prod int int))), pdivmod ) 19.39/18.22 ( (fun int (fun int (product_prod int int))), norm_frac ) 19.39/18.22 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 19.39/18.22 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 19.39/18.22 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 19.39/18.22 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 19.39/18.22 ( (fun real nat), natfloor ) 19.39/18.22 ( (fun real nat), natceiling ) 19.39/18.22 ( (fun int quickcheck_code_int), quickcheck_of_int ) 19.39/18.22 ( (fun int (fun int (fun int bool))), wset ) 19.39/18.22 ( (fun int (fun int (fun int bool))), bnorRset ) 19.39/18.22 ( (fun int (fun int (fun int bool))), zcong ) 19.39/18.22 ( (fun int (fun int (fun int bool))), noXRRset ) 19.39/18.22 ( (fun int (fun int (fun int bool))), zcongm ) 19.39/18.22 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 19.39/18.22 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 19.39/18.22 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 19.39/18.22 ( (fun int real), (real_1 int) ) 19.39/18.22 ( (fun complex nat), (size_size complex) ) 19.39/18.22 ( (fun complex nat), complex_size ) 19.39/18.22 ( (fun int (list int)), quickc666637781d_zero ) 19.39/18.22 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 19.39/18.22 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 19.39/18.22 ( (fun (product_prod int int) rat), frct ) 19.39/18.22 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 19.39/18.22 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 19.39/18.22 ( (fun (fun nat rat) bool), vanishes ) 19.39/18.22 ( (fun int (fun int rat)), fract ) 19.39/18.22 ( (fun code_code_numeral int), code_int_of ) 19.39/18.22 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 19.39/18.22 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 19.39/18.22 ( (fun code_code_numeral nat), code_c271388182l_size ) 19.39/18.22 ( (fun real (fun real complex)), complex_1 ) 19.39/18.22 ( (fun real (fun real complex)), rcis ) 19.39/18.22 ( (fun int (fun nat nat)), nat_aux ) 19.39/18.22 ( (fun rat real), ratreal ) 19.39/18.22 ( (fun quickcheck_code_int int), quickcheck_int_of ) 19.39/18.22 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 19.39/18.22 ( (fun rat (product_prod int int)), quotient_of ) 19.39/18.22 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 19.39/18.22 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 19.39/18.22 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 19.39/18.22 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 19.39/18.22 ) 19.39/18.22 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_140484 $$unsorted) (BOUND_VARIABLE_140485 $$unsorted)) (or (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_140485) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_140484) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_140485) BOUND_VARIABLE_140484)) _let_3))) ))))) 19.39/18.22 ( nat, (one_one nat), (one_one nat) ) 19.39/18.22 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 19.39/18.22 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.22 ) 19.39/18.22 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_1) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) X_1) (one_one int))) zEven))) )))) 19.39/18.22 ( (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)))) ) 19.39/18.22 ) 19.39/18.22 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (ord_less real))) (let ((_let_3 (one_one real))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP int real (number_number_of real) min_1)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X_1) _let_3))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) arcsin) X_1) (hAPP real real (inverse_inverse real) (hAPP real real sqrt (hAPP real real (hAPP real _let_1 (minus_minus real) _let_3) (hAPP nat real (hAPP real (fun nat real) (power_power real) X_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))) ))))) 19.39/18.22 ( (zero_zero real) ) 19.39/18.22 ( (one_one real) ) 19.39/18.22 ( pi ) 19.39/18.22 ( (hAPP int real (number_number_of real) min_1) ) 19.39/18.22 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.22 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 19.39/18.22 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.22 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.22 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 19.39/18.22 ) 19.39/18.22 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) K))) (forall ((P_1 $$unsorted) (K $$unsorted) (I $$unsorted)) (or (not (hBOOL (hAPP int bool _let_0 I))) (not (hBOOL (hAPP int bool P_1 K))) (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_0 I_2))) (not (hBOOL (hAPP int bool P_1 I_2))) (hBOOL (hAPP int bool P_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) I_2) (one_one int))))) )) (hBOOL (hAPP int bool P_1 I))) )) 19.39/18.22 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), s ) 19.39/18.22 ( (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int), t ) 19.39/18.22 ( nat_neg, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 19.39/18.22 ( (hAPP int (fun int bool) (ord_less int) pls), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.39/18.22 ( (hAPP int (fun int bool) (ord_less_eq int) pls), min_1, min_1 ) 19.39/18.22 ( nat_is_nat, (zero_zero int), skv_9 ) 19.39/18.22 ( (even_odd_even int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.22 ( (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))), (zero_zero int), min_1 ) 19.39/18.22 ( (hAPP int (fun int bool) (ord_less int) min_1), (zero_zero int), skv_3 ) 19.39/18.22 ( (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1, pls ) 19.39/18.22 ( (hAPP int (fun int bool) (ord_less int) t), (zero_zero int), (one_one int) ) 19.39/18.22 ) 19.39/18.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140532 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_140532) (zero_zero int))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_140532)) (zero_zero X_a))))) ) 19.39/18.23 ( real, (zero_zero int) ) 19.39/18.23 ( real, (one_one int) ) 19.39/18.23 ) 19.39/18.23 (instantiation (forall ((P_5 $$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))) ) 19.39/18.23 ( (zero_zero nat) ) 19.39/18.23 ( (one_one nat) ) 19.39/18.23 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.23 ) 19.39/18.23 (instantiation (let ((_let_0 (zero_zero nat))) (let ((_let_1 (fun X_a bool))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool (finite_finite_1 X_a) A_3))) (and (not (forall ((X_2 $$unsorted)) (not (hBOOL (hAPP _let_1 bool (hAPP X_a (fun _let_1 bool) (member X_a) X_2) A_3))) )) (not (= _let_0 (one_one nat)))) (= _let_0 (hAPP _let_1 nat (finite_card X_a) A_3))) ))) 19.39/18.23 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 19.39/18.23 ) 19.39/18.23 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (sgn_sgn X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_140631 $$unsorted) (BOUND_VARIABLE_140632 $$unsorted)) (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_140631) BOUND_VARIABLE_140632)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_140631)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_140632)))) )))) 19.39/18.23 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.39/18.23 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.39/18.23 ( 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)))))) ) 19.39/18.23 ( 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 ) 19.39/18.23 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 19.39/18.23 ( 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) ) 19.39/18.23 ( 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 ) 19.39/18.23 ( 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_1 ) 19.39/18.23 ( complex, ii, ii ) 19.39/18.23 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 19.39/18.23 ( 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 ) 19.39/18.23 ) 19.39/18.23 (instantiation (let ((_let_0 (fun real bool))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (or (not (forall ((X_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X_2) (zero_zero real))) )) (= (hAPP real real F Y_1) (hAPP real real F X_1))) )) 19.39/18.23 ( (zero_zero real), (zero_zero real), sqrt ) 19.39/18.23 ( (zero_zero real), (zero_zero real), tan ) 19.39/18.23 ( (zero_zero real), (zero_zero real), cos ) 19.39/18.23 ( (zero_zero real), (zero_zero real), (inverse_inverse real) ) 19.39/18.23 ( (zero_zero real), (zero_zero real), sin ) 19.39/18.23 ( (zero_zero real), (zero_zero real), arctan ) 19.39/18.23 ( (zero_zero real), (zero_zero real), (sgn_sgn real) ) 19.39/18.23 ( (zero_zero real), pi, sin ) 19.39/18.23 ( (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)))), cos ) 19.39/18.23 ( (zero_zero real), (hAPP real real (hAPP 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 ) 19.39/18.23 ( (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 (hAPP int int bit1 pls))))), tan ) 19.39/18.23 ( (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 bit0 (hAPP int int bit1 pls))))), sin ) 19.39/18.23 ( (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 bit1 (hAPP int int bit1 pls)))), tan ) 19.39/18.23 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))), arctan ) 19.39/18.23 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))), arctan ) 19.39/18.23 ( (one_one real), (one_one real), (uminus_uminus real) ) 19.39/18.23 ( (one_one real), (one_one real), ln ) 19.39/18.23 ( (one_one real), (one_one real), arctan ) 19.39/18.23 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), sqrt ) 19.39/18.23 ( (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) ) 19.39/18.23 ( (one_one real), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), (uminus_uminus real) ) 19.39/18.23 ( pi, (zero_zero real), sin ) 19.39/18.23 ( 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)))) ) 19.39/18.23 ( pi, pi, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))) ) 19.39/18.23 ( pi, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _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)))) ) 19.39/18.23 ( pi, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), tan ) 19.39/18.23 ( 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 ) 19.39/18.23 ( (hAPP int real (number_number_of real) (hAPP 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) ) 19.39/18.23 ( (hAPP int real (number_number_of real) (hAPP 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)) ) 19.39/18.23 ( (hAPP int real (number_number_of real) (hAPP 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))))) ) 19.39/18.23 ( (hAPP int real (number_number_of real) (hAPP 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)))) ) 19.39/18.23 ( (hAPP int real (number_number_of real) (hAPP 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))))) ) 19.39/18.23 ( (hAPP int real (number_number_of 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) ) 19.39/18.23 ( (hAPP int real (number_number_of real) (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) ) 19.39/18.23 ( (hAPP int 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 ) 19.39/18.23 ( (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)))), (hAPP real (fun real real) (inverse_divide real) (one_one real)) ) 19.39/18.23 ( (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 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))), cos ) 19.39/18.23 ( (hAPP int 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)) ) 19.39/18.23 ( (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), cos ) 19.39/18.23 ( (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 real real (hAPP 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) ) 19.39/18.23 ( (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 real real (hAPP 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 ) 19.39/18.23 ( (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), (one_one real), (uminus_uminus real) ) 19.39/18.23 ( (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), (hAPP real real (hAPP 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 ) 19.39/18.23 ( (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), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))), sin ) 19.39/18.23 ( (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) ) 19.39/18.23 ( (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), 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)))) ) 19.39/18.23 ( (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) ) 19.39/18.23 ( (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))))), (zero_zero real), tan ) 19.39/18.23 ( (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))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), cos ) 19.39/18.23 ( (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))))), (hAPP real real (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 ) 19.39/18.23 ( (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))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))), cos ) 19.39/18.23 ( (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))))), (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 ) 19.39/18.23 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (one_one real), sqrt ) 19.39/18.23 ( (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 ) 19.39/18.23 ( (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))), sqrt ) 19.39/18.24 ( (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) ) 19.39/18.24 ( (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))), (hAPP real (fun real real) (inverse_divide real) (one_one real)) ) 19.39/18.24 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), sin ) 19.39/18.24 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), sin ) 19.39/18.24 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))), cos ) 19.39/18.24 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))), sin ) 19.39/18.24 ( (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))))), pi, tan ) 19.39/18.24 ( (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))))), pi, cos ) 19.39/18.24 ( (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))))), pi, sin ) 19.39/18.24 ( (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))))), (hAPP real 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 ) 19.39/18.24 ( (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))))), (hAPP real 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 ) 19.39/18.24 ( (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))))), (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 ) 19.39/18.24 ( (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)))), pi, cos ) 19.39/18.24 ( (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)))), (hAPP real real (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 ) 19.39/18.24 ( (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)))), (hAPP real real (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 ) 19.39/18.24 ( (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)))), (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 ) 19.39/18.24 ( (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 bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real real) (inverse_divide real) (one_one real)) ) 19.39/18.24 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))), arctan ) 19.39/18.24 ( (hAPP real real arctan (hAPP real real (hAPP 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))))) ) 19.39/18.24 ( (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 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)) ) 19.39/18.24 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP 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 ) 19.39/18.24 ( (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1))))))))) ) 19.39/18.24 ( skv_14, skv_14, cos ) 19.39/18.24 ) 19.39/18.24 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (not (hBOOL (hAPP X_a bool (iszero X_a) (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 pls)))))) ) 19.39/18.24 ( real ) 19.39/18.24 ( nat ) 19.39/18.24 ( int ) 19.39/18.24 ( complex ) 19.39/18.24 ( rat ) 19.39/18.24 ( quickcheck_code_int ) 19.39/18.24 ( code_code_numeral ) 19.39/18.24 ) 19.39/18.24 (instantiation (let ((_let_0 (fun X_a (fun X_a X_a)))) (let ((_let_1 (fun X_a (fun nat X_a)))) (forall ((X_a $$unsorted)) (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))) ))) 19.39/18.24 ( bool ) 19.39/18.24 ( real ) 19.39/18.24 ( nat ) 19.39/18.24 ( (fun nat bool) ) 19.39/18.24 ( (fun nat nat) ) 19.39/18.24 ( int ) 19.39/18.24 ( (fun int bool) ) 19.39/18.24 ( (fun real bool) ) 19.39/18.24 ( (fun real real) ) 19.39/18.24 ( complex ) 19.39/18.24 ( (fun nat real) ) 19.39/18.24 ( (fun int int) ) 19.39/18.24 ( rat ) 19.39/18.24 ( (fun bool bool) ) 19.39/18.24 ( (fun int (fun int bool)) ) 19.39/18.24 ( quickcheck_code_int ) 19.39/18.24 ( (fun nat (fun nat bool)) ) 19.39/18.24 ( (product_prod real real) ) 19.39/18.24 ( (product_prod int int) ) 19.39/18.24 ( (fun nat (product_prod int int)) ) 19.39/18.24 ( (product_prod nat nat) ) 19.39/18.24 ( (fun (product_prod nat nat) bool) ) 19.39/18.24 ( (fun nat (fun (product_prod nat nat) bool)) ) 19.39/18.24 ( (fun nat (product_prod nat nat)) ) 19.39/18.24 ( (fun (product_prod int int) bool) ) 19.39/18.24 ( code_code_numeral ) 19.39/18.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 19.39/18.24 ( (fun (product_prod int int) int) ) 19.39/18.24 ( (fun int (fun int (fun int bool))) ) 19.39/18.24 ( (fun int real) ) 19.39/18.24 ) 19.39/18.24 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int (fun int bool) (dvd_dvd int) K_4))) (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (or (not (= (one_one int) (hAPP int int (hAPP int _let_0 (gcd_gcd int) K_4) N))) (not (hBOOL (hAPP int bool _let_1 (hAPP int int (hAPP int _let_0 (times_times int) M) N)))) (hBOOL (hAPP int bool _let_1 M))) ))) 19.39/18.24 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1 ) 19.39/18.24 ) 19.39/18.24 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (times_times int) (one_one int)) Z_1) (ti int Z_1)) ) 19.39/18.24 ( pls ) 19.39/18.24 ( m ) 19.39/18.24 ( min_1 ) 19.39/18.24 ( s ) 19.39/18.24 ( s1 ) 19.39/18.24 ( t ) 19.39/18.24 ) 19.39/18.24 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140761 $$unsorted)) (or (not (monoid_mult X_a)) (= (ti X_a BOUND_VARIABLE_140761) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_140761) (one_one nat)))) ) 19.39/18.24 ( bool, fFalse ) 19.39/18.24 ( bool, fTrue ) 19.39/18.24 ( real, pi ) 19.39/18.24 ( real, (hAPP int real (number_number_of real) min_1) ) 19.39/18.24 ( 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)))) ) 19.39/18.24 ( (fun nat bool), (even_odd_even nat) ) 19.39/18.24 ( (fun nat bool), prime ) 19.39/18.24 ( (fun nat nat), suc ) 19.39/18.24 ( (fun nat nat), (fact_fact nat) ) 19.39/18.24 ( (fun nat nat), (size_size nat) ) 19.39/18.24 ( (fun nat nat), fact ) 19.39/18.24 ( (fun nat nat), nat_size ) 19.39/18.24 ( int, pls ) 19.39/18.24 ( int, m ) 19.39/18.24 ( int, min_1 ) 19.39/18.24 ( int, s ) 19.39/18.24 ( int, s1 ) 19.39/18.24 ( int, t ) 19.39/18.24 ( int, skv_8 ) 19.39/18.24 ( (fun int bool), zprime ) 19.39/18.24 ( (fun int bool), nat_neg ) 19.39/18.24 ( (fun int bool), zEven ) 19.39/18.24 ( (fun int bool), nat_is_nat ) 19.39/18.24 ( (fun int bool), zOdd ) 19.39/18.24 ( (fun int bool), (even_odd_even int) ) 19.39/18.24 ( (fun int bool), twoSqu1091635170sum2sq ) 19.39/18.24 ( (fun int nat), nat_1 ) 19.39/18.24 ( (fun int nat), phi ) 19.39/18.24 ( (fun real real), sqrt ) 19.39/18.24 ( (fun real real), tan ) 19.39/18.24 ( (fun real real), cos ) 19.39/18.24 ( (fun real real), arccos ) 19.39/18.24 ( (fun real real), ln ) 19.39/18.24 ( (fun real real), sin ) 19.39/18.24 ( (fun real real), arctan ) 19.39/18.24 ( (fun real real), arcsin ) 19.39/18.24 ( complex, ii ) 19.39/18.24 ( (fun complex complex), cnj ) 19.39/18.24 ( (fun complex complex), expi ) 19.39/18.24 ( (fun nat real), (real_1 nat) ) 19.39/18.24 ( (fun nat real), cos_coeff ) 19.39/18.24 ( (fun nat real), sin_coeff ) 19.39/18.24 ( (fun int int), bit0 ) 19.39/18.24 ( (fun int int), bit1 ) 19.39/18.24 ( (fun int int), pred ) 19.39/18.24 ( (fun int int), succ ) 19.39/18.24 ( (fun int int), (fact_fact int) ) 19.39/18.24 ( (fun int int), zfact ) 19.39/18.24 ( (fun bool bool), fNot ) 19.39/18.24 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 19.39/18.24 ( (fun bool (fun bool bool)), fconj ) 19.39/18.24 ( (fun bool (fun bool bool)), fdisj ) 19.39/18.24 ( (fun bool (fun bool bool)), fimplies ) 19.39/18.24 ( (fun int (fun int bool)), sRStar ) 19.39/18.24 ( (fun int (fun int bool)), quadRes ) 19.39/18.24 ( (fun int (fun int bool)), norRRset ) 19.39/18.24 ( (fun int (fun int bool)), d22set ) 19.39/18.24 ( (fun int (fun int bool)), sr ) 19.39/18.24 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 19.39/18.24 ( (fun nat (fun nat nat)), nat_gcd ) 19.39/18.24 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 19.39/18.24 ( (fun nat (fun nat nat)), nat_lcm ) 19.39/18.24 ( (fun nat (fun real real)), root ) 19.39/18.24 ( (fun real (fun real real)), log ) 19.39/18.24 ( (fun real (fun real real)), powr ) 19.39/18.24 ( (fun nat (fun nat bool)), coprime ) 19.39/18.24 ( (fun (fun int bool) int), (the int) ) 19.39/18.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 19.39/18.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 19.39/18.24 ( (fun nat (fun nat (product_prod int int))), bezw ) 19.39/18.24 ( (fun (fun int bool) bool), nat_nat_set ) 19.39/18.24 ( (filter nat), sequentially ) 19.39/18.24 ( (fun (product_prod nat nat) bool), pred_nat ) 19.39/18.24 ( (fun (product_prod int int) bool), frac_1 ) 19.39/18.24 ( (fun real complex), cis ) 19.39/18.24 ( (fun complex real), im ) 19.39/18.24 ( (fun complex real), re ) 19.39/18.24 ( (fun complex real), arg ) 19.39/18.24 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 19.39/18.24 ( (fun int (fun int int)), int_gcd ) 19.39/18.24 ( (fun int (fun int int)), multInv ) 19.39/18.24 ( (fun int (fun int int)), legacy_zgcd ) 19.39/18.24 ( (fun int (fun int int)), z3mod ) 19.39/18.24 ( (fun int (fun int int)), inv ) 19.39/18.24 ( (fun int (fun int int)), (gcd_gcd int) ) 19.39/18.24 ( (fun int (fun int int)), standardRes ) 19.39/18.24 ( (fun int (fun int int)), legendre ) 19.39/18.24 ( (fun int (fun int int)), nat_tsub ) 19.39/18.24 ( (fun int (fun int int)), z3div ) 19.39/18.24 ( (fun int (fun int int)), int_lcm ) 19.39/18.24 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 19.39/18.24 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 19.39/18.24 ( (fun int (fun (fun int bool) bool)), rsetR ) 19.39/18.24 ( (fun int (fun (fun int bool) bool)), resSet ) 19.39/18.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 19.39/18.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 19.39/18.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 19.39/18.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 19.39/18.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 19.39/18.24 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 19.39/18.24 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 19.39/18.24 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 19.39/18.24 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 19.39/18.24 ( (fun int (fun int (product_prod int int))), negDivAlg ) 19.39/18.24 ( (fun int (fun int (product_prod int int))), divmod_int ) 19.39/18.24 ( (fun int (fun int (product_prod int int))), posDivAlg ) 19.39/18.24 ( (fun int (fun int (product_prod int int))), pdivmod ) 19.39/18.24 ( (fun int (fun int (product_prod int int))), norm_frac ) 19.39/18.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 19.39/18.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 19.39/18.24 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 19.39/18.24 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 19.39/18.24 ( (fun real nat), natfloor ) 19.39/18.24 ( (fun real nat), natceiling ) 19.39/18.24 ( (fun int quickcheck_code_int), quickcheck_of_int ) 19.39/18.24 ( (fun int (fun int (fun int bool))), wset ) 19.39/18.24 ( (fun int (fun int (fun int bool))), bnorRset ) 19.39/18.24 ( (fun int (fun int (fun int bool))), zcong ) 19.39/18.24 ( (fun int (fun int (fun int bool))), noXRRset ) 19.39/18.24 ( (fun int (fun int (fun int bool))), zcongm ) 19.39/18.24 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 19.39/18.24 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 19.39/18.24 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 19.39/18.24 ( (fun int real), (real_1 int) ) 19.39/18.24 ( (fun complex nat), (size_size complex) ) 19.39/18.24 ( (fun complex nat), complex_size ) 19.39/18.24 ( (fun int (list int)), quickc666637781d_zero ) 19.39/18.24 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 19.39/18.24 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 19.39/18.24 ( (fun (product_prod int int) rat), frct ) 19.39/18.24 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 19.39/18.24 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 19.39/18.24 ( (fun (fun nat rat) bool), vanishes ) 19.39/18.24 ( (fun int (fun int rat)), fract ) 19.39/18.24 ( (fun code_code_numeral int), code_int_of ) 19.39/18.24 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 19.39/18.25 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 19.39/18.25 ( (fun code_code_numeral nat), code_c271388182l_size ) 19.39/18.25 ( (fun real (fun real complex)), complex_1 ) 19.39/18.25 ( (fun real (fun real complex)), rcis ) 19.39/18.25 ( (fun int (fun nat nat)), nat_aux ) 19.39/18.25 ( (fun rat real), ratreal ) 19.39/18.25 ( (fun quickcheck_code_int int), quickcheck_int_of ) 19.39/18.25 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 19.39/18.25 ( (fun rat (product_prod int int)), quotient_of ) 19.39/18.25 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 19.39/18.25 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 19.39/18.25 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 19.39/18.25 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 19.39/18.25 ) 19.39/18.25 (instantiation (let ((_let_0 (one_one X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_140801 $$unsorted)) (or (not (field_inverse_zero X_a)) (= (= _let_0 (ti X_a BOUND_VARIABLE_140801)) (= _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_140801)))) )) 19.39/18.25 ( bool, fFalse ) 19.39/18.25 ( bool, fTrue ) 19.39/18.25 ( real, (zero_zero real) ) 19.39/18.25 ( real, pi ) 19.39/18.25 ( (fun nat bool), (even_odd_even nat) ) 19.39/18.25 ( (fun nat bool), prime ) 19.39/18.25 ( (fun nat nat), suc ) 19.39/18.25 ( (fun nat nat), (fact_fact nat) ) 19.39/18.25 ( (fun nat nat), (size_size nat) ) 19.39/18.25 ( (fun nat nat), fact ) 19.39/18.25 ( (fun nat nat), nat_size ) 19.39/18.25 ( int, pls ) 19.39/18.25 ( int, m ) 19.39/18.25 ( int, min_1 ) 19.39/18.25 ( int, s ) 19.39/18.25 ( int, s1 ) 19.39/18.25 ( int, t ) 19.39/18.25 ( (fun int bool), zprime ) 19.39/18.25 ( (fun int bool), nat_neg ) 19.39/18.25 ( (fun int bool), zEven ) 19.39/18.25 ( (fun int bool), nat_is_nat ) 19.39/18.25 ( (fun int bool), zOdd ) 19.39/18.25 ( (fun int bool), (even_odd_even int) ) 19.39/18.25 ( (fun int bool), twoSqu1091635170sum2sq ) 19.39/18.25 ( (fun int nat), nat_1 ) 19.39/18.25 ( (fun int nat), phi ) 19.39/18.25 ( (fun real real), sqrt ) 19.39/18.25 ( (fun real real), tan ) 19.39/18.25 ( (fun real real), cos ) 19.39/18.25 ( (fun real real), arccos ) 19.39/18.25 ( (fun real real), ln ) 19.39/18.25 ( (fun real real), sin ) 19.39/18.25 ( (fun real real), arctan ) 19.39/18.25 ( (fun real real), arcsin ) 19.39/18.25 ( complex, ii ) 19.39/18.25 ( (fun complex complex), cnj ) 19.39/18.25 ( (fun complex complex), expi ) 19.39/18.25 ( (fun nat real), (real_1 nat) ) 19.39/18.25 ( (fun nat real), cos_coeff ) 19.39/18.25 ( (fun nat real), sin_coeff ) 19.39/18.25 ( (fun int int), bit0 ) 19.39/18.25 ( (fun int int), bit1 ) 19.39/18.25 ( (fun int int), pred ) 19.39/18.25 ( (fun int int), succ ) 19.39/18.25 ( (fun int int), (fact_fact int) ) 19.39/18.25 ( (fun int int), zfact ) 19.39/18.25 ( (fun bool bool), fNot ) 19.39/18.25 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 19.39/18.25 ( (fun bool (fun bool bool)), fconj ) 19.39/18.25 ( (fun bool (fun bool bool)), fdisj ) 19.39/18.25 ( (fun bool (fun bool bool)), fimplies ) 19.39/18.25 ( (fun int (fun int bool)), sRStar ) 19.39/18.25 ( (fun int (fun int bool)), quadRes ) 19.39/18.25 ( (fun int (fun int bool)), norRRset ) 19.39/18.25 ( (fun int (fun int bool)), d22set ) 19.39/18.25 ( (fun int (fun int bool)), sr ) 19.39/18.25 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 19.39/18.25 ( (fun nat (fun nat nat)), nat_gcd ) 19.39/18.25 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 19.39/18.25 ( (fun nat (fun nat nat)), nat_lcm ) 19.39/18.25 ( (fun nat (fun real real)), root ) 19.39/18.25 ( (fun real (fun real real)), log ) 19.39/18.25 ( (fun real (fun real real)), powr ) 19.39/18.25 ( (fun nat (fun nat bool)), coprime ) 19.39/18.25 ( (fun (fun int bool) int), (the int) ) 19.39/18.25 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 19.39/18.25 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 19.39/18.25 ( (fun nat (fun nat (product_prod int int))), bezw ) 19.39/18.25 ( (fun (fun int bool) bool), nat_nat_set ) 19.39/18.25 ( (filter nat), sequentially ) 19.39/18.25 ( (fun (product_prod nat nat) bool), pred_nat ) 19.39/18.25 ( (fun (product_prod int int) bool), frac_1 ) 19.39/18.25 ( (fun real complex), cis ) 19.39/18.25 ( (fun complex real), im ) 19.39/18.25 ( (fun complex real), re ) 19.39/18.25 ( (fun complex real), arg ) 19.39/18.25 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 19.39/18.25 ( (fun int (fun int int)), int_gcd ) 19.39/18.25 ( (fun int (fun int int)), multInv ) 19.39/18.25 ( (fun int (fun int int)), legacy_zgcd ) 19.39/18.25 ( (fun int (fun int int)), z3mod ) 19.39/18.25 ( (fun int (fun int int)), inv ) 19.39/18.25 ( (fun int (fun int int)), (gcd_gcd int) ) 19.39/18.25 ( (fun int (fun int int)), standardRes ) 19.39/18.25 ( (fun int (fun int int)), legendre ) 19.39/18.25 ( (fun int (fun int int)), nat_tsub ) 19.39/18.25 ( (fun int (fun int int)), z3div ) 19.39/18.25 ( (fun int (fun int int)), int_lcm ) 19.39/18.25 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 19.39/18.25 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 19.39/18.25 ( (fun int (fun (fun int bool) bool)), rsetR ) 19.39/18.25 ( (fun int (fun (fun int bool) bool)), resSet ) 19.39/18.25 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 19.39/18.25 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 19.39/18.25 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 19.39/18.25 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 19.39/18.25 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 19.39/18.25 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 19.39/18.25 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 19.39/18.25 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 19.39/18.25 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 19.39/18.25 ( (fun int (fun int (product_prod int int))), negDivAlg ) 19.39/18.25 ( (fun int (fun int (product_prod int int))), divmod_int ) 19.39/18.25 ( (fun int (fun int (product_prod int int))), posDivAlg ) 19.39/18.25 ( (fun int (fun int (product_prod int int))), pdivmod ) 19.39/18.25 ( (fun int (fun int (product_prod int int))), norm_frac ) 19.39/18.25 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 19.39/18.25 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 19.39/18.25 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 19.39/18.25 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 19.39/18.25 ( (fun real nat), natfloor ) 19.39/18.25 ( (fun real nat), natceiling ) 19.39/18.25 ( (fun int quickcheck_code_int), quickcheck_of_int ) 19.39/18.25 ( (fun int (fun int (fun int bool))), wset ) 19.39/18.25 ( (fun int (fun int (fun int bool))), bnorRset ) 19.39/18.25 ( (fun int (fun int (fun int bool))), zcong ) 19.39/18.25 ( (fun int (fun int (fun int bool))), noXRRset ) 19.39/18.25 ( (fun int (fun int (fun int bool))), zcongm ) 19.39/18.25 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 19.39/18.25 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 19.39/18.25 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 19.39/18.25 ( (fun int real), (real_1 int) ) 19.39/18.25 ( (fun complex nat), (size_size complex) ) 19.39/18.25 ( (fun complex nat), complex_size ) 19.39/18.25 ( (fun int (list int)), quickc666637781d_zero ) 19.39/18.25 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 19.39/18.25 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 19.39/18.25 ( (fun (product_prod int int) rat), frct ) 19.39/18.25 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 19.39/18.25 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 19.39/18.25 ( (fun (fun nat rat) bool), vanishes ) 19.39/18.25 ( (fun int (fun int rat)), fract ) 19.39/18.25 ( (fun code_code_numeral int), code_int_of ) 19.39/18.25 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 19.39/18.25 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 19.39/18.25 ( (fun code_code_numeral nat), code_c271388182l_size ) 19.39/18.25 ( (fun real (fun real complex)), complex_1 ) 19.39/18.25 ( (fun real (fun real complex)), rcis ) 19.39/18.25 ( (fun int (fun nat nat)), nat_aux ) 19.39/18.25 ( (fun rat real), ratreal ) 19.39/18.25 ( (fun quickcheck_code_int int), quickcheck_int_of ) 19.39/18.25 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 19.39/18.25 ( (fun rat (product_prod int int)), quotient_of ) 19.39/18.25 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 19.39/18.25 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 19.39/18.25 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 19.39/18.25 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 19.39/18.25 ) 19.39/18.25 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_140826 $$unsorted) (BOUND_VARIABLE_140827 $$unsorted) (BOUND_VARIABLE_140828 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_140828)) (not (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_140826) BOUND_VARIABLE_140828) (ti X_a BOUND_VARIABLE_140827))) (= (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_140827) BOUND_VARIABLE_140828) (ti X_a BOUND_VARIABLE_140826))) )) 19.39/18.25 ( 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, pi ) 19.39/18.25 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), min_1, min_1 ) 19.39/18.25 ( 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))), m, m ) 19.39/18.25 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), s, s ) 19.39/18.25 ( complex, ii, ii, ii ) 19.39/18.25 ) 19.39/18.25 (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)))) ) 19.39/18.25 ( (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))) ) 19.39/18.25 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.25 ( 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))) ) 19.39/18.25 ( skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.39/18.25 ) 19.39/18.25 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (one_one real))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP nat (fun real real) root N_1) X_1)) _let_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) _let_2)))) )))) 19.39/18.25 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.25 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.25 ( (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))) ) 19.39/18.25 ( (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))) ) 19.39/18.25 ) 19.39/18.25 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140971 $$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_140971)) (hAPP real real (abs_abs real) (hAPP int real (ring_1_of_int real) BOUND_VARIABLE_140971)))) ) 19.39/18.25 ( real, (zero_zero int) ) 19.39/18.25 ( real, (one_one int) ) 19.39/18.25 ) 19.39/18.25 (instantiation (let ((_let_0 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) W_1)))) (forall ((W_1 $$unsorted) (Ma $$unsorted)) (= (= Ma (hAPP int nat nat_1 W_1)) (and (or _let_0 (= (zero_zero nat) Ma)) (or (not _let_0) (= (ti int W_1) (hAPP nat int (semiring_1_of_nat int) Ma))))) )) 19.39/18.25 ( (zero_zero int), (zero_zero nat) ) 19.39/18.25 ( (one_one int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.39/18.25 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.25 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP nat nat suc (zero_zero nat)) ) 19.39/18.25 ) 19.39/18.25 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_141058 $$unsorted) (BOUND_VARIABLE_141059 $$unsorted) (BOUND_VARIABLE_141060 $$unsorted)) (or (not (order X_a)) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a BOUND_VARIABLE_141060 N_2)) (hAPP nat X_a BOUND_VARIABLE_141060 (hAPP nat nat suc N_2)))) )) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) BOUND_VARIABLE_141058) BOUND_VARIABLE_141059))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a BOUND_VARIABLE_141060 BOUND_VARIABLE_141058)) (hAPP nat X_a BOUND_VARIABLE_141060 BOUND_VARIABLE_141059)))) ))) 19.39/18.25 ( int, (zero_zero nat), (zero_zero nat), (semiring_1_of_nat int) ) 19.39/18.25 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)), (semiring_1_of_nat int) ) 19.39/18.25 ( int, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (semiring_1_of_nat int) ) 19.39/18.25 ( int, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), (semiring_1_of_nat int) ) 19.39/18.25 ) 19.39/18.25 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_141119))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_141118 $$unsorted) (BOUND_VARIABLE_141119 $$unsorted) (BOUND_VARIABLE_141120 $$unsorted)) (or (not (comm_semiring_1 X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_141120))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_141118) BOUND_VARIABLE_141120)))) )) 19.39/18.25 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1 ) 19.39/18.25 ) 19.39/18.25 (instantiation (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (times_times X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_141146 $$unsorted) (BOUND_VARIABLE_141147 $$unsorted)) (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_141147))) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_141146)) BOUND_VARIABLE_141147) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_141146) BOUND_VARIABLE_141147)))) )))) 19.39/18.25 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.39/18.25 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.39/18.25 ( 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)))))) ) 19.39/18.25 ( 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 ) 19.39/18.25 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 19.39/18.25 ( 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))), (zero_zero int) ) 19.39/18.25 ( 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 ) 19.39/18.26 ( 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))), skv_1 ) 19.39/18.26 ( complex, ii, ii ) 19.39/18.26 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 19.39/18.26 ( 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 ) 19.39/18.26 ) 19.39/18.26 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_141204 $$unsorted) (BOUND_VARIABLE_141205 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_141205))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_141204) _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_141205) BOUND_VARIABLE_141204)) _let_2))) )))) 19.39/18.26 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 19.39/18.26 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.39/18.26 ( 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))) ) 19.39/18.26 ( 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)))) ) 19.39/18.26 ( 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)))) ) 19.39/18.26 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 19.39/18.26 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 19.39/18.26 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 19.39/18.26 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 19.39/18.26 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 19.39/18.26 ( 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) ) 19.39/18.26 ) 19.39/18.26 (instantiation (forall ((Z_1 $$unsorted)) (= (ti int Z_1) (hAPP int int (hAPP int (fun int int) (plus_plus int) (zero_zero int)) Z_1)) ) 19.39/18.26 ( pls ) 19.39/18.26 ( m ) 19.39/18.26 ( min_1 ) 19.39/18.26 ( s ) 19.39/18.26 ( s1 ) 19.39/18.26 ( t ) 19.39/18.26 ) 19.39/18.26 (instantiation (let ((_let_0 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_141238 $$unsorted)) (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_141238)) (one_one X_a)) (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_141238) (hAPP int int (uminus_uminus int) (hAPP int int bit1 pls)))))) )) 19.39/18.26 ( code_code_numeral, pls ) 19.39/18.26 ) 19.39/18.26 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun nat real))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (one_one real)))) (hBOOL (hAPP _let_2 bool (monoseq real) (hAPP real _let_2 (power_power real) X_1)))) )))) 19.39/18.26 ( (zero_zero real) ) 19.39/18.26 ( pi ) 19.39/18.26 ( (hAPP int real (number_number_of real) min_1) ) 19.39/18.26 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.26 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.26 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.26 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.26 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.26 ( skv_6 ) 19.39/18.26 ( skv_11 ) 19.39/18.26 ( skv_12 ) 19.39/18.26 ( skv_14 ) 19.39/18.26 ) 19.39/18.26 (instantiation (let ((_let_0 (fun nat real))) (let ((_let_1 (fun (filter nat) bool))) (forall ((X_3 $$unsorted)) (or (not (forall ((R_2 $$unsorted)) (not (forall ((N_3 $$unsorted)) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N_3) N_2))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) R_2) (hAPP nat real X_3 N_2)))) )) )) )) (hBOOL (hAPP (filter nat) bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (tendsto nat real) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) X_3)) (zero_zero real)) sequentially))) ))) 19.39/18.26 ( (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) ) 19.39/18.26 ) 19.39/18.26 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (ord_less X_a))) (let ((_let_3 (zero_zero X_a))) (let ((_let_4 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_3) BOUND_VARIABLE_141330)))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_141330) _let_3)))) (let ((_let_6 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_141331) BOUND_VARIABLE_141330))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_141329 $$unsorted) (BOUND_VARIABLE_141330 $$unsorted) (BOUND_VARIABLE_141331 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_141329) BOUND_VARIABLE_141330)) BOUND_VARIABLE_141331)) (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_141329))) (or _let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_3) BOUND_VARIABLE_141331))))) (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_141329) _let_6)))))) )))))))) 19.39/18.26 ( real, (zero_zero real), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.26 ( 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))) ) 19.39/18.26 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.26 ) 19.39/18.26 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) N_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_1))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP real nat natceiling X_1)) (hAPP int nat (number_number_of nat) N_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (hAPP int real (number_number_of real) N_1))))) ))) 19.39/18.26 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.39/18.26 ( skv_14, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.39/18.26 ) 19.39/18.26 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_141437))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_141436 $$unsorted) (BOUND_VARIABLE_141437 $$unsorted) (BOUND_VARIABLE_141438 $$unsorted)) (or (not (comm_semiring_1 X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_141438))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_141438) BOUND_VARIABLE_141436)))) )) 19.39/18.26 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.39/18.26 ) 19.39/18.26 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)))) (forall ((X $$unsorted) (N $$unsorted) (M $$unsorted)) (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 (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)))) ))) 19.39/18.26 ( (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))) ) 19.39/18.26 ( (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))) ) 19.39/18.26 ) 19.39/18.26 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_141483 $$unsorted) (BOUND_VARIABLE_141484 $$unsorted)) (or (not (linord581940658strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_141484) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_141483) _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_141484) BOUND_VARIABLE_141483)))) )))) 19.39/18.26 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.26 ( 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))))) ) 19.39/18.26 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.26 ( 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)))) ) 19.39/18.26 ( 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))) ) 19.39/18.26 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.26 ( 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))) ) 19.39/18.26 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.39/18.26 ( complex, ii, ii ) 19.39/18.26 ( 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)) ) 19.39/18.26 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.26 ) 19.39/18.26 (instantiation (let ((_let_0 (hAPP int (fun int int) (minus_minus int) min_1))) (forall ((L_4 $$unsorted)) (= (hAPP int int _let_0 (hAPP int int bit0 L_4)) (hAPP int int bit1 (hAPP int int _let_0 L_4))) )) 19.39/18.26 ( pls ) 19.39/18.26 ( (hAPP int int bit1 pls) ) 19.39/18.26 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.39/18.26 ( min_1 ) 19.39/18.26 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.39/18.26 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.39/18.26 ) 19.39/18.26 (instantiation (let ((_let_0 (fun real bool))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) X))) (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP real real ln X)) (hAPP real real (hAPP real (fun real real) (minus_minus real) X) (one_one real))))) )) 19.39/18.26 ( (one_one real) ) 19.39/18.26 ( pi ) 19.39/18.26 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.26 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.26 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 19.39/18.26 ( skv_2 ) 19.39/18.26 ( skv_10 ) 19.39/18.26 ( skv_13 ) 19.39/18.26 ) 19.39/18.26 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_141631 $$unsorted) (BOUND_VARIABLE_141632 $$unsorted)) (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_141631) BOUND_VARIABLE_141632)) BOUND_VARIABLE_141632))) )) 19.39/18.26 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.39/18.27 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.39/18.27 ( 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)))))) ) 19.39/18.27 ( 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 ) 19.39/18.27 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 19.39/18.27 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 19.39/18.27 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 19.39/18.27 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_1 ) 19.39/18.27 ( complex, ii, ii ) 19.39/18.27 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 19.39/18.27 ( 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 ) 19.39/18.27 ) 19.39/18.27 (instantiation (forall ((N_1 $$unsorted) (Ma $$unsorted)) (or (= (zero_zero int) (ti int Ma)) (= (= (one_one int) (hAPP int int (abs_abs int) N_1)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int (fun int int) (times_times int) Ma) N_1)) Ma)))) ) 19.39/18.27 ( (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))) ) 19.39/18.27 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.27 ( 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))) ) 19.39/18.27 ( skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.39/18.27 ) 19.39/18.27 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (number_number_of int))) (let ((_let_4 (product_prod int int))) (let ((_let_5 (fun int _let_4))) (let ((_let_6 (product_Pair int int))) (let ((_let_7 (fun _let_4 bool))) (let ((_let_8 (hAPP int _let_5 negDivAlg A_2))) (let ((_let_9 (hAPP int _let_4 _let_8 B_1))) (let ((_let_10 (hAPP int int (hAPP int (fun int int) (plus_plus int) A_2) B_1))) (let ((_let_11 (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) _let_10)))) (let ((_let_12 (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B_1) _let_2)))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP _let_4 bool (hAPP (fun _let_4 _let_7) _let_7 (accp _let_4) negDivAlg_rel) (hAPP int _let_4 (hAPP int _let_5 _let_6 A_2) B_1)))) (and (or _let_11 _let_12 (= _let_9 (hAPP _let_4 _let_4 (hAPP int (fun _let_4 _let_4) adjust B_1) (hAPP int _let_4 _let_8 (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int _let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) B_1))))) (or (and (not _let_12) (not _let_11)) (= _let_9 (hAPP int _let_4 (hAPP int _let_5 _let_6 (hAPP int int _let_3 min_1)) _let_10))))) )))))))))))))) 19.39/18.27 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 19.39/18.27 ( (hAPP nat int (hAPP 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) ) 19.39/18.27 ) 19.39/18.27 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (div_div nat))) (let ((_let_3 (ord_less nat))) (forall ((M $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_3 (zero_zero nat)) N))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_3 M) N)) (= (hAPP nat nat (hAPP nat _let_1 _let_2 M) N) (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)))) ))))) 19.39/18.27 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.27 ) 19.39/18.27 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP real (fun real real) (plus_plus real) (one_one real)) X)) (hAPP real real (exp real) X)))) ))) 19.39/18.27 ( pi ) 19.39/18.27 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.27 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.27 ( skv_6 ) 19.39/18.27 ( skv_11 ) 19.39/18.27 ( skv_12 ) 19.39/18.27 ( skv_14 ) 19.39/18.27 ) 19.39/18.27 (instantiation (let ((_let_0 (of_real X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_141812 $$unsorted)) (or (not (real_algebra_1 X_a)) (= (hAPP real X_a _let_0 (hAPP real real (uminus_uminus real) BOUND_VARIABLE_141812)) (hAPP X_a X_a (uminus_uminus X_a) (hAPP real X_a _let_0 BOUND_VARIABLE_141812)))) )) 19.39/18.27 ( complex, (one_one real) ) 19.39/18.27 ) 19.39/18.27 (instantiation (let ((_let_0 (product_prod int int))) (forall ((K_4 $$unsorted)) (= (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) (hAPP int int (number_number_of int) K_4)) (one_one int)) (hAPP rat _let_0 quotient_of (hAPP int rat (number_number_of rat) K_4))) )) 19.39/18.27 ( pls ) 19.39/18.27 ( (hAPP int int bit1 pls) ) 19.39/18.27 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.39/18.27 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.27 ( min_1 ) 19.39/18.27 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.39/18.27 ) 19.39/18.27 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted) (W_1 $$unsorted)) (= (= (hAPP real complex (hAPP real (fun real complex) complex_1 A_2) B_1) (hAPP int complex (number_number_of complex) W_1)) (and (= A_2 (hAPP int real (number_number_of real) W_1)) (= (zero_zero real) B_1))) ) 19.39/18.27 ( (zero_zero real), (zero_zero real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.39/18.27 ( (one_one real), (zero_zero real), min_1 ) 19.39/18.27 ) 19.39/18.27 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (hAPP int _let_0 (dvd_dvd int) K_4))) (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (or (not (= (one_one int) (hAPP int int (hAPP int _let_1 legacy_zgcd N) K_4))) (not (hBOOL (hAPP int bool _let_2 (hAPP int int (hAPP int _let_1 (times_times int) M) N)))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) M))) (hBOOL (hAPP int bool _let_2 M))) )))) 19.39/18.27 ( (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))), skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.39/18.27 ) 19.39/18.27 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_141849 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (not (number_ring X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_141849))) (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_141849) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls))))))) )) 19.39/18.27 ( real, (one_one real) ) 19.39/18.27 ( real, pi ) 19.39/18.27 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.39/18.27 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 19.39/18.27 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.27 ) 19.39/18.27 (instantiation (let ((_let_0 (number_number_of nat))) (forall ((V $$unsorted)) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V))) (= (hAPP nat nat suc (hAPP int nat _let_0 V)) (hAPP int nat _let_0 (hAPP int int succ V)))) )) 19.39/18.27 ( pls ) 19.39/18.27 ( (hAPP int int bit1 pls) ) 19.39/18.27 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.39/18.27 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.27 ( min_1 ) 19.39/18.27 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.39/18.27 ) 19.39/18.27 (instantiation (forall ((V $$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)))) ) 19.39/18.27 ( pls ) 19.39/18.27 ( (hAPP int int bit1 pls) ) 19.39/18.27 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.39/18.27 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.27 ( min_1 ) 19.39/18.27 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.39/18.27 ) 19.39/18.27 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141906 $$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_141906)) (one_one int))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_141906) (one_one X_a))))) ) 19.39/18.27 ( real, (zero_zero real) ) 19.39/18.27 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.27 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.27 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.27 ( real, skv_14 ) 19.39/18.27 ( int, (zero_zero int) ) 19.39/18.27 ( int, (one_one int) ) 19.39/18.27 ( int, min_1 ) 19.39/18.27 ) 19.39/18.27 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (forall ((X $$unsorted)) (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)))) )))) 19.39/18.27 ( (zero_zero real) ) 19.39/18.27 ( (one_one real) ) 19.39/18.27 ( pi ) 19.39/18.27 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.27 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.27 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 19.39/18.27 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 19.39/18.27 ( (hAPP real real (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))))) ) 19.39/18.27 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 19.39/18.27 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.27 ( (hAPP real 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))))) ) 19.39/18.27 ( (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)))) ) 19.39/18.27 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 19.39/18.27 ( skv_14 ) 19.39/18.27 ) 19.39/18.27 (instantiation (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a real))) (let ((_let_3 (fun X_a X_b))) (let ((_let_4 (norm_norm X_b))) (let ((_let_5 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_142036))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_142034 $$unsorted) (BOUND_VARIABLE_142035 $$unsorted) (BOUND_VARIABLE_142036 $$unsorted)) (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_3 (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_142034) BOUND_VARIABLE_142035) _let_5))) (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (tendsto X_a real) (hAPP _let_3 _let_2 (hAPP (fun X_b real) (fun _let_3 _let_2) (combb X_b real X_a) _let_4) BOUND_VARIABLE_142034)) (hAPP X_b real _let_4 BOUND_VARIABLE_142035)) _let_5))) ))))))) 19.39/18.27 ( 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)))) ) 19.39/18.27 ) 19.39/18.27 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142058 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (one_one X_a)) BOUND_VARIABLE_142058)) (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_142058))))) ) 19.39/18.27 ( int, t ) 19.39/18.27 ) 19.39/18.27 (instantiation (forall ((N $$unsorted)) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) N) (hAPP nat nat suc (hAPP nat nat suc N))) ) 19.39/18.27 ( (zero_zero nat) ) 19.39/18.27 ( (hAPP nat nat suc (zero_zero nat)) ) 19.39/18.27 ) 19.39/18.27 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) Z_1) (zero_zero int)) (ti int Z_1)) ) 19.39/18.27 ( pls ) 19.39/18.27 ( m ) 19.39/18.27 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 19.39/18.27 ( min_1 ) 19.39/18.27 ( s ) 19.39/18.27 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.27 ( s1 ) 19.39/18.27 ( t ) 19.39/18.27 ) 19.39/18.27 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)))) (forall ((B $$unsorted) (A_1 $$unsorted)) (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))))) )) 19.39/18.28 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.28 ( 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))))) ) 19.39/18.28 ( (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.28 ( (hAPP real real arctan (hAPP real real (hAPP 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)))) ) 19.39/18.28 ) 19.39/18.28 (instantiation (let ((_let_0 (semiring_1_of_nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_142213 $$unsorted) (BOUND_VARIABLE_142214 $$unsorted)) (or (not (semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_142213)) (hAPP nat X_a _let_0 BOUND_VARIABLE_142214)) (hAPP nat X_a _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) BOUND_VARIABLE_142213) BOUND_VARIABLE_142214)))) )) 19.39/18.28 ( int, (one_one nat), (one_one nat) ) 19.39/18.28 ) 19.39/18.28 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int pred K_4) (hAPP int int (hAPP int (fun int int) (plus_plus int) K_4) min_1)) ) 19.39/18.28 ( pls ) 19.39/18.28 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 19.39/18.28 ( min_1 ) 19.39/18.28 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.28 ) 19.39/18.28 (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_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real (norm_norm X_a) (hAPP real X_a (of_real X_a) X_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real (norm_norm real) X_2)) K_2))) )) ))) ) 19.39/18.28 ( real ) 19.39/18.28 ( complex ) 19.39/18.28 ) 19.39/18.28 (instantiation (let ((_let_0 (semiring_1_of_nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_142332 $$unsorted)) (or (not (semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (one_one X_a)) (hAPP nat X_a _let_0 BOUND_VARIABLE_142332)) (hAPP nat X_a _let_0 (hAPP nat nat suc BOUND_VARIABLE_142332)))) )) 19.39/18.28 ( real, (zero_zero nat) ) 19.39/18.28 ( int, (zero_zero nat) ) 19.39/18.28 ( int, (hAPP nat nat suc (zero_zero nat)) ) 19.39/18.28 ( int, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 19.39/18.28 ) 19.39/18.28 (instantiation (let ((_let_0 (real_1 int))) (forall ((N $$unsorted) (D $$unsorted)) (or (= (zero_zero int) (ti int D)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) D) N))) (= (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_0 N)) (hAPP int real _let_0 D)) (hAPP int real _let_0 (hAPP int int (hAPP int (fun int int) (div_div int) N) D)))) )) 19.39/18.28 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.39/18.28 ) 19.39/18.28 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (one_one real)))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool _let_0 X))) (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt X)))) )) 19.39/18.28 ( (zero_zero real) ) 19.39/18.28 ( (one_one real) ) 19.39/18.28 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.28 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.39/18.28 ) 19.39/18.28 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_4 (one_one real))) (let ((_let_5 (abs_abs real))) (let ((_let_6 (hAPP int real (number_number_of real) _let_3))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real _let_5 X)) (hAPP real real (hAPP real _let_2 (inverse_divide real) _let_4) _let_6)))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real _let_5 (hAPP real real (hAPP real _let_2 (minus_minus real) (hAPP real real ln (hAPP real real (hAPP real _let_2 (plus_plus real) _let_4) X))) X))) (hAPP real real (hAPP real _let_2 (times_times real) _let_6) (hAPP nat real (hAPP real (fun nat real) (power_power real) X) (hAPP int nat (number_number_of nat) _let_3)))))) )))))))) 19.39/18.28 ( (hAPP int real (number_number_of real) min_1) ) 19.39/18.28 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.28 ) 19.39/18.28 (instantiation (let ((_let_0 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_142408))) (let ((_let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_142409))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_142408 $$unsorted) (BOUND_VARIABLE_142409 $$unsorted)) (or (not (ab_sem1668676832m_mult X_a)) (= _let_1 (hAPP X_a X_a _let_0 _let_1))) ))) 19.39/18.28 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.39/18.28 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.39/18.28 ( 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)))))) ) 19.39/18.28 ( 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 ) 19.39/18.28 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 19.39/18.28 ( 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))), (zero_zero int) ) 19.39/18.28 ( 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 ) 19.39/18.28 ( 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_1 ) 19.39/18.28 ( complex, ii, ii ) 19.39/18.28 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 19.39/18.28 ( 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 ) 19.39/18.28 ) 19.39/18.28 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142449 $$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_142449))))) ) 19.39/18.28 ( real, (hAPP nat nat suc (zero_zero nat)) ) 19.39/18.28 ( int, (hAPP nat nat suc (zero_zero nat)) ) 19.39/18.28 ) 19.39/18.28 (instantiation (let ((_let_0 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_142473 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a _let_0 (hAPP int int succ BOUND_VARIABLE_142473)) (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_142473)))) )) 19.39/18.28 ( nat, pls ) 19.39/18.28 ( nat, (hAPP int int bit1 pls) ) 19.39/18.28 ( nat, min_1 ) 19.39/18.28 ( int, pls ) 19.39/18.28 ( int, min_1 ) 19.39/18.28 ( quickcheck_code_int, pls ) 19.39/18.28 ( quickcheck_code_int, min_1 ) 19.39/18.28 ( code_code_numeral, pls ) 19.39/18.28 ( code_code_numeral, min_1 ) 19.39/18.28 ) 19.39/18.28 (instantiation (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_142530))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_142530 $$unsorted) (BOUND_VARIABLE_142531 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_142531))) (hBOOL (hAPP X_a bool _let_3 (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_142530) BOUND_VARIABLE_142531)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 _let_2) _let_2))))) ))))) 19.39/18.28 ( nat, (one_one nat), (one_one nat) ) 19.39/18.28 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 19.39/18.28 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 19.39/18.28 ) 19.39/18.28 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142551 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_142551)) (zero_zero int))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_142551) (zero_zero X_a))))) ) 19.39/18.28 ( real, (zero_zero real) ) 19.39/18.28 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.28 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.28 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.28 ( real, skv_14 ) 19.39/18.28 ( int, (zero_zero int) ) 19.39/18.28 ( int, (one_one int) ) 19.39/18.28 ( int, min_1 ) 19.39/18.28 ) 19.39/18.28 (instantiation (let ((_let_0 (real_1 int))) (forall ((N $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real _let_0 N)) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real _let_0 X)) (one_one real))))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) N) X))) )) 19.39/18.28 ( (zero_zero int), (one_one int) ) 19.39/18.28 ( (zero_zero int), min_1 ) 19.39/18.28 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.28 ( (zero_zero int), s ) 19.39/18.28 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 19.39/18.28 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.39/18.28 ( (zero_zero int), skv_3 ) 19.39/18.28 ( (zero_zero int), skv_9 ) 19.39/18.28 ( (one_one int), t ) 19.39/18.28 ( min_1, pls ) 19.39/18.28 ( min_1, min_1 ) 19.39/18.28 ) 19.39/18.28 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_142681 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_142681))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_142681)))) )) 19.39/18.28 ( real, (zero_zero real) ) 19.39/18.28 ( complex, ii ) 19.39/18.28 ) 19.39/18.28 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142698 $$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_142698) (ti X_a BOUND_VARIABLE_142698))) ) 19.39/18.28 ( bool, fFalse ) 19.39/18.28 ( bool, fTrue ) 19.39/18.28 ( real, pi ) 19.39/18.28 ( (fun nat bool), (even_odd_even nat) ) 19.39/18.28 ( (fun nat bool), prime ) 19.39/18.28 ( (fun nat nat), suc ) 19.39/18.28 ( (fun nat nat), (fact_fact nat) ) 19.39/18.28 ( (fun nat nat), (size_size nat) ) 19.39/18.28 ( (fun nat nat), fact ) 19.39/18.28 ( (fun nat nat), nat_size ) 19.39/18.28 ( int, pls ) 19.39/18.28 ( int, m ) 19.39/18.28 ( int, min_1 ) 19.39/18.28 ( int, s ) 19.39/18.28 ( int, s1 ) 19.39/18.28 ( int, t ) 19.39/18.28 ( (fun int bool), zprime ) 19.39/18.28 ( (fun int bool), nat_neg ) 19.39/18.28 ( (fun int bool), zEven ) 19.39/18.28 ( (fun int bool), nat_is_nat ) 19.39/18.28 ( (fun int bool), zOdd ) 19.39/18.28 ( (fun int bool), (even_odd_even int) ) 19.39/18.28 ( (fun int bool), twoSqu1091635170sum2sq ) 19.39/18.28 ( (fun int nat), nat_1 ) 19.39/18.28 ( (fun int nat), phi ) 19.39/18.28 ( (fun real real), sqrt ) 19.39/18.28 ( (fun real real), tan ) 19.39/18.28 ( (fun real real), cos ) 19.39/18.28 ( (fun real real), arccos ) 19.39/18.28 ( (fun real real), ln ) 19.39/18.28 ( (fun real real), sin ) 19.39/18.28 ( (fun real real), arctan ) 19.39/18.28 ( (fun real real), arcsin ) 19.39/18.28 ( complex, ii ) 19.39/18.28 ( (fun complex complex), cnj ) 19.39/18.28 ( (fun complex complex), expi ) 19.39/18.28 ( (fun nat real), (real_1 nat) ) 19.39/18.28 ( (fun nat real), cos_coeff ) 19.39/18.28 ( (fun nat real), sin_coeff ) 19.39/18.28 ( (fun int int), bit0 ) 19.39/18.28 ( (fun int int), bit1 ) 19.39/18.28 ( (fun int int), pred ) 19.39/18.28 ( (fun int int), succ ) 19.39/18.28 ( (fun int int), (fact_fact int) ) 19.39/18.28 ( (fun int int), zfact ) 19.39/18.28 ( (fun bool bool), fNot ) 19.39/18.28 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 19.39/18.28 ( (fun bool (fun bool bool)), fconj ) 19.39/18.28 ( (fun bool (fun bool bool)), fdisj ) 19.39/18.28 ( (fun bool (fun bool bool)), fimplies ) 19.39/18.28 ( (fun int (fun int bool)), sRStar ) 19.39/18.28 ( (fun int (fun int bool)), quadRes ) 19.39/18.28 ( (fun int (fun int bool)), norRRset ) 19.39/18.28 ( (fun int (fun int bool)), d22set ) 19.39/18.28 ( (fun int (fun int bool)), sr ) 19.39/18.28 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 19.39/18.28 ( (fun nat (fun nat nat)), nat_gcd ) 19.39/18.28 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 19.39/18.28 ( (fun nat (fun nat nat)), nat_lcm ) 19.39/18.28 ( (fun nat (fun real real)), root ) 19.39/18.28 ( (fun real (fun real real)), log ) 19.39/18.28 ( (fun real (fun real real)), powr ) 19.39/18.28 ( (fun nat (fun nat bool)), coprime ) 19.39/18.28 ( (fun (fun int bool) int), (the int) ) 19.39/18.28 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 19.39/18.28 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 19.39/18.28 ( (fun nat (fun nat (product_prod int int))), bezw ) 19.39/18.28 ( (fun (fun int bool) bool), nat_nat_set ) 19.39/18.28 ( (filter nat), sequentially ) 19.39/18.28 ( (fun (product_prod nat nat) bool), pred_nat ) 19.39/18.28 ( (fun (product_prod int int) bool), frac_1 ) 19.39/18.28 ( (fun real complex), cis ) 19.39/18.28 ( (fun complex real), im ) 19.39/18.28 ( (fun complex real), re ) 19.39/18.28 ( (fun complex real), arg ) 19.39/18.28 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 19.39/18.28 ( (fun int (fun int int)), int_gcd ) 19.39/18.28 ( (fun int (fun int int)), multInv ) 19.39/18.28 ( (fun int (fun int int)), legacy_zgcd ) 19.39/18.28 ( (fun int (fun int int)), z3mod ) 19.39/18.28 ( (fun int (fun int int)), inv ) 19.39/18.28 ( (fun int (fun int int)), (gcd_gcd int) ) 19.39/18.28 ( (fun int (fun int int)), standardRes ) 19.39/18.28 ( (fun int (fun int int)), legendre ) 19.39/18.28 ( (fun int (fun int int)), nat_tsub ) 19.39/18.29 ( (fun int (fun int int)), z3div ) 19.39/18.29 ( (fun int (fun int int)), int_lcm ) 19.39/18.29 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 19.39/18.29 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 19.39/18.29 ( (fun int (fun (fun int bool) bool)), rsetR ) 19.39/18.29 ( (fun int (fun (fun int bool) bool)), resSet ) 19.39/18.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 19.39/18.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 19.39/18.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 19.39/18.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 19.39/18.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 19.39/18.29 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 19.39/18.29 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 19.39/18.29 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 19.39/18.29 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 19.39/18.29 ( (fun int (fun int (product_prod int int))), negDivAlg ) 19.39/18.29 ( (fun int (fun int (product_prod int int))), divmod_int ) 19.39/18.29 ( (fun int (fun int (product_prod int int))), posDivAlg ) 19.39/18.29 ( (fun int (fun int (product_prod int int))), pdivmod ) 19.39/18.29 ( (fun int (fun int (product_prod int int))), norm_frac ) 19.39/18.29 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 19.39/18.29 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 19.39/18.29 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 19.39/18.29 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 19.39/18.29 ( (fun real nat), natfloor ) 19.39/18.29 ( (fun real nat), natceiling ) 19.39/18.29 ( (fun int quickcheck_code_int), quickcheck_of_int ) 19.39/18.29 ( (fun int (fun int (fun int bool))), wset ) 19.39/18.29 ( (fun int (fun int (fun int bool))), bnorRset ) 19.39/18.29 ( (fun int (fun int (fun int bool))), zcong ) 19.39/18.29 ( (fun int (fun int (fun int bool))), noXRRset ) 19.39/18.29 ( (fun int (fun int (fun int bool))), zcongm ) 19.39/18.29 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 19.39/18.29 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 19.39/18.29 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 19.39/18.29 ( (fun int real), (real_1 int) ) 19.39/18.29 ( (fun complex nat), (size_size complex) ) 19.39/18.29 ( (fun complex nat), complex_size ) 19.39/18.29 ( (fun int (list int)), quickc666637781d_zero ) 19.39/18.29 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 19.39/18.29 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 19.39/18.29 ( (fun (product_prod int int) rat), frct ) 19.39/18.29 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 19.39/18.29 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 19.39/18.29 ( (fun (fun nat rat) bool), vanishes ) 19.39/18.29 ( (fun int (fun int rat)), fract ) 19.39/18.29 ( (fun code_code_numeral int), code_int_of ) 19.39/18.29 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 19.39/18.29 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 19.39/18.29 ( (fun code_code_numeral nat), code_c271388182l_size ) 19.39/18.29 ( (fun real (fun real complex)), complex_1 ) 19.39/18.29 ( (fun real (fun real complex)), rcis ) 19.39/18.29 ( (fun int (fun nat nat)), nat_aux ) 19.39/18.29 ( (fun rat real), ratreal ) 19.39/18.29 ( (fun quickcheck_code_int int), quickcheck_int_of ) 19.39/18.29 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 19.39/18.29 ( (fun rat (product_prod int int)), quotient_of ) 19.39/18.29 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 19.39/18.29 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 19.39/18.29 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 19.39/18.29 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 19.39/18.29 ) 19.39/18.29 (instantiation (let ((_let_0 (fun nat bool))) (forall ((M $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) (hAPP nat nat suc M)) N))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) N))) )) 19.39/18.29 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.29 ) 19.39/18.29 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_2) P_5))) (not (hBOOL (hAPP int bool zprime P_5))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP int int (hAPP int _let_1 legendre A_1) P_5)) (hAPP nat int (hAPP int (fun nat int) (power_power int) A_1) (hAPP int nat nat_1 (hAPP int int (hAPP int _let_1 (div_div int) (hAPP int int (hAPP int _let_1 (minus_minus int) P_5) (one_one int))) _let_2)))) P_5))) )))) 19.39/18.29 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.39/18.29 ) 19.39/18.29 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_142749 $$unsorted)) (or (not (linord219039673up_add X_a)) (= (= _let_0 (ti X_a BOUND_VARIABLE_142749)) (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_142749) BOUND_VARIABLE_142749)))) )) 19.39/18.29 ( bool, fFalse ) 19.39/18.29 ( bool, fTrue ) 19.39/18.29 ( real, pi ) 19.39/18.29 ( nat, (one_one nat) ) 19.39/18.29 ( (fun nat bool), (even_odd_even nat) ) 19.39/18.29 ( (fun nat bool), prime ) 19.39/18.29 ( (fun nat nat), suc ) 19.39/18.29 ( (fun nat nat), (fact_fact nat) ) 19.39/18.29 ( (fun nat nat), (size_size nat) ) 19.39/18.29 ( (fun nat nat), fact ) 19.39/18.29 ( (fun nat nat), nat_size ) 19.39/18.29 ( int, pls ) 19.39/18.29 ( int, m ) 19.39/18.29 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 19.39/18.29 ( int, min_1 ) 19.39/18.29 ( int, s ) 19.39/18.29 ( 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)))) ) 19.39/18.29 ( int, s1 ) 19.39/18.29 ( int, t ) 19.39/18.29 ( (fun int bool), zprime ) 19.39/18.29 ( (fun int bool), nat_neg ) 19.39/18.29 ( (fun int bool), zEven ) 19.39/18.29 ( (fun int bool), nat_is_nat ) 19.39/18.29 ( (fun int bool), zOdd ) 19.39/18.29 ( (fun int bool), (even_odd_even int) ) 19.39/18.29 ( (fun int bool), twoSqu1091635170sum2sq ) 19.39/18.29 ( (fun int nat), nat_1 ) 19.39/18.29 ( (fun int nat), phi ) 19.39/18.29 ( (fun real real), sqrt ) 19.39/18.29 ( (fun real real), tan ) 19.39/18.29 ( (fun real real), cos ) 19.39/18.29 ( (fun real real), arccos ) 19.39/18.29 ( (fun real real), ln ) 19.39/18.29 ( (fun real real), sin ) 19.39/18.29 ( (fun real real), arctan ) 19.39/18.29 ( (fun real real), arcsin ) 19.39/18.29 ( complex, ii ) 19.39/18.29 ( (fun complex complex), cnj ) 19.39/18.29 ( (fun complex complex), expi ) 19.39/18.29 ( (fun nat real), (real_1 nat) ) 19.39/18.29 ( (fun nat real), cos_coeff ) 19.39/18.29 ( (fun nat real), sin_coeff ) 19.39/18.29 ( (fun int int), bit0 ) 19.39/18.29 ( (fun int int), bit1 ) 19.39/18.29 ( (fun int int), pred ) 19.39/18.29 ( (fun int int), succ ) 19.39/18.29 ( (fun int int), (fact_fact int) ) 19.39/18.29 ( (fun int int), zfact ) 19.39/18.29 ( (fun bool bool), fNot ) 19.39/18.29 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 19.39/18.29 ( (fun bool (fun bool bool)), fconj ) 19.39/18.29 ( (fun bool (fun bool bool)), fdisj ) 19.39/18.29 ( (fun bool (fun bool bool)), fimplies ) 19.39/18.29 ( (fun int (fun int bool)), sRStar ) 19.39/18.29 ( (fun int (fun int bool)), quadRes ) 19.39/18.29 ( (fun int (fun int bool)), norRRset ) 19.39/18.29 ( (fun int (fun int bool)), d22set ) 19.39/18.29 ( (fun int (fun int bool)), sr ) 19.39/18.29 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 19.39/18.29 ( (fun nat (fun nat nat)), nat_gcd ) 19.39/18.29 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 19.39/18.29 ( (fun nat (fun nat nat)), nat_lcm ) 19.39/18.29 ( (fun nat (fun real real)), root ) 19.39/18.29 ( (fun real (fun real real)), log ) 19.39/18.29 ( (fun real (fun real real)), powr ) 19.39/18.29 ( (fun nat (fun nat bool)), coprime ) 19.39/18.29 ( (fun (fun int bool) int), (the int) ) 19.39/18.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 19.39/18.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 19.39/18.29 ( (fun nat (fun nat (product_prod int int))), bezw ) 19.39/18.29 ( (fun (fun int bool) bool), nat_nat_set ) 19.39/18.29 ( (filter nat), sequentially ) 19.39/18.29 ( (fun (product_prod nat nat) bool), pred_nat ) 19.39/18.29 ( (fun (product_prod int int) bool), frac_1 ) 19.39/18.29 ( (fun real complex), cis ) 19.39/18.29 ( (fun complex real), im ) 19.39/18.29 ( (fun complex real), re ) 19.39/18.29 ( (fun complex real), arg ) 19.39/18.29 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 19.39/18.29 ( (fun int (fun int int)), int_gcd ) 19.39/18.29 ( (fun int (fun int int)), multInv ) 19.39/18.29 ( (fun int (fun int int)), legacy_zgcd ) 19.39/18.29 ( (fun int (fun int int)), z3mod ) 19.39/18.29 ( (fun int (fun int int)), inv ) 19.39/18.29 ( (fun int (fun int int)), (gcd_gcd int) ) 19.39/18.29 ( (fun int (fun int int)), standardRes ) 19.39/18.29 ( (fun int (fun int int)), legendre ) 19.39/18.29 ( (fun int (fun int int)), nat_tsub ) 19.39/18.29 ( (fun int (fun int int)), z3div ) 19.39/18.29 ( (fun int (fun int int)), int_lcm ) 19.39/18.29 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 19.39/18.29 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 19.39/18.29 ( (fun int (fun (fun int bool) bool)), rsetR ) 19.39/18.29 ( (fun int (fun (fun int bool) bool)), resSet ) 19.39/18.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 19.39/18.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 19.39/18.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 19.39/18.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 19.39/18.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 19.39/18.29 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 19.39/18.29 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 19.39/18.29 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 19.39/18.29 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 19.39/18.29 ( (fun int (fun int (product_prod int int))), negDivAlg ) 19.39/18.29 ( (fun int (fun int (product_prod int int))), divmod_int ) 19.39/18.29 ( (fun int (fun int (product_prod int int))), posDivAlg ) 19.39/18.29 ( (fun int (fun int (product_prod int int))), pdivmod ) 19.39/18.29 ( (fun int (fun int (product_prod int int))), norm_frac ) 19.39/18.29 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 19.39/18.29 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 19.39/18.29 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 19.39/18.29 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 19.39/18.29 ( (fun real nat), natfloor ) 19.39/18.29 ( (fun real nat), natceiling ) 19.39/18.29 ( (fun int quickcheck_code_int), quickcheck_of_int ) 19.39/18.29 ( (fun int (fun int (fun int bool))), wset ) 19.39/18.29 ( (fun int (fun int (fun int bool))), bnorRset ) 19.39/18.29 ( (fun int (fun int (fun int bool))), zcong ) 19.39/18.29 ( (fun int (fun int (fun int bool))), noXRRset ) 19.39/18.29 ( (fun int (fun int (fun int bool))), zcongm ) 19.39/18.29 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 19.39/18.29 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 19.39/18.29 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 19.39/18.29 ( (fun int real), (real_1 int) ) 19.39/18.29 ( (fun complex nat), (size_size complex) ) 19.39/18.29 ( (fun complex nat), complex_size ) 19.39/18.29 ( (fun int (list int)), quickc666637781d_zero ) 19.39/18.29 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 19.39/18.29 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 19.39/18.29 ( (fun (product_prod int int) rat), frct ) 19.39/18.29 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 19.39/18.29 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 19.39/18.29 ( (fun (fun nat rat) bool), vanishes ) 19.39/18.29 ( (fun int (fun int rat)), fract ) 19.39/18.29 ( (fun code_code_numeral int), code_int_of ) 19.39/18.29 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 19.39/18.29 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 19.39/18.29 ( (fun code_code_numeral nat), code_c271388182l_size ) 19.39/18.29 ( (fun real (fun real complex)), complex_1 ) 19.39/18.29 ( (fun real (fun real complex)), rcis ) 19.39/18.29 ( (fun int (fun nat nat)), nat_aux ) 19.39/18.29 ( (fun rat real), ratreal ) 19.39/18.29 ( (fun quickcheck_code_int int), quickcheck_int_of ) 19.39/18.29 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 19.39/18.29 ( (fun rat (product_prod int int)), quotient_of ) 19.39/18.29 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 19.39/18.29 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 19.39/18.29 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 19.39/18.29 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 19.39/18.29 ) 19.39/18.29 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_142779 $$unsorted) (BOUND_VARIABLE_142780 $$unsorted)) (or (not (no_zero_divisors X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_142780)) (= _let_0 (ti X_a BOUND_VARIABLE_142779)) (not (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_142780) BOUND_VARIABLE_142779)))) )) 19.39/18.29 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.29 ( 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))))) ) 19.39/18.29 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.29 ( 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)))) ) 19.39/18.29 ( 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))) ) 19.39/18.29 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.39/18.29 ( 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))) ) 19.39/18.29 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.39/18.29 ( complex, ii, ii ) 19.39/18.29 ( 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)) ) 19.39/18.29 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.39/18.29 ) 19.39/18.29 (instantiation (let ((_let_0 (zero_zero real))) (forall ((Y $$unsorted)) (or (= _let_0 Y) (= _let_0 (hAPP real real cos (hAPP complex real arg (hAPP real complex (hAPP real (fun real complex) complex_1 _let_0) Y))))) )) 19.39/18.29 ( (zero_zero real) ) 19.39/18.29 ( (one_one real) ) 19.39/18.29 ) 19.39/18.29 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (finite_finite T_1)) (not (finite_finite T_2)) (finite_finite (fun T_2 T_1))) ) 19.39/18.29 ( bool, bool ) 19.39/18.29 ( bool, (fun bool bool) ) 19.39/18.29 ( real, bool ) 19.39/18.29 ( real, real ) 19.39/18.29 ( real, nat ) 19.39/18.29 ( real, (fun int bool) ) 19.39/18.29 ( real, (fun real bool) ) 19.39/18.29 ( real, (fun real real) ) 19.39/18.29 ( real, complex ) 19.39/18.29 ( real, (fun nat real) ) 19.39/18.29 ( real, (fun bool bool) ) 19.39/18.29 ( real, (fun int (fun int bool)) ) 19.39/18.29 ( real, (fun (filter real) bool) ) 19.39/18.29 ( real, (fun (filter nat) bool) ) 19.39/18.29 ( real, (fun real complex) ) 19.39/18.29 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 19.39/18.29 ( real, (fun nat (product_prod real real)) ) 19.39/18.29 ( real, (fun real (fun nat (product_prod real real))) ) 19.39/18.29 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 19.39/18.29 ( real, (fun int (fun int (fun bool bool))) ) 19.39/18.29 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 19.39/18.29 ( real, (fun (fun int real) (fun int bool)) ) 19.39/18.29 ( real, (fun int (fun nat bool)) ) 19.39/18.29 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 19.39/18.30 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 19.39/18.30 ( real, (fun int (fun nat (fun bool bool))) ) 19.39/18.30 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 19.39/18.30 ( real, (fun (fun nat real) (fun nat bool)) ) 19.39/18.30 ( nat, bool ) 19.39/18.30 ( nat, real ) 19.39/18.30 ( nat, nat ) 19.39/18.30 ( nat, (fun nat bool) ) 19.39/18.30 ( nat, (fun nat nat) ) 19.39/18.30 ( nat, int ) 19.39/18.30 ( nat, (fun real real) ) 19.39/18.30 ( nat, complex ) 19.39/18.30 ( nat, (fun int int) ) 19.39/18.30 ( nat, rat ) 19.39/18.30 ( nat, (fun bool bool) ) 19.39/18.30 ( nat, (fun nat (fun nat bool)) ) 19.39/18.30 ( nat, (product_prod real real) ) 19.39/18.30 ( nat, (product_prod int int) ) 19.39/18.30 ( nat, (fun nat (product_prod int int)) ) 19.39/18.30 ( nat, (product_prod nat nat) ) 19.39/18.30 ( nat, (fun (product_prod nat nat) bool) ) 19.39/18.30 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 19.39/18.30 ( nat, (fun nat (product_prod nat nat)) ) 19.39/18.30 ( (fun nat bool), bool ) 19.39/18.30 ( (fun nat bool), (fun nat bool) ) 19.39/18.30 ( (fun nat bool), (fun nat (fun bool bool)) ) 19.39/18.30 ( (fun nat bool), (fun int (fun nat bool)) ) 19.39/18.30 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 19.39/18.30 ( (fun nat nat), (fun nat real) ) 19.39/18.30 ( (fun nat nat), (fun nat (fun nat nat)) ) 19.39/18.30 ( (fun nat nat), (fun nat (fun nat bool)) ) 19.39/18.30 ( int, bool ) 19.39/18.30 ( int, real ) 19.39/18.30 ( int, nat ) 19.39/18.30 ( int, (fun nat bool) ) 19.39/18.30 ( int, (fun nat nat) ) 19.39/18.30 ( int, int ) 19.39/18.30 ( int, (fun int bool) ) 19.39/18.30 ( int, (fun nat int) ) 19.39/18.30 ( int, (fun real real) ) 19.39/18.30 ( int, (fun nat real) ) 19.39/18.30 ( int, (fun int int) ) 19.39/18.30 ( int, rat ) 19.39/18.30 ( int, (fun int rat) ) 19.39/18.30 ( int, (fun bool bool) ) 19.39/18.30 ( int, (fun int (fun bool bool)) ) 19.39/18.30 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 19.39/18.30 ( int, (fun int (fun int bool)) ) 19.39/18.30 ( int, quickcheck_code_int ) 19.39/18.30 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 19.39/18.30 ( int, (product_prod int int) ) 19.39/18.30 ( int, (fun int (product_prod int int)) ) 19.39/18.30 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 19.39/18.30 ( int, (fun (fun int bool) bool) ) 19.39/18.30 ( int, (fun (product_prod int int) bool) ) 19.39/18.30 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 19.39/18.30 ( int, (product_prod int (product_prod int int)) ) 19.39/18.30 ( int, (fun int (product_prod int (product_prod int int))) ) 19.39/18.30 ( int, (fun (fun int int) (fun int bool)) ) 19.39/18.30 ( int, (fun int (fun (product_prod int int) bool)) ) 19.39/18.30 ( int, (fun int (fun (fun int bool) bool)) ) 19.39/18.30 ( int, (list int) ) 19.39/18.30 ( int, (fun nat (fun bool bool)) ) 19.39/18.30 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 19.39/18.30 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 19.39/18.30 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 19.39/18.30 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 19.39/18.30 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 19.39/18.30 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 19.39/18.30 ( int, (fun (product_prod int int) int) ) 19.39/18.30 ( int, (fun int (fun int (fun int bool))) ) 19.39/18.30 ( int, (fun int real) ) 19.39/18.30 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 19.39/18.30 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 19.39/18.30 ( (fun int bool), bool ) 19.39/18.30 ( (fun int bool), int ) 19.39/18.30 ( (fun int bool), (fun int bool) ) 19.39/18.30 ( (fun int bool), (fun int (fun bool bool)) ) 19.39/18.30 ( (fun int bool), (fun int (fun int bool)) ) 19.39/18.30 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 19.39/18.30 ( (fun int bool), (fun int (fun int int)) ) 19.39/18.30 ( (fun int bool), (fun real (fun int (fun int bool))) ) 19.39/18.30 ( (fun real bool), real ) 19.39/18.30 ( (fun real bool), (fun real bool) ) 19.39/18.30 ( (fun real bool), (fun real (fun bool bool)) ) 19.39/18.30 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 19.39/18.30 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 19.39/18.30 ( (fun real real), (fun real real) ) 19.39/18.30 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 19.39/18.30 ( (fun real real), (fun real (fun real real)) ) 19.39/18.30 ( (fun real real), (fun real (fun real bool)) ) 19.39/18.30 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 19.39/18.30 ( complex, real ) 19.39/18.30 ( complex, nat ) 19.39/18.30 ( complex, complex ) 19.39/18.30 ( (fun nat real), (fun nat bool) ) 19.39/18.30 ( (fun nat real), (fun nat real) ) 19.39/18.30 ( (fun nat real), (fun nat (fun real real)) ) 19.39/18.30 ( (fun nat real), (fun int (fun nat real)) ) 19.39/18.30 ( (fun int int), (fun int bool) ) 19.39/18.30 ( (fun int int), (fun int int) ) 19.39/18.30 ( (fun int int), (fun int (fun int bool)) ) 19.39/18.30 ( (fun int int), (fun int (fun int int)) ) 19.39/18.30 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 19.39/18.30 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 19.39/18.30 ( rat, real ) 19.39/18.30 ( rat, (product_prod int int) ) 19.39/18.30 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 19.39/18.30 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 19.39/18.30 ( (fun int (fun int bool)), (fun int bool) ) 19.39/18.30 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 19.39/18.30 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 19.39/18.30 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 19.39/18.30 ( quickcheck_code_int, nat ) 19.39/18.30 ( quickcheck_code_int, int ) 19.39/18.30 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 19.39/18.30 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 19.39/18.30 ( (product_prod real real), bool ) 19.39/18.30 ( (product_prod int int), bool ) 19.39/18.30 ( (product_prod int int), int ) 19.39/18.30 ( (product_prod int int), (fun int bool) ) 19.39/18.30 ( (product_prod int int), (fun int int) ) 19.39/18.30 ( (product_prod int int), rat ) 19.39/18.30 ( (product_prod int int), (fun bool bool) ) 19.39/18.30 ( (product_prod int int), (product_prod int int) ) 19.39/18.30 ( (product_prod int int), (fun (product_prod int int) bool) ) 19.39/18.30 ( (product_prod int int), (fun (product_prod int int) int) ) 19.39/18.30 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 19.39/18.30 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 19.39/18.30 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 19.39/18.30 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 19.39/18.30 ( (filter real), bool ) 19.39/18.30 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 19.39/18.30 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 19.39/18.30 ( (filter nat), bool ) 19.39/18.30 ( (product_prod nat nat), bool ) 19.39/18.30 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 19.39/18.30 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 19.39/18.30 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 19.39/18.30 ( code_code_numeral, nat ) 19.39/18.30 ( code_code_numeral, (fun nat nat) ) 19.39/18.30 ( code_code_numeral, int ) 19.39/18.30 ( code_code_numeral, code_code_numeral ) 19.39/18.30 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 19.39/18.30 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 19.39/18.30 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 19.39/18.30 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 19.39/18.30 ( (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))) ) 19.39/18.30 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 19.39/18.30 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 19.39/18.30 ( (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))) ) 19.39/18.30 ( (fun nat rat), bool ) 19.39/18.30 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 19.39/18.30 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 19.39/18.30 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 19.39/18.30 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 19.39/18.30 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 19.39/18.30 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 19.39/18.30 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 19.39/18.30 ( (fun int real), (fun int bool) ) 19.39/18.30 ( (fun int real), (fun int real) ) 19.39/18.30 ( (fun int real), (fun int (fun int real)) ) 19.39/18.30 ( (fun int real), (fun int (fun real real)) ) 19.39/18.30 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 19.39/18.30 ( (fun real (fun int bool)), (fun real bool) ) 19.39/18.30 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 19.39/18.30 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 19.39/18.30 ( (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)))) ) 19.39/18.30 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 19.39/18.30 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 19.39/18.30 ( (fun int (fun int real)), (fun int (fun int bool)) ) 19.39/18.30 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 19.39/18.30 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 19.39/18.30 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 19.39/18.30 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 19.39/18.30 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 19.39/18.30 ( (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))) ) 19.39/18.30 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 19.39/18.30 ( (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))) ) 19.39/18.30 ( (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))) ) 19.39/18.30 ( (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)))) ) 19.39/18.30 ( (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)))) ) 19.39/18.30 ( (fun int (fun nat bool)), (fun int bool) ) 19.39/18.30 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 19.39/18.30 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 19.39/18.30 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 19.39/18.30 ( (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))) ) 19.39/18.30 ( (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)))) ) 19.39/18.30 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 19.39/18.30 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 19.39/18.30 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 19.39/18.30 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 19.39/18.30 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 19.39/18.30 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 19.39/18.30 ) 19.39/18.30 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP int real (real_1 int) N))) (forall ((N $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) _let_1) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_1) (one_one real))))) (= (ti int N) (hAPP real int (archim2085082626_floor real) X))) ))) 19.55/18.30 ( (zero_zero int), pi ) 19.55/18.30 ( (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.30 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.30 ( (zero_zero int), skv_6 ) 19.55/18.30 ( (zero_zero int), skv_11 ) 19.55/18.30 ( (zero_zero int), skv_12 ) 19.55/18.30 ( (zero_zero int), skv_14 ) 19.55/18.30 ) 19.55/18.30 (instantiation (let ((_let_0 (fun real bool))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) Y_1) X_1))) (= X_1 (hAPP _let_0 real (complete_Sup_Sup real) (hAPP real _let_0 (hAPP real (fun real _let_0) (ord_atLeastLessThan real) Y_1) X_1)))) )) 19.55/18.30 ( (zero_zero real), pi ) 19.55/18.30 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.30 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.30 ( (zero_zero real), skv_2 ) 19.55/18.30 ( (zero_zero real), skv_10 ) 19.55/18.30 ( (zero_zero real), skv_13 ) 19.55/18.30 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.30 ( pi, (zero_zero real) ) 19.55/18.30 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.30 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.30 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 19.55/18.30 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.55/18.30 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 19.55/18.30 ) 19.55/18.30 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142881 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_142881) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_142881) (hAPP int X_a (number_number_of X_a) min_1)))) ) 19.55/18.30 ( real, (one_one real) ) 19.55/18.30 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.30 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.30 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 19.55/18.30 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.30 ( 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))))) ) 19.55/18.30 ( int, pls ) 19.55/18.30 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.30 ( int, (one_one int) ) 19.55/18.30 ( 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))) ) 19.55/18.30 ( int, min_1 ) 19.55/18.30 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.30 ( complex, ii ) 19.55/18.30 ( complex, (one_one complex) ) 19.55/18.30 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.30 ( 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)) ) 19.55/18.30 ) 19.55/18.30 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_142904 $$unsorted) (BOUND_VARIABLE_142905 $$unsorted) (BOUND_VARIABLE_142906 $$unsorted) (BOUND_VARIABLE_142907 $$unsorted)) (or (not (ordered_ab_group_add X_a)) (not (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_142904) BOUND_VARIABLE_142905) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_142906) BOUND_VARIABLE_142907))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_142906) BOUND_VARIABLE_142907)) (hBOOL (hAPP X_a bool (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_142904) BOUND_VARIABLE_142905)))) ))))) 19.55/18.31 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 19.55/18.31 ( 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_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 19.55/18.31 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral), (zero_zero code_code_numeral), (one_one code_code_numeral) ) 19.55/18.31 ) 19.55/18.31 (instantiation (let ((_let_0 (fun real bool))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) Y_1) X_1))) (= X_1 (hAPP _let_0 real (complete_Sup_Sup real) (hAPP real _let_0 (hAPP real (fun real _let_0) (ord_gr676655987ssThan real) Y_1) X_1)))) )) 19.55/18.31 ( (zero_zero real), pi ) 19.55/18.31 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.31 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.31 ( (zero_zero real), skv_2 ) 19.55/18.31 ( (zero_zero real), skv_10 ) 19.55/18.31 ( (zero_zero real), skv_13 ) 19.55/18.31 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.31 ( pi, (zero_zero real) ) 19.55/18.31 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.31 ( (hAPP real real (hAPP real (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))) ) 19.55/18.31 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP 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) ) 19.55/18.31 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.55/18.31 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP 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 ) 19.55/18.31 ) 19.55/18.31 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun _let_0 _let_0))) (let ((_let_7 (combs real bool bool))) (let ((_let_8 (hAPP (fun bool _let_3) (fun _let_0 _let_5) (combb bool _let_3 real) fconj))) (let ((_let_9 (combc real real bool))) (forall ((Y_1 $$unsorted)) (= (hAPP real real arccos Y_1) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_5 _let_6 _let_7 (hAPP _let_0 _let_5 _let_8 (hAPP real _let_0 _let_1 (zero_zero real)))) (hAPP _let_0 _let_0 (hAPP _let_5 _let_6 _let_7 (hAPP _let_0 _let_5 _let_8 (hAPP real _let_0 (hAPP _let_4 _let_4 _let_9 _let_1) pi))) (hAPP real _let_0 (hAPP _let_4 _let_4 _let_9 (hAPP _let_2 _let_4 (hAPP _let_4 (fun _let_2 _let_4) (combb real _let_0 real) (fequal real)) cos)) Y_1))))) ))))))))))) 19.55/18.31 ( (zero_zero real) ) 19.55/18.31 ) 19.55/18.31 (instantiation (let ((_let_0 (fun nat bool))) (forall ((N_1 $$unsorted)) (= (hAPP _let_0 nat (hAPP (fun nat nat) (fun _let_0 nat) (big_co302546470etprod nat nat) (combi nat)) (hAPP nat _let_0 (hAPP nat (fun nat _let_0) (ord_atLeastAtMost nat) (one_one nat)) N_1)) (hAPP nat nat (fact_fact nat) N_1)) )) 19.55/18.31 ( (zero_zero nat) ) 19.55/18.31 ( (hAPP nat nat suc (zero_zero nat)) ) 19.55/18.31 ) 19.55/18.31 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_143105 $$unsorted) (BOUND_VARIABLE_143106 $$unsorted)) (or (not (ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_143105) BOUND_VARIABLE_143106) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_143105)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_143106)))) )))) 19.55/18.31 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.55/18.31 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.55/18.31 ( 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)))))) ) 19.55/18.31 ( 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 ) 19.55/18.31 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 19.55/18.31 ( 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))), (zero_zero int) ) 19.55/18.31 ( 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))), t ) 19.55/18.31 ( 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_1 ) 19.55/18.31 ( complex, ii, ii ) 19.55/18.31 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 19.55/18.31 ( 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 ) 19.55/18.31 ) 19.55/18.31 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP nat (fun real real) root N))) (forall ((X $$unsorted) (Y $$unsorted) (N $$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 _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)))) )))) 19.55/18.31 ( (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))) ) 19.55/18.31 ( (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))) ) 19.55/18.31 ) 19.55/18.31 (instantiation (let ((_let_0 (fun nat bool))) (forall ((M $$unsorted) (N $$unsorted)) (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))) )) 19.55/18.31 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.31 ) 19.55/18.31 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143158 $$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_143158) (zero_zero X_a)))) ) 19.55/18.31 ( 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))) ) 19.55/18.31 ) 19.55/18.31 (instantiation (forall ((N $$unsorted)) (= (hAPP nat nat suc N) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)) N)) ) 19.55/18.31 ( (zero_zero nat) ) 19.55/18.31 ( (hAPP nat nat suc (zero_zero nat)) ) 19.55/18.31 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 19.55/18.31 ( (one_one nat) ) 19.55/18.31 ) 19.55/18.31 (instantiation (let ((_let_0 (hBOOL P_2))) (let ((_let_1 (hBOOL P_1))) (let ((_let_2 (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X_1))))) (forall ((P_2 $$unsorted) (P_1 $$unsorted) (X_1 $$unsorted)) (or (and (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X_1)) (= (not _let_0) _let_1)) (= (or _let_2 _let_1) (or _let_2 _let_0))) )))) 19.55/18.31 ( (let ((_let_0 (fun int int))) (hAPP int bool zprime (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 zprime (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (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) pls) ) 19.55/18.31 ( (let ((_let_0 (fun int int))) (hAPP int bool zprime (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (fun real _let_0))) (let ((_let_3 (filter real))) (let ((_let_4 (fun _let_3 bool))) (hAPP _let_3 bool (hAPP real _let_4 (hAPP _let_0 (fun real _let_4) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_0 real) _let_1) cos)) sin)) (zero_zero real)) (hAPP real _let_3 (at real) (hAPP real real (hAPP real _let_0 _let_1 pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))), (hAPP int int (number_number_of int) pls) ) 19.55/18.31 ( (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (fun real _let_0))) (let ((_let_3 (filter real))) (let ((_let_4 (fun _let_3 bool))) (hAPP _let_3 bool (hAPP real _let_4 (hAPP _let_0 (fun real _let_4) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_0 real) _let_1) cos)) sin)) (zero_zero real)) (hAPP real _let_3 (at real) (hAPP real real (hAPP real _let_0 _let_1 pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun int int))) (hAPP int bool zprime (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_1 ) 19.55/18.31 ( (hAPP int bool zprime (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int bool zprime (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))), s ) 19.55/18.31 ( (hAPP int bool zprime (hAPP int int (number_number_of int) (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 (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), s ) 19.55/18.31 ( (hAPP real bool (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))))), (hAPP int bool zprime (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 bit1 pls))) ) 19.55/18.31 ( (let ((_let_0 (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 real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) _let_0)) _let_0)), (let ((_let_0 (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 real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) _let_0)) _let_0)), (one_one int) ) 19.55/18.31 ( (let ((_let_0 (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 real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) _let_0)) _let_0)), (hAPP int bool nat_neg (hAPP int int (number_number_of int) pls)), (one_one int) ) 19.55/18.31 ( fTrue, fTrue, skv_3 ) 19.55/18.31 ( fTrue, (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))) (zero_zero int)), skv_3 ) 19.55/18.31 ( (hAPP int bool nat_neg (hAPP int int (number_number_of int) pls)), (let ((_let_0 (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 real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) _let_0)) _let_0)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.55/18.31 ( (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))) (zero_zero int)), fTrue, skv_9 ) 19.55/18.31 ) 19.55/18.31 (instantiation (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (inverse_inverse X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_143197 $$unsorted)) (or (not (linordered_field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_143197)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_143197)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_143197)))) ))) 19.55/18.31 ( bool, fFalse ) 19.55/18.31 ( bool, fTrue ) 19.55/18.31 ( real, (zero_zero real) ) 19.55/18.31 ( real, pi ) 19.55/18.31 ( (fun nat bool), (even_odd_even nat) ) 19.55/18.31 ( (fun nat bool), prime ) 19.55/18.31 ( (fun nat nat), suc ) 19.55/18.31 ( (fun nat nat), (fact_fact nat) ) 19.55/18.32 ( (fun nat nat), (size_size nat) ) 19.55/18.32 ( (fun nat nat), fact ) 19.55/18.32 ( (fun nat nat), nat_size ) 19.55/18.32 ( int, pls ) 19.55/18.32 ( int, m ) 19.55/18.32 ( int, min_1 ) 19.55/18.32 ( int, s ) 19.55/18.32 ( int, s1 ) 19.55/18.32 ( int, t ) 19.55/18.32 ( (fun int bool), zprime ) 19.55/18.32 ( (fun int bool), nat_neg ) 19.55/18.32 ( (fun int bool), zEven ) 19.55/18.32 ( (fun int bool), nat_is_nat ) 19.55/18.32 ( (fun int bool), zOdd ) 19.55/18.32 ( (fun int bool), (even_odd_even int) ) 19.55/18.32 ( (fun int bool), twoSqu1091635170sum2sq ) 19.55/18.32 ( (fun int nat), nat_1 ) 19.55/18.32 ( (fun int nat), phi ) 19.55/18.32 ( (fun real real), sqrt ) 19.55/18.32 ( (fun real real), tan ) 19.55/18.32 ( (fun real real), cos ) 19.55/18.32 ( (fun real real), arccos ) 19.55/18.32 ( (fun real real), ln ) 19.55/18.32 ( (fun real real), sin ) 19.55/18.32 ( (fun real real), arctan ) 19.55/18.32 ( (fun real real), arcsin ) 19.55/18.32 ( complex, ii ) 19.55/18.32 ( (fun complex complex), cnj ) 19.55/18.32 ( (fun complex complex), expi ) 19.55/18.32 ( (fun nat real), (real_1 nat) ) 19.55/18.32 ( (fun nat real), cos_coeff ) 19.55/18.32 ( (fun nat real), sin_coeff ) 19.55/18.32 ( (fun int int), bit0 ) 19.55/18.32 ( (fun int int), bit1 ) 19.55/18.32 ( (fun int int), pred ) 19.55/18.32 ( (fun int int), succ ) 19.55/18.32 ( (fun int int), (fact_fact int) ) 19.55/18.32 ( (fun int int), zfact ) 19.55/18.32 ( (fun bool bool), fNot ) 19.55/18.32 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 19.55/18.32 ( (fun bool (fun bool bool)), fconj ) 19.55/18.32 ( (fun bool (fun bool bool)), fdisj ) 19.55/18.32 ( (fun bool (fun bool bool)), fimplies ) 19.55/18.32 ( (fun int (fun int bool)), sRStar ) 19.55/18.32 ( (fun int (fun int bool)), quadRes ) 19.55/18.32 ( (fun int (fun int bool)), norRRset ) 19.55/18.32 ( (fun int (fun int bool)), d22set ) 19.55/18.32 ( (fun int (fun int bool)), sr ) 19.55/18.32 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 19.55/18.32 ( (fun nat (fun nat nat)), nat_gcd ) 19.55/18.32 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 19.55/18.32 ( (fun nat (fun nat nat)), nat_lcm ) 19.55/18.32 ( (fun nat (fun real real)), root ) 19.55/18.32 ( (fun real (fun real real)), log ) 19.55/18.32 ( (fun real (fun real real)), powr ) 19.55/18.32 ( (fun nat (fun nat bool)), coprime ) 19.55/18.32 ( (fun (fun int bool) int), (the int) ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 19.55/18.32 ( (fun nat (fun nat (product_prod int int))), bezw ) 19.55/18.32 ( (fun (fun int bool) bool), nat_nat_set ) 19.55/18.32 ( (filter nat), sequentially ) 19.55/18.32 ( (fun (product_prod nat nat) bool), pred_nat ) 19.55/18.32 ( (fun (product_prod int int) bool), frac_1 ) 19.55/18.32 ( (fun real complex), cis ) 19.55/18.32 ( (fun complex real), im ) 19.55/18.32 ( (fun complex real), re ) 19.55/18.32 ( (fun complex real), arg ) 19.55/18.32 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 19.55/18.32 ( (fun int (fun int int)), int_gcd ) 19.55/18.32 ( (fun int (fun int int)), multInv ) 19.55/18.32 ( (fun int (fun int int)), legacy_zgcd ) 19.55/18.32 ( (fun int (fun int int)), z3mod ) 19.55/18.32 ( (fun int (fun int int)), inv ) 19.55/18.32 ( (fun int (fun int int)), (gcd_gcd int) ) 19.55/18.32 ( (fun int (fun int int)), standardRes ) 19.55/18.32 ( (fun int (fun int int)), legendre ) 19.55/18.32 ( (fun int (fun int int)), nat_tsub ) 19.55/18.32 ( (fun int (fun int int)), z3div ) 19.55/18.32 ( (fun int (fun int int)), int_lcm ) 19.55/18.32 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 19.55/18.32 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 19.55/18.32 ( (fun int (fun (fun int bool) bool)), rsetR ) 19.55/18.32 ( (fun int (fun (fun int bool) bool)), resSet ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 19.55/18.32 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 19.55/18.32 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 19.55/18.32 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 19.55/18.32 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 19.55/18.32 ( (fun int (fun int (product_prod int int))), negDivAlg ) 19.55/18.32 ( (fun int (fun int (product_prod int int))), divmod_int ) 19.55/18.32 ( (fun int (fun int (product_prod int int))), posDivAlg ) 19.55/18.32 ( (fun int (fun int (product_prod int int))), pdivmod ) 19.55/18.32 ( (fun int (fun int (product_prod int int))), norm_frac ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 19.55/18.32 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 19.55/18.32 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 19.55/18.32 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 19.55/18.32 ( (fun real nat), natfloor ) 19.55/18.32 ( (fun real nat), natceiling ) 19.55/18.32 ( (fun int quickcheck_code_int), quickcheck_of_int ) 19.55/18.32 ( (fun int (fun int (fun int bool))), wset ) 19.55/18.32 ( (fun int (fun int (fun int bool))), bnorRset ) 19.55/18.32 ( (fun int (fun int (fun int bool))), zcong ) 19.55/18.32 ( (fun int (fun int (fun int bool))), noXRRset ) 19.55/18.32 ( (fun int (fun int (fun int bool))), zcongm ) 19.55/18.32 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 19.55/18.32 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 19.55/18.32 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 19.55/18.32 ( (fun int real), (real_1 int) ) 19.55/18.32 ( (fun complex nat), (size_size complex) ) 19.55/18.32 ( (fun complex nat), complex_size ) 19.55/18.32 ( (fun int (list int)), quickc666637781d_zero ) 19.55/18.32 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 19.55/18.32 ( (fun (product_prod int int) rat), frct ) 19.55/18.32 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 19.55/18.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 19.55/18.32 ( (fun (fun nat rat) bool), vanishes ) 19.55/18.32 ( (fun int (fun int rat)), fract ) 19.55/18.32 ( (fun code_code_numeral int), code_int_of ) 19.55/18.32 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 19.55/18.32 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 19.55/18.32 ( (fun code_code_numeral nat), code_c271388182l_size ) 19.55/18.32 ( (fun real (fun real complex)), complex_1 ) 19.55/18.32 ( (fun real (fun real complex)), rcis ) 19.55/18.32 ( (fun int (fun nat nat)), nat_aux ) 19.55/18.32 ( (fun rat real), ratreal ) 19.55/18.32 ( (fun quickcheck_code_int int), quickcheck_int_of ) 19.55/18.32 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 19.55/18.32 ( (fun rat (product_prod int int)), quotient_of ) 19.55/18.32 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 19.55/18.32 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 19.55/18.32 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 19.55/18.32 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 19.55/18.32 ) 19.55/18.32 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143226 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_143226)) (= (one_one X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_143226) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_143226)))) ) 19.55/18.32 ( bool, fFalse ) 19.55/18.32 ( bool, fTrue ) 19.55/18.32 ( real, (zero_zero real) ) 19.55/18.32 ( real, pi ) 19.55/18.32 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.32 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.32 ( 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))))) ) 19.55/18.32 ( (fun nat bool), (even_odd_even nat) ) 19.55/18.32 ( (fun nat bool), prime ) 19.55/18.32 ( (fun nat nat), suc ) 19.55/18.32 ( (fun nat nat), (fact_fact nat) ) 19.55/18.32 ( (fun nat nat), (size_size nat) ) 19.55/18.32 ( (fun nat nat), fact ) 19.55/18.32 ( (fun nat nat), nat_size ) 19.55/18.32 ( int, pls ) 19.55/18.32 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.32 ( int, m ) 19.55/18.32 ( 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))) ) 19.55/18.32 ( int, min_1 ) 19.55/18.32 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.32 ( int, s ) 19.55/18.32 ( int, s1 ) 19.55/18.32 ( int, t ) 19.55/18.32 ( (fun int bool), zprime ) 19.55/18.32 ( (fun int bool), nat_neg ) 19.55/18.32 ( (fun int bool), zEven ) 19.55/18.32 ( (fun int bool), nat_is_nat ) 19.55/18.32 ( (fun int bool), zOdd ) 19.55/18.32 ( (fun int bool), (even_odd_even int) ) 19.55/18.32 ( (fun int bool), twoSqu1091635170sum2sq ) 19.55/18.32 ( (fun int nat), nat_1 ) 19.55/18.32 ( (fun int nat), phi ) 19.55/18.32 ( (fun real real), sqrt ) 19.55/18.32 ( (fun real real), tan ) 19.55/18.32 ( (fun real real), cos ) 19.55/18.32 ( (fun real real), arccos ) 19.55/18.32 ( (fun real real), ln ) 19.55/18.32 ( (fun real real), sin ) 19.55/18.32 ( (fun real real), arctan ) 19.55/18.32 ( (fun real real), arcsin ) 19.55/18.32 ( complex, ii ) 19.55/18.32 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.32 ( 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)) ) 19.55/18.32 ( (fun complex complex), cnj ) 19.55/18.32 ( (fun complex complex), expi ) 19.55/18.32 ( (fun nat real), (real_1 nat) ) 19.55/18.32 ( (fun nat real), cos_coeff ) 19.55/18.32 ( (fun nat real), sin_coeff ) 19.55/18.32 ( (fun int int), bit0 ) 19.55/18.32 ( (fun int int), bit1 ) 19.55/18.32 ( (fun int int), pred ) 19.55/18.32 ( (fun int int), succ ) 19.55/18.32 ( (fun int int), (fact_fact int) ) 19.55/18.32 ( (fun int int), zfact ) 19.55/18.32 ( (fun bool bool), fNot ) 19.55/18.32 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 19.55/18.32 ( (fun bool (fun bool bool)), fconj ) 19.55/18.32 ( (fun bool (fun bool bool)), fdisj ) 19.55/18.32 ( (fun bool (fun bool bool)), fimplies ) 19.55/18.32 ( (fun int (fun int bool)), sRStar ) 19.55/18.32 ( (fun int (fun int bool)), quadRes ) 19.55/18.32 ( (fun int (fun int bool)), norRRset ) 19.55/18.32 ( (fun int (fun int bool)), d22set ) 19.55/18.32 ( (fun int (fun int bool)), sr ) 19.55/18.32 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 19.55/18.32 ( (fun nat (fun nat nat)), nat_gcd ) 19.55/18.32 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 19.55/18.32 ( (fun nat (fun nat nat)), nat_lcm ) 19.55/18.32 ( (fun nat (fun real real)), root ) 19.55/18.32 ( (fun real (fun real real)), log ) 19.55/18.32 ( (fun real (fun real real)), powr ) 19.55/18.32 ( (fun nat (fun nat bool)), coprime ) 19.55/18.32 ( (fun (fun int bool) int), (the int) ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 19.55/18.32 ( (fun nat (fun nat (product_prod int int))), bezw ) 19.55/18.32 ( (fun (fun int bool) bool), nat_nat_set ) 19.55/18.32 ( (filter nat), sequentially ) 19.55/18.32 ( (fun (product_prod nat nat) bool), pred_nat ) 19.55/18.32 ( (fun (product_prod int int) bool), frac_1 ) 19.55/18.32 ( (fun real complex), cis ) 19.55/18.32 ( (fun complex real), im ) 19.55/18.32 ( (fun complex real), re ) 19.55/18.32 ( (fun complex real), arg ) 19.55/18.32 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 19.55/18.32 ( (fun int (fun int int)), int_gcd ) 19.55/18.32 ( (fun int (fun int int)), multInv ) 19.55/18.32 ( (fun int (fun int int)), legacy_zgcd ) 19.55/18.32 ( (fun int (fun int int)), z3mod ) 19.55/18.32 ( (fun int (fun int int)), inv ) 19.55/18.32 ( (fun int (fun int int)), (gcd_gcd int) ) 19.55/18.32 ( (fun int (fun int int)), standardRes ) 19.55/18.32 ( (fun int (fun int int)), legendre ) 19.55/18.32 ( (fun int (fun int int)), nat_tsub ) 19.55/18.32 ( (fun int (fun int int)), z3div ) 19.55/18.32 ( (fun int (fun int int)), int_lcm ) 19.55/18.32 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 19.55/18.32 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 19.55/18.32 ( (fun int (fun (fun int bool) bool)), rsetR ) 19.55/18.32 ( (fun int (fun (fun int bool) bool)), resSet ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 19.55/18.32 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 19.55/18.32 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 19.55/18.32 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 19.55/18.32 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 19.55/18.32 ( (fun int (fun int (product_prod int int))), negDivAlg ) 19.55/18.32 ( (fun int (fun int (product_prod int int))), divmod_int ) 19.55/18.32 ( (fun int (fun int (product_prod int int))), posDivAlg ) 19.55/18.32 ( (fun int (fun int (product_prod int int))), pdivmod ) 19.55/18.32 ( (fun int (fun int (product_prod int int))), norm_frac ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 19.55/18.32 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 19.55/18.32 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 19.55/18.32 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 19.55/18.32 ( (fun real nat), natfloor ) 19.55/18.32 ( (fun real nat), natceiling ) 19.55/18.32 ( (fun int quickcheck_code_int), quickcheck_of_int ) 19.55/18.32 ( (fun int (fun int (fun int bool))), wset ) 19.55/18.32 ( (fun int (fun int (fun int bool))), bnorRset ) 19.55/18.32 ( (fun int (fun int (fun int bool))), zcong ) 19.55/18.32 ( (fun int (fun int (fun int bool))), noXRRset ) 19.55/18.32 ( (fun int (fun int (fun int bool))), zcongm ) 19.55/18.32 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 19.55/18.32 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 19.55/18.32 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 19.55/18.32 ( (fun int real), (real_1 int) ) 19.55/18.32 ( (fun complex nat), (size_size complex) ) 19.55/18.32 ( (fun complex nat), complex_size ) 19.55/18.32 ( (fun int (list int)), quickc666637781d_zero ) 19.55/18.32 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 19.55/18.32 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 19.55/18.32 ( (fun (product_prod int int) rat), frct ) 19.55/18.32 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 19.55/18.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 19.55/18.32 ( (fun (fun nat rat) bool), vanishes ) 19.55/18.32 ( (fun int (fun int rat)), fract ) 19.55/18.32 ( (fun code_code_numeral int), code_int_of ) 19.55/18.32 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 19.55/18.32 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 19.55/18.32 ( (fun code_code_numeral nat), code_c271388182l_size ) 19.55/18.32 ( (fun real (fun real complex)), complex_1 ) 19.55/18.32 ( (fun real (fun real complex)), rcis ) 19.55/18.32 ( (fun int (fun nat nat)), nat_aux ) 19.55/18.32 ( (fun rat real), ratreal ) 19.55/18.32 ( (fun quickcheck_code_int int), quickcheck_int_of ) 19.55/18.32 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 19.55/18.32 ( (fun rat (product_prod int int)), quotient_of ) 19.55/18.32 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 19.55/18.32 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 19.55/18.32 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 19.55/18.32 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 19.55/18.32 ) 19.55/18.32 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (div_div int))) (let ((_let_2 (abs_abs int))) (forall ((Y $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) Y) X))) (= (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_2 X)) (hAPP int int _let_2 Y)) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 X) Y)))) )))) 19.55/18.32 ( (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) (hAPP nat int (hAPP 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)) ) 19.55/18.32 ) 19.55/18.32 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (ord_less int))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 _let_1) B_1))) (= (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less rat) (hAPP int rat (hAPP int (fun int rat) fract A_2) B_1)) (zero_zero rat))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 A_2) _let_1)))) )))) 19.55/18.32 ( (zero_zero int), (one_one int) ) 19.55/18.32 ( (one_one int), (one_one int) ) 19.55/18.32 ) 19.55/18.32 (instantiation (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_143391 $$unsorted)) (or (not (real_normed_field X_a)) (not (hBOOL (hAPP _let_1 bool (summable X_a) BOUND_VARIABLE_143391))) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_143391) (zero_zero X_a)) sequentially))) ))) 19.55/18.32 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 19.55/18.32 ) 19.55/18.32 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (or (hBOOL (hAPP _let_0 bool (finite_finite_1 X_a) A_3)) (= (zero_zero nat) (hAPP _let_0 nat (finite_card X_a) A_3))) )) 19.55/18.32 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 19.55/18.32 ) 19.55/18.32 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (minus T_1)) (minus (fun T_2 T_1))) ) 19.55/18.32 ( bool, bool ) 19.55/18.32 ( bool, (fun bool bool) ) 19.55/18.32 ( real, bool ) 19.55/18.32 ( real, real ) 19.55/18.32 ( real, nat ) 19.55/18.32 ( real, (fun int bool) ) 19.55/18.32 ( real, (fun real bool) ) 19.55/18.33 ( real, (fun real real) ) 19.55/18.33 ( real, complex ) 19.55/18.33 ( real, (fun nat real) ) 19.55/18.33 ( real, (fun bool bool) ) 19.55/18.33 ( real, (fun int (fun int bool)) ) 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(one_one int)) _let_4)))) (forall ((W $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_0) _let_4))) (and (or (not _let_6) (= (hAPP int _let_2 (hAPP int (fun int _let_2) (product_Pair int int) _let_0) (one_one int)) _let_5)) (or _let_6 (= _let_5 (hAPP _let_2 _let_2 (hAPP int (fun _let_2 _let_2) adjust _let_4) (hAPP int _let_2 _let_3 (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int _let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) _let_4))))))) )))))))) 19.55/18.33 ( pls ) 19.55/18.33 ( (hAPP int int bit1 pls) ) 19.55/18.33 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.55/18.33 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.33 ( min_1 ) 19.55/18.33 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.55/18.33 ) 19.55/18.33 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP complex real re Z_1)) (hAPP complex real (norm_norm complex) Z_1)) (hAPP complex real re (hAPP complex complex (sgn_sgn complex) Z_1))) ) 19.55/18.33 ( (one_one complex) ) 19.55/18.33 ) 19.55/18.33 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_143472 $$unsorted) (BOUND_VARIABLE_143473 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_143472) BOUND_VARIABLE_143473) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_143473) BOUND_VARIABLE_143472))) ))) 19.55/18.33 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.33 ( 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))))) ) 19.55/18.33 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.55/18.33 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.55/18.33 ( 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)))))) ) 19.55/18.33 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.34 ( 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 ) 19.55/18.34 ( 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)))) ) 19.55/18.34 ( 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))) ) 19.55/18.34 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 19.55/18.34 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.34 ( 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))), (zero_zero int) ) 19.55/18.34 ( 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))), t ) 19.55/18.34 ( 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))), skv_1 ) 19.55/18.34 ( 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))) ) 19.55/18.34 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.55/18.34 ( complex, ii, ii ) 19.55/18.34 ( 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)) ) 19.55/18.34 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 19.55/18.34 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.34 ( 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 ) 19.55/18.34 ) 19.55/18.34 (instantiation (let ((_let_0 (one_one X_a))) (let ((_let_1 (ti X_a BOUND_VARIABLE_143491))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_143491 $$unsorted)) (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_143491) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (= _let_0 _let_1) (= (hAPP X_a X_a (uminus_uminus X_a) _let_0) _let_1)))) ))) 19.55/18.34 ( bool, fFalse ) 19.55/18.34 ( bool, fTrue ) 19.55/18.34 ( real, pi ) 19.55/18.34 ( real, (hAPP int real (number_number_of real) min_1) ) 19.55/18.34 ( 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)))) ) 19.55/18.34 ( (fun nat bool), (even_odd_even nat) ) 19.55/18.34 ( (fun nat bool), prime ) 19.55/18.34 ( (fun nat nat), suc ) 19.55/18.34 ( (fun nat nat), (fact_fact nat) ) 19.55/18.34 ( (fun nat nat), (size_size nat) ) 19.55/18.34 ( (fun nat nat), fact ) 19.55/18.34 ( (fun nat nat), nat_size ) 19.55/18.34 ( int, pls ) 19.55/18.34 ( int, m ) 19.55/18.34 ( int, min_1 ) 19.55/18.34 ( int, s ) 19.55/18.34 ( int, s1 ) 19.55/18.34 ( int, t ) 19.55/18.34 ( int, skv_8 ) 19.55/18.34 ( (fun int bool), zprime ) 19.55/18.34 ( (fun int bool), nat_neg ) 19.55/18.34 ( (fun int bool), zEven ) 19.55/18.34 ( (fun int bool), nat_is_nat ) 19.55/18.34 ( (fun int bool), zOdd ) 19.55/18.34 ( (fun int bool), (even_odd_even int) ) 19.55/18.34 ( (fun int bool), twoSqu1091635170sum2sq ) 19.55/18.34 ( (fun int nat), nat_1 ) 19.55/18.34 ( (fun int nat), phi ) 19.55/18.34 ( (fun real real), sqrt ) 19.55/18.34 ( (fun real real), tan ) 19.55/18.34 ( (fun real real), cos ) 19.55/18.34 ( (fun real real), arccos ) 19.55/18.34 ( (fun real real), ln ) 19.55/18.34 ( (fun real real), sin ) 19.55/18.34 ( (fun real real), arctan ) 19.55/18.34 ( (fun real real), arcsin ) 19.55/18.34 ( complex, ii ) 19.55/18.34 ( (fun complex complex), cnj ) 19.55/18.34 ( (fun complex complex), expi ) 19.55/18.34 ( (fun nat real), (real_1 nat) ) 19.55/18.34 ( (fun nat real), cos_coeff ) 19.55/18.34 ( (fun nat real), sin_coeff ) 19.55/18.34 ( (fun int int), bit0 ) 19.55/18.34 ( (fun int int), bit1 ) 19.55/18.34 ( (fun int int), pred ) 19.55/18.34 ( (fun int int), succ ) 19.55/18.34 ( (fun int int), (fact_fact int) ) 19.55/18.34 ( (fun int int), zfact ) 19.55/18.34 ( (fun bool bool), fNot ) 19.55/18.34 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 19.55/18.34 ( (fun bool (fun bool bool)), fconj ) 19.55/18.34 ( (fun bool (fun bool bool)), fdisj ) 19.55/18.34 ( (fun bool (fun bool bool)), fimplies ) 19.55/18.34 ( (fun int (fun int bool)), sRStar ) 19.55/18.34 ( (fun int (fun int bool)), quadRes ) 19.55/18.34 ( (fun int (fun int bool)), norRRset ) 19.55/18.34 ( (fun int (fun int bool)), d22set ) 19.55/18.34 ( (fun int (fun int bool)), sr ) 19.55/18.34 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 19.55/18.34 ( (fun nat (fun nat nat)), nat_gcd ) 19.55/18.34 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 19.55/18.34 ( (fun nat (fun nat nat)), nat_lcm ) 19.55/18.34 ( (fun nat (fun real real)), root ) 19.55/18.34 ( (fun real (fun real real)), log ) 19.55/18.34 ( (fun real (fun real real)), powr ) 19.55/18.34 ( (fun nat (fun nat bool)), coprime ) 19.55/18.34 ( (fun (fun int bool) int), (the int) ) 19.55/18.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 19.55/18.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 19.55/18.34 ( (fun nat (fun nat (product_prod int int))), bezw ) 19.55/18.34 ( (fun (fun int bool) bool), nat_nat_set ) 19.55/18.34 ( (filter nat), sequentially ) 19.55/18.34 ( (fun (product_prod nat nat) bool), pred_nat ) 19.55/18.34 ( (fun (product_prod int int) bool), frac_1 ) 19.55/18.34 ( (fun real complex), cis ) 19.55/18.34 ( (fun complex real), im ) 19.55/18.34 ( (fun complex real), re ) 19.55/18.34 ( (fun complex real), arg ) 19.55/18.34 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 19.55/18.34 ( (fun int (fun int int)), int_gcd ) 19.55/18.34 ( (fun int (fun int int)), multInv ) 19.55/18.34 ( (fun int (fun int int)), legacy_zgcd ) 19.55/18.34 ( (fun int (fun int int)), z3mod ) 19.55/18.34 ( (fun int (fun int int)), inv ) 19.55/18.34 ( (fun int (fun int int)), (gcd_gcd int) ) 19.55/18.34 ( (fun int (fun int int)), standardRes ) 19.55/18.34 ( (fun int (fun int int)), legendre ) 19.55/18.34 ( (fun int (fun int int)), nat_tsub ) 19.55/18.34 ( (fun int (fun int int)), z3div ) 19.55/18.34 ( (fun int (fun int int)), int_lcm ) 19.55/18.34 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 19.55/18.34 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 19.55/18.34 ( (fun int (fun (fun int bool) bool)), rsetR ) 19.55/18.34 ( (fun int (fun (fun int bool) bool)), resSet ) 19.55/18.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 19.55/18.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 19.55/18.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 19.55/18.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 19.55/18.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 19.55/18.34 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 19.55/18.34 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 19.55/18.34 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 19.55/18.34 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 19.55/18.34 ( (fun int (fun int (product_prod int int))), negDivAlg ) 19.55/18.34 ( (fun int (fun int (product_prod int int))), divmod_int ) 19.55/18.34 ( (fun int (fun int (product_prod int int))), posDivAlg ) 19.55/18.34 ( (fun int (fun int (product_prod int int))), pdivmod ) 19.55/18.34 ( (fun int (fun int (product_prod int int))), norm_frac ) 19.55/18.34 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 19.55/18.34 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 19.55/18.34 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 19.55/18.34 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 19.55/18.34 ( (fun real nat), natfloor ) 19.55/18.34 ( (fun real nat), natceiling ) 19.55/18.34 ( (fun int quickcheck_code_int), quickcheck_of_int ) 19.55/18.34 ( (fun int (fun int (fun int bool))), wset ) 19.55/18.34 ( (fun int (fun int (fun int bool))), bnorRset ) 19.55/18.34 ( (fun int (fun int (fun int bool))), zcong ) 19.55/18.34 ( (fun int (fun int (fun int bool))), noXRRset ) 19.55/18.34 ( (fun int (fun int (fun int bool))), zcongm ) 19.55/18.34 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 19.55/18.34 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 19.55/18.34 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 19.55/18.34 ( (fun int real), (real_1 int) ) 19.55/18.34 ( (fun complex nat), (size_size complex) ) 19.55/18.34 ( (fun complex nat), complex_size ) 19.55/18.34 ( (fun int (list int)), quickc666637781d_zero ) 19.55/18.34 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 19.55/18.34 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 19.55/18.34 ( (fun (product_prod int int) rat), frct ) 19.55/18.34 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 19.55/18.34 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 19.55/18.34 ( (fun (fun nat rat) bool), vanishes ) 19.55/18.34 ( (fun int (fun int rat)), fract ) 19.55/18.34 ( (fun code_code_numeral int), code_int_of ) 19.55/18.34 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 19.55/18.34 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 19.55/18.34 ( (fun code_code_numeral nat), code_c271388182l_size ) 19.55/18.34 ( (fun real (fun real complex)), complex_1 ) 19.55/18.34 ( (fun real (fun real complex)), rcis ) 19.55/18.34 ( (fun int (fun nat nat)), nat_aux ) 19.55/18.34 ( (fun rat real), ratreal ) 19.55/18.34 ( (fun quickcheck_code_int int), quickcheck_int_of ) 19.55/18.34 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 19.55/18.34 ( (fun rat (product_prod int int)), quotient_of ) 19.55/18.34 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 19.55/18.34 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 19.55/18.34 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 19.55/18.34 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 19.55/18.34 ) 19.55/18.34 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_1) zEven))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Y_1) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) X_1) Y_1)) zEven))) )))) 19.55/18.34 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.34 ) 19.55/18.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143694 $$unsorted)) (or (not (number_ring X_a)) (not (field_inverse_zero X_a)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_143694) (hAPP int X_a (number_number_of X_a) pls)))) ) 19.55/18.34 ( real, (one_one real) ) 19.55/18.34 ( real, pi ) 19.55/18.34 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.55/18.34 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 19.55/18.34 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.34 ) 19.55/18.34 (instantiation (let ((_let_0 (abs_abs X_a))) (forall ((X_a $$unsorted)) (or (not (abs_if X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 19.55/18.34 ( bool ) 19.55/18.34 ( real ) 19.55/18.34 ( nat ) 19.55/18.34 ( (fun nat bool) ) 19.55/18.34 ( int ) 19.55/18.34 ( (fun int bool) ) 19.55/18.34 ( (fun real bool) ) 19.55/18.34 ( (fun real real) ) 19.55/18.34 ( complex ) 19.55/18.34 ( (fun nat real) ) 19.55/18.34 ( (fun int int) ) 19.55/18.34 ( rat ) 19.55/18.34 ( (fun int (fun int bool)) ) 19.55/18.34 ( (product_prod int int) ) 19.55/18.34 ( (fun (product_prod int int) bool) ) 19.55/18.34 ( code_code_numeral ) 19.55/18.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 19.55/18.34 ( (fun (product_prod int int) int) ) 19.55/18.34 ( (fun int (fun int (fun int bool))) ) 19.55/18.34 ( (fun int real) ) 19.55/18.34 ) 19.55/18.34 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_143716 $$unsorted)) (or (not (group_add X_a)) (= (= _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_143716)) (= _let_0 (ti X_a BOUND_VARIABLE_143716)))) )) 19.55/18.34 ( bool, fFalse ) 19.55/18.34 ( bool, fTrue ) 19.55/18.34 ( real, (one_one real) ) 19.55/18.34 ( real, pi ) 19.55/18.34 ( 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)))) ) 19.55/18.34 ( 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) ) 19.55/18.34 ( (fun nat bool), (even_odd_even nat) ) 19.55/18.34 ( (fun nat bool), prime ) 19.55/18.34 ( (fun nat nat), suc ) 19.55/18.34 ( (fun nat nat), (fact_fact nat) ) 19.55/18.34 ( (fun nat nat), (size_size nat) ) 19.55/18.34 ( (fun nat nat), fact ) 19.55/18.34 ( (fun nat nat), nat_size ) 19.55/18.34 ( int, pls ) 19.55/18.34 ( int, m ) 19.55/18.34 ( int, (one_one int) ) 19.55/18.34 ( int, min_1 ) 19.55/18.34 ( int, s ) 19.55/18.34 ( int, s1 ) 19.55/18.34 ( int, t ) 19.55/18.34 ( (fun int bool), zprime ) 19.55/18.34 ( (fun int bool), nat_neg ) 19.55/18.34 ( (fun int bool), zEven ) 19.55/18.34 ( (fun int bool), nat_is_nat ) 19.55/18.34 ( (fun int bool), zOdd ) 19.55/18.34 ( (fun int bool), (even_odd_even int) ) 19.55/18.34 ( (fun int bool), twoSqu1091635170sum2sq ) 19.55/18.34 ( (fun int nat), nat_1 ) 19.55/18.34 ( (fun int nat), phi ) 19.55/18.34 ( (fun real real), sqrt ) 19.55/18.34 ( (fun real real), tan ) 19.55/18.34 ( (fun real real), cos ) 19.55/18.34 ( (fun real real), arccos ) 19.55/18.34 ( (fun real real), ln ) 19.55/18.34 ( (fun real real), sin ) 19.55/18.34 ( (fun real real), arctan ) 19.55/18.34 ( (fun real real), arcsin ) 19.55/18.34 ( complex, ii ) 19.55/18.34 ( complex, (one_one complex) ) 19.55/18.34 ( (fun complex complex), cnj ) 19.55/18.34 ( (fun complex complex), expi ) 19.55/18.34 ( (fun nat real), (real_1 nat) ) 19.55/18.34 ( (fun nat real), cos_coeff ) 19.55/18.34 ( (fun nat real), sin_coeff ) 19.55/18.34 ( (fun int int), bit0 ) 19.55/18.34 ( (fun int int), bit1 ) 19.55/18.34 ( (fun int int), pred ) 19.55/18.34 ( (fun int int), succ ) 19.55/18.34 ( (fun int int), (fact_fact int) ) 19.55/18.34 ( (fun int int), zfact ) 19.55/18.34 ( (fun bool bool), fNot ) 19.55/18.34 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 19.55/18.34 ( (fun bool (fun bool bool)), fconj ) 19.55/18.34 ( (fun bool (fun bool bool)), fdisj ) 19.55/18.34 ( (fun bool (fun bool bool)), fimplies ) 19.55/18.34 ( (fun int (fun int bool)), sRStar ) 19.55/18.34 ( (fun int (fun int bool)), quadRes ) 19.55/18.34 ( (fun int (fun int bool)), norRRset ) 19.55/18.34 ( (fun int (fun int bool)), d22set ) 19.55/18.34 ( (fun int (fun int bool)), sr ) 19.55/18.34 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 19.55/18.34 ( (fun nat (fun nat nat)), nat_gcd ) 19.55/18.34 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 19.55/18.34 ( (fun nat (fun nat nat)), nat_lcm ) 19.55/18.34 ( (fun nat (fun real real)), root ) 19.55/18.34 ( (fun real (fun real real)), log ) 19.55/18.34 ( (fun real (fun real real)), powr ) 19.55/18.34 ( (fun nat (fun nat bool)), coprime ) 19.55/18.34 ( (fun (fun int bool) int), (the int) ) 19.55/18.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 19.55/18.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 19.55/18.34 ( (fun nat (fun nat (product_prod int int))), bezw ) 19.55/18.34 ( (fun (fun int bool) bool), nat_nat_set ) 19.55/18.34 ( (filter nat), sequentially ) 19.55/18.34 ( (fun (product_prod nat nat) bool), pred_nat ) 19.55/18.34 ( (fun (product_prod int int) bool), frac_1 ) 19.55/18.34 ( (fun real complex), cis ) 19.55/18.34 ( (fun complex real), im ) 19.55/18.34 ( (fun complex real), re ) 19.55/18.34 ( (fun complex real), arg ) 19.55/18.34 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 19.55/18.34 ( (fun int (fun int int)), int_gcd ) 19.55/18.34 ( (fun int (fun int int)), multInv ) 19.55/18.34 ( (fun int (fun int int)), legacy_zgcd ) 19.55/18.34 ( (fun int (fun int int)), z3mod ) 19.55/18.34 ( (fun int (fun int int)), inv ) 19.55/18.34 ( (fun int (fun int int)), (gcd_gcd int) ) 19.55/18.34 ( (fun int (fun int int)), standardRes ) 19.55/18.34 ( (fun int (fun int int)), legendre ) 19.55/18.34 ( (fun int (fun int int)), nat_tsub ) 19.55/18.34 ( (fun int (fun int int)), z3div ) 19.55/18.34 ( (fun int (fun int int)), int_lcm ) 19.55/18.34 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 19.55/18.34 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 19.55/18.34 ( (fun int (fun (fun int bool) bool)), rsetR ) 19.55/18.34 ( (fun int (fun (fun int bool) bool)), resSet ) 19.55/18.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 19.55/18.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 19.55/18.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 19.55/18.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 19.55/18.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 19.55/18.35 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 19.55/18.35 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 19.55/18.35 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 19.55/18.35 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 19.55/18.35 ( (fun int (fun int (product_prod int int))), negDivAlg ) 19.55/18.35 ( (fun int (fun int (product_prod int int))), divmod_int ) 19.55/18.35 ( (fun int (fun int (product_prod int int))), posDivAlg ) 19.55/18.35 ( (fun int (fun int (product_prod int int))), pdivmod ) 19.55/18.35 ( (fun int (fun int (product_prod int int))), norm_frac ) 19.55/18.35 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 19.55/18.35 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 19.55/18.35 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 19.55/18.35 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 19.55/18.35 ( (fun real nat), natfloor ) 19.55/18.35 ( (fun real nat), natceiling ) 19.55/18.35 ( (fun int quickcheck_code_int), quickcheck_of_int ) 19.55/18.35 ( (fun int (fun int (fun int bool))), wset ) 19.55/18.35 ( (fun int (fun int (fun int bool))), bnorRset ) 19.55/18.35 ( (fun int (fun int (fun int bool))), zcong ) 19.55/18.35 ( (fun int (fun int (fun int bool))), noXRRset ) 19.55/18.35 ( (fun int (fun int (fun int bool))), zcongm ) 19.55/18.35 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 19.55/18.35 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 19.55/18.35 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 19.55/18.35 ( (fun int real), (real_1 int) ) 19.55/18.35 ( (fun complex nat), (size_size complex) ) 19.55/18.35 ( (fun complex nat), complex_size ) 19.55/18.35 ( (fun int (list int)), quickc666637781d_zero ) 19.55/18.35 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 19.55/18.35 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 19.55/18.35 ( (fun (product_prod int int) rat), frct ) 19.55/18.35 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 19.55/18.35 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 19.55/18.35 ( (fun (fun nat rat) bool), vanishes ) 19.55/18.35 ( (fun int (fun int rat)), fract ) 19.55/18.35 ( (fun code_code_numeral int), code_int_of ) 19.55/18.35 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 19.55/18.35 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 19.55/18.35 ( (fun code_code_numeral nat), code_c271388182l_size ) 19.55/18.35 ( (fun real (fun real complex)), complex_1 ) 19.55/18.35 ( (fun real (fun real complex)), rcis ) 19.55/18.35 ( (fun int (fun nat nat)), nat_aux ) 19.55/18.35 ( (fun rat real), ratreal ) 19.55/18.35 ( (fun quickcheck_code_int int), quickcheck_int_of ) 19.55/18.35 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 19.55/18.35 ( (fun rat (product_prod int int)), quotient_of ) 19.55/18.35 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 19.55/18.35 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 19.55/18.35 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 19.55/18.35 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 19.55/18.35 ) 19.55/18.35 (instantiation (let ((_let_0 (zero_zero real))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (= _let_0 (hAPP real real (hAPP nat (fun real real) root N_1) X_1)) (= _let_0 X_1))) )) 19.55/18.35 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.35 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.35 ( (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))) ) 19.55/18.35 ( (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))) ) 19.55/18.35 ) 19.55/18.35 (instantiation (let ((_let_0 (product_apsnd X_c X_b X_a))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted)) (= _let_0 (ti (fun (fun X_c X_b) (fun (product_prod X_a X_c) (product_prod X_a X_b))) _let_0)) )) 19.55/18.35 ( int, int, int ) 19.55/18.35 ) 19.55/18.35 (instantiation (let ((_let_0 (one_one X_a))) (forall ((X_a $$unsorted)) (or (not (one X_a)) (= _let_0 (ti X_a _let_0))) )) 19.55/18.35 ( real ) 19.55/18.35 ( nat ) 19.55/18.35 ( int ) 19.55/18.35 ( complex ) 19.55/18.35 ( rat ) 19.55/18.35 ( quickcheck_code_int ) 19.55/18.35 ( code_code_numeral ) 19.55/18.35 ) 19.55/18.35 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_143842 $$unsorted)) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_143842)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_143842)) BOUND_VARIABLE_143842)))) ))) 19.55/18.35 ( real, (one_one real) ) 19.55/18.35 ( real, pi ) 19.55/18.35 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.35 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 19.55/18.35 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.35 ( real, skv_6 ) 19.55/18.35 ( real, skv_11 ) 19.55/18.35 ( real, skv_12 ) 19.55/18.35 ( real, skv_14 ) 19.55/18.35 ( int, pls ) 19.55/18.35 ( int, (one_one int) ) 19.55/18.35 ( int, min_1 ) 19.55/18.35 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.35 ( int, s ) 19.55/18.35 ( int, (hAPP int int (number_number_of int) pls) ) 19.55/18.35 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.55/18.35 ( int, skv_3 ) 19.55/18.35 ( int, skv_9 ) 19.55/18.35 ( complex, ii ) 19.55/18.35 ( complex, (one_one complex) ) 19.55/18.35 ) 19.55/18.35 (instantiation (let ((_let_0 (iszero X_a))) (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (= _let_0 (ti (fun X_a bool) _let_0))) )) 19.55/18.35 ( bool ) 19.55/18.35 ( real ) 19.55/18.35 ( nat ) 19.55/18.35 ( (fun nat bool) ) 19.55/18.35 ( int ) 19.55/18.35 ( (fun int bool) ) 19.55/18.35 ( complex ) 19.55/18.35 ( rat ) 19.55/18.35 ( quickcheck_code_int ) 19.55/18.35 ( (product_prod real real) ) 19.55/18.35 ( (product_prod int int) ) 19.55/18.35 ( (filter real) ) 19.55/18.35 ( (filter nat) ) 19.55/18.35 ( (product_prod nat nat) ) 19.55/18.35 ( code_code_numeral ) 19.55/18.35 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 19.55/18.35 ( (fun nat rat) ) 19.55/18.35 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 19.55/18.35 ) 19.55/18.35 (instantiation (let ((_let_0 (fun nat nat))) (forall ((X_2 $$unsorted)) (or (hBOOL (hAPP nat bool (even_odd_even nat) X_2)) (= (hAPP nat real sin_coeff X_2) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) (hAPP nat nat (hAPP nat _let_0 (div_div nat) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) X_2) (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_2))))) )) 19.55/18.35 ( (zero_zero nat) ) 19.55/18.35 ( (hAPP nat nat suc (zero_zero nat)) ) 19.55/18.35 ( (one_one nat) ) 19.55/18.35 ) 19.55/18.35 (instantiation (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) X_2))) (= (zero_zero real) (hAPP nat real sin_coeff X_2))) ) 19.55/18.35 ( (zero_zero nat) ) 19.55/18.35 ( (one_one nat) ) 19.55/18.35 ) 19.55/18.35 (instantiation (forall ((N $$unsorted)) (= (hAPP quickcheck_code_int int quickcheck_int_of (hAPP int quickcheck_code_int quickcheck_of_int N)) (ti int N)) ) 19.55/18.35 ( (zero_zero int) ) 19.55/18.35 ( pls ) 19.55/18.35 ( (hAPP int int bit1 pls) ) 19.55/18.35 ( m ) 19.55/18.35 ( (one_one int) ) 19.55/18.35 ( min_1 ) 19.55/18.35 ( s ) 19.55/18.35 ( s1 ) 19.55/18.35 ( t ) 19.55/18.35 ) 19.55/18.35 (instantiation (let ((_let_0 (strict_mono nat X_a))) (forall ((X_a $$unsorted)) (or (not (order X_a)) (= _let_0 (ti (fun (fun nat (fun nat bool)) (fun (fun nat X_a) bool)) _let_0))) )) 19.55/18.35 ( bool ) 19.55/18.35 ( real ) 19.55/18.35 ( nat ) 19.55/18.35 ( (fun nat bool) ) 19.55/18.35 ( (fun nat nat) ) 19.55/18.35 ( int ) 19.55/18.35 ( (fun real real) ) 19.55/18.35 ( complex ) 19.55/18.35 ( (fun int int) ) 19.55/18.35 ( rat ) 19.55/18.35 ( (fun bool bool) ) 19.55/18.35 ( quickcheck_code_int ) 19.55/18.35 ( (fun nat (fun nat bool)) ) 19.55/18.35 ( (product_prod real real) ) 19.55/18.35 ( (product_prod int int) ) 19.55/18.35 ( (fun nat (product_prod int int)) ) 19.55/18.35 ( (product_prod nat nat) ) 19.55/18.35 ( (fun (product_prod nat nat) bool) ) 19.55/18.35 ( (fun nat (fun (product_prod nat nat) bool)) ) 19.55/18.35 ( (fun nat (product_prod nat nat)) ) 19.55/18.35 ( code_code_numeral ) 19.55/18.35 ) 19.55/18.35 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (forall ((N $$unsorted)) (= (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))) ))) 19.55/18.35 ( (zero_zero nat) ) 19.55/18.35 ( (one_one nat) ) 19.55/18.35 ) 19.55/18.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143888 $$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_143888) (hAPP int X_a (ring_1_of_int X_a) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_143888))))) ) 19.55/18.35 ( real, (zero_zero real) ) 19.55/18.35 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.35 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.35 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.35 ( real, skv_14 ) 19.55/18.35 ( int, (zero_zero int) ) 19.55/18.35 ( int, (one_one int) ) 19.55/18.35 ( int, min_1 ) 19.55/18.35 ) 19.55/18.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143922 $$unsorted) (BOUND_VARIABLE_143923 $$unsorted)) (or (not (linorder X_a)) (= (= (ti X_a BOUND_VARIABLE_143922) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_min X_a) BOUND_VARIABLE_143922) BOUND_VARIABLE_143923)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_143922) BOUND_VARIABLE_143923)))) ) 19.55/18.35 ( real, (zero_zero real), pi ) 19.55/18.35 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.35 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.35 ( real, (zero_zero real), skv_6 ) 19.55/18.35 ( real, (zero_zero real), skv_11 ) 19.55/18.35 ( real, (zero_zero real), skv_12 ) 19.55/18.35 ( real, (zero_zero real), skv_14 ) 19.55/18.35 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.55/18.35 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.35 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.55/18.35 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.35 ( int, (zero_zero int), (one_one int) ) 19.55/18.35 ( int, (zero_zero int), min_1 ) 19.55/18.35 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.35 ( int, (zero_zero int), s ) 19.55/18.35 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 19.55/18.35 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.55/18.35 ( int, (zero_zero int), skv_3 ) 19.55/18.35 ( int, (zero_zero int), skv_9 ) 19.55/18.35 ( int, (one_one int), t ) 19.55/18.35 ( int, min_1, pls ) 19.55/18.35 ( int, min_1, min_1 ) 19.55/18.35 ) 19.55/18.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143947 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_143947)) (= (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_143947) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) (one_one X_a)) BOUND_VARIABLE_143947))) ) 19.55/18.35 ( bool, fFalse ) 19.55/18.35 ( bool, fTrue ) 19.55/18.35 ( real, (zero_zero real) ) 19.55/18.35 ( real, pi ) 19.55/18.35 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.35 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 19.55/18.35 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.35 ( 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))))))))) ) 19.55/18.35 ( (fun nat bool), (even_odd_even nat) ) 19.55/18.35 ( (fun nat bool), prime ) 19.55/18.35 ( (fun nat nat), suc ) 19.55/18.35 ( (fun nat nat), (fact_fact nat) ) 19.55/18.35 ( (fun nat nat), (size_size nat) ) 19.55/18.35 ( (fun nat nat), fact ) 19.55/18.35 ( (fun nat nat), nat_size ) 19.55/18.35 ( int, pls ) 19.55/18.35 ( int, m ) 19.55/18.35 ( int, min_1 ) 19.55/18.35 ( int, s ) 19.55/18.35 ( int, s1 ) 19.55/18.35 ( int, t ) 19.55/18.35 ( (fun int bool), zprime ) 19.55/18.35 ( (fun int bool), nat_neg ) 19.55/18.35 ( (fun int bool), zEven ) 19.55/18.35 ( (fun int bool), nat_is_nat ) 19.55/18.35 ( (fun int bool), zOdd ) 19.55/18.35 ( (fun int bool), (even_odd_even int) ) 19.55/18.35 ( (fun int bool), twoSqu1091635170sum2sq ) 19.55/18.35 ( (fun int nat), nat_1 ) 19.55/18.35 ( (fun int nat), phi ) 19.55/18.35 ( (fun real real), sqrt ) 19.55/18.35 ( (fun real real), tan ) 19.55/18.35 ( (fun real real), cos ) 19.55/18.35 ( (fun real real), arccos ) 19.55/18.35 ( (fun real real), ln ) 19.55/18.35 ( (fun real real), sin ) 19.55/18.35 ( (fun real real), arctan ) 19.55/18.35 ( (fun real real), arcsin ) 19.55/18.35 ( complex, ii ) 19.55/18.35 ( (fun complex complex), cnj ) 19.55/18.35 ( (fun complex complex), expi ) 19.55/18.35 ( (fun nat real), (real_1 nat) ) 19.55/18.35 ( (fun nat real), cos_coeff ) 19.55/18.35 ( (fun nat real), sin_coeff ) 19.55/18.35 ( (fun int int), bit0 ) 19.55/18.35 ( (fun int int), bit1 ) 19.55/18.35 ( (fun int int), pred ) 19.55/18.35 ( (fun int int), succ ) 19.55/18.35 ( (fun int int), (fact_fact int) ) 19.55/18.35 ( (fun int int), zfact ) 19.55/18.35 ( (fun bool bool), fNot ) 19.55/18.35 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 19.55/18.35 ( (fun bool (fun bool bool)), fconj ) 19.55/18.35 ( (fun bool (fun bool bool)), fdisj ) 19.55/18.35 ( (fun bool (fun bool bool)), fimplies ) 19.55/18.35 ( (fun int (fun int bool)), sRStar ) 19.55/18.35 ( (fun int (fun int bool)), quadRes ) 19.55/18.35 ( (fun int (fun int bool)), norRRset ) 19.55/18.35 ( (fun int (fun int bool)), d22set ) 19.55/18.35 ( (fun int (fun int bool)), sr ) 19.55/18.35 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 19.55/18.35 ( (fun nat (fun nat nat)), nat_gcd ) 19.55/18.35 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 19.55/18.35 ( (fun nat (fun nat nat)), nat_lcm ) 19.55/18.35 ( (fun nat (fun real real)), root ) 19.55/18.35 ( (fun real (fun real real)), log ) 19.55/18.35 ( (fun real (fun real real)), powr ) 19.55/18.35 ( (fun nat (fun nat bool)), coprime ) 19.55/18.35 ( (fun (fun int bool) int), (the int) ) 19.55/18.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 19.55/18.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 19.55/18.35 ( (fun nat (fun nat (product_prod int int))), bezw ) 19.55/18.35 ( (fun (fun int bool) bool), nat_nat_set ) 19.55/18.35 ( (filter nat), sequentially ) 19.55/18.35 ( (fun (product_prod nat nat) bool), pred_nat ) 19.55/18.35 ( (fun (product_prod int int) bool), frac_1 ) 19.55/18.35 ( (fun real complex), cis ) 19.55/18.35 ( (fun complex real), im ) 19.55/18.35 ( (fun complex real), re ) 19.55/18.35 ( (fun complex real), arg ) 19.55/18.35 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 19.55/18.35 ( (fun int (fun int int)), int_gcd ) 19.55/18.35 ( (fun int (fun int int)), multInv ) 19.55/18.35 ( (fun int (fun int int)), legacy_zgcd ) 19.55/18.35 ( (fun int (fun int int)), z3mod ) 19.55/18.35 ( (fun int (fun int int)), inv ) 19.55/18.35 ( (fun int (fun int int)), (gcd_gcd int) ) 19.55/18.35 ( (fun int (fun int int)), standardRes ) 19.55/18.35 ( (fun int (fun int int)), legendre ) 19.55/18.35 ( (fun int (fun int int)), nat_tsub ) 19.55/18.35 ( (fun int (fun int int)), z3div ) 19.55/18.35 ( (fun int (fun int int)), int_lcm ) 19.55/18.35 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 19.55/18.35 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 19.55/18.35 ( (fun int (fun (fun int bool) bool)), rsetR ) 19.55/18.35 ( (fun int (fun (fun int bool) bool)), resSet ) 19.55/18.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 19.55/18.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 19.55/18.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 19.55/18.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 19.55/18.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 19.55/18.35 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 19.55/18.35 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 19.55/18.35 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 19.55/18.35 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 19.55/18.35 ( (fun int (fun int (product_prod int int))), negDivAlg ) 19.55/18.35 ( (fun int (fun int (product_prod int int))), divmod_int ) 19.55/18.35 ( (fun int (fun int (product_prod int int))), posDivAlg ) 19.55/18.35 ( (fun int (fun int (product_prod int int))), pdivmod ) 19.55/18.35 ( (fun int (fun int (product_prod int int))), norm_frac ) 19.55/18.35 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 19.55/18.35 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 19.55/18.35 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 19.55/18.35 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 19.55/18.35 ( (fun real nat), natfloor ) 19.55/18.35 ( (fun real nat), natceiling ) 19.55/18.35 ( (fun int quickcheck_code_int), quickcheck_of_int ) 19.55/18.35 ( (fun int (fun int (fun int bool))), wset ) 19.55/18.35 ( (fun int (fun int (fun int bool))), bnorRset ) 19.55/18.35 ( (fun int (fun int (fun int bool))), zcong ) 19.55/18.35 ( (fun int (fun int (fun int bool))), noXRRset ) 19.55/18.35 ( (fun int (fun int (fun int bool))), zcongm ) 19.55/18.35 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 19.55/18.35 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 19.55/18.35 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 19.55/18.35 ( (fun int real), (real_1 int) ) 19.55/18.35 ( (fun complex nat), (size_size complex) ) 19.55/18.35 ( (fun complex nat), complex_size ) 19.55/18.35 ( (fun int (list int)), quickc666637781d_zero ) 19.55/18.35 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 19.55/18.35 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 19.55/18.35 ( (fun (product_prod int int) rat), frct ) 19.55/18.35 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 19.55/18.36 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 19.55/18.36 ( (fun (fun nat rat) bool), vanishes ) 19.55/18.36 ( (fun int (fun int rat)), fract ) 19.55/18.36 ( (fun code_code_numeral int), code_int_of ) 19.55/18.36 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 19.55/18.36 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 19.55/18.36 ( (fun code_code_numeral nat), code_c271388182l_size ) 19.55/18.36 ( (fun real (fun real complex)), complex_1 ) 19.55/18.36 ( (fun real (fun real complex)), rcis ) 19.55/18.36 ( (fun int (fun nat nat)), nat_aux ) 19.55/18.36 ( (fun rat real), ratreal ) 19.55/18.36 ( (fun quickcheck_code_int int), quickcheck_int_of ) 19.55/18.36 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 19.55/18.36 ( (fun rat (product_prod int int)), quotient_of ) 19.55/18.36 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 19.55/18.36 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 19.55/18.36 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 19.55/18.36 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 19.55/18.36 ) 19.55/18.36 (instantiation (let ((_let_0 (uminus_uminus int))) (forall ((Z_1 $$unsorted)) (= (hAPP int int _let_0 (hAPP int int _let_0 Z_1)) (ti int Z_1)) )) 19.55/18.36 ( pls ) 19.55/18.36 ( m ) 19.55/18.36 ( (one_one int) ) 19.55/18.36 ( min_1 ) 19.55/18.36 ( s ) 19.55/18.36 ( s1 ) 19.55/18.36 ( t ) 19.55/18.36 ) 19.55/18.36 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_143974))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_143974 $$unsorted) (BOUND_VARIABLE_143975 $$unsorted)) (or (not (linordered_field X_a)) (not (forall ((E $$unsorted)) (or (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) E))) (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_143975) E)))) )) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_143975))) )) 19.55/18.36 ( real, (zero_zero real), pi ) 19.55/18.36 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.36 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.36 ( real, (zero_zero real), skv_6 ) 19.55/18.36 ( real, (zero_zero real), skv_11 ) 19.55/18.36 ( real, (zero_zero real), skv_12 ) 19.55/18.36 ( real, (zero_zero real), skv_14 ) 19.55/18.36 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.55/18.36 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.36 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.55/18.36 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.36 ( int, (zero_zero int), (one_one int) ) 19.55/18.36 ( int, (zero_zero int), min_1 ) 19.55/18.36 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.36 ( int, (zero_zero int), s ) 19.55/18.36 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 19.55/18.36 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.55/18.36 ( int, (zero_zero int), skv_3 ) 19.55/18.36 ( int, (zero_zero int), skv_9 ) 19.55/18.36 ( int, (one_one int), t ) 19.55/18.36 ( int, min_1, pls ) 19.55/18.36 ( int, min_1, min_1 ) 19.55/18.36 ) 19.55/18.36 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((W_1 $$unsorted) (Z $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) Z))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP int nat nat_1 W_1)) (hAPP int nat nat_1 Z))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 W_1) Z)))) ))) 19.55/18.36 ( (zero_zero int), (zero_zero int) ) 19.55/18.36 ( (zero_zero int), (one_one int) ) 19.55/18.36 ( (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))) ) 19.55/18.36 ( (zero_zero int), min_1 ) 19.55/18.36 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.36 ( min_1, (zero_zero int) ) 19.55/18.36 ( min_1, min_1 ) 19.55/18.36 ( 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))) ) 19.55/18.36 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 19.55/18.36 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int 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real)) ) 19.55/18.37 ( (fun int real), (fun int (fun real real)) ) 19.55/18.37 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 19.55/18.37 ( (fun real (fun int bool)), (fun real bool) ) 19.55/18.37 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 19.55/18.37 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 19.55/18.37 ( (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)))) ) 19.55/18.37 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 19.55/18.37 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 19.55/18.37 ( (fun int (fun int real)), (fun int (fun int bool)) ) 19.55/18.37 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 19.55/18.37 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 19.55/18.37 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 19.55/18.37 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 19.55/18.37 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 19.55/18.37 ( (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))) ) 19.55/18.37 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 19.55/18.37 ( (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))) ) 19.55/18.37 ( (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))) ) 19.55/18.37 ( (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)))) ) 19.55/18.37 ( (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)))) ) 19.55/18.37 ( (fun int (fun nat bool)), (fun int bool) ) 19.55/18.37 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 19.55/18.37 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 19.55/18.37 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 19.55/18.37 ( (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))) ) 19.55/18.37 ( (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)))) ) 19.55/18.37 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 19.55/18.37 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 19.55/18.37 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 19.55/18.37 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 19.55/18.37 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 19.55/18.37 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 19.55/18.37 ) 19.55/18.37 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_144215 $$unsorted) (BOUND_VARIABLE_144216 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_144216)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_144215) BOUND_VARIABLE_144216) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_144215)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_144216)))) )))) 19.55/18.37 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.37 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 19.55/18.37 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.37 ( 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))))))))) ) 19.55/18.37 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.37 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.37 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 19.55/18.37 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.55/18.37 ( 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))) ) 19.55/18.37 ( 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))) ) 19.55/18.37 ( 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))) ) 19.55/18.37 ) 19.55/18.37 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (forall ((X $$unsorted)) (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))) )))) 19.55/18.37 ( (zero_zero real) ) 19.55/18.37 ( pi ) 19.55/18.37 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 19.55/18.37 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 19.55/18.37 ( (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)))) ) 19.55/18.37 ) 19.55/18.37 (instantiation (let ((_let_0 (archim2085082626_floor X_a))) (forall ((X_a $$unsorted)) (or (not (archim1727834104eiling X_a)) (= _let_0 (ti (fun X_a int) _let_0))) )) 19.55/18.37 ( real ) 19.55/18.37 ( nat ) 19.55/18.37 ( int ) 19.55/18.37 ( (fun int bool) ) 19.55/18.37 ( rat ) 19.55/18.37 ( quickcheck_code_int ) 19.55/18.37 ( (product_prod int int) ) 19.55/18.37 ( code_code_numeral ) 19.55/18.37 ) 19.55/18.37 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((Z_1 $$unsorted) (Z_4 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) Z_4))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Z_4) Z_1))) (= (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat nat_1 Z_1)) (hAPP int nat nat_1 Z_4)) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) Z_1) Z_4)))) ))) 19.55/18.37 ( pls, min_1 ) 19.55/18.37 ( (one_one int), (zero_zero int) ) 19.55/18.37 ( min_1, (zero_zero int) ) 19.55/18.37 ( min_1, min_1 ) 19.55/18.37 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 19.55/18.37 ( s, (zero_zero int) ) 19.55/18.37 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 19.55/18.37 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 19.55/18.37 ( t, (one_one int) ) 19.55/18.37 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 19.55/18.37 ( skv_3, (zero_zero int) ) 19.55/18.37 ( skv_9, (zero_zero int) ) 19.55/18.37 ) 19.55/18.37 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_144364 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_144364))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_144364)))) )) 19.55/18.37 ( real, (zero_zero real) ) 19.55/18.37 ( rat, (zero_zero rat) ) 19.55/18.37 ) 19.55/18.37 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (plus_plus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_144423 $$unsorted) (BOUND_VARIABLE_144424 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_144423) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_144424) BOUND_VARIABLE_144423)) (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_144424) (one_one X_a))) BOUND_VARIABLE_144423))) )))) 19.55/18.37 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.37 ( 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))))) ) 19.55/18.37 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.37 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int 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)))) ) 19.55/18.37 ( 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) ) 19.55/18.37 ( 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))) ) 19.55/18.37 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.55/18.37 ( 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) ) 19.55/18.37 ( 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))) ) 19.55/18.37 ( int, skv_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 bit0 (hAPP int int bit1 pls))))) m) ) 19.55/18.37 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.55/18.37 ( complex, ii, ii ) 19.55/18.37 ( 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)) ) 19.55/18.37 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.37 ) 19.55/18.37 (instantiation (let ((_let_0 (archim2085082626_floor X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_144444 $$unsorted) (BOUND_VARIABLE_144445 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_144444) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_144445))) (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP X_a int _let_0 BOUND_VARIABLE_144444)) (hAPP int int (number_number_of int) BOUND_VARIABLE_144445)))) )) 19.55/18.37 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), min_1 ) 19.55/18.37 ( code_code_numeral, (zero_zero code_code_numeral), (hAPP int int bit1 pls) ) 19.55/18.37 ) 19.55/18.37 (instantiation (let ((_let_0 (fun nat bool))) (forall ((N_4 $$unsorted)) (= (not (forall ((M_2 $$unsorted)) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP nat (fun _let_0 bool) (member nat) X_2) N_4))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) X_2) M_2))) )) )) (hBOOL (hAPP _let_0 bool (finite_finite_1 nat) N_4))) )) 19.55/18.37 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 19.55/18.37 ) 19.55/18.37 (instantiation (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_144485))) (let ((_let_2 (hAPP nat X_a _let_1 (hAPP int nat _let_0 BOUND_VARIABLE_144486)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_144485 $$unsorted) (BOUND_VARIABLE_144486 $$unsorted)) (or (not (monoid_mult X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) _let_2) _let_2) (hAPP nat X_a _let_1 (hAPP int nat _let_0 (hAPP int int bit0 BOUND_VARIABLE_144486))))) )))) 19.55/18.38 ( int, s, (hAPP int int bit1 pls) ) 19.55/18.38 ( int, s1, (hAPP int int bit1 pls) ) 19.55/18.38 ( int, skv_8, (hAPP int int bit1 pls) ) 19.55/18.38 ( complex, ii, (hAPP int int bit1 pls) ) 19.55/18.38 ) 19.55/18.38 (instantiation (forall ((P_1 $$unsorted) (I $$unsorted)) (= (hBOOL (hAPP nat bool P_1 (hAPP int nat nat_1 I))) (and (forall ((N_2 $$unsorted)) (or (not (= (hAPP nat int (semiring_1_of_nat int) N_2) (ti int I))) (hBOOL (hAPP nat bool P_1 N_2))) ) (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)))))) ) 19.55/18.38 ( (even_odd_even nat), (zero_zero int) ) 19.55/18.38 ( (even_odd_even nat), (one_one int) ) 19.55/18.38 ( (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))) ) 19.55/18.38 ( prime, (zero_zero int) ) 19.55/18.38 ( prime, (one_one int) ) 19.55/18.38 ( prime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.38 ) 19.55/18.38 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_1) zEven)) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP nat int (hAPP int (fun nat int) (power_power int) X_1) N_1)) zEven)))) )))) 19.55/18.38 ( s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.38 ( s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.38 ( skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.55/18.38 ) 19.55/18.38 (instantiation (let ((_let_0 (times_times X_a))) (forall ((X_a $$unsorted)) (or (not (power X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0))) )) 19.55/18.38 ( bool ) 19.55/18.38 ( real ) 19.55/18.38 ( nat ) 19.55/18.38 ( (fun nat bool) ) 19.55/18.38 ( int ) 19.55/18.38 ( (fun int bool) ) 19.55/18.38 ( (fun real bool) ) 19.55/18.38 ( (fun real real) ) 19.55/18.38 ( complex ) 19.55/18.38 ( (fun nat real) ) 19.55/18.38 ( (fun int int) ) 19.55/18.38 ( rat ) 19.55/18.38 ( (fun int (fun int bool)) ) 19.55/18.38 ( quickcheck_code_int ) 19.55/18.38 ( (product_prod int int) ) 19.55/18.38 ( (fun (product_prod int int) bool) ) 19.55/18.38 ( code_code_numeral ) 19.55/18.38 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 19.55/18.38 ( (fun (product_prod int int) int) ) 19.55/18.38 ( (fun int (fun int (fun int bool))) ) 19.55/18.38 ( (fun int real) ) 19.55/18.38 ) 19.55/18.38 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_144646 $$unsorted) (BOUND_VARIABLE_144647 $$unsorted)) (or (not (ring_n68954251visors X_a)) (= (or (= _let_0 (ti X_a BOUND_VARIABLE_144647)) (= _let_0 (ti X_a BOUND_VARIABLE_144646))) (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_144646) BOUND_VARIABLE_144647)))) )) 19.55/18.38 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.55/18.38 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.55/18.38 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 19.55/18.38 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 19.55/18.38 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 19.55/18.38 ( 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))), (zero_zero int) ) 19.55/18.38 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 19.55/18.38 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1 ) 19.55/18.38 ( complex, ii, ii ) 19.55/18.38 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 19.55/18.38 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 19.55/18.38 ) 19.55/18.38 (instantiation (let ((_let_0 (zero_zero int))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (number_number_of nat))) (let ((_let_3 (hAPP int int _let_1 V_2))) (let ((_let_4 (hBOOL (hAPP int bool nat_neg _let_3)))) (let ((_let_5 (hAPP int int _let_1 V_1))) (let ((_let_6 (hBOOL (hAPP int bool nat_neg _let_5)))) (forall ((V_1 $$unsorted) (V_2 $$unsorted)) (= (and (or _let_6 (and (or _let_4 (= (ti int V_2) (ti int V_1))) (or (not _let_4) (= _let_0 _let_5)))) (or (not _let_6) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) _let_3) _let_0)))) (= (hAPP int nat _let_2 V_2) (hAPP int nat _let_2 V_1))) )))))))) 19.70/18.42 ( pls, pls ) 19.70/18.42 ( (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 19.70/18.42 ( (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.70/18.42 ( (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))) ) 19.70/18.42 ( min_1, min_1 ) 19.70/18.42 ( (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.70/18.42 ) 19.70/18.42 (instantiation (let ((_let_0 (abs_abs int))) (forall ((W $$unsorted) (Z_1 $$unsorted)) (= (hAPP int nat nat_1 (hAPP int int _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) W) Z_1))) (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP int nat nat_1 (hAPP int int _let_0 W))) (hAPP int nat nat_1 (hAPP int int _let_0 Z_1)))) )) 19.70/18.42 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 19.70/18.42 ( (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))), (zero_zero int) ) 19.70/18.42 ( (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 ) 19.70/18.42 ( (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_1 ) 19.70/18.42 ) 19.70/18.42 (instantiation (let ((_let_0 (one_one X_a))) (let ((_let_1 (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_144739)))) (let ((_let_2 (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_144739))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_144732 $$unsorted) (BOUND_VARIABLE_144739 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (sgn_if X_a)) (and (or (not (= _let_0 (ti X_a BOUND_VARIABLE_144732))) (= _let_0 (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_144732))) (or (= _let_0 (ti X_a BOUND_VARIABLE_144739)) (and (or (not _let_1) (= _let_0 _let_2)) (or _let_1 (= (hAPP X_a X_a (uminus_uminus X_a) _let_0) _let_2))))))) )))) 19.70/18.42 ( bool, fFalse, fFalse ) 19.70/18.42 ( bool, fTrue, fTrue ) 19.70/18.42 ( real, pi, pi ) 19.70/18.42 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat) ) 19.70/18.42 ( (fun nat bool), prime, prime ) 19.70/18.42 ( (fun nat nat), suc, suc ) 19.70/18.42 ( (fun nat nat), (fact_fact nat), (fact_fact nat) ) 19.70/18.42 ( (fun nat nat), (size_size nat), (size_size nat) ) 19.70/18.42 ( (fun nat nat), fact, fact ) 19.70/18.42 ( (fun nat nat), nat_size, nat_size ) 19.70/18.42 ( int, pls, pls ) 19.70/18.42 ( int, m, m ) 19.70/18.42 ( int, min_1, min_1 ) 19.70/18.42 ( int, s, s ) 19.70/18.42 ( int, s1, s1 ) 19.70/18.42 ( int, t, t ) 19.70/18.42 ( (fun int bool), zprime, zprime ) 19.70/18.42 ( (fun int bool), nat_neg, nat_neg ) 19.70/18.42 ( (fun int bool), zEven, zEven ) 19.70/18.42 ( (fun int bool), nat_is_nat, nat_is_nat ) 19.70/18.42 ( (fun int bool), zOdd, zOdd ) 19.70/18.42 ( (fun int bool), (even_odd_even int), (even_odd_even int) ) 19.70/18.42 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 19.70/18.42 ( (fun int nat), nat_1, nat_1 ) 19.70/18.42 ( (fun int nat), phi, phi ) 19.70/18.42 ( (fun real real), sqrt, sqrt ) 19.70/18.42 ( (fun real real), tan, tan ) 19.70/18.42 ( (fun real real), cos, cos ) 19.70/18.42 ( (fun real real), arccos, arccos ) 19.70/18.42 ( (fun real real), ln, ln ) 19.70/18.42 ( (fun real real), sin, sin ) 19.70/18.42 ( (fun real real), arctan, arctan ) 19.70/18.42 ( (fun real real), arcsin, arcsin ) 19.70/18.42 ( complex, ii, ii ) 19.70/18.42 ( (fun complex complex), cnj, cnj ) 19.70/18.42 ( (fun complex complex), expi, expi ) 19.70/18.42 ( (fun nat real), (real_1 nat), (real_1 nat) ) 19.70/18.42 ( (fun nat real), cos_coeff, cos_coeff ) 19.70/18.42 ( (fun nat real), sin_coeff, sin_coeff ) 19.70/18.42 ( (fun int int), bit0, bit0 ) 19.70/18.42 ( (fun int int), bit1, bit1 ) 19.70/18.42 ( (fun int int), pred, pred ) 19.70/18.42 ( (fun int int), succ, succ ) 19.70/18.42 ( (fun int int), (fact_fact int), (fact_fact int) ) 19.70/18.42 ( (fun int int), zfact, zfact ) 19.70/18.42 ( (fun bool bool), fNot, fNot ) 19.70/18.42 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset ) 19.70/18.42 ( (fun bool (fun bool bool)), fconj, fconj ) 19.70/18.42 ( (fun bool (fun bool bool)), fdisj, fdisj ) 19.70/18.42 ( (fun bool (fun bool bool)), fimplies, fimplies ) 19.70/18.42 ( (fun int (fun int bool)), sRStar, sRStar ) 19.70/18.42 ( (fun int (fun int bool)), quadRes, quadRes ) 19.70/18.42 ( (fun int (fun int bool)), norRRset, norRRset ) 19.70/18.42 ( (fun int (fun int bool)), d22set, d22set ) 19.70/18.42 ( (fun int (fun int bool)), sr, sr ) 19.70/18.42 ( (fun int (fun int bool)), quickc1265749348ro_rel, quickc1265749348ro_rel ) 19.70/18.42 ( (fun nat (fun nat nat)), nat_gcd, nat_gcd ) 19.70/18.42 ( (fun nat (fun nat nat)), (gcd_gcd nat), (gcd_gcd nat) ) 19.70/18.42 ( (fun nat (fun nat nat)), nat_lcm, nat_lcm ) 19.70/18.42 ( (fun nat (fun real real)), root, root ) 19.70/18.42 ( (fun real (fun real real)), log, log ) 19.70/18.42 ( (fun real (fun real real)), powr, powr ) 19.70/18.42 ( (fun nat (fun nat bool)), coprime, coprime ) 19.70/18.42 ( (fun (fun int bool) int), (the int), (the int) ) 19.70/18.42 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, normalize ) 19.70/18.42 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, negateSnd ) 19.70/18.42 ( (fun nat (fun nat (product_prod int int))), bezw, bezw ) 19.70/18.42 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set ) 19.70/18.42 ( (filter nat), sequentially, sequentially ) 19.70/18.42 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat ) 19.70/18.42 ( (fun (product_prod int int) bool), frac_1, frac_1 ) 19.70/18.42 ( (fun real complex), cis, cis ) 19.70/18.42 ( (fun complex real), im, im ) 19.70/18.42 ( (fun complex real), re, re ) 19.70/18.42 ( (fun complex real), arg, arg ) 19.70/18.42 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral ) 19.70/18.42 ( (fun int (fun int int)), int_gcd, int_gcd ) 19.70/18.42 ( (fun int (fun int int)), multInv, multInv ) 19.70/18.42 ( (fun int (fun int int)), legacy_zgcd, legacy_zgcd ) 19.70/18.42 ( (fun int (fun int int)), z3mod, z3mod ) 19.70/18.42 ( (fun int (fun int int)), inv, inv ) 19.70/18.42 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int) ) 19.70/18.42 ( (fun int (fun int int)), standardRes, standardRes ) 19.70/18.42 ( (fun int (fun int int)), legendre, legendre ) 19.70/18.42 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 19.70/18.42 ( (fun int (fun int int)), z3div, z3div ) 19.70/18.42 ( (fun int (fun int int)), int_lcm, int_lcm ) 19.70/18.42 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than2 ) 19.70/18.42 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than ) 19.70/18.42 ( (fun int (fun (fun int bool) bool)), rsetR, rsetR ) 19.70/18.42 ( (fun int (fun (fun int bool) bool)), resSet, resSet ) 19.70/18.42 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, lazy_small_lazy_rel ) 19.70/18.42 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, posDivAlg_rel ) 19.70/18.42 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, upto_rel ) 19.70/18.42 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, negDivAlg_rel ) 19.70/18.42 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, norm_frac_rel ) 19.70/18.42 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_less ) 19.70/18.42 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_leq ) 19.70/18.42 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel ) 19.70/18.42 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd ) 19.70/18.42 ( (fun int (fun int (product_prod int int))), negDivAlg, negDivAlg ) 19.70/18.42 ( (fun int (fun int (product_prod int int))), divmod_int, divmod_int ) 19.70/18.42 ( (fun int (fun int (product_prod int int))), posDivAlg, posDivAlg ) 19.70/18.42 ( (fun int (fun int (product_prod int int))), pdivmod, pdivmod ) 19.70/18.43 ( (fun int (fun int (product_prod int int))), norm_frac, norm_frac ) 19.70/18.43 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust ) 19.70/18.43 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, bolzano_bisect ) 19.70/18.43 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 19.70/18.43 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 19.70/18.43 ( (fun real nat), natfloor, natfloor ) 19.70/18.43 ( (fun real nat), natceiling, natceiling ) 19.70/18.43 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int ) 19.70/18.43 ( (fun int (fun int (fun int bool))), wset, wset ) 19.70/18.43 ( (fun int (fun int (fun int bool))), bnorRset, bnorRset ) 19.70/18.43 ( (fun int (fun int (fun int bool))), zcong, zcong ) 19.70/18.43 ( (fun int (fun int (fun int bool))), noXRRset, noXRRset ) 19.70/18.43 ( (fun int (fun int (fun int bool))), zcongm, zcongm ) 19.70/18.43 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair ) 19.70/18.43 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS ) 19.70/18.43 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral ) 19.70/18.43 ( (fun int real), (real_1 int), (real_1 int) ) 19.70/18.43 ( (fun complex nat), (size_size complex), (size_size complex) ) 19.70/18.43 ( (fun complex nat), complex_size, complex_size ) 19.70/18.43 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero ) 19.70/18.43 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel ) 19.70/18.43 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel ) 19.70/18.43 ( (fun (product_prod int int) rat), frct, frct ) 19.70/18.43 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux ) 19.70/18.43 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel ) 19.70/18.43 ( (fun (fun nat rat) bool), vanishes, vanishes ) 19.70/18.43 ( (fun int (fun int rat)), fract, fract ) 19.70/18.43 ( (fun code_code_numeral int), code_int_of, code_int_of ) 19.70/18.43 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat ) 19.70/18.43 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral) ) 19.70/18.43 ( (fun code_code_numeral nat), code_c271388182l_size, code_c271388182l_size ) 19.70/18.43 ( (fun real (fun real complex)), complex_1, complex_1 ) 19.70/18.43 ( (fun real (fun real complex)), rcis, rcis ) 19.70/18.43 ( (fun int (fun nat nat)), nat_aux, nat_aux ) 19.70/18.43 ( (fun rat real), ratreal, ratreal ) 19.70/18.43 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of ) 19.70/18.43 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int ) 19.70/18.43 ( (fun rat (product_prod int int)), quotient_of, quotient_of ) 19.70/18.43 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR ) 19.70/18.43 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 19.70/18.43 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of ) 19.70/18.43 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda, xzgcda ) 19.70/18.43 ) 19.70/18.43 (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)))))) ) 19.70/18.43 ( (zero_zero real) ) 19.70/18.43 ( (one_one real) ) 19.70/18.43 ( pi ) 19.70/18.43 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.43 ( (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)))) ) 19.70/18.43 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.70/18.43 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.43 ( skv_6 ) 19.70/18.43 ( skv_11 ) 19.70/18.43 ( skv_12 ) 19.70/18.43 ( skv_14 ) 19.70/18.43 ) 19.70/18.43 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_144771 $$unsorted)) (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_144771)) (ring_1_Ints X_a)))) )) 19.70/18.43 ( real, (zero_zero int) ) 19.70/18.43 ( real, (one_one int) ) 19.70/18.43 ) 19.70/18.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144799 $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (= (hAPP X_a real (norm_norm X_a) (hAPP real X_a (of_real X_a) BOUND_VARIABLE_144799)) (hAPP real real (abs_abs real) BOUND_VARIABLE_144799))) ) 19.70/18.43 ( complex, pi ) 19.70/18.43 ( complex, (hAPP int real (number_number_of real) min_1) ) 19.70/18.43 ( complex, (hAPP real real (uminus_uminus real) (one_one real)) ) 19.70/18.43 ) 19.70/18.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144946 $$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_144946))) (= (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_144946) (ti X_a BOUND_VARIABLE_144946))) ) 19.70/18.43 ( bool, fFalse ) 19.70/18.43 ( bool, fTrue ) 19.70/18.43 ( real, pi ) 19.70/18.43 ( 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)))) ) 19.70/18.43 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.43 ( real, skv_2 ) 19.70/18.43 ( real, skv_10 ) 19.70/18.43 ( real, skv_13 ) 19.70/18.43 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.43 ( (fun nat bool), (even_odd_even nat) ) 19.70/18.43 ( (fun nat bool), prime ) 19.70/18.43 ( (fun nat nat), suc ) 19.70/18.43 ( (fun nat nat), (fact_fact nat) ) 19.70/18.43 ( (fun nat nat), (size_size nat) ) 19.70/18.43 ( (fun nat nat), fact ) 19.70/18.43 ( (fun nat nat), nat_size ) 19.70/18.43 ( int, (zero_zero int) ) 19.70/18.43 ( int, pls ) 19.70/18.43 ( int, m ) 19.70/18.43 ( int, (one_one int) ) 19.70/18.43 ( 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))) ) 19.70/18.43 ( int, min_1 ) 19.70/18.43 ( int, s ) 19.70/18.43 ( int, s1 ) 19.70/18.43 ( int, t ) 19.70/18.43 ( (fun int bool), zprime ) 19.70/18.43 ( (fun int bool), nat_neg ) 19.70/18.43 ( (fun int bool), zEven ) 19.70/18.43 ( (fun int bool), nat_is_nat ) 19.70/18.43 ( (fun int bool), zOdd ) 19.70/18.43 ( (fun int bool), (even_odd_even int) ) 19.70/18.43 ( (fun int bool), twoSqu1091635170sum2sq ) 19.70/18.43 ( (fun int nat), nat_1 ) 19.70/18.43 ( (fun int nat), phi ) 19.70/18.43 ( (fun real real), sqrt ) 19.70/18.43 ( (fun real real), tan ) 19.70/18.43 ( (fun real real), cos ) 19.70/18.43 ( (fun real real), arccos ) 19.70/18.43 ( (fun real real), ln ) 19.70/18.43 ( (fun real real), sin ) 19.70/18.43 ( (fun real real), arctan ) 19.70/18.43 ( (fun real real), arcsin ) 19.70/18.43 ( complex, ii ) 19.70/18.43 ( (fun complex complex), cnj ) 19.70/18.43 ( (fun complex complex), expi ) 19.70/18.43 ( (fun nat real), (real_1 nat) ) 19.70/18.43 ( (fun nat real), cos_coeff ) 19.70/18.43 ( (fun nat real), sin_coeff ) 19.70/18.43 ( (fun int int), bit0 ) 19.70/18.43 ( (fun int int), bit1 ) 19.70/18.43 ( (fun int int), pred ) 19.70/18.43 ( (fun int int), succ ) 19.70/18.43 ( (fun int int), (fact_fact int) ) 19.70/18.43 ( (fun int int), zfact ) 19.70/18.43 ( (fun bool bool), fNot ) 19.70/18.43 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 19.70/18.43 ( (fun bool (fun bool bool)), fconj ) 19.70/18.43 ( (fun bool (fun bool bool)), fdisj ) 19.70/18.43 ( (fun bool (fun bool bool)), fimplies ) 19.70/18.43 ( (fun int (fun int bool)), sRStar ) 19.70/18.43 ( (fun int (fun int bool)), quadRes ) 19.70/18.43 ( (fun int (fun int bool)), norRRset ) 19.70/18.43 ( (fun int (fun int bool)), d22set ) 19.70/18.43 ( (fun int (fun int bool)), sr ) 19.70/18.43 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 19.70/18.43 ( (fun nat (fun nat nat)), nat_gcd ) 19.70/18.43 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 19.70/18.43 ( (fun nat (fun nat nat)), nat_lcm ) 19.70/18.43 ( (fun nat (fun real real)), root ) 19.70/18.43 ( (fun real (fun real real)), log ) 19.70/18.43 ( (fun real (fun real real)), powr ) 19.70/18.43 ( (fun nat (fun nat bool)), coprime ) 19.70/18.43 ( (fun (fun int bool) int), (the int) ) 19.70/18.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 19.70/18.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 19.70/18.43 ( (fun nat (fun nat (product_prod int int))), bezw ) 19.70/18.43 ( (fun (fun int bool) bool), nat_nat_set ) 19.70/18.43 ( (filter nat), sequentially ) 19.70/18.43 ( (fun (product_prod nat nat) bool), pred_nat ) 19.70/18.43 ( (fun (product_prod int int) bool), frac_1 ) 19.70/18.43 ( (fun real complex), cis ) 19.70/18.43 ( (fun complex real), im ) 19.70/18.43 ( (fun complex real), re ) 19.70/18.43 ( (fun complex real), arg ) 19.70/18.43 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 19.70/18.43 ( (fun int (fun int int)), int_gcd ) 19.70/18.43 ( (fun int (fun int int)), multInv ) 19.70/18.43 ( (fun int (fun int int)), legacy_zgcd ) 19.70/18.43 ( (fun int (fun int int)), z3mod ) 19.70/18.43 ( (fun int (fun int int)), inv ) 19.70/18.43 ( (fun int (fun int int)), (gcd_gcd int) ) 19.70/18.43 ( (fun int (fun int int)), standardRes ) 19.70/18.43 ( (fun int (fun int int)), legendre ) 19.70/18.43 ( (fun int (fun int int)), nat_tsub ) 19.70/18.43 ( (fun int (fun int int)), z3div ) 19.70/18.43 ( (fun int (fun int int)), int_lcm ) 19.70/18.43 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 19.70/18.43 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 19.70/18.43 ( (fun int (fun (fun int bool) bool)), rsetR ) 19.70/18.43 ( (fun int (fun (fun int bool) bool)), resSet ) 19.70/18.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 19.70/18.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 19.70/18.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 19.70/18.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 19.70/18.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 19.70/18.43 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 19.70/18.43 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 19.70/18.43 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 19.70/18.43 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 19.70/18.43 ( (fun int (fun int (product_prod int int))), negDivAlg ) 19.70/18.43 ( (fun int (fun int (product_prod int int))), divmod_int ) 19.70/18.43 ( (fun int (fun int (product_prod int int))), posDivAlg ) 19.70/18.43 ( (fun int (fun int (product_prod int int))), pdivmod ) 19.70/18.43 ( (fun int (fun int (product_prod int int))), norm_frac ) 19.70/18.43 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 19.70/18.43 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 19.70/18.43 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 19.70/18.43 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 19.70/18.43 ( (fun real nat), natfloor ) 19.70/18.43 ( (fun real nat), natceiling ) 19.70/18.43 ( (fun int quickcheck_code_int), quickcheck_of_int ) 19.70/18.43 ( (fun int (fun int (fun int bool))), wset ) 19.70/18.43 ( (fun int (fun int (fun int bool))), bnorRset ) 19.70/18.43 ( (fun int (fun int (fun int bool))), zcong ) 19.70/18.43 ( (fun int (fun int (fun int bool))), noXRRset ) 19.70/18.43 ( (fun int (fun int (fun int bool))), zcongm ) 19.70/18.43 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 19.70/18.43 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 19.70/18.43 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 19.70/18.43 ( (fun int real), (real_1 int) ) 19.70/18.43 ( (fun complex nat), (size_size complex) ) 19.70/18.43 ( (fun complex nat), complex_size ) 19.70/18.43 ( (fun int (list int)), quickc666637781d_zero ) 19.70/18.43 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 19.70/18.43 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 19.70/18.43 ( (fun (product_prod int int) rat), frct ) 19.70/18.43 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 19.70/18.43 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 19.70/18.43 ( (fun (fun nat rat) bool), vanishes ) 19.70/18.43 ( (fun int (fun int rat)), fract ) 19.70/18.43 ( (fun code_code_numeral int), code_int_of ) 19.70/18.43 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 19.70/18.43 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 19.70/18.43 ( (fun code_code_numeral nat), code_c271388182l_size ) 19.70/18.43 ( (fun real (fun real complex)), complex_1 ) 19.70/18.43 ( (fun real (fun real complex)), rcis ) 19.70/18.43 ( (fun int (fun nat nat)), nat_aux ) 19.70/18.43 ( (fun rat real), ratreal ) 19.70/18.43 ( (fun quickcheck_code_int int), quickcheck_int_of ) 19.70/18.43 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 19.70/18.43 ( (fun rat (product_prod int int)), quotient_of ) 19.70/18.43 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 19.70/18.43 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 19.70/18.43 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 19.70/18.43 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 19.70/18.43 ) 19.70/18.43 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_145025 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (= (not (= _let_0 (ti X_a BOUND_VARIABLE_145025))) (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_145025))))) )) 19.70/18.43 ( bool, fFalse ) 19.70/18.43 ( bool, fTrue ) 19.70/18.43 ( real, pi ) 19.70/18.43 ( (fun nat bool), (even_odd_even nat) ) 19.70/18.43 ( (fun nat bool), prime ) 19.70/18.43 ( (fun nat nat), suc ) 19.70/18.43 ( (fun nat nat), (fact_fact nat) ) 19.70/18.43 ( (fun nat nat), (size_size nat) ) 19.70/18.43 ( (fun nat nat), fact ) 19.70/18.43 ( (fun nat nat), nat_size ) 19.70/18.43 ( int, pls ) 19.70/18.43 ( int, m ) 19.70/18.43 ( int, min_1 ) 19.70/18.43 ( int, s ) 19.70/18.43 ( int, s1 ) 19.70/18.43 ( int, t ) 19.70/18.43 ( (fun int bool), zprime ) 19.70/18.43 ( (fun int bool), nat_neg ) 19.70/18.43 ( (fun int bool), zEven ) 19.70/18.43 ( (fun int bool), nat_is_nat ) 19.70/18.43 ( (fun int bool), zOdd ) 19.70/18.43 ( (fun int bool), (even_odd_even int) ) 19.70/18.43 ( (fun int bool), twoSqu1091635170sum2sq ) 19.70/18.43 ( (fun int nat), nat_1 ) 19.70/18.43 ( (fun int nat), phi ) 19.70/18.43 ( (fun real real), sqrt ) 19.70/18.43 ( (fun real real), tan ) 19.70/18.43 ( (fun real real), cos ) 19.70/18.43 ( (fun real real), arccos ) 19.70/18.43 ( (fun real real), ln ) 19.70/18.43 ( (fun real real), sin ) 19.70/18.43 ( (fun real real), arctan ) 19.70/18.43 ( (fun real real), arcsin ) 19.70/18.43 ( complex, ii ) 19.70/18.43 ( (fun complex complex), cnj ) 19.70/18.43 ( (fun complex complex), expi ) 19.70/18.43 ( (fun nat real), (real_1 nat) ) 19.70/18.43 ( (fun nat real), cos_coeff ) 19.70/18.43 ( (fun nat real), sin_coeff ) 19.70/18.43 ( (fun int int), bit0 ) 19.70/18.43 ( (fun int int), bit1 ) 19.70/18.43 ( (fun int int), pred ) 19.70/18.43 ( (fun int int), succ ) 19.70/18.43 ( (fun int int), (fact_fact int) ) 19.70/18.43 ( (fun int int), zfact ) 19.70/18.43 ( (fun bool bool), fNot ) 19.70/18.43 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 19.70/18.43 ( (fun bool (fun bool bool)), fconj ) 19.70/18.43 ( (fun bool (fun bool bool)), fdisj ) 19.70/18.43 ( (fun bool (fun bool bool)), fimplies ) 19.70/18.43 ( (fun int (fun int bool)), sRStar ) 19.70/18.43 ( (fun int (fun int bool)), quadRes ) 19.70/18.43 ( (fun int (fun int bool)), norRRset ) 19.70/18.43 ( (fun int (fun int bool)), d22set ) 19.70/18.43 ( (fun int (fun int bool)), sr ) 19.70/18.43 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 19.70/18.43 ( (fun nat (fun nat nat)), nat_gcd ) 19.70/18.43 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 19.70/18.43 ( (fun nat (fun nat nat)), nat_lcm ) 19.70/18.43 ( (fun nat (fun real real)), root ) 19.70/18.43 ( (fun real (fun real real)), log ) 19.70/18.43 ( (fun real (fun real real)), powr ) 19.70/18.43 ( (fun nat (fun nat bool)), coprime ) 19.70/18.43 ( (fun (fun int bool) int), (the int) ) 19.70/18.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 19.70/18.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 19.70/18.43 ( (fun nat (fun nat (product_prod int int))), bezw ) 19.70/18.43 ( (fun (fun int bool) bool), nat_nat_set ) 19.70/18.43 ( (filter nat), sequentially ) 19.70/18.43 ( (fun (product_prod nat nat) bool), pred_nat ) 19.70/18.43 ( (fun (product_prod int int) bool), frac_1 ) 19.70/18.43 ( (fun real complex), cis ) 19.70/18.43 ( (fun complex real), im ) 19.70/18.43 ( (fun complex real), re ) 19.70/18.43 ( (fun complex real), arg ) 19.70/18.43 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 19.70/18.43 ( (fun int (fun int int)), int_gcd ) 19.70/18.43 ( (fun int (fun int int)), multInv ) 19.70/18.43 ( (fun int (fun int int)), legacy_zgcd ) 19.70/18.43 ( (fun int (fun int int)), z3mod ) 19.70/18.43 ( (fun int (fun int int)), inv ) 19.70/18.43 ( (fun int (fun int int)), (gcd_gcd int) ) 19.70/18.43 ( (fun int (fun int int)), standardRes ) 19.70/18.43 ( (fun int (fun int int)), legendre ) 19.70/18.43 ( (fun int (fun int int)), nat_tsub ) 19.70/18.43 ( (fun int (fun int int)), z3div ) 19.70/18.43 ( (fun int (fun int int)), int_lcm ) 19.70/18.43 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 19.70/18.43 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 19.70/18.43 ( (fun int (fun (fun int bool) bool)), rsetR ) 19.70/18.43 ( (fun int (fun (fun int bool) bool)), resSet ) 19.70/18.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 19.70/18.43 ( (let ((_let_0 (product_prod 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(product_prod int int))), pdivmod ) 19.70/18.43 ( (fun int (fun int (product_prod int int))), norm_frac ) 19.70/18.43 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 19.70/18.43 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 19.70/18.43 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 19.70/18.43 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 19.70/18.44 ( (fun real nat), natfloor ) 19.70/18.44 ( (fun real nat), natceiling ) 19.70/18.44 ( (fun int quickcheck_code_int), quickcheck_of_int ) 19.70/18.44 ( (fun int (fun int (fun int bool))), wset ) 19.70/18.44 ( (fun int (fun int (fun int bool))), bnorRset ) 19.70/18.44 ( (fun int (fun int (fun int bool))), zcong ) 19.70/18.44 ( (fun int (fun int (fun int bool))), noXRRset ) 19.70/18.44 ( (fun int (fun int (fun int bool))), zcongm ) 19.70/18.44 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 19.70/18.44 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 19.70/18.44 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 19.70/18.44 ( (fun int real), (real_1 int) ) 19.70/18.44 ( (fun complex nat), (size_size complex) ) 19.70/18.44 ( (fun complex nat), complex_size ) 19.70/18.44 ( (fun int (list int)), quickc666637781d_zero ) 19.70/18.44 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 19.70/18.44 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 19.70/18.44 ( (fun (product_prod int int) rat), frct ) 19.70/18.44 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 19.70/18.44 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 19.70/18.44 ( (fun (fun nat rat) bool), vanishes ) 19.70/18.44 ( (fun int (fun int rat)), fract ) 19.70/18.44 ( (fun code_code_numeral int), code_int_of ) 19.70/18.44 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 19.70/18.44 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 19.70/18.44 ( (fun code_code_numeral nat), code_c271388182l_size ) 19.70/18.44 ( (fun real (fun real complex)), complex_1 ) 19.70/18.44 ( (fun real (fun real complex)), rcis ) 19.70/18.44 ( (fun int (fun nat nat)), nat_aux ) 19.70/18.44 ( (fun rat real), ratreal ) 19.70/18.44 ( (fun quickcheck_code_int int), quickcheck_int_of ) 19.70/18.44 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 19.70/18.44 ( (fun rat (product_prod int int)), quotient_of ) 19.70/18.44 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 19.70/18.44 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 19.70/18.44 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 19.70/18.44 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 19.70/18.44 ) 19.70/18.44 (instantiation (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))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted) (M $$unsorted)) (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))) ))))) 19.70/18.44 ( (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))) ) 19.70/18.44 ) 19.70/18.44 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_145131 $$unsorted) (BOUND_VARIABLE_145132 $$unsorted)) (or (not (linorder X_a)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_145131) BOUND_VARIABLE_145132)) (= (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_145132) BOUND_VARIABLE_145131))) (= (ti X_a BOUND_VARIABLE_145131) (ti X_a BOUND_VARIABLE_145132)))) ))) 19.70/18.44 ( real, (zero_zero real), pi ) 19.70/18.44 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.44 ( 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))))) ) 19.70/18.44 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.44 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.44 ( real, (zero_zero real), skv_2 ) 19.70/18.44 ( real, (zero_zero real), skv_10 ) 19.70/18.44 ( real, (zero_zero real), skv_13 ) 19.70/18.44 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.44 ( real, pi, (zero_zero real) ) 19.70/18.44 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.44 ( 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)) ) 19.70/18.44 ( 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)))) ) 19.70/18.44 ( 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)))), (zero_zero real) ) 19.70/18.44 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.44 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 19.70/18.44 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 19.70/18.44 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.70/18.44 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.70/18.44 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 19.70/18.44 ( 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)), pi ) 19.70/18.44 ( real, skv_2, (zero_zero real) ) 19.70/18.44 ( real, skv_10, (zero_zero real) ) 19.70/18.44 ( real, skv_13, (zero_zero real) ) 19.70/18.44 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.44 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 19.70/18.44 ( int, (zero_zero int), (zero_zero int) ) 19.70/18.44 ( int, (zero_zero int), (one_one int) ) 19.70/18.44 ( 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))) ) 19.70/18.44 ( int, (zero_zero int), min_1 ) 19.70/18.44 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 19.70/18.44 ( int, (zero_zero int), t ) 19.70/18.44 ( int, (one_one int), (zero_zero int) ) 19.70/18.44 ( int, (one_one int), t ) 19.70/18.44 ( 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))), (zero_zero int) ) 19.70/18.44 ( 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))), s ) 19.70/18.44 ( 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 ) 19.70/18.44 ( 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_3 ) 19.70/18.44 ( 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_9 ) 19.70/18.44 ( int, min_1, (zero_zero int) ) 19.70/18.44 ( int, min_1, min_1 ) 19.70/18.44 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.70/18.44 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 19.70/18.44 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 19.70/18.44 ( int, t, (zero_zero int) ) 19.70/18.44 ( int, t, (one_one int) ) 19.70/18.44 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.70/18.44 ( 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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 19.70/18.44 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.70/18.44 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.70/18.44 ) 19.70/18.44 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (hAPP int int bit1 pls))) (let ((_let_3 (times_times nat))) (let ((_let_4 (hAPP int (fun int int) (minus_minus int) P_5))) (let ((_let_5 (hAPP int nat nat_1 (hAPP int int _let_4 (hAPP int int _let_1 (hAPP int int bit0 _let_2)))))) (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int _let_1 (hAPP int int bit1 (hAPP int int bit0 _let_2)))) P_5))) (= (hAPP nat nat (hAPP nat _let_0 _let_3 _let_5) _let_5) (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_3 (hAPP int nat nat_1 (hAPP int int _let_4 (one_one int)))) (hAPP int nat nat_1 (hAPP int int _let_4 (hAPP int int _let_1 (hAPP int int bit1 _let_2)))))))) ))))))) 19.70/18.44 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.44 ) 19.70/18.44 (instantiation (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_145211 $$unsorted) (BOUND_VARIABLE_145212 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 (minus_minus X_a) BOUND_VARIABLE_145211) BOUND_VARIABLE_145212))) (hAPP X_a X_a (hAPP X_a _let_1 (plus_plus X_a) (hAPP X_a X_a _let_0 BOUND_VARIABLE_145211)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_145212))))) ))) 19.70/18.44 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 19.70/18.44 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 19.70/18.44 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 19.70/18.44 ) 19.70/18.44 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int bit0 K_4) (hAPP int int pred (hAPP int int bit1 K_4))) ) 19.70/18.44 ( pls ) 19.70/18.44 ( (hAPP int int bit1 pls) ) 19.70/18.44 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.70/18.44 ( min_1 ) 19.70/18.44 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.70/18.44 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.70/18.44 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 19.70/18.44 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 19.70/18.44 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 19.70/18.44 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 19.70/18.44 ) 19.70/18.44 (instantiation (let ((_let_0 (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (number_number_of int) min_1)) (hAPP (fun X_a bool) nat (finite_card X_a) A_3)))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (or (not (hBOOL (hAPP (fun X_a bool) bool (finite_finite_1 X_a) A_3))) (= (one_one int) (hAPP int int (hAPP int (fun int int) (times_times int) _let_0) _let_0))) )) 19.70/18.44 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 19.70/18.44 ) 19.70/18.44 (instantiation (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_145243))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_145242 $$unsorted) (BOUND_VARIABLE_145243 $$unsorted)) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP nat bool (even_odd_even nat) _let_2))) (= (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_145242) _let_2) (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_145242)) _let_2))) )))) 19.70/18.44 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.70/18.44 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.70/18.44 ( int, skv_8, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.70/18.44 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.70/18.44 ) 19.70/18.44 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_145284 $$unsorted) (BOUND_VARIABLE_145285 $$unsorted)) (or (not (ordere453448008miring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_145285))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_145284) _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_145285) BOUND_VARIABLE_145284)) _let_2))) )))) 19.70/18.44 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.44 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 19.70/18.44 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.45 ( 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)))) ) 19.70/18.45 ( 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))) ) 19.70/18.45 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.45 ( 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))) ) 19.70/18.45 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.70/18.45 ( complex, ii, ii ) 19.70/18.45 ( 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)) ) 19.70/18.45 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.45 ) 19.70/18.45 (instantiation (let ((_let_0 (product_prod int int))) (forall ((K_4 $$unsorted)) (= (zero_zero rat) (hAPP _let_0 rat frct (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) K_4) (zero_zero int)))) )) 19.70/18.45 ( (zero_zero int) ) 19.70/18.45 ( (one_one int) ) 19.70/18.45 ( s ) 19.70/18.45 ) 19.70/18.45 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_145316 $$unsorted) (BOUND_VARIABLE_145317 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_145317))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) BOUND_VARIABLE_145316))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_145317) BOUND_VARIABLE_145316)))) )) 19.70/18.45 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 19.70/18.45 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 19.70/18.45 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 19.70/18.45 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 19.70/18.45 ) 19.70/18.45 (instantiation (let ((_let_0 (field_char_0_Rats X_a))) (forall ((X_a $$unsorted)) (or (not (field_char_0 X_a)) (= _let_0 (ti (fun X_a bool) _let_0))) )) 19.70/18.45 ( bool ) 19.70/18.45 ( real ) 19.70/18.45 ( nat ) 19.70/18.45 ( (fun nat bool) ) 19.70/18.45 ( int ) 19.70/18.45 ( (fun int bool) ) 19.70/18.45 ( complex ) 19.70/18.45 ( rat ) 19.70/18.45 ( (product_prod real real) ) 19.70/18.45 ( (product_prod int int) ) 19.70/18.45 ( (filter real) ) 19.70/18.45 ( (filter nat) ) 19.70/18.45 ( (product_prod nat nat) ) 19.70/18.45 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 19.70/18.45 ( (fun nat rat) ) 19.70/18.45 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 19.70/18.45 ) 19.70/18.45 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)))) (forall ((X $$unsorted) (N $$unsorted) (M $$unsorted)) (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 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))) ))) 19.70/18.45 ( (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))) ) 19.70/18.45 ( (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))) ) 19.70/18.45 ) 19.70/18.45 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 _let_0) X))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X) (one_one real)))) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real ln X)) _let_0))) )))) 19.70/18.45 ( (one_one real) ) 19.70/18.45 ( pi ) 19.70/18.45 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.45 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.45 ( skv_2 ) 19.70/18.45 ( skv_10 ) 19.70/18.45 ( skv_13 ) 19.70/18.45 ) 19.70/18.45 (instantiation (forall ((X $$unsorted)) (= (hAPP real real (uminus_uminus real) (hAPP complex real im X)) (hAPP complex real im (hAPP complex complex cnj X))) ) 19.70/18.45 ( ii ) 19.70/18.45 ( (zero_zero complex) ) 19.70/18.45 ( (one_one complex) ) 19.70/18.45 ) 19.70/18.45 (instantiation (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 int X_a (number_number_of X_a) BOUND_VARIABLE_145499))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_3) _let_4)))) (let ((_let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_4) _let_3)))) (let ((_let_7 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_145500) _let_4))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_145498 $$unsorted) (BOUND_VARIABLE_145499 $$unsorted) (BOUND_VARIABLE_145500 $$unsorted)) (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_145498) _let_4)) BOUND_VARIABLE_145500)) (and (or _let_5 (and (or (not _let_6) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_7) BOUND_VARIABLE_145498))) (or _let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_3) BOUND_VARIABLE_145500))))) (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_145498) _let_7)))))) ))))))))) 19.70/18.45 ( 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))) ) 19.70/18.45 ) 19.70/18.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145537 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)) BOUND_VARIABLE_145537)) (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_145537))))) ) 19.70/18.45 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.45 ) 19.70/18.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145614 $$unsorted) (BOUND_VARIABLE_145615 $$unsorted) (BOUND_VARIABLE_145616 $$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_145615) BOUND_VARIABLE_145616) (ti X_a BOUND_VARIABLE_145614))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_145615) BOUND_VARIABLE_145614))) ) 19.70/18.45 ( 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))))), pi ) 19.70/18.45 ( int, m, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 19.70/18.45 ( int, min_1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 19.70/18.45 ( 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))), t ) 19.70/18.45 ( 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))), skv_1 ) 19.70/18.45 ( complex, ii, ii, ii ) 19.70/18.45 ) 19.70/18.45 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_145634 $$unsorted)) (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_145634) BOUND_VARIABLE_145634))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_145634)))) )) 19.70/18.45 ( nat, (one_one nat) ) 19.70/18.45 ( 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) ) 19.70/18.45 ( 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)))) ) 19.70/18.45 ) 19.70/18.45 (instantiation (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)))) (forall ((N_1 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool _let_1 N_1))) (= (hAPP int int (hAPP int (fun int int) (minus_minus int) N_1) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (hAPP _let_0 nat (finite_card int) (hAPP _let_0 _let_0 (collect int) (hAPP _let_0 _let_0 (hAPP _let_3 (fun _let_0 _let_0) (combs int bool bool) (hAPP _let_0 _let_3 (hAPP (fun bool _let_2) (fun _let_0 _let_3) (combb bool _let_2 int) fconj) _let_1)) (hAPP int _let_0 (hAPP _let_4 _let_4 (combc int int bool) _let_0) N_1)))))))) )))))) 19.70/18.45 ( (zero_zero int) ) 19.70/18.45 ( (one_one int) ) 19.70/18.45 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.70/18.45 ( min_1 ) 19.70/18.45 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.45 ) 19.70/18.45 (instantiation (let ((_let_0 (fun nat X_a))) (let ((_let_1 (hAPP nat nat suc BOUND_VARIABLE_145659))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_145658 $$unsorted) (BOUND_VARIABLE_145659 $$unsorted)) (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_145658 _let_1)) (hAPP nat X_a (hAPP _let_0 _let_0 (diffs X_a) BOUND_VARIABLE_145658) BOUND_VARIABLE_145659))) ))) 19.70/18.45 ( bool, (even_odd_even nat), (zero_zero nat) ) 19.70/18.45 ( bool, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)) ) 19.70/18.45 ( bool, prime, (zero_zero nat) ) 19.70/18.45 ( bool, prime, (hAPP nat nat suc (zero_zero nat)) ) 19.70/18.45 ( real, (real_1 nat), (zero_zero nat) ) 19.70/18.45 ( nat, suc, (zero_zero nat) ) 19.70/18.45 ( nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 19.70/18.45 ( nat, (fact_fact nat), (zero_zero nat) ) 19.70/18.45 ( nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (zero_zero nat) ) 19.70/18.45 ( (fun nat nat), (plus_plus nat), (zero_zero nat) ) 19.70/18.45 ( (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)) ) 19.70/18.45 ( (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) ) 19.70/18.45 ( int, (semiring_1_of_nat int), (zero_zero nat) ) 19.70/18.45 ( int, (semiring_1_of_nat int), (hAPP nat nat suc (zero_zero nat)) ) 19.70/18.45 ( int, (semiring_1_of_nat int), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 19.70/18.45 ( int, (hAPP int (fun nat int) (power_power int) s), (hAPP nat nat suc (zero_zero nat)) ) 19.70/18.45 ( int, (hAPP int (fun nat int) (power_power int) s1), (hAPP nat nat suc (zero_zero nat)) ) 19.70/18.45 ( int, (hAPP int (fun nat int) (power_power int) skv_8), (hAPP nat nat suc (zero_zero nat)) ) 19.70/18.45 ( (fun real real), root, (hAPP nat nat suc (zero_zero nat)) ) 19.70/18.45 ( complex, (hAPP complex (fun nat complex) (power_power complex) ii), (hAPP nat nat suc (zero_zero nat)) ) 19.70/18.45 ( (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)) ) 19.70/18.45 ) 19.70/18.45 (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))) ) 19.70/18.45 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.45 ) 19.70/18.45 (instantiation (forall ((X_a $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (= (one_one real) (hAPP X_a real (norm_norm X_a) (one_one X_a)))) ) 19.70/18.45 ( real ) 19.70/18.45 ( nat ) 19.70/18.45 ( int ) 19.70/18.45 ( complex ) 19.70/18.45 ( rat ) 19.70/18.45 ( quickcheck_code_int ) 19.70/18.45 ( code_code_numeral ) 19.70/18.45 ) 19.70/18.45 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (fun (filter nat) bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_145700 $$unsorted) (BOUND_VARIABLE_145701 $$unsorted) (BOUND_VARIABLE_145702 $$unsorted)) (or (not (metric_space X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_2 (hAPP (fun nat X_a) (fun X_a _let_2) (tendsto nat X_a) BOUND_VARIABLE_145701) BOUND_VARIABLE_145702) sequentially))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) BOUND_VARIABLE_145700))) (not (forall ((No $$unsorted)) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) (hAPP nat X_a BOUND_VARIABLE_145701 N_2)) BOUND_VARIABLE_145702)) BOUND_VARIABLE_145700))) )) ))) )))) 19.70/18.45 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 19.70/18.45 ) 19.70/18.45 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_1) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Y_1) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) X_1) Y_1)) zEven))) )))) 19.70/18.45 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.45 ) 19.70/18.45 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))))) (forall ((X $$unsorted)) (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))))) ))) 19.70/18.45 ( (zero_zero nat) ) 19.70/18.45 ( (one_one nat) ) 19.70/18.45 ) 19.70/18.45 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_145799 $$unsorted) (BOUND_VARIABLE_145800 $$unsorted)) (or (not (linorder X_a)) (= (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_145799) BOUND_VARIABLE_145800))) (or (= (ti X_a BOUND_VARIABLE_145800) (ti X_a BOUND_VARIABLE_145799)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_145800) BOUND_VARIABLE_145799))))) ))) 19.70/18.46 ( real, (zero_zero real), pi ) 19.70/18.46 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.46 ( 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))))) ) 19.70/18.46 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.46 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.46 ( real, (zero_zero real), skv_2 ) 19.70/18.46 ( real, (zero_zero real), skv_10 ) 19.70/18.46 ( real, (zero_zero real), skv_13 ) 19.70/18.46 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.46 ( real, pi, (zero_zero real) ) 19.70/18.46 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.46 ( 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)) ) 19.70/18.46 ( 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)))) ) 19.70/18.46 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.70/18.46 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.46 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 19.70/18.46 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 19.70/18.46 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.70/18.46 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.70/18.46 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 19.70/18.46 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 19.70/18.46 ( real, skv_2, (zero_zero real) ) 19.70/18.46 ( real, skv_10, (zero_zero real) ) 19.70/18.46 ( real, skv_13, (zero_zero real) ) 19.70/18.46 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.46 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 19.70/18.46 ( int, (zero_zero int), (zero_zero int) ) 19.70/18.46 ( int, (zero_zero int), (one_one int) ) 19.70/18.46 ( 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))) ) 19.70/18.46 ( int, (zero_zero int), min_1 ) 19.70/18.46 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 19.70/18.46 ( int, (zero_zero int), t ) 19.70/18.46 ( int, (one_one int), (zero_zero int) ) 19.70/18.46 ( int, (one_one int), t ) 19.70/18.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 19.70/18.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 19.70/18.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 19.70/18.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_3 ) 19.70/18.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_9 ) 19.70/18.46 ( int, min_1, (zero_zero int) ) 19.70/18.46 ( int, min_1, min_1 ) 19.70/18.46 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.70/18.46 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 19.70/18.46 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 19.70/18.46 ( int, t, (zero_zero int) ) 19.70/18.46 ( int, t, (one_one int) ) 19.70/18.46 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.70/18.46 ( 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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 19.70/18.46 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.70/18.46 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.70/18.46 ) 19.70/18.46 (instantiation (let ((_let_0 (max X_a))) (forall ((X_a $$unsorted)) (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))) )) 19.70/18.46 ( bool ) 19.70/18.46 ( real ) 19.70/18.46 ( nat ) 19.70/18.46 ( (fun nat bool) ) 19.70/18.46 ( int ) 19.70/18.46 ( (fun int bool) ) 19.70/18.46 ( (fun real bool) ) 19.70/18.46 ( (fun real real) ) 19.70/18.46 ( complex ) 19.70/18.46 ( (fun nat real) ) 19.70/18.46 ( (fun int int) ) 19.70/18.46 ( rat ) 19.70/18.46 ( (fun int (fun int bool)) ) 19.70/18.46 ( quickcheck_code_int ) 19.70/18.46 ( (product_prod real real) ) 19.70/18.46 ( (product_prod int int) ) 19.70/18.46 ( (filter real) ) 19.70/18.46 ( (filter nat) ) 19.70/18.46 ( (product_prod nat nat) ) 19.70/18.46 ( (fun (product_prod int int) bool) ) 19.70/18.46 ( code_code_numeral ) 19.70/18.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 19.70/18.46 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 19.70/18.46 ( (fun nat rat) ) 19.70/18.46 ( (fun (product_prod int int) int) ) 19.70/18.46 ( (fun int (fun int (fun int bool))) ) 19.70/18.46 ( (fun int real) ) 19.70/18.46 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 19.70/18.46 ) 19.70/18.46 (instantiation (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_145930))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_145930 $$unsorted) (BOUND_VARIABLE_145931 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP nat X_a _let_0 (hAPP nat nat suc BOUND_VARIABLE_145931)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_145931)) BOUND_VARIABLE_145930))) )) 19.70/18.46 ( int, s, (hAPP nat nat suc (zero_zero nat)) ) 19.70/18.46 ( int, s1, (hAPP nat nat suc (zero_zero nat)) ) 19.70/18.46 ( int, skv_8, (hAPP nat nat suc (zero_zero nat)) ) 19.70/18.46 ( complex, ii, (hAPP nat nat suc (zero_zero nat)) ) 19.70/18.46 ) 19.70/18.46 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_145976 $$unsorted) (BOUND_VARIABLE_145977 $$unsorted)) (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_145977))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_145977) (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_145977) (hAPP nat nat suc BOUND_VARIABLE_145976))) BOUND_VARIABLE_145977))) ))) 19.70/18.46 ( int, (hAPP nat nat suc (zero_zero nat)), s ) 19.70/18.46 ( int, (hAPP nat nat suc (zero_zero nat)), s1 ) 19.70/18.46 ( int, (hAPP nat nat suc (zero_zero nat)), skv_8 ) 19.70/18.46 ( complex, (hAPP nat nat suc (zero_zero nat)), ii ) 19.70/18.46 ) 19.70/18.46 (instantiation (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_146020 $$unsorted) (BOUND_VARIABLE_146021 $$unsorted)) (or (not (metric_space X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_146020) BOUND_VARIABLE_146021) sequentially))) (hBOOL (hAPP _let_1 bool (cauchy X_a) BOUND_VARIABLE_146020))) ))) 19.70/18.46 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 19.70/18.46 ) 19.70/18.46 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (hAPP real _let_0 _let_1 I_1))) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (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))) )))) 19.70/18.46 ( 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))) ) 19.70/18.46 ( (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)))) ) 19.70/18.46 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), skv_14 ) 19.70/18.46 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.70/18.46 ) 19.70/18.46 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (ord_less real))) (let ((_let_4 (hAPP real _let_0 _let_3 A_2))) (let ((_let_5 (hAPP real _let_0 _let_1 A_2))) (forall ((X_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_4 B_1))) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_5 X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) B_1))) (hBOOL (hAPP real bool (hAPP _let_2 _let_0 (isCont real real) F) X_2))) )) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_4 X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_3 X_2) B_1))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (deriv real) F) X_2) (zero_zero real)))) )) (not (hBOOL (hAPP real bool _let_5 X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) B_1))) (= (hAPP real real F X_1) (hAPP real real F A_2))) ))))))) 19.70/18.46 ( (zero_zero real), (sgn_sgn real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.70/18.46 ( (one_one real), (uminus_uminus real), (zero_zero real), skv_13 ) 19.70/18.46 ( pi, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), pi, (zero_zero real) ) 19.70/18.46 ( pi, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP 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 ) 19.70/18.46 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), sqrt, (zero_zero real), skv_2 ) 19.70/18.46 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), cos, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 19.70/18.46 ( (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 real real (hAPP real (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))) ) 19.70/18.46 ( (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))))), (zero_zero real), pi ) 19.70/18.46 ( (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)))), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.46 ( (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), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.46 ( (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))))), cos, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.46 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), sqrt, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.46 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))), cos, pi, (zero_zero real) ) 19.70/18.47 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))), sin, (zero_zero real), skv_10 ) 19.70/18.47 ) 19.70/18.47 (instantiation (let ((_let_0 (sgn_sgn int))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (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)))) )) 19.70/18.47 ( (zero_zero int), (one_one int) ) 19.70/18.47 ( (one_one int), (one_one int) ) 19.70/18.47 ) 19.70/18.47 (instantiation (let ((_let_0 (fun nat X_a))) (let ((_let_1 (power_power X_a))) (let ((_let_2 (inverse_inverse X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_146103 $$unsorted) (BOUND_VARIABLE_146104 $$unsorted)) (or (not (divisi14063676e_zero X_a)) (= (hAPP X_a X_a _let_2 (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146103) BOUND_VARIABLE_146104)) (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_146103)) BOUND_VARIABLE_146104))) )))) 19.70/18.47 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.47 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.47 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.47 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.47 ) 19.70/18.47 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_146140 $$unsorted) (BOUND_VARIABLE_146141 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146140) BOUND_VARIABLE_146141) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146141) BOUND_VARIABLE_146140))) ))) 19.70/18.47 ( nat, (one_one nat), (one_one nat) ) 19.70/18.47 ( 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), (one_one int) ) 19.70/18.47 ( 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) ) 19.70/18.47 ( 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)))) ) 19.70/18.47 ( int, (hAPP nat int (hAPP 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) ) 19.70/18.47 ) 19.70/18.47 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (hAPP real _let_0 _let_1 A_2))) (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 B_1))) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) B_1))) (not (hBOOL (hAPP real bool _let_2 X_2))) (not (forall ((Y_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) Y_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X_2) Y_2)))) ))) )) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real F A_2)) (hAPP real real F B_1)))) )))) 19.70/18.47 ( sqrt, (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.47 ( cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 19.70/18.47 ) 19.70/18.47 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (fun int int))) (let ((_let_4 (ord_less int))) (let ((_let_5 (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 _let_2) B_8)))) (forall ((A_9 $$unsorted) (B_8 $$unsorted) (Y $$unsorted) (R_6 $$unsorted)) (or (not (= (ti int A_9) (hAPP int int (hAPP int _let_3 (plus_plus int) (hAPP int int (hAPP int _let_3 (times_times int) B_8) Y)) R_6))) (and (not _let_5) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 R_6) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 B_8) R_6))))) (and _let_5 (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 R_6) B_8))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) R_6))))) (= _let_2 (ti int B_8)) (= (hAPP int int (hAPP int _let_3 (div_div int) A_9) B_8) (ti int Y))) ))))))) 19.70/18.47 ( min_1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, (one_one int) ) 19.70/18.47 ) 19.70/18.47 (instantiation (let ((_let_0 (uminus_uminus X_a))) (forall ((X_a $$unsorted)) (or (not (uminus X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 19.70/18.47 ( bool ) 19.70/18.47 ( real ) 19.70/18.47 ( nat ) 19.70/18.47 ( (fun nat bool) ) 19.70/18.47 ( int ) 19.70/18.47 ( (fun int bool) ) 19.70/18.47 ( (fun real bool) ) 19.70/18.47 ( (fun real real) ) 19.70/18.47 ( complex ) 19.70/18.47 ( (fun nat real) ) 19.70/18.47 ( (fun int int) ) 19.70/18.47 ( rat ) 19.70/18.47 ( (fun int (fun int bool)) ) 19.70/18.47 ( (product_prod int int) ) 19.70/18.47 ( (fun (product_prod int int) bool) ) 19.70/18.47 ( code_code_numeral ) 19.70/18.47 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 19.70/18.47 ( (fun (product_prod int int) int) ) 19.70/18.47 ( (fun int (fun int (fun int bool))) ) 19.70/18.47 ( (fun int real) ) 19.70/18.47 ) 19.70/18.47 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_146306 $$unsorted) (BOUND_VARIABLE_146307 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_146306)) BOUND_VARIABLE_146307))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_146306)) BOUND_VARIABLE_146307))) ))) 19.70/18.47 ( int, pls, (one_one int) ) 19.70/18.47 ( int, pls, min_1 ) 19.70/18.47 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.47 ( int, pls, s ) 19.70/18.47 ( int, pls, (hAPP int int (number_number_of int) pls) ) 19.70/18.47 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.70/18.47 ( int, pls, skv_3 ) 19.70/18.47 ( int, pls, skv_9 ) 19.70/18.47 ( int, (one_one int), pls ) 19.70/18.47 ( int, (one_one int), min_1 ) 19.70/18.47 ) 19.70/18.47 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_146330 $$unsorted) (BOUND_VARIABLE_146331 $$unsorted)) (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_146330) BOUND_VARIABLE_146331)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_146330)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_146331)))) )))) 19.70/18.47 ( nat, (one_one nat), (one_one nat) ) 19.70/18.47 ( 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), (one_one int) ) 19.70/18.47 ( int, (hAPP nat int (hAPP 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) ) 19.70/18.47 ) 19.70/18.47 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_146390 $$unsorted) (BOUND_VARIABLE_146391 $$unsorted)) (or (not (ring_1 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_146391) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_146391) BOUND_VARIABLE_146390)) _let_3))) ))))) 19.70/18.47 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 19.70/18.47 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 19.70/18.47 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 19.70/18.47 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 19.70/18.47 ) 19.70/18.47 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_146465 $$unsorted) (BOUND_VARIABLE_146466 $$unsorted)) (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_146465)) BOUND_VARIABLE_146466))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_146466)) BOUND_VARIABLE_146465))) )))) 19.70/18.47 ( int, pls, (one_one int) ) 19.70/18.47 ( int, pls, min_1 ) 19.70/18.47 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.47 ( int, pls, s ) 19.70/18.47 ( int, pls, (hAPP int int (number_number_of int) pls) ) 19.70/18.47 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.70/18.47 ( int, pls, skv_3 ) 19.70/18.47 ( int, pls, skv_9 ) 19.70/18.47 ( int, (one_one int), pls ) 19.70/18.47 ( int, (one_one int), min_1 ) 19.70/18.47 ( int, min_1, pls ) 19.70/18.47 ( int, min_1, (one_one int) ) 19.70/18.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), pls ) 19.70/18.47 ( int, s, pls ) 19.70/18.47 ( int, (hAPP int int (number_number_of int) pls), pls ) 19.70/18.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), pls ) 19.70/18.47 ( int, skv_3, pls ) 19.70/18.47 ( int, skv_9, pls ) 19.70/18.47 ) 19.70/18.47 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X))) (= X (hAPP real real (exp real) (hAPP real real ln X)))) ) 19.70/18.47 ( (one_one real) ) 19.70/18.47 ( pi ) 19.70/18.47 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.47 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.47 ( skv_2 ) 19.70/18.47 ( skv_10 ) 19.70/18.47 ( skv_13 ) 19.70/18.47 ) 19.70/18.47 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (let ((_let_3 (filter X_a))) (let ((_let_4 (fun _let_3 bool))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_146539 $$unsorted) (BOUND_VARIABLE_146540 $$unsorted) (BOUND_VARIABLE_146541 $$unsorted) (BOUND_VARIABLE_146542 $$unsorted)) (or (not (real_normed_vector X_b)) (not (real_normed_vector X_a)) (not (hBOOL (hAPP _let_3 bool (hAPP X_b _let_4 (hAPP (fun X_a X_b) (fun X_b _let_4) (tendsto X_a X_b) BOUND_VARIABLE_146540) BOUND_VARIABLE_146541) (hAPP X_a _let_3 (at X_a) BOUND_VARIABLE_146542)))) (not (hBOOL (hAPP real bool _let_2 BOUND_VARIABLE_146539))) (not (forall ((S_1 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 S_1))) (not (forall ((X_2 $$unsorted)) (or (= (ti X_a X_2) (ti X_a BOUND_VARIABLE_146542)) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (norm_norm X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) X_2) BOUND_VARIABLE_146542))) S_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_b real (norm_norm X_b) (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (minus_minus X_b) (hAPP X_a X_b BOUND_VARIABLE_146540 X_2)) BOUND_VARIABLE_146541))) BOUND_VARIABLE_146539))) ))) ))) )))))) 19.70/18.47 ( real, real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.47 ) 19.70/18.47 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_146589 $$unsorted) (BOUND_VARIABLE_146590 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146590) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_2) BOUND_VARIABLE_146589))) (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_146590) BOUND_VARIABLE_146589)) _let_2))) )))) 19.70/18.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 19.70/18.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.70/18.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.70/18.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 19.70/18.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 19.70/18.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 19.70/18.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 19.70/18.47 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 19.70/18.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 19.70/18.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (one_one real) ) 19.70/18.47 ) 19.70/18.47 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP nat _let_1 root N_1))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (hBOOL (hAPP nat bool (even_odd_even nat) N_1)) (= (zero_zero real) X_1) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) _let_2) X_1) (hAPP real real (inverse_inverse real) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP nat real (real_1 nat) N_1)) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real _let_2 X_1)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N_1) (hAPP nat nat suc (zero_zero nat))))))))) )))) 19.70/18.47 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.47 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.47 ( (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))) ) 19.70/18.47 ( (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))) ) 19.70/18.47 ) 19.70/18.47 (instantiation (forall ((Ma $$unsorted) (Z $$unsorted)) (= (and (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Z)) (= Ma (hAPP int nat nat_1 Z))) (= (hAPP nat int (semiring_1_of_nat int) Ma) (ti int Z))) ) 19.70/18.47 ( (zero_zero nat), min_1 ) 19.70/18.47 ( (hAPP nat nat suc (zero_zero nat)), (hAPP int int (number_number_of int) pls) ) 19.70/18.47 ( (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))) ) 19.70/18.47 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), s ) 19.70/18.47 ) 19.70/18.47 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (inverse_inverse X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_146823 $$unsorted) (BOUND_VARIABLE_146824 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146823) BOUND_VARIABLE_146824))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_146823))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_146824)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_146823)))) )))) 19.70/18.47 ( real, (zero_zero real), pi ) 19.70/18.47 ( 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)))) ) 19.70/18.47 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.47 ( real, (zero_zero real), skv_6 ) 19.70/18.47 ( real, (zero_zero real), skv_11 ) 19.70/18.47 ( real, (zero_zero real), skv_12 ) 19.70/18.47 ( real, (zero_zero real), skv_14 ) 19.70/18.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.70/18.47 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.48 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.70/18.48 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.48 ( int, (zero_zero int), (one_one int) ) 19.70/18.48 ( int, (zero_zero int), min_1 ) 19.70/18.48 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.48 ( int, (zero_zero int), s ) 19.70/18.48 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 19.70/18.48 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.70/18.48 ( int, (zero_zero int), skv_3 ) 19.70/18.48 ( int, (zero_zero int), skv_9 ) 19.70/18.48 ( int, (one_one int), t ) 19.70/18.48 ( int, min_1, pls ) 19.70/18.48 ( int, min_1, min_1 ) 19.70/18.48 ) 19.70/18.48 (instantiation (let ((_let_0 (exp X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_146853 $$unsorted)) (or (not (real_normed_field X_a)) (not (banach X_a)) (= (hAPP X_a X_a _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_146853)) (hAPP X_a X_a (inverse_inverse X_a) (hAPP X_a X_a _let_0 BOUND_VARIABLE_146853)))) )) 19.70/18.48 ( real, (one_one real) ) 19.70/18.48 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.48 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 19.70/18.48 ( int, pls ) 19.70/18.48 ( int, (one_one int) ) 19.70/18.48 ( int, min_1 ) 19.70/18.48 ( complex, ii ) 19.70/18.48 ( complex, (one_one complex) ) 19.70/18.48 ) 19.70/18.48 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_146876 $$unsorted) (BOUND_VARIABLE_146877 $$unsorted)) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146877) BOUND_VARIABLE_146876)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_146876)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_146877))))) )))) 19.70/18.48 ( real, (zero_zero real), pi ) 19.70/18.48 ( 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))))) ) 19.70/18.48 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.48 ( real, pi, (zero_zero real) ) 19.70/18.48 ( 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)) ) 19.70/18.48 ( 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)))) ) 19.70/18.48 ( 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)))), (zero_zero real) ) 19.70/18.48 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 19.70/18.48 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.70/18.48 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 19.70/18.48 ( real, skv_2, (zero_zero real) ) 19.70/18.48 ( real, skv_10, (zero_zero real) ) 19.70/18.48 ( real, skv_13, (zero_zero real) ) 19.70/18.48 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 19.70/18.48 ( int, (zero_zero int), (zero_zero int) ) 19.70/18.48 ( int, (zero_zero int), min_1 ) 19.70/18.48 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 19.70/18.48 ( int, (zero_zero int), t ) 19.70/18.48 ( int, pls, pls ) 19.70/18.48 ( int, pls, (one_one int) ) 19.70/18.48 ( int, (one_one int), (zero_zero int) ) 19.70/18.48 ( int, (one_one int), pls ) 19.70/18.48 ( int, (one_one int), (one_one int) ) 19.70/18.48 ( int, (one_one int), t ) 19.70/18.48 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 19.70/18.48 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 19.70/18.48 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 19.70/18.48 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_3 ) 19.70/18.48 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_9 ) 19.70/18.48 ( int, min_1, (zero_zero int) ) 19.70/18.48 ( int, min_1, min_1 ) 19.70/18.48 ( 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) (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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 19.70/18.48 ) 19.70/18.48 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_146917 $$unsorted) (BOUND_VARIABLE_146918 $$unsorted)) (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_146917)) BOUND_VARIABLE_146918)) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146917) BOUND_VARIABLE_146918)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_146917)) BOUND_VARIABLE_146918))))) ))) 19.70/18.48 ( real, (zero_zero real), pi ) 19.70/18.48 ( 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)))) ) 19.70/18.48 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.48 ( real, (zero_zero real), skv_6 ) 19.70/18.48 ( real, (zero_zero real), skv_11 ) 19.70/18.48 ( real, (zero_zero real), skv_12 ) 19.70/18.48 ( real, (zero_zero real), skv_14 ) 19.70/18.48 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.70/18.48 ( 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))) ) 19.70/18.48 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.70/18.48 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.48 ( int, (zero_zero int), (one_one int) ) 19.70/18.48 ( int, (zero_zero int), min_1 ) 19.70/18.48 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.48 ( int, (zero_zero int), s ) 19.70/18.48 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 19.70/18.48 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.70/18.48 ( int, (zero_zero int), skv_3 ) 19.70/18.48 ( int, (zero_zero int), skv_9 ) 19.70/18.48 ( int, pls, (one_one int) ) 19.70/18.48 ( int, pls, min_1 ) 19.70/18.48 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.48 ( int, pls, s ) 19.70/18.48 ( int, pls, (hAPP int int (number_number_of int) pls) ) 19.70/18.48 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.70/18.48 ( int, pls, skv_3 ) 19.70/18.48 ( int, pls, skv_9 ) 19.70/18.48 ( int, (one_one int), pls ) 19.70/18.48 ( int, (one_one int), min_1 ) 19.70/18.48 ( int, (one_one int), t ) 19.70/18.48 ( int, min_1, pls ) 19.70/18.48 ( int, min_1, min_1 ) 19.70/18.48 ) 19.70/18.48 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int (fun int int) standardRes Ma))) (forall ((X1_2 $$unsorted) (X2_2 $$unsorted) (Ma $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) Ma))) (= (= (hAPP int int _let_1 X1_2) (hAPP int int _let_1 X2_2)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong X1_2) X2_2) Ma)))) ))) 19.70/18.48 ( (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)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.70/18.48 ( (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)))), (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))) ) 19.70/18.48 ( 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))) ) 19.70/18.48 ( s1, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.70/18.48 ( s1, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.70/18.48 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.70/18.48 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.70/18.48 ) 19.70/18.48 (instantiation (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_146961)))) (let ((_let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146961) _let_2)))) (let ((_let_7 (hAPP X_a _let_0 _let_3 BOUND_VARIABLE_146959))) (let ((_let_8 (hAPP X_a X_a (hAPP X_a _let_4 (times_times X_a) BOUND_VARIABLE_146959) BOUND_VARIABLE_146961))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_146959 $$unsorted) (BOUND_VARIABLE_146960 $$unsorted) (BOUND_VARIABLE_146961 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (= (and (or _let_5 (and (or _let_6 (hBOOL (hAPP X_a bool _let_7 _let_2))) (or (not _let_6) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 BOUND_VARIABLE_146960) _let_8))))) (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 _let_8) BOUND_VARIABLE_146960)))) (hBOOL (hAPP X_a bool _let_7 (hAPP X_a X_a (hAPP X_a _let_4 (inverse_divide X_a) BOUND_VARIABLE_146960) BOUND_VARIABLE_146961))))) )))))))))) 19.70/18.48 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.48 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 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real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.70/18.48 ) 19.70/18.48 (instantiation (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (= (hAPP int quickcheck_code_int quickcheck_of_int Ma) (hAPP int quickcheck_code_int quickcheck_of_int N_1)) (= (ti int N_1) (ti int Ma))) ) 19.70/18.48 ( (zero_zero int), (one_one int) ) 19.70/18.48 ( (hAPP int int bit1 pls), (zero_zero int) ) 19.70/18.48 ( (one_one int), (zero_zero int) ) 19.70/18.48 ( (one_one int), (hAPP int int bit1 pls) ) 19.70/18.48 ( (one_one int), (one_one int) ) 19.70/18.48 ) 19.70/18.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147011 $$unsorted)) (or (not (linordered_idom X_a)) (= (= (one_one X_a) (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_147011)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_147011)))) ) 19.70/18.48 ( real, (zero_zero real) ) 19.70/18.48 ( real, pi ) 19.70/18.48 ( 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)))) ) 19.70/18.48 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.70/18.48 ( real, skv_2 ) 19.70/18.48 ( real, skv_10 ) 19.70/18.48 ( real, skv_13 ) 19.70/18.48 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.70/18.48 ( int, (zero_zero int) ) 19.70/18.48 ( int, (one_one int) ) 19.70/18.48 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.70/18.48 ( int, min_1 ) 19.70/18.48 ( rat, (zero_zero rat) ) 19.70/18.48 ) 19.70/18.48 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (dvd_dvd nat))) (let ((_let_4 (fun _let_0 _let_0))) (let ((_let_5 (fun nat _let_1))) (let ((_let_6 (fun _let_0 _let_5))) (let ((_let_7 (fun _let_2 _let_2))) (let ((_let_8 (fun nat _let_4))) (let ((_let_9 (fun nat _let_5))) (let ((_let_10 (fun nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_147034 $$unsorted) (BOUND_VARIABLE_147035 $$unsorted) (BOUND_VARIABLE_147036 $$unsorted)) (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_8 _let_7 (combs nat _let_0 _let_0) (hAPP _let_9 _let_8 (hAPP (fun _let_5 _let_4) (fun _let_9 _let_8) (combb _let_5 _let_4 nat) (combs nat bool bool)) (hAPP _let_2 _let_9 (hAPP _let_6 (fun _let_2 _let_9) (combb _let_0 _let_5 nat) (hAPP (fun bool _let_1) _let_6 (combb bool _let_1 nat) fconj)) _let_3))) (hAPP _let_2 _let_2 (hAPP _let_4 _let_7 (combb _let_0 _let_0 nat) (hAPP _let_1 _let_4 (combb bool bool nat) fNot)) (hAPP _let_2 _let_2 (combc nat nat bool) _let_3)))) BOUND_VARIABLE_147036))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_3 BOUND_VARIABLE_147035) BOUND_VARIABLE_147034)) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_3 BOUND_VARIABLE_147034) BOUND_VARIABLE_147035))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a BOUND_VARIABLE_147036 BOUND_VARIABLE_147034)) (hAPP nat X_a BOUND_VARIABLE_147036 BOUND_VARIABLE_147035)))) )))))))))))) 19.70/18.49 ( int, (zero_zero nat), (zero_zero nat), (semiring_1_of_nat int) ) 19.70/18.49 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)), (semiring_1_of_nat int) ) 19.70/18.49 ) 19.70/18.49 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int nat))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun int _let_3))) (forall ((P_1 $$unsorted)) (= (hAPP _let_0 _let_0 (collect nat) P_1) (hAPP _let_1 _let_0 (hAPP _let_2 (fun _let_1 _let_0) (image int nat) nat_1) (hAPP _let_1 _let_1 (collect int) (hAPP _let_1 _let_1 (hAPP _let_4 (fun _let_1 _let_1) (combs int bool bool) (hAPP _let_1 _let_4 (hAPP (fun bool _let_3) (fun _let_1 _let_4) (combb bool _let_3 int) fconj) (hAPP int _let_1 (ord_less_eq int) (zero_zero int)))) (hAPP _let_2 _let_1 (hAPP _let_0 (fun _let_2 _let_1) (combb nat bool int) P_1) nat_1))))) )))))) 19.70/18.49 ( prime ) 19.70/18.49 ) 19.70/18.49 (instantiation (let ((_let_0 (fun int int))) (forall ((X_1 $$unsorted)) (= (not (forall ((Y_2 $$unsorted)) (not (= (ti int X_1) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) Y_2)) (one_one int)))) )) (not (hBOOL (hAPP int bool (even_odd_even int) X_1)))) )) 19.70/18.49 ( (zero_zero int) ) 19.70/18.49 ( (one_one int) ) 19.85/18.49 ) 19.85/18.49 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147126 $$unsorted)) (or (not (real_normed_vector X_a)) (= (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_147126)) (= (zero_zero real) (hAPP X_a real (norm_norm X_a) BOUND_VARIABLE_147126)))) ) 19.85/18.49 ( bool, fFalse ) 19.85/18.49 ( bool, fTrue ) 19.85/18.49 ( real, pi ) 19.85/18.49 ( (fun nat bool), (even_odd_even nat) ) 19.85/18.49 ( (fun nat bool), prime ) 19.85/18.49 ( (fun nat nat), suc ) 19.85/18.49 ( (fun nat nat), (fact_fact nat) ) 19.85/18.49 ( (fun nat nat), (size_size nat) ) 19.85/18.49 ( (fun nat nat), fact ) 19.85/18.49 ( (fun nat nat), nat_size ) 19.85/18.49 ( int, pls ) 19.85/18.49 ( int, m ) 19.85/18.49 ( int, min_1 ) 19.85/18.49 ( int, s ) 19.85/18.49 ( int, s1 ) 19.85/18.49 ( int, t ) 19.85/18.49 ( (fun int bool), zprime ) 19.85/18.49 ( (fun int bool), nat_neg ) 19.85/18.49 ( (fun int bool), zEven ) 19.85/18.49 ( (fun int bool), nat_is_nat ) 19.85/18.49 ( (fun int bool), zOdd ) 19.85/18.49 ( (fun int bool), (even_odd_even int) ) 19.85/18.49 ( (fun int bool), twoSqu1091635170sum2sq ) 19.85/18.49 ( (fun int nat), nat_1 ) 19.85/18.49 ( (fun int nat), phi ) 19.85/18.49 ( (fun real real), sqrt ) 19.85/18.49 ( (fun real real), tan ) 19.85/18.49 ( (fun real real), cos ) 19.85/18.49 ( (fun real real), arccos ) 19.85/18.49 ( (fun real real), ln ) 19.85/18.49 ( (fun real real), sin ) 19.85/18.49 ( (fun real real), arctan ) 19.85/18.49 ( (fun real real), arcsin ) 19.85/18.49 ( complex, ii ) 19.85/18.49 ( (fun complex complex), cnj ) 19.85/18.49 ( (fun complex complex), expi ) 19.85/18.49 ( (fun nat real), (real_1 nat) ) 19.85/18.49 ( (fun nat real), cos_coeff ) 19.85/18.49 ( (fun nat real), sin_coeff ) 19.85/18.49 ( (fun int int), bit0 ) 19.85/18.49 ( (fun int int), bit1 ) 19.85/18.49 ( (fun int int), pred ) 19.85/18.49 ( (fun int int), succ ) 19.85/18.49 ( (fun int int), (fact_fact int) ) 19.85/18.49 ( (fun int int), zfact ) 19.85/18.49 ( (fun bool bool), fNot ) 19.85/18.49 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 19.85/18.49 ( (fun bool (fun bool bool)), fconj ) 19.85/18.49 ( (fun bool (fun bool bool)), fdisj ) 19.85/18.49 ( (fun bool (fun bool bool)), fimplies ) 19.85/18.49 ( (fun int (fun int bool)), sRStar ) 19.85/18.49 ( (fun int (fun int bool)), quadRes ) 19.85/18.49 ( (fun int (fun int bool)), norRRset ) 19.85/18.49 ( (fun int (fun int bool)), d22set ) 19.85/18.49 ( (fun int (fun int bool)), sr ) 19.85/18.49 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 19.85/18.49 ( (fun nat (fun nat nat)), nat_gcd ) 19.85/18.49 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 19.85/18.49 ( (fun nat (fun nat nat)), nat_lcm ) 19.85/18.49 ( (fun nat (fun real real)), root ) 19.85/18.49 ( (fun real (fun real real)), log ) 19.85/18.49 ( (fun real (fun real real)), powr ) 19.85/18.49 ( (fun nat (fun nat bool)), coprime ) 19.85/18.49 ( (fun (fun int bool) int), (the int) ) 19.85/18.49 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 19.85/18.49 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 19.85/18.49 ( (fun nat (fun nat (product_prod int int))), bezw ) 19.85/18.49 ( (fun (fun int bool) bool), nat_nat_set ) 19.85/18.49 ( (filter 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int_ge_less_than2 ) 19.85/18.49 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 19.85/18.49 ( (fun int (fun (fun int bool) bool)), rsetR ) 19.85/18.49 ( (fun int (fun (fun int bool) bool)), resSet ) 19.85/18.49 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 19.85/18.49 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 19.85/18.49 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 19.85/18.49 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 19.85/18.49 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 19.85/18.49 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 19.85/18.49 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 19.85/18.49 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 19.85/18.49 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 19.85/18.49 ( (fun int (fun int (product_prod int int))), negDivAlg ) 19.85/18.49 ( (fun int (fun int (product_prod int int))), divmod_int ) 19.85/18.49 ( (fun int (fun int (product_prod int int))), posDivAlg ) 19.85/18.49 ( (fun int (fun int (product_prod int int))), pdivmod ) 19.85/18.49 ( (fun int (fun int (product_prod int int))), norm_frac ) 19.85/18.49 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 19.85/18.49 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 19.85/18.49 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 19.85/18.49 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 19.85/18.49 ( (fun real nat), natfloor ) 19.85/18.49 ( (fun real nat), natceiling ) 19.85/18.49 ( (fun int quickcheck_code_int), quickcheck_of_int ) 19.85/18.49 ( (fun int (fun int (fun int bool))), wset ) 19.85/18.49 ( (fun int (fun int (fun int bool))), bnorRset ) 19.85/18.49 ( (fun int (fun int (fun int bool))), zcong ) 19.85/18.49 ( (fun int (fun int (fun int bool))), noXRRset ) 19.85/18.49 ( (fun int (fun int (fun int bool))), zcongm ) 19.85/18.49 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 19.85/18.49 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 19.85/18.49 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 19.85/18.49 ( (fun int real), (real_1 int) ) 19.85/18.49 ( (fun complex nat), (size_size complex) ) 19.85/18.49 ( (fun complex nat), complex_size ) 19.85/18.49 ( (fun int (list int)), quickc666637781d_zero ) 19.85/18.49 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 19.85/18.49 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 19.85/18.49 ( (fun (product_prod int int) rat), frct ) 19.85/18.49 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 19.85/18.49 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 19.85/18.49 ( (fun (fun nat rat) bool), vanishes ) 19.85/18.49 ( (fun int (fun int rat)), fract ) 19.85/18.49 ( (fun code_code_numeral int), code_int_of ) 19.85/18.49 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 19.85/18.49 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 19.85/18.49 ( (fun code_code_numeral nat), code_c271388182l_size ) 19.85/18.49 ( (fun real (fun real complex)), complex_1 ) 19.85/18.49 ( (fun real (fun real complex)), rcis ) 19.85/18.49 ( (fun int (fun nat nat)), nat_aux ) 19.85/18.49 ( (fun rat real), ratreal ) 19.85/18.49 ( (fun quickcheck_code_int int), quickcheck_int_of ) 19.85/18.49 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 19.85/18.49 ( (fun rat (product_prod int int)), quotient_of ) 19.85/18.49 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 19.85/18.49 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 19.85/18.49 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 19.85/18.49 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 19.85/18.49 ) 19.85/18.49 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (fun nat _let_3))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_147145 $$unsorted)) (or (not (banach X_a)) (not (real_normed_field X_a)) (= (hAPP _let_2 X_a (suminf X_a) (hAPP _let_2 _let_2 (hAPP _let_4 (fun _let_2 _let_2) (combs nat X_a X_a) (hAPP _let_1 _let_4 (hAPP (fun real _let_3) (fun _let_1 _let_4) (combb real _let_3 nat) (scaleR_scaleR X_a)) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) (fact_fact nat))))) (hAPP X_a _let_2 (power_power X_a) BOUND_VARIABLE_147145))) (hAPP X_a X_a (exp X_a) BOUND_VARIABLE_147145))) )))))) 19.85/18.49 ( real, (hAPP int real (number_number_of real) min_1) ) 19.85/18.49 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.85/18.49 ( int, s ) 19.85/18.49 ( int, s1 ) 19.85/18.49 ( int, skv_8 ) 19.85/18.49 ( complex, ii ) 19.85/18.49 ) 19.85/18.49 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_147169 $$unsorted) (BOUND_VARIABLE_147170 $$unsorted) (BOUND_VARIABLE_147171 $$unsorted)) (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_147171))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_147169) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_147170) BOUND_VARIABLE_147171)))) (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_147169) BOUND_VARIABLE_147171)) BOUND_VARIABLE_147170))) )))) 19.85/18.49 ( real, (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.85/18.49 ( 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))) ) 19.85/18.49 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.85/18.49 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 19.85/18.49 ) 19.85/18.49 (instantiation (forall ((K_4 $$unsorted)) (= (ti int K_4) (hAPP int int (hAPP int (fun int int) (plus_plus int) K_4) pls)) ) 19.85/18.49 ( pls ) 19.85/18.49 ( m ) 19.85/18.49 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 19.85/18.49 ( min_1 ) 19.85/18.49 ( s ) 19.85/18.49 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.85/18.49 ( s1 ) 19.85/18.49 ( t ) 19.85/18.49 ) 19.85/18.49 (instantiation (forall ((X_a $$unsorted)) (or (not (number_semiring X_a)) (= (hAPP int X_a (number_number_of X_a) pls) (zero_zero X_a))) ) 19.85/18.49 ( real ) 19.85/18.49 ( nat ) 19.85/18.49 ( int ) 19.85/18.49 ( complex ) 19.85/18.49 ( rat ) 19.85/18.49 ( quickcheck_code_int ) 19.85/18.49 ( code_code_numeral ) 19.85/18.49 ) 19.85/18.49 (instantiation (forall ((N $$unsorted)) (= (hAPP real int (archimedean_ceiling real) (hAPP nat real (real_1 nat) N)) (hAPP nat int (semiring_1_of_nat int) N)) ) 19.85/18.49 ( (zero_zero nat) ) 19.85/18.49 ( (hAPP nat nat suc (zero_zero nat)) ) 19.85/18.49 ( (one_one nat) ) 19.85/18.49 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.85/18.49 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.85/18.49 ) 19.85/18.49 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP int int (uminus_uminus int) A_1) (hAPP int int (hAPP int (fun int int) (div_div int) A_1) (hAPP int int (number_number_of int) min_1))) ) 19.85/18.49 ( pls ) 19.85/18.49 ( (one_one int) ) 19.85/18.49 ( min_1 ) 19.85/18.49 ) 19.85/18.49 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted)) (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)))) )) 19.85/18.49 ( real ) 19.85/18.49 ( nat ) 19.85/18.49 ( int ) 19.85/18.49 ( complex ) 19.85/18.49 ( rat ) 19.85/18.49 ( quickcheck_code_int ) 19.85/18.49 ( code_code_numeral ) 19.85/18.49 ) 19.85/18.49 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 Y))) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_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))))))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) (hAPP real real tan X_2))))) ))) )))) 19.85/18.49 ( pi ) 19.85/18.49 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.85/18.49 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.85/18.49 ( skv_2 ) 19.85/18.49 ( skv_10 ) 19.85/18.49 ( skv_13 ) 19.85/18.49 ) 19.85/18.49 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (semiri532925092at_aux X_a))) (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (= _let_1 (ti (fun _let_0 (fun nat _let_0)) _let_1))) ))) 19.85/18.49 ( bool ) 19.85/18.50 ( real ) 19.85/18.50 ( nat ) 19.85/18.50 ( (fun nat bool) ) 19.85/18.50 ( int ) 19.85/18.50 ( (fun int bool) ) 19.85/18.50 ( (fun real bool) ) 19.85/18.50 ( (fun real real) ) 19.85/18.50 ( complex ) 19.85/18.50 ( (fun nat real) ) 19.85/18.50 ( (fun int int) ) 19.85/18.50 ( rat ) 19.85/18.50 ( (fun int (fun int bool)) ) 19.85/18.50 ( quickcheck_code_int ) 19.85/18.50 ( (product_prod int int) ) 19.85/18.50 ( (fun (product_prod int int) bool) ) 19.85/18.50 ( code_code_numeral ) 19.85/18.50 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 19.85/18.50 ( (fun (product_prod int int) int) ) 19.85/18.50 ( (fun int (fun int (fun int bool))) ) 19.85/18.50 ( (fun int real) ) 19.85/18.50 ) 19.85/18.50 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (hAPP int _let_0 _let_1 (zero_zero int)))) (forall ((B $$unsorted) (M $$unsorted) (A_1 $$unsorted)) (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)))) )))) 19.85/18.50 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.85/18.50 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.85/18.50 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.85/18.50 ( 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 ) 19.85/18.50 ( (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)))) ) 19.85/18.50 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s1 ) 19.85/18.50 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 19.85/18.50 ) 19.85/18.50 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((X $$unsorted) (Y $$unsorted)) (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)))) ))) 19.85/18.50 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.85/18.50 ) 19.85/18.50 (instantiation (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_147438 $$unsorted)) (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_147438) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_147438)))) ))) 19.85/18.50 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.85/18.50 ) 19.85/18.50 (instantiation (let ((_let_0 (inverse_inverse real))) (let ((_let_1 (hAPP nat (fun real real) root N))) (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))) (= (hAPP real real _let_0 (hAPP real real _let_1 X)) (hAPP real real _let_1 (hAPP real real _let_0 X)))) ))) 19.85/18.50 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.85/18.50 ) 19.85/18.50 (instantiation (let ((_let_0 (semiring_1_of_nat int))) (forall ((X $$unsorted) (Y $$unsorted)) (= (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))) )) 19.85/18.50 ( (one_one nat), (one_one nat) ) 19.85/18.50 ) 19.85/18.50 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (uminus T_1)) (uminus (fun T_2 T_1))) ) 19.85/18.50 ( bool, bool ) 19.85/18.50 ( bool, (fun bool bool) ) 19.85/18.50 ( real, bool ) 19.85/18.50 ( real, real ) 19.85/18.50 ( real, nat ) 19.85/18.50 ( real, (fun int bool) ) 19.85/18.50 ( real, (fun real bool) ) 19.85/18.50 ( real, (fun real real) ) 19.85/18.50 ( real, complex ) 19.85/18.50 ( real, (fun nat real) ) 19.85/18.50 ( real, (fun bool bool) ) 19.85/18.50 ( real, (fun int (fun int bool)) ) 19.85/18.50 ( real, (fun (filter real) bool) ) 19.85/18.50 ( real, (fun (filter nat) bool) ) 19.85/18.50 ( real, (fun real complex) ) 19.85/18.50 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 19.85/18.50 ( real, (fun nat (product_prod real real)) ) 19.87/18.50 ( real, (fun real (fun nat (product_prod real real))) ) 19.87/18.50 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 19.87/18.50 ( real, (fun int (fun int (fun bool bool))) ) 19.87/18.50 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 19.87/18.50 ( real, (fun (fun int real) (fun int bool)) ) 19.87/18.50 ( real, (fun int (fun nat bool)) ) 19.87/18.50 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 19.87/18.50 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 19.87/18.50 ( real, (fun int (fun nat (fun bool bool))) ) 19.87/18.50 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 19.87/18.50 ( real, (fun (fun nat real) (fun nat bool)) ) 19.87/18.50 ( nat, bool ) 19.87/18.50 ( nat, real ) 19.87/18.50 ( nat, nat ) 19.87/18.50 ( nat, (fun nat bool) ) 19.87/18.50 ( nat, (fun nat nat) ) 19.87/18.50 ( nat, int ) 19.87/18.50 ( nat, (fun real real) ) 19.87/18.50 ( nat, complex ) 19.87/18.50 ( nat, (fun int int) ) 19.87/18.50 ( nat, rat ) 19.87/18.50 ( nat, (fun bool bool) ) 19.87/18.50 ( nat, (fun nat (fun nat bool)) ) 19.87/18.50 ( nat, (product_prod real real) ) 19.87/18.50 ( nat, (product_prod int int) ) 19.87/18.50 ( nat, (fun nat (product_prod int int)) ) 19.87/18.50 ( nat, (product_prod nat nat) ) 19.87/18.50 ( nat, (fun (product_prod nat nat) bool) ) 19.87/18.50 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 19.87/18.50 ( nat, (fun nat (product_prod nat nat)) ) 19.87/18.50 ( (fun nat bool), bool ) 19.87/18.50 ( (fun nat bool), (fun nat bool) ) 19.87/18.50 ( (fun nat bool), (fun nat (fun bool bool)) ) 19.87/18.50 ( (fun nat bool), (fun int (fun nat bool)) ) 19.87/18.50 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 19.87/18.50 ( (fun nat nat), (fun nat real) ) 19.87/18.50 ( (fun nat nat), (fun nat (fun nat nat)) ) 19.87/18.50 ( (fun nat nat), (fun nat (fun nat bool)) ) 19.87/18.50 ( int, bool ) 19.87/18.50 ( int, real ) 19.87/18.50 ( int, nat ) 19.87/18.50 ( int, (fun nat bool) ) 19.87/18.50 ( int, (fun nat nat) ) 19.87/18.50 ( int, int ) 19.87/18.50 ( int, (fun int bool) ) 19.87/18.50 ( int, (fun nat int) ) 19.87/18.50 ( int, (fun real real) ) 19.87/18.50 ( int, (fun nat real) ) 19.87/18.50 ( int, (fun int int) ) 19.87/18.50 ( int, rat ) 19.87/18.50 ( int, (fun int rat) ) 19.87/18.50 ( int, (fun bool bool) ) 19.87/18.50 ( int, (fun int (fun bool bool)) ) 19.87/18.50 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 19.87/18.50 ( int, (fun int (fun int bool)) ) 19.87/18.50 ( int, quickcheck_code_int ) 19.87/18.50 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 19.87/18.50 ( int, (product_prod int int) ) 19.87/18.50 ( int, (fun int (product_prod int int)) ) 19.87/18.50 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 19.87/18.50 ( int, (fun (fun int bool) bool) ) 19.87/18.50 ( int, (fun (product_prod int int) bool) ) 19.87/18.50 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 19.87/18.50 ( int, (product_prod int (product_prod int int)) ) 19.87/18.50 ( int, (fun int (product_prod int (product_prod int int))) ) 19.87/18.50 ( int, (fun (fun int int) (fun int bool)) ) 19.87/18.50 ( int, (fun int (fun (product_prod int int) bool)) ) 19.87/18.50 ( int, (fun int (fun (fun int bool) bool)) ) 19.87/18.50 ( int, (list int) ) 19.87/18.50 ( int, (fun nat (fun bool bool)) ) 19.87/18.50 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 19.87/18.50 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 19.87/18.50 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 19.87/18.50 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 19.87/18.50 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 19.87/18.50 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 19.87/18.50 ( int, (fun (product_prod int int) int) ) 19.87/18.50 ( int, (fun int (fun int (fun int bool))) ) 19.87/18.50 ( int, (fun int real) ) 19.87/18.50 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 19.87/18.50 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 19.87/18.50 ( (fun int bool), bool ) 19.87/18.50 ( (fun int bool), int ) 19.87/18.50 ( (fun int bool), (fun int bool) ) 19.87/18.50 ( (fun int bool), (fun int (fun bool bool)) ) 19.87/18.50 ( (fun int bool), (fun int (fun int bool)) ) 19.87/18.50 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 19.87/18.50 ( (fun int bool), (fun int (fun int int)) ) 19.87/18.50 ( (fun int bool), (fun real (fun int (fun int bool))) ) 19.87/18.50 ( (fun real bool), real ) 19.87/18.50 ( (fun real bool), (fun real bool) ) 19.87/18.50 ( (fun real bool), (fun real (fun bool bool)) ) 19.87/18.50 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 19.87/18.50 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 19.87/18.50 ( (fun real real), (fun real real) ) 19.87/18.50 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 19.87/18.50 ( (fun real real), (fun real (fun real real)) ) 19.87/18.50 ( (fun real real), (fun real (fun real bool)) ) 19.87/18.50 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 19.87/18.50 ( complex, real ) 19.87/18.50 ( complex, nat ) 19.87/18.50 ( complex, complex ) 19.87/18.50 ( (fun nat real), (fun nat bool) ) 19.87/18.50 ( (fun nat real), (fun nat real) ) 19.87/18.50 ( (fun nat real), (fun nat (fun real real)) ) 19.87/18.50 ( (fun nat real), (fun int (fun nat real)) ) 19.87/18.50 ( (fun int int), (fun int bool) ) 19.87/18.50 ( (fun int int), (fun int int) ) 19.87/18.50 ( (fun int int), (fun int (fun int bool)) ) 19.87/18.50 ( (fun int int), (fun int (fun int int)) ) 19.87/18.50 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 19.87/18.50 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 19.87/18.50 ( rat, real ) 19.87/18.50 ( rat, (product_prod int int) ) 19.87/18.50 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 19.87/18.50 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 19.87/18.50 ( (fun int (fun int bool)), (fun int bool) ) 19.87/18.50 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 19.87/18.50 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 19.87/18.50 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 19.87/18.50 ( quickcheck_code_int, nat ) 19.87/18.50 ( quickcheck_code_int, int ) 19.87/18.50 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 19.87/18.50 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 19.87/18.50 ( (product_prod real real), bool ) 19.87/18.50 ( (product_prod int int), bool ) 19.87/18.50 ( (product_prod int int), int ) 19.87/18.50 ( (product_prod int int), (fun int bool) ) 19.87/18.50 ( (product_prod int int), (fun int int) ) 19.87/18.50 ( (product_prod int int), rat ) 19.87/18.50 ( (product_prod int int), (fun bool bool) ) 19.87/18.50 ( (product_prod int int), (product_prod int int) ) 19.87/18.50 ( (product_prod int int), (fun (product_prod int int) bool) ) 19.87/18.50 ( (product_prod int int), (fun (product_prod int int) int) ) 19.87/18.50 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 19.87/18.50 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 19.87/18.50 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 19.87/18.50 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 19.87/18.50 ( (filter real), bool ) 19.87/18.50 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 19.87/18.50 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 19.87/18.50 ( (filter nat), bool ) 19.87/18.50 ( (product_prod nat nat), bool ) 19.87/18.50 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 19.87/18.50 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 19.87/18.50 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 19.87/18.50 ( code_code_numeral, nat ) 19.87/18.50 ( code_code_numeral, (fun nat nat) ) 19.87/18.50 ( code_code_numeral, int ) 19.87/18.50 ( code_code_numeral, code_code_numeral ) 19.87/18.50 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 19.87/18.50 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 19.87/18.50 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 19.87/18.50 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 19.87/18.50 ( (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))) ) 19.87/18.50 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 19.87/18.50 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 19.87/18.50 ( (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))) ) 19.87/18.50 ( (fun nat rat), bool ) 19.87/18.50 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 19.87/18.50 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 19.87/18.50 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 19.87/18.50 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 19.87/18.50 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 19.87/18.50 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 19.87/18.50 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 19.87/18.50 ( (fun int real), (fun int bool) ) 19.87/18.50 ( (fun int real), (fun int real) ) 19.87/18.50 ( (fun int real), (fun int (fun int real)) ) 19.87/18.50 ( (fun int real), (fun int (fun real real)) ) 19.87/18.50 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 19.87/18.50 ( (fun real (fun int bool)), (fun real bool) ) 19.87/18.50 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 19.87/18.50 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 19.87/18.50 ( (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)))) ) 19.87/18.50 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 19.87/18.50 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 19.87/18.50 ( (fun int (fun int real)), (fun int (fun int bool)) ) 19.87/18.50 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 19.87/18.50 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 19.87/18.50 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 19.87/18.50 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 19.87/18.50 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 19.87/18.50 ( (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))) ) 19.87/18.50 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 19.88/18.51 ( (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))) ) 19.88/18.51 ( (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))) ) 19.88/18.51 ( (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)))) ) 19.88/18.51 ( (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)))) ) 19.88/18.51 ( (fun int (fun nat bool)), (fun int bool) ) 19.88/18.51 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 19.88/18.51 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 19.88/18.51 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 19.88/18.51 ( (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))) ) 19.88/18.51 ( (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)))) ) 19.88/18.51 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 19.88/18.51 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 19.88/18.51 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 19.88/18.51 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 19.88/18.51 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 19.88/18.51 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 19.88/18.51 ) 19.88/18.51 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (forall ((X $$unsorted) (Y $$unsorted)) (= (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))) ))) 19.88/18.51 ( ii, ii ) 19.88/18.51 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 19.88/18.51 ( (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 ) 19.88/18.51 ) 19.88/18.51 (instantiation (forall ((N $$unsorted)) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N) (one_one nat)) (hAPP nat nat suc N)) ) 19.88/18.51 ( (zero_zero nat) ) 19.88/18.51 ( (hAPP nat nat suc (zero_zero nat)) ) 19.88/18.51 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 19.88/18.51 ( (one_one nat) ) 19.88/18.51 ) 19.88/18.51 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147520 $$unsorted)) (or (not (sgn_div_norm X_a)) (= (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) (hAPP real real (inverse_inverse real) (hAPP X_a real (norm_norm X_a) BOUND_VARIABLE_147520))) BOUND_VARIABLE_147520) (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_147520))) ) 19.88/18.51 ( real, (zero_zero real) ) 19.88/18.51 ( rat, (zero_zero rat) ) 19.88/18.51 ) 19.88/18.51 (instantiation (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hilbert_Eps _let_0))) (let ((_let_3 (fun X_b bool))) (let ((_let_4 (fun X_a _let_3))) (let ((_let_5 (fun _let_0 X_b))) (let ((_let_6 (fun _let_0 _let_3))) (let ((_let_7 (fun _let_0 X_a))) (forall ((X_a $$unsorted) (X_b $$unsorted) (P_1 $$unsorted)) (= (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))) ))))))))) 19.88/18.51 ( 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))) ) 19.88/18.51 ( int, int, (fequal int) ) 19.88/18.51 ( int, int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun 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_5 _let_5))) (let ((_let_7 (fun _let_1 _let_5))) (let ((_let_8 (fun int _let_1))) (let ((_let_9 (fun int _let_5))) (hAPP _let_5 _let_5 (hAPP _let_4 _let_6 (combb _let_0 _let_0 int) (hAPP _let_3 _let_4 (combs int bool bool) (hAPP _let_0 _let_3 (hAPP (fun bool _let_2) (fun _let_0 _let_3) (combb bool _let_2 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int))))) (hAPP int _let_5 (hAPP _let_9 _let_9 (combc int int _let_0) (hAPP _let_9 _let_9 (hAPP _let_6 (fun _let_9 _let_9) (combb _let_5 _let_5 int) (combc int int bool)) (hAPP _let_8 _let_9 (hAPP _let_7 (fun _let_8 _let_9) (combb _let_1 _let_5 int) (hAPP _let_5 _let_7 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int))))))))))))) ) 19.88/18.51 ( (product_prod int int), (product_prod int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (product_prod int int))) (let ((_let_4 (product_snd int int))) (let ((_let_5 (fun _let_3 (fun _let_3 bool)))) (let ((_let_6 (fun _let_3 int))) (let ((_let_7 (fun _let_3 _let_2))) (let ((_let_8 (fun (fun _let_3 bool) (fun _let_3 bool)))) (let ((_let_9 (fun _let_6 (fun _let_3 bool)))) (let ((_let_10 (fun _let_3 _let_0))) (let ((_let_11 (fun _let_6 _let_10))) (let ((_let_12 (hAPP (fun int _let_0) _let_11 (combb int _let_0 _let_3) (fequal int)))) (let ((_let_13 (fun _let_3 _let_1))) (let ((_let_14 (fun _let_6 _let_6))) (let ((_let_15 (fun _let_3 _let_8))) (let ((_let_16 (fun _let_5 _let_5))) (let ((_let_17 (hAPP (fun _let_3 bool) _let_7 (hAPP (fun bool _let_2) (fun (fun _let_3 bool) _let_7) (combb bool _let_2 _let_3) fconj) (hAPP (fun _let_3 bool) (fun _let_3 bool) (hAPP _let_2 _let_8 (combb bool bool _let_3) fNot) (hAPP int (fun _let_3 bool) (hAPP _let_10 (fun int (fun _let_3 bool)) (combc _let_3 int bool) (hAPP _let_6 _let_10 _let_12 _let_4)) (zero_zero int)))))) (let ((_let_18 (fun _let_3 _let_6))) (let ((_let_19 (fun _let_3 _let_9))) (let ((_let_20 (fun _let_3 _let_10))) (let ((_let_21 (fun _let_3 _let_14))) (let ((_let_22 (fun _let_6 _let_18))) (let ((_let_23 (hAPP _let_6 _let_13 (hAPP (fun int _let_1) (fun _let_6 _let_13) (combb int _let_1 _let_3) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_6))) (hAPP _let_5 _let_5 (hAPP _let_15 _let_16 (combs _let_3 (fun _let_3 bool) (fun _let_3 bool)) (hAPP _let_7 _let_15 (hAPP (fun _let_2 _let_8) (fun _let_7 _let_15) (combb _let_2 _let_8 _let_3) (combb bool bool _let_3)) _let_17)) (hAPP _let_5 _let_5 (hAPP _let_8 _let_16 (combb (fun _let_3 bool) (fun _let_3 bool) _let_3) (hAPP _let_7 _let_8 (combs _let_3 bool bool) _let_17)) (hAPP _let_18 _let_5 (hAPP _let_19 (fun _let_18 _let_5) (combs _let_3 _let_6 (fun _let_3 bool)) (hAPP _let_20 _let_19 (hAPP (fun _let_10 _let_9) (fun _let_20 _let_19) (combb _let_10 _let_9 _let_3) (combs _let_3 int bool)) (hAPP _let_18 _let_20 (hAPP _let_11 (fun _let_18 _let_20) (combb _let_6 _let_10 _let_3) _let_12) (hAPP _let_6 _let_18 (hAPP _let_21 _let_22 (combc _let_3 _let_6 _let_6) (hAPP _let_13 _let_21 (hAPP (fun _let_1 _let_14) (fun _let_13 _let_21) (combb _let_1 _let_14 _let_3) (combb int int _let_3)) _let_23)) _let_4)))) (hAPP _let_6 _let_18 (hAPP _let_24 _let_22 (combb int _let_6 _let_3) (hAPP _let_13 _let_24 (combc _let_3 int int) _let_23)) _let_4))))))))))))))))))))))))))))) ) 19.88/18.51 ) 19.88/18.51 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_147601 $$unsorted)) (or (not (metric_space X_a)) (not (comm_monoid_add X_a)) (= (hAPP _let_2 X_a (suminf X_a) BOUND_VARIABLE_147601) (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_147601)) (hAPP nat _let_1 (ord_atLeastLessThan nat) (zero_zero nat)))))) ))))) 19.88/18.51 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (combc nat nat nat))) (let ((_let_4 (fun nat _let_0))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun _let_1 _let_4))) (let ((_let_7 (combb real _let_0 nat))) (hAPP _let_1 _let_1 (hAPP _let_4 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_4 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 19.88/18.51 ) 19.88/18.51 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (ti X_a BOUND_VARIABLE_147624))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_147624 $$unsorted) (BOUND_VARIABLE_147625 $$unsorted)) (or (not (idom X_a)) (= (or (= (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_147625) _let_2) (= _let_2 (ti X_a BOUND_VARIABLE_147625))) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_147625) BOUND_VARIABLE_147625) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_147624) BOUND_VARIABLE_147624)))) )))) 19.88/18.51 ( real, pi, (one_one real) ) 19.88/18.51 ( int, m, min_1 ) 19.88/18.51 ( int, min_1, (one_one int) ) 19.88/18.51 ( int, s, pls ) 19.88/18.51 ( complex, ii, (one_one complex) ) 19.88/18.51 ) 19.88/18.51 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (one_one real))) (forall ((X $$unsorted)) (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) _let_3))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_2 (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_2 (plus_plus real) _let_3) X))))) ))))) 19.88/18.51 ( pi ) 19.88/18.51 ( (hAPP int real (number_number_of real) min_1) ) 19.88/18.51 ( (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)))) ) 19.88/18.51 ( (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)))) ) 19.88/18.51 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.51 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 19.88/18.51 ( skv_6 ) 19.88/18.51 ( skv_11 ) 19.88/18.51 ( skv_12 ) 19.88/18.51 ( skv_14 ) 19.88/18.51 ) 19.88/18.51 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_147686))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_147686 $$unsorted) (BOUND_VARIABLE_147687 $$unsorted)) (or (not (archim1727834104eiling X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) _let_1) (one_one X_a))) BOUND_VARIABLE_147687))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_147687) _let_1))) (= (ti int BOUND_VARIABLE_147686) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_147687))) ))) 19.88/18.51 ( real, (zero_zero int), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.51 ) 19.88/18.51 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (one_one int))) (let ((_let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_4 (fun int _let_0))) (forall ((X $$unsorted) (P_5 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_3) P_5))) (not (hBOOL (hAPP int bool zprime P_5))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_4 zcong X) (zero_zero int)) P_5)) (not (hBOOL (hAPP int bool (hAPP int _let_0 quadRes P_5) X))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_4 zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) X) (hAPP int nat nat_1 (hAPP int int (hAPP int _let_1 (div_div int) (hAPP int int (hAPP int _let_1 (minus_minus int) P_5) _let_2)) _let_3)))) _let_2) P_5))) )))))) 19.88/18.51 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.51 ) 19.88/18.51 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (plus_plus nat))) (let ((_let_3 (ord_less nat))) (forall ((Ma $$unsorted) (K $$unsorted) (F $$unsorted)) (or (not (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_3 M_2) N_2))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_3 (hAPP nat nat F M_2)) (hAPP nat nat F N_2)))) )) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) (hAPP nat nat (hAPP nat _let_1 _let_2 (hAPP nat nat F Ma)) K)) (hAPP nat nat F (hAPP nat nat (hAPP nat _let_1 _let_2 Ma) K))))) ))))) 19.88/18.51 ( (hAPP nat nat suc (zero_zero nat)), (one_one nat), (fact_fact nat) ) 19.88/18.51 ( (one_one nat), (one_one nat), suc ) 19.88/18.51 ) 19.88/18.51 (instantiation (let ((_let_0 (hAPP int int (number_number_of int) V_1))) (forall ((Ma $$unsorted) (V_1 $$unsorted)) (= (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))) (= _let_0 (hAPP nat int (semiring_1_of_nat int) Ma))) )) 19.88/18.51 ( (zero_zero nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.88/18.51 ( (hAPP nat nat suc (zero_zero nat)), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.51 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), pls ) 19.88/18.51 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), min_1 ) 19.88/18.51 ) 19.88/18.51 (instantiation (let ((_let_0 (power_power X_a))) (forall ((X_a $$unsorted)) (or (not (power X_a)) (= _let_0 (ti (fun X_a (fun nat X_a)) _let_0))) )) 19.88/18.51 ( bool ) 19.88/18.51 ( real ) 19.88/18.51 ( nat ) 19.88/18.51 ( (fun nat bool) ) 19.88/18.51 ( (fun nat nat) ) 19.88/18.51 ( int ) 19.88/18.51 ( (fun real real) ) 19.88/18.51 ( complex ) 19.88/18.51 ( (fun int int) ) 19.88/18.51 ( rat ) 19.88/18.51 ( (fun bool bool) ) 19.88/18.51 ( quickcheck_code_int ) 19.88/18.51 ( (fun nat (fun nat bool)) ) 19.88/18.51 ( (product_prod real real) ) 19.88/18.51 ( (product_prod int int) ) 19.88/18.51 ( (fun nat (product_prod int int)) ) 19.88/18.51 ( (product_prod nat nat) ) 19.88/18.51 ( (fun (product_prod nat nat) bool) ) 19.88/18.51 ( (fun nat (fun (product_prod nat nat) bool)) ) 19.88/18.51 ( (fun nat (product_prod nat nat)) ) 19.88/18.51 ( code_code_numeral ) 19.88/18.51 ) 19.88/18.51 (instantiation (let ((_let_0 (hAPP nat (fun nat nat) (plus_plus nat) M))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP nat nat suc (hAPP nat nat _let_0 N)) (hAPP nat nat _let_0 (hAPP nat nat suc N))) )) 19.88/18.51 ( (one_one nat), (zero_zero nat) ) 19.88/18.51 ( (one_one nat), (one_one nat) ) 19.88/18.51 ) 19.88/18.51 (instantiation (let ((_let_0 (fun int bool))) (forall ((A_1 $$unsorted) (B $$unsorted)) (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))) )) 19.88/18.52 ( (zero_zero int), (zero_zero int) ) 19.88/18.52 ( (zero_zero int), (one_one int) ) 19.88/18.52 ( (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))) ) 19.88/18.52 ( (zero_zero int), min_1 ) 19.88/18.52 ( min_1, (zero_zero int) ) 19.88/18.52 ( min_1, min_1 ) 19.88/18.52 ( 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))) ) 19.88/18.52 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 19.88/18.52 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 19.88/18.52 ( t, (zero_zero int) ) 19.88/18.52 ( t, (one_one int) ) 19.88/18.52 ( 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))) ) 19.88/18.52 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.52 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.52 ) 19.88/18.52 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (hAPP int int (hAPP int _let_1 (minus_minus int) P_5) (one_one int)))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_2) P_5))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_3 zcong A_1) (zero_zero int)) P_5)) (hBOOL (hAPP int bool (hAPP int _let_0 quadRes P_5) A_1)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_3 zcong (hAPP int int zfact _let_4)) (hAPP nat int (hAPP int (fun nat int) (power_power int) A_1) (hAPP int nat nat_1 (hAPP int int (hAPP int _let_1 (div_div int) _let_4) _let_2)))) P_5))) )))))) 19.88/18.52 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.52 ) 19.88/18.52 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148010 $$unsorted) (BOUND_VARIABLE_148011 $$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_148010) BOUND_VARIABLE_148011))) (= (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_148010) (ti X_a BOUND_VARIABLE_148011))) ) 19.88/18.52 ( nat, (one_one nat), (one_one nat) ) 19.88/18.52 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 19.88/18.52 ( int, (hAPP nat int (hAPP 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) ) 19.88/18.52 ) 19.88/18.52 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148039 $$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_148039) (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_148039))) ) 19.88/18.52 ( real, (zero_zero real) ) 19.88/18.52 ( real, (one_one real) ) 19.88/18.52 ( real, pi ) 19.88/18.52 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.52 ( 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))))) ) 19.88/18.52 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.52 ( 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)) ) 19.88/18.52 ( nat, (zero_zero nat) ) 19.88/18.52 ( int, (zero_zero int) ) 19.88/18.52 ( int, min_1 ) 19.88/18.52 ( int, s ) 19.88/18.52 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 19.88/18.52 ( int, t ) 19.88/18.52 ( int, skv_3 ) 19.88/18.52 ( int, skv_9 ) 19.88/18.52 ( rat, (zero_zero rat) ) 19.88/18.52 ) 19.88/18.52 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (= (= (ti int L) (ti int K)) (= (hAPP int int bit0 K) (hAPP int int bit0 L))) ) 19.88/18.52 ( pls, s1 ) 19.88/18.52 ( m, s ) 19.88/18.52 ( min_1, m ) 19.88/18.52 ( min_1, min_1 ) 19.88/18.52 ( min_1, s ) 19.88/18.52 ( s, min_1 ) 19.88/18.52 ( s1, t ) 19.88/18.52 ( t, pls ) 19.88/18.52 ( t, s1 ) 19.88/18.52 ( t, t ) 19.88/18.52 ) 19.88/18.52 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (forall ((Z_3 $$unsorted) (Z $$unsorted)) (or (not (hBOOL (hAPP int bool _let_0 Z))) (not (hBOOL (hAPP int bool _let_0 Z_3))) (= (= (hAPP int nat nat_1 Z_3) (hAPP int nat nat_1 Z)) (= (ti int Z_3) (ti int Z)))) )) 19.88/18.52 ( (one_one int), (one_one int) ) 19.88/18.52 ( (one_one int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.88/18.52 ( min_1, (hAPP int int (number_number_of int) pls) ) 19.88/18.52 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 19.88/18.52 ( s, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.52 ( s, s ) 19.88/18.52 ( (hAPP int int (number_number_of int) pls), min_1 ) 19.88/18.52 ( (hAPP int int (number_number_of int) pls), (hAPP int int (number_number_of int) pls) ) 19.88/18.52 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (one_one int) ) 19.88/18.52 ( skv_3, skv_3 ) 19.88/18.52 ( skv_3, skv_9 ) 19.88/18.52 ( skv_9, skv_3 ) 19.88/18.52 ) 19.88/18.52 (instantiation (let ((_let_0 (fun real bool))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) X_1))) (hBOOL (hAPP real bool (hAPP (fun real real) _let_0 (isCont real real) ln) X_1))) )) 19.88/18.52 ( pi ) 19.88/18.52 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.52 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.52 ( skv_2 ) 19.88/18.52 ( skv_10 ) 19.88/18.52 ( skv_13 ) 19.88/18.52 ) 19.88/18.52 (instantiation (let ((_let_0 (zero_zero int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (product_Pair int int))) (forall ((P_5 $$unsorted)) (= (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))) ))))) 19.88/18.52 ( (zero_zero int) ) 19.88/18.52 ( (one_one int) ) 19.88/18.52 ( s ) 19.88/18.52 ) 19.88/18.52 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_148163 $$unsorted)) (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_148163)) (ring_1_Ints X_a)))) )) 19.88/18.52 ( real, (zero_zero nat) ) 19.88/18.52 ( real, (one_one nat) ) 19.88/18.52 ( int, (zero_zero nat) ) 19.88/18.52 ( int, (hAPP nat nat suc (zero_zero nat)) ) 19.88/18.52 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.52 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.88/18.52 ) 19.88/18.52 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (inverse_inverse X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_148181 $$unsorted) (BOUND_VARIABLE_148182 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148181) BOUND_VARIABLE_148182))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_148181))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_148182)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_148181)))) )))) 19.88/18.52 ( real, (zero_zero real), pi ) 19.88/18.52 ( 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)))) ) 19.88/18.52 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.52 ( real, (zero_zero real), skv_2 ) 19.88/18.52 ( real, (zero_zero real), skv_10 ) 19.88/18.52 ( real, (zero_zero real), skv_13 ) 19.88/18.52 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.52 ( real, pi, (zero_zero real) ) 19.88/18.52 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.52 ( real, (hAPP real real (hAPP real (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))) ) 19.88/18.52 ( 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) ) 19.88/18.52 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.88/18.52 ( 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 ) 19.88/18.52 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.52 ( int, (zero_zero int), (zero_zero int) ) 19.88/18.52 ( int, (zero_zero int), (one_one int) ) 19.88/18.52 ( 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))) ) 19.88/18.52 ( int, (zero_zero int), min_1 ) 19.88/18.52 ( int, min_1, (zero_zero int) ) 19.88/18.52 ( int, min_1, min_1 ) 19.88/18.52 ( 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))) ) 19.88/18.52 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 19.88/18.52 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 19.88/18.52 ( int, t, (zero_zero int) ) 19.88/18.52 ( int, t, (one_one int) ) 19.88/18.52 ( 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))) ) 19.88/18.52 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.52 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.52 ) 19.88/18.52 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (comple44059174attice T_1)) (comple44059174attice (fun T_2 T_1))) ) 19.88/18.52 ( bool, bool ) 19.88/18.52 ( bool, (fun bool bool) ) 19.88/18.52 ( real, bool ) 19.88/18.52 ( real, real ) 19.88/18.52 ( real, nat ) 19.88/18.52 ( real, (fun int bool) ) 19.88/18.52 ( real, (fun real bool) ) 19.88/18.52 ( real, (fun real real) ) 19.88/18.52 ( real, complex ) 19.88/18.52 ( real, (fun nat real) ) 19.88/18.52 ( real, (fun bool bool) ) 19.88/18.52 ( real, (fun int (fun int bool)) ) 19.88/18.52 ( real, (fun (filter real) bool) ) 19.88/18.52 ( real, (fun (filter nat) bool) ) 19.88/18.52 ( real, (fun real complex) ) 19.88/18.52 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 19.88/18.52 ( real, (fun nat (product_prod real real)) ) 19.88/18.52 ( real, (fun real (fun nat (product_prod real real))) ) 19.88/18.52 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 19.88/18.52 ( real, (fun int (fun int (fun bool bool))) ) 19.88/18.52 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 19.88/18.52 ( real, (fun (fun int real) (fun int bool)) ) 19.88/18.52 ( real, (fun int (fun nat bool)) ) 19.88/18.52 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 19.88/18.52 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 19.88/18.52 ( real, (fun int (fun nat (fun bool bool))) ) 19.88/18.52 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 19.88/18.52 ( real, (fun (fun nat real) (fun nat bool)) ) 19.88/18.52 ( nat, bool ) 19.88/18.52 ( nat, real ) 19.88/18.52 ( nat, nat ) 19.88/18.52 ( nat, (fun nat bool) ) 19.88/18.52 ( nat, (fun nat nat) ) 19.88/18.52 ( nat, int ) 19.88/18.52 ( nat, (fun real real) ) 19.88/18.52 ( nat, complex ) 19.88/18.52 ( nat, (fun int int) ) 19.88/18.52 ( nat, rat ) 19.88/18.52 ( nat, (fun bool bool) ) 19.88/18.52 ( nat, (fun nat (fun nat bool)) ) 19.88/18.52 ( nat, (product_prod real real) ) 19.88/18.52 ( nat, (product_prod int int) ) 19.88/18.52 ( nat, (fun nat (product_prod int int)) ) 19.88/18.52 ( nat, (product_prod nat nat) ) 19.88/18.52 ( nat, (fun (product_prod nat nat) bool) ) 19.88/18.52 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 19.88/18.52 ( nat, (fun nat (product_prod nat nat)) ) 19.88/18.52 ( (fun nat bool), bool ) 19.88/18.52 ( (fun nat bool), (fun nat bool) ) 19.88/18.52 ( (fun nat bool), (fun nat (fun bool bool)) ) 19.88/18.52 ( (fun nat bool), (fun int (fun nat bool)) ) 19.88/18.52 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 19.88/18.52 ( (fun nat nat), (fun nat real) ) 19.88/18.52 ( (fun nat nat), (fun nat (fun nat nat)) ) 19.88/18.52 ( (fun nat nat), (fun nat (fun nat bool)) ) 19.88/18.52 ( int, bool ) 19.88/18.52 ( int, real ) 19.88/18.52 ( int, nat ) 19.88/18.52 ( int, (fun nat bool) ) 19.88/18.52 ( int, (fun nat nat) ) 19.88/18.52 ( int, int ) 19.88/18.52 ( int, (fun int bool) ) 19.88/18.52 ( int, (fun nat int) ) 19.88/18.52 ( int, (fun real real) ) 19.88/18.52 ( int, (fun nat real) ) 19.88/18.52 ( int, (fun int int) ) 19.88/18.52 ( int, rat ) 19.88/18.52 ( int, (fun int rat) ) 19.88/18.52 ( int, (fun bool bool) ) 19.88/18.52 ( int, (fun int (fun bool bool)) ) 19.88/18.52 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 19.88/18.52 ( int, (fun int (fun int bool)) ) 19.88/18.52 ( int, quickcheck_code_int ) 19.88/18.52 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 19.88/18.52 ( int, (product_prod int int) ) 19.88/18.52 ( int, (fun int (product_prod int int)) ) 19.88/18.52 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 19.88/18.52 ( int, (fun (fun int bool) bool) ) 19.88/18.52 ( int, (fun (product_prod int int) bool) ) 19.88/18.52 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 19.88/18.52 ( int, (product_prod int (product_prod int int)) ) 19.88/18.52 ( int, (fun int (product_prod int (product_prod int int))) ) 19.88/18.52 ( int, (fun (fun int int) (fun int bool)) ) 19.88/18.52 ( int, (fun int (fun (product_prod int int) bool)) ) 19.88/18.52 ( int, (fun int (fun (fun int bool) bool)) ) 19.88/18.52 ( int, (list int) ) 19.88/18.52 ( int, (fun nat (fun bool bool)) ) 19.88/18.52 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 19.88/18.52 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 19.88/18.53 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 19.88/18.53 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 19.88/18.53 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 19.88/18.53 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 19.88/18.53 ( int, (fun (product_prod int int) int) ) 19.88/18.53 ( int, (fun int (fun int (fun int bool))) ) 19.88/18.53 ( int, (fun int real) ) 19.88/18.53 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 19.88/18.53 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 19.88/18.53 ( (fun int bool), bool ) 19.88/18.53 ( (fun int bool), int ) 19.88/18.53 ( (fun int bool), (fun int bool) ) 19.88/18.53 ( (fun int bool), (fun int (fun bool bool)) ) 19.88/18.53 ( (fun int bool), (fun int (fun int bool)) ) 19.88/18.53 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 19.88/18.53 ( (fun int bool), (fun int (fun int int)) ) 19.88/18.53 ( (fun int bool), (fun real (fun int (fun int bool))) ) 19.88/18.53 ( (fun real bool), real ) 19.88/18.53 ( (fun real bool), (fun real bool) ) 19.88/18.53 ( (fun real bool), (fun real (fun bool bool)) ) 19.88/18.53 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 19.88/18.53 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 19.88/18.53 ( (fun real real), (fun real real) ) 19.88/18.53 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 19.88/18.53 ( (fun real real), (fun real (fun real real)) ) 19.88/18.53 ( (fun real real), (fun real (fun real bool)) ) 19.88/18.53 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 19.88/18.53 ( complex, real ) 19.88/18.53 ( complex, nat ) 19.88/18.53 ( complex, complex ) 19.88/18.53 ( (fun nat real), (fun nat bool) ) 19.88/18.53 ( (fun nat real), (fun nat real) ) 19.88/18.53 ( (fun nat real), (fun nat (fun real real)) ) 19.88/18.53 ( (fun nat real), (fun int (fun nat real)) ) 19.88/18.53 ( (fun int int), (fun int bool) ) 19.88/18.53 ( (fun int int), (fun int int) ) 19.88/18.53 ( (fun int int), (fun int (fun int bool)) ) 19.88/18.53 ( (fun int int), (fun int (fun int int)) ) 19.88/18.53 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 19.88/18.53 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 19.88/18.53 ( rat, real ) 19.88/18.53 ( rat, (product_prod int int) ) 19.88/18.53 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 19.88/18.53 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 19.88/18.53 ( (fun int (fun int bool)), (fun int bool) ) 19.88/18.53 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 19.88/18.53 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 19.88/18.53 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 19.88/18.53 ( quickcheck_code_int, nat ) 19.88/18.53 ( quickcheck_code_int, int ) 19.88/18.53 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 19.88/18.53 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 19.88/18.53 ( (product_prod real real), bool ) 19.88/18.53 ( (product_prod int int), bool ) 19.88/18.53 ( (product_prod int int), int ) 19.88/18.53 ( (product_prod int int), (fun int bool) ) 19.88/18.53 ( (product_prod int int), (fun int int) ) 19.88/18.53 ( (product_prod int int), rat ) 19.88/18.53 ( (product_prod int int), (fun bool bool) ) 19.88/18.53 ( (product_prod int int), (product_prod int int) ) 19.88/18.53 ( (product_prod int int), (fun (product_prod int int) bool) ) 19.88/18.53 ( (product_prod int int), (fun (product_prod int int) int) ) 19.88/18.53 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 19.88/18.53 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 19.88/18.53 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 19.88/18.53 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 19.88/18.53 ( (filter real), bool ) 19.88/18.53 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 19.88/18.53 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 19.88/18.53 ( (filter nat), bool ) 19.88/18.53 ( (product_prod nat nat), bool ) 19.88/18.53 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 19.88/18.53 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 19.88/18.53 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 19.88/18.53 ( code_code_numeral, nat ) 19.88/18.53 ( code_code_numeral, (fun nat nat) ) 19.88/18.53 ( code_code_numeral, int ) 19.88/18.53 ( code_code_numeral, code_code_numeral ) 19.88/18.53 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 19.88/18.53 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 19.88/18.53 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 19.88/18.53 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 19.88/18.53 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 19.88/18.53 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 19.88/18.53 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 19.88/18.53 ( (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))) ) 19.88/18.53 ( (fun nat rat), bool ) 19.88/18.53 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 19.88/18.53 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 19.88/18.53 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 19.88/18.53 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 19.88/18.53 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 19.88/18.53 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 19.88/18.53 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 19.88/18.53 ( (fun int real), (fun int bool) ) 19.88/18.53 ( (fun int real), (fun int real) ) 19.88/18.53 ( (fun int real), (fun int (fun int real)) ) 19.88/18.53 ( (fun int real), (fun int (fun real real)) ) 19.88/18.53 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 19.88/18.53 ( (fun real (fun int bool)), (fun real bool) ) 19.88/18.53 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 19.88/18.53 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 19.88/18.53 ( (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)))) ) 19.88/18.53 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 19.88/18.53 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 19.88/18.53 ( (fun int (fun int real)), (fun int (fun int bool)) ) 19.88/18.53 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 19.88/18.53 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 19.88/18.53 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 19.88/18.53 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 19.88/18.53 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 19.88/18.53 ( (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))) ) 19.88/18.53 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 19.88/18.53 ( (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))) ) 19.88/18.53 ( (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))) ) 19.88/18.53 ( (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)))) ) 19.88/18.53 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))) ) 19.88/18.53 ( (fun int (fun nat bool)), (fun int bool) ) 19.88/18.53 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 19.88/18.53 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 19.88/18.53 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 19.88/18.53 ( (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))) ) 19.88/18.53 ( (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)))) ) 19.88/18.53 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 19.88/18.53 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 19.88/18.53 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 19.88/18.53 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 19.88/18.53 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 19.88/18.53 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 19.88/18.53 ) 19.88/18.53 (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))))) ) 19.88/18.53 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.53 ) 19.88/18.53 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (forall ((A_2 $$unsorted) (Ma $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_2) Ma))) (hBOOL (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) (hAPP int _let_0 (hAPP int (fun int _let_0) bnorRset A_2) Ma)) (hAPP int _let_1 rsetR Ma)))) ))) 19.88/18.53 ( (zero_zero int), (zero_zero int) ) 19.88/18.53 ( (zero_zero int), (one_one int) ) 19.88/18.53 ( (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))) ) 19.88/18.53 ( (zero_zero int), min_1 ) 19.88/18.53 ( min_1, (zero_zero int) ) 19.88/18.53 ( min_1, min_1 ) 19.88/18.53 ( 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))) ) 19.88/18.53 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 19.88/18.53 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 19.88/18.53 ( t, (zero_zero int) ) 19.88/18.53 ( t, (one_one int) ) 19.88/18.53 ( 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))) ) 19.88/18.53 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.53 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.53 ) 19.88/18.53 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_148236 $$unsorted) (BOUND_VARIABLE_148237 $$unsorted)) (or (not (group_add X_a)) (= (ti X_a BOUND_VARIABLE_148236) (hAPP X_a X_a (hAPP X_a _let_0 (minus_minus X_a) (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_148236) BOUND_VARIABLE_148237)) BOUND_VARIABLE_148237))) )) 19.88/18.53 ( nat, (one_one nat), (one_one nat) ) 19.88/18.53 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 19.88/18.53 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 19.88/18.53 ) 19.88/18.53 (instantiation (let ((_let_0 (fun (product_prod X_a X_b) bool))) (let ((_let_1 (hAPP (product_prod X_a X_b) (fun _let_0 bool) (member (product_prod X_a X_b)) (hAPP X_b (product_prod X_a X_b) (hAPP X_a (fun X_b (product_prod X_a X_b)) (product_Pair X_a X_b) X_2) Xa)))) (forall ((X_a $$unsorted) (X_b $$unsorted) (S $$unsorted) (R_3 $$unsorted)) (= (forall ((X_2 $$unsorted) (Xa $$unsorted)) (= (hBOOL (hAPP _let_0 bool _let_1 S)) (hBOOL (hAPP _let_0 bool _let_1 R_3))) ) (= (ti _let_0 R_3) (ti _let_0 S))) ))) 19.88/18.53 ( nat, nat, pred_nat, pred_nat ) 19.88/18.53 ( int, int, frac_1, frac_1 ) 19.88/18.53 ( (product_prod int int), (product_prod int int), ratrel, ratrel ) 19.88/18.53 ( (product_prod nat nat), (product_prod nat nat), pair_less, pair_less ) 19.88/18.53 ( (product_prod nat nat), (product_prod nat nat), pair_less, pair_leq ) 19.88/18.53 ( (product_prod nat nat), (product_prod nat nat), pair_leq, pair_less ) 19.88/18.53 ) 19.88/18.53 (instantiation (let ((_let_0 (number_number_of X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (plus_plus X_a))) (let ((_let_3 (hAPP int X_a _let_0 BOUND_VARIABLE_148269))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_148269 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (zero_zero X_a)) _let_3)) _let_3) (hAPP int X_a _let_0 (hAPP int int bit0 BOUND_VARIABLE_148269)))) ))))) 19.88/18.53 ( real, (hAPP int int bit1 pls) ) 19.88/18.53 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.88/18.53 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.88/18.53 ( nat, pls ) 19.88/18.53 ( nat, (hAPP int int bit1 pls) ) 19.88/18.53 ( int, pls ) 19.88/18.53 ( int, (hAPP int int bit1 pls) ) 19.88/18.53 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.88/18.53 ( complex, (hAPP int int bit1 pls) ) 19.88/18.53 ( quickcheck_code_int, pls ) 19.88/18.53 ( code_code_numeral, pls ) 19.88/18.53 ) 19.88/18.53 (instantiation (forall ((X_a $$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)))) ) 19.88/18.53 ( bool ) 19.88/18.53 ( real ) 19.88/18.53 ( nat ) 19.88/18.53 ( (fun nat bool) ) 19.88/18.53 ( int ) 19.88/18.53 ( (fun int bool) ) 19.88/18.53 ( complex ) 19.88/18.53 ( rat ) 19.88/18.53 ( quickcheck_code_int ) 19.88/18.53 ( (product_prod real real) ) 19.88/18.53 ( (product_prod int int) ) 19.88/18.53 ( (filter real) ) 19.88/18.53 ( (filter nat) ) 19.88/18.53 ( (product_prod nat nat) ) 19.88/18.53 ( code_code_numeral ) 19.88/18.53 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 19.88/18.53 ( (fun nat rat) ) 19.88/18.53 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 19.88/18.53 ) 19.88/18.53 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (times_times X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_148301 $$unsorted) (BOUND_VARIABLE_148302 $$unsorted) (BOUND_VARIABLE_148303 $$unsorted)) (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_148301) BOUND_VARIABLE_148302)) BOUND_VARIABLE_148303) (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_148301) BOUND_VARIABLE_148303)) (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_148302) BOUND_VARIABLE_148303)))) )))) 19.88/18.53 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (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) ) 19.88/18.53 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (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 ) 19.88/18.53 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (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_1 ) 19.88/18.54 ) 19.88/18.54 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (real_1 int))) (forall ((N $$unsorted) (M $$unsorted) (R_4 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP int real _let_1 M)) R_4))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) R_4) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real _let_1 N)) (one_one real))))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) M) N))) ))) 19.88/18.54 ( (zero_zero int), (zero_zero int), pi ) 19.88/18.54 ( (one_one int), (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.54 ) 19.88/18.54 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (inverse_inverse X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_148333 $$unsorted) (BOUND_VARIABLE_148334 $$unsorted)) (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_148333)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_148334)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_148334) (zero_zero X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148334) BOUND_VARIABLE_148333))) )))) 19.88/18.54 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.54 ( real, pi, (zero_zero real) ) 19.88/18.54 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.54 ( 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)))) ) 19.88/18.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 19.88/18.54 ( 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)))), (zero_zero real) ) 19.88/18.54 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.88/18.54 ( real, skv_6, (zero_zero real) ) 19.88/18.54 ( real, skv_11, (zero_zero real) ) 19.88/18.54 ( real, skv_12, (zero_zero real) ) 19.88/18.54 ( real, skv_14, (zero_zero real) ) 19.88/18.54 ( int, pls, min_1 ) 19.88/18.54 ( int, (one_one int), (zero_zero int) ) 19.88/18.54 ( int, min_1, (zero_zero int) ) 19.88/18.54 ( int, min_1, min_1 ) 19.88/18.54 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 19.88/18.54 ( int, s, (zero_zero int) ) 19.88/18.54 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 19.88/18.54 ( int, t, (one_one int) ) 19.88/18.54 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 19.88/18.54 ( int, skv_3, (zero_zero int) ) 19.88/18.54 ( int, skv_9, (zero_zero int) ) 19.88/18.54 ) 19.88/18.54 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (hAPP nat (fun real real) root N_1))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) Y_1)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real _let_2 X_1)) (hAPP real real _let_2 Y_1))))) )))) 19.88/18.54 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.54 ) 19.88/18.54 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148419))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_148419 $$unsorted) (BOUND_VARIABLE_148420 $$unsorted) (BOUND_VARIABLE_148421 $$unsorted)) (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_148420)) BOUND_VARIABLE_148421) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148420) BOUND_VARIABLE_148421)))) )))) 19.88/18.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.88/18.54 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.88/18.54 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi), ii ) 19.88/18.54 ) 19.88/18.54 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((X $$unsorted)) (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))) ))) 19.88/18.54 ( (zero_zero real) ) 19.88/18.54 ( (one_one real) ) 19.88/18.54 ( pi ) 19.88/18.54 ( (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)))) ) 19.88/18.54 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.54 ( skv_6 ) 19.88/18.54 ( skv_11 ) 19.88/18.54 ( skv_12 ) 19.88/18.54 ( skv_14 ) 19.88/18.54 ) 19.88/18.54 (instantiation (let ((_let_0 (fun nat real))) (let ((_let_1 (fun (filter nat) bool))) (forall ((C_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP real real (abs_abs real) C_1)) (one_one real)))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (tendsto nat real) (hAPP real _let_0 (power_power real) C_1)) (zero_zero real)) sequentially))) ))) 19.88/18.54 ( (hAPP int real (number_number_of real) min_1) ) 19.88/18.54 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.54 ) 19.88/18.54 (instantiation (let ((_let_0 (archimedean_ceiling X_a))) (forall ((X_a $$unsorted)) (or (not (archim1727834104eiling X_a)) (= _let_0 (ti (fun X_a int) _let_0))) )) 19.88/18.54 ( real ) 19.88/18.54 ( nat ) 19.88/18.54 ( int ) 19.88/18.54 ( (fun int bool) ) 19.88/18.54 ( rat ) 19.88/18.54 ( quickcheck_code_int ) 19.88/18.54 ( (product_prod int int) ) 19.88/18.54 ( code_code_numeral ) 19.88/18.54 ) 19.88/18.54 (instantiation (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_148461))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_148461 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 BOUND_VARIABLE_148461)) (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))) )))) 19.88/18.54 ( real, (hAPP int int bit1 pls) ) 19.88/18.54 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.88/18.54 ( real, min_1 ) 19.88/18.54 ( 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))))))) ) 19.88/18.54 ( nat, pls ) 19.88/18.54 ( nat, (hAPP int int bit1 pls) ) 19.88/18.54 ( int, pls ) 19.88/18.54 ( int, (hAPP int int bit1 pls) ) 19.88/18.54 ( int, min_1 ) 19.88/18.54 ( complex, min_1 ) 19.88/18.54 ( quickcheck_code_int, pls ) 19.88/18.54 ( code_code_numeral, pls ) 19.88/18.54 ) 19.88/18.54 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_148508 $$unsorted) (BOUND_VARIABLE_148509 $$unsorted) (BOUND_VARIABLE_148510 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148510) (zero_zero X_a)))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148508) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_148509) BOUND_VARIABLE_148510))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148509) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_148508) BOUND_VARIABLE_148510))))) )))) 19.88/18.54 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.88/18.54 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.88/18.54 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 19.88/18.54 ) 19.88/18.54 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_148626 $$unsorted) (BOUND_VARIABLE_148627 $$unsorted)) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148626) BOUND_VARIABLE_148627))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148627) BOUND_VARIABLE_148626))) (= (ti X_a BOUND_VARIABLE_148626) (ti X_a BOUND_VARIABLE_148627))) ))) 19.88/18.54 ( real, (zero_zero real), pi ) 19.88/18.54 ( 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)))) ) 19.88/18.54 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.54 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.54 ( real, (zero_zero real), skv_6 ) 19.88/18.54 ( real, (zero_zero real), skv_11 ) 19.88/18.54 ( real, (zero_zero real), skv_12 ) 19.88/18.54 ( real, (zero_zero real), skv_14 ) 19.88/18.54 ( real, pi, (zero_zero real) ) 19.88/18.54 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 19.88/18.54 ( 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)))) ) 19.88/18.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 19.88/18.54 ( 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)))), (zero_zero real) ) 19.88/18.54 ( 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))) ) 19.88/18.54 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.88/18.54 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 19.88/18.54 ( real, skv_6, (zero_zero real) ) 19.88/18.54 ( real, skv_11, (zero_zero real) ) 19.88/18.54 ( real, skv_12, (zero_zero real) ) 19.88/18.54 ( real, skv_14, (zero_zero real) ) 19.88/18.54 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.54 ( int, (zero_zero int), (one_one int) ) 19.88/18.54 ( int, (zero_zero int), min_1 ) 19.88/18.54 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.54 ( int, (zero_zero int), s ) 19.88/18.54 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 19.88/18.54 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.88/18.54 ( int, (zero_zero int), skv_3 ) 19.88/18.54 ( int, (zero_zero int), skv_9 ) 19.88/18.54 ( int, pls, min_1 ) 19.88/18.54 ( int, (one_one int), (zero_zero int) ) 19.88/18.54 ( int, (one_one int), t ) 19.88/18.54 ( int, min_1, (zero_zero int) ) 19.88/18.54 ( int, min_1, pls ) 19.88/18.54 ( int, min_1, min_1 ) 19.88/18.54 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 19.88/18.54 ( int, s, (zero_zero int) ) 19.88/18.54 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 19.88/18.54 ( int, t, (one_one int) ) 19.88/18.54 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 19.88/18.54 ( int, skv_3, (zero_zero int) ) 19.88/18.54 ( int, skv_9, (zero_zero int) ) 19.88/18.54 ) 19.88/18.54 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun nat real))) (let ((_let_5 (fun nat _let_3))) (let ((_let_6 (fun (filter nat) bool))) (forall ((A_2 $$unsorted)) (or (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_6 (hAPP _let_4 (fun real _let_6) (tendsto nat real) A_2) _let_0) sequentially))) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 _let_0) (hAPP nat real A_2 N_2))) )) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP nat real A_2 (hAPP nat nat suc N_2))) (hAPP nat real A_2 N_2))) )) (hBOOL (hAPP _let_4 bool (summable real) (hAPP _let_4 _let_4 (hAPP _let_5 (fun _let_4 _let_4) (combs nat real real) (hAPP _let_4 _let_5 (hAPP (fun real _let_3) (fun _let_4 _let_5) (combb real _let_3 nat) (times_times real)) (hAPP real _let_4 (power_power real) (hAPP int real (number_number_of real) min_1)))) A_2)))) )))))))) 19.88/18.54 ( (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 19.88/18.55 ) 19.88/18.55 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_148702 $$unsorted) (BOUND_VARIABLE_148703 $$unsorted) (BOUND_VARIABLE_148704 $$unsorted)) (or (not (semiring_div X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_148704)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_148704) BOUND_VARIABLE_148703))) (= (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_148702) BOUND_VARIABLE_148704) (ti X_a BOUND_VARIABLE_148703)) (= (ti X_a BOUND_VARIABLE_148702) (hAPP X_a X_a (hAPP X_a _let_0 (div_div X_a) BOUND_VARIABLE_148703) BOUND_VARIABLE_148704)))) )) 19.88/18.55 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.55 ) 19.88/18.55 (instantiation (forall ((X $$unsorted)) (= (hAPP real nat natfloor X) (hAPP int nat nat_1 (hAPP real int (archim2085082626_floor real) X))) ) 19.88/18.55 ( (zero_zero real) ) 19.88/18.55 ( (one_one real) ) 19.88/18.55 ) 19.88/18.55 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (let ((_let_2 (inverse_inverse X_a))) (let ((_let_3 (times_times X_a))) (let ((_let_4 (zero_zero X_a))) (let ((_let_5 (hAPP X_a X_a _let_2 BOUND_VARIABLE_148751))) (let ((_let_6 (hAPP X_a X_a _let_2 BOUND_VARIABLE_148750))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_148750 $$unsorted) (BOUND_VARIABLE_148751 $$unsorted)) (or (not (division_ring X_a)) (= _let_4 (ti X_a BOUND_VARIABLE_148751)) (= _let_4 (ti X_a BOUND_VARIABLE_148750)) (= (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_148750) BOUND_VARIABLE_148751))) _let_6) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 _let_5) _let_6))) )))))))) 19.88/18.55 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 19.88/18.55 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 19.88/18.55 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 19.88/18.55 ) 19.88/18.55 (instantiation (let ((_let_0 (norm_norm X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_148776 $$unsorted) (BOUND_VARIABLE_148777 $$unsorted)) (or (not (real_normed_vector X_a)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (minus_minus real) (hAPP X_a real _let_0 BOUND_VARIABLE_148776)) (hAPP X_a real _let_0 BOUND_VARIABLE_148777))) (hAPP X_a real _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_148776) BOUND_VARIABLE_148777))))) )) 19.88/18.55 ( nat, (one_one nat), (one_one nat) ) 19.88/18.55 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 19.88/18.55 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 19.88/18.55 ) 19.88/18.55 (instantiation (let ((_let_0 (zero_zero real))) (forall ((X_1 $$unsorted)) (= (= _let_0 (hAPP real real sqrt X_1)) (= _let_0 X_1)) )) 19.88/18.55 ( (zero_zero real) ) 19.88/18.55 ( (one_one real) ) 19.88/18.55 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.55 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.88/18.55 ) 19.88/18.55 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int rat (number_number_of rat) K_4) (hAPP int rat (hAPP int (fun int rat) fract (hAPP int int (number_number_of int) K_4)) (one_one int))) ) 19.88/18.55 ( pls ) 19.88/18.55 ( (hAPP int int bit1 pls) ) 19.88/18.55 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 19.88/18.55 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.55 ( min_1 ) 19.88/18.55 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 19.88/18.55 ) 19.88/18.55 (instantiation (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP int (fun int bool) (ord_less_eq int) V_1))) (forall ((V_1 $$unsorted) (V_2 $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP int nat _let_0 V_1)) (hAPP int nat _let_0 V_2))) (or (hBOOL (hAPP int bool _let_1 V_2)) (hBOOL (hAPP int bool _let_1 pls)))) ))) 19.88/18.55 ( (zero_zero int), (one_one int) ) 19.88/18.55 ( (zero_zero int), min_1 ) 19.88/18.55 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.55 ( (zero_zero int), s ) 19.88/18.55 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 19.88/18.55 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.88/18.55 ( (zero_zero int), skv_3 ) 19.88/18.55 ( (zero_zero int), skv_9 ) 19.88/18.55 ( (one_one int), t ) 19.88/18.55 ( min_1, pls ) 19.88/18.55 ( min_1, min_1 ) 19.88/18.55 ) 19.88/18.55 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_148954 $$unsorted) (BOUND_VARIABLE_148955 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_148955))) (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_148955) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_148955) BOUND_VARIABLE_148954))))) )) 19.88/18.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 19.88/18.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 19.88/18.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 19.88/18.55 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 19.88/18.55 ) 19.88/18.55 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_148979 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (= (= _let_0 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_148979)) (= _let_0 (ti X_a BOUND_VARIABLE_148979)))) )) 19.88/18.55 ( bool, fFalse ) 19.88/18.55 ( bool, fTrue ) 19.88/18.55 ( real, pi ) 19.88/18.55 ( (fun nat bool), (even_odd_even nat) ) 19.88/18.55 ( (fun nat bool), prime ) 19.88/18.55 ( (fun nat nat), suc ) 19.88/18.55 ( (fun nat nat), (fact_fact nat) ) 19.88/18.55 ( (fun nat nat), (size_size nat) ) 19.88/18.55 ( (fun nat nat), fact ) 19.88/18.55 ( (fun nat nat), nat_size ) 19.88/18.55 ( int, pls ) 19.88/18.55 ( int, m ) 19.88/18.55 ( int, min_1 ) 19.88/18.55 ( int, s ) 19.88/18.55 ( int, s1 ) 19.88/18.55 ( int, t ) 19.88/18.55 ( (fun int bool), zprime ) 19.88/18.55 ( (fun int bool), nat_neg ) 19.88/18.55 ( (fun int bool), zEven ) 19.88/18.55 ( (fun int bool), nat_is_nat ) 19.88/18.55 ( (fun int bool), zOdd ) 19.88/18.55 ( (fun int bool), (even_odd_even int) ) 19.88/18.55 ( (fun int bool), twoSqu1091635170sum2sq ) 19.88/18.55 ( (fun int nat), nat_1 ) 19.88/18.55 ( (fun int nat), phi ) 19.88/18.55 ( (fun real real), sqrt ) 19.88/18.55 ( (fun real real), tan ) 19.88/18.55 ( (fun real real), cos ) 19.88/18.55 ( (fun real real), arccos ) 19.88/18.55 ( (fun real real), ln ) 19.88/18.55 ( (fun real real), sin ) 19.88/18.55 ( (fun real real), arctan ) 19.88/18.55 ( (fun real real), arcsin ) 19.88/18.55 ( complex, ii ) 19.88/18.55 ( (fun complex complex), cnj ) 19.88/18.55 ( (fun complex complex), expi ) 19.88/18.55 ( (fun nat real), (real_1 nat) ) 19.88/18.55 ( (fun nat real), cos_coeff ) 19.88/18.55 ( (fun nat real), sin_coeff ) 19.88/18.55 ( (fun int int), bit0 ) 19.88/18.55 ( (fun int int), bit1 ) 19.88/18.55 ( (fun int int), pred ) 19.88/18.55 ( (fun int int), succ ) 19.88/18.55 ( (fun int int), (fact_fact int) ) 19.88/18.55 ( (fun int int), zfact ) 19.88/18.55 ( (fun bool bool), fNot ) 19.88/18.55 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 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int)), nat_tsub ) 19.88/18.55 ( (fun int (fun int int)), z3div ) 19.88/18.55 ( (fun int (fun int int)), int_lcm ) 19.88/18.55 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 19.88/18.55 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 19.88/18.55 ( (fun int (fun (fun int bool) bool)), rsetR ) 19.88/18.55 ( (fun int (fun (fun int bool) bool)), resSet ) 19.88/18.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 19.88/18.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 19.88/18.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 19.88/18.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 19.88/18.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 19.88/18.55 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), 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twoSqu1094008024sum2sq ) 19.88/18.55 ( (fun real nat), natfloor ) 19.88/18.55 ( (fun real nat), natceiling ) 19.88/18.55 ( (fun int quickcheck_code_int), quickcheck_of_int ) 19.88/18.55 ( (fun int (fun int (fun int bool))), wset ) 19.88/18.55 ( (fun int (fun int (fun int bool))), bnorRset ) 19.88/18.55 ( (fun int (fun int (fun int bool))), zcong ) 19.88/18.55 ( (fun int (fun int (fun int bool))), noXRRset ) 19.88/18.55 ( (fun int (fun int (fun int bool))), zcongm ) 19.88/18.55 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 19.88/18.55 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 19.88/18.55 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 19.88/18.55 ( (fun int real), (real_1 int) ) 19.88/18.55 ( (fun complex nat), (size_size complex) ) 19.88/18.55 ( (fun complex nat), complex_size ) 19.88/18.55 ( (fun int (list int)), quickc666637781d_zero ) 19.88/18.55 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 19.88/18.55 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 19.88/18.55 ( (fun (product_prod int int) rat), frct ) 19.88/18.55 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 19.88/18.55 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 19.88/18.55 ( (fun (fun nat rat) bool), vanishes ) 19.88/18.55 ( (fun int (fun int rat)), fract ) 19.88/18.55 ( (fun code_code_numeral int), code_int_of ) 19.88/18.55 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 19.88/18.55 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 19.88/18.55 ( (fun code_code_numeral nat), code_c271388182l_size ) 19.88/18.55 ( (fun real (fun real complex)), complex_1 ) 19.88/18.55 ( (fun real (fun real complex)), rcis ) 19.88/18.55 ( (fun int (fun nat nat)), nat_aux ) 19.88/18.55 ( (fun rat real), ratreal ) 19.88/18.55 ( (fun quickcheck_code_int int), quickcheck_int_of ) 19.88/18.55 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 19.88/18.55 ( (fun rat (product_prod int int)), quotient_of ) 19.88/18.55 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 19.88/18.55 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 19.88/18.55 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 19.88/18.55 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 19.88/18.55 ) 19.88/18.55 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (abs_abs int))) (let ((_let_2 (dvd_dvd int))) (forall ((A_1 $$unsorted) (B $$unsorted)) (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))) )))) 19.88/18.55 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 19.88/18.55 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.55 ) 19.88/18.55 (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))) ))) ) 19.88/18.55 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.55 ) 19.88/18.55 (instantiation (forall ((X_1 $$unsorted)) (= (= (zero_zero real) (hAPP int real (real_1 int) X_1)) (= (zero_zero int) (ti int X_1))) ) 19.88/18.55 ( (zero_zero int) ) 19.88/18.55 ( pls ) 19.88/18.55 ( m ) 19.88/18.55 ( (one_one int) ) 19.88/18.55 ( min_1 ) 19.88/18.55 ( s ) 19.88/18.55 ( s1 ) 19.88/18.55 ( t ) 19.88/18.55 ) 19.88/18.55 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (ord_less real))) (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 A_2) B_1))) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_2) X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) B_1))) (not (forall ((Y_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (zero_zero real)) Y_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X_2) Y_2)))) ))) )) (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP real real F A_2)) (hAPP real real F B_1)))) )))) 19.88/18.55 ( sqrt, (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.55 ( sqrt, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.55 ( cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 19.88/18.55 ) 19.88/18.55 (instantiation (let ((_let_0 (fun nat X_a))) (let ((_let_1 (diffs X_a))) (forall ((X_a $$unsorted)) (or (not (ring_1 X_a)) (= _let_1 (ti (fun _let_0 _let_0) _let_1))) ))) 19.88/18.55 ( bool ) 19.88/18.55 ( real ) 19.88/18.55 ( nat ) 19.88/18.55 ( (fun nat bool) ) 19.88/18.55 ( (fun nat nat) ) 19.88/18.55 ( int ) 19.88/18.55 ( (fun real real) ) 19.88/18.55 ( complex ) 19.88/18.55 ( (fun int int) ) 19.88/18.55 ( rat ) 19.88/18.55 ( (fun bool bool) ) 19.88/18.55 ( (fun nat (fun nat bool)) ) 19.88/18.55 ( (product_prod real real) ) 19.88/18.55 ( (product_prod int int) ) 19.88/18.55 ( (fun nat (product_prod int int)) ) 19.88/18.55 ( (product_prod nat nat) ) 19.88/18.56 ( (fun (product_prod nat nat) bool) ) 19.88/18.56 ( (fun nat (fun (product_prod nat nat) bool)) ) 19.88/18.56 ( (fun nat (product_prod nat nat)) ) 19.88/18.56 ) 19.88/18.56 (instantiation (forall ((N $$unsorted)) (not (= (zero_zero real) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) N)))) ) 19.88/18.56 ( (zero_zero nat) ) 19.88/18.56 ( (hAPP nat nat suc (zero_zero nat)) ) 19.88/18.56 ) 19.88/18.56 (instantiation (let ((_let_0 (number_number_of nat))) (forall ((V_3 $$unsorted) (V $$unsorted)) (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_3)) (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP int nat _let_0 V)) (hAPP int nat _let_0 V_3)))) )) 19.88/18.56 ( (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))) ) 19.88/18.56 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.56 ( 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))) ) 19.88/18.56 ( skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.56 ) 19.88/18.56 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149281 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_149281) (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_149281))))) ) 19.88/18.56 ( real, (one_one real) ) 19.88/18.56 ( 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)))) ) 19.88/18.56 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 19.88/18.56 ( int, pls ) 19.88/18.56 ( int, (one_one int) ) 19.88/18.56 ( int, min_1 ) 19.88/18.56 ( complex, ii ) 19.88/18.56 ( complex, (one_one complex) ) 19.88/18.56 ) 19.88/18.56 (instantiation (let ((_let_0 (one_one real))) (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) Y)) _let_0))) (= (hAPP real real sqrt (hAPP real real (hAPP real (fun real real) (minus_minus real) _let_0) (hAPP nat real (hAPP real (fun nat real) (power_power real) Y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real real sin (hAPP real real arccos Y)))) )) 19.88/18.56 ( (hAPP int real (number_number_of real) min_1) ) 19.88/18.56 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.56 ) 19.88/18.56 (instantiation (let ((_let_0 (inverse_divide X_a))) (forall ((X_a $$unsorted)) (or (not (inverse X_a)) (not (real_normed_vector X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0))) )) 19.88/18.56 ( bool ) 19.88/18.56 ( real ) 19.88/18.56 ( nat ) 19.88/18.56 ( (fun nat bool) ) 19.88/18.56 ( int ) 19.88/18.56 ( (fun int bool) ) 19.88/18.56 ( (fun real bool) ) 19.88/18.56 ( (fun real real) ) 19.88/18.56 ( complex ) 19.88/18.56 ( (fun nat real) ) 19.88/18.56 ( (fun int int) ) 19.88/18.56 ( rat ) 19.88/18.56 ( (fun int (fun int bool)) ) 19.88/18.56 ( (product_prod int int) ) 19.88/18.56 ( (fun (product_prod int int) bool) ) 19.88/18.56 ( code_code_numeral ) 19.88/18.56 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 19.88/18.56 ( (fun (product_prod int int) int) ) 19.88/18.56 ( (fun int (fun int (fun int bool))) ) 19.88/18.56 ( (fun int real) ) 19.88/18.56 ) 19.88/18.56 (instantiation (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_149329))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_149329 $$unsorted) (BOUND_VARIABLE_149330 $$unsorted)) (or (not (idom X_a)) (= (or (= _let_3 (ti X_a BOUND_VARIABLE_149330)) (= _let_3 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_149330))) (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_149330) _let_0) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_149329) _let_0)))) ))))) 19.88/18.56 ( bool, fFalse, fTrue ) 19.88/18.56 ( bool, fTrue, fFalse ) 19.88/18.56 ( bool, fTrue, fTrue ) 19.88/18.56 ( real, pi, pi ) 19.88/18.56 ( (fun nat bool), (even_odd_even nat), prime ) 19.88/18.56 ( (fun nat bool), prime, (even_odd_even nat) ) 19.88/18.56 ( (fun nat bool), prime, prime ) 19.88/18.56 ( (fun nat nat), suc, suc ) 19.88/18.56 ( (fun nat nat), suc, nat_size ) 19.88/18.56 ( (fun nat nat), (fact_fact nat), (fact_fact nat) ) 19.88/18.56 ( (fun nat nat), (size_size nat), fact ) 19.88/18.56 ( (fun nat nat), fact, (size_size nat) ) 19.88/18.56 ( (fun nat nat), fact, fact ) 19.88/18.56 ( (fun nat nat), nat_size, suc ) 19.88/18.56 ( int, pls, s1 ) 19.88/18.56 ( int, m, m ) 19.88/18.56 ( int, m, t ) 19.88/18.56 ( int, min_1, min_1 ) 19.88/18.56 ( int, min_1, s ) 19.88/18.56 ( int, s, min_1 ) 19.88/18.56 ( int, s1, pls ) 19.88/18.56 ( int, s1, s1 ) 19.88/18.56 ( int, t, m ) 19.88/18.56 ( (fun int bool), zprime, twoSqu1091635170sum2sq ) 19.88/18.56 ( (fun int bool), nat_neg, nat_is_nat ) 19.88/18.56 ( (fun int bool), zEven, (even_odd_even int) ) 19.88/18.56 ( (fun int bool), nat_is_nat, nat_neg ) 19.88/18.56 ( (fun int bool), nat_is_nat, nat_is_nat ) 19.88/18.56 ( (fun int bool), zOdd, zOdd ) 19.88/18.56 ( (fun int bool), (even_odd_even int), zEven ) 19.88/18.56 ( (fun int bool), (even_odd_even int), (even_odd_even int) ) 19.88/18.56 ( (fun int bool), twoSqu1091635170sum2sq, zprime ) 19.88/18.56 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 19.88/18.56 ( (fun int nat), nat_1, phi ) 19.88/18.56 ( (fun int nat), phi, nat_1 ) 19.88/18.56 ( (fun int nat), phi, phi ) 19.88/18.56 ( (fun real real), sqrt, ln ) 19.88/18.56 ( (fun real real), 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(product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel ) 19.88/18.56 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel ) 19.88/18.56 ( (fun (product_prod int int) rat), frct, frct ) 19.88/18.56 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux ) 19.88/18.56 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel ) 19.88/18.56 ( (fun (fun nat rat) bool), vanishes, vanishes ) 19.88/18.56 ( (fun int (fun int rat)), fract, fract ) 19.88/18.56 ( (fun code_code_numeral int), code_int_of, code_int_of ) 19.88/18.56 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat ) 19.88/18.56 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral) ) 19.88/18.56 ( (fun code_code_numeral nat), (size_size code_code_numeral), code_c271388182l_size ) 19.88/18.56 ( (fun code_code_numeral nat), code_c271388182l_size, (size_size code_code_numeral) ) 19.88/18.56 ( (fun real (fun real complex)), complex_1, complex_1 ) 19.88/18.56 ( (fun real (fun real complex)), complex_1, rcis ) 19.88/18.56 ( (fun real (fun real complex)), rcis, complex_1 ) 19.88/18.56 ( (fun int (fun nat nat)), nat_aux, nat_aux ) 19.88/18.56 ( (fun rat real), ratreal, ratreal ) 19.88/18.56 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of ) 19.88/18.56 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int ) 19.88/18.56 ( (fun rat (product_prod int int)), quotient_of, quotient_of ) 19.88/18.56 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR ) 19.88/18.56 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 19.88/18.56 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of ) 19.88/18.56 ( (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 ) 19.88/18.56 ) 19.88/18.56 (instantiation (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))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (= (hAPP X_b _let_1 (hAPP X_a (fun X_b _let_1) (product_Pair X_a X_b) X_1) Y_1) (hAPP _let_2 _let_1 (the _let_1) (hAPP _let_4 _let_2 (product_prod_case X_a X_b bool) (hAPP _let_3 _let_4 (hAPP _let_6 (fun _let_3 _let_4) (combc X_a _let_3 _let_3) (hAPP _let_7 _let_6 (hAPP (fun _let_0 _let_5) (fun _let_7 _let_6) (combb _let_0 _let_5 X_a) (combb bool bool X_b)) (hAPP _let_8 _let_7 (hAPP (fun bool _let_0) (fun _let_8 _let_7) (combb bool _let_0 X_a) fconj) (hAPP X_a _let_8 (fequal X_a) X_1)))) (hAPP X_b _let_3 (fequal X_b) Y_1))))) )))))))))) 19.88/18.56 ( int, int, (zero_zero int), (one_one int) ) 19.88/18.56 ( int, int, (one_one int), (one_one int) ) 19.88/18.56 ( int, int, s, (one_one int) ) 19.88/18.56 ) 19.88/18.56 (instantiation (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_149368))) (let ((_let_3 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_149370))) (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_149367 $$unsorted) (BOUND_VARIABLE_149368 $$unsorted) (BOUND_VARIABLE_149369 $$unsorted) (BOUND_VARIABLE_149370 $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (not (metric_space X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 _let_2 BOUND_VARIABLE_149369) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 _let_2 BOUND_VARIABLE_149367) _let_3))) (= (ti X_b BOUND_VARIABLE_149369) (ti X_b BOUND_VARIABLE_149367))) ))))) 19.88/18.56 ( real, real, (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.56 ) 19.88/18.56 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_149464 $$unsorted)) (or (not (number_semiring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_149464) (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_149464) BOUND_VARIABLE_149464))) )) 19.88/18.56 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.56 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.56 ( 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))))) ) 19.88/18.57 ( nat, (one_one nat) ) 19.88/18.57 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.57 ( 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) ) 19.88/18.57 ( 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))) ) 19.88/18.57 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.57 ( 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)))) ) 19.88/18.57 ( complex, ii ) 19.88/18.57 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.57 ( 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)) ) 19.88/18.57 ) 19.88/18.57 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) Z) Z_3))) (forall ((Z $$unsorted) (Z_3 $$unsorted)) (or (hBOOL (hAPP int bool nat_neg Z_3)) (= (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) (hAPP int nat nat_1 Z)) (hAPP int nat nat_1 Z_3)) (hAPP nat nat (hAPP nat _let_0 (hAPP bool (fun nat _let_0) (if nat) (hAPP int bool nat_neg _let_1)) (zero_zero nat)) (hAPP int nat nat_1 _let_1)))) ))) 19.88/18.57 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 19.88/18.57 ) 19.88/18.57 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_b bool))) (let ((_let_3 (hAPP X_b _let_2 (ord_less X_b) BOUND_VARIABLE_149556))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_149556 $$unsorted) (BOUND_VARIABLE_149557 $$unsorted) (BOUND_VARIABLE_149558 $$unsorted) (BOUND_VARIABLE_149559 $$unsorted)) (or (not (order X_a)) (not (order X_b)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_149558) BOUND_VARIABLE_149559))) (not (hBOOL (hAPP X_b bool _let_3 (hAPP X_a X_b BOUND_VARIABLE_149557 BOUND_VARIABLE_149558)))) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 Y_2) X_2))) (hBOOL (hAPP X_b bool (hAPP X_b _let_2 (ord_less_eq X_b) (hAPP X_a X_b BOUND_VARIABLE_149557 Y_2)) (hAPP X_a X_b BOUND_VARIABLE_149557 X_2)))) )) (hBOOL (hAPP X_b bool _let_3 (hAPP X_a X_b BOUND_VARIABLE_149557 BOUND_VARIABLE_149559)))) ))))) 19.88/18.57 ( real, real, (zero_zero real), tan, (zero_zero real), pi ) 19.88/18.57 ( real, real, (one_one real), sqrt, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.57 ( real, real, pi, 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 int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.57 ( 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))), pi ) 19.88/18.57 ( 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), skv_11 ) 19.88/18.57 ( real, real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (sgn_sgn 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)))) ) 19.88/18.57 ( 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)), sin, (zero_zero real), skv_6 ) 19.88/18.57 ( nat, int, (zero_zero nat), (number_number_of nat), pls, s ) 19.88/18.57 ( int, int, (zero_zero int), (number_number_of int), min_1, min_1 ) 19.88/18.57 ( int, int, min_1, bit0, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.57 ( int, int, s, (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int), t ) 19.88/18.57 ( int, int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), bit1, pls, (hAPP int int (number_number_of int) pls) ) 19.88/18.57 ( int, int, t, (number_number_of int), pls, min_1 ) 19.88/18.57 ( int, int, skv_3, succ, min_1, pls ) 19.88/18.57 ( int, int, skv_9, pred, pls, (one_one int) ) 19.88/18.57 ) 19.88/18.57 (instantiation (let ((_let_0 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (forall ((P_5 $$unsorted)) (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))))) )) 19.88/18.57 ( (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)))) ) 19.88/18.57 ) 19.88/18.57 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (minus_minus real))) (let ((_let_2 (times_times real))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_2 (hAPP real real sin X)) (hAPP real real cos Y))) (hAPP real real (hAPP real _let_0 _let_2 (hAPP real real cos X)) (hAPP real real sin Y))) (hAPP real real sin (hAPP real real (hAPP real _let_0 _let_1 X) Y))) )))) 19.88/18.57 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 19.88/18.57 ) 19.88/18.57 (instantiation (let ((_let_0 (hAPP X_a X_c B_1_1 B_2_1))) (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= _let_0 (ti X_c _let_0)) )) 19.88/18.57 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 19.88/18.57 ( 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)))) ) 19.88/18.57 ( 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)))) ) 19.88/18.57 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_6 ) 19.88/18.57 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 19.88/18.57 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 19.88/18.57 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_14 ) 19.88/18.57 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 19.88/18.57 ( 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)))) ) 19.88/18.57 ( 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)))) ) 19.88/18.57 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 19.88/18.57 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_10 ) 19.88/18.57 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_13 ) 19.88/18.57 ( 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))) ) 19.88/18.57 ( 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)))) ) 19.88/18.57 ( 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) ) 19.88/18.57 ( 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) ) 19.88/18.57 ( 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) ) 19.88/18.57 ( bool, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 19.88/18.57 ( 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))) ) 19.88/18.57 ( 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 ) 19.88/18.57 ( bool, real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 19.88/18.57 ( 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)))) ) 19.88/18.57 ( 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 ) 19.88/18.57 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) skv_14), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.57 ( bool, nat, (even_odd_even nat), (zero_zero nat) ) 19.88/18.57 ( bool, nat, (even_odd_even nat), (one_one nat) ) 19.88/18.57 ( 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))) ) 19.88/18.57 ( bool, nat, prime, (zero_zero nat) ) 19.88/18.57 ( bool, nat, prime, (one_one nat) ) 19.88/18.57 ( bool, nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.57 ( bool, (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 19.88/18.57 ( 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) ) 19.88/18.57 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 19.88/18.57 ( 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))) ) 19.88/18.57 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 19.88/18.57 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 19.88/18.57 ( 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))) ) 19.88/18.57 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_3 ) 19.88/18.57 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_9 ) 19.88/18.57 ( 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))) ) 19.88/18.57 ( bool, int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.57 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 19.88/18.57 ( 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))) ) 19.88/18.57 ( bool, int, nat_neg, (one_one int) ) 19.88/18.57 ( bool, int, nat_neg, (hAPP int int (number_number_of int) min_1) ) 19.88/18.57 ( bool, int, nat_neg, (hAPP int int (number_number_of int) pls) ) 19.88/18.57 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), (zero_zero int) ) 19.88/18.57 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 19.88/18.57 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 19.88/18.57 ( bool, int, nat_is_nat, (zero_zero int) ) 19.88/18.57 ( bool, int, nat_is_nat, (one_one int) ) 19.88/18.57 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.57 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.88/18.57 ( bool, int, (even_odd_even int), (zero_zero int) ) 19.88/18.57 ( bool, int, (even_odd_even int), (one_one int) ) 19.88/18.57 ( 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))) ) 19.88/18.57 ( bool, int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))), (zero_zero int) ) 19.88/18.57 ( bool, int, (hAPP int (fun int bool) (ord_less int) min_1), (zero_zero int) ) 19.88/18.57 ( bool, int, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 19.88/18.57 ( bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 19.88/18.57 ( 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))) ) 19.88/18.57 ( 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))) ) 19.88/18.57 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 19.88/18.57 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 19.88/18.57 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 19.88/18.57 ( 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) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.57 ( bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 19.88/18.58 ( bool, int, (hAPP int (fun int bool) (ord_less int) t), (zero_zero int) ) 19.88/18.58 ( bool, int, (hAPP int (fun int bool) (ord_less int) t), (one_one int) ) 19.88/18.58 ( 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))) ) 19.88/18.58 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.58 ( bool, int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.58 ( bool, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun int bool) (ord_less 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)))), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 19.88/18.58 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_3), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.58 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_3)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.58 ( 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_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.58 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_9), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.58 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_9)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 19.88/18.58 ( bool, (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 19.88/18.58 ( 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)) ) 19.88/18.58 ( 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))))) ) 19.88/18.58 ( bool, (filter nat), (trivial_limit nat), sequentially ) 19.88/18.58 ( bool, (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 19.88/18.58 ( real, real, sqrt, (zero_zero real) ) 19.88/18.58 ( real, real, sqrt, (one_one real) ) 19.88/18.58 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.58 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 19.88/18.58 ( real, real, (uminus_uminus real), (one_one real) ) 19.88/18.58 ( real, real, (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 19.88/18.58 ( real, real, (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 19.88/18.58 ( real, real, tan, (zero_zero real) ) 19.88/18.58 ( real, real, tan, pi ) 19.88/18.58 ( 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))))) ) 19.88/18.58 ( 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))))) ) 19.88/18.58 ( 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)))) ) 19.88/18.58 ( real, real, cos, (zero_zero real) ) 19.88/18.58 ( real, real, cos, pi ) 19.88/18.58 ( real, real, cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.58 ( 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)))) ) 19.88/18.58 ( 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) ) 19.88/18.58 ( 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))))) ) 19.88/18.58 ( real, real, cos, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 19.88/18.58 ( 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))))) ) 19.88/18.58 ( 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)))) ) 19.88/18.58 ( real, real, cos, skv_14 ) 19.88/18.58 ( real, real, ln, (one_one real) ) 19.88/18.58 ( real, real, (inverse_inverse real), (zero_zero real) ) 19.88/18.58 ( real, real, sin, (zero_zero real) ) 19.88/18.58 ( real, real, sin, pi ) 19.88/18.58 ( 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)))) ) 19.88/18.58 ( 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) ) 19.88/18.58 ( 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))))) ) 19.88/18.58 ( real, real, sin, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 19.88/18.58 ( 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))))) ) 19.88/18.58 ( 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)))) ) 19.88/18.58 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 19.88/18.58 ( real, 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)))) ) 19.88/18.58 ( real, real, (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)))) ) 19.88/18.58 ( 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))) ) 19.88/18.58 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 19.88/18.58 ( real, real, (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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 19.88/18.58 ( real, real, arctan, (zero_zero real) ) 19.88/18.58 ( real, real, arctan, (one_one real) ) 19.88/18.58 ( real, real, arctan, (hAPP real real (hAPP 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))))) ) 19.88/18.58 ( real, real, arctan, (hAPP real real (hAPP 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)))))))))) ) 19.88/18.58 ( 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)))))) ) 19.88/18.58 ( real, real, (sgn_sgn real), (zero_zero real) ) 19.88/18.58 ( 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))) ) 19.88/18.58 ( 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 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(let ((_let_6 (fun _let_1 _let_4))) (let ((_let_7 (combb real _let_0 nat))) (hAPP _let_1 _let_1 (hAPP _let_4 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_4 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 19.88/18.59 ( real, rat, ratreal, (zero_zero rat) ) 19.88/18.59 ( real, rat, ratreal, 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(inverse_divide real)) (real_1 int))))) ) 20.18/18.72 ( (let ((_let_0 (fun nat real))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))) ) 20.18/18.72 ( (let ((_let_0 (fun nat real))) (fun (fun int (fun real real)) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat real))) (fun (fun real real) (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (combb (fun real real) (fun _let_0 _let_0) int)), (combb real real nat) ) 20.18/18.72 ) 20.18/18.72 (instantiation (let ((_let_0 (hAPP int (fun int rat) fract (zero_zero int)))) (forall ((A_1 $$unsorted) (C $$unsorted)) (= (hAPP int rat _let_0 C) (hAPP int rat _let_0 A_1)) )) 20.18/18.72 ( (one_one int), (one_one int) ) 20.18/18.72 ) 20.18/18.72 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (forall ((X $$unsorted) (P_5 $$unsorted)) (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))) ))) 20.18/18.72 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.72 ) 20.18/18.72 (instantiation (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_149787))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_149787 $$unsorted) (BOUND_VARIABLE_149788 $$unsorted) (BOUND_VARIABLE_149789 $$unsorted)) (or (not (linord893533164strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_149788) BOUND_VARIABLE_149789))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_149787))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_149788)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_149789)))) )))) 20.18/18.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1, (zero_zero int) ) 20.18/18.72 ) 20.18/18.72 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (forall ((Y $$unsorted) (X $$unsorted)) (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)))) )) 20.18/18.72 ( (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))) ) 20.18/18.72 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.72 ( 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))) ) 20.18/18.72 ( skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.18/18.72 ) 20.18/18.72 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 (hAPP real real ln X)))) (not (hBOOL (hAPP real bool _let_2 X))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) X))) )))) 20.18/18.72 ( (one_one real) ) 20.18/18.72 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.72 ) 20.18/18.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149911 $$unsorted)) (or (not (ab_group_add X_a)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_149911)) BOUND_VARIABLE_149911))) ) 20.18/18.72 ( real, (one_one real) ) 20.18/18.72 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.72 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 20.18/18.72 ( int, pls ) 20.18/18.72 ( int, (one_one int) ) 20.18/18.72 ( int, min_1 ) 20.18/18.72 ( complex, ii ) 20.18/18.72 ( complex, (one_one complex) ) 20.18/18.72 ) 20.18/18.72 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP real complex (of_real complex) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP complex real re Z_1))) (hAPP complex complex (hAPP complex (fun complex complex) (plus_plus complex) Z_1) (hAPP complex complex cnj Z_1))) ) 20.18/18.72 ( ii ) 20.18/18.72 ( (zero_zero complex) ) 20.18/18.72 ( (one_one complex) ) 20.18/18.72 ) 20.18/18.72 (instantiation (let ((_let_0 (norm_norm X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_149961 $$unsorted)) (or (not (real_normed_vector X_a)) (= (hAPP X_a real _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_149961)) (hAPP X_a real _let_0 BOUND_VARIABLE_149961))) )) 20.18/18.72 ( real, (one_one real) ) 20.18/18.72 ( 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)))) ) 20.18/18.72 ( 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) ) 20.18/18.72 ( int, pls ) 20.18/18.72 ( int, (one_one int) ) 20.18/18.72 ( int, min_1 ) 20.18/18.72 ( complex, ii ) 20.18/18.72 ( complex, (one_one complex) ) 20.18/18.72 ) 20.18/18.72 (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))) ) 20.18/18.72 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 20.18/18.72 ) 20.18/18.72 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (power_power real))) (forall ((N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= _let_0 (hAPP real real (hAPP real _let_1 (times_times real) (hAPP real real (hAPP real _let_1 (inverse_divide real) (hAPP nat real (hAPP real _let_2 _let_3 (hAPP int real (number_number_of real) min_1)) (hAPP nat nat (hAPP nat (fun nat nat) (div_div nat) N) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) N)))) (hAPP nat real (hAPP real _let_2 _let_3 _let_0) N)))) ))))) 20.18/18.72 ( (zero_zero nat) ) 20.18/18.72 ( (hAPP nat nat suc (zero_zero nat)) ) 20.18/18.72 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.72 ) 20.18/18.72 (instantiation (let ((_let_0 (fun (filter X_a) bool))) (let ((_let_1 (fun X_a X_b))) (let ((_let_2 (fun X_a real))) (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_150062 $$unsorted) (BOUND_VARIABLE_150063 $$unsorted)) (let ((_let_0 (filter X_a))) (or (not (real_normed_vector X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (tendsto X_a real) (hAPP _let_1 _let_2 (hAPP (fun X_b real) (fun _let_1 _let_2) (combb X_b real X_a) (norm_norm X_b)) BOUND_VARIABLE_150062)) (zero_zero real)) BOUND_VARIABLE_150063))) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_0 (hAPP _let_1 (fun X_b _let_0) (tendsto X_a X_b) BOUND_VARIABLE_150062) (zero_zero X_b)) BOUND_VARIABLE_150063)))) )))) 20.18/18.72 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 20.18/18.72 ( nat, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), sequentially ) 20.18/18.72 ) 20.18/18.72 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_150119 $$unsorted) (BOUND_VARIABLE_150120 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_150120) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_150119) _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_150120) BOUND_VARIABLE_150119)))) )))) 20.18/18.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 20.18/18.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 20.18/18.72 ( 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))) ) 20.18/18.72 ( 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)))) ) 20.18/18.72 ( 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)))) ) 20.18/18.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 20.18/18.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 20.18/18.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 20.18/18.72 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 20.18/18.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 20.18/18.72 ( 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) ) 20.18/18.72 ) 20.18/18.72 (instantiation (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_150149))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_150149 $$unsorted) (BOUND_VARIABLE_150150 $$unsorted) (BOUND_VARIABLE_150151 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_150150) BOUND_VARIABLE_150151))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_150149))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_150150)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_150151)))) )))) 20.18/18.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1, (zero_zero int) ) 20.18/18.72 ) 20.18/18.72 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (forall ((Y_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root N_1) Y_1))) (hBOOL (hAPP real bool _let_0 Y_1)))) )) 20.18/18.72 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.72 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.72 ( (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))) ) 20.18/18.72 ( (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))) ) 20.18/18.72 ) 20.18/18.72 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_150284 $$unsorted) (BOUND_VARIABLE_150285 $$unsorted) (BOUND_VARIABLE_150286 $$unsorted)) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_150285) BOUND_VARIABLE_150286))) (not (= (ti X_a BOUND_VARIABLE_150285) (ti X_a BOUND_VARIABLE_150284))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_150284) BOUND_VARIABLE_150286))) ))) 20.18/18.72 ( 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))) ) 20.18/18.72 ( int, pls, (zero_zero int), (zero_zero int) ) 20.18/18.72 ( int, m, (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))) ) 20.18/18.72 ( int, min_1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 20.18/18.72 ( int, s, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.18/18.72 ( int, s1, t, (zero_zero int) ) 20.18/18.72 ( int, t, (zero_zero int), (one_one int) ) 20.18/18.72 ) 20.18/18.72 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (fun nat _let_3))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_150336 $$unsorted)) (or (not (banach X_a)) (not (real_n2089651433ebra_1 X_a)) (hBOOL (hAPP _let_1 bool (summable real) (hAPP _let_2 _let_1 (hAPP (fun X_a real) (fun _let_2 _let_1) (combb X_a real nat) (norm_norm X_a)) (hAPP _let_2 _let_2 (hAPP _let_4 (fun _let_2 _let_2) (combs nat X_a X_a) (hAPP _let_1 _let_4 (hAPP (fun real _let_3) (fun _let_1 _let_4) (combb real _let_3 nat) (scaleR_scaleR X_a)) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) (fact_fact nat))))) (hAPP X_a _let_2 (power_power X_a) BOUND_VARIABLE_150336)))))) )))))) 20.18/18.73 ( real, (hAPP int real (number_number_of real) min_1) ) 20.18/18.73 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.73 ( int, s ) 20.18/18.73 ( int, s1 ) 20.18/18.73 ( int, skv_8 ) 20.18/18.73 ( complex, ii ) 20.18/18.73 ) 20.18/18.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150372 $$unsorted)) (or (not (number_ring X_a)) (= (ti X_a BOUND_VARIABLE_150372) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_150372) (hAPP int X_a (number_number_of X_a) pls)))) ) 20.18/18.73 ( bool, fFalse ) 20.18/18.73 ( bool, fTrue ) 20.18/18.73 ( real, pi ) 20.18/18.73 ( nat, (one_one nat) ) 20.18/18.73 ( (fun nat bool), (even_odd_even nat) ) 20.18/18.73 ( (fun nat bool), prime ) 20.18/18.73 ( (fun nat nat), suc ) 20.18/18.73 ( (fun nat nat), (fact_fact nat) ) 20.18/18.73 ( (fun nat nat), (size_size nat) ) 20.18/18.73 ( (fun nat nat), fact ) 20.18/18.73 ( (fun nat nat), nat_size ) 20.18/18.73 ( int, pls ) 20.18/18.73 ( int, m ) 20.18/18.73 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 20.18/18.73 ( int, min_1 ) 20.18/18.73 ( int, s ) 20.18/18.73 ( 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)))) ) 20.18/18.73 ( int, s1 ) 20.18/18.73 ( int, t ) 20.18/18.73 ( (fun int bool), zprime ) 20.18/18.73 ( (fun int bool), nat_neg ) 20.18/18.73 ( (fun int bool), zEven ) 20.18/18.73 ( (fun int bool), nat_is_nat ) 20.18/18.73 ( (fun int bool), zOdd ) 20.18/18.73 ( (fun int bool), (even_odd_even int) ) 20.18/18.73 ( (fun int bool), twoSqu1091635170sum2sq ) 20.18/18.73 ( (fun int nat), nat_1 ) 20.18/18.73 ( (fun int nat), phi ) 20.18/18.73 ( (fun real real), sqrt ) 20.18/18.73 ( (fun real real), tan ) 20.18/18.73 ( (fun real real), cos ) 20.18/18.73 ( (fun real real), arccos ) 20.18/18.73 ( (fun real real), ln ) 20.18/18.73 ( (fun real real), sin ) 20.18/18.73 ( (fun real real), arctan ) 20.18/18.73 ( (fun real real), arcsin ) 20.18/18.73 ( complex, ii ) 20.18/18.73 ( (fun complex complex), cnj ) 20.18/18.73 ( (fun complex complex), expi ) 20.18/18.73 ( (fun nat real), (real_1 nat) ) 20.18/18.73 ( (fun nat real), cos_coeff ) 20.18/18.73 ( (fun nat real), sin_coeff ) 20.18/18.73 ( (fun int int), bit0 ) 20.18/18.73 ( (fun int int), bit1 ) 20.18/18.73 ( (fun int int), pred ) 20.18/18.73 ( (fun int int), succ ) 20.18/18.73 ( (fun int int), (fact_fact int) ) 20.18/18.73 ( (fun int int), zfact ) 20.18/18.73 ( (fun bool bool), fNot ) 20.18/18.73 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 20.18/18.73 ( (fun bool (fun bool bool)), fconj ) 20.18/18.73 ( (fun bool (fun bool bool)), fdisj ) 20.18/18.73 ( (fun bool (fun bool bool)), fimplies ) 20.18/18.73 ( (fun int (fun int bool)), sRStar ) 20.18/18.73 ( (fun int (fun int bool)), quadRes ) 20.18/18.73 ( (fun int (fun int bool)), norRRset ) 20.18/18.73 ( (fun int (fun int bool)), d22set ) 20.18/18.73 ( (fun int (fun int bool)), sr ) 20.18/18.73 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 20.18/18.73 ( (fun nat (fun nat nat)), nat_gcd ) 20.18/18.73 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 20.18/18.73 ( (fun nat (fun nat nat)), nat_lcm ) 20.18/18.73 ( (fun nat (fun real real)), root ) 20.18/18.73 ( (fun real (fun real real)), log ) 20.18/18.73 ( (fun real (fun real real)), powr ) 20.18/18.73 ( (fun nat (fun nat bool)), coprime ) 20.18/18.73 ( (fun (fun int bool) int), (the int) ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 20.18/18.73 ( (fun nat (fun nat (product_prod int int))), bezw ) 20.18/18.73 ( (fun (fun int bool) bool), nat_nat_set ) 20.18/18.73 ( (filter nat), sequentially ) 20.18/18.73 ( (fun (product_prod nat nat) bool), pred_nat ) 20.18/18.73 ( (fun (product_prod int int) bool), frac_1 ) 20.18/18.73 ( (fun real complex), cis ) 20.18/18.73 ( (fun complex real), im ) 20.18/18.73 ( (fun complex real), re ) 20.18/18.73 ( (fun complex real), arg ) 20.18/18.73 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 20.18/18.73 ( (fun int (fun int int)), int_gcd ) 20.18/18.73 ( (fun int (fun int int)), multInv ) 20.18/18.73 ( (fun int (fun int int)), legacy_zgcd ) 20.18/18.73 ( (fun int (fun int int)), z3mod ) 20.18/18.73 ( (fun int (fun int int)), inv ) 20.18/18.73 ( (fun int (fun int int)), (gcd_gcd int) ) 20.18/18.73 ( (fun int (fun int int)), standardRes ) 20.18/18.73 ( (fun int (fun int int)), legendre ) 20.18/18.73 ( (fun int (fun int int)), nat_tsub ) 20.18/18.73 ( (fun int (fun int int)), z3div ) 20.18/18.73 ( (fun int (fun int int)), int_lcm ) 20.18/18.73 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 20.18/18.73 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 20.18/18.73 ( (fun int (fun (fun int bool) bool)), rsetR ) 20.18/18.73 ( (fun int (fun (fun int bool) bool)), resSet ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 20.18/18.73 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 20.18/18.73 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 20.18/18.73 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 20.18/18.73 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 20.18/18.73 ( (fun int (fun int (product_prod int int))), negDivAlg ) 20.18/18.73 ( (fun int (fun int (product_prod int int))), divmod_int ) 20.18/18.73 ( (fun int (fun int (product_prod int int))), posDivAlg ) 20.18/18.73 ( (fun int (fun int (product_prod int int))), pdivmod ) 20.18/18.73 ( (fun int (fun int (product_prod int int))), norm_frac ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 20.18/18.73 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 20.18/18.73 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 20.18/18.73 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 20.18/18.73 ( (fun real nat), natfloor ) 20.18/18.73 ( (fun real nat), natceiling ) 20.18/18.73 ( (fun int quickcheck_code_int), quickcheck_of_int ) 20.18/18.73 ( (fun int (fun int (fun int bool))), wset ) 20.18/18.73 ( (fun int (fun int (fun int bool))), bnorRset ) 20.18/18.73 ( (fun int (fun int (fun int bool))), zcong ) 20.18/18.73 ( (fun int (fun int (fun int bool))), noXRRset ) 20.18/18.73 ( (fun int (fun int (fun int bool))), zcongm ) 20.18/18.73 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 20.18/18.73 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 20.18/18.73 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 20.18/18.73 ( (fun int real), (real_1 int) ) 20.18/18.73 ( (fun complex nat), (size_size complex) ) 20.18/18.73 ( (fun complex nat), complex_size ) 20.18/18.73 ( (fun int (list int)), quickc666637781d_zero ) 20.18/18.73 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 20.18/18.73 ( (fun (product_prod int int) rat), frct ) 20.18/18.73 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 20.18/18.73 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 20.18/18.73 ( (fun (fun nat rat) bool), vanishes ) 20.18/18.73 ( (fun int (fun int rat)), fract ) 20.18/18.73 ( (fun code_code_numeral int), code_int_of ) 20.18/18.73 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 20.18/18.73 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 20.18/18.73 ( (fun code_code_numeral nat), code_c271388182l_size ) 20.18/18.73 ( (fun real (fun real complex)), complex_1 ) 20.18/18.73 ( (fun real (fun real complex)), rcis ) 20.18/18.73 ( (fun int (fun nat nat)), nat_aux ) 20.18/18.73 ( (fun rat real), ratreal ) 20.18/18.73 ( (fun quickcheck_code_int int), quickcheck_int_of ) 20.18/18.73 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 20.18/18.73 ( (fun rat (product_prod int int)), quotient_of ) 20.18/18.73 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 20.18/18.73 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 20.18/18.73 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 20.18/18.73 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 20.18/18.73 ) 20.18/18.73 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (ord_less real))) (let ((_let_4 (hAPP real _let_0 _let_3 A_2))) (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_4 B_1))) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_2) X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) B_1))) (hBOOL (hAPP real bool (hAPP _let_2 _let_0 (isCont real real) F) X_2))) )) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_4 X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_3 X_2) B_1))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (deriv real) F) X_2) (zero_zero real)))) )) (= (hAPP real real F B_1) (hAPP real real F A_2))) )))))) 20.18/18.73 ( sqrt, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP 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) ) 20.18/18.73 ( tan, pi, (zero_zero real) ) 20.18/18.73 ( cos, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP 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 ) 20.18/18.73 ( 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)))) ) 20.18/18.73 ( (hAPP real (fun real real) (inverse_divide real) pi), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.73 ( (hAPP real (fun real real) (inverse_divide 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))) ) 20.18/18.73 ( (sgn_sgn real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 20.18/18.73 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), (zero_zero real), pi ) 20.18/18.73 ) 20.18/18.73 (instantiation (let ((_let_0 (sgn_sgn X_a))) (forall ((X_a $$unsorted)) (or (not (sgn_div_norm X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 20.18/18.73 ( bool ) 20.18/18.73 ( real ) 20.18/18.73 ( nat ) 20.18/18.73 ( (fun nat bool) ) 20.18/18.73 ( int ) 20.18/18.73 ( (fun int bool) ) 20.18/18.73 ( (fun real bool) ) 20.18/18.73 ( (fun real real) ) 20.18/18.73 ( complex ) 20.18/18.73 ( (fun nat real) ) 20.18/18.73 ( (fun int int) ) 20.18/18.73 ( rat ) 20.18/18.73 ( (fun int (fun int bool)) ) 20.18/18.73 ( (product_prod int int) ) 20.18/18.73 ( (fun (product_prod int int) bool) ) 20.18/18.73 ( code_code_numeral ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 20.18/18.73 ( (fun (product_prod int int) int) ) 20.18/18.73 ( (fun int (fun int (fun int bool))) ) 20.18/18.73 ( (fun int real) ) 20.18/18.73 ) 20.18/18.73 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_150515))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_150515 $$unsorted)) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool _let_0 (zero_zero X_a))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_150515))))) )) 20.18/18.73 ( real, (zero_zero real) ) 20.18/18.73 ( real, (one_one real) ) 20.18/18.73 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.73 ( 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)))) ) 20.18/18.73 ( 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) ) 20.18/18.73 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.73 ( real, skv_14 ) 20.18/18.73 ( int, (zero_zero int) ) 20.18/18.73 ( int, pls ) 20.18/18.73 ( int, (one_one int) ) 20.18/18.73 ( int, min_1 ) 20.18/18.73 ( complex, ii ) 20.18/18.73 ( complex, (one_one complex) ) 20.18/18.73 ) 20.18/18.73 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_150535 $$unsorted)) (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_150535) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (= _let_0 (ti X_a BOUND_VARIABLE_150535)))) )) 20.18/18.73 ( bool, fFalse ) 20.18/18.73 ( bool, fTrue ) 20.18/18.73 ( real, pi ) 20.18/18.73 ( real, (hAPP int real (number_number_of real) min_1) ) 20.18/18.73 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.73 ( (fun nat bool), (even_odd_even nat) ) 20.18/18.73 ( (fun nat bool), prime ) 20.18/18.73 ( (fun nat nat), suc ) 20.18/18.73 ( (fun nat nat), (fact_fact nat) ) 20.18/18.73 ( (fun nat nat), (size_size nat) ) 20.18/18.73 ( (fun nat nat), fact ) 20.18/18.73 ( (fun nat nat), nat_size ) 20.18/18.73 ( int, pls ) 20.18/18.73 ( int, m ) 20.18/18.73 ( int, min_1 ) 20.18/18.73 ( int, s ) 20.18/18.73 ( int, s1 ) 20.18/18.73 ( int, t ) 20.18/18.73 ( int, skv_8 ) 20.18/18.73 ( (fun int bool), zprime ) 20.18/18.73 ( (fun int bool), nat_neg ) 20.18/18.73 ( (fun int bool), zEven ) 20.18/18.73 ( (fun int bool), nat_is_nat ) 20.18/18.73 ( (fun int bool), zOdd ) 20.18/18.73 ( (fun int bool), (even_odd_even int) ) 20.18/18.73 ( (fun int bool), twoSqu1091635170sum2sq ) 20.18/18.73 ( (fun int nat), nat_1 ) 20.18/18.73 ( (fun int nat), phi ) 20.18/18.73 ( (fun real real), sqrt ) 20.18/18.73 ( (fun real real), tan ) 20.18/18.73 ( (fun real real), cos ) 20.18/18.73 ( (fun real real), arccos ) 20.18/18.73 ( (fun real real), ln ) 20.18/18.73 ( (fun real real), sin ) 20.18/18.73 ( (fun real real), arctan ) 20.18/18.73 ( (fun real real), arcsin ) 20.18/18.73 ( complex, ii ) 20.18/18.73 ( (fun complex complex), cnj ) 20.18/18.73 ( (fun complex complex), expi ) 20.18/18.73 ( (fun nat real), (real_1 nat) ) 20.18/18.73 ( (fun nat real), cos_coeff ) 20.18/18.73 ( (fun nat real), sin_coeff ) 20.18/18.73 ( (fun int int), bit0 ) 20.18/18.73 ( (fun int int), bit1 ) 20.18/18.73 ( (fun int int), pred ) 20.18/18.73 ( (fun int int), succ ) 20.18/18.73 ( (fun int int), (fact_fact int) ) 20.18/18.73 ( (fun int int), zfact ) 20.18/18.73 ( (fun bool bool), fNot ) 20.18/18.73 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 20.18/18.73 ( (fun bool (fun bool bool)), fconj ) 20.18/18.73 ( (fun bool (fun bool bool)), fdisj ) 20.18/18.73 ( (fun bool (fun bool bool)), fimplies ) 20.18/18.73 ( (fun int (fun int bool)), sRStar ) 20.18/18.73 ( (fun int (fun int bool)), quadRes ) 20.18/18.73 ( (fun int (fun int bool)), norRRset ) 20.18/18.73 ( (fun int (fun int bool)), d22set ) 20.18/18.73 ( (fun int (fun int bool)), sr ) 20.18/18.73 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 20.18/18.73 ( (fun nat (fun nat nat)), nat_gcd ) 20.18/18.73 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 20.18/18.73 ( (fun nat (fun nat nat)), nat_lcm ) 20.18/18.73 ( (fun nat (fun real real)), root ) 20.18/18.73 ( (fun real (fun real real)), log ) 20.18/18.73 ( (fun real (fun real real)), powr ) 20.18/18.73 ( (fun nat (fun nat bool)), coprime ) 20.18/18.73 ( (fun (fun int bool) int), (the int) ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 20.18/18.73 ( (fun nat (fun nat (product_prod int int))), bezw ) 20.18/18.73 ( (fun (fun int bool) bool), nat_nat_set ) 20.18/18.73 ( (filter nat), sequentially ) 20.18/18.73 ( (fun (product_prod nat nat) bool), pred_nat ) 20.18/18.73 ( (fun (product_prod int int) bool), frac_1 ) 20.18/18.73 ( (fun real complex), cis ) 20.18/18.73 ( (fun complex real), im ) 20.18/18.73 ( (fun complex real), re ) 20.18/18.73 ( (fun complex real), arg ) 20.18/18.73 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 20.18/18.73 ( (fun int (fun int int)), int_gcd ) 20.18/18.73 ( (fun int (fun int int)), multInv ) 20.18/18.73 ( (fun int (fun int int)), legacy_zgcd ) 20.18/18.73 ( (fun int (fun int int)), z3mod ) 20.18/18.73 ( (fun int (fun int int)), inv ) 20.18/18.73 ( (fun int (fun int int)), (gcd_gcd int) ) 20.18/18.73 ( (fun int (fun int int)), standardRes ) 20.18/18.73 ( (fun int (fun int int)), legendre ) 20.18/18.73 ( (fun int (fun int int)), nat_tsub ) 20.18/18.73 ( (fun int (fun int int)), z3div ) 20.18/18.73 ( (fun int (fun int int)), int_lcm ) 20.18/18.73 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 20.18/18.73 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 20.18/18.73 ( (fun int (fun (fun int bool) bool)), rsetR ) 20.18/18.73 ( (fun int (fun (fun int bool) bool)), resSet ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 20.18/18.73 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 20.18/18.73 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 20.18/18.73 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 20.18/18.73 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 20.18/18.73 ( (fun int (fun int (product_prod int int))), negDivAlg ) 20.18/18.73 ( (fun int (fun int (product_prod int int))), divmod_int ) 20.18/18.73 ( (fun int (fun int (product_prod int int))), posDivAlg ) 20.18/18.73 ( (fun int (fun int (product_prod int int))), pdivmod ) 20.18/18.73 ( (fun int (fun int (product_prod int int))), norm_frac ) 20.18/18.73 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 20.18/18.74 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 20.18/18.74 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 20.18/18.74 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 20.18/18.74 ( (fun real nat), natfloor ) 20.18/18.74 ( (fun real nat), natceiling ) 20.18/18.74 ( (fun int quickcheck_code_int), quickcheck_of_int ) 20.18/18.74 ( (fun int (fun int (fun int bool))), wset ) 20.18/18.74 ( (fun int (fun int (fun int bool))), bnorRset ) 20.18/18.74 ( (fun int (fun int (fun int bool))), zcong ) 20.18/18.74 ( (fun int (fun int (fun int bool))), noXRRset ) 20.18/18.74 ( (fun int (fun int (fun int bool))), zcongm ) 20.18/18.74 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 20.18/18.74 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 20.18/18.74 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 20.18/18.74 ( (fun int real), (real_1 int) ) 20.18/18.74 ( (fun complex nat), (size_size complex) ) 20.18/18.74 ( (fun complex nat), complex_size ) 20.18/18.74 ( (fun int (list int)), quickc666637781d_zero ) 20.18/18.74 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 20.18/18.74 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 20.18/18.74 ( (fun (product_prod int int) rat), frct ) 20.18/18.74 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 20.18/18.74 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 20.18/18.74 ( (fun (fun nat rat) bool), vanishes ) 20.18/18.74 ( (fun int (fun int rat)), fract ) 20.18/18.74 ( (fun code_code_numeral int), code_int_of ) 20.18/18.74 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 20.18/18.74 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 20.18/18.74 ( (fun code_code_numeral nat), code_c271388182l_size ) 20.18/18.74 ( (fun real (fun real complex)), complex_1 ) 20.18/18.74 ( (fun real (fun real complex)), rcis ) 20.18/18.74 ( (fun int (fun nat nat)), nat_aux ) 20.18/18.74 ( (fun rat real), ratreal ) 20.18/18.74 ( (fun quickcheck_code_int int), quickcheck_int_of ) 20.18/18.74 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 20.18/18.74 ( (fun rat (product_prod int int)), quotient_of ) 20.18/18.74 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 20.18/18.74 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 20.18/18.74 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 20.18/18.74 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 20.18/18.74 ) 20.18/18.74 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (fun int int))) (let ((_let_4 (ord_less int))) (let ((_let_5 (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 _let_2) B_8)))) (forall ((A_9 $$unsorted) (B_8 $$unsorted) (Q_6 $$unsorted) (Y $$unsorted)) (or (not (= (hAPP int int (hAPP int _let_3 (plus_plus int) (hAPP int int (hAPP int _let_3 (times_times int) B_8) Q_6)) Y) (ti int A_9))) (and _let_5 (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 Y) B_8))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) Y))))) (and (not _let_5) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 B_8) Y))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Y) _let_2))))) (= _let_2 (ti int B_8)) (= (ti int Y) (hAPP int int (hAPP int _let_3 (div_mod int) A_9) B_8))) ))))))) 20.18/18.74 ( min_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) ) 20.18/18.74 ) 20.18/18.74 (instantiation (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_150625))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_150625 $$unsorted)) (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_150625))) (hAPP _let_0 real (suminf real) _let_3)))) ))))) 20.18/18.74 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (combc nat nat nat))) (let ((_let_4 (fun nat _let_0))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun _let_1 _let_4))) (let ((_let_7 (combb real _let_0 nat))) (hAPP _let_1 _let_1 (hAPP _let_4 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_4 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 20.18/18.74 ) 20.18/18.74 (instantiation (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_150649))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_150649 $$unsorted) (BOUND_VARIABLE_150650 $$unsorted)) (or (not (field_inverse_zero X_a)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_150650)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_150650)))) ))) 20.18/18.74 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.74 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.18/18.74 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.74 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 20.18/18.74 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.74 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.74 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.18/18.74 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.18/18.74 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.74 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.74 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.74 ) 20.18/18.74 (instantiation (forall ((K_4 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) K_4))) (not (forall ((N_2 $$unsorted)) (or (not (= (hAPP nat int (semiring_1_of_nat int) N_2) (ti int K_4))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_2)))) ))) ) 20.18/18.74 ( (zero_zero int) ) 20.18/18.74 ( (one_one int) ) 20.18/18.74 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.18/18.74 ( min_1 ) 20.18/18.74 ) 20.18/18.74 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (ring_1_Ints X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_150818 $$unsorted) (BOUND_VARIABLE_150819 $$unsorted)) (or (not (ring_1 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_150819) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_150818) _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_150819) BOUND_VARIABLE_150818)) _let_3))) ))))) 20.18/18.74 ( 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 bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 20.18/18.74 ( int, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.74 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 20.18/18.74 ) 20.18/18.74 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_150849 $$unsorted) (BOUND_VARIABLE_150850 $$unsorted)) (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_150849) BOUND_VARIABLE_150850)))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_150849))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_150850))) )) 20.18/18.74 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 20.18/18.74 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 20.18/18.74 ( 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)))))) ) 20.18/18.74 ( 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 ) 20.18/18.74 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 20.18/18.74 ( 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) ) 20.18/18.74 ( 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 ) 20.18/18.74 ( 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_1 ) 20.18/18.74 ( complex, ii, ii ) 20.18/18.74 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 20.18/18.74 ( 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 ) 20.18/18.74 ) 20.18/18.74 (instantiation (forall ((Nat_1 $$unsorted)) (= (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))) (hAPP nat nat nat_size (hAPP nat nat suc Nat_1))) ) 20.18/18.74 ( (zero_zero nat) ) 20.18/18.74 ( (hAPP nat nat suc (zero_zero nat)) ) 20.18/18.74 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 20.18/18.74 ) 20.18/18.74 (instantiation (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_150873))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_150872 $$unsorted) (BOUND_VARIABLE_150873 $$unsorted)) (or (not (linordered_idom X_a)) (= (and (not (hBOOL (hAPP nat bool (even_odd_even nat) _let_3))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_150872) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_150872) _let_3)) _let_2)))) ))))) 20.18/18.74 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.18/18.74 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.18/18.74 ( int, skv_8, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.18/18.74 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.18/18.74 ) 20.18/18.74 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int (fun int bool) (dvd_dvd int) I_1))) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (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))) ))) 20.18/18.74 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_1 ) 20.18/18.74 ) 20.18/18.74 (instantiation (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_150903))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_150903 $$unsorted) (BOUND_VARIABLE_150904 $$unsorted)) (or (not (power X_a)) (= (hAPP nat X_a _let_0 (hAPP nat nat suc BOUND_VARIABLE_150904)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_150903) (hAPP nat X_a _let_0 BOUND_VARIABLE_150904)))) )) 20.18/18.74 ( int, s, (hAPP nat nat suc (zero_zero nat)) ) 20.18/18.74 ( int, s1, (hAPP nat nat suc (zero_zero nat)) ) 20.18/18.74 ( int, skv_8, (hAPP nat nat suc (zero_zero nat)) ) 20.18/18.74 ( complex, ii, (hAPP nat nat suc (zero_zero nat)) ) 20.18/18.74 ) 20.18/18.74 (instantiation (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (forall ((X $$unsorted)) (= (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real sin X)) _let_2) (hAPP real real (hAPP real (fun real real) (minus_minus real) (one_one real)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real cos X)) _let_2))) )))) 20.18/18.74 ( (zero_zero real) ) 20.18/18.74 ( pi ) 20.18/18.74 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.74 ( (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)))) ) 20.18/18.74 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 20.18/18.74 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 20.18/18.74 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 20.18/18.74 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 20.18/18.74 ( (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)))) ) 20.18/18.75 ( skv_14 ) 20.18/18.75 ) 20.18/18.75 (instantiation (let ((_let_0 (zero_zero real))) (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) _let_0) Y))) (= _let_0 (hAPP real real cos (hAPP complex real arg (hAPP real complex (hAPP real (fun real complex) complex_1 _let_0) Y))))) )) 20.18/18.75 ( (zero_zero real) ) 20.18/18.75 ( (one_one real) ) 20.18/18.75 ( pi ) 20.18/18.75 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.75 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.75 ( skv_2 ) 20.18/18.75 ( skv_10 ) 20.18/18.75 ( skv_13 ) 20.18/18.75 ) 20.18/18.75 (instantiation (let ((_let_0 (product_prod_case X_a X_b X_c))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (= _let_0 (ti (fun (fun X_a (fun X_b X_c)) (fun (product_prod X_a X_b) X_c)) _let_0)) )) 20.18/18.75 ( real, real, bool ) 20.18/18.75 ( nat, nat, bool ) 20.18/18.75 ( nat, nat, (fun (product_prod nat nat) bool) ) 20.18/18.75 ( int, int, bool ) 20.18/18.75 ( int, int, int ) 20.18/18.75 ( int, int, (fun int bool) ) 20.18/18.75 ( int, int, (fun int int) ) 20.18/18.75 ( int, int, rat ) 20.18/18.75 ( int, int, (fun bool bool) ) 20.18/18.75 ( int, int, (product_prod int int) ) 20.18/18.75 ( int, int, (fun (product_prod int int) bool) ) 20.18/18.75 ( int, int, (fun (product_prod int int) int) ) 20.18/18.75 ( int, int, (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 20.18/18.75 ( int, int, (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 20.18/18.75 ( int, int, (fun (product_prod int int) (fun int bool)) ) 20.18/18.75 ( int, int, (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 20.18/18.79 ( (product_prod int int), (product_prod int int), bool ) 20.18/18.79 ( (product_prod nat nat), (product_prod nat nat), bool ) 20.18/18.79 ) 20.18/18.79 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_151029 $$unsorted) (BOUND_VARIABLE_151030 $$unsorted)) (or (not (comple44059174attice X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_151029) BOUND_VARIABLE_151030))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_151029) (hAPP _let_0 X_a (complete_Sup_Sup X_a) BOUND_VARIABLE_151030)))) )) 20.18/18.79 ( int, (one_one int), zEven ) 20.18/18.79 ) 20.18/18.79 (instantiation (let ((_let_0 (ord_atMost X_a))) (forall ((X_a $$unsorted)) (or (not (ord X_a)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0))) )) 20.18/18.79 ( bool ) 20.18/18.79 ( real ) 20.18/18.79 ( nat ) 20.18/18.79 ( (fun nat bool) ) 20.18/18.79 ( int ) 20.18/18.79 ( (fun int bool) ) 20.18/18.79 ( rat ) 20.18/18.79 ( quickcheck_code_int ) 20.18/18.79 ( (product_prod real real) ) 20.18/18.79 ( (product_prod int int) ) 20.18/18.79 ( (filter real) ) 20.18/18.79 ( (filter nat) ) 20.18/18.79 ( (product_prod nat nat) ) 20.18/18.79 ( code_code_numeral ) 20.18/18.79 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 20.18/18.79 ( (fun nat rat) ) 20.18/18.79 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 20.18/18.79 ) 20.18/18.79 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) ln) X_1) (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) X_1)))) ))) 20.18/18.79 ( pi ) 20.18/18.79 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.79 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.79 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.18/18.79 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.79 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.79 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 20.18/18.79 ( skv_2 ) 20.18/18.79 ( skv_10 ) 20.18/18.79 ( skv_13 ) 20.18/18.79 ) 20.18/18.79 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (minus_minus int) K_4) (one_one int)) (hAPP int int pred K_4)) ) 20.18/18.79 ( pls ) 20.18/18.79 ( min_1 ) 20.18/18.79 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.79 ) 20.18/18.79 (instantiation (forall ((X_1 $$unsorted)) (= (= X_1 (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real sqrt X_1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X_1))) ) 20.18/18.79 ( (zero_zero real) ) 20.18/18.79 ( (one_one real) ) 20.18/18.79 ( pi ) 20.18/18.79 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.79 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.79 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.18/18.79 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.79 ( skv_6 ) 20.18/18.79 ( skv_11 ) 20.18/18.79 ( skv_12 ) 20.18/18.79 ( skv_14 ) 20.18/18.79 ) 20.18/18.79 (instantiation (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_151101 $$unsorted) (BOUND_VARIABLE_151102 $$unsorted)) (or (not (linordered_idom X_a)) (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_151101)) BOUND_VARIABLE_151102) (hAPP X_a X_a _let_0 (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_151101) BOUND_VARIABLE_151102)))) )))) 20.18/18.79 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.79 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.79 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.79 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.79 ) 20.18/18.79 (instantiation (let ((_let_0 (fun int bool))) (forall ((Ma $$unsorted) (W_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) W_1))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP int nat nat_1 W_1)) Ma)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W_1) (hAPP nat int (semiring_1_of_nat int) Ma))))) )) 20.18/18.79 ( (zero_zero nat), (zero_zero int) ) 20.18/18.79 ( (zero_zero nat), min_1 ) 20.18/18.79 ( (zero_zero nat), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 20.18/18.79 ( (zero_zero nat), t ) 20.18/18.79 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero int) ) 20.18/18.79 ( (hAPP nat nat suc (zero_zero nat)), t ) 20.18/18.79 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 20.18/18.79 ) 20.18/18.79 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_151134 $$unsorted) (BOUND_VARIABLE_151135 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_151134) BOUND_VARIABLE_151135))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_151134)) BOUND_VARIABLE_151135))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_151134)) BOUND_VARIABLE_151135))) ))) 20.18/18.79 ( real, (zero_zero real), pi ) 20.18/18.79 ( 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)))) ) 20.18/18.79 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.18/18.79 ( real, (zero_zero real), skv_6 ) 20.18/18.79 ( real, (zero_zero real), skv_11 ) 20.18/18.79 ( real, (zero_zero real), skv_12 ) 20.18/18.79 ( real, (zero_zero real), skv_14 ) 20.18/18.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 20.18/18.79 ( 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))) ) 20.18/18.79 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 20.18/18.79 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.79 ( int, (zero_zero int), (one_one int) ) 20.18/18.79 ( int, (zero_zero int), min_1 ) 20.18/18.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.79 ( int, (zero_zero int), s ) 20.18/18.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 20.18/18.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.18/18.79 ( int, (zero_zero int), skv_3 ) 20.18/18.79 ( int, (zero_zero int), skv_9 ) 20.18/18.79 ( int, pls, (one_one int) ) 20.18/18.79 ( int, pls, min_1 ) 20.18/18.79 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.79 ( int, pls, s ) 20.18/18.79 ( int, pls, (hAPP int int (number_number_of int) pls) ) 20.18/18.79 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.18/18.79 ( int, pls, skv_3 ) 20.18/18.79 ( int, pls, skv_9 ) 20.18/18.79 ( int, (one_one int), pls ) 20.18/18.79 ( int, (one_one int), min_1 ) 20.18/18.79 ( int, (one_one int), t ) 20.18/18.79 ( int, min_1, pls ) 20.18/18.79 ( int, min_1, min_1 ) 20.18/18.79 ) 20.18/18.79 (instantiation (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))) (forall ((X $$unsorted)) (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)))) ))))) 20.18/18.79 ( (zero_zero real) ) 20.18/18.79 ( pi ) 20.18/18.79 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.79 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 20.18/18.79 ( (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 (hAPP int int bit1 pls))))) ) 20.18/18.79 ( (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 bit0 (hAPP int int bit1 pls))))) ) 20.18/18.79 ( (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)))) ) 20.18/18.79 ) 20.18/18.79 (instantiation (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 (number_number_of nat))) (let ((_let_3 (semiring_1_of_nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_151227 $$unsorted) (BOUND_VARIABLE_151237 $$unsorted)) (or (not (number_ring X_a)) (and (or (not (hBOOL (hAPP int bool _let_0 (hAPP int int _let_1 BOUND_VARIABLE_151227)))) (= (hAPP nat X_a _let_3 (hAPP int nat _let_2 BOUND_VARIABLE_151227)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_151227))) (or (hBOOL (hAPP int bool _let_0 (hAPP int int _let_1 BOUND_VARIABLE_151237))) (= (zero_zero X_a) (hAPP nat X_a _let_3 (hAPP int nat _let_2 BOUND_VARIABLE_151237)))))) ))))) 20.18/18.79 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.18/18.79 ( int, min_1, min_1 ) 20.18/18.79 ( complex, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.18/18.79 ( rat, pls, pls ) 20.18/18.79 ) 20.18/18.79 (instantiation (let ((_let_0 (fun (filter X_a) bool))) (let ((_let_1 (fun X_a X_b))) (let ((_let_2 (fun X_b _let_0))) (let ((_let_3 (tendsto X_a X_b))) (let ((_let_4 (inverse_inverse X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_151297 $$unsorted) (BOUND_VARIABLE_151298 $$unsorted) (BOUND_VARIABLE_151299 $$unsorted)) (let ((_let_0 (filter X_a))) (or (not (real_n1866405975lgebra X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_0 (hAPP _let_1 _let_2 _let_3 BOUND_VARIABLE_151297) BOUND_VARIABLE_151298) BOUND_VARIABLE_151299))) (= (zero_zero X_b) (ti X_b BOUND_VARIABLE_151298)) (hBOOL (hAPP _let_0 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_151297)) (hAPP X_b X_b _let_4 BOUND_VARIABLE_151298)) BOUND_VARIABLE_151299)))) )))))) 20.31/18.79 ( nat, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))), (zero_zero real), sequentially ) 20.31/18.79 ) 20.31/18.79 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_b bool))) (let ((_let_3 (ord_less X_b))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_151362 $$unsorted) (BOUND_VARIABLE_151363 $$unsorted) (BOUND_VARIABLE_151364 $$unsorted) (BOUND_VARIABLE_151365 $$unsorted)) (or (not (order X_b)) (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_151364) BOUND_VARIABLE_151365))) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_2 (ord_less_eq X_b) BOUND_VARIABLE_151362) (hAPP X_a X_b BOUND_VARIABLE_151363 BOUND_VARIABLE_151364)))) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 Y_2) X_2))) (hBOOL (hAPP X_b bool (hAPP X_b _let_2 _let_3 (hAPP X_a X_b BOUND_VARIABLE_151363 Y_2)) (hAPP X_a X_b BOUND_VARIABLE_151363 X_2)))) )) (hBOOL (hAPP X_b bool (hAPP X_b _let_2 _let_3 BOUND_VARIABLE_151362) (hAPP X_a X_b BOUND_VARIABLE_151363 BOUND_VARIABLE_151365)))) ))))) 20.31/18.80 ( real, real, (zero_zero real), (sgn_sgn 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)))) ) 20.31/18.80 ( real, real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), tan, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.31/18.80 ( real, real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (uminus_uminus real), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.31/18.80 ( real, real, (hAPP real real cos (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 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.31/18.80 ( real, int, skv_14, (number_number_of real), min_1, min_1 ) 20.31/18.80 ( 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))) ) 20.31/18.80 ( int, int, (one_one int), (number_number_of int), pls, (one_one int) ) 20.31/18.80 ( int, int, min_1, (number_number_of int), min_1, (zero_zero int) ) 20.31/18.80 ) 20.31/18.80 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_151410 $$unsorted) (BOUND_VARIABLE_151411 $$unsorted)) (or (not (order X_a)) (= (= (ti X_a BOUND_VARIABLE_151411) (ti X_a BOUND_VARIABLE_151410)) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_151410) BOUND_VARIABLE_151411)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_151411) BOUND_VARIABLE_151410))))) ))) 20.31/18.80 ( real, (zero_zero real), pi ) 20.31/18.80 ( 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)))) ) 20.31/18.80 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.31/18.80 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.31/18.80 ( real, (zero_zero real), skv_6 ) 20.31/18.80 ( real, (zero_zero real), skv_11 ) 20.31/18.80 ( real, (zero_zero real), skv_12 ) 20.31/18.80 ( real, (zero_zero real), skv_14 ) 20.31/18.80 ( real, pi, (zero_zero real) ) 20.31/18.80 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.31/18.80 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 20.31/18.80 ( 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)))) ) 20.31/18.80 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 20.31/18.80 ( 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)))), (zero_zero real) ) 20.31/18.80 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.31/18.80 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 20.33/18.80 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 20.33/18.80 ( real, skv_6, (zero_zero real) ) 20.33/18.80 ( real, skv_11, (zero_zero real) ) 20.33/18.80 ( real, skv_12, (zero_zero real) ) 20.33/18.80 ( real, skv_14, (zero_zero real) ) 20.33/18.80 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.33/18.80 ( int, (zero_zero int), (one_one int) ) 20.33/18.80 ( int, (zero_zero int), min_1 ) 20.33/18.80 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.33/18.80 ( int, (zero_zero int), s ) 20.33/18.80 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 20.33/18.80 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.33/18.80 ( int, (zero_zero int), skv_3 ) 20.33/18.80 ( int, (zero_zero int), skv_9 ) 20.33/18.80 ( int, pls, min_1 ) 20.33/18.80 ( int, (one_one int), (zero_zero int) ) 20.33/18.80 ( int, (one_one int), t ) 20.33/18.80 ( int, min_1, (zero_zero int) ) 20.33/18.80 ( int, min_1, pls ) 20.33/18.80 ( int, min_1, min_1 ) 20.33/18.80 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 20.33/18.80 ( int, s, (zero_zero int) ) 20.33/18.80 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 20.33/18.80 ( int, t, (one_one int) ) 20.33/18.80 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 20.33/18.80 ( int, skv_3, (zero_zero int) ) 20.33/18.80 ( int, skv_9, (zero_zero int) ) 20.33/18.80 ) 20.33/18.80 (instantiation (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (inverse_divide X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_151438 $$unsorted) (BOUND_VARIABLE_151439 $$unsorted)) (or (not (linordered_field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_151439)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_151438)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_151439)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_151438) BOUND_VARIABLE_151439)))) )))) 20.33/18.80 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.33/18.80 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.33/18.80 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.33/18.80 ( 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))))))))) ) 20.33/18.80 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.33/18.80 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.33/18.80 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.33/18.80 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.33/18.80 ( 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))) ) 20.33/18.80 ( 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))) ) 20.33/18.80 ( 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))) ) 20.33/18.80 ) 20.33/18.80 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (hAPP int int (hAPP int _let_0 _let_1 W) Z_1) (hAPP int int (hAPP int _let_0 _let_1 Z_1) W)) ))) 20.33/18.80 ( (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 bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 20.33/18.80 ( (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) ) 20.33/18.80 ( (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)))) ) 20.33/18.80 ( (hAPP nat int (hAPP 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) ) 20.33/18.80 ) 20.33/18.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151556 $$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_151556) (zero_zero X_a)))) (= (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_151556) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_151556))) ) 20.33/18.80 ( real, (zero_zero real) ) 20.33/18.80 ( real, (one_one real) ) 20.33/18.80 ( real, pi ) 20.33/18.80 ( 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)))) ) 20.33/18.80 ( 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) ) 20.33/18.80 ( 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))))) ) 20.33/18.80 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.33/18.80 ( 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)) ) 20.33/18.80 ( nat, (zero_zero nat) ) 20.33/18.80 ( int, (zero_zero int) ) 20.33/18.80 ( int, pls ) 20.33/18.80 ( int, (one_one int) ) 20.33/18.80 ( int, min_1 ) 20.33/18.80 ( int, s ) 20.33/18.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 20.33/18.80 ( int, t ) 20.33/18.80 ( int, skv_3 ) 20.33/18.80 ( int, skv_9 ) 20.33/18.80 ( complex, ii ) 20.33/18.80 ( complex, (one_one complex) ) 20.33/18.80 ) 20.33/18.80 (instantiation (let ((_let_0 (fun nat nat))) (forall ((M $$unsorted) (N $$unsorted)) (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)))) )) 20.33/18.80 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.33/18.80 ) 20.33/18.80 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (hAPP int _let_1 zcong A_1))) (forall ((D $$unsorted) (C $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 B) M))) (not (= (ti int C) (ti int B))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong C) D) M))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 D) M))) )))) 20.33/18.80 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.33/18.80 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.33/18.80 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (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_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.33/18.80 ( 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))) ) 20.33/18.80 ( (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))) ) 20.33/18.80 ( skv_3, s1, s1, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.33/18.80 ( skv_9, s1, s1, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.33/18.80 ) 20.33/18.80 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (fun nat _let_1))) (let ((_let_4 (fun (filter nat) bool))) (forall ((Sa $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) _let_0) Sa))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_4 (hAPP _let_2 (fun real _let_4) (tendsto nat real) (hAPP real _let_2 (hAPP _let_3 (fun real _let_2) (combc nat real real) (hAPP _let_2 _let_3 (hAPP (fun real _let_1) (fun _let_2 _let_3) (combb real _let_1 nat) powr) (real_1 nat))) (hAPP real real (uminus_uminus real) Sa))) _let_0) sequentially))) )))))) 20.33/18.80 ( (one_one real) ) 20.33/18.80 ( pi ) 20.33/18.80 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.33/18.80 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 20.33/18.80 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.33/18.80 ( skv_2 ) 20.33/18.80 ( skv_10 ) 20.33/18.80 ( skv_13 ) 20.33/18.80 ) 20.33/18.80 (instantiation (let ((_let_0 (semiring_1_of_nat int))) (let ((_let_1 (zero_zero nat))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (and (= _let_1 Ma) (= _let_1 N_1)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP nat int _let_0 N_1)) (hAPP int int (uminus_uminus int) (hAPP nat int _let_0 Ma))))) ))) 20.33/18.80 ( (zero_zero nat), (zero_zero nat) ) 20.33/18.80 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 20.33/18.80 ) 20.33/18.80 (instantiation (let ((_let_0 (fun X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (G $$unsorted)) (or (not (forall ((X_2 $$unsorted)) (= (hAPP X_a X_b G X_2) (hAPP X_a X_b F X_2)) )) (= (ti _let_0 F) (ti _let_0 G))) )) 20.33/18.80 ( bool, bool, fNot, fNot ) 20.33/18.80 ( bool, (fun bool bool), fconj, fdisj ) 20.33/18.80 ( bool, (fun bool bool), fconj, fimplies ) 20.33/18.80 ( bool, (fun bool bool), fdisj, fconj ) 20.33/18.80 ( bool, (fun bool bool), fdisj, fdisj ) 20.33/18.80 ( bool, (fun bool bool), fimplies, fdisj ) 20.33/18.80 ( real, real, sqrt, arcsin ) 20.33/18.80 ( real, real, tan, tan ) 20.33/18.80 ( real, real, tan, arccos ) 20.33/18.80 ( real, real, cos, cos ) 20.33/18.80 ( real, real, cos, arctan ) 20.33/18.80 ( real, real, arccos, tan ) 20.33/18.80 ( real, real, arccos, sin ) 20.33/18.80 ( real, real, ln, sqrt ) 20.33/18.80 ( real, real, ln, arcsin ) 20.33/18.80 ( real, real, sin, tan ) 20.33/18.80 ( real, real, arctan, cos ) 20.33/18.80 ( real, real, arcsin, ln ) 20.33/18.80 ( real, real, arcsin, arcsin ) 20.33/18.80 ( real, nat, natfloor, natceiling ) 20.33/18.80 ( real, nat, natceiling, natfloor ) 20.33/18.80 ( real, nat, natceiling, natceiling ) 20.33/18.80 ( real, (fun real real), log, powr ) 20.33/18.80 ( real, (fun real real), powr, log ) 20.33/18.80 ( real, (fun real real), powr, powr ) 20.33/18.80 ( real, complex, cis, cis ) 20.33/18.80 ( real, (fun real complex), complex_1, complex_1 ) 20.33/18.80 ( real, (fun real complex), complex_1, rcis ) 20.33/18.80 ( real, (fun real complex), rcis, complex_1 ) 20.33/18.80 ( nat, bool, (even_odd_even nat), prime ) 20.33/18.80 ( nat, bool, prime, (even_odd_even nat) ) 20.33/18.80 ( nat, bool, prime, prime ) 20.33/18.80 ( nat, real, (real_1 nat), (real_1 nat) ) 20.33/18.81 ( nat, real, (real_1 nat), sin_coeff ) 20.33/18.81 ( nat, real, cos_coeff, (real_1 nat) ) 20.33/18.81 ( nat, real, sin_coeff, (real_1 nat) ) 20.33/18.81 ( nat, real, sin_coeff, cos_coeff ) 20.33/18.81 ( nat, nat, suc, suc ) 20.33/18.81 ( nat, nat, suc, nat_size ) 20.33/18.81 ( nat, nat, (fact_fact nat), (size_size nat) ) 20.33/18.81 ( nat, nat, (size_size nat), (fact_fact nat) ) 20.33/18.81 ( nat, nat, (size_size nat), (size_size nat) ) 20.33/18.81 ( nat, nat, fact, suc ) 20.33/18.81 ( nat, nat, nat_size, suc ) 20.33/18.81 ( nat, nat, nat_size, fact ) 20.33/18.81 ( nat, (fun nat bool), coprime, coprime ) 20.33/18.81 ( nat, (fun nat nat), nat_gcd, nat_gcd ) 20.33/18.81 ( nat, (fun nat nat), nat_gcd, nat_lcm ) 20.33/18.81 ( nat, (fun nat nat), (gcd_gcd nat), nat_gcd ) 20.33/18.81 ( nat, (fun nat nat), nat_lcm, nat_gcd ) 20.33/18.81 ( nat, (fun nat nat), nat_lcm, (gcd_gcd nat) ) 20.33/18.81 ( nat, (fun real real), root, root ) 20.33/18.81 ( nat, (fun nat (fun nat bool)), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 20.33/18.81 ( nat, (fun nat (product_prod int int)), bezw, bezw ) 20.33/18.81 ( nat, (fun nat (fun (product_prod nat nat) bool)), divmod_nat_rel, divmod_nat_rel ) 20.33/18.81 ( nat, (fun nat (product_prod nat nat)), divmod_nat, divmod_nat ) 20.33/18.81 ( int, bool, zprime, zprime ) 20.33/18.81 ( int, bool, zprime, (even_odd_even int) ) 20.33/18.81 ( int, bool, nat_neg, nat_is_nat ) 20.33/18.81 ( int, bool, nat_neg, twoSqu1091635170sum2sq ) 20.33/18.81 ( int, bool, zEven, zprime ) 20.33/18.81 ( int, bool, nat_is_nat, nat_neg ) 20.33/18.81 ( int, bool, nat_is_nat, nat_is_nat ) 20.33/18.81 ( int, bool, zOdd, zOdd ) 20.33/18.81 ( int, bool, (even_odd_even int), zprime ) 20.33/18.81 ( int, bool, (even_odd_even int), zEven ) 20.33/18.81 ( int, bool, twoSqu1091635170sum2sq, nat_is_nat ) 20.33/18.81 ( int, real, (real_1 int), (real_1 int) ) 20.33/18.81 ( int, nat, nat_1, phi ) 20.33/18.81 ( int, nat, phi, nat_1 ) 20.33/18.81 ( int, nat, phi, phi ) 20.33/18.81 ( int, (fun nat nat), nat_aux, nat_aux ) 20.33/18.81 ( int, int, bit0, bit0 ) 20.33/18.81 ( int, int, bit0, (fact_fact int) ) 20.33/18.81 ( int, int, bit1, bit0 ) 20.33/18.81 ( int, int, pred, succ ) 20.33/18.81 ( int, int, pred, zfact ) 20.33/18.81 ( int, int, succ, zfact ) 20.33/18.81 ( int, int, (fact_fact int), bit0 ) 20.33/18.81 ( int, int, (fact_fact int), bit1 ) 20.33/18.81 ( int, int, zfact, pred ) 20.33/18.81 ( int, int, zfact, zfact ) 20.33/18.81 ( int, (fun int bool), sRStar, sRStar ) 20.33/18.81 ( int, (fun int bool), sRStar, d22set ) 20.33/18.81 ( int, (fun int bool), quadRes, sRStar ) 20.33/18.81 ( int, (fun int bool), norRRset, sr ) 20.33/18.81 ( int, (fun int bool), norRRset, quickc1265749348ro_rel ) 20.33/18.81 ( int, (fun int bool), d22set, sRStar ) 20.33/18.81 ( int, (fun int bool), d22set, quadRes ) 20.33/18.81 ( int, (fun int bool), sr, norRRset ) 20.33/18.81 ( int, (fun int bool), sr, sr ) 20.33/18.81 ( int, (fun int bool), quickc1265749348ro_rel, sr ) 20.33/18.81 ( int, (fun int int), int_gcd, multInv ) 20.33/18.81 ( int, (fun int int), int_gcd, int_lcm ) 20.33/18.81 ( int, (fun int int), multInv, int_lcm ) 20.33/18.81 ( int, (fun int int), legacy_zgcd, legacy_zgcd ) 20.33/18.81 ( int, (fun int int), legacy_zgcd, inv ) 20.33/18.81 ( int, (fun int int), z3mod, (gcd_gcd int) ) 20.33/18.81 ( int, (fun int int), z3mod, z3div ) 20.34/18.81 ( int, (fun int int), inv, legacy_zgcd ) 20.34/18.81 ( int, (fun int int), inv, nat_tsub ) 20.34/18.81 ( int, (fun int int), (gcd_gcd int), z3div ) 20.34/18.81 ( int, (fun int int), standardRes, legendre ) 20.34/18.81 ( int, (fun int int), legendre, standardRes ) 20.34/18.81 ( int, (fun int int), legendre, legendre ) 20.34/18.81 ( int, (fun int int), nat_tsub, legacy_zgcd ) 20.34/18.81 ( int, (fun int int), z3div, z3mod ) 20.34/18.81 ( int, (fun int int), z3div, z3div ) 20.34/18.81 ( int, (fun int int), int_lcm, int_gcd ) 20.34/18.81 ( int, (fun int int), int_lcm, int_lcm ) 20.34/18.81 ( int, (fun int rat), fract, fract ) 20.34/18.81 ( int, (fun int (fun int bool)), wset, wset ) 20.34/18.81 ( int, (fun int (fun int bool)), wset, bnorRset ) 20.34/18.81 ( int, (fun int (fun int bool)), bnorRset, wset ) 20.34/18.81 ( int, (fun int (fun int bool)), bnorRset, zcong ) 20.34/18.81 ( int, (fun int (fun int bool)), zcong, wset ) 20.34/18.81 ( int, (fun int (fun int bool)), noXRRset, zcongm ) 20.34/18.81 ( int, (fun int (fun int bool)), zcongm, noXRRset ) 20.34/18.81 ( int, (fun int (fun int bool)), zcongm, zcongm ) 20.34/18.81 ( int, quickcheck_code_int, quickcheck_of_int, quickcheck_of_int ) 20.34/18.81 ( int, (fun int (product_prod int int)), negDivAlg, pdivmod ) 20.34/18.81 ( int, (fun int (product_prod int int)), divmod_int, negDivAlg ) 20.34/18.81 ( int, (fun int (product_prod int int)), divmod_int, pdivmod ) 20.34/18.81 ( int, (fun int (product_prod int int)), posDivAlg, posDivAlg ) 20.34/18.81 ( int, (fun int (product_prod int int)), posDivAlg, norm_frac ) 20.34/18.81 ( int, (fun int (product_prod int int)), pdivmod, divmod_int ) 20.34/18.81 ( int, (fun int (product_prod int int)), pdivmod, pdivmod ) 20.34/18.81 ( int, (fun int (product_prod int int)), norm_frac, posDivAlg ) 20.34/18.81 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), adjust, adjust ) 20.34/18.81 ( int, (fun (fun int bool) bool), rsetR, resSet ) 20.34/18.81 ( int, (fun (fun int bool) bool), resSet, rsetR ) 20.34/18.81 ( int, (fun (fun int bool) bool), resSet, resSet ) 20.34/18.81 ( int, (fun (product_prod int int) bool), int_ge_less_than2, int_ge_less_than ) 20.34/18.81 ( int, (fun (product_prod int int) bool), int_ge_less_than, int_ge_less_than2 ) 20.34/18.81 ( int, (fun (product_prod int int) bool), int_ge_less_than, int_ge_less_than ) 20.34/18.81 ( int, (fun int (product_prod int (product_prod int int))), xzgcd, xzgcd ) 20.34/18.81 ( int, (fun int (fun (product_prod int int) bool)), divmod_int_rel, divmod_int_rel ) 20.34/18.81 ( int, (fun int (fun (fun int bool) bool)), setS, setS ) 20.34/18.81 ( int, (list int), quickc666637781d_zero, quickc666637781d_zero ) 20.34/18.81 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))), xzgcda, xzgcda ) 20.34/18.81 ( int, (fun int (fun int (fun int bool))), multInvPair, multInvPair ) 20.34/18.81 ( (fun int bool), bool, nat_nat_set, nat_nat_set ) 20.34/18.81 ( (fun int bool), int, (the int), (the int) ) 20.34/18.81 ( (fun int bool), (fun int bool), is_RRset, is_RRset ) 20.34/18.81 ( (fun int bool), (fun int (fun int int)), rRset2norRR, rRset2norRR ) 20.34/18.81 ( (fun real bool), real, (complete_Sup_Sup real), (complete_Sup_Sup real) ) 20.34/18.81 ( complex, real, im, im ) 20.34/18.81 ( complex, real, im, re ) 20.34/18.81 ( complex, real, re, im ) 20.34/18.81 ( complex, real, re, arg ) 20.34/18.81 ( complex, real, arg, im ) 20.34/18.81 ( complex, nat, (size_size complex), complex_size ) 20.34/18.81 ( complex, nat, complex_size, (size_size complex) ) 20.34/18.81 ( complex, nat, complex_size, complex_size ) 20.34/18.81 ( complex, complex, cnj, cnj ) 20.34/18.81 ( complex, complex, cnj, expi ) 20.34/18.81 ( complex, complex, expi, cnj ) 20.34/18.81 ( rat, real, ratreal, ratreal ) 20.34/18.81 ( rat, (product_prod int int), quotient_of, quotient_of ) 20.34/18.81 ( quickcheck_code_int, nat, quickcheck_nat_of, quickcheck_nat_of ) 20.34/18.81 ( quickcheck_code_int, int, quickcheck_int_of, quickcheck_int_of ) 20.34/18.81 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)), quickc495462417de_int, quickc495462417de_int ) 20.34/18.81 ( (product_prod int int), bool, frac_1, frac_1 ) 20.34/18.81 ( (product_prod int int), int, twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 20.34/18.81 ( (product_prod int int), rat, frct, frct ) 20.34/18.81 ( (product_prod int int), (product_prod int int), normalize, negateSnd ) 20.34/18.81 ( (product_prod int int), (product_prod int int), negateSnd, normalize ) 20.34/18.81 ( (product_prod int int), (product_prod int int), negateSnd, negateSnd ) 20.34/18.81 ( (product_prod int int), (fun (product_prod int int) bool), lazy_small_lazy_rel, upto_rel ) 20.34/18.81 ( (product_prod int int), (fun (product_prod int int) bool), posDivAlg_rel, posDivAlg_rel ) 20.34/18.81 ( (product_prod int int), (fun (product_prod int int) bool), posDivAlg_rel, negDivAlg_rel ) 20.34/18.81 ( (product_prod int int), (fun (product_prod int int) bool), upto_rel, lazy_small_lazy_rel ) 20.34/18.81 ( (product_prod int int), (fun (product_prod int int) bool), upto_rel, upto_rel ) 20.34/18.81 ( (product_prod int int), (fun (product_prod int int) bool), negDivAlg_rel, posDivAlg_rel ) 20.34/18.81 ( (product_prod int int), (fun (product_prod int int) bool), negDivAlg_rel, norm_frac_rel ) 20.34/18.81 ( (product_prod int int), (fun (product_prod int int) bool), norm_frac_rel, posDivAlg_rel ) 20.34/18.81 ( (product_prod nat nat), bool, pred_nat, pred_nat ) 20.34/18.81 ( (product_prod nat nat), (fun (product_prod nat nat) bool), nat_gcd_rel, nat_gcd_rel ) 20.34/18.81 ( code_code_numeral, nat, (size_size code_code_numeral), (size_size code_code_numeral) ) 20.34/18.81 ( code_code_numeral, nat, (size_size code_code_numeral), code_c271388182l_size ) 20.34/18.81 ( code_code_numeral, nat, code_c271388182l_size, (size_size code_code_numeral) ) 20.34/18.81 ( code_code_numeral, (fun nat nat), code_nat_of_aux, code_nat_of_aux ) 20.34/18.81 ( code_code_numeral, int, code_int_of, code_int_of ) 20.34/18.81 ( code_code_numeral, code_code_numeral, code_S1047413653umeral, code_S1047413653umeral ) 20.34/18.81 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)), code_d418564891umeral, code_d418564891umeral ) 20.34/18.81 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool, pair_less, pair_less ) 20.34/18.81 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool, pair_less, pair_leq ) 20.34/18.81 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool, pair_leq, pair_less ) 20.34/18.81 ( (fun nat rat), bool, vanishes, vanishes ) 20.34/18.81 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))), bolzano_bisect, bolzano_bisect ) 20.34/18.81 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool, ratrel, ratrel ) 20.34/18.81 ) 20.34/18.81 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP real real sqrt (hAPP real real (hAPP real _let_0 _let_1 X) Y)) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real sqrt X)) (hAPP real real sqrt Y))) ))) 20.34/18.81 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.34/18.81 ) 20.34/18.81 (instantiation (let ((_let_0 (fun nat bool))) (forall ((U_1 $$unsorted)) (= (hAPP _let_0 nat (finite_card nat) (hAPP nat _let_0 (ord_atMost nat) U_1)) (hAPP nat nat suc U_1)) )) 20.34/18.81 ( (zero_zero nat) ) 20.34/18.81 ( (hAPP nat nat suc (zero_zero nat)) ) 20.34/18.81 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 20.34/18.81 ) 20.34/18.81 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (fact_fact nat))) (forall ((N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (hAPP nat nat (hAPP nat _let_0 (times_times nat) N) (hAPP nat nat _let_1 (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) N) (one_one nat)))) (hAPP nat nat _let_1 N))) ))) 20.34/18.81 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.81 ) 20.34/18.81 (instantiation (forall ((N_1 $$unsorted)) (= (not (hBOOL (hAPP nat bool (even_odd_even nat) N_1))) (not (forall ((M_2 $$unsorted)) (not (= N_1 (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) M_2)))) ))) ) 20.34/18.81 ( (zero_zero nat) ) 20.34/18.81 ( (one_one nat) ) 20.34/18.81 ) 20.34/18.81 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_151927 $$unsorted) (BOUND_VARIABLE_151928 $$unsorted)) (or (not (linordered_idom X_a)) (= (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_151927)) BOUND_VARIABLE_151928)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_151927) BOUND_VARIABLE_151928))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_151927)) BOUND_VARIABLE_151928)))) ))) 20.34/18.81 ( real, (zero_zero real), pi ) 20.34/18.81 ( 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)))) ) 20.34/18.81 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.81 ( real, (zero_zero real), skv_2 ) 20.34/18.81 ( real, (zero_zero real), skv_10 ) 20.34/18.81 ( real, (zero_zero real), skv_13 ) 20.34/18.81 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.81 ( real, pi, (zero_zero real) ) 20.34/18.81 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.81 ( 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)))), (zero_zero real) ) 20.34/18.81 ( 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 int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.81 ( real, (hAPP real real (hAPP 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 ) 20.34/18.81 ( 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) ) 20.34/18.81 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 20.34/18.81 ( 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 ) 20.34/18.81 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.81 ( int, (zero_zero int), (zero_zero int) ) 20.34/18.81 ( int, (zero_zero int), (one_one int) ) 20.34/18.81 ( 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))) ) 20.34/18.81 ( int, (zero_zero int), min_1 ) 20.34/18.81 ( int, pls, (zero_zero int) ) 20.34/18.81 ( int, pls, (one_one int) ) 20.34/18.81 ( 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))) ) 20.34/18.81 ( int, pls, min_1 ) 20.34/18.81 ( int, (one_one int), (zero_zero int) ) 20.34/18.81 ( int, (one_one int), min_1 ) 20.34/18.81 ( int, min_1, (zero_zero int) ) 20.34/18.81 ( int, min_1, min_1 ) 20.34/18.81 ( 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))) ) 20.34/18.81 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 20.34/18.81 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 20.34/18.81 ( int, t, (zero_zero int) ) 20.34/18.81 ( int, t, (one_one int) ) 20.34/18.81 ( 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))) ) 20.34/18.81 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.34/18.81 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.34/18.81 ) 20.34/18.81 (instantiation (forall ((W $$unsorted)) (= (hAPP int rat (number_number_of rat) W) (hAPP int rat (hAPP int (fun int rat) fract W) (one_one int))) ) 20.34/18.81 ( (zero_zero int) ) 20.34/18.81 ( (one_one int) ) 20.34/18.81 ) 20.34/18.81 (instantiation (let ((_let_0 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_152008 $$unsorted) (BOUND_VARIABLE_152009 $$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_152008) BOUND_VARIABLE_152009)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_152008)) (hAPP int X_a _let_0 BOUND_VARIABLE_152009))))) )) 20.34/18.81 ( nat, pls, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.81 ( int, pls, pls ) 20.34/18.81 ( int, pls, (hAPP int int bit1 pls) ) 20.34/18.81 ) 20.34/18.81 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (hAPP int int (hAPP int _let_0 _let_1 W) Z_1) (hAPP int int (hAPP int _let_0 _let_1 Z_1) W)) ))) 20.34/18.81 ( (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))) ) 20.34/18.81 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 20.34/18.81 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.81 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 20.34/18.81 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 20.34/18.81 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_1 ) 20.34/18.81 ( 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))) ) 20.34/18.81 ( skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.34/18.81 ) 20.34/18.81 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (forall ((U $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) U))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP real (fun real real) (inverse_divide real) U) (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) U))) ))) 20.34/18.82 ( (one_one real) ) 20.34/18.82 ( pi ) 20.34/18.82 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.82 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.34/18.82 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.34/18.82 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.82 ( skv_2 ) 20.34/18.82 ( skv_10 ) 20.34/18.82 ( skv_13 ) 20.34/18.82 ) 20.34/18.82 (instantiation (let ((_let_0 (product_prod int int))) (forall ((K_4 $$unsorted)) (= (hAPP _let_0 rat frct (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) (hAPP int int (number_number_of int) K_4)) (one_one int))) (hAPP int rat (number_number_of rat) K_4)) )) 20.34/18.82 ( pls ) 20.34/18.82 ( (hAPP int int bit1 pls) ) 20.34/18.82 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.82 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.82 ( min_1 ) 20.34/18.82 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 20.34/18.82 ) 20.34/18.82 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (let ((_let_1 (hAPP int nat (number_number_of nat) BOUND_VARIABLE_152062))) (let ((_let_2 (hBOOL (hAPP nat bool (even_odd_even nat) _let_1)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_152061 $$unsorted) (BOUND_VARIABLE_152062 $$unsorted)) (or (not (linordered_idom X_a)) (= (or _let_2 (and (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_152061)) (not _let_2))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_152061) _let_1))))) )))) 20.34/18.82 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.82 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.82 ( int, skv_8, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.82 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.82 ) 20.34/18.82 (instantiation (let ((_let_0 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_1 (hAPP real (fun real real) (plus_plus real) (one_one real)))) (forall ((X $$unsorted)) (let ((_let_0 (fun real real))) (= (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real (number_number_of real) _let_0)) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (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))) ))) 20.34/18.82 ( (one_one real) ) 20.34/18.82 ( pi ) 20.34/18.82 ( (hAPP int real (number_number_of real) min_1) ) 20.34/18.82 ( (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)))) ) 20.34/18.82 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.34/18.82 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.34/18.82 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.82 ) 20.34/18.82 (instantiation (let ((_let_0 (iszero X_a))) (let ((_let_1 (number_number_of X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_152087 $$unsorted)) (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_152087)))) (hBOOL (hAPP X_a bool _let_0 (hAPP int X_a _let_1 BOUND_VARIABLE_152087))))) ))) 20.34/18.82 ( real, (hAPP int int bit1 pls) ) 20.34/18.82 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.82 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 20.34/18.82 ( nat, pls ) 20.34/18.82 ( nat, (hAPP int int bit1 pls) ) 20.34/18.82 ( int, pls ) 20.34/18.82 ( int, (hAPP int int bit1 pls) ) 20.34/18.82 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.82 ( complex, (hAPP int int bit1 pls) ) 20.34/18.82 ( quickcheck_code_int, pls ) 20.34/18.82 ( code_code_numeral, pls ) 20.34/18.82 ) 20.34/18.82 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (let ((_let_3 (filter X_a))) (let ((_let_4 (fun _let_3 bool))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_152139 $$unsorted) (BOUND_VARIABLE_152140 $$unsorted) (BOUND_VARIABLE_152141 $$unsorted)) (or (not (real_normed_vector X_b)) (not (real_normed_vector X_a)) (= (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 R_2))) (not (forall ((S_1 $$unsorted)) (or (not (forall ((X_2 $$unsorted)) (or (= (ti X_a X_2) (ti X_a BOUND_VARIABLE_152141)) (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_2) BOUND_VARIABLE_152141))) 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_152139 X_2)) BOUND_VARIABLE_152140))) R_2))) )) (not (hBOOL (hAPP real bool _let_2 S_1)))) ))) ) (hBOOL (hAPP _let_3 bool (hAPP X_b _let_4 (hAPP (fun X_a X_b) (fun X_b _let_4) (tendsto X_a X_b) BOUND_VARIABLE_152139) BOUND_VARIABLE_152140) (hAPP X_a _let_3 (at X_a) BOUND_VARIABLE_152141))))) )))))) 20.34/18.82 ( 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)))) ) 20.34/18.82 ) 20.34/18.82 (instantiation (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))))) (forall ((X $$unsorted)) (= (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real cos X)) _let_2) (hAPP real real (hAPP real (fun real real) (minus_minus real) (one_one real)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real sin X)) _let_2))) )))) 20.34/18.82 ( (zero_zero real) ) 20.34/18.82 ( pi ) 20.34/18.82 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.82 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.82 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 20.34/18.82 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 20.34/18.82 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 20.34/18.82 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 20.34/18.82 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.34/18.82 ( skv_14 ) 20.34/18.82 ) 20.34/18.82 (instantiation (let ((_let_0 (one_one X_a))) (forall ((X_a $$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)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) _let_0) _let_0)))) )) 20.34/18.82 ( bool ) 20.34/18.82 ( real ) 20.34/18.82 ( nat ) 20.34/18.82 ( (fun nat bool) ) 20.34/18.82 ( int ) 20.34/18.82 ( (fun int bool) ) 20.34/18.82 ( (fun real bool) ) 20.34/18.82 ( (fun real real) ) 20.34/18.82 ( complex ) 20.34/18.82 ( (fun nat real) ) 20.34/18.82 ( (fun int int) ) 20.34/18.82 ( rat ) 20.34/18.82 ( (fun int (fun int bool)) ) 20.34/18.82 ( quickcheck_code_int ) 20.34/18.82 ( (product_prod real real) ) 20.34/18.82 ( (product_prod int int) ) 20.34/18.82 ( (filter real) ) 20.34/18.82 ( (filter nat) ) 20.34/18.82 ( (product_prod nat nat) ) 20.34/18.82 ( (fun (product_prod int int) bool) ) 20.34/18.82 ( code_code_numeral ) 20.34/18.82 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 20.34/18.82 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 20.34/18.82 ( (fun nat rat) ) 20.34/18.82 ( (fun (product_prod int int) int) ) 20.34/18.82 ( (fun int (fun int (fun int bool))) ) 20.34/18.82 ( (fun int real) ) 20.34/18.82 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 20.34/18.82 ) 20.34/18.82 (instantiation (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (hBOOL (hAPP X_a bool (iszero X_a) (zero_zero X_a)))) ) 20.34/18.82 ( real ) 20.34/18.82 ( nat ) 20.34/18.82 ( int ) 20.34/18.82 ( complex ) 20.34/18.82 ( rat ) 20.34/18.82 ( quickcheck_code_int ) 20.34/18.82 ( code_code_numeral ) 20.34/18.82 ) 20.34/18.82 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (uminus_uminus real))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun _let_1 _let_1))) (forall ((X_1 $$unsorted)) (= (hAPP _let_1 real (suminf real) (hAPP _let_1 _let_1 (hAPP _let_0 _let_4 (combb real real nat) _let_2) (hAPP _let_1 _let_1 (hAPP _let_3 _let_4 (combs nat real real) (hAPP _let_1 _let_3 (hAPP (fun real _let_0) (fun _let_1 _let_3) (combb real _let_0 nat) (times_times real)) sin_coeff)) (hAPP real _let_1 (power_power real) X_1)))) (hAPP real real _let_2 (hAPP real real sin X_1))) )))))) 20.34/18.82 ( (zero_zero real) ) 20.34/18.82 ( pi ) 20.34/18.82 ( (hAPP int real (number_number_of real) min_1) ) 20.34/18.82 ( (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)))) ) 20.34/18.82 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 20.34/18.82 ( (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)))) ) 20.34/18.82 ( (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 (hAPP int int bit1 pls))))) ) 20.34/18.82 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 20.34/18.82 ( (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 bit0 (hAPP int int bit1 pls))))) ) 20.34/18.82 ( (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)))) ) 20.34/18.82 ) 20.34/18.82 (instantiation (let ((_let_0 (fun X_a (fun X_a bool)))) (forall ((X_a $$unsorted)) (or (not (linorder X_a)) (= (hAPP _let_0 (fun X_a (fun X_a X_a)) (min X_a) (hAPP _let_0 _let_0 (combc X_a X_a bool) (ord_less_eq X_a))) (ord_max X_a))) )) 20.34/18.82 ( bool ) 20.34/18.82 ( real ) 20.34/18.82 ( nat ) 20.34/18.82 ( (fun nat bool) ) 20.34/18.82 ( int ) 20.34/18.82 ( (fun int bool) ) 20.34/18.82 ( (fun real bool) ) 20.34/18.82 ( (fun real real) ) 20.34/18.82 ( complex ) 20.34/18.82 ( (fun nat real) ) 20.34/18.82 ( (fun int int) ) 20.34/18.82 ( rat ) 20.34/18.82 ( (fun int (fun int bool)) ) 20.34/18.82 ( quickcheck_code_int ) 20.34/18.82 ( (product_prod real real) ) 20.34/18.82 ( (product_prod int int) ) 20.34/18.82 ( (filter real) ) 20.34/18.82 ( (filter nat) ) 20.34/18.82 ( (product_prod nat nat) ) 20.34/18.82 ( (fun (product_prod int int) bool) ) 20.34/18.82 ( code_code_numeral ) 20.34/18.82 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 20.34/18.82 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 20.34/18.82 ( (fun nat rat) ) 20.34/18.82 ( (fun (product_prod int int) int) ) 20.34/18.82 ( (fun int (fun int (fun int bool))) ) 20.34/18.82 ( (fun int real) ) 20.34/18.82 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 20.34/18.82 ) 20.34/18.82 (instantiation (let ((_let_0 (fun (filter X_a) bool))) (let ((_let_1 (hAPP (fun X_a X_b) (fun X_b _let_0) (tendsto X_a X_b) BOUND_VARIABLE_152359))) (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_152358 $$unsorted) (BOUND_VARIABLE_152359 $$unsorted) (BOUND_VARIABLE_152360 $$unsorted) (BOUND_VARIABLE_152361 $$unsorted)) (let ((_let_0 (filter X_a))) (or (not (t2_space X_b)) (hBOOL (hAPP _let_0 bool (trivial_limit X_a) BOUND_VARIABLE_152361)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_152360) BOUND_VARIABLE_152361))) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_152358) BOUND_VARIABLE_152361))) (= (ti X_b BOUND_VARIABLE_152358) (ti X_b BOUND_VARIABLE_152360)))) ))) 20.34/18.82 ( nat, real, (zero_zero real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real), sequentially ) 20.34/18.82 ) 20.34/18.82 (instantiation (let ((_let_0 (min X_a))) (forall ((X_a $$unsorted)) (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))) )) 20.34/18.82 ( bool ) 20.34/18.82 ( real ) 20.34/18.82 ( nat ) 20.34/18.82 ( (fun nat bool) ) 20.34/18.82 ( int ) 20.34/18.82 ( (fun int bool) ) 20.34/18.82 ( (fun real bool) ) 20.34/18.82 ( (fun real real) ) 20.34/18.82 ( complex ) 20.34/18.82 ( (fun nat real) ) 20.34/18.82 ( (fun int int) ) 20.34/18.82 ( rat ) 20.34/18.82 ( (fun int (fun int bool)) ) 20.34/18.82 ( quickcheck_code_int ) 20.34/18.82 ( (product_prod real real) ) 20.34/18.82 ( (product_prod int int) ) 20.34/18.82 ( (filter real) ) 20.34/18.82 ( (filter nat) ) 20.34/18.82 ( (product_prod nat nat) ) 20.34/18.82 ( (fun (product_prod int int) bool) ) 20.34/18.82 ( code_code_numeral ) 20.34/18.82 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 20.34/18.82 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 20.34/18.82 ( (fun nat rat) ) 20.34/18.82 ( (fun (product_prod int int) int) ) 20.34/18.82 ( (fun int (fun int (fun int bool))) ) 20.34/18.82 ( (fun int real) ) 20.34/18.82 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 20.34/18.82 ) 20.34/18.82 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152388 $$unsorted) (BOUND_VARIABLE_152389 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_152388)) BOUND_VARIABLE_152389)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_152388) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_152389))))) ) 20.34/18.82 ( real, (zero_zero int), pi ) 20.34/18.82 ( real, (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.82 ( real, (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.82 ( real, (zero_zero int), skv_2 ) 20.34/18.82 ( real, (zero_zero int), skv_10 ) 20.34/18.82 ( real, (zero_zero int), skv_13 ) 20.34/18.82 ( real, (one_one int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.82 ) 20.34/18.82 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (fun (filter nat) bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_152424 $$unsorted) (BOUND_VARIABLE_152425 $$unsorted)) (or (not (metric_space X_a)) (not (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) R_2))) (not (forall ((No $$unsorted)) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) (hAPP nat X_a BOUND_VARIABLE_152424 N_2)) BOUND_VARIABLE_152425)) R_2))) )) ))) )) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_2 (hAPP (fun nat X_a) (fun X_a _let_2) (tendsto nat X_a) BOUND_VARIABLE_152424) BOUND_VARIABLE_152425) sequentially))) )))) 20.34/18.82 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 20.34/18.82 ) 20.34/18.82 (instantiation (forall ((I $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) I) (zero_zero int))) (= (zero_zero nat) (hAPP int nat nat_1 I))) ) 20.34/18.82 ( (zero_zero int) ) 20.34/18.82 ( (one_one int) ) 20.34/18.82 ( min_1 ) 20.34/18.82 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.82 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.34/18.82 ) 20.34/18.82 (instantiation (let ((_let_0 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X_1)))) (let ((_let_1 (hBOOL P_1))) (let ((_let_2 (hBOOL P_2))) (forall ((P_2 $$unsorted) (P_1 $$unsorted) (X_1 $$unsorted)) (or (and _let_0 (= (not _let_1) _let_2)) (= (and _let_0 _let_1) (and _let_2 _let_0))) )))) 20.34/18.82 ( (let ((_let_0 (fun int int))) (hAPP int bool zprime (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 zprime (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (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) pls) ) 20.34/18.83 ( (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (fun real _let_0))) (let ((_let_3 (filter real))) (let ((_let_4 (fun _let_3 bool))) (hAPP _let_3 bool (hAPP real _let_4 (hAPP _let_0 (fun real _let_4) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_0 real) _let_1) cos)) sin)) (zero_zero real)) (hAPP real _let_3 (at real) (hAPP real real (hAPP real _let_0 _let_1 pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (fun real _let_0))) (let ((_let_3 (filter real))) (let ((_let_4 (fun _let_3 bool))) (hAPP _let_3 bool (hAPP real _let_4 (hAPP _let_0 (fun real _let_4) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_0 real) _let_1) cos)) sin)) (zero_zero real)) (hAPP real _let_3 (at real) (hAPP real real (hAPP real _let_0 _let_1 pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))), min_1 ) 20.34/18.83 ( (hAPP int bool zprime (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int bool zprime (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))), s ) 20.34/18.83 ( (hAPP real bool (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))))), (hAPP real bool (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))))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.83 ( (let ((_let_0 (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 real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) _let_0)) _let_0)), (let ((_let_0 (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 real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) _let_0)) _let_0)), (one_one int) ) 20.34/18.83 ( fTrue, fTrue, skv_3 ) 20.34/18.83 ( (hAPP int bool nat_neg (hAPP int int (number_number_of int) pls)), (hAPP int bool nat_neg (hAPP int int (number_number_of int) pls)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.34/18.83 ( (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))) (zero_zero int)), (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))) (zero_zero int)), skv_9 ) 20.34/18.83 ) 20.34/18.83 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152539 $$unsorted)) (or (not (linordered_idom X_a)) (not (number_ring X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_152539)) (zero_zero X_a))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_152539) pls)))) ) 20.34/18.83 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.83 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.83 ( real, min_1 ) 20.34/18.83 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.83 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 20.34/18.83 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.34/18.83 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 20.34/18.83 ( nat, pls ) 20.34/18.83 ( nat, (hAPP int int bit1 pls) ) 20.34/18.83 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.83 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 20.34/18.83 ( int, pls ) 20.34/18.83 ( int, (hAPP int int bit1 pls) ) 20.34/18.83 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.83 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.83 ( int, min_1 ) 20.34/18.83 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 20.34/18.83 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.83 ( complex, min_1 ) 20.34/18.83 ( quickcheck_code_int, (zero_zero int) ) 20.34/18.83 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 20.34/18.83 ( quickcheck_code_int, (one_one int) ) 20.34/18.83 ( code_code_numeral, pls ) 20.34/18.83 ( code_code_numeral, (hAPP int int bit1 pls) ) 20.34/18.83 ) 20.34/18.83 (instantiation (let ((_let_0 (fun int bool))) (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) N_1))) (= (hAPP int int (fact_fact int) N_1) (hAPP _let_0 int (hAPP (fun int int) (fun _let_0 int) (big_co302546470etprod int int) (combi int)) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastAtMost int) (one_one int)) N_1)))) )) 20.34/18.83 ( (zero_zero int) ) 20.34/18.83 ( (one_one int) ) 20.34/18.83 ( min_1 ) 20.34/18.83 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.83 ( s ) 20.34/18.83 ( (hAPP int int (number_number_of int) pls) ) 20.34/18.83 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.34/18.83 ( skv_3 ) 20.34/18.83 ( skv_9 ) 20.34/18.83 ) 20.34/18.83 (instantiation (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (inverse_divide X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_152617 $$unsorted) (BOUND_VARIABLE_152618 $$unsorted)) (or (not (real_normed_field X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_152617)) BOUND_VARIABLE_152618) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_152617) BOUND_VARIABLE_152618)))) )))) 20.34/18.83 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.83 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.34/18.83 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.83 ( 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))))))))) ) 20.34/18.83 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.83 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.83 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.34/18.83 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.34/18.83 ( 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))) ) 20.34/18.83 ( 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))) ) 20.34/18.83 ( 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))) ) 20.34/18.83 ) 20.34/18.83 (instantiation (let ((_let_0 (fun nat int))) (let ((_let_1 (fun int int))) (let ((_let_2 (power_power int))) (let ((_let_3 (minus_minus int))) (let ((_let_4 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (hAPP int int (hAPP int _let_1 _let_3 (hAPP nat int (hAPP int _let_0 _let_2 A_1) _let_4)) (hAPP nat int (hAPP int _let_0 _let_2 B) _let_4)) (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int (hAPP int _let_1 (plus_plus int) A_1) B)) (hAPP int int (hAPP int _let_1 _let_3 A_1) B))) )))))) 20.34/18.83 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 20.34/18.83 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 20.34/18.83 ) 20.34/18.83 (instantiation (let ((_let_0 (times_times X_a))) (forall ((X_a $$unsorted)) (or (not (dvd X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0))) )) 20.34/18.83 ( bool ) 20.34/18.83 ( real ) 20.34/18.83 ( nat ) 20.34/18.83 ( (fun nat bool) ) 20.34/18.83 ( int ) 20.34/18.83 ( (fun int bool) ) 20.34/18.83 ( (fun real bool) ) 20.34/18.83 ( (fun real real) ) 20.34/18.83 ( complex ) 20.34/18.83 ( (fun nat real) ) 20.34/18.83 ( (fun int int) ) 20.34/18.83 ( rat ) 20.34/18.83 ( (fun int (fun int bool)) ) 20.34/18.83 ( quickcheck_code_int ) 20.34/18.83 ( (product_prod int int) ) 20.34/18.83 ( (fun (product_prod int int) bool) ) 20.34/18.83 ( code_code_numeral ) 20.34/18.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 20.34/18.83 ( (fun (product_prod int int) int) ) 20.34/18.83 ( (fun int (fun int (fun int bool))) ) 20.34/18.83 ( (fun int real) ) 20.34/18.83 ) 20.34/18.83 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (let ((_let_1 (number_number_of int))) (forall ((N $$unsorted)) (or (not (hBOOL (hAPP int bool _let_0 (hAPP int int _let_1 N)))) (and (hBOOL (hAPP int bool _let_0 (hAPP int int _let_1 (hAPP int int bit1 N)))) (hBOOL (hAPP int bool _let_0 (hAPP int int _let_1 (hAPP int int bit0 N)))))) ))) 20.34/18.83 ( pls ) 20.34/18.83 ( (hAPP int int bit1 pls) ) 20.34/18.83 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.83 ( min_1 ) 20.34/18.83 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 20.34/18.83 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.34/18.83 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.34/18.83 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 20.34/18.83 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 20.34/18.83 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 20.34/18.83 ) 20.34/18.83 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int _let_0 (ord_less_eq int) (zero_zero int)))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_1 X_1))) (not (hBOOL (hAPP int bool _let_1 Y_1))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) X_1) Y_1)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP int nat nat_1 X_1)) (hAPP int nat nat_1 Y_1))))) ))) 20.34/18.83 ( (zero_zero int), (zero_zero int) ) 20.34/18.83 ( (zero_zero int), min_1 ) 20.34/18.83 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 20.34/18.83 ( (zero_zero int), t ) 20.34/18.83 ( (one_one int), (zero_zero int) ) 20.34/18.83 ( (one_one int), t ) 20.34/18.83 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 20.34/18.83 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 20.34/18.83 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 20.34/18.83 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_3 ) 20.34/18.83 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_9 ) 20.34/18.83 ( min_1, (zero_zero int) ) 20.34/18.83 ( min_1, min_1 ) 20.34/18.83 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 20.34/18.83 ( (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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 20.34/18.83 ) 20.34/18.83 (instantiation (forall ((X_1 $$unsorted)) (= (= X_1 (hAPP real real (hAPP real (fun real real) powr X_1) (one_one real))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X_1))) ) 20.34/18.83 ( pi ) 20.34/18.83 ( (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)))) ) 20.34/18.83 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.83 ( skv_2 ) 20.34/18.83 ( skv_10 ) 20.34/18.83 ( skv_13 ) 20.34/18.83 ) 20.34/18.83 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (fun (filter nat) bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_152840 $$unsorted) (BOUND_VARIABLE_152841 $$unsorted)) (or (not (real_normed_vector X_a)) (not (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) R_2))) (not (forall ((No $$unsorted)) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_2))) (hBOOL (hAPP real bool (hAPP real _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) (hAPP nat X_a BOUND_VARIABLE_152840 N_2)) BOUND_VARIABLE_152841))) R_2))) )) ))) )) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_2 (hAPP (fun nat X_a) (fun X_a _let_2) (tendsto nat X_a) BOUND_VARIABLE_152840) BOUND_VARIABLE_152841) sequentially))) )))) 20.34/18.83 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 20.34/18.83 ) 20.34/18.83 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_152878 $$unsorted)) (or (not (field_inverse_zero X_a)) (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_152878) _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_152878)) _let_3))) ))))) 20.34/18.83 ( real, (zero_zero real) ) 20.34/18.83 ( complex, ii ) 20.34/18.83 ) 20.34/18.83 (instantiation (forall ((N $$unsorted)) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls)))) N) (hAPP nat nat suc (hAPP nat nat suc (hAPP nat nat suc N)))) ) 20.34/18.83 ( (zero_zero nat) ) 20.34/18.83 ) 20.34/18.83 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP real real cos (hAPP real real (hAPP real _let_0 (minus_minus real) X) Y)) (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real cos Y)) (hAPP real real cos X))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real sin Y)) (hAPP real real sin X)))) ))) 20.34/18.83 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 20.34/18.84 ) 20.34/18.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153002 $$unsorted)) (or (not (semiring_div X_a)) (= (ti X_a BOUND_VARIABLE_153002) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (div_div X_a) BOUND_VARIABLE_153002) (one_one X_a)))) ) 20.34/18.84 ( bool, fFalse ) 20.34/18.84 ( bool, fTrue ) 20.34/18.84 ( real, pi ) 20.34/18.84 ( (fun nat bool), (even_odd_even nat) ) 20.34/18.84 ( (fun nat bool), prime ) 20.34/18.84 ( (fun nat nat), suc ) 20.34/18.84 ( (fun nat nat), (fact_fact nat) ) 20.34/18.84 ( (fun nat nat), (size_size nat) ) 20.34/18.84 ( (fun nat nat), fact ) 20.34/18.84 ( (fun nat nat), nat_size ) 20.34/18.84 ( int, pls ) 20.34/18.84 ( int, m ) 20.34/18.84 ( int, min_1 ) 20.34/18.84 ( int, s ) 20.34/18.84 ( int, s1 ) 20.34/18.84 ( int, t ) 20.34/18.84 ( (fun int bool), zprime ) 20.34/18.84 ( (fun int bool), nat_neg ) 20.34/18.84 ( (fun int bool), zEven ) 20.34/18.84 ( (fun int bool), nat_is_nat ) 20.34/18.84 ( (fun int bool), zOdd ) 20.34/18.84 ( (fun int bool), (even_odd_even int) ) 20.34/18.84 ( (fun int bool), twoSqu1091635170sum2sq ) 20.34/18.84 ( (fun int nat), nat_1 ) 20.34/18.84 ( (fun int nat), phi ) 20.34/18.84 ( (fun real real), sqrt ) 20.34/18.84 ( (fun real real), tan ) 20.34/18.84 ( (fun real real), cos ) 20.34/18.84 ( (fun real real), arccos ) 20.34/18.84 ( (fun real real), ln ) 20.34/18.84 ( (fun real real), sin ) 20.34/18.84 ( (fun real real), arctan ) 20.34/18.84 ( (fun real real), arcsin ) 20.34/18.84 ( complex, ii ) 20.34/18.84 ( (fun complex complex), cnj ) 20.34/18.84 ( (fun complex complex), expi ) 20.34/18.84 ( (fun nat real), (real_1 nat) ) 20.34/18.84 ( (fun nat real), cos_coeff ) 20.34/18.84 ( (fun nat real), sin_coeff ) 20.34/18.84 ( (fun int int), bit0 ) 20.34/18.84 ( (fun int int), bit1 ) 20.34/18.84 ( (fun int int), pred ) 20.34/18.84 ( (fun int int), succ ) 20.34/18.84 ( (fun int int), (fact_fact int) ) 20.34/18.84 ( (fun int int), zfact ) 20.34/18.84 ( (fun bool bool), fNot ) 20.34/18.84 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 20.34/18.84 ( (fun bool (fun bool bool)), fconj ) 20.34/18.84 ( (fun bool (fun bool bool)), fdisj ) 20.34/18.84 ( (fun bool (fun bool bool)), fimplies ) 20.34/18.84 ( (fun int (fun int bool)), sRStar ) 20.34/18.84 ( (fun int (fun int bool)), quadRes ) 20.34/18.84 ( (fun int (fun int bool)), norRRset ) 20.34/18.84 ( (fun int (fun int bool)), d22set ) 20.34/18.84 ( (fun int (fun int bool)), sr ) 20.34/18.84 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 20.34/18.84 ( (fun nat (fun nat nat)), nat_gcd ) 20.34/18.84 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 20.34/18.84 ( (fun nat (fun nat nat)), nat_lcm ) 20.34/18.84 ( (fun nat (fun real real)), root ) 20.34/18.84 ( (fun real (fun real real)), log ) 20.34/18.84 ( (fun real (fun real real)), powr ) 20.34/18.84 ( (fun nat (fun nat bool)), coprime ) 20.34/18.84 ( (fun (fun int bool) int), (the int) ) 20.34/18.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 20.34/18.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 20.34/18.84 ( (fun nat (fun nat (product_prod int int))), bezw ) 20.34/18.84 ( (fun (fun int bool) bool), nat_nat_set ) 20.34/18.84 ( (filter nat), sequentially ) 20.34/18.84 ( (fun (product_prod nat nat) bool), pred_nat ) 20.34/18.84 ( (fun (product_prod int int) bool), frac_1 ) 20.34/18.84 ( (fun real complex), cis ) 20.34/18.84 ( (fun complex real), im ) 20.34/18.84 ( (fun complex real), re ) 20.34/18.84 ( (fun complex real), arg ) 20.34/18.84 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 20.34/18.84 ( (fun int (fun int int)), int_gcd ) 20.34/18.84 ( (fun int (fun int int)), multInv ) 20.34/18.84 ( (fun int (fun int int)), legacy_zgcd ) 20.34/18.84 ( (fun int (fun int int)), z3mod ) 20.34/18.84 ( (fun int (fun int int)), inv ) 20.34/18.84 ( (fun int (fun int int)), (gcd_gcd int) ) 20.34/18.84 ( (fun int (fun int int)), standardRes ) 20.34/18.84 ( (fun int (fun int int)), legendre ) 20.34/18.84 ( (fun int (fun int int)), nat_tsub ) 20.34/18.84 ( (fun int (fun int int)), z3div ) 20.34/18.84 ( (fun int (fun int int)), int_lcm ) 20.34/18.84 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 20.34/18.84 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 20.34/18.84 ( (fun int (fun (fun int bool) bool)), rsetR ) 20.34/18.84 ( (fun int (fun (fun int bool) bool)), resSet ) 20.34/18.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 20.34/18.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 20.34/18.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 20.34/18.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 20.34/18.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 20.34/18.84 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 20.34/18.84 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 20.34/18.84 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 20.34/18.84 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 20.34/18.84 ( (fun int (fun int (product_prod int int))), negDivAlg ) 20.34/18.84 ( (fun int (fun int (product_prod int int))), divmod_int ) 20.34/18.84 ( (fun int (fun int (product_prod int int))), posDivAlg ) 20.34/18.84 ( (fun int (fun int (product_prod int int))), pdivmod ) 20.34/18.84 ( (fun int (fun int (product_prod int int))), norm_frac ) 20.34/18.84 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 20.34/18.84 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 20.34/18.84 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 20.34/18.84 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 20.34/18.84 ( (fun real nat), natfloor ) 20.34/18.84 ( (fun real nat), natceiling ) 20.34/18.84 ( (fun int quickcheck_code_int), quickcheck_of_int ) 20.34/18.84 ( (fun int (fun int (fun int bool))), wset ) 20.34/18.84 ( (fun int (fun int (fun int bool))), bnorRset ) 20.34/18.84 ( (fun int (fun int (fun int bool))), zcong ) 20.34/18.84 ( (fun int (fun int (fun int bool))), noXRRset ) 20.34/18.84 ( (fun int (fun int (fun int bool))), zcongm ) 20.34/18.84 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 20.34/18.84 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 20.34/18.84 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 20.34/18.84 ( (fun int real), (real_1 int) ) 20.34/18.84 ( (fun complex nat), (size_size complex) ) 20.34/18.84 ( (fun complex nat), complex_size ) 20.34/18.84 ( (fun int (list int)), quickc666637781d_zero ) 20.34/18.84 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 20.34/18.84 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 20.34/18.84 ( (fun (product_prod int int) rat), frct ) 20.34/18.84 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 20.34/18.84 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 20.34/18.84 ( (fun (fun nat rat) bool), vanishes ) 20.34/18.84 ( (fun int (fun int rat)), fract ) 20.34/18.84 ( (fun code_code_numeral int), code_int_of ) 20.34/18.84 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 20.34/18.84 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 20.34/18.84 ( (fun code_code_numeral nat), code_c271388182l_size ) 20.34/18.84 ( (fun real (fun real complex)), complex_1 ) 20.34/18.84 ( (fun real (fun real complex)), rcis ) 20.34/18.84 ( (fun int (fun nat nat)), nat_aux ) 20.34/18.84 ( (fun rat real), ratreal ) 20.34/18.84 ( (fun quickcheck_code_int int), quickcheck_int_of ) 20.34/18.84 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 20.34/18.84 ( (fun rat (product_prod int int)), quotient_of ) 20.34/18.84 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 20.34/18.84 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 20.34/18.84 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 20.34/18.84 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 20.34/18.84 ) 20.34/18.84 (instantiation (let ((_let_0 (fun nat X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (times_times X_a))) (let ((_let_3 (suminf X_a))) (let ((_let_4 (fun nat _let_1))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_153079 $$unsorted) (BOUND_VARIABLE_153080 $$unsorted)) (or (not (real_normed_algebra X_a)) (not (hBOOL (hAPP _let_0 bool (summable X_a) BOUND_VARIABLE_153080))) (= (hAPP _let_0 X_a _let_3 (hAPP X_a _let_0 (hAPP _let_4 (fun X_a _let_0) (combc nat X_a X_a) (hAPP _let_0 _let_4 (hAPP (fun X_a _let_1) (fun _let_0 _let_4) (combb X_a _let_1 nat) _let_2) BOUND_VARIABLE_153080)) BOUND_VARIABLE_153079)) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP _let_0 X_a _let_3 BOUND_VARIABLE_153080)) BOUND_VARIABLE_153079))) )))))) 20.34/18.84 ( real, (one_one real), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) ) 20.34/18.84 ) 20.34/18.84 (instantiation (let ((_let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) N))) (forall ((M $$unsorted) (N $$unsorted)) (or (not (= (zero_zero nat) _let_0)) (= (one_one nat) (hAPP nat nat (fact_fact nat) _let_0))) )) 20.34/18.84 ( (one_one nat), (one_one nat) ) 20.34/18.84 ) 20.34/18.84 (instantiation (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))) (forall ((M $$unsorted) (N $$unsorted)) (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)))))) )))) 20.34/18.84 ( (one_one nat), (one_one nat) ) 20.34/18.84 ) 20.34/18.84 (instantiation (let ((_let_0 (fun int rat))) (forall ((M $$unsorted) (N $$unsorted)) (or (= (zero_zero int) (ti int N)) (= (hAPP int rat (hAPP int _let_0 fract (hAPP int int (hAPP int (fun int int) (plus_plus int) M) N)) 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)))) )) 20.34/18.84 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 20.34/18.84 ( (hAPP nat int (hAPP 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) ) 20.34/18.84 ) 20.34/18.84 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (forall ((X $$unsorted)) (or (= (zero_zero real) X) (= (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (sgn_sgn real) X)) pi)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP real real arctan X)) (hAPP real real arctan (hAPP real real (hAPP real _let_0 _let_1 (one_one real)) X)))) ))) 20.34/18.84 ( (zero_zero real) ) 20.34/18.84 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.84 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.34/18.84 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.84 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 20.34/18.84 ) 20.34/18.84 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_153170 $$unsorted)) (or (not (number_ring X_a)) (not (field_inverse_zero X_a)) (= (hAPP X_a X_a (uminus_uminus X_a) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (one_one X_a)) BOUND_VARIABLE_153170)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP int X_a (number_number_of X_a) min_1)) BOUND_VARIABLE_153170))) ))) 20.34/18.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.84 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.34/18.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 20.34/18.84 ) 20.34/18.84 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (let ((_let_2 (hAPP int int (number_number_of int) (hAPP int int pred V_1)))) (forall ((V_1 $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP int nat (number_number_of nat) V_1)) (hAPP nat nat suc N_1))) (or (hBOOL (hAPP int bool nat_neg _let_2)) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP int nat nat_1 _let_2)) N_1)))) )))) 20.34/18.84 ( pls, (hAPP nat nat suc (zero_zero nat)) ) 20.34/18.84 ) 20.34/18.84 (instantiation (let ((_let_0 (uminus_uminus real))) (forall ((X $$unsorted)) (= (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)) )) 20.34/18.84 ( ii ) 20.34/18.84 ( (zero_zero complex) ) 20.34/18.84 ( (one_one complex) ) 20.34/18.84 ) 20.34/18.84 (instantiation (let ((_let_0 (product_prod int int))) (forall ((K_4 $$unsorted)) (= (zero_zero rat) (hAPP _let_0 rat frct (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) (zero_zero int)) K_4))) )) 20.34/18.84 ( (one_one int) ) 20.34/18.84 ) 20.34/18.84 (instantiation (let ((_let_0 (zero_zero int))) (let ((_let_1 (fun int int))) (let ((_let_2 (ti int A_1))) (let ((_let_3 (ti int B))) (let ((_let_4 (hAPP int _let_1 (times_times int) (hAPP int int (hAPP int _let_1 legacy_zgcd A_1) B)))) (forall ((B $$unsorted) (A_1 $$unsorted)) (or (and (= _let_0 _let_2) (= _let_0 _let_3)) (not (forall ((C_4 $$unsorted) (D_3 $$unsorted)) (or (not (= (one_one int) (hAPP int int (hAPP int _let_1 legacy_zgcd C_4) D_3))) (not (= _let_3 (hAPP int int _let_4 D_3))) (not (= _let_2 (hAPP int int _let_4 C_4)))) ))) )))))) 20.34/18.84 ( pls, pls ) 20.34/18.84 ( m, m ) 20.34/18.84 ( min_1, min_1 ) 20.34/18.84 ( s, s ) 20.34/18.84 ( s1, s1 ) 20.34/18.84 ( t, t ) 20.34/18.84 ) 20.34/18.84 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_153361))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_153361 $$unsorted) (BOUND_VARIABLE_153362 $$unsorted) (BOUND_VARIABLE_153363 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_153363))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_153362))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_153363) BOUND_VARIABLE_153362)))) )) 20.34/18.84 ( nat, (zero_zero nat), (one_one nat), (one_one nat) ) 20.34/18.84 ( int, (zero_zero int), (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 20.34/18.84 ( int, s, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 20.34/18.84 ( int, t, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 20.34/18.84 ( int, skv_3, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 20.34/18.84 ( int, skv_9, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 20.34/18.84 ) 20.34/18.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153422 $$unsorted)) (or (not (semiring_1 X_a)) (= (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_153422)) (hBOOL (hAPP X_a bool (iszero X_a) BOUND_VARIABLE_153422)))) ) 20.34/18.84 ( bool, fFalse ) 20.34/18.84 ( bool, fTrue ) 20.34/18.84 ( real, pi ) 20.34/18.84 ( (fun nat bool), (even_odd_even nat) ) 20.34/18.84 ( (fun nat bool), prime ) 20.34/18.84 ( (fun nat nat), suc ) 20.34/18.84 ( (fun nat nat), (fact_fact nat) ) 20.34/18.84 ( (fun nat nat), (size_size nat) ) 20.34/18.84 ( (fun nat nat), fact ) 20.34/18.84 ( (fun nat nat), nat_size ) 20.34/18.84 ( int, pls ) 20.34/18.84 ( int, m ) 20.34/18.84 ( int, min_1 ) 20.34/18.84 ( int, s ) 20.34/18.84 ( int, s1 ) 20.34/18.84 ( int, t ) 20.34/18.84 ( (fun int bool), zprime ) 20.34/18.84 ( (fun int bool), nat_neg ) 20.34/18.84 ( (fun int bool), zEven ) 20.34/18.84 ( (fun int bool), nat_is_nat ) 20.34/18.84 ( (fun int bool), zOdd ) 20.34/18.84 ( (fun int bool), (even_odd_even int) ) 20.34/18.84 ( (fun int bool), twoSqu1091635170sum2sq ) 20.34/18.84 ( (fun int nat), nat_1 ) 20.34/18.84 ( (fun int nat), phi ) 20.34/18.84 ( (fun real real), sqrt ) 20.34/18.84 ( (fun real real), tan ) 20.34/18.84 ( (fun real real), cos ) 20.34/18.84 ( (fun real real), arccos ) 20.34/18.84 ( (fun real real), ln ) 20.34/18.84 ( (fun real real), sin ) 20.34/18.84 ( (fun real real), arctan ) 20.34/18.84 ( (fun real real), arcsin ) 20.34/18.84 ( complex, ii ) 20.34/18.84 ( (fun complex complex), cnj ) 20.34/18.84 ( (fun complex complex), expi ) 20.34/18.84 ( (fun nat real), (real_1 nat) ) 20.34/18.84 ( (fun nat real), cos_coeff ) 20.34/18.84 ( (fun nat real), sin_coeff ) 20.34/18.84 ( (fun int int), bit0 ) 20.34/18.84 ( (fun int int), bit1 ) 20.34/18.84 ( (fun int int), pred ) 20.34/18.84 ( (fun int int), succ ) 20.34/18.84 ( (fun int int), (fact_fact int) ) 20.34/18.84 ( (fun int int), zfact ) 20.34/18.84 ( (fun bool bool), fNot ) 20.34/18.84 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 20.34/18.84 ( (fun bool (fun bool bool)), fconj ) 20.34/18.84 ( (fun bool (fun bool bool)), fdisj ) 20.34/18.84 ( (fun bool (fun bool bool)), fimplies ) 20.34/18.84 ( (fun int (fun int bool)), sRStar ) 20.34/18.84 ( (fun int (fun int bool)), quadRes ) 20.34/18.84 ( (fun int (fun int bool)), norRRset ) 20.34/18.84 ( (fun int (fun int bool)), d22set ) 20.34/18.84 ( (fun int (fun int bool)), sr ) 20.34/18.84 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 20.34/18.84 ( (fun nat (fun nat nat)), nat_gcd ) 20.34/18.85 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 20.34/18.85 ( (fun nat (fun nat nat)), nat_lcm ) 20.34/18.85 ( (fun nat (fun real real)), root ) 20.34/18.85 ( (fun real (fun real real)), log ) 20.34/18.85 ( (fun real (fun real real)), powr ) 20.34/18.85 ( (fun nat (fun nat bool)), coprime ) 20.34/18.85 ( (fun (fun int bool) int), (the int) ) 20.34/18.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 20.34/18.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 20.34/18.85 ( (fun nat (fun nat (product_prod int int))), bezw ) 20.34/18.85 ( (fun (fun int bool) bool), nat_nat_set ) 20.34/18.85 ( (filter nat), sequentially ) 20.34/18.85 ( (fun (product_prod nat nat) bool), pred_nat ) 20.34/18.85 ( (fun (product_prod int int) bool), frac_1 ) 20.34/18.85 ( (fun real complex), cis ) 20.34/18.85 ( (fun complex real), im ) 20.34/18.85 ( (fun complex real), re ) 20.34/18.85 ( (fun complex real), arg ) 20.34/18.85 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 20.34/18.85 ( (fun int (fun int int)), int_gcd ) 20.34/18.85 ( (fun int (fun int int)), multInv ) 20.34/18.85 ( (fun int (fun int int)), legacy_zgcd ) 20.34/18.85 ( (fun int (fun int int)), z3mod ) 20.34/18.85 ( (fun int (fun int int)), inv ) 20.34/18.85 ( (fun int (fun int int)), (gcd_gcd int) ) 20.34/18.85 ( (fun int (fun int int)), standardRes ) 20.34/18.85 ( (fun int (fun int int)), legendre ) 20.34/18.85 ( (fun int (fun int int)), nat_tsub ) 20.34/18.85 ( (fun int (fun int int)), z3div ) 20.34/18.85 ( (fun int (fun int int)), int_lcm ) 20.34/18.85 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 20.34/18.85 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 20.34/18.85 ( (fun int (fun (fun int bool) bool)), rsetR ) 20.34/18.85 ( (fun int (fun (fun int bool) bool)), resSet ) 20.34/18.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 20.34/18.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 20.34/18.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 20.34/18.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 20.34/18.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 20.34/18.85 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 20.34/18.85 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 20.34/18.85 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 20.34/18.85 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 20.34/18.85 ( (fun int (fun int (product_prod int int))), negDivAlg ) 20.34/18.85 ( (fun int (fun int (product_prod int int))), divmod_int ) 20.34/18.85 ( (fun int (fun int (product_prod int int))), posDivAlg ) 20.34/18.85 ( (fun int (fun int (product_prod int int))), pdivmod ) 20.34/18.85 ( (fun int (fun int (product_prod int int))), norm_frac ) 20.34/18.85 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 20.34/18.85 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 20.34/18.85 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 20.34/18.85 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 20.34/18.85 ( (fun real nat), natfloor ) 20.34/18.85 ( (fun real nat), natceiling ) 20.34/18.85 ( (fun int quickcheck_code_int), quickcheck_of_int ) 20.34/18.85 ( (fun int (fun int (fun int bool))), wset ) 20.34/18.85 ( (fun int (fun int (fun int bool))), bnorRset ) 20.34/18.85 ( (fun int (fun int (fun int bool))), zcong ) 20.34/18.85 ( (fun int (fun int (fun int bool))), noXRRset ) 20.34/18.85 ( (fun int (fun int (fun int bool))), zcongm ) 20.34/18.85 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 20.34/18.85 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 20.34/18.85 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 20.34/18.85 ( (fun int real), (real_1 int) ) 20.34/18.85 ( (fun complex nat), (size_size complex) ) 20.34/18.85 ( (fun complex nat), complex_size ) 20.34/18.85 ( (fun int (list int)), quickc666637781d_zero ) 20.34/18.85 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 20.34/18.85 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 20.34/18.85 ( (fun (product_prod int int) rat), frct ) 20.34/18.85 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 20.34/18.85 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 20.34/18.85 ( (fun (fun nat rat) bool), vanishes ) 20.34/18.85 ( (fun int (fun int rat)), fract ) 20.34/18.85 ( (fun code_code_numeral int), code_int_of ) 20.34/18.85 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 20.34/18.85 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 20.34/18.85 ( (fun code_code_numeral nat), code_c271388182l_size ) 20.34/18.85 ( (fun real (fun real complex)), complex_1 ) 20.34/18.85 ( (fun real (fun real complex)), rcis ) 20.34/18.85 ( (fun int (fun nat nat)), nat_aux ) 20.34/18.85 ( (fun rat real), ratreal ) 20.34/18.85 ( (fun quickcheck_code_int int), quickcheck_int_of ) 20.34/18.85 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 20.34/18.85 ( (fun rat (product_prod int int)), quotient_of ) 20.34/18.85 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 20.34/18.85 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 20.34/18.85 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 20.34/18.85 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 20.34/18.85 ) 20.34/18.85 (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)))) ) 20.34/18.85 ( (zero_zero real) ) 20.34/18.85 ( pi ) 20.34/18.85 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.85 ( (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)))) ) 20.34/18.85 ( (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) ) 20.34/18.85 ( (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))))) ) 20.34/18.85 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 20.34/18.85 ( (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))))) ) 20.34/18.85 ( (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)))) ) 20.34/18.85 ( skv_14 ) 20.34/18.85 ) 20.34/18.85 (instantiation (let ((_let_0 (ti X_a A_1))) (let ((_let_1 (product_prod X_b X_a))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X $$unsorted) (Y $$unsorted) (A_1 $$unsorted)) (or (not (= _let_0 (hAPP _let_1 X_a (product_snd X_b X_a) (hAPP X_a _let_1 (hAPP X_b (fun X_a _let_1) (product_Pair X_b X_a) X) Y)))) (= (ti X_a Y) _let_0)) ))) 20.34/18.85 ( int, int, (zero_zero int), (one_one int), min_1 ) 20.34/18.85 ( int, int, (one_one int), (one_one int), s ) 20.34/18.85 ( int, int, s, (one_one int), m ) 20.34/18.85 ) 20.34/18.85 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X_1))) (= (hBOOL (hAPP int bool (even_odd_even int) X_1)) (hBOOL (hAPP nat bool (even_odd_even nat) (hAPP int nat nat_1 X_1))))) ) 20.34/18.85 ( (zero_zero int) ) 20.34/18.85 ( (one_one int) ) 20.34/18.85 ( min_1 ) 20.34/18.85 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.85 ( s ) 20.34/18.85 ( (hAPP int int (number_number_of int) pls) ) 20.34/18.85 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.34/18.85 ( skv_3 ) 20.34/18.85 ( skv_9 ) 20.34/18.85 ) 20.34/18.85 (instantiation (let ((_let_0 (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_153497))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_153497 $$unsorted) (BOUND_VARIABLE_153498 $$unsorted) (BOUND_VARIABLE_153499 $$unsorted)) (or (not (cancel146912293up_add X_a)) (not (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_153498) (hAPP X_a X_a _let_0 BOUND_VARIABLE_153499))) (= (ti X_a BOUND_VARIABLE_153499) (ti X_a BOUND_VARIABLE_153498))) )) 20.34/18.85 ( nat, (one_one nat), (one_one nat), (one_one nat) ) 20.34/18.85 ( 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) ) 20.34/18.85 ( 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) ) 20.34/18.85 ) 20.34/18.85 (instantiation (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_b))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (fun X_a X_b))) (let ((_let_4 (filter X_a))) (let ((_let_5 (fun _let_4 bool))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_153601 $$unsorted) (BOUND_VARIABLE_153602 $$unsorted) (BOUND_VARIABLE_153603 $$unsorted) (BOUND_VARIABLE_153604 $$unsorted)) (let ((_let_0 (filter nat))) (or (not (metric_space X_b)) (not (metric_space X_a)) (not (hBOOL (hAPP _let_4 bool (hAPP X_b _let_5 (hAPP _let_3 (fun X_b _let_5) (tendsto X_a X_b) BOUND_VARIABLE_153601) BOUND_VARIABLE_153602) (hAPP X_a _let_4 (at X_a) BOUND_VARIABLE_153603)))) (not (forall ((N_2 $$unsorted)) (not (= (ti X_a BOUND_VARIABLE_153603) (hAPP nat X_a BOUND_VARIABLE_153604 N_2))) )) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_0 (hAPP _let_2 (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_153604) BOUND_VARIABLE_153603) sequentially))) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_0 (hAPP _let_1 (fun X_b _let_0) (tendsto nat X_b) (hAPP _let_2 _let_1 (hAPP _let_3 (fun _let_2 _let_1) (combb X_a X_b nat) BOUND_VARIABLE_153601) BOUND_VARIABLE_153604)) BOUND_VARIABLE_153602) sequentially)))) ))))))) 20.34/18.85 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 20.34/18.85 ) 20.34/18.85 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X))) (not (forall ((N_2 $$unsorted)) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (inverse_inverse real) (hAPP nat real (real_1 nat) (hAPP nat nat suc N_2)))) X))) ))) ))) 20.34/18.85 ( pi ) 20.34/18.85 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.85 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.85 ( skv_2 ) 20.34/18.85 ( skv_10 ) 20.34/18.85 ( skv_13 ) 20.34/18.85 ) 20.34/18.85 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (field_char_0_Rats X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_153665 $$unsorted)) (or (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_153665) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_153665)) _let_3))) ))))) 20.34/18.85 ( real, (one_one real) ) 20.34/18.85 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.85 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 20.34/18.85 ( int, pls ) 20.34/18.85 ( int, (one_one int) ) 20.34/18.85 ( int, min_1 ) 20.34/18.85 ( complex, ii ) 20.34/18.85 ( complex, (one_one complex) ) 20.34/18.85 ) 20.34/18.85 (instantiation (forall ((N $$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))) ) 20.34/18.85 ( (zero_zero nat) ) 20.34/18.85 ( (one_one nat) ) 20.34/18.85 ) 20.34/18.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153690 $$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_153690) (ti X_a BOUND_VARIABLE_153690))) ) 20.34/18.85 ( bool, fFalse ) 20.34/18.85 ( bool, fTrue ) 20.34/18.85 ( real, pi ) 20.34/18.85 ( (fun nat bool), (even_odd_even nat) ) 20.34/18.85 ( (fun nat bool), prime ) 20.34/18.85 ( (fun nat nat), suc ) 20.34/18.85 ( (fun nat nat), (fact_fact nat) ) 20.34/18.85 ( (fun nat nat), (size_size nat) ) 20.34/18.85 ( (fun nat nat), fact ) 20.34/18.85 ( (fun nat nat), nat_size ) 20.34/18.85 ( int, pls ) 20.34/18.85 ( int, m ) 20.34/18.85 ( int, min_1 ) 20.34/18.85 ( int, s ) 20.34/18.85 ( int, s1 ) 20.34/18.85 ( int, t ) 20.34/18.85 ( (fun int bool), zprime ) 20.34/18.85 ( (fun int bool), nat_neg ) 20.34/18.85 ( (fun int bool), zEven ) 20.34/18.85 ( (fun int bool), nat_is_nat ) 20.34/18.85 ( (fun int bool), zOdd ) 20.34/18.85 ( (fun int bool), (even_odd_even int) ) 20.34/18.85 ( (fun int bool), twoSqu1091635170sum2sq ) 20.34/18.85 ( (fun int nat), nat_1 ) 20.34/18.85 ( (fun int nat), phi ) 20.34/18.85 ( (fun real real), sqrt ) 20.34/18.85 ( (fun real real), tan ) 20.34/18.85 ( (fun real real), cos ) 20.34/18.85 ( (fun real real), arccos ) 20.34/18.85 ( (fun real real), ln ) 20.34/18.85 ( (fun real real), sin ) 20.34/18.85 ( (fun real real), arctan ) 20.34/18.85 ( (fun real real), arcsin ) 20.34/18.85 ( complex, ii ) 20.34/18.85 ( (fun complex complex), cnj ) 20.34/18.85 ( (fun complex complex), expi ) 20.34/18.85 ( (fun nat real), (real_1 nat) ) 20.34/18.85 ( (fun nat real), cos_coeff ) 20.34/18.85 ( (fun nat real), sin_coeff ) 20.34/18.85 ( (fun int int), bit0 ) 20.34/18.85 ( (fun int int), bit1 ) 20.34/18.85 ( (fun int int), pred ) 20.34/18.85 ( (fun int int), succ ) 20.34/18.85 ( (fun int int), (fact_fact int) ) 20.34/18.85 ( (fun int int), zfact ) 20.34/18.85 ( (fun bool bool), fNot ) 20.34/18.85 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 20.34/18.85 ( (fun bool (fun bool bool)), fconj ) 20.34/18.85 ( (fun bool (fun bool bool)), fdisj ) 20.34/18.85 ( (fun bool (fun bool bool)), fimplies ) 20.34/18.85 ( (fun int (fun int bool)), sRStar ) 20.34/18.85 ( (fun int (fun int bool)), quadRes ) 20.34/18.85 ( (fun int (fun int bool)), norRRset ) 20.34/18.85 ( (fun int (fun int bool)), d22set ) 20.34/18.85 ( (fun int (fun int bool)), sr ) 20.34/18.85 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 20.34/18.85 ( (fun nat (fun nat nat)), nat_gcd ) 20.34/18.85 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 20.34/18.85 ( (fun nat (fun nat nat)), nat_lcm ) 20.34/18.85 ( (fun nat (fun real real)), root ) 20.34/18.85 ( (fun real (fun real real)), log ) 20.34/18.85 ( (fun real (fun real real)), powr ) 20.34/18.85 ( (fun nat (fun nat bool)), coprime ) 20.34/18.85 ( (fun (fun int bool) int), (the int) ) 20.34/18.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 20.34/18.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 20.34/18.85 ( (fun nat (fun nat (product_prod int int))), bezw ) 20.34/18.85 ( (fun (fun int bool) bool), nat_nat_set ) 20.34/18.85 ( (filter nat), sequentially ) 20.34/18.85 ( (fun (product_prod nat nat) bool), pred_nat ) 20.34/18.85 ( (fun (product_prod int int) bool), frac_1 ) 20.34/18.85 ( (fun real complex), cis ) 20.34/18.85 ( (fun complex real), im ) 20.34/18.85 ( (fun complex real), re ) 20.34/18.85 ( (fun complex real), arg ) 20.34/18.85 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 20.34/18.85 ( (fun int (fun int int)), int_gcd ) 20.34/18.85 ( (fun int (fun int int)), multInv ) 20.34/18.85 ( (fun int (fun int int)), legacy_zgcd ) 20.34/18.85 ( (fun int (fun int int)), z3mod ) 20.34/18.85 ( (fun int (fun int int)), inv ) 20.34/18.85 ( (fun int (fun int int)), (gcd_gcd int) ) 20.34/18.85 ( (fun int (fun int int)), standardRes ) 20.34/18.85 ( (fun int (fun int int)), legendre ) 20.34/18.85 ( (fun int (fun int int)), nat_tsub ) 20.34/18.85 ( (fun int (fun int int)), z3div ) 20.34/18.85 ( (fun int (fun int int)), int_lcm ) 20.34/18.85 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 20.34/18.85 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 20.34/18.85 ( (fun int (fun (fun int bool) bool)), rsetR ) 20.34/18.85 ( (fun int (fun (fun int bool) bool)), resSet ) 20.34/18.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 20.34/18.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 20.34/18.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 20.34/18.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 20.34/18.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 20.34/18.85 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 20.34/18.85 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 20.34/18.85 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 20.34/18.85 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 20.34/18.85 ( (fun int (fun int (product_prod int int))), negDivAlg ) 20.34/18.85 ( (fun int (fun int (product_prod int int))), divmod_int ) 20.34/18.85 ( (fun int (fun int (product_prod int int))), posDivAlg ) 20.34/18.85 ( (fun int (fun int (product_prod int int))), pdivmod ) 20.34/18.85 ( (fun int (fun int (product_prod int int))), norm_frac ) 20.34/18.85 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 20.34/18.85 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 20.34/18.85 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 20.34/18.85 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 20.34/18.85 ( (fun real nat), natfloor ) 20.34/18.85 ( (fun real nat), natceiling ) 20.34/18.85 ( (fun int quickcheck_code_int), quickcheck_of_int ) 20.34/18.85 ( (fun int (fun int (fun int bool))), wset ) 20.34/18.85 ( (fun int (fun int (fun int bool))), bnorRset ) 20.34/18.85 ( (fun int (fun int (fun int bool))), zcong ) 20.34/18.86 ( (fun int (fun int (fun int bool))), noXRRset ) 20.34/18.86 ( (fun int (fun int (fun int bool))), zcongm ) 20.34/18.86 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 20.34/18.86 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 20.34/18.86 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 20.34/18.86 ( (fun int real), (real_1 int) ) 20.34/18.86 ( (fun complex nat), (size_size complex) ) 20.34/18.86 ( (fun complex nat), complex_size ) 20.34/18.86 ( (fun int (list int)), quickc666637781d_zero ) 20.34/18.86 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 20.34/18.86 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 20.34/18.86 ( (fun (product_prod int int) rat), frct ) 20.34/18.86 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 20.34/18.86 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 20.34/18.86 ( (fun (fun nat rat) bool), vanishes ) 20.34/18.86 ( (fun int (fun int rat)), fract ) 20.34/18.86 ( (fun code_code_numeral int), code_int_of ) 20.34/18.86 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 20.34/18.86 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 20.34/18.86 ( (fun code_code_numeral nat), code_c271388182l_size ) 20.34/18.86 ( (fun real (fun real complex)), complex_1 ) 20.34/18.86 ( (fun real (fun real complex)), rcis ) 20.34/18.86 ( (fun int (fun nat nat)), nat_aux ) 20.34/18.86 ( (fun rat real), ratreal ) 20.34/18.86 ( (fun quickcheck_code_int int), quickcheck_int_of ) 20.34/18.86 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 20.34/18.86 ( (fun rat (product_prod int int)), quotient_of ) 20.34/18.86 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 20.34/18.86 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 20.34/18.86 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 20.34/18.86 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 20.34/18.86 ) 20.34/18.86 (instantiation (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))))) (forall ((X $$unsorted)) (or (hBOOL (hAPP int bool (even_odd_even int) X)) (= (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 X) _let_2)) _let_4) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 X) _let_4)) _let_2))) )))))) 20.34/18.86 ( (zero_zero int) ) 20.34/18.86 ( (one_one int) ) 20.34/18.86 ) 20.34/18.86 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (finite_finite_1 X_a) A_3))) (= (hAPP _let_1 nat (finite_card _let_0) (hAPP _let_0 _let_1 (pow X_a) A_3)) (hAPP nat nat (hAPP nat (fun nat nat) (power_power nat) (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat)))) (hAPP _let_0 nat (finite_card X_a) A_3)))) ))) 20.34/18.86 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 20.34/18.86 ) 20.34/18.86 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_153742 $$unsorted) (BOUND_VARIABLE_153743 $$unsorted) (BOUND_VARIABLE_153744 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_153744) (zero_zero X_a)))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_153743) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_153742) BOUND_VARIABLE_153744))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_153742) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_153743) BOUND_VARIABLE_153744))))) )))) 20.34/18.86 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.86 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 20.34/18.86 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 20.34/18.86 ) 20.34/18.86 (instantiation (let ((_let_0 (times_times X_a))) (forall ((X_a $$unsorted)) (or (not (semiring X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0))) )) 20.34/18.86 ( bool ) 20.34/18.86 ( real ) 20.34/18.86 ( nat ) 20.34/18.86 ( (fun nat bool) ) 20.34/18.86 ( int ) 20.34/18.86 ( (fun int bool) ) 20.34/18.86 ( (fun real bool) ) 20.34/18.86 ( (fun real real) ) 20.34/18.86 ( complex ) 20.34/18.86 ( (fun nat real) ) 20.34/18.86 ( (fun int int) ) 20.34/18.86 ( rat ) 20.34/18.86 ( (fun int (fun int bool)) ) 20.34/18.86 ( quickcheck_code_int ) 20.34/18.86 ( (product_prod int int) ) 20.34/18.86 ( (fun (product_prod int int) bool) ) 20.34/18.86 ( code_code_numeral ) 20.34/18.86 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 20.34/18.86 ( (fun (product_prod int int) int) ) 20.34/18.86 ( (fun int (fun int (fun int bool))) ) 20.34/18.86 ( (fun int real) ) 20.34/18.86 ) 20.34/18.86 (instantiation (let ((_let_0 (uminus_uminus int))) (forall ((K_4 $$unsorted)) (= (hAPP int int bit0 (hAPP int int _let_0 K_4)) (hAPP int int _let_0 (hAPP int int bit0 K_4))) )) 20.34/18.86 ( pls ) 20.34/18.86 ( (one_one int) ) 20.34/18.86 ( min_1 ) 20.34/18.86 ) 20.34/18.86 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_153985 $$unsorted) (BOUND_VARIABLE_153986 $$unsorted)) (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_153985) BOUND_VARIABLE_153986)))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_153986))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_153985))) )) 20.34/18.86 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 20.34/18.86 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 20.34/18.86 ( 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)))))) ) 20.34/18.86 ( 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 ) 20.34/18.86 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 20.34/18.86 ( 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) ) 20.34/18.86 ( 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 ) 20.34/18.86 ( 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_1 ) 20.34/18.86 ( complex, ii, ii ) 20.34/18.86 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 20.34/18.86 ( 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 ) 20.34/18.86 ) 20.34/18.86 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (ord_less real))) (forall ((B $$unsorted) (A_1 $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 A_1) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X) B))) (not (forall ((D_3 $$unsorted)) (or (not (forall ((Y_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP real real (abs_abs real) (hAPP real real (hAPP real (fun real real) (minus_minus real) X) Y_2))) D_3))) (and (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_1) Y_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_2) B)))) )) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (zero_zero real)) D_3)))) ))) )))) 20.34/18.86 ( (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 20.34/18.86 ( pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 20.34/18.86 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.86 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 20.34/18.86 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), pi ) 20.34/18.86 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi, (zero_zero real) ) 20.34/18.86 ) 20.34/18.86 (instantiation (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (fun X_a _let_0))) (let ((_let_3 (tendsto nat X_a))) (let ((_let_4 (inverse_inverse X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_154119 $$unsorted) (BOUND_VARIABLE_154120 $$unsorted)) (let ((_let_0 (filter nat))) (or (not (real_n1866405975lgebra X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_0 (hAPP _let_1 _let_2 _let_3 BOUND_VARIABLE_154119) BOUND_VARIABLE_154120) sequentially))) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_154120)) (hBOOL (hAPP _let_0 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_154119)) (hAPP X_a X_a _let_4 BOUND_VARIABLE_154120)) sequentially)))) )))))) 20.34/18.86 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))), (zero_zero real) ) 20.34/18.86 ) 20.34/18.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154147 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_154147) (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_154147)) (zero_zero X_a))))) ) 20.34/18.86 ( real, (zero_zero int) ) 20.34/18.86 ( real, (one_one int) ) 20.34/18.86 ) 20.34/18.86 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (ord_less int))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (zero_zero int)) Z_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 X) (hAPP int int (hAPP int _let_1 (times_times int) Y) Z_1)))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_1 (div_div int) X) Z_1)) Y))) )))) 20.34/18.86 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 20.34/18.86 ) 20.34/18.86 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_154226))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_154225 $$unsorted) (BOUND_VARIABLE_154226 $$unsorted) (BOUND_VARIABLE_154227 $$unsorted)) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_154227))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_154227) BOUND_VARIABLE_154225))) (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_154225))) ))) 20.34/18.86 ( real, pi, pi, (zero_zero real) ) 20.34/18.86 ( real, pi, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.86 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.86 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 20.34/18.86 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 20.34/18.86 ( int, pls, (zero_zero int), min_1 ) 20.34/18.86 ( int, min_1, min_1, min_1 ) 20.34/18.86 ( int, min_1, t, (zero_zero int) ) 20.34/18.86 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), min_1, (zero_zero int) ) 20.34/18.86 ( int, s, (zero_zero int), (zero_zero int) ) 20.34/18.86 ( int, (hAPP int int (number_number_of int) pls), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 20.34/18.86 ( int, t, (zero_zero int), (one_one int) ) 20.34/18.86 ) 20.34/18.86 (instantiation (let ((_let_0 (lim X_a))) (forall ((X_a $$unsorted)) (or (not (metric_space X_a)) (= _let_0 (ti (fun (fun nat X_a) X_a) _let_0))) )) 20.34/18.86 ( bool ) 20.34/18.86 ( real ) 20.34/18.86 ( nat ) 20.34/18.86 ( (fun nat bool) ) 20.34/18.86 ( (fun nat nat) ) 20.34/18.86 ( int ) 20.34/18.86 ( (fun real real) ) 20.34/18.86 ( complex ) 20.34/18.86 ( (fun int int) ) 20.34/18.86 ( rat ) 20.34/18.86 ( (fun bool bool) ) 20.34/18.86 ( (fun nat (fun nat bool)) ) 20.34/18.86 ( (product_prod real real) ) 20.34/18.86 ( (product_prod int int) ) 20.34/18.87 ( (fun nat (product_prod int int)) ) 20.34/18.87 ( (product_prod nat nat) ) 20.34/18.87 ( (fun (product_prod nat nat) bool) ) 20.34/18.87 ( (fun nat (fun (product_prod nat nat) bool)) ) 20.34/18.87 ( (fun nat (product_prod nat nat)) ) 20.34/18.87 ) 20.34/18.87 (instantiation (let ((_let_0 (sgn_sgn X_a))) (forall ((X_a $$unsorted)) (or (not (sgn_if X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 20.34/18.87 ( bool ) 20.34/18.87 ( real ) 20.34/18.87 ( nat ) 20.34/18.87 ( (fun nat bool) ) 20.34/18.87 ( int ) 20.34/18.87 ( (fun int bool) ) 20.34/18.87 ( (fun real bool) ) 20.34/18.87 ( (fun real real) ) 20.34/18.87 ( complex ) 20.34/18.87 ( (fun nat real) ) 20.34/18.87 ( (fun int int) ) 20.34/18.87 ( rat ) 20.34/18.87 ( (fun int (fun int bool)) ) 20.34/18.87 ( (product_prod int int) ) 20.34/18.87 ( (fun (product_prod int int) bool) ) 20.34/18.87 ( code_code_numeral ) 20.34/18.87 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 20.34/18.87 ( (fun (product_prod int int) int) ) 20.34/18.87 ( (fun int (fun int (fun int bool))) ) 20.34/18.87 ( (fun int real) ) 20.34/18.87 ) 20.34/18.87 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_154272 $$unsorted) (BOUND_VARIABLE_154273 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_154273) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_154272) _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_154273) BOUND_VARIABLE_154272)) _let_2))) )))) 20.34/18.87 ( nat, (one_one nat), (one_one nat) ) 20.34/18.87 ( 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) ) 20.34/18.87 ( 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)))) ) 20.34/18.87 ) 20.34/18.87 (instantiation (let ((_let_0 (fun int bool))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_1) zEven))) (not (forall ((K_1 $$unsorted)) (not (= (ti int X_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)))) K_1))) ))) )) 20.34/18.87 ( (one_one int) ) 20.34/18.87 ) 20.34/18.87 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (ord_less 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_154363) BOUND_VARIABLE_154364))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_154363 $$unsorted) (BOUND_VARIABLE_154364 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (= (and (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) _let_4) _let_1))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_154363) BOUND_VARIABLE_154364))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_1) _let_4))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_154364) BOUND_VARIABLE_154363)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 (hAPP X_a X_a _let_3 BOUND_VARIABLE_154363)) (hAPP X_a X_a _let_3 BOUND_VARIABLE_154364))))) )))))) 20.34/18.87 ( real, (zero_zero real), pi ) 20.34/18.87 ( 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)))) ) 20.34/18.87 ( 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))))) ) 20.34/18.87 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.87 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.87 ( real, (zero_zero real), skv_2 ) 20.34/18.87 ( real, (zero_zero real), skv_10 ) 20.34/18.87 ( real, (zero_zero real), skv_13 ) 20.34/18.87 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.87 ( real, pi, (zero_zero real) ) 20.34/18.87 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.87 ( 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)) ) 20.34/18.87 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 20.34/18.87 ( 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)))) ) 20.34/18.87 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 20.34/18.87 ( 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) ) 20.34/18.87 ( 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))) ) 20.34/18.87 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 20.34/18.87 ( 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)))))) ) 20.34/18.87 ( 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) ) 20.34/18.87 ( 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 ) 20.34/18.87 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 20.34/18.87 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 20.34/18.87 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 20.34/18.87 ( 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 ) 20.34/18.87 ( real, skv_2, (zero_zero real) ) 20.34/18.87 ( real, skv_10, (zero_zero real) ) 20.34/18.87 ( real, skv_13, (zero_zero real) ) 20.34/18.87 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.87 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 20.34/18.87 ( int, (zero_zero int), (zero_zero int) ) 20.34/18.87 ( int, (zero_zero int), (one_one int) ) 20.34/18.87 ( 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))) ) 20.34/18.87 ( int, (zero_zero int), min_1 ) 20.34/18.87 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 20.34/18.87 ( int, (zero_zero int), t ) 20.34/18.87 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 20.34/18.87 ( int, (one_one int), (zero_zero int) ) 20.34/18.87 ( int, (one_one int), t ) 20.34/18.87 ( 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))), (zero_zero int) ) 20.34/18.87 ( 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))), s ) 20.34/18.87 ( 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))), t ) 20.34/18.87 ( 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_1 ) 20.34/18.87 ( 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_3 ) 20.34/18.87 ( 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_9 ) 20.34/18.87 ( int, min_1, (zero_zero int) ) 20.34/18.87 ( int, min_1, min_1 ) 20.34/18.87 ( 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))) ) 20.34/18.87 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 20.34/18.87 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 20.34/18.87 ( int, t, (zero_zero int) ) 20.34/18.87 ( int, t, (one_one int) ) 20.34/18.87 ( 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))) ) 20.34/18.87 ( 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) (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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 20.34/18.87 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.34/18.87 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.34/18.87 ( complex, ii, ii ) 20.34/18.87 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 20.34/18.87 ( 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 ) 20.34/18.87 ) 20.34/18.87 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (forall ((A_1 $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (not (hBOOL (hAPP real bool _let_0 A_1))) (not (forall ((R_2 $$unsorted)) (or (not (= A_1 (hAPP nat real (hAPP real (fun nat real) (power_power real) R_2) N))) (not (hBOOL (hAPP real bool _let_0 R_2)))) ))) )) 20.34/18.87 ( (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)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.87 ) 20.34/18.87 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (let ((_let_1 (hAPP int nat (number_number_of nat) BOUND_VARIABLE_154478))) (let ((_let_2 (hBOOL (hAPP nat bool (even_odd_even nat) _let_1)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_154477 $$unsorted) (BOUND_VARIABLE_154478 $$unsorted)) (or (not (linordered_idom X_a)) (= (or (and _let_2 (not (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_154477)))) (and (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_154477)) (not _let_2)) (= (zero_zero nat) _let_1)) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_154477) _let_1))))) )))) 20.34/18.87 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.87 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.87 ( int, skv_8, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.87 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.87 ) 20.34/18.87 (instantiation (forall ((W_1 $$unsorted) (Z $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) W_1) Z)) (not (forall ((N_2 $$unsorted)) (not (= (ti int Z) (hAPP int int (hAPP int (fun int int) (plus_plus int) W_1) (hAPP nat int (semiring_1_of_nat int) N_2)))) ))) ) 20.34/18.87 ( (zero_zero int), (one_one int) ) 20.34/18.87 ( (zero_zero int), min_1 ) 20.34/18.87 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.87 ( (zero_zero int), s ) 20.34/18.87 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 20.34/18.87 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.34/18.87 ( (zero_zero int), skv_3 ) 20.34/18.87 ( (zero_zero int), skv_9 ) 20.34/18.87 ( (one_one int), t ) 20.34/18.87 ( min_1, pls ) 20.34/18.87 ( min_1, min_1 ) 20.34/18.87 ) 20.34/18.87 (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)))) ) 20.34/18.87 ( (zero_zero nat), pi ) 20.34/18.87 ( (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)))) ) 20.34/18.87 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.87 ( (zero_zero nat), skv_6 ) 20.34/18.87 ( (zero_zero nat), skv_11 ) 20.34/18.87 ( (zero_zero nat), skv_12 ) 20.34/18.87 ( (zero_zero nat), skv_14 ) 20.34/18.87 ) 20.34/18.87 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_154572 $$unsorted) (BOUND_VARIABLE_154573 $$unsorted)) (or (not (group_add X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) (hAPP X_a X_a (hAPP X_a _let_0 (minus_minus X_a) BOUND_VARIABLE_154572) BOUND_VARIABLE_154573)) BOUND_VARIABLE_154573) (ti X_a BOUND_VARIABLE_154572))) )) 20.34/18.87 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 20.34/18.88 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 20.34/18.88 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 20.34/18.88 ) 20.34/18.88 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (forall ((X_1 $$unsorted)) (= (hAPP _let_0 real (the real) (hAPP real _let_0 (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) (exp real))) X_1)) (hAPP real real ln X_1)) )))) 20.34/18.88 ( (one_one real) ) 20.34/18.88 ) 20.34/18.88 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (or (not (forall ((J_1 $$unsorted)) (or (not (= Ma (hAPP nat nat suc J_1))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 J_1) N_1)))) )) (= (zero_zero nat) Ma)) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Ma) (hAPP nat nat suc N_1)))) ))) 20.34/18.88 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 20.34/18.88 ) 20.34/18.88 (instantiation (let ((_let_0 (real_1 int))) (forall ((X $$unsorted)) (= (hAPP int real _let_0 (hAPP int int (uminus_uminus int) X)) (hAPP real real (uminus_uminus real) (hAPP int real _let_0 X))) )) 20.34/18.88 ( pls ) 20.34/18.88 ( (one_one int) ) 20.34/18.88 ( min_1 ) 20.34/18.88 ) 20.34/18.88 (instantiation (let ((_let_0 (fun (filter X_a) bool))) (let ((_let_1 (fun X_a real))) (let ((_let_2 (fun X_a X_b))) (let ((_let_3 (norm_norm X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_154688 $$unsorted) (BOUND_VARIABLE_154689 $$unsorted) (BOUND_VARIABLE_154690 $$unsorted)) (let ((_let_0 (filter X_a))) (or (not (real_normed_vector X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_0 (hAPP _let_2 (fun X_b _let_0) (tendsto X_a X_b) BOUND_VARIABLE_154688) BOUND_VARIABLE_154689) BOUND_VARIABLE_154690))) (hBOOL (hAPP _let_0 bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (tendsto X_a real) (hAPP _let_2 _let_1 (hAPP (fun X_b real) (fun _let_2 _let_1) (combb X_b real X_a) _let_3) BOUND_VARIABLE_154688)) (hAPP X_b real _let_3 BOUND_VARIABLE_154689)) BOUND_VARIABLE_154690)))) ))))) 20.34/18.88 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 20.34/18.88 ( nat, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real), sequentially ) 20.34/18.88 ) 20.34/18.88 (instantiation (let ((_let_0 (hAPP nat int (hAPP int (fun nat int) (power_power int) Z_1) (hAPP int nat (number_number_of nat) W)))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (hAPP nat int (hAPP int (fun nat int) (power_power int) Z_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 W))) (hAPP int int (hAPP int (fun int int) (times_times int) _let_0) _let_0)) )) 20.34/18.88 ( s, (hAPP int int bit1 pls) ) 20.34/18.88 ( s1, (hAPP int int bit1 pls) ) 20.34/18.88 ( skv_8, (hAPP int int bit1 pls) ) 20.34/18.88 ) 20.34/18.88 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_lessThan nat))) (let ((_let_2 (hAPP (fun nat X_a) (fun _let_0 X_a) (big_co1399186613setsum nat X_a) BOUND_VARIABLE_154763))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_154763 $$unsorted) (BOUND_VARIABLE_154764 $$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) (hAPP _let_0 X_a _let_2 (hAPP nat _let_0 _let_1 BOUND_VARIABLE_154764))) (hAPP nat X_a BOUND_VARIABLE_154763 BOUND_VARIABLE_154764)) (hAPP _let_0 X_a _let_2 (hAPP nat _let_0 _let_1 (hAPP nat nat suc BOUND_VARIABLE_154764))))) )))) 20.34/18.88 ( bool, (even_odd_even nat), (zero_zero nat) ) 20.34/18.88 ( bool, (even_odd_even nat), (one_one nat) ) 20.34/18.88 ( 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))) ) 20.34/18.88 ( bool, prime, (zero_zero nat) ) 20.34/18.88 ( bool, prime, (one_one nat) ) 20.34/18.88 ( bool, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.88 ( real, (real_1 nat), (zero_zero nat) ) 20.34/18.88 ( real, (real_1 nat), (one_one nat) ) 20.34/18.88 ( nat, suc, (zero_zero nat) ) 20.34/18.88 ( nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 20.34/18.88 ( nat, suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 20.34/18.88 ( nat, (fact_fact nat), (zero_zero nat) ) 20.34/18.88 ( nat, (fact_fact nat), (hAPP nat nat suc (zero_zero nat)) ) 20.34/18.88 ( nat, (size_size nat), (zero_zero nat) ) 20.34/18.88 ( nat, fact, (zero_zero nat) ) 20.34/18.88 ( nat, nat_size, (zero_zero nat) ) 20.34/18.88 ( nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (one_one nat) ) 20.34/18.88 ( (fun nat bool), (ord_less nat), (zero_zero nat) ) 20.34/18.88 ( (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) ) 20.34/18.88 ( (fun nat nat), (plus_plus nat), (one_one nat) ) 20.34/18.88 ( (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))) ) 20.34/18.88 ( (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) ) 20.34/18.88 ( int, (semiring_1_of_nat int), (zero_zero nat) ) 20.34/18.88 ( int, (semiring_1_of_nat int), (hAPP nat nat suc (zero_zero nat)) ) 20.34/18.88 ( int, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.88 ( int, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.34/18.88 ( int, (hAPP int (fun nat int) (power_power int) s), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.88 ( 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))) ) 20.34/18.88 ( int, (hAPP int (fun nat int) (power_power int) skv_8), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.88 ( (fun real real), root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.88 ( 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))) ) 20.34/18.88 ( (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))) ) 20.34/18.88 ) 20.34/18.88 (instantiation (let ((_let_0 (fun int bool))) (forall ((P_4 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_4))) (= (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) P_4) zOdd)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) P_4)))) )) 20.34/18.88 ( (one_one int) ) 20.34/18.88 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.34/18.88 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.88 ) 20.34/18.88 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (times_times X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_154878 $$unsorted) (BOUND_VARIABLE_154879 $$unsorted)) (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_154878) (one_one X_a))) BOUND_VARIABLE_154879) (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_154878) BOUND_VARIABLE_154879)) BOUND_VARIABLE_154879))) )))) 20.34/18.88 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 20.34/18.88 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 20.34/18.88 ( 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)))))) ) 20.34/18.88 ( 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 ) 20.34/18.88 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 20.34/18.88 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (zero_zero int) ) 20.34/18.88 ( int, (hAPP int int (hAPP int (fun int int) (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 ) 20.34/18.88 ( int, (hAPP int int (hAPP int (fun int int) (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_1 ) 20.34/18.88 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 20.34/18.88 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 20.34/18.88 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_1 ) 20.34/18.88 ( complex, ii, ii ) 20.34/18.88 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 20.34/18.88 ( 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 ) 20.34/18.88 ) 20.34/18.88 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (forall ((L $$unsorted) (U_1 $$unsorted)) (= (hAPP _let_0 nat (finite_card int) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastAtMost int) L) U_1)) (hAPP int nat nat_1 (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (minus_minus int) U_1) L)) (one_one int)))) ))) 20.34/18.88 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.88 ) 20.34/18.88 (instantiation (let ((_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)))))) (forall ((X $$unsorted)) (= (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real _let_0 (hAPP real real sin X))) (hAPP real real cos X)) (hAPP real real sin (hAPP real real _let_0 X))) )) 20.34/18.88 ( (zero_zero real) ) 20.34/18.88 ( pi ) 20.34/18.88 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.88 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.88 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 20.34/18.88 ( (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 20.34/18.88 ( (hAPP real real (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))))) ) 20.34/18.88 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 20.34/18.88 ( (hAPP real 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))))) ) 20.34/18.88 ( (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)))) ) 20.34/18.88 ( skv_14 ) 20.34/18.88 ) 20.34/18.88 (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)))) ) 20.34/18.88 ( real ) 20.34/18.88 ( nat ) 20.34/18.88 ( int ) 20.34/18.88 ( complex ) 20.34/18.88 ( rat ) 20.34/18.88 ( quickcheck_code_int ) 20.34/18.88 ( code_code_numeral ) 20.34/18.88 ) 20.34/18.88 (instantiation (forall ((W $$unsorted)) (not (= ii (hAPP int complex (number_number_of complex) W))) ) 20.34/18.88 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.88 ( min_1 ) 20.34/18.88 ) 20.34/18.88 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (power_power real))) (let ((_let_3 (inverse_divide real))) (let ((_let_4 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_5 (fun real complex))) (let ((_let_6 (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP nat real (hAPP real _let_1 _let_2 A_1) _let_4)) (hAPP nat real (hAPP real _let_1 _let_2 B) _let_4)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (hAPP complex complex (inverse_inverse complex) (hAPP real complex (hAPP real _let_5 complex_1 A_1) B)) (hAPP real complex (hAPP real _let_5 complex_1 (hAPP real real (hAPP real _let_0 _let_3 A_1) _let_6)) (hAPP real real (hAPP real _let_0 _let_3 (hAPP real real (uminus_uminus real) B)) _let_6))) )))))))) 20.34/18.88 ( (zero_zero real), (one_one real) ) 20.34/18.88 ) 20.34/18.88 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (hAPP real _let_1 (times_times real) (hAPP int real (number_number_of real) _let_2)))) (let ((_let_4 (hAPP real real _let_3 X))) (let ((_let_5 (hAPP real real tan X))) (forall ((X $$unsorted)) (or (= _let_0 (hAPP real real cos X)) (= _let_0 (hAPP real real cos _let_4)) (= (hAPP real real (hAPP real _let_1 (inverse_divide real) (hAPP real real _let_3 _let_5)) (hAPP real real (hAPP real _let_1 (minus_minus real) (one_one real)) (hAPP nat real (hAPP real (fun nat real) (power_power real) _let_5) (hAPP int nat (number_number_of nat) _let_2)))) (hAPP real real tan _let_4))) ))))))) 20.34/18.89 ( (zero_zero real) ) 20.34/18.89 ( pi ) 20.34/18.89 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.89 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 20.34/18.89 ( (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 20.34/18.89 ( (hAPP real real (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))))) ) 20.34/18.89 ( (hAPP real 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))))) ) 20.34/18.89 ( (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)))) ) 20.34/18.89 ) 20.34/18.89 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_atMost X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_155086 $$unsorted) (BOUND_VARIABLE_155087 $$unsorted)) (or (not (linorder X_a)) (= (= (ti X_a BOUND_VARIABLE_155087) (ti X_a BOUND_VARIABLE_155086)) (= (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_155086) (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_155087)))) ))) 20.34/18.89 ( bool, fFalse, fTrue ) 20.34/18.89 ( bool, fTrue, fFalse ) 20.34/18.89 ( bool, fTrue, fTrue ) 20.34/18.89 ( real, pi, pi ) 20.34/18.89 ( (fun nat bool), (even_odd_even nat), prime ) 20.34/18.89 ( (fun nat bool), prime, (even_odd_even nat) ) 20.34/18.89 ( (fun nat bool), prime, prime ) 20.34/18.89 ( (fun nat nat), suc, suc ) 20.34/18.89 ( (fun nat nat), suc, fact ) 20.34/18.89 ( (fun nat nat), suc, nat_size ) 20.34/18.89 ( (fun nat nat), (fact_fact nat), (size_size nat) ) 20.34/18.89 ( (fun nat nat), (size_size nat), (fact_fact nat) ) 20.34/18.89 ( (fun nat nat), (size_size nat), (size_size nat) ) 20.34/18.89 ( (fun nat nat), fact, nat_size ) 20.34/18.89 ( (fun nat nat), nat_size, suc ) 20.34/18.89 ( int, pls, s1 ) 20.34/18.89 ( int, m, s ) 20.34/18.89 ( int, min_1, m ) 20.34/18.89 ( int, min_1, min_1 ) 20.34/18.89 ( int, min_1, s ) 20.34/18.89 ( int, s, min_1 ) 20.34/18.89 ( int, s1, t ) 20.34/18.89 ( int, t, pls ) 20.34/18.89 ( int, t, s1 ) 20.34/18.89 ( int, t, t ) 20.34/18.89 ( (fun int bool), zprime, zprime ) 20.34/18.89 ( (fun int bool), zprime, zEven ) 20.34/18.89 ( (fun int bool), zprime, (even_odd_even int) ) 20.34/18.89 ( (fun int bool), nat_neg, nat_is_nat ) 20.34/18.89 ( (fun int bool), zEven, (even_odd_even int) ) 20.34/18.89 ( (fun int bool), nat_is_nat, nat_neg ) 20.34/18.89 ( (fun int bool), nat_is_nat, nat_is_nat ) 20.34/18.89 ( (fun int bool), nat_is_nat, twoSqu1091635170sum2sq ) 20.34/18.89 ( (fun int bool), zOdd, zOdd ) 20.34/18.89 ( (fun int bool), (even_odd_even int), zprime ) 20.34/18.89 ( (fun int bool), twoSqu1091635170sum2sq, nat_neg ) 20.34/18.89 ( (fun int nat), nat_1, phi ) 20.34/18.89 ( (fun int nat), phi, nat_1 ) 20.34/18.89 ( (fun int nat), phi, phi ) 20.34/18.89 ( (fun real real), sqrt, ln ) 20.34/18.89 ( (fun real real), tan, tan ) 20.34/18.89 ( (fun real real), tan, arccos ) 20.34/18.89 ( (fun real real), tan, sin ) 20.34/18.89 ( (fun real real), cos, cos ) 20.34/18.89 ( (fun real real), cos, arctan ) 20.34/18.89 ( (fun real real), arccos, tan ) 20.34/18.89 ( (fun real real), ln, arcsin ) 20.34/18.89 ( (fun real real), sin, arccos ) 20.34/18.89 ( (fun real real), arctan, cos ) 20.34/18.89 ( (fun real real), arcsin, sqrt ) 20.34/18.89 ( (fun real real), arcsin, ln ) 20.34/18.89 ( (fun real real), arcsin, arcsin ) 20.34/18.89 ( complex, ii, ii ) 20.34/18.89 ( (fun complex complex), cnj, cnj ) 20.34/18.89 ( (fun complex complex), cnj, expi ) 20.34/18.89 ( (fun complex complex), expi, cnj ) 20.34/18.89 ( (fun nat real), (real_1 nat), (real_1 nat) ) 20.34/18.89 ( (fun nat real), (real_1 nat), cos_coeff ) 20.34/18.89 ( (fun nat real), (real_1 nat), sin_coeff ) 20.34/18.89 ( (fun nat real), cos_coeff, sin_coeff ) 20.34/18.89 ( (fun nat real), sin_coeff, (real_1 nat) ) 20.34/18.89 ( (fun int int), bit0, bit0 ) 20.34/18.89 ( (fun int int), bit0, bit1 ) 20.34/18.89 ( (fun int int), bit0, (fact_fact int) ) 20.34/18.89 ( (fun int int), bit1, (fact_fact int) ) 20.34/18.89 ( (fun int int), pred, zfact ) 20.34/18.89 ( (fun int int), succ, pred ) 20.34/18.89 ( (fun int int), (fact_fact int), bit0 ) 20.34/18.89 ( (fun int int), zfact, pred ) 20.34/18.89 ( (fun int int), zfact, succ ) 20.34/18.89 ( (fun int int), zfact, zfact ) 20.34/18.89 ( (fun bool bool), fNot, fNot ) 20.34/18.89 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset ) 20.34/18.89 ( (fun bool (fun bool bool)), fconj, fdisj ) 20.34/18.89 ( (fun bool (fun bool bool)), fdisj, fconj ) 20.34/18.89 ( (fun bool (fun bool bool)), fdisj, fdisj ) 20.34/18.89 ( (fun bool (fun bool bool)), fdisj, fimplies ) 20.34/18.89 ( (fun bool (fun bool bool)), fimplies, fconj ) 20.34/18.89 ( (fun int (fun int bool)), sRStar, sRStar ) 20.34/18.89 ( (fun int (fun int bool)), sRStar, quadRes ) 20.34/18.89 ( (fun int (fun int bool)), sRStar, d22set ) 20.34/18.89 ( (fun int (fun int bool)), quadRes, d22set ) 20.34/18.89 ( (fun int (fun int bool)), norRRset, sr ) 20.34/18.89 ( (fun int (fun int bool)), d22set, sRStar ) 20.34/18.89 ( (fun int (fun int bool)), sr, norRRset ) 20.34/18.89 ( (fun int (fun int bool)), sr, sr ) 20.34/18.89 ( (fun int (fun int bool)), sr, quickc1265749348ro_rel ) 20.34/18.89 ( (fun int (fun int bool)), quickc1265749348ro_rel, norRRset ) 20.34/18.89 ( (fun nat (fun nat nat)), nat_gcd, nat_gcd ) 20.34/18.89 ( (fun nat (fun nat nat)), nat_gcd, (gcd_gcd nat) ) 20.34/18.89 ( (fun nat (fun nat nat)), nat_gcd, nat_lcm ) 20.34/18.89 ( (fun nat (fun nat nat)), (gcd_gcd nat), nat_lcm ) 20.34/18.89 ( (fun nat (fun nat nat)), nat_lcm, nat_gcd ) 20.34/18.89 ( (fun nat (fun real real)), root, root ) 20.34/18.89 ( (fun real (fun real real)), log, powr ) 20.34/18.89 ( (fun real (fun real real)), powr, log ) 20.34/18.89 ( (fun real (fun real real)), powr, powr ) 20.34/18.89 ( (fun nat (fun nat bool)), coprime, coprime ) 20.34/18.89 ( (fun (fun int bool) int), (the int), (the int) ) 20.34/18.89 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, negateSnd ) 20.34/18.89 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, normalize ) 20.34/18.89 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, negateSnd ) 20.34/18.89 ( (fun nat (fun nat (product_prod int int))), bezw, bezw ) 20.34/18.89 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set ) 20.34/18.89 ( (filter nat), sequentially, sequentially ) 20.34/18.89 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat ) 20.34/18.89 ( (fun (product_prod int int) bool), frac_1, frac_1 ) 20.34/18.89 ( (fun real complex), cis, cis ) 20.34/18.89 ( (fun complex real), im, im ) 20.34/18.89 ( (fun complex real), im, re ) 20.34/18.89 ( (fun complex real), im, arg ) 20.34/18.89 ( (fun complex real), re, im ) 20.34/18.89 ( (fun complex real), arg, re ) 20.34/18.89 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral ) 20.34/18.89 ( (fun int (fun int int)), int_gcd, int_lcm ) 20.34/18.89 ( (fun int (fun int int)), multInv, int_gcd ) 20.34/18.89 ( (fun int (fun int int)), legacy_zgcd, legacy_zgcd ) 20.34/18.89 ( (fun int (fun int int)), legacy_zgcd, inv ) 20.34/18.89 ( (fun int (fun int int)), legacy_zgcd, nat_tsub ) 20.34/18.89 ( (fun int (fun int int)), z3mod, z3div ) 20.34/18.89 ( (fun int (fun int int)), inv, legacy_zgcd ) 20.34/18.89 ( (fun int (fun int int)), (gcd_gcd int), z3mod ) 20.34/18.89 ( (fun int (fun int int)), standardRes, legendre ) 20.34/18.89 ( (fun int (fun int int)), legendre, standardRes ) 20.34/18.89 ( (fun int (fun int int)), legendre, legendre ) 20.34/18.89 ( (fun int (fun int int)), nat_tsub, inv ) 20.34/18.89 ( (fun int (fun int int)), z3div, z3mod ) 20.34/18.89 ( (fun int (fun int int)), z3div, (gcd_gcd int) ) 20.34/18.89 ( (fun int (fun int int)), z3div, z3div ) 20.34/18.89 ( (fun int (fun int int)), int_lcm, int_gcd ) 20.34/18.89 ( (fun int (fun int int)), int_lcm, multInv ) 20.34/18.89 ( (fun int (fun int int)), int_lcm, int_lcm ) 20.34/18.89 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than ) 20.34/18.89 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than2 ) 20.34/18.89 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than ) 20.34/18.89 ( (fun int (fun (fun int bool) bool)), rsetR, resSet ) 20.34/18.89 ( (fun int (fun (fun int bool) bool)), resSet, rsetR ) 20.34/18.89 ( (fun int (fun (fun int bool) bool)), resSet, resSet ) 20.34/18.89 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, upto_rel ) 20.34/18.89 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, posDivAlg_rel ) 20.34/18.89 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, negDivAlg_rel ) 20.34/18.89 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, norm_frac_rel ) 20.34/18.89 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, lazy_small_lazy_rel ) 20.34/18.89 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, upto_rel ) 20.34/18.89 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, posDivAlg_rel ) 20.34/18.89 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, negDivAlg_rel ) 20.34/18.89 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_less ) 20.34/18.89 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_leq ) 20.34/18.89 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_less ) 20.34/18.89 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel ) 20.34/18.89 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd ) 20.34/18.89 ( (fun int (fun int (product_prod int int))), negDivAlg, divmod_int ) 20.34/18.89 ( (fun int (fun int (product_prod int int))), divmod_int, pdivmod ) 20.34/18.89 ( (fun int (fun int (product_prod int int))), posDivAlg, posDivAlg ) 20.34/18.89 ( (fun int (fun int (product_prod int int))), posDivAlg, norm_frac ) 20.34/18.89 ( (fun int (fun int (product_prod int int))), pdivmod, negDivAlg ) 20.34/18.89 ( (fun int (fun int (product_prod int int))), pdivmod, divmod_int ) 20.34/18.89 ( (fun int (fun int (product_prod int int))), pdivmod, pdivmod ) 20.34/18.89 ( (fun int (fun int (product_prod int int))), norm_frac, posDivAlg ) 20.34/18.89 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust ) 20.34/18.89 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, bolzano_bisect ) 20.34/18.89 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 20.34/18.89 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 20.34/18.89 ( (fun real nat), natfloor, natceiling ) 20.34/18.89 ( (fun real nat), natceiling, natfloor ) 20.34/18.89 ( (fun real nat), natceiling, natceiling ) 20.34/18.89 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int ) 20.34/18.89 ( (fun int (fun int (fun int bool))), wset, wset ) 20.34/18.89 ( (fun int (fun int (fun int bool))), wset, bnorRset ) 20.34/18.89 ( (fun int (fun int (fun int bool))), wset, zcong ) 20.34/18.89 ( (fun int (fun int (fun int bool))), bnorRset, wset ) 20.34/18.89 ( (fun int (fun int (fun int bool))), zcong, bnorRset ) 20.34/18.89 ( (fun int (fun int (fun int bool))), noXRRset, zcongm ) 20.34/18.89 ( (fun int (fun int (fun int bool))), zcongm, noXRRset ) 20.34/18.89 ( (fun int (fun int (fun int bool))), zcongm, zcongm ) 20.34/18.89 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair ) 20.34/18.89 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS ) 20.34/18.89 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral ) 20.34/18.89 ( (fun int real), (real_1 int), (real_1 int) ) 20.34/18.89 ( (fun complex nat), (size_size complex), complex_size ) 20.34/18.89 ( (fun complex nat), complex_size, (size_size complex) ) 20.34/18.89 ( (fun complex nat), complex_size, complex_size ) 20.34/18.89 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero ) 20.34/18.89 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel ) 20.34/18.89 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel ) 20.34/18.89 ( (fun (product_prod int int) rat), frct, frct ) 20.34/18.89 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux ) 20.34/18.89 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel ) 20.34/18.89 ( (fun (fun nat rat) bool), vanishes, vanishes ) 20.34/18.89 ( (fun int (fun int rat)), fract, fract ) 20.34/18.89 ( (fun code_code_numeral int), code_int_of, code_int_of ) 20.34/18.89 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat ) 20.34/18.89 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral) ) 20.34/18.89 ( (fun code_code_numeral nat), (size_size code_code_numeral), code_c271388182l_size ) 20.34/18.89 ( (fun code_code_numeral nat), code_c271388182l_size, (size_size code_code_numeral) ) 20.34/18.89 ( (fun real (fun real complex)), complex_1, complex_1 ) 20.34/18.89 ( (fun real (fun real complex)), complex_1, rcis ) 20.34/18.89 ( (fun real (fun real complex)), rcis, complex_1 ) 20.34/18.89 ( (fun int (fun nat nat)), nat_aux, nat_aux ) 20.34/18.89 ( (fun rat real), ratreal, ratreal ) 20.34/18.89 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of ) 20.34/18.89 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int ) 20.34/18.89 ( (fun rat (product_prod int int)), quotient_of, quotient_of ) 20.34/18.89 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR ) 20.34/18.89 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 20.34/18.89 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of ) 20.34/18.89 ( (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 ) 20.34/18.89 ) 20.34/18.89 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP int nat (number_number_of nat) BOUND_VARIABLE_155102))) (let ((_let_4 (hBOOL (hAPP nat bool (even_odd_even nat) _let_3)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_155101 $$unsorted) (BOUND_VARIABLE_155102 $$unsorted)) (or (not (linordered_idom X_a)) (= (and (not (= (zero_zero nat) _let_3)) (or (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_155101) _let_2)) (not _let_4)) (and (= _let_2 (ti X_a BOUND_VARIABLE_155101)) _let_4))) (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_155101) _let_3)) _let_2)))) )))))) 20.34/18.89 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.89 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.89 ( int, skv_8, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.89 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.34/18.89 ) 20.34/18.89 (instantiation (forall ((X $$unsorted)) (or (not (= (one_one real) (hAPP real real cos X))) (= (zero_zero real) (hAPP real real sin X))) ) 20.34/18.89 ( (zero_zero real) ) 20.34/18.89 ( pi ) 20.34/18.89 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.89 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.89 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 20.34/18.89 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 20.34/18.89 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 20.34/18.89 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 20.34/18.89 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.34/18.89 ( skv_14 ) 20.34/18.89 ) 20.34/18.89 (instantiation (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a real))) (let ((_let_3 (fun X_a X_b))) (let ((_let_4 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_155181))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_155180 $$unsorted) (BOUND_VARIABLE_155181 $$unsorted)) (or (not (real_normed_vector X_b)) (not (topological_space X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_3 (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_155180) (zero_zero X_b)) _let_4))) (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (tendsto X_a real) (hAPP _let_3 _let_2 (hAPP (fun X_b real) (fun _let_3 _let_2) (combb X_b real X_a) (norm_norm X_b)) BOUND_VARIABLE_155180)) (zero_zero real)) _let_4))) )))))) 20.34/18.89 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.89 ) 20.34/18.89 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (power_power real))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_4 (hAPP complex real im X))) (forall ((X $$unsorted)) (= (hAPP complex real im (hAPP complex complex (inverse_inverse complex) X)) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP real real (uminus_uminus real) _let_4)) (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP nat real (hAPP real _let_1 _let_2 (hAPP complex real re X)) _let_3)) (hAPP nat real (hAPP real _let_1 _let_2 _let_4) _let_3)))) )))))) 20.34/18.89 ( ii ) 20.34/18.89 ( (zero_zero complex) ) 20.34/18.89 ( (one_one complex) ) 20.34/18.89 ) 20.34/18.89 (instantiation (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))) (forall ((A_1 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (times_times int) A_1) (hAPP nat int _let_2 (hAPP int nat _let_1 (hAPP int int bit0 _let_0)))) (hAPP nat int _let_2 (hAPP int nat _let_1 (hAPP int int bit1 _let_0)))) )))) 20.34/18.90 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.90 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.34/18.90 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.90 ( s ) 20.34/18.90 ( s1 ) 20.34/18.90 ( skv_8 ) 20.34/18.90 ) 20.34/18.90 (instantiation (let ((_let_0 (fun int bool))) (forall ((Ma $$unsorted) (X_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 quadRes Ma) X_1)) (not (forall ((Y_2 $$unsorted)) (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_2) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) X_1) Ma))) ))) )) 20.34/18.90 ( (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))), (hAPP int int (number_number_of int) min_1) ) 20.34/18.90 ) 20.34/18.90 (instantiation (let ((_let_0 (fun int int))) (forall ((N $$unsorted) (M $$unsorted)) (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))) )) 20.34/18.90 ( (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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 20.34/18.90 ) 20.34/18.90 (instantiation (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_155227))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_155227 $$unsorted) (BOUND_VARIABLE_155228 $$unsorted) (BOUND_VARIABLE_155229 $$unsorted)) (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_155228)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_155229)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_155227))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_155228) BOUND_VARIABLE_155229))) )))) 20.34/18.90 ( 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))), skv_1, (zero_zero int) ) 20.34/18.90 ) 20.34/18.90 (instantiation (let ((_let_0 (real_1 nat))) (forall ((N $$unsorted)) (= (hAPP nat real _let_0 (hAPP nat nat suc N)) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real _let_0 N)) (one_one real))) )) 20.34/18.90 ( (zero_zero nat) ) 20.34/18.90 ( (hAPP nat nat suc (zero_zero nat)) ) 20.34/18.90 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 20.34/18.90 ) 20.34/18.90 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (div_div nat))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (forall ((N $$unsorted)) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) N))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 N) _let_2) (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N) (one_one nat))) _let_2))) )))) 20.34/18.90 ( (zero_zero nat) ) 20.34/18.90 ( (one_one nat) ) 20.34/18.90 ) 20.34/18.90 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP nat real (real_1 nat) N))) (forall ((N $$unsorted) (X $$unsorted)) (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))) ))) 20.34/18.90 ( (zero_zero nat), pi ) 20.34/18.90 ( (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)))) ) 20.34/18.90 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.90 ( (zero_zero nat), skv_6 ) 20.34/18.90 ( (zero_zero nat), skv_11 ) 20.34/18.90 ( (zero_zero nat), skv_12 ) 20.34/18.90 ( (zero_zero nat), skv_14 ) 20.34/18.90 ) 20.34/18.90 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (= (hAPP real complex cis (hAPP real real (hAPP real (fun real real) (minus_minus real) A_1) B)) (hAPP complex complex (hAPP complex (fun complex complex) (inverse_divide complex) (hAPP real complex cis A_1)) (hAPP real complex cis B))) ) 20.34/18.90 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 20.34/18.90 ) 20.34/18.90 (instantiation (let ((_let_0 (fun nat X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (fun nat _let_1))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_155373 $$unsorted)) (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_155373)) (hAPP X_a _let_0 (power_power X_a) (zero_zero X_a)))) (hAPP nat X_a BOUND_VARIABLE_155373 (zero_zero nat)))) )))) 20.34/18.90 ( bool, (even_odd_even nat) ) 20.34/18.90 ( bool, prime ) 20.34/18.90 ( real, (real_1 nat) ) 20.34/18.90 ( real, (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) ) 20.34/18.90 ( nat, suc ) 20.34/18.90 ( nat, (fact_fact nat) ) 20.34/18.90 ( nat, (size_size nat) ) 20.34/18.90 ( nat, fact ) 20.34/18.90 ( nat, nat_size ) 20.34/18.90 ( (fun nat bool), (ord_less nat) ) 20.34/18.90 ( (fun nat bool), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))) ) 20.34/18.90 ( int, (semiring_1_of_nat int) ) 20.34/18.90 ) 20.34/18.90 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (one_one real))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X) _let_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real ln (hAPP real real (hAPP real (fun real real) (minus_minus real) _let_2) X))) (hAPP real real (uminus_uminus real) X)))) )))) 20.34/18.90 ( (zero_zero real) ) 20.34/18.90 ( (one_one real) ) 20.34/18.90 ( pi ) 20.34/18.90 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.90 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 20.34/18.90 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 20.34/18.90 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.90 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.90 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 20.34/18.90 ( skv_6 ) 20.34/18.90 ( skv_11 ) 20.34/18.90 ( skv_12 ) 20.34/18.90 ( skv_14 ) 20.34/18.90 ) 20.34/18.90 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (hAPP int _let_0 _let_1 I_1))) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (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))) )))) 20.34/18.90 ( pls, min_1, min_1 ) 20.34/18.90 ( min_1, (zero_zero int), min_1 ) 20.34/18.90 ( min_1, min_1, pls ) 20.34/18.90 ( (hAPP int int (number_number_of int) pls), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 20.34/18.90 ( t, (zero_zero int), (one_one int) ) 20.34/18.90 ) 20.34/18.90 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_155446 $$unsorted) (BOUND_VARIABLE_155447 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_155447) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_155446) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_155447) BOUND_VARIABLE_155446)) _let_2))) )))) 20.34/18.90 ( nat, (one_one nat), (one_one nat) ) 20.34/18.90 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 20.34/18.90 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.90 ) 20.34/18.90 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (filter X_a))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun X_a X_b))) (let ((_let_5 (fun X_b _let_3))) (let ((_let_6 (tendsto X_a X_b))) (let ((_let_7 (hAPP X_a _let_2 (at X_a) BOUND_VARIABLE_155499))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_155496 $$unsorted) (BOUND_VARIABLE_155497 $$unsorted) (BOUND_VARIABLE_155498 $$unsorted) (BOUND_VARIABLE_155499 $$unsorted) (BOUND_VARIABLE_155500 $$unsorted)) (or (not (topological_space X_b)) (not (real_normed_vector X_a)) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) BOUND_VARIABLE_155500))) (not (forall ((X_2 $$unsorted)) (or (= (ti X_a X_2) (ti X_a BOUND_VARIABLE_155499)) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (norm_norm X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) X_2) BOUND_VARIABLE_155499))) BOUND_VARIABLE_155500))) (= (hAPP X_a X_b BOUND_VARIABLE_155498 X_2) (hAPP X_a X_b BOUND_VARIABLE_155497 X_2))) )) (not (hBOOL (hAPP _let_2 bool (hAPP X_b _let_3 (hAPP _let_4 _let_5 _let_6 BOUND_VARIABLE_155498) BOUND_VARIABLE_155496) _let_7))) (hBOOL (hAPP _let_2 bool (hAPP X_b _let_3 (hAPP _let_4 _let_5 _let_6 BOUND_VARIABLE_155497) BOUND_VARIABLE_155496) _let_7))) ))))))))) 20.34/18.90 ( real, real, (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.90 ) 20.34/18.90 (instantiation (let ((_let_0 (fun nat real))) (let ((_let_1 (filter real))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun (filter nat) bool))) (let ((_let_4 (fun real X_a))) (let ((_let_5 (fun nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_155557 $$unsorted) (BOUND_VARIABLE_155558 $$unsorted) (BOUND_VARIABLE_155559 $$unsorted)) (let ((_let_0 (filter nat))) (or (not (metric_space X_a)) (= (hBOOL (hAPP _let_1 bool (hAPP X_a _let_2 (hAPP _let_4 (fun X_a _let_2) (tendsto real X_a) BOUND_VARIABLE_155557) BOUND_VARIABLE_155558) (hAPP real _let_1 (at real) BOUND_VARIABLE_155559))) (forall ((S_2 $$unsorted)) (or (not (forall ((N_2 $$unsorted)) (not (= (hAPP nat real S_2 N_2) BOUND_VARIABLE_155559)) )) (not (hBOOL (hAPP _let_0 bool (hAPP real _let_3 (hAPP _let_0 (fun real _let_3) (tendsto nat real) S_2) BOUND_VARIABLE_155559) sequentially))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_3 (hAPP _let_5 (fun X_a _let_3) (tendsto nat X_a) (hAPP _let_0 _let_5 (hAPP _let_4 (fun _let_0 _let_5) (combb real X_a nat) BOUND_VARIABLE_155557) S_2)) BOUND_VARIABLE_155558) sequentially))) )))) ))))))) 20.34/18.90 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.34/18.90 ) 20.34/18.90 (instantiation (forall ((A_1 $$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))) ) 20.34/18.90 ( m ) 20.34/18.90 ( min_1 ) 20.34/18.90 ( s ) 20.34/18.90 ( s1 ) 20.34/18.90 ( t ) 20.34/18.90 ) 20.34/18.90 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (ord_less real))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 Y) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) pi))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP real real cos X)) (hAPP real real cos Y)))) )))) 20.34/18.90 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 20.34/18.90 ) 20.34/18.90 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (div_mod nat))) (forall ((M $$unsorted) (N $$unsorted)) (or (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N)) (= (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))) ))) 20.34/18.90 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.34/18.90 ) 20.34/18.90 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_155668 $$unsorted) (BOUND_VARIABLE_155669 $$unsorted)) (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_155668) BOUND_VARIABLE_155669))) (= _let_0 (ti X_a BOUND_VARIABLE_155669)) (= _let_0 (ti X_a BOUND_VARIABLE_155668))) )) 20.34/18.90 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 20.34/18.90 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 20.34/18.90 ( 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)))))) ) 20.34/18.90 ( 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))))), pi ) 20.52/18.91 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 20.52/18.91 ( 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) ) 20.52/18.91 ( 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 ) 20.52/18.91 ( 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_1 ) 20.52/18.91 ( complex, ii, ii ) 20.52/18.91 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 20.52/18.91 ( 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 ) 20.52/18.91 ) 20.52/18.91 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155689 $$unsorted)) (or (not (linordered_ring X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_155689) BOUND_VARIABLE_155689)))) ) 20.52/18.91 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.91 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.52/18.91 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 20.52/18.91 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.52/18.91 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.52/18.91 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.91 ( complex, ii ) 20.52/18.91 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.91 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 20.52/18.91 ) 20.52/18.91 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int _let_0 (gcd_gcd int) M))) (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (= (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)) (hAPP int int _let_1 N)) ))) 20.52/18.91 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 20.52/18.91 ) 20.52/18.91 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (div_div X_a))) (let ((_let_2 (plus_plus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_155766 $$unsorted) (BOUND_VARIABLE_155767 $$unsorted)) (or (not (semiring_div X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_155767)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_155766) BOUND_VARIABLE_155767)) (one_one X_a)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_155767) BOUND_VARIABLE_155766)) BOUND_VARIABLE_155767))) )))) 20.52/18.91 ( nat, (one_one nat), (one_one nat) ) 20.52/18.91 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 20.52/18.91 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.52/18.91 ) 20.52/18.91 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (ord_less_eq X_a))) (let ((_let_4 (fun X_a X_a))) (let ((_let_5 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_155807))) (let ((_let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) _let_5)))) (let ((_let_7 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_5) _let_2)))) (let ((_let_8 (hAPP X_a _let_0 _let_3 BOUND_VARIABLE_155805))) (let ((_let_9 (hAPP X_a X_a (hAPP X_a _let_4 (times_times X_a) BOUND_VARIABLE_155805) _let_5))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_155805 $$unsorted) (BOUND_VARIABLE_155806 $$unsorted) (BOUND_VARIABLE_155807 $$unsorted)) (or (not (number X_a)) (not (linord1117847801e_zero X_a)) (= (and (or _let_6 (and (or _let_7 (hBOOL (hAPP X_a bool _let_8 _let_2))) (or (not _let_7) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 BOUND_VARIABLE_155806) _let_9))))) (or (not _let_6) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 _let_9) BOUND_VARIABLE_155806)))) (hBOOL (hAPP X_a bool _let_8 (hAPP X_a X_a (hAPP X_a _let_4 (inverse_divide X_a) BOUND_VARIABLE_155806) _let_5))))) ))))))))))) 20.52/18.91 ( real, (zero_zero real), pi, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.52/18.91 ) 20.52/18.91 (instantiation (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_155862))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_155862 $$unsorted) (BOUND_VARIABLE_155863 $$unsorted) (BOUND_VARIABLE_155864 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP nat X_a _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) BOUND_VARIABLE_155863) BOUND_VARIABLE_155864)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_155863)) (hAPP nat X_a _let_0 BOUND_VARIABLE_155864)))) )) 20.52/18.91 ( int, s, (one_one nat), (one_one nat) ) 20.52/18.91 ( int, s1, (one_one nat), (one_one nat) ) 20.52/18.91 ( int, skv_8, (one_one nat), (one_one nat) ) 20.52/18.91 ( complex, ii, (one_one nat), (one_one nat) ) 20.52/18.91 ) 20.52/18.91 (instantiation (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (inverse_inverse X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_155942 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_155942)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_155942)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_155942)))) ))) 20.52/18.91 ( bool, fFalse ) 20.52/18.91 ( bool, fTrue ) 20.52/18.91 ( real, (zero_zero real) ) 20.52/18.91 ( real, (one_one real) ) 20.52/18.91 ( real, pi ) 20.52/18.91 ( 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)))) ) 20.52/18.91 ( 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) ) 20.52/18.91 ( (fun nat bool), (even_odd_even nat) ) 20.52/18.91 ( (fun nat bool), prime ) 20.52/18.91 ( (fun nat nat), suc ) 20.52/18.91 ( (fun nat nat), (fact_fact nat) ) 20.52/18.91 ( (fun nat nat), (size_size nat) ) 20.52/18.91 ( (fun nat nat), fact ) 20.52/18.91 ( (fun nat nat), nat_size ) 20.52/18.91 ( int, pls ) 20.52/18.91 ( int, m ) 20.52/18.91 ( int, (one_one int) ) 20.52/18.91 ( int, min_1 ) 20.52/18.91 ( int, s ) 20.52/18.91 ( int, s1 ) 20.52/18.91 ( int, t ) 20.52/18.91 ( (fun int bool), zprime ) 20.52/18.91 ( (fun int bool), nat_neg ) 20.52/18.91 ( (fun int bool), zEven ) 20.52/18.91 ( (fun int bool), nat_is_nat ) 20.52/18.91 ( (fun int bool), zOdd ) 20.52/18.91 ( (fun int bool), (even_odd_even int) ) 20.52/18.91 ( (fun int bool), twoSqu1091635170sum2sq ) 20.52/18.91 ( (fun int nat), nat_1 ) 20.52/18.91 ( (fun int nat), phi ) 20.52/18.91 ( (fun real real), sqrt ) 20.52/18.91 ( (fun real real), tan ) 20.52/18.91 ( (fun real real), cos ) 20.52/18.91 ( (fun real real), arccos ) 20.52/18.91 ( (fun real real), ln ) 20.52/18.91 ( (fun real real), sin ) 20.52/18.91 ( (fun real real), arctan ) 20.52/18.91 ( (fun real real), arcsin ) 20.52/18.91 ( complex, ii ) 20.52/18.91 ( complex, (one_one complex) ) 20.52/18.91 ( (fun complex complex), cnj ) 20.52/18.91 ( (fun complex complex), expi ) 20.52/18.91 ( (fun nat real), (real_1 nat) ) 20.52/18.91 ( (fun nat real), cos_coeff ) 20.52/18.91 ( (fun nat real), sin_coeff ) 20.52/18.91 ( (fun int int), bit0 ) 20.52/18.91 ( (fun int int), bit1 ) 20.52/18.91 ( (fun int int), pred ) 20.52/18.91 ( (fun int int), succ ) 20.52/18.91 ( (fun int int), (fact_fact int) ) 20.52/18.91 ( (fun int int), zfact ) 20.52/18.91 ( (fun bool bool), fNot ) 20.52/18.91 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 20.52/18.91 ( (fun bool (fun bool bool)), fconj ) 20.52/18.91 ( (fun bool (fun bool bool)), fdisj ) 20.52/18.91 ( (fun bool (fun bool bool)), fimplies ) 20.52/18.91 ( (fun int (fun int bool)), sRStar ) 20.52/18.91 ( (fun int (fun int bool)), quadRes ) 20.52/18.91 ( (fun int (fun int bool)), norRRset ) 20.52/18.91 ( (fun int (fun int bool)), d22set ) 20.52/18.91 ( (fun int (fun int bool)), sr ) 20.52/18.91 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 20.52/18.91 ( (fun nat (fun nat nat)), nat_gcd ) 20.52/18.91 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 20.52/18.91 ( (fun nat (fun nat nat)), nat_lcm ) 20.52/18.91 ( (fun nat (fun real real)), root ) 20.52/18.91 ( (fun real (fun real real)), log ) 20.52/18.91 ( (fun real (fun real real)), powr ) 20.52/18.91 ( (fun nat (fun nat bool)), coprime ) 20.52/18.91 ( (fun (fun int bool) int), (the int) ) 20.52/18.91 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 20.52/18.91 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 20.52/18.91 ( (fun nat (fun nat (product_prod int int))), bezw ) 20.52/18.91 ( (fun (fun int bool) bool), nat_nat_set ) 20.52/18.91 ( (filter nat), sequentially ) 20.52/18.91 ( (fun (product_prod nat nat) bool), pred_nat ) 20.52/18.91 ( (fun (product_prod int int) bool), frac_1 ) 20.52/18.91 ( (fun real complex), cis ) 20.52/18.91 ( (fun complex real), im ) 20.52/18.91 ( (fun complex real), re ) 20.52/18.91 ( (fun complex real), arg ) 20.52/18.91 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 20.52/18.91 ( (fun int (fun int int)), int_gcd ) 20.52/18.91 ( (fun int (fun int int)), multInv ) 20.52/18.91 ( (fun int (fun int int)), legacy_zgcd ) 20.52/18.91 ( (fun int (fun int int)), z3mod ) 20.52/18.91 ( (fun int (fun int int)), inv ) 20.52/18.91 ( (fun int (fun int int)), (gcd_gcd int) ) 20.52/18.91 ( (fun int (fun int int)), standardRes ) 20.52/18.91 ( (fun int (fun int int)), legendre ) 20.52/18.91 ( (fun int (fun int int)), nat_tsub ) 20.52/18.91 ( (fun int (fun int int)), z3div ) 20.52/18.91 ( (fun int (fun int int)), int_lcm ) 20.52/18.91 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 20.52/18.91 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 20.52/18.91 ( (fun int (fun (fun int bool) bool)), rsetR ) 20.52/18.91 ( (fun int (fun (fun int bool) bool)), resSet ) 20.52/18.91 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 20.52/18.91 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 20.52/18.91 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 20.52/18.91 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 20.52/18.91 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 20.52/18.91 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 20.52/18.91 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 20.52/18.91 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 20.52/18.91 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 20.52/18.91 ( (fun int (fun int (product_prod int int))), negDivAlg ) 20.52/18.91 ( (fun int (fun int (product_prod int int))), divmod_int ) 20.52/18.91 ( (fun int (fun int (product_prod int int))), posDivAlg ) 20.52/18.91 ( (fun int (fun int (product_prod int int))), pdivmod ) 20.52/18.91 ( (fun int (fun int (product_prod int int))), norm_frac ) 20.52/18.91 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 20.52/18.91 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 20.52/18.91 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 20.52/18.91 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 20.52/18.91 ( (fun real nat), natfloor ) 20.52/18.91 ( (fun real nat), natceiling ) 20.52/18.91 ( (fun int quickcheck_code_int), quickcheck_of_int ) 20.52/18.91 ( (fun int (fun int (fun int bool))), wset ) 20.52/18.91 ( (fun int (fun int (fun int bool))), bnorRset ) 20.52/18.91 ( (fun int (fun int (fun int bool))), zcong ) 20.52/18.91 ( (fun int (fun int (fun int bool))), noXRRset ) 20.52/18.91 ( (fun int (fun int (fun int bool))), zcongm ) 20.52/18.91 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 20.52/18.91 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 20.52/18.91 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 20.52/18.91 ( (fun int real), (real_1 int) ) 20.52/18.91 ( (fun complex nat), (size_size complex) ) 20.52/18.91 ( (fun complex nat), complex_size ) 20.52/18.91 ( (fun int (list int)), quickc666637781d_zero ) 20.52/18.91 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 20.52/18.91 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 20.52/18.91 ( (fun (product_prod int int) rat), frct ) 20.52/18.91 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 20.52/18.91 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 20.52/18.91 ( (fun (fun nat rat) bool), vanishes ) 20.52/18.91 ( (fun int (fun int rat)), fract ) 20.52/18.91 ( (fun code_code_numeral int), code_int_of ) 20.52/18.91 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 20.52/18.91 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 20.52/18.91 ( (fun code_code_numeral nat), code_c271388182l_size ) 20.52/18.91 ( (fun real (fun real complex)), complex_1 ) 20.52/18.91 ( (fun real (fun real complex)), rcis ) 20.52/18.91 ( (fun int (fun nat nat)), nat_aux ) 20.52/18.91 ( (fun rat real), ratreal ) 20.52/18.91 ( (fun quickcheck_code_int int), quickcheck_int_of ) 20.52/18.91 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 20.52/18.91 ( (fun rat (product_prod int int)), quotient_of ) 20.52/18.91 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 20.52/18.91 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 20.52/18.91 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 20.52/18.91 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 20.52/18.91 ) 20.52/18.91 (instantiation (let ((_let_0 (one_one real))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (= _let_0 X_1) (= _let_0 (hAPP real real (hAPP nat (fun real real) root N_1) X_1)))) )) 20.52/18.91 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.91 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.91 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.91 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.91 ) 20.52/18.91 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_155967 $$unsorted) (BOUND_VARIABLE_155968 $$unsorted) (BOUND_VARIABLE_155969 $$unsorted)) (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_155969))) (= (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_155967) BOUND_VARIABLE_155969)) BOUND_VARIABLE_155968)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_155967) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_155968) BOUND_VARIABLE_155969))))) )))) 20.52/18.91 ( real, (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 20.52/18.91 ( 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))) ) 20.52/18.91 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 20.52/18.92 ) 20.52/18.92 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_156000 $$unsorted) (BOUND_VARIABLE_156001 $$unsorted) (BOUND_VARIABLE_156002 $$unsorted)) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_156001) BOUND_VARIABLE_156002))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_156002) BOUND_VARIABLE_156000))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_156001) BOUND_VARIABLE_156000))) ))) 20.52/18.92 ( real, (zero_zero real), (zero_zero real), pi ) 20.52/18.92 ( 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)))) ) 20.52/18.92 ( 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 real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 20.52/18.92 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 20.52/18.92 ( int, (zero_zero int), (zero_zero int), min_1 ) 20.52/18.92 ( int, (zero_zero int), (one_one int), t ) 20.52/18.92 ( int, (one_one int), min_1, pls ) 20.52/18.92 ( 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))), (zero_zero int), s ) 20.52/18.92 ( 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))), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 20.52/18.92 ( 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))), (zero_zero int), skv_3 ) 20.52/18.92 ( 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))), (zero_zero int), skv_9 ) 20.52/18.92 ( int, min_1, min_1, min_1 ) 20.52/18.92 ) 20.52/18.92 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) _let_2)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) _let_2))) (= X (hAPP real real arcsin (hAPP real real sin X)))) )))) 20.52/18.92 ( (zero_zero real) ) 20.52/18.92 ( pi ) 20.52/18.92 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.92 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.52/18.92 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 20.52/18.92 ( (hAPP real real (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))))) ) 20.52/18.92 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 20.52/18.92 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.52/18.92 ( (hAPP real 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))))) ) 20.52/18.92 ( (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)))) ) 20.52/18.92 ( skv_14 ) 20.52/18.92 ) 20.52/18.92 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (fun int (fun int bool)))) (let ((_let_3 (fun (fun int bool) bool))) (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool zprime P_4))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) P_4))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_2 zcong A_2) (zero_zero int)) P_4)) (hBOOL (hAPP int bool (hAPP int _let_0 quadRes P_4) A_2)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_2 zcong (hAPP _let_0 int (hAPP _let_0 (fun _let_0 int) (big_co302546470etprod int int) (combi int)) (hAPP _let_3 _let_0 (complete_Sup_Sup _let_0) (hAPP int _let_3 (hAPP int (fun int _let_3) setS A_2) P_4)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) A_2) (hAPP int nat nat_1 (hAPP int int (hAPP int _let_0 (div_div int) (hAPP int int (hAPP int _let_0 (minus_minus int) P_4) (one_one int))) _let_1)))) P_4)))) ))))) 20.52/18.92 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.52/18.92 ) 20.52/18.92 (instantiation (let ((_let_0 (fun X_a (fun X_a X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_156091 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (semiring_1 X_a)) (= (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_156091) (hAPP X_a X_a (hAPP nat _let_0 (hAPP _let_0 (fun nat _let_0) (semiri532925092at_aux X_a) (hAPP X_a _let_0 (hAPP _let_0 _let_0 (combc X_a X_a X_a) (plus_plus X_a)) (one_one X_a))) BOUND_VARIABLE_156091) (zero_zero X_a))))) )) 20.52/18.92 ( real, (zero_zero nat) ) 20.52/18.92 ( real, (one_one nat) ) 20.52/18.92 ( int, (zero_zero nat) ) 20.52/18.92 ( int, (hAPP nat nat suc (zero_zero nat)) ) 20.52/18.92 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.92 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.52/18.92 ) 20.52/18.92 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP nat (fun real real) root N_1))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real _let_2 X_1)) (hAPP real real _let_2 Y_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) Y_1)))) )))) 20.52/18.92 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.92 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.92 ) 20.52/18.92 (instantiation (forall ((N $$unsorted)) (= (hAPP complex real re (hAPP nat complex (semiring_1_of_nat complex) N)) (hAPP nat real (semiring_1_of_nat real) N)) ) 20.52/18.92 ( (zero_zero nat) ) 20.52/18.92 ( (one_one nat) ) 20.52/18.92 ) 20.52/18.92 (instantiation (let ((_let_0 (real_1 int))) (forall ((X $$unsorted) (Y $$unsorted)) (= (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))) )) 20.52/18.92 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 20.52/18.92 ( (hAPP nat int (hAPP 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) ) 20.52/18.92 ) 20.52/18.92 (instantiation (let ((_let_0 (hAPP nat nat suc (zero_zero nat)))) (forall ((X $$unsorted)) (or (hBOOL (hAPP nat bool (even_odd_even nat) X)) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) X) (hAPP nat nat suc _let_0)))) )) 20.52/18.92 ( (zero_zero nat) ) 20.52/18.92 ( (one_one nat) ) 20.52/18.92 ) 20.52/18.92 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (hAPP int (fun int _let_1) posDivAlg A_1))) (forall ((A_1 $$unsorted) (B $$unsorted)) (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))))) )))) 20.52/18.92 ( (zero_zero int), (zero_zero int) ) 20.52/18.92 ( (zero_zero int), (one_one int) ) 20.52/18.92 ( (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))) ) 20.52/18.92 ( (zero_zero int), min_1 ) 20.52/18.92 ( min_1, (zero_zero int) ) 20.52/18.92 ( min_1, min_1 ) 20.52/18.92 ( 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))) ) 20.52/18.92 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 20.52/18.92 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 20.52/18.92 ( t, (zero_zero int) ) 20.52/18.92 ( t, (one_one int) ) 20.52/18.92 ( 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))) ) 20.52/18.92 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.52/18.92 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.52/18.92 ) 20.52/18.92 (instantiation (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))) (forall ((A_1 $$unsorted) (B $$unsorted)) (or (and (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B) _let_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_1) B)))) (= (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))) ))))) 20.52/18.92 ( (zero_zero int), (zero_zero int) ) 20.52/18.92 ( (zero_zero int), (one_one int) ) 20.52/18.92 ( (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))) ) 20.52/18.92 ( (zero_zero int), min_1 ) 20.52/18.92 ( min_1, (zero_zero int) ) 20.52/18.92 ( min_1, min_1 ) 20.52/18.92 ( 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))) ) 20.52/18.92 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 20.52/18.92 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 20.52/18.92 ( t, (zero_zero int) ) 20.52/18.92 ( t, (one_one int) ) 20.52/18.92 ( 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))) ) 20.52/18.92 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.52/18.92 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.52/18.92 ) 20.52/18.92 (instantiation (let ((_let_0 (norm_norm X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_156352 $$unsorted) (BOUND_VARIABLE_156353 $$unsorted)) (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_156352)) (hAPP X_a real _let_0 BOUND_VARIABLE_156353))) (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_156352) BOUND_VARIABLE_156353))))) )) 20.52/18.92 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 20.52/18.92 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 20.52/18.92 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 20.52/18.92 ) 20.52/18.92 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (ord_less real))) (let ((_let_5 (real_1 nat))) (let ((_let_6 (times_times real))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_4 _let_0) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 _let_0) X))) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real (hAPP real _let_3 _let_6 (hAPP nat real _let_5 N_2)) Y)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_4 X) (hAPP real real (hAPP real _let_3 _let_6 (hAPP nat real _let_5 (hAPP nat nat suc N_2))) Y))))) ))) )))))))) 20.52/18.93 ( pi, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.52/18.93 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.52/18.93 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 20.52/18.93 ( skv_6, skv_2 ) 20.52/18.93 ( skv_11, skv_10 ) 20.52/18.93 ( skv_12, skv_13 ) 20.52/18.93 ) 20.52/18.93 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (dvd_dvd X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_156386 $$unsorted) (BOUND_VARIABLE_156387 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_156386) BOUND_VARIABLE_156387)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_156386)) BOUND_VARIABLE_156387)))) ))) 20.52/18.93 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 20.52/18.93 ) 20.52/18.93 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (forall ((X $$unsorted) (Y $$unsorted)) (= (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)))) ))) 20.52/18.93 ( ii, ii ) 20.52/18.93 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 20.52/18.93 ( (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 ) 20.52/18.93 ) 20.52/18.93 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_156404 $$unsorted) (BOUND_VARIABLE_156405 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_156404) BOUND_VARIABLE_156405))) (or (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_156405)) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_156404))))) )) 20.52/18.93 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.93 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.93 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.93 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.93 ) 20.52/18.93 (instantiation (let ((_let_0 (ord_max X_a))) (forall ((X_a $$unsorted)) (or (not (ord X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0))) )) 20.52/18.93 ( bool ) 20.52/18.93 ( real ) 20.52/18.93 ( nat ) 20.52/18.93 ( (fun nat bool) ) 20.52/18.93 ( int ) 20.52/18.93 ( (fun int bool) ) 20.52/18.93 ( (fun real bool) ) 20.52/18.93 ( (fun real real) ) 20.52/18.93 ( complex ) 20.52/18.93 ( (fun nat real) ) 20.52/18.93 ( (fun int int) ) 20.52/18.93 ( rat ) 20.52/18.93 ( (fun int (fun int bool)) ) 20.52/18.93 ( quickcheck_code_int ) 20.52/18.93 ( (product_prod int int) ) 20.52/18.93 ( (fun (product_prod int int) bool) ) 20.52/18.93 ( code_code_numeral ) 20.52/18.93 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 20.52/18.93 ( (fun (product_prod int int) int) ) 20.52/18.93 ( (fun int (fun int (fun int bool))) ) 20.52/18.93 ( (fun int real) ) 20.52/18.93 ) 20.52/18.93 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (times_times real))) (let ((_let_3 (norm_norm X_a))) (forall ((X_a $$unsorted)) (or (not (real_normed_algebra X_a)) (not (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) K_2))) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP X_a real _let_3 (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_1 _let_2 (hAPP real real (hAPP real _let_1 _let_2 (hAPP X_a real _let_3 A_4)) (hAPP X_a real _let_3 B_4))) K_2))) ))) ))) ))))) 20.52/18.93 ( real ) 20.52/18.93 ( complex ) 20.52/18.93 ) 20.52/18.93 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (P_1 $$unsorted)) (= (hAPP _let_0 _let_0 (collect X_a) P_1) (ti _let_0 P_1)) )) 20.52/18.93 ( bool, fNot ) 20.52/18.93 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (fun (fun int bool) (fun int bool)))) (let ((_let_6 (fun (fun int bool) _let_4))) (let ((_let_7 (fun int (fun int bool)))) (let ((_let_8 (fun (fun int bool) bool))) (let ((_let_9 (fun real _let_0))) (let ((_let_10 (fun _let_7 (fun int bool)))) (let ((_let_11 (fEx int))) (let ((_let_12 (fun int _let_5))) (let ((_let_13 (fun int real))) (let ((_let_14 (fun real (fun int bool)))) (let ((_let_15 (fun real _let_7))) (let ((_let_16 (fun (fun int bool) _let_7))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun int _let_4))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_19 _let_12))) (let ((_let_22 (fun _let_7 _let_19))) (let ((_let_23 (fun int _let_13))) (let ((_let_24 (fun _let_23 _let_7))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun _let_13 (fun int bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun _let_13 _let_13))) (let ((_let_29 (fun int _let_28))) (let ((_let_30 (fun int _let_1))) (hAPP _let_14 _let_0 (hAPP _let_8 (fun _let_14 _let_0) (combb (fun int bool) bool real) _let_11) (hAPP _let_15 _let_14 (hAPP _let_10 (fun _let_15 _let_14) (combb _let_7 (fun int bool) real) (hAPP _let_8 _let_10 (combb (fun int bool) bool int) _let_11)) (hAPP (fun int bool) _let_15 (hAPP _let_17 (fun (fun int bool) _let_15) (combc real (fun int bool) _let_7) (hAPP _let_18 _let_17 (hAPP (fun _let_12 _let_16) (fun _let_18 _let_17) (combb _let_12 _let_16 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_20 _let_18 (hAPP _let_21 (fun _let_20 _let_18) (combb _let_19 _let_12 real) (hAPP (fun _let_4 _let_5) _let_21 (combb _let_4 _let_5 int) (combs int bool bool))) (hAPP _let_15 _let_20 (hAPP _let_22 (fun _let_15 _let_20) (combb _let_7 _let_19 real) (hAPP _let_6 _let_22 (combb (fun int bool) _let_4 int) (hAPP (fun bool _let_3) _let_6 (combb bool _let_3 int) fconj))) (hAPP _let_23 _let_15 (hAPP _let_25 (fun _let_23 _let_15) (combc real _let_23 _let_7) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb _let_13 (fun int bool) int)) (hAPP _let_9 _let_27 (hAPP (fun _let_0 _let_26) (fun _let_9 _let_27) (combb _let_0 _let_26 real) (combb real bool int)) (fequal real)))) (hAPP _let_13 _let_23 (hAPP _let_29 (fun _let_13 _let_23) (combc int _let_13 _let_13) (hAPP _let_30 _let_29 (hAPP (fun _let_1 _let_28) (fun _let_30 _let_29) (combb _let_1 _let_28 int) (combb real real int)) (hAPP _let_13 _let_30 (hAPP (fun real _let_1) (fun _let_13 _let_30) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_3 _let_5 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_7 _let_7 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))))))))) ) 20.52/18.93 ( real, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun (fun nat real) (fun nat real)))) (let ((_let_5 (fun nat (fun nat bool)))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun (fun 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int)) (hAPP _let_13 _let_11 (hAPP _let_14 (fun _let_13 _let_11) (combb (fun int (fun nat bool)) _let_0 real) (hAPP (fun (fun nat bool) bool) _let_14 (combb (fun nat bool) bool int) (fEx nat))) (hAPP (fun nat bool) _let_13 (hAPP _let_16 (fun (fun nat bool) _let_13) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_18 _let_16 (hAPP (fun _let_17 _let_15) (fun _let_18 _let_16) (combb _let_17 _let_15 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_20 _let_18 (hAPP _let_21 (fun _let_20 _let_18) (combb _let_19 _let_17 real) (hAPP (fun _let_8 _let_7) _let_21 (combb _let_8 _let_7 int) (combs nat bool bool))) (hAPP _let_13 _let_20 (hAPP _let_22 (fun _let_13 _let_20) (combb (fun int (fun nat bool)) _let_19 real) (hAPP _let_9 _let_22 (combb (fun nat bool) _let_8 int) (hAPP (fun bool _let_3) _let_9 (combb bool _let_3 nat) fconj))) (hAPP _let_23 _let_13 (hAPP _let_25 (fun _let_23 _let_13) (combc real _let_23 (fun int (fun nat bool))) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_23 (hAPP _let_28 (fun (fun nat real) _let_23) (combc int (fun nat real) (fun nat real)) (hAPP _let_12 _let_28 (hAPP (fun _let_2 _let_4) (fun _let_12 _let_28) (combb _let_2 _let_4 int) (combb real real nat)) (hAPP _let_10 _let_12 (hAPP (fun real _let_2) (fun _let_10 _let_12) (combb real _let_2 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_3 _let_7 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_5 _let_5 (combc nat nat bool) (fequal nat)) (zero_zero nat))))))))))))))))))))))))))))))))))) ) 20.52/18.93 ( nat, (even_odd_even nat) ) 20.52/18.93 ( nat, prime ) 20.52/18.93 ( int, zprime ) 20.52/18.93 ( int, nat_neg ) 20.52/18.93 ( int, zEven ) 20.52/18.93 ( int, nat_is_nat ) 20.52/18.93 ( int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (fun int _let_1))) (hAPP _let_2 _let_0 (hAPP (fun _let_0 bool) (fun _let_2 _let_0) (combb _let_0 bool int) (fEx int)) (hAPP _let_1 _let_2 (hAPP _let_4 (fun _let_1 _let_2) (combc int _let_1 _let_0) (hAPP _let_2 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_2 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_1 (hAPP _let_5 _let_5 (combc int int int) (hAPP _let_1 _let_5 (hAPP _let_5 (fun _let_1 _let_5) (combb int _let_1 int) (plus_plus int)) (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int)))))))))) ) 20.52/18.93 ( int, zOdd ) 20.52/18.93 ( int, (even_odd_even int) ) 20.52/18.93 ( int, twoSqu1091635170sum2sq ) 20.52/18.93 ( int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_2 _let_0 (hAPP (fun _let_0 bool) (fun _let_2 _let_0) (combb _let_0 bool int) (fEx int)) (hAPP _let_1 _let_2 (hAPP _let_4 (fun _let_1 _let_2) (combc int _let_1 _let_0) (hAPP _let_2 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_2 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))) ) 20.52/18.93 ( (fun int bool), nat_nat_set ) 20.52/18.93 ( (product_prod int int), frac_1 ) 20.52/18.93 ( (product_prod nat nat), pred_nat ) 20.52/18.93 ( (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)))) ) 20.52/18.93 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_less ) 20.52/18.93 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_leq ) 20.52/18.93 ( (fun nat rat), vanishes ) 20.52/18.93 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), ratrel ) 20.52/18.93 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (product_prod int int))) (let ((_let_4 (product_snd int int))) (let ((_let_5 (fun _let_3 (fun _let_3 bool)))) (let ((_let_6 (fun _let_3 int))) (let ((_let_7 (fun _let_3 _let_2))) (let ((_let_8 (fun (fun _let_3 bool) (fun _let_3 bool)))) (let ((_let_9 (fun _let_6 (fun _let_3 bool)))) (let ((_let_10 (fun _let_3 _let_0))) (let ((_let_11 (fun _let_6 _let_10))) (let ((_let_12 (hAPP (fun int _let_0) _let_11 (combb int _let_0 _let_3) (fequal int)))) (let ((_let_13 (fun _let_3 _let_1))) (let ((_let_14 (fun _let_6 _let_6))) (let ((_let_15 (fun _let_3 _let_8))) (let ((_let_16 (fun _let_5 _let_5))) (let ((_let_17 (hAPP (fun _let_3 bool) _let_7 (hAPP (fun bool _let_2) (fun (fun _let_3 bool) _let_7) (combb bool _let_2 _let_3) fconj) (hAPP (fun _let_3 bool) (fun _let_3 bool) (hAPP _let_2 _let_8 (combb bool bool _let_3) fNot) (hAPP int (fun _let_3 bool) (hAPP _let_10 (fun int (fun _let_3 bool)) (combc _let_3 int bool) (hAPP _let_6 _let_10 _let_12 _let_4)) (zero_zero int)))))) (let ((_let_18 (fun _let_3 _let_6))) (let ((_let_19 (fun _let_3 _let_9))) (let ((_let_20 (fun _let_3 _let_10))) (let ((_let_21 (fun _let_3 _let_14))) (let ((_let_22 (fun _let_6 _let_18))) (let ((_let_23 (hAPP _let_6 _let_13 (hAPP (fun int _let_1) (fun _let_6 _let_13) (combb int _let_1 _let_3) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_6))) (hAPP _let_5 (fun (product_prod _let_3 _let_3) bool) (product_prod_case 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(hAPP _let_13 _let_24 (combc _let_3 int int) _let_23)) _let_4)))))))))))))))))))))))))))))) ) 20.52/18.93 ) 20.52/18.93 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (forall ((N $$unsorted)) (= _let_1 (hAPP int int (hAPP int _let_0 (gcd_gcd int) (hAPP int int (hAPP int _let_0 (plus_plus int) N) _let_1)) N)) ))) 20.52/18.93 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 20.52/18.93 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.52/18.94 ) 20.52/18.94 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (real_1 nat))) (forall ((R_4 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) R_4))) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP nat real _let_2 N_2)) R_4))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) R_4) (hAPP nat real _let_2 (hAPP nat nat suc N_2)))))) ))) )))) 20.52/18.94 ( pi ) 20.52/18.94 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.52/18.94 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.52/18.94 ( skv_6 ) 20.52/18.94 ( skv_11 ) 20.52/18.94 ( skv_12 ) 20.52/18.94 ( skv_14 ) 20.52/18.94 ) 20.52/18.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156477 $$unsorted)) (or (not (real_algebra_1 X_a)) (= (= (zero_zero real) BOUND_VARIABLE_156477) (= (zero_zero X_a) (hAPP real X_a (of_real X_a) BOUND_VARIABLE_156477)))) ) 20.52/18.94 ( complex, pi ) 20.52/18.94 ( complex, (hAPP int real (number_number_of real) min_1) ) 20.52/18.94 ( complex, (hAPP real real (uminus_uminus real) (one_one real)) ) 20.52/18.94 ) 20.52/18.94 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_156495))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_156495 $$unsorted) (BOUND_VARIABLE_156496 $$unsorted) (BOUND_VARIABLE_156497 $$unsorted)) (or (not (linord581940658strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_156496) BOUND_VARIABLE_156497))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_156495) (zero_zero X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_156497)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_156496)))) )))) 20.52/18.94 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int), skv_1 ) 20.52/18.94 ) 20.52/18.94 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted)) (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)))) )) 20.52/18.94 ( real ) 20.52/18.94 ( nat ) 20.52/18.94 ( int ) 20.52/18.94 ( complex ) 20.52/18.94 ( rat ) 20.52/18.94 ( quickcheck_code_int ) 20.52/18.94 ( code_code_numeral ) 20.52/18.94 ) 20.52/18.94 (instantiation (let ((_let_0 (real_1 int))) (forall ((X $$unsorted) (Y $$unsorted)) (= (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))) )) 20.52/18.94 ( (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)))), (hAPP int int (number_number_of int) min_1) ) 20.52/18.94 ) 20.52/18.94 (instantiation (let ((_let_0 (fun int bool))) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool nat_nat_set A_3))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_1) A_3))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) X_1))) )) 20.52/18.94 ( (one_one int), zEven ) 20.52/18.94 ) 20.52/18.94 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (not (= Ma N_1)) (or (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 N_1) Ma)) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Ma) N_1)))) ))) 20.52/18.94 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.94 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 20.52/18.94 ) 20.52/18.94 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real real))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) _let_0) X))) (not (= _let_0 (hAPP real real cos X))) (not (forall ((N_2 $$unsorted)) (or (hBOOL (hAPP nat bool (even_odd_even nat) N_2)) (not (= X (hAPP real real (hAPP real _let_1 (times_times real) (hAPP nat real (real_1 nat) N_2)) (hAPP real real (hAPP real _let_1 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ))) ))) 20.52/18.94 ( (zero_zero real) ) 20.52/18.94 ( pi ) 20.52/18.94 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.94 ( (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)))) ) 20.52/18.94 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 20.52/18.94 ( (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 (hAPP int int bit1 pls))))) ) 20.52/18.94 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 20.52/18.94 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.52/18.94 ( (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 bit0 (hAPP int int bit1 pls))))) ) 20.52/18.94 ( (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)))) ) 20.52/18.94 ( skv_6 ) 20.52/18.94 ( skv_11 ) 20.52/18.94 ( skv_12 ) 20.52/18.94 ( skv_14 ) 20.52/18.94 ) 20.52/18.94 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (ord_less int))) (forall ((M $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 _let_1) X))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 X) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong X) _let_1) M)))) )))) 20.52/18.94 ( (zero_zero int), (zero_zero int) ) 20.52/18.94 ( (zero_zero int), min_1 ) 20.52/18.94 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 20.52/18.94 ( (zero_zero int), t ) 20.52/18.94 ( (one_one int), (zero_zero int) ) 20.52/18.94 ( (one_one int), t ) 20.52/18.94 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 20.52/18.94 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 20.52/18.94 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 20.52/18.94 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_3 ) 20.52/18.94 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_9 ) 20.52/18.94 ( min_1, (zero_zero int) ) 20.52/18.94 ( min_1, min_1 ) 20.52/18.94 ( (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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 20.52/18.94 ) 20.52/18.94 (instantiation (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP nat bool prime P_5))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) P_5))) ) 20.52/18.94 ( (zero_zero nat) ) 20.52/18.94 ( (one_one nat) ) 20.52/18.94 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.94 ) 20.52/18.94 (instantiation (let ((_let_0 (zero_zero real))) (forall ((X_1 $$unsorted)) (= (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) _let_0) (hAPP real real (hAPP real (fun real real) (times_times real) X_1) X_1)))) (= _let_0 X_1)) )) 20.52/18.94 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.94 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.52/18.94 ( (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))))) ) 20.52/18.94 ) 20.52/18.94 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (one_one real)))) (hBOOL (hAPP real bool (hAPP (fun real real) _let_0 (isCont real real) arccos) X_1))) ))) 20.52/18.94 ( (zero_zero real) ) 20.52/18.94 ( (one_one real) ) 20.52/18.94 ( pi ) 20.52/18.94 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.52/18.94 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 20.52/18.94 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.52/18.94 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 20.52/18.94 ) 20.52/18.94 (instantiation (forall ((X $$unsorted)) (= (hAPP real real (uminus_uminus real) (hAPP complex real re X)) (hAPP complex real re (hAPP complex complex (uminus_uminus complex) X))) ) 20.52/18.94 ( ii ) 20.52/18.94 ( (one_one complex) ) 20.52/18.94 ) 20.52/18.94 (instantiation (let ((_let_0 (fun int bool))) (forall ((B $$unsorted) (A_1 $$unsorted)) (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))) )) 20.52/18.94 ( (zero_zero int), (zero_zero int) ) 20.52/18.94 ( (zero_zero int), min_1 ) 20.52/18.94 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 20.52/18.94 ( (zero_zero int), t ) 20.52/18.94 ( (one_one int), (zero_zero int) ) 20.52/18.94 ( (one_one int), t ) 20.52/18.94 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 20.52/18.94 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 20.52/18.94 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 20.52/18.94 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_3 ) 20.52/18.94 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_9 ) 20.52/18.94 ( min_1, (zero_zero int) ) 20.52/18.94 ( min_1, min_1 ) 20.52/18.94 ( (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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 20.52/18.94 ) 20.52/18.94 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_156721 $$unsorted) (BOUND_VARIABLE_156722 $$unsorted)) (or (not (comm_ring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP nat X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_156721) _let_0)) (hAPP nat X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_156722) _let_0)) (hAPP X_a X_a (hAPP X_a _let_1 (times_times X_a) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_156721) BOUND_VARIABLE_156722)) (hAPP X_a X_a (hAPP X_a _let_1 (plus_plus X_a) BOUND_VARIABLE_156721) BOUND_VARIABLE_156722)))) )))))) 20.52/18.94 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 20.52/18.94 ( nat, (one_one nat), (one_one nat) ) 20.52/18.94 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 20.52/18.94 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 20.52/18.94 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 20.52/18.94 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 20.52/18.94 ) 20.52/18.94 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_156751 $$unsorted) (BOUND_VARIABLE_156752 $$unsorted) (BOUND_VARIABLE_156753 $$unsorted)) (or (not (cancel_semigroup_add X_a)) (not (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_156753) BOUND_VARIABLE_156752) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_156751) BOUND_VARIABLE_156752))) (= (ti X_a BOUND_VARIABLE_156751) (ti X_a BOUND_VARIABLE_156753))) ))) 20.52/18.94 ( nat, (one_one nat), (one_one nat), (one_one nat) ) 20.52/18.94 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 20.52/18.94 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.52/18.95 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 20.52/18.95 ) 20.52/18.95 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (div_mod int) A_1) (zero_zero int)) (ti int A_1)) ) 20.52/18.95 ( pls ) 20.52/18.95 ( m ) 20.52/18.95 ( min_1 ) 20.52/18.95 ( s ) 20.52/18.95 ( s1 ) 20.52/18.95 ( t ) 20.52/18.95 ) 20.52/18.95 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_156906 $$unsorted)) (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_156906)) (field_char_0_Rats X_a)))) )) 20.52/18.95 ( real, (zero_zero int) ) 20.52/18.95 ( real, (one_one int) ) 20.52/18.95 ) 20.52/18.95 (instantiation (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_156920))) (let ((_let_3 (hAPP int X_a _let_1 BOUND_VARIABLE_156921))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_156920 $$unsorted) (BOUND_VARIABLE_156921 $$unsorted)) (or (not (number X_a)) (not (linorder X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) _let_2) _let_3)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_3) _let_2))))) ))))) 20.52/18.95 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)), pls ) 20.52/18.95 ( int, pls, pls ) 20.52/18.95 ( int, pls, (hAPP int int bit1 pls) ) 20.52/18.95 ( int, pls, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.52/18.95 ( int, pls, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 20.52/18.95 ( int, (hAPP int int bit1 pls), pls ) 20.52/18.95 ) 20.52/18.95 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted)) (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)))) )) 20.52/18.95 ( real ) 20.52/18.95 ( nat ) 20.52/18.95 ( int ) 20.52/18.95 ( complex ) 20.52/18.95 ( rat ) 20.52/18.95 ( quickcheck_code_int ) 20.52/18.95 ( code_code_numeral ) 20.52/18.95 ) 20.52/18.95 (instantiation (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_157003))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_156999 $$unsorted) (BOUND_VARIABLE_157000 $$unsorted) (BOUND_VARIABLE_157001 $$unsorted) (BOUND_VARIABLE_157002 $$unsorted) (BOUND_VARIABLE_157003 $$unsorted)) (or (not (semiri456707255roduct X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_157003)) (= (ti X_a BOUND_VARIABLE_156999) (ti X_a BOUND_VARIABLE_157000)) (not (= (ti X_a BOUND_VARIABLE_157001) (ti X_a BOUND_VARIABLE_157002))) (not (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_157001) (hAPP X_a X_a _let_2 BOUND_VARIABLE_156999)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_157002) (hAPP X_a X_a _let_2 BOUND_VARIABLE_157000))))) )))) 20.52/18.95 ( bool, fFalse, 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int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq, twoSqu1094008024sum2sq, twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 20.52/18.98 ( (fun real nat), natfloor, natceiling, natfloor, natfloor, natfloor ) 20.52/18.98 ( (fun real nat), natceiling, natfloor, natceiling, natceiling, natceiling ) 20.52/18.98 ( (fun real nat), natceiling, natceiling, natfloor, natfloor, natceiling ) 20.52/18.98 ( (fun real nat), natceiling, natceiling, natfloor, natceiling, natceiling ) 20.52/18.98 ( (fun real nat), natceiling, natceiling, natceiling, natfloor, natceiling ) 20.52/18.98 ( (fun real nat), natceiling, natceiling, natceiling, natceiling, natceiling ) 20.52/18.98 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int, quickcheck_of_int, quickcheck_of_int, quickcheck_of_int ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, wset, wset, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, wset, bnorRset, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, wset, zcong, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, wset, noXRRset, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, wset, zcongm, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, bnorRset, wset, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, bnorRset, bnorRset, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, bnorRset, zcong, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, bnorRset, noXRRset, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, bnorRset, zcongm, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, zcong, wset, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, zcong, bnorRset, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, zcong, zcong, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, zcong, noXRRset, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, zcong, zcongm, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, noXRRset, wset, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, noXRRset, bnorRset, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, noXRRset, zcong, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, noXRRset, noXRRset, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, noXRRset, zcongm, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, zcongm, wset, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, zcongm, bnorRset, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, zcongm, zcong, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, zcongm, noXRRset, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, wset, zcongm, zcongm, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), wset, bnorRset, wset, wset, wset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), bnorRset, wset, bnorRset, bnorRset, bnorRset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), zcong, zcong, zcong, zcong, zcong ) 20.52/18.98 ( (fun int (fun int (fun int bool))), zcong, zcong, zcong, noXRRset, zcong ) 20.52/18.98 ( (fun int (fun int (fun int bool))), zcong, zcong, zcong, zcongm, zcong ) 20.52/18.98 ( (fun int (fun int (fun int bool))), zcong, zcong, noXRRset, zcong, zcong ) 20.52/18.98 ( (fun int (fun int (fun int bool))), zcong, zcong, noXRRset, noXRRset, zcong ) 20.52/18.98 ( (fun int (fun int (fun int bool))), zcong, zcong, noXRRset, zcongm, zcong ) 20.52/18.98 ( (fun int (fun int (fun int bool))), zcong, zcong, zcongm, zcong, zcong ) 20.52/18.98 ( (fun int (fun int (fun int bool))), zcong, zcong, zcongm, noXRRset, zcong ) 20.52/18.98 ( (fun int (fun int (fun int bool))), zcong, zcong, zcongm, zcongm, zcong ) 20.52/18.98 ( (fun int (fun int (fun int bool))), zcong, zcongm, zcong, zcong, zcong ) 20.52/18.98 ( (fun int (fun int (fun int bool))), noXRRset, noXRRset, noXRRset, noXRRset, noXRRset ) 20.52/18.98 ( (fun int (fun int (fun int bool))), zcongm, zcong, zcongm, zcongm, zcongm ) 20.52/18.98 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair, multInvPair, multInvPair, multInvPair ) 20.52/18.98 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS, setS, setS, setS ) 20.52/18.98 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral, code_d418564891umeral, code_d418564891umeral, code_d418564891umeral ) 20.52/18.98 ( (fun int real), (real_1 int), (real_1 int), (real_1 int), (real_1 int), (real_1 int) ) 20.52/18.98 ( (fun complex nat), (size_size complex), complex_size, (size_size complex), (size_size complex), (size_size complex) ) 20.52/18.98 ( (fun complex nat), complex_size, (size_size complex), complex_size, complex_size, complex_size ) 20.52/18.98 ( (fun complex nat), complex_size, complex_size, (size_size complex), (size_size complex), complex_size ) 20.52/18.98 ( (fun complex nat), complex_size, complex_size, (size_size complex), complex_size, complex_size ) 20.52/18.98 ( (fun complex nat), complex_size, complex_size, complex_size, (size_size complex), complex_size ) 20.52/18.98 ( (fun complex nat), complex_size, complex_size, complex_size, complex_size, complex_size ) 20.52/18.98 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero, quickc666637781d_zero, quickc666637781d_zero, quickc666637781d_zero ) 20.52/18.98 ( (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 ) 20.52/18.98 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel, ratrel, ratrel, ratrel ) 20.52/18.98 ( (fun (product_prod int int) rat), frct, frct, frct, frct, frct ) 20.52/18.98 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux, code_nat_of_aux, code_nat_of_aux, code_nat_of_aux ) 20.52/18.98 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel, nat_gcd_rel, nat_gcd_rel, nat_gcd_rel ) 20.52/18.98 ( (fun (fun nat rat) bool), vanishes, vanishes, vanishes, vanishes, vanishes ) 20.52/18.98 ( (fun int (fun int rat)), fract, fract, fract, fract, fract ) 20.52/18.98 ( (fun code_code_numeral int), code_int_of, code_int_of, code_int_of, code_int_of, code_int_of ) 20.52/18.98 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat, divmod_nat, divmod_nat, divmod_nat ) 20.52/18.98 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral), (size_size code_code_numeral), (size_size code_code_numeral), (size_size code_code_numeral) ) 20.52/18.98 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral), (size_size code_code_numeral), code_c271388182l_size, (size_size code_code_numeral) ) 20.52/18.98 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral), code_c271388182l_size, (size_size code_code_numeral), (size_size code_code_numeral) ) 20.52/18.98 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral), code_c271388182l_size, code_c271388182l_size, (size_size code_code_numeral) ) 20.52/18.98 ( (fun code_code_numeral nat), (size_size code_code_numeral), code_c271388182l_size, (size_size code_code_numeral), (size_size code_code_numeral), (size_size code_code_numeral) ) 20.52/18.98 ( (fun code_code_numeral nat), code_c271388182l_size, (size_size code_code_numeral), code_c271388182l_size, code_c271388182l_size, code_c271388182l_size ) 20.52/18.98 ( (fun real (fun real complex)), complex_1, complex_1, complex_1, complex_1, complex_1 ) 20.52/18.98 ( (fun real (fun real complex)), complex_1, complex_1, complex_1, rcis, complex_1 ) 20.52/18.98 ( (fun real (fun real complex)), complex_1, complex_1, rcis, complex_1, complex_1 ) 20.52/18.98 ( (fun real (fun real complex)), complex_1, complex_1, rcis, rcis, complex_1 ) 20.52/18.98 ( (fun real (fun real complex)), complex_1, rcis, complex_1, complex_1, complex_1 ) 20.52/18.98 ( (fun real (fun real complex)), rcis, complex_1, rcis, rcis, rcis ) 20.52/18.98 ( (fun int (fun nat nat)), nat_aux, nat_aux, nat_aux, nat_aux, nat_aux ) 20.52/18.98 ( (fun rat real), ratreal, ratreal, ratreal, ratreal, ratreal ) 20.52/18.98 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of, quickcheck_int_of, quickcheck_int_of, quickcheck_int_of ) 20.52/18.98 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int, quickc495462417de_int, quickc495462417de_int, quickc495462417de_int ) 20.52/18.98 ( (fun rat (product_prod int int)), quotient_of, quotient_of, quotient_of, quotient_of, quotient_of ) 20.52/18.98 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR, rRset2norRR, rRset2norRR, rRset2norRR ) 20.52/18.98 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real), (complete_Sup_Sup real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 20.52/18.98 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of, quickcheck_nat_of, quickcheck_nat_of, quickcheck_nat_of ) 20.52/18.98 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda, xzgcda, xzgcda, xzgcda, xzgcda ) 20.52/18.98 ) 20.52/18.98 (instantiation (let ((_let_0 (fun nat bool))) (forall ((N_1 $$unsorted) (P_1 $$unsorted)) (or (hBOOL (hAPP nat bool P_1 (zero_zero nat))) (not (hBOOL (hAPP nat bool P_1 N_1))) (not (forall ((K_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool P_1 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) K_1) (one_one nat))))) (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) I_2) K_1))) (not (hBOOL (hAPP nat bool P_1 I_2)))) )) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) K_1) N_1)))) ))) )) 20.52/18.98 ( (zero_zero nat), (even_odd_even nat) ) 20.52/18.98 ( (zero_zero nat), prime ) 20.52/18.98 ( (one_one nat), (even_odd_even nat) ) 20.52/18.98 ( (one_one nat), prime ) 20.52/18.98 ( (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)) ) 20.52/18.98 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), prime ) 20.52/18.98 ) 20.52/18.98 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (zero_zero X_a))) (let ((_let_4 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_3) BOUND_VARIABLE_157072)))) (let ((_let_5 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_157070))) (let ((_let_6 (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) _let_5) BOUND_VARIABLE_157072))) (let ((_let_7 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_157072) _let_3)))) (let ((_let_8 (hAPP X_a _let_0 _let_1 _let_5))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_157070 $$unsorted) (BOUND_VARIABLE_157071 $$unsorted) (BOUND_VARIABLE_157072 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (not (number X_a)) (= (and (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_6) BOUND_VARIABLE_157071))) (or _let_4 (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_157071) _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_157071) BOUND_VARIABLE_157072))))) )))))))))) 20.52/18.99 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (zero_zero real), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 20.52/18.99 ( real, (hAPP 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 20.52/18.99 ) 20.52/18.99 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (forall ((Z_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) Z_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) Z_1)))) ))) 20.52/18.99 ( (one_one int) ) 20.52/18.99 ( min_1 ) 20.52/18.99 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.99 ( s ) 20.52/18.99 ( (hAPP int int (number_number_of int) pls) ) 20.52/18.99 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.52/18.99 ( skv_3 ) 20.52/18.99 ( skv_9 ) 20.52/18.99 ) 20.52/18.99 (instantiation (let ((_let_0 (ring_1_of_int X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_157137 $$unsorted) (BOUND_VARIABLE_157138 $$unsorted)) (or (not (ring_char_0 X_a)) (= (= (ti int BOUND_VARIABLE_157138) (ti int BOUND_VARIABLE_157137)) (= (hAPP int X_a _let_0 BOUND_VARIABLE_157138) (hAPP int X_a _let_0 BOUND_VARIABLE_157137)))) )) 20.52/18.99 ( real, min_1, s ) 20.52/18.99 ( int, m, t ) 20.52/18.99 ( complex, m, m ) 20.52/18.99 ( complex, t, m ) 20.52/18.99 ( rat, min_1, min_1 ) 20.52/18.99 ( rat, s, min_1 ) 20.52/18.99 ) 20.52/18.99 (instantiation (let ((_let_0 (number_number_of X_a))) (forall ((X_a $$unsorted)) (or (not (number X_a)) (= _let_0 (ti (fun int X_a) _let_0))) )) 20.52/18.99 ( bool ) 20.52/18.99 ( real ) 20.52/18.99 ( nat ) 20.52/18.99 ( (fun nat bool) ) 20.52/18.99 ( (fun nat nat) ) 20.52/18.99 ( int ) 20.52/18.99 ( (fun int bool) ) 20.52/18.99 ( (fun nat int) ) 20.52/18.99 ( (fun real real) ) 20.52/18.99 ( complex ) 20.52/18.99 ( (fun nat real) ) 20.52/18.99 ( (fun int int) ) 20.52/18.99 ( rat ) 20.52/18.99 ( (fun int rat) ) 20.52/18.99 ( (fun bool bool) ) 20.52/18.99 ( (fun int (fun bool bool)) ) 20.52/18.99 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 20.52/18.99 ( (fun int (fun int bool)) ) 20.52/18.99 ( quickcheck_code_int ) 20.52/18.99 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 20.52/18.99 ( (product_prod int int) ) 20.52/18.99 ( (fun int (product_prod int int)) ) 20.52/18.99 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 20.52/18.99 ( (fun (fun int bool) bool) ) 20.52/18.99 ( (fun (product_prod int int) bool) ) 20.52/18.99 ( code_code_numeral ) 20.52/18.99 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 20.52/18.99 ( (product_prod int (product_prod int int)) ) 20.52/18.99 ( (fun int (product_prod int (product_prod int int))) ) 20.52/18.99 ( (fun (fun int int) (fun int bool)) ) 20.52/18.99 ( (fun int (fun (product_prod int int) bool)) ) 20.52/18.99 ( (fun int (fun (fun int bool) bool)) ) 20.52/18.99 ( (list int) ) 20.52/18.99 ( (fun nat (fun bool bool)) ) 20.52/18.99 ( (fun int (fun int (product_prod int (product_prod int int)))) ) 20.52/18.99 ( (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 20.52/18.99 ( (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 20.52/18.99 ( (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 20.52/18.99 ( (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 20.52/18.99 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 20.52/18.99 ( (fun (product_prod int int) int) ) 20.52/18.99 ( (fun int (fun int (fun int bool))) ) 20.52/18.99 ( (fun int real) ) 20.52/18.99 ( (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 20.52/18.99 ( (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 20.52/18.99 ) 20.52/18.99 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (forall ((X $$unsorted)) (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 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(hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 20.52/18.99 ) 20.52/18.99 (instantiation (let ((_let_0 (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_157338))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_157338 $$unsorted) (BOUND_VARIABLE_157339 $$unsorted) (BOUND_VARIABLE_157340 $$unsorted)) (or (not (cancel_semigroup_add X_a)) (= (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_157340) (hAPP X_a X_a _let_0 BOUND_VARIABLE_157339)) (= (ti X_a BOUND_VARIABLE_157339) (ti X_a BOUND_VARIABLE_157340)))) )) 20.52/18.99 ( nat, (one_one nat), (one_one nat), (one_one nat) ) 20.52/18.99 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (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) ) 20.52/18.99 ( int, (hAPP nat int (hAPP 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) ) 20.52/18.99 ) 20.52/18.99 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less X_b))) (let ((_let_2 (fun X_a bool))) (let ((_let_3 (ord_less X_a))) (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_157374 $$unsorted) (BOUND_VARIABLE_157375 $$unsorted) (BOUND_VARIABLE_157376 $$unsorted) (BOUND_VARIABLE_157377 $$unsorted)) (or (not (order X_b)) (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_2 (ord_less_eq X_a) BOUND_VARIABLE_157375) (hAPP X_b X_a BOUND_VARIABLE_157376 BOUND_VARIABLE_157377)))) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_157377) BOUND_VARIABLE_157374))) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (or (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 X_2) Y_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_2 _let_3 (hAPP X_b X_a BOUND_VARIABLE_157376 X_2)) (hAPP X_b X_a BOUND_VARIABLE_157376 Y_2)))) )) (hBOOL (hAPP X_a bool (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_157375) (hAPP X_b X_a BOUND_VARIABLE_157376 BOUND_VARIABLE_157374)))) ))))) 20.52/18.99 ( 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)))), (zero_zero real), (sgn_sgn real), (zero_zero real) ) 20.52/18.99 ( real, real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), pi ) 20.52/18.99 ( real, real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int 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20.52/18.99 ) 20.52/18.99 (instantiation (let ((_let_0 (fun nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_157454 $$unsorted) (BOUND_VARIABLE_157455 $$unsorted)) (or (not (comm_monoid_add X_a)) (not (t2_space X_a)) (= (and (hBOOL (hAPP _let_0 bool (summable X_a) BOUND_VARIABLE_157454)) (= (hAPP _let_0 X_a (suminf X_a) BOUND_VARIABLE_157454) (ti X_a BOUND_VARIABLE_157455))) (hBOOL (hAPP X_a bool (hAPP _let_0 (fun X_a bool) (sums X_a) BOUND_VARIABLE_157454) BOUND_VARIABLE_157455)))) )) 20.52/18.99 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 20.52/18.99 ) 20.52/18.99 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_157479 $$unsorted) (BOUND_VARIABLE_157480 $$unsorted)) (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_157480))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_157479))) (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_157480) BOUND_VARIABLE_157479)))) )) 20.52/18.99 ( nat, (one_one nat), (one_one nat) ) 20.52/18.99 ( 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) ) 20.52/18.99 ( 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)))) ) 20.52/18.99 ) 20.52/18.99 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_157544 $$unsorted) (BOUND_VARIABLE_157545 $$unsorted)) (or (not (field_inverse_zero X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_157544) BOUND_VARIABLE_157545) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_157544)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_157545)))) )))) 20.52/18.99 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.99 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.52/18.99 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.52/18.99 ( 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))))))))) ) 20.52/18.99 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.52/18.99 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.52/18.99 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.52/18.99 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.52/18.99 ( 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))) ) 20.52/18.99 ( 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))) ) 20.52/18.99 ( 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))) ) 20.52/18.99 ) 20.52/18.99 (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))) ) 20.52/18.99 ( (zero_zero real) ) 20.52/18.99 ( pi ) 20.67/18.99 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/18.99 ( (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 pls)))) ) 20.67/18.99 ( (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) ) 20.67/18.99 ( (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))))) ) 20.67/18.99 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 20.67/18.99 ( (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))))) ) 20.67/18.99 ( (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)))) ) 20.67/19.00 ( skv_14 ) 20.67/19.00 ) 20.67/19.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157611 $$unsorted)) (or (not (linorder X_a)) (= (ti X_a BOUND_VARIABLE_157611) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_max X_a) BOUND_VARIABLE_157611) BOUND_VARIABLE_157611))) ) 20.67/19.00 ( bool, fFalse ) 20.67/19.00 ( bool, fTrue ) 20.67/19.00 ( real, pi ) 20.67/19.00 ( (fun nat bool), (even_odd_even nat) ) 20.67/19.00 ( (fun nat bool), prime ) 20.67/19.00 ( (fun nat nat), suc ) 20.67/19.00 ( (fun nat nat), (fact_fact nat) ) 20.67/19.00 ( (fun nat nat), (size_size nat) ) 20.67/19.00 ( (fun nat nat), fact ) 20.67/19.00 ( (fun nat nat), nat_size ) 20.67/19.00 ( int, pls ) 20.67/19.00 ( int, m ) 20.67/19.00 ( int, min_1 ) 20.67/19.00 ( int, s ) 20.67/19.00 ( int, s1 ) 20.67/19.00 ( int, t ) 20.67/19.00 ( (fun int bool), zprime ) 20.67/19.00 ( (fun int bool), nat_neg ) 20.67/19.00 ( (fun int bool), zEven ) 20.67/19.00 ( (fun int bool), nat_is_nat ) 20.67/19.00 ( (fun int bool), zOdd ) 20.67/19.00 ( (fun int bool), (even_odd_even int) ) 20.67/19.00 ( (fun int bool), twoSqu1091635170sum2sq ) 20.67/19.00 ( (fun int nat), nat_1 ) 20.67/19.00 ( (fun int nat), phi ) 20.67/19.00 ( (fun real real), sqrt ) 20.67/19.00 ( (fun real real), tan ) 20.67/19.00 ( (fun real real), cos ) 20.67/19.00 ( (fun real real), arccos ) 20.67/19.00 ( (fun real real), ln ) 20.67/19.00 ( (fun real real), sin ) 20.67/19.00 ( (fun real real), arctan ) 20.67/19.00 ( (fun real real), arcsin ) 20.67/19.00 ( complex, ii ) 20.67/19.00 ( (fun complex complex), cnj ) 20.67/19.00 ( (fun complex complex), expi ) 20.67/19.00 ( (fun nat real), (real_1 nat) ) 20.67/19.00 ( (fun nat real), cos_coeff ) 20.67/19.00 ( (fun nat real), sin_coeff ) 20.67/19.00 ( (fun int int), bit0 ) 20.67/19.00 ( (fun int int), bit1 ) 20.67/19.00 ( (fun int int), pred ) 20.67/19.00 ( (fun int int), succ ) 20.67/19.00 ( (fun int int), (fact_fact int) ) 20.67/19.00 ( (fun int int), zfact ) 20.67/19.00 ( (fun bool bool), fNot ) 20.67/19.00 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 20.67/19.00 ( (fun bool (fun bool bool)), fconj ) 20.67/19.00 ( (fun bool (fun bool bool)), fdisj ) 20.67/19.00 ( (fun bool (fun bool bool)), fimplies ) 20.67/19.00 ( (fun int (fun int bool)), sRStar ) 20.67/19.00 ( (fun int (fun int bool)), quadRes ) 20.67/19.00 ( (fun int (fun int bool)), norRRset ) 20.67/19.00 ( (fun int (fun int bool)), d22set ) 20.67/19.00 ( (fun int (fun int bool)), sr ) 20.67/19.00 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 20.67/19.00 ( (fun nat (fun nat nat)), nat_gcd ) 20.67/19.00 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 20.67/19.00 ( (fun nat (fun nat nat)), nat_lcm ) 20.67/19.00 ( (fun nat (fun real real)), root ) 20.67/19.00 ( (fun real (fun real real)), log ) 20.67/19.00 ( (fun real (fun real real)), powr ) 20.67/19.00 ( (fun nat (fun nat bool)), coprime ) 20.67/19.00 ( (fun (fun int bool) int), (the int) ) 20.67/19.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 20.67/19.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 20.67/19.00 ( (fun nat (fun nat (product_prod int int))), bezw ) 20.67/19.00 ( (fun (fun int bool) bool), nat_nat_set ) 20.67/19.00 ( (filter nat), sequentially ) 20.67/19.00 ( (fun (product_prod nat nat) bool), pred_nat ) 20.67/19.00 ( (fun (product_prod int int) bool), frac_1 ) 20.67/19.00 ( (fun real complex), cis ) 20.67/19.00 ( (fun complex real), im ) 20.67/19.00 ( (fun complex real), re ) 20.67/19.00 ( (fun complex real), arg ) 20.67/19.00 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 20.67/19.00 ( (fun int (fun int int)), int_gcd ) 20.67/19.00 ( (fun int (fun int int)), multInv ) 20.67/19.00 ( (fun int (fun int int)), legacy_zgcd ) 20.67/19.00 ( (fun int (fun int int)), z3mod ) 20.67/19.00 ( (fun int (fun int int)), inv ) 20.67/19.00 ( (fun int (fun int int)), (gcd_gcd int) ) 20.67/19.00 ( (fun int (fun int int)), standardRes ) 20.67/19.00 ( (fun int (fun int int)), legendre ) 20.67/19.00 ( (fun int (fun int int)), nat_tsub ) 20.67/19.00 ( (fun int (fun int int)), z3div ) 20.67/19.00 ( (fun int (fun int int)), int_lcm ) 20.67/19.00 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 20.67/19.00 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 20.67/19.00 ( (fun int (fun (fun int bool) bool)), rsetR ) 20.67/19.00 ( (fun int (fun (fun int bool) bool)), resSet ) 20.67/19.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 20.67/19.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 20.67/19.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 20.67/19.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 20.67/19.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 20.67/19.00 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 20.67/19.00 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 20.67/19.00 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 20.67/19.00 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 20.67/19.00 ( (fun int (fun int (product_prod int int))), negDivAlg ) 20.67/19.00 ( (fun int (fun int (product_prod int int))), divmod_int ) 20.67/19.00 ( (fun int (fun int (product_prod int int))), posDivAlg ) 20.67/19.00 ( (fun int (fun int (product_prod int int))), pdivmod ) 20.67/19.00 ( (fun int (fun int (product_prod int int))), norm_frac ) 20.67/19.00 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 20.67/19.00 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 20.67/19.00 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 20.67/19.00 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 20.67/19.00 ( (fun real nat), natfloor ) 20.67/19.00 ( (fun real nat), natceiling ) 20.67/19.00 ( (fun int quickcheck_code_int), quickcheck_of_int ) 20.67/19.00 ( (fun int (fun int (fun int bool))), wset ) 20.67/19.00 ( (fun int (fun int (fun int bool))), bnorRset ) 20.67/19.00 ( (fun int (fun int (fun int bool))), zcong ) 20.67/19.00 ( (fun int (fun int (fun int bool))), noXRRset ) 20.67/19.00 ( (fun int (fun int (fun int bool))), zcongm ) 20.67/19.00 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 20.67/19.00 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 20.67/19.00 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 20.67/19.00 ( (fun int real), (real_1 int) ) 20.67/19.00 ( (fun complex nat), (size_size complex) ) 20.67/19.00 ( (fun complex nat), complex_size ) 20.67/19.00 ( (fun int (list int)), quickc666637781d_zero ) 20.67/19.00 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 20.67/19.00 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 20.67/19.00 ( (fun (product_prod int int) rat), frct ) 20.67/19.00 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 20.67/19.00 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 20.67/19.00 ( (fun (fun nat rat) bool), vanishes ) 20.67/19.00 ( (fun int (fun int rat)), fract ) 20.67/19.00 ( (fun code_code_numeral int), code_int_of ) 20.67/19.00 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 20.67/19.00 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 20.67/19.00 ( (fun code_code_numeral nat), code_c271388182l_size ) 20.67/19.00 ( (fun real (fun real complex)), complex_1 ) 20.67/19.00 ( (fun real (fun real complex)), rcis ) 20.67/19.00 ( (fun int (fun nat nat)), nat_aux ) 20.67/19.00 ( (fun rat real), ratreal ) 20.67/19.00 ( (fun quickcheck_code_int int), quickcheck_int_of ) 20.67/19.00 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 20.67/19.00 ( (fun rat (product_prod int int)), quotient_of ) 20.67/19.00 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 20.67/19.00 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 20.67/19.00 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 20.67/19.00 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 20.67/19.00 ) 20.67/19.00 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_157629 $$unsorted) (BOUND_VARIABLE_157630 $$unsorted)) (or (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_157630) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_157629) _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_157630) BOUND_VARIABLE_157629)) _let_3))) ))))) 20.67/19.00 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.00 ( 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))))) ) 20.67/19.00 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.00 ( 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)))) ) 20.67/19.00 ( 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))) ) 20.67/19.00 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.00 ( 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))) ) 20.67/19.00 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.00 ( complex, ii, ii ) 20.67/19.00 ( 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)) ) 20.67/19.00 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.00 ) 20.67/19.00 (instantiation (let ((_let_0 (filter real))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (of_real X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_157677 $$unsorted)) (or (not (real_algebra_1 X_a)) (not (real_normed_vector X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 (hAPP (fun real X_a) (fun X_a _let_1) (tendsto real X_a) _let_2) (hAPP real X_a _let_2 BOUND_VARIABLE_157677)) (hAPP real _let_0 (at real) BOUND_VARIABLE_157677)))) )))) 20.67/19.00 ( complex, pi ) 20.67/19.00 ( complex, (hAPP int real (number_number_of real) min_1) ) 20.67/19.00 ( complex, (hAPP real real (uminus_uminus real) (one_one real)) ) 20.67/19.00 ) 20.67/19.00 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_157699))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_157699 $$unsorted) (BOUND_VARIABLE_157700 $$unsorted) (BOUND_VARIABLE_157701 $$unsorted)) (or (not (order X_a)) (not (= (ti X_a BOUND_VARIABLE_157700) (ti X_a BOUND_VARIABLE_157701))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_157701))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_157700))) )) 20.67/19.00 ( real, (zero_zero real), pi, pi ) 20.67/19.00 ( int, (zero_zero int), min_1, min_1 ) 20.67/19.00 ( int, (one_one int), m, m ) 20.67/19.00 ( int, min_1, s, s ) 20.67/19.00 ) 20.67/19.00 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (ord_less int))) (let ((_let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (forall ((P_4 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 _let_3) P_4))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) P_4) zOdd))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (zero_zero int)) (hAPP int int (hAPP int _let_1 (div_div int) (hAPP int int (hAPP int _let_1 (minus_minus int) P_4) (one_one int))) _let_3)))) ))))) 20.67/19.00 ( (one_one int) ) 20.67/19.00 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.00 ) 20.67/19.00 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (let ((_let_3 (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) _let_2)))) (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) (one_one real)))) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_3 X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) _let_2))) (not (forall ((Y_2 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_3 Y_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_2) _let_2))) (not (= Y (hAPP real real sin Y_2))) (= X_2 Y_2)) )) (not (= Y (hAPP real real sin X_2)))) ))) ))))) 20.67/19.00 ( (zero_zero real) ) 20.67/19.00 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.00 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.00 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.00 ( skv_14 ) 20.67/19.00 ) 20.67/19.00 (instantiation (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (ord_less_eq X_a))) (let ((_let_3 (fun nat X_a))) (let ((_let_4 (power_power X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_157769 $$unsorted) (BOUND_VARIABLE_157770 $$unsorted)) (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_157769) _let_0)) (hAPP nat X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_157770) _let_0)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 (zero_zero X_a)) BOUND_VARIABLE_157770))) (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_157769) BOUND_VARIABLE_157770))) )))))) 20.67/19.00 ( real, (zero_zero real), pi ) 20.67/19.00 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.00 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.00 ( real, (zero_zero real), skv_6 ) 20.67/19.00 ( real, (zero_zero real), skv_11 ) 20.67/19.00 ( real, (zero_zero real), skv_12 ) 20.67/19.00 ( real, (zero_zero real), skv_14 ) 20.67/19.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 20.67/19.00 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.00 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 20.67/19.00 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.00 ( int, (zero_zero int), (one_one int) ) 20.67/19.00 ( int, (zero_zero int), min_1 ) 20.67/19.00 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.00 ( int, (zero_zero int), s ) 20.67/19.00 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 20.67/19.00 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.67/19.00 ( int, (zero_zero int), skv_3 ) 20.67/19.00 ( int, (zero_zero int), skv_9 ) 20.67/19.00 ( int, (one_one int), t ) 20.67/19.00 ( int, min_1, pls ) 20.67/19.00 ( int, min_1, min_1 ) 20.67/19.00 ) 20.67/19.00 (instantiation (let ((_let_0 (zero_zero real))) (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) Y) _let_0))) (= _let_0 (hAPP real real cos (hAPP complex real arg (hAPP real complex (hAPP real (fun real complex) complex_1 _let_0) Y))))) )) 20.67/19.00 ( (zero_zero real) ) 20.67/19.00 ( (one_one real) ) 20.67/19.00 ( pi ) 20.67/19.00 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.00 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 20.67/19.00 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.00 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 20.67/19.00 ) 20.67/19.00 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_157806 $$unsorted) (BOUND_VARIABLE_157807 $$unsorted)) (or (not (semiring_div X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_157807)) (= (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_157807) BOUND_VARIABLE_157806)) BOUND_VARIABLE_157807) (ti X_a BOUND_VARIABLE_157806))) )) 20.67/19.01 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.01 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 20.67/19.01 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.01 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.01 ( 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))) ) 20.67/19.01 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.01 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.01 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.01 ( complex, ii, ii ) 20.67/19.01 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 20.67/19.01 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.01 ) 20.67/19.01 (instantiation (let ((_let_0 (fun int int))) (forall ((A_1 $$unsorted) (B $$unsorted)) (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))))) )) 20.67/19.01 ( (zero_zero int), (one_one int) ) 20.67/19.01 ( (one_one int), (one_one int) ) 20.67/19.01 ) 20.67/19.01 (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))) ) 20.67/19.01 ( (zero_zero int), (one_one int) ) 20.67/19.01 ( (one_one int), (one_one int) ) 20.67/19.01 ) 20.67/19.01 (instantiation (let ((_let_0 (exp X_a))) (forall ((X_a $$unsorted)) (or (not (banach X_a)) (not (real_normed_field X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 20.67/19.01 ( bool ) 20.67/19.01 ( real ) 20.67/19.01 ( nat ) 20.67/19.01 ( (fun nat bool) ) 20.67/19.01 ( int ) 20.67/19.01 ( (fun int bool) ) 20.67/19.01 ( (fun real bool) ) 20.67/19.01 ( (fun real real) ) 20.67/19.01 ( complex ) 20.67/19.01 ( (fun nat real) ) 20.67/19.01 ( (fun int int) ) 20.67/19.01 ( (fun int (fun int bool)) ) 20.67/19.01 ( (product_prod int int) ) 20.67/19.01 ( (fun (product_prod int int) bool) ) 20.67/19.01 ( code_code_numeral ) 20.67/19.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 20.67/19.01 ( (fun (product_prod int int) int) ) 20.67/19.01 ( (fun int (fun int (fun int bool))) ) 20.67/19.01 ( (fun int real) ) 20.67/19.01 ) 20.67/19.01 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 (plus_plus int) A_1) B))) (let ((_let_4 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) _let_3)))) (let ((_let_5 (hAPP int (fun int _let_2) negDivAlg A_1))) (let ((_let_6 (hAPP int _let_2 _let_5 B))) (forall ((A_1 $$unsorted) (B $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) B))) (and (or (not _let_4) (= (hAPP int _let_2 (hAPP int (fun int _let_2) (product_Pair int int) (hAPP int int _let_1 min_1)) _let_3) _let_6)) (or _let_4 (= _let_6 (hAPP _let_2 _let_2 (hAPP int (fun _let_2 _let_2) adjust B) (hAPP int _let_2 _let_5 (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int _let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) B))))))) )))))))) 20.67/19.01 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 20.67/19.01 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 20.67/19.01 ) 20.67/19.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157868 $$unsorted) (BOUND_VARIABLE_157869 $$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_157868)) (hAPP int int (number_number_of int) BOUND_VARIABLE_157869))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_157868) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_157869))))) ) 20.67/19.01 ( 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 int bit0 (hAPP int int bit1 pls)) ) 20.67/19.01 ( real, skv_14, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.67/19.01 ( int, (zero_zero int), pls ) 20.67/19.01 ( int, (zero_zero int), (hAPP int int bit1 pls) ) 20.67/19.01 ( int, (zero_zero int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.67/19.01 ( int, (zero_zero int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 20.67/19.01 ( int, min_1, pls ) 20.67/19.01 ) 20.67/19.01 (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))) ) 20.67/19.01 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.01 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.01 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.01 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.01 ) 20.67/19.01 (instantiation (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))))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP int bool (even_odd_even int) X))) (= (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) X) (one_one int))) _let_2) (hAPP int int (hAPP int _let_0 _let_1 X) _let_2))) )))) 20.67/19.01 ( (zero_zero int) ) 20.67/19.01 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 20.67/19.01 ( (one_one int) ) 20.67/19.01 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.01 ) 20.67/19.01 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (hAPP X_a _let_0 (ord_less_eq X_a) _let_1))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_157969 $$unsorted) (BOUND_VARIABLE_157970 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_157970))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_1) BOUND_VARIABLE_157969))) (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_157970) BOUND_VARIABLE_157969)))) )))) 20.67/19.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 20.67/19.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 20.67/19.01 ( 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))) ) 20.67/19.01 ( 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)))) ) 20.67/19.01 ( 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)))) ) 20.67/19.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 20.67/19.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 20.67/19.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 20.67/19.01 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 20.67/19.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 20.67/19.01 ( 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) ) 20.67/19.01 ) 20.67/19.01 (instantiation (let ((_let_0 (one_one X_a))) (let ((_let_1 (ti X_a BOUND_VARIABLE_157997))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_157997 $$unsorted)) (or (not (ring_11004092258visors X_a)) (= (or (= _let_0 _let_1) (= (hAPP X_a X_a (uminus_uminus X_a) _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_157997) BOUND_VARIABLE_157997)))) ))) 20.67/19.01 ( bool, fFalse ) 20.67/19.01 ( bool, fTrue ) 20.67/19.01 ( real, pi ) 20.67/19.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.01 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 20.67/19.01 ( (fun nat bool), (even_odd_even nat) ) 20.67/19.01 ( (fun nat bool), prime ) 20.67/19.01 ( (fun nat nat), suc ) 20.67/19.01 ( (fun nat nat), (fact_fact nat) ) 20.67/19.01 ( (fun nat nat), (size_size nat) ) 20.67/19.01 ( (fun nat nat), fact ) 20.67/19.01 ( (fun nat nat), nat_size ) 20.67/19.01 ( int, pls ) 20.67/19.01 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.01 ( int, m ) 20.67/19.01 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.01 ( int, min_1 ) 20.67/19.01 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.01 ( int, s ) 20.67/19.01 ( int, s1 ) 20.67/19.01 ( int, t ) 20.67/19.01 ( (fun int bool), zprime ) 20.67/19.01 ( (fun int bool), nat_neg ) 20.67/19.01 ( (fun int bool), zEven ) 20.67/19.01 ( (fun int bool), nat_is_nat ) 20.67/19.01 ( (fun int bool), zOdd ) 20.67/19.01 ( (fun int bool), (even_odd_even int) ) 20.67/19.01 ( (fun int bool), twoSqu1091635170sum2sq ) 20.67/19.01 ( (fun int nat), nat_1 ) 20.67/19.01 ( (fun int nat), phi ) 20.67/19.01 ( (fun real real), sqrt ) 20.67/19.01 ( (fun real real), tan ) 20.67/19.01 ( (fun real real), cos ) 20.67/19.01 ( (fun real real), arccos ) 20.67/19.01 ( (fun real real), ln ) 20.67/19.01 ( (fun real real), sin ) 20.67/19.01 ( (fun real real), arctan ) 20.67/19.01 ( (fun real real), arcsin ) 20.67/19.01 ( complex, ii ) 20.67/19.01 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.01 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 20.67/19.01 ( (fun complex complex), cnj ) 20.67/19.01 ( (fun complex complex), expi ) 20.67/19.01 ( (fun nat real), (real_1 nat) ) 20.67/19.01 ( (fun nat real), cos_coeff ) 20.67/19.01 ( (fun nat real), sin_coeff ) 20.67/19.01 ( (fun int int), bit0 ) 20.67/19.01 ( (fun int int), bit1 ) 20.67/19.01 ( (fun int int), pred ) 20.67/19.01 ( (fun int int), succ ) 20.67/19.01 ( (fun int int), (fact_fact int) ) 20.67/19.01 ( (fun int int), zfact ) 20.67/19.01 ( (fun bool bool), fNot ) 20.67/19.01 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 20.67/19.01 ( (fun bool (fun bool bool)), fconj ) 20.67/19.01 ( (fun bool (fun bool bool)), fdisj ) 20.67/19.01 ( (fun bool (fun bool bool)), fimplies ) 20.67/19.01 ( (fun int (fun int bool)), sRStar ) 20.67/19.01 ( (fun int (fun int bool)), quadRes ) 20.67/19.01 ( (fun int (fun int bool)), norRRset ) 20.67/19.01 ( (fun int (fun int bool)), d22set ) 20.67/19.01 ( (fun int (fun int bool)), sr ) 20.67/19.01 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 20.67/19.01 ( (fun nat (fun nat nat)), nat_gcd ) 20.67/19.01 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 20.67/19.01 ( (fun nat (fun nat nat)), nat_lcm ) 20.67/19.01 ( (fun nat (fun real real)), root ) 20.67/19.01 ( (fun real (fun real real)), log ) 20.67/19.01 ( (fun real (fun real real)), powr ) 20.67/19.01 ( (fun nat (fun nat bool)), coprime ) 20.67/19.01 ( (fun (fun int bool) int), (the int) ) 20.67/19.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 20.67/19.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 20.67/19.01 ( (fun nat (fun nat (product_prod int int))), bezw ) 20.67/19.01 ( (fun (fun int bool) bool), nat_nat_set ) 20.67/19.01 ( (filter nat), sequentially ) 20.67/19.01 ( (fun (product_prod nat nat) bool), pred_nat ) 20.67/19.01 ( (fun (product_prod int int) bool), frac_1 ) 20.67/19.01 ( (fun real complex), cis ) 20.67/19.01 ( (fun complex real), im ) 20.67/19.01 ( (fun complex real), re ) 20.67/19.01 ( (fun complex real), arg ) 20.67/19.01 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 20.67/19.01 ( (fun int (fun int int)), int_gcd ) 20.67/19.01 ( (fun int (fun int int)), multInv ) 20.67/19.01 ( (fun int (fun int int)), legacy_zgcd ) 20.67/19.01 ( (fun int (fun int int)), z3mod ) 20.67/19.01 ( (fun int (fun int int)), inv ) 20.67/19.01 ( (fun int (fun int int)), (gcd_gcd int) ) 20.67/19.01 ( (fun int (fun int int)), standardRes ) 20.67/19.01 ( (fun int (fun int int)), legendre ) 20.67/19.01 ( (fun int (fun int int)), nat_tsub ) 20.67/19.01 ( (fun int (fun int int)), z3div ) 20.67/19.01 ( (fun int (fun int int)), int_lcm ) 20.67/19.01 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 20.67/19.01 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 20.67/19.01 ( (fun int (fun (fun int bool) bool)), rsetR ) 20.67/19.01 ( (fun int (fun (fun int bool) bool)), resSet ) 20.67/19.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 20.67/19.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 20.67/19.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 20.67/19.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 20.67/19.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 20.67/19.01 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 20.67/19.01 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 20.67/19.01 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 20.67/19.01 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 20.67/19.01 ( (fun int (fun int (product_prod int int))), negDivAlg ) 20.67/19.01 ( (fun int (fun int (product_prod int int))), divmod_int ) 20.67/19.01 ( (fun int (fun int (product_prod int int))), posDivAlg ) 20.67/19.01 ( (fun int (fun int (product_prod int int))), pdivmod ) 20.67/19.01 ( (fun int (fun int (product_prod int int))), norm_frac ) 20.67/19.01 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 20.67/19.01 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 20.67/19.01 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 20.67/19.01 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 20.67/19.01 ( (fun real nat), natfloor ) 20.67/19.01 ( (fun real nat), natceiling ) 20.67/19.01 ( (fun int quickcheck_code_int), quickcheck_of_int ) 20.67/19.01 ( (fun int (fun int (fun int bool))), wset ) 20.67/19.01 ( (fun int (fun int (fun int bool))), bnorRset ) 20.67/19.02 ( (fun int (fun int (fun int bool))), zcong ) 20.67/19.02 ( (fun int (fun int (fun int bool))), noXRRset ) 20.67/19.02 ( (fun int (fun int (fun int bool))), zcongm ) 20.67/19.02 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 20.67/19.02 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 20.67/19.02 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 20.67/19.02 ( (fun int real), (real_1 int) ) 20.67/19.02 ( (fun complex nat), (size_size complex) ) 20.67/19.02 ( (fun complex nat), complex_size ) 20.67/19.02 ( (fun int (list int)), quickc666637781d_zero ) 20.67/19.02 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 20.67/19.02 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 20.67/19.02 ( (fun (product_prod int int) rat), frct ) 20.67/19.02 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 20.67/19.02 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 20.67/19.02 ( (fun (fun nat rat) bool), vanishes ) 20.67/19.02 ( (fun int (fun int rat)), fract ) 20.67/19.02 ( (fun code_code_numeral int), code_int_of ) 20.67/19.02 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 20.67/19.02 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 20.67/19.02 ( (fun code_code_numeral nat), code_c271388182l_size ) 20.67/19.02 ( (fun real (fun real complex)), complex_1 ) 20.67/19.02 ( (fun real (fun real complex)), rcis ) 20.67/19.02 ( (fun int (fun nat nat)), nat_aux ) 20.67/19.02 ( (fun rat real), ratreal ) 20.67/19.02 ( (fun quickcheck_code_int int), quickcheck_int_of ) 20.67/19.02 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 20.67/19.02 ( (fun rat (product_prod int int)), quotient_of ) 20.67/19.02 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 20.67/19.02 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 20.67/19.02 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 20.67/19.02 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 20.67/19.02 ) 20.67/19.02 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_158058 $$unsorted) (BOUND_VARIABLE_158059 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP nat X_a (hAPP X_a _let_4 _let_5 (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_158058) BOUND_VARIABLE_158059)) _let_1) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 (hAPP X_a X_a (hAPP X_a _let_2 (plus_plus X_a) (hAPP nat X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_158058) _let_1)) (hAPP nat X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_158059) _let_1))) (hAPP X_a X_a (hAPP X_a _let_2 _let_6 (hAPP X_a X_a (hAPP X_a _let_2 _let_6 (hAPP int X_a (number_number_of X_a) _let_0)) BOUND_VARIABLE_158058)) BOUND_VARIABLE_158059)))) )))))))) 20.67/19.02 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 20.67/19.02 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 20.67/19.02 ( complex, (hAPP real complex (of_real complex) pi), ii ) 20.67/19.02 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 20.67/19.02 ) 20.67/19.02 (instantiation (let ((_let_0 (one_one int))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) Ma))) (= (= _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) Ma) N_1)) (and (= _let_0 (ti int N_1)) (= _let_0 (ti int Ma))))) )) 20.67/19.02 ( (zero_zero int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.02 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.02 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.02 ( skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.02 ) 20.67/19.02 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (forall ((X $$unsorted)) (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)))) )))) 20.67/19.02 ( (zero_zero real) ) 20.67/19.02 ( (one_one real) ) 20.67/19.02 ( pi ) 20.67/19.02 ( (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)))) ) 20.67/19.02 ( (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) ) 20.67/19.02 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 20.67/19.02 ( (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))))) ) 20.67/19.02 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 20.67/19.02 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.02 ( (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))))) ) 20.67/19.02 ( (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)))) ) 20.67/19.02 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 20.67/19.02 ) 20.67/19.02 (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))) ) 20.67/19.02 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.02 ) 20.67/19.02 (instantiation (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) Y))) (not (forall ((X_2 $$unsorted)) (not (= Y (hAPP real real (exp real) X_2))) ))) ) 20.67/19.02 ( pi ) 20.67/19.02 ( (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)))) ) 20.67/19.02 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.02 ( skv_2 ) 20.67/19.02 ( skv_10 ) 20.67/19.02 ( skv_13 ) 20.67/19.02 ) 20.67/19.02 (instantiation (forall ((W $$unsorted)) (= (hAPP int int (number_number_of int) W) (hAPP int int (ring_1_of_int int) W)) ) 20.67/19.02 ( pls ) 20.67/19.02 ( (hAPP int int bit1 pls) ) 20.67/19.02 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.67/19.02 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.02 ( min_1 ) 20.67/19.02 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 20.67/19.02 ) 20.67/19.02 (instantiation (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_158293))) (let ((_let_3 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_158295))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_158292 $$unsorted) (BOUND_VARIABLE_158293 $$unsorted) (BOUND_VARIABLE_158294 $$unsorted) (BOUND_VARIABLE_158295 $$unsorted)) (or (not (topological_space X_a)) (not (topological_space X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 _let_2 BOUND_VARIABLE_158294) _let_3))) (not (= (ti X_b BOUND_VARIABLE_158292) (ti X_b BOUND_VARIABLE_158294))) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 _let_2 BOUND_VARIABLE_158292) _let_3))) ))))) 20.67/19.02 ( real, real, pi, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.02 ) 20.67/19.02 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (product_Pair int int))) (let ((_let_5 (fun _let_2 bool))) (let ((_let_6 (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_2) B_1)))) (let ((_let_7 (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B_1) _let_1)))) (let ((_let_8 (hAPP int _let_2 (hAPP int _let_3 posDivAlg A_2) B_1))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP _let_2 bool (hAPP (fun _let_2 _let_5) _let_5 (accp _let_2) posDivAlg_rel) (hAPP int _let_2 (hAPP int _let_3 _let_4 A_2) B_1)))) (and (or _let_6 _let_7 (= (hAPP _let_2 _let_2 (hAPP int (fun _let_2 _let_2) adjust B_1) (hAPP int _let_2 (hAPP int _let_3 posDivAlg A_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_1))) _let_8)) (or (and (not _let_7) (not _let_6)) (= _let_8 (hAPP int _let_2 (hAPP int _let_3 _let_4 _let_1) A_2))))) )))))))))) 20.67/19.02 ( (zero_zero int), (zero_zero int) ) 20.67/19.02 ( (zero_zero int), (one_one int) ) 20.67/19.02 ( (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))) ) 20.67/19.02 ( (zero_zero int), min_1 ) 20.67/19.02 ( (one_one int), (one_one int) ) 20.67/19.02 ( min_1, (zero_zero int) ) 20.67/19.02 ( min_1, min_1 ) 20.67/19.02 ( s, (one_one int) ) 20.67/19.02 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.02 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 20.67/19.02 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 20.67/19.02 ( t, (zero_zero int) ) 20.67/19.02 ( t, (one_one int) ) 20.67/19.02 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.02 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.02 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.02 ) 20.67/19.02 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_158338 $$unsorted)) (or (not (linordered_idom X_a)) (= (= _let_0 (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_158338)) (= _let_0 (ti X_a BOUND_VARIABLE_158338)))) )) 20.67/19.02 ( bool, fFalse ) 20.67/19.02 ( bool, fTrue ) 20.67/19.02 ( real, (zero_zero real) ) 20.67/19.02 ( real, pi ) 20.67/19.02 ( (fun nat bool), (even_odd_even nat) ) 20.67/19.02 ( (fun nat bool), prime ) 20.67/19.02 ( (fun nat nat), suc ) 20.67/19.02 ( (fun nat nat), (fact_fact nat) ) 20.67/19.02 ( (fun nat nat), (size_size nat) ) 20.67/19.02 ( (fun nat nat), fact ) 20.67/19.02 ( (fun nat nat), nat_size ) 20.67/19.02 ( int, pls ) 20.67/19.02 ( int, m ) 20.67/19.02 ( int, min_1 ) 20.67/19.02 ( int, s ) 20.67/19.02 ( int, s1 ) 20.67/19.02 ( int, t ) 20.67/19.02 ( (fun int bool), zprime ) 20.67/19.02 ( (fun int bool), nat_neg ) 20.67/19.02 ( (fun int bool), zEven ) 20.67/19.02 ( (fun int bool), nat_is_nat ) 20.67/19.02 ( (fun int bool), zOdd ) 20.67/19.02 ( (fun int bool), (even_odd_even int) ) 20.67/19.02 ( (fun int bool), twoSqu1091635170sum2sq ) 20.67/19.02 ( (fun int nat), nat_1 ) 20.67/19.02 ( (fun int nat), phi ) 20.67/19.02 ( (fun real real), sqrt ) 20.67/19.02 ( (fun real real), tan ) 20.67/19.02 ( (fun real real), cos ) 20.67/19.02 ( (fun real real), arccos ) 20.67/19.02 ( (fun real real), ln ) 20.67/19.02 ( (fun real real), sin ) 20.67/19.02 ( (fun real real), arctan ) 20.67/19.02 ( (fun real real), arcsin ) 20.67/19.02 ( complex, ii ) 20.67/19.02 ( (fun complex complex), cnj ) 20.67/19.02 ( (fun complex complex), expi ) 20.67/19.02 ( (fun nat real), (real_1 nat) ) 20.67/19.02 ( (fun nat real), cos_coeff ) 20.67/19.02 ( (fun nat real), sin_coeff ) 20.67/19.02 ( (fun int int), bit0 ) 20.67/19.02 ( (fun int int), bit1 ) 20.67/19.02 ( (fun int int), pred ) 20.67/19.02 ( (fun int int), succ ) 20.67/19.02 ( (fun int int), (fact_fact int) ) 20.67/19.02 ( (fun int int), zfact ) 20.67/19.02 ( rat, (zero_zero rat) ) 20.67/19.02 ( (fun bool bool), fNot ) 20.67/19.02 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 20.67/19.02 ( (fun bool (fun bool bool)), fconj ) 20.67/19.02 ( (fun bool (fun bool bool)), fdisj ) 20.67/19.02 ( (fun bool (fun bool bool)), fimplies ) 20.67/19.02 ( (fun int (fun int bool)), sRStar ) 20.67/19.02 ( (fun int (fun int bool)), quadRes ) 20.67/19.02 ( (fun int (fun int bool)), norRRset ) 20.67/19.02 ( (fun int (fun int bool)), d22set ) 20.67/19.02 ( (fun int (fun int bool)), sr ) 20.67/19.02 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 20.67/19.02 ( (fun nat (fun nat nat)), nat_gcd ) 20.67/19.02 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 20.67/19.02 ( (fun nat (fun nat nat)), nat_lcm ) 20.67/19.02 ( (fun nat (fun real real)), root ) 20.67/19.02 ( (fun real (fun real real)), log ) 20.67/19.02 ( (fun real (fun real real)), powr ) 20.67/19.02 ( (fun nat (fun nat bool)), coprime ) 20.67/19.02 ( (fun (fun int bool) int), (the int) ) 20.67/19.02 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 20.67/19.02 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 20.67/19.02 ( (fun nat (fun nat (product_prod int int))), bezw ) 20.67/19.02 ( (fun (fun int bool) bool), nat_nat_set ) 20.67/19.02 ( (filter nat), sequentially ) 20.67/19.02 ( (fun (product_prod nat nat) bool), pred_nat ) 20.67/19.02 ( (fun (product_prod int int) bool), frac_1 ) 20.67/19.02 ( (fun real complex), cis ) 20.67/19.02 ( (fun complex real), im ) 20.67/19.02 ( (fun complex real), re ) 20.67/19.02 ( (fun complex real), arg ) 20.67/19.02 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 20.67/19.02 ( (fun int (fun int int)), int_gcd ) 20.67/19.02 ( (fun int (fun int int)), multInv ) 20.67/19.02 ( (fun int (fun int int)), legacy_zgcd ) 20.67/19.02 ( (fun int (fun int int)), z3mod ) 20.67/19.02 ( (fun int (fun int int)), inv ) 20.67/19.02 ( (fun int (fun int int)), (gcd_gcd int) ) 20.67/19.02 ( (fun int (fun int int)), standardRes ) 20.67/19.02 ( (fun int (fun int int)), legendre ) 20.67/19.02 ( (fun int (fun int int)), nat_tsub ) 20.67/19.02 ( (fun int (fun int int)), z3div ) 20.67/19.02 ( (fun int (fun int int)), int_lcm ) 20.67/19.02 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 20.67/19.02 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 20.67/19.02 ( (fun int (fun (fun int bool) bool)), rsetR ) 20.67/19.02 ( (fun int (fun (fun int bool) bool)), resSet ) 20.67/19.02 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 20.67/19.02 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 20.67/19.02 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 20.67/19.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 20.67/19.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 20.67/19.03 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 20.67/19.03 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 20.67/19.03 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 20.67/19.03 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 20.67/19.03 ( (fun int (fun int (product_prod int int))), negDivAlg ) 20.67/19.03 ( (fun int (fun int (product_prod int int))), divmod_int ) 20.67/19.03 ( (fun int (fun int (product_prod int int))), posDivAlg ) 20.67/19.03 ( (fun int (fun int (product_prod int int))), pdivmod ) 20.67/19.03 ( (fun int (fun int (product_prod int int))), norm_frac ) 20.67/19.03 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 20.67/19.03 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 20.67/19.03 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 20.67/19.03 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 20.67/19.03 ( (fun real nat), natfloor ) 20.67/19.03 ( (fun real nat), natceiling ) 20.67/19.03 ( (fun int quickcheck_code_int), quickcheck_of_int ) 20.67/19.03 ( (fun int (fun int (fun int bool))), wset ) 20.67/19.03 ( (fun int (fun int (fun int bool))), bnorRset ) 20.67/19.03 ( (fun int (fun int (fun int bool))), zcong ) 20.67/19.03 ( (fun int (fun int (fun int bool))), noXRRset ) 20.67/19.03 ( (fun int (fun int (fun int bool))), zcongm ) 20.67/19.03 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 20.67/19.03 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 20.67/19.03 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 20.67/19.03 ( (fun int real), (real_1 int) ) 20.67/19.03 ( (fun complex nat), (size_size complex) ) 20.67/19.03 ( (fun complex nat), complex_size ) 20.67/19.03 ( (fun int (list int)), quickc666637781d_zero ) 20.67/19.03 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 20.67/19.03 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 20.67/19.03 ( (fun (product_prod int int) rat), frct ) 20.67/19.03 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 20.67/19.03 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 20.67/19.03 ( (fun (fun nat rat) bool), vanishes ) 20.67/19.03 ( (fun int (fun int rat)), fract ) 20.67/19.03 ( (fun code_code_numeral int), code_int_of ) 20.67/19.03 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 20.67/19.03 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 20.67/19.03 ( (fun code_code_numeral nat), code_c271388182l_size ) 20.67/19.03 ( (fun real (fun real complex)), complex_1 ) 20.67/19.03 ( (fun real (fun real complex)), rcis ) 20.67/19.03 ( (fun int (fun nat nat)), nat_aux ) 20.67/19.03 ( (fun rat real), ratreal ) 20.67/19.03 ( (fun quickcheck_code_int int), quickcheck_int_of ) 20.67/19.03 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 20.67/19.03 ( (fun rat (product_prod int int)), quotient_of ) 20.67/19.03 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 20.67/19.03 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 20.67/19.03 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 20.67/19.03 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 20.67/19.03 ) 20.67/19.03 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_158361 $$unsorted) (BOUND_VARIABLE_158362 $$unsorted)) (or (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_158362) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_158361) _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_158362) BOUND_VARIABLE_158361)) _let_3))) ))))) 20.67/19.03 ( 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 bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 20.67/19.03 ( int, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.03 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 20.67/19.03 ) 20.67/19.03 (instantiation (let ((_let_0 (fun int rat))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (hAPP rat rat (uminus_uminus rat) (hAPP int rat (hAPP int _let_0 fract A_1) B)) (hAPP int rat (hAPP int _let_0 fract (hAPP int int (uminus_uminus int) A_1)) B)) )) 20.67/19.03 ( pls, (one_one int) ) 20.67/19.03 ) 20.67/19.03 (instantiation (forall ((X_a $$unsorted)) (or (not (real_algebra_1 X_a)) (= (hAPP real X_a (of_real X_a) (zero_zero real)) (zero_zero X_a))) ) 20.67/19.03 ( real ) 20.67/19.03 ( nat ) 20.67/19.03 ( int ) 20.67/19.03 ( complex ) 20.67/19.03 ( rat ) 20.67/19.03 ( quickcheck_code_int ) 20.67/19.03 ( code_code_numeral ) 20.67/19.03 ) 20.67/19.03 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (forall ((B $$unsorted) (A_1 $$unsorted)) (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))) ))) 20.67/19.03 ( (zero_zero int), (zero_zero int) ) 20.67/19.03 ( (zero_zero int), (one_one int) ) 20.67/19.03 ( (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))) ) 20.67/19.03 ( (zero_zero int), min_1 ) 20.67/19.03 ( min_1, (zero_zero int) ) 20.67/19.03 ( min_1, min_1 ) 20.67/19.03 ( 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))) ) 20.67/19.03 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 20.67/19.03 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 20.67/19.03 ( t, (zero_zero int) ) 20.67/19.03 ( t, (one_one int) ) 20.67/19.03 ( 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))) ) 20.67/19.03 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.03 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.03 ) 20.67/19.03 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (let ((_let_2 (filter real))) (let ((_let_3 (fun _let_2 bool))) (forall ((F $$unsorted) (L $$unsorted) (C_1 $$unsorted)) (or (not (hBOOL (hAPP _let_2 bool (hAPP real _let_3 (hAPP _let_0 (fun real _let_3) (tendsto real real) F) L) (hAPP real _let_2 (at real) C_1)))) (not (hBOOL (hAPP real bool _let_1 L))) (not (forall ((R_2 $$unsorted)) (or (not (forall ((X_2 $$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 _let_0 (minus_minus real) C_1) X_2))) R_2))) (= C_1 X_2) (hBOOL (hAPP real bool _let_1 (hAPP real real F X_2)))) )) (not (hBOOL (hAPP real bool _let_1 R_2)))) ))) ))))) 20.67/19.03 ( (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)))) ) 20.67/19.03 ) 20.67/19.03 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (inverse_inverse X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_158441 $$unsorted) (BOUND_VARIABLE_158442 $$unsorted)) (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_158441)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_158442)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_158441))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_158442) BOUND_VARIABLE_158441))) )))) 20.67/19.03 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.03 ( real, pi, (zero_zero real) ) 20.67/19.03 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.03 ( 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)))) ) 20.67/19.03 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 20.67/19.03 ( 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)))), (zero_zero real) ) 20.67/19.03 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 20.67/19.03 ( real, skv_6, (zero_zero real) ) 20.67/19.03 ( real, skv_11, (zero_zero real) ) 20.67/19.03 ( real, skv_12, (zero_zero real) ) 20.67/19.03 ( real, skv_14, (zero_zero real) ) 20.67/19.03 ( int, pls, min_1 ) 20.67/19.03 ( int, (one_one int), (zero_zero int) ) 20.67/19.03 ( int, min_1, (zero_zero int) ) 20.67/19.03 ( int, min_1, min_1 ) 20.67/19.03 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 20.67/19.03 ( int, s, (zero_zero int) ) 20.67/19.03 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 20.67/19.03 ( int, t, (one_one int) ) 20.67/19.03 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 20.67/19.03 ( int, skv_3, (zero_zero int) ) 20.67/19.03 ( int, skv_9, (zero_zero int) ) 20.67/19.03 ) 20.67/19.03 (instantiation (let ((_let_0 (hAPP int int (number_number_of int) min_1))) (forall ((B $$unsorted)) (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))) )) 20.67/19.03 ( (zero_zero int) ) 20.67/19.03 ( (one_one int) ) 20.67/19.03 ( (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))) ) 20.67/19.03 ( min_1 ) 20.67/19.03 ) 20.67/19.03 (instantiation (let ((_let_0 (fun real bool))) (forall ((N $$unsorted) (X $$unsorted)) (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))) )) 20.67/19.03 ( (zero_zero nat), pi ) 20.67/19.03 ( (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))))) ) 20.67/19.03 ( (zero_zero nat), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.03 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 20.67/19.03 ) 20.67/19.03 (instantiation (let ((_let_0 (abs_abs X_a))) (forall ((X_a $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 20.67/19.03 ( bool ) 20.67/19.03 ( real ) 20.67/19.03 ( nat ) 20.67/19.03 ( (fun nat bool) ) 20.67/19.03 ( int ) 20.67/19.03 ( (fun int bool) ) 20.67/19.03 ( (fun real bool) ) 20.67/19.03 ( (fun real real) ) 20.67/19.03 ( complex ) 20.67/19.03 ( (fun nat real) ) 20.67/19.03 ( (fun int int) ) 20.67/19.03 ( rat ) 20.67/19.03 ( (fun int (fun int bool)) ) 20.67/19.03 ( (product_prod int int) ) 20.67/19.03 ( (fun (product_prod int int) bool) ) 20.67/19.03 ( code_code_numeral ) 20.67/19.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 20.67/19.03 ( (fun (product_prod int int) int) ) 20.67/19.03 ( (fun int (fun int (fun int bool))) ) 20.67/19.03 ( (fun int real) ) 20.67/19.03 ) 20.67/19.03 (instantiation (let ((_let_0 (norm_norm X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_158505 $$unsorted) (BOUND_VARIABLE_158506 $$unsorted)) (or (not (real_normed_field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_158506)) (= (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_158505) BOUND_VARIABLE_158506)) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP X_a real _let_0 BOUND_VARIABLE_158505)) (hAPP X_a real _let_0 BOUND_VARIABLE_158506)))) )) 20.67/19.03 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.03 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.67/19.03 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.03 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 20.67/19.03 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.03 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.03 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.67/19.03 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.67/19.03 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.03 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.03 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.03 ) 20.67/19.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158613 $$unsorted) (BOUND_VARIABLE_158614 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_158613)) BOUND_VARIABLE_158614)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int (number_number_of int) BOUND_VARIABLE_158613)) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_158614))))) ) 20.67/19.03 ( nat, pls, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.03 ( int, pls, (zero_zero int) ) 20.67/19.03 ( int, pls, (one_one int) ) 20.67/19.03 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.03 ( int, pls, min_1 ) 20.67/19.03 ) 20.67/19.03 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) pi))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real cos X)) (hAPP real real cos Y)))) ))) 20.67/19.03 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 20.67/19.03 ) 20.67/19.03 (instantiation (let ((_let_0 (scaleR_scaleR X_a))) (forall ((X_a $$unsorted)) (or (not (real_vector X_a)) (= _let_0 (ti (fun real (fun X_a X_a)) _let_0))) )) 20.67/19.03 ( bool ) 20.67/19.04 ( real ) 20.67/19.04 ( nat ) 20.67/19.04 ( (fun nat bool) ) 20.67/19.04 ( int ) 20.67/19.04 ( (fun int bool) ) 20.67/19.04 ( (fun real bool) ) 20.67/19.04 ( (fun real real) ) 20.67/19.04 ( complex ) 20.67/19.04 ( (fun nat real) ) 20.67/19.04 ( (fun int int) ) 20.67/19.04 ( (fun int (fun int bool)) ) 20.67/19.04 ( (product_prod int int) ) 20.67/19.04 ( (fun (product_prod int int) bool) ) 20.67/19.04 ( code_code_numeral ) 20.67/19.04 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 20.67/19.04 ( (fun (product_prod int int) int) ) 20.67/19.04 ( (fun int (fun int (fun int bool))) ) 20.67/19.04 ( (fun int real) ) 20.67/19.04 ) 20.67/19.04 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_158653 $$unsorted) (BOUND_VARIABLE_158654 $$unsorted)) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_158653) BOUND_VARIABLE_158654))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_158654) BOUND_VARIABLE_158653))) (= (ti X_a BOUND_VARIABLE_158654) (ti X_a BOUND_VARIABLE_158653))) ))) 20.67/19.04 ( real, (zero_zero real), pi ) 20.67/19.04 ( 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)))) ) 20.67/19.04 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.04 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.04 ( real, (zero_zero real), skv_6 ) 20.67/19.04 ( real, (zero_zero real), skv_11 ) 20.67/19.04 ( real, (zero_zero real), skv_12 ) 20.67/19.04 ( real, (zero_zero real), skv_14 ) 20.67/19.04 ( real, pi, (zero_zero real) ) 20.67/19.04 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.04 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 20.67/19.04 ( 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)))) ) 20.67/19.04 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 20.67/19.04 ( 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) ) 20.67/19.04 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.04 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 20.67/19.04 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 20.67/19.04 ( real, skv_6, (zero_zero real) ) 20.67/19.04 ( real, skv_11, (zero_zero real) ) 20.67/19.04 ( real, skv_12, (zero_zero real) ) 20.67/19.04 ( real, skv_14, (zero_zero real) ) 20.67/19.04 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.04 ( int, (zero_zero int), (one_one int) ) 20.67/19.04 ( int, (zero_zero int), min_1 ) 20.67/19.04 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.04 ( int, (zero_zero int), s ) 20.67/19.04 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 20.67/19.04 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.67/19.04 ( int, (zero_zero int), skv_3 ) 20.67/19.04 ( int, (zero_zero int), skv_9 ) 20.67/19.04 ( int, pls, min_1 ) 20.67/19.04 ( int, (one_one int), (zero_zero int) ) 20.67/19.04 ( int, (one_one int), t ) 20.67/19.04 ( int, min_1, (zero_zero int) ) 20.67/19.04 ( int, min_1, pls ) 20.67/19.04 ( int, min_1, min_1 ) 20.67/19.04 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 20.67/19.04 ( int, s, (zero_zero int) ) 20.67/19.04 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 20.67/19.04 ( int, t, (one_one int) ) 20.67/19.04 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 20.67/19.04 ( int, skv_3, (zero_zero int) ) 20.67/19.04 ( int, skv_9, (zero_zero int) ) 20.67/19.04 ) 20.67/19.04 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) (forall ((X $$unsorted)) (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) _let_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real cos (hAPP real real (hAPP real (fun real real) (times_times real) _let_2) X))) (one_one real)))) )))) 20.67/19.04 ( pi ) 20.67/19.04 ( (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)))) ) 20.67/19.04 ( (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 20.67/19.04 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.04 ( skv_2 ) 20.67/19.04 ( skv_10 ) 20.67/19.04 ( skv_13 ) 20.67/19.04 ) 20.67/19.04 (instantiation (let ((_let_0 (hAPP nat (fun nat nat) (plus_plus nat) K))) (forall ((K $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (= (= (hAPP nat nat _let_0 Ma) (hAPP nat nat _let_0 N_1)) (= Ma N_1)) )) 20.67/19.04 ( (one_one nat), (one_one nat), (one_one nat) ) 20.67/19.04 ) 20.67/19.04 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_158706 $$unsorted) (BOUND_VARIABLE_158707 $$unsorted)) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_158706) BOUND_VARIABLE_158707)) (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_158706) BOUND_VARIABLE_158707)) (zero_zero X_a))))) ))) 20.67/19.04 ( real, (zero_zero real), pi ) 20.67/19.04 ( 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)))) ) 20.67/19.04 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.04 ( real, (zero_zero real), skv_2 ) 20.67/19.04 ( real, (zero_zero real), skv_10 ) 20.67/19.04 ( real, (zero_zero real), skv_13 ) 20.67/19.04 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.04 ( real, pi, (zero_zero real) ) 20.67/19.04 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.04 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.04 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 20.67/19.04 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 20.67/19.04 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 20.67/19.04 ( 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)), pi ) 20.67/19.04 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.04 ( int, (zero_zero int), (zero_zero int) ) 20.67/19.04 ( int, (zero_zero int), (one_one int) ) 20.67/19.04 ( 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))) ) 20.67/19.04 ( int, (zero_zero int), min_1 ) 20.67/19.04 ( int, min_1, (zero_zero int) ) 20.67/19.04 ( int, min_1, min_1 ) 20.67/19.04 ( 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))) ) 20.67/19.04 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 20.67/19.04 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 20.67/19.04 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 20.67/19.04 ( int, t, (zero_zero int) ) 20.67/19.04 ( int, t, (one_one int) ) 20.67/19.04 ( 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))) ) 20.67/19.04 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.04 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.04 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 20.67/19.04 ) 20.67/19.04 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (fun nat _let_3))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_158726 $$unsorted)) (or (not (real_normed_field X_a)) (not (banach X_a)) (hBOOL (hAPP X_a bool (hAPP _let_2 (fun X_a bool) (sums X_a) (hAPP _let_2 _let_2 (hAPP _let_4 (fun _let_2 _let_2) (combs nat X_a X_a) (hAPP _let_1 _let_4 (hAPP (fun real _let_3) (fun _let_1 _let_4) (combb real _let_3 nat) (scaleR_scaleR X_a)) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) (fact_fact nat))))) (hAPP X_a _let_2 (power_power X_a) BOUND_VARIABLE_158726))) (hAPP X_a X_a (exp X_a) BOUND_VARIABLE_158726)))) )))))) 20.67/19.04 ( real, (hAPP int real (number_number_of real) min_1) ) 20.67/19.04 ( 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)))) ) 20.67/19.04 ( int, s ) 20.67/19.04 ( int, s1 ) 20.67/19.04 ( int, skv_8 ) 20.67/19.04 ( complex, ii ) 20.67/19.04 ) 20.67/19.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158739 $$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_158739))))) ) 20.67/19.04 ( real, (hAPP nat nat suc (zero_zero nat)) ) 20.67/19.04 ( int, (hAPP nat nat suc (zero_zero nat)) ) 20.67/19.04 ) 20.67/19.04 (instantiation (let ((_let_0 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_158767 $$unsorted) (BOUND_VARIABLE_158768 $$unsorted)) (or (not (semiring_div X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_158767) BOUND_VARIABLE_158768))) (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_158767) (hAPP X_a X_a (hAPP X_a _let_0 (div_div X_a) BOUND_VARIABLE_158768) BOUND_VARIABLE_158767)) (ti X_a BOUND_VARIABLE_158768))) )) 20.67/19.04 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 20.67/19.04 ) 20.67/19.04 (instantiation (let ((_let_0 (fun int bool))) (forall ((Z $$unsorted) (W_1 $$unsorted)) (= (and (not (= (ti int Z) (ti int W_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) Z) W_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) Z) W_1))) )) 20.67/19.04 ( (zero_zero int), (zero_zero int) ) 20.67/19.04 ( (zero_zero int), (one_one int) ) 20.67/19.04 ( (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))) ) 20.67/19.04 ( (zero_zero int), min_1 ) 20.67/19.04 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.04 ( (zero_zero int), s ) 20.67/19.04 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 20.67/19.04 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.67/19.04 ( (zero_zero int), skv_3 ) 20.67/19.04 ( (zero_zero int), skv_9 ) 20.67/19.04 ( (one_one int), t ) 20.67/19.04 ( min_1, (zero_zero int) ) 20.67/19.04 ( min_1, pls ) 20.67/19.04 ( min_1, min_1 ) 20.67/19.04 ( 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))) ) 20.67/19.04 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 20.67/19.04 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 20.67/19.04 ( t, (zero_zero int) ) 20.67/19.04 ( t, (one_one int) ) 20.67/19.04 ( 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))) ) 20.67/19.04 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.04 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.04 ) 20.67/19.04 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (one_one 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_1 (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) M)) _let_2))) (forall ((M $$unsorted)) (or (not (hBOOL (hAPP int bool zprime _let_3))) (= _let_2 (hAPP int int (hAPP int _let_0 legendre (hAPP int int _let_1 min_1)) _let_3))) ))))) 20.67/19.05 ( m ) 20.67/19.05 ) 20.67/19.05 (instantiation (forall ((N_1 $$unsorted)) (= (= (zero_zero nat) N_1) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP nat real (real_1 nat) N_1)) (zero_zero real)))) ) 20.67/19.05 ( (zero_zero nat) ) 20.67/19.05 ( (one_one nat) ) 20.67/19.05 ) 20.67/19.05 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (power_power real))) (let ((_let_4 (one_one real))) (let ((_let_5 (fun nat _let_1))) (let ((_let_6 (fun _let_2 _let_2))) (let ((_let_7 (combs nat real real))) (let ((_let_8 (fun (fun nat nat) _let_2))) (let ((_let_9 (combb nat real nat))) (let ((_let_10 (hAPP (fun real _let_1) (fun _let_2 _let_5) (combb real _let_1 nat) (times_times real)))) (let ((_let_11 (hAPP _let_5 _let_6 _let_7 (hAPP _let_2 _let_5 _let_10 (hAPP real _let_2 _let_3 (hAPP int real (number_number_of real) min_1)))))) (let ((_let_12 (suminf real))) (let ((_let_13 (fun real _let_2))) (let ((_let_14 (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (let ((_let_15 (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) (combc nat nat nat) (hAPP (fun nat nat) (fun nat (fun nat nat)) (hAPP (fun nat (fun nat nat)) (fun (fun nat nat) (fun nat (fun nat nat))) (combb nat (fun nat nat) nat) (plus_plus nat)) _let_14)) (one_one nat)))) (let ((_let_16 (fun _let_13 _let_13))) (let ((_let_17 (combb _let_2 _let_2 real))) (let ((_let_18 (fun real _let_8))) (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (hAPP real real (abs_abs real) X_1)) _let_4))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) (hAPP _let_13 _let_1 (hAPP (fun _let_2 real) (fun _let_13 _let_1) (combb _let_2 real real) _let_12) (hAPP _let_13 _let_13 (hAPP _let_6 _let_16 _let_17 _let_11) (hAPP _let_13 _let_13 (hAPP _let_6 _let_16 _let_17 (hAPP _let_5 _let_6 _let_7 (hAPP _let_2 _let_5 _let_10 (hAPP _let_2 _let_2 (hAPP _let_1 _let_6 (combb real real nat) (hAPP real _let_1 (inverse_divide real) _let_4)) (hAPP _let_0 _let_2 (hAPP _let_2 _let_8 _let_9 (real_1 nat)) _let_15))))) (hAPP _let_0 _let_13 (hAPP _let_18 (fun _let_0 _let_13) (combc real _let_0 _let_2) (hAPP _let_13 _let_18 (hAPP (fun _let_2 _let_8) (fun _let_13 _let_18) (combb _let_2 _let_8 real) _let_9) _let_3)) _let_15))))) X_1) (hAPP _let_2 real _let_12 (hAPP _let_2 _let_2 _let_11 (hAPP _let_0 _let_2 (hAPP _let_2 _let_8 _let_9 (hAPP real _let_2 _let_3 X_1)) _let_14))))))) )))))))))))))))))))) 20.67/19.05 ( (hAPP int real (number_number_of real) min_1) ) 20.67/19.05 ( (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)))) ) 20.67/19.05 ) 20.67/19.05 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (product_prod X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool (hAPP (fun X_a _let_0) (fun _let_1 bool) (product_prod_case X_a X_b bool) F) (hAPP X_b _let_1 (hAPP X_a (fun X_b _let_1) (product_Pair X_a X_b) A_2) B_1)))) (hBOOL (hAPP X_b bool (hAPP X_a _let_0 F A_2) B_1))) ))) 20.67/19.05 ( real, real, (ord_less_eq real), (zero_zero real), pi ) 20.67/19.05 ( 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)))) ) 20.67/19.05 ( 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)))) ) 20.67/19.05 ( real, real, (ord_less_eq real), (zero_zero real), skv_6 ) 20.67/19.05 ( real, real, (ord_less_eq real), (zero_zero real), skv_11 ) 20.67/19.05 ( real, real, (ord_less_eq real), (zero_zero real), skv_12 ) 20.67/19.05 ( real, real, (ord_less_eq real), (zero_zero real), skv_14 ) 20.67/19.05 ( real, real, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 20.67/19.05 ( 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))) ) 20.67/19.05 ( 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) ) 20.67/19.05 ( real, real, (ord_less_eq real), skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.05 ( real, real, (ord_less real), (zero_zero real), pi ) 20.67/19.05 ( 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)))) ) 20.67/19.05 ( 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)))) ) 20.67/19.05 ( real, real, (ord_less real), (zero_zero real), skv_2 ) 20.67/19.05 ( real, real, (ord_less real), (zero_zero real), skv_10 ) 20.67/19.05 ( real, real, (ord_less real), (zero_zero real), skv_13 ) 20.67/19.05 ( 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)))) ) 20.67/19.05 ( real, real, (ord_less real), pi, (zero_zero real) ) 20.67/19.05 ( 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)))) ) 20.67/19.05 ( 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))) ) 20.67/19.05 ( 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) ) 20.67/19.05 ( 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) ) 20.67/19.05 ( 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 ) 20.67/19.05 ( 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))))) ) 20.67/19.05 ( real, (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real (fun (filter nat) bool)) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real), sequentially ) 20.67/19.05 ( nat, nat, (ord_less nat), (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.05 ( int, int, (ord_less_eq int), (zero_zero int), (one_one int) ) 20.67/19.05 ( int, int, (ord_less_eq int), (zero_zero int), min_1 ) 20.67/19.05 ( 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))) ) 20.67/19.05 ( int, int, (ord_less_eq int), (zero_zero int), s ) 20.67/19.05 ( int, int, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 20.67/19.05 ( 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))) ) 20.67/19.05 ( int, int, (ord_less_eq int), (zero_zero int), skv_3 ) 20.67/19.05 ( int, int, (ord_less_eq int), (zero_zero int), skv_9 ) 20.67/19.05 ( int, int, (ord_less_eq int), (one_one int), t ) 20.67/19.05 ( int, int, (ord_less_eq int), min_1, pls ) 20.67/19.05 ( int, int, (ord_less_eq int), min_1, min_1 ) 20.67/19.05 ( int, int, (ord_less int), (zero_zero int), (zero_zero int) ) 20.67/19.05 ( int, int, (ord_less int), (zero_zero int), (one_one int) ) 20.67/19.05 ( 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))) ) 20.67/19.05 ( int, int, (ord_less int), (zero_zero int), min_1 ) 20.67/19.05 ( int, int, (ord_less int), min_1, (zero_zero int) ) 20.67/19.05 ( int, int, (ord_less int), min_1, min_1 ) 20.67/19.05 ( 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))) ) 20.67/19.05 ( int, int, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 20.67/19.05 ( int, int, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 20.67/19.05 ( int, int, (ord_less int), t, (zero_zero int) ) 20.67/19.05 ( int, int, (ord_less int), t, (one_one int) ) 20.67/19.05 ( 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))) ) 20.67/19.05 ( int, int, (ord_less int), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.05 ( int, int, (ord_less int), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.05 ( int, int, (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 20.67/19.05 ( int, int, quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 20.67/19.05 ( 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))) ) 20.67/19.05 ( int, int, (hAPP int (fun int (fun int bool)) zcong s1), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.05 ( int, int, (hAPP int (fun int (fun int bool)) zcong s1), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.05 ( int, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.05 ( 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))) ) 20.67/19.05 ( int, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.05 ( int, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.05 ( int, (fun int bool), (member int), (one_one int), zEven ) 20.67/19.05 ( (fun int nat), (fun int bool), (nat_tr1645093318rphism int nat), nat_1, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 20.67/19.05 ( (fun nat int), (fun nat bool), (nat_tr1645093318rphism nat int), (semiring_1_of_nat int), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 20.67/19.05 ( (fun nat real), real, (sums real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 20.67/19.05 ) 20.67/19.05 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (power_power 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_0 (plus_plus real) (hAPP nat real (hAPP real _let_1 _let_2 (hAPP complex real re X)) _let_4)) (hAPP nat real (hAPP real _let_1 _let_2 _let_5) _let_4)))) (forall ((X $$unsorted)) (= (hAPP complex complex (inverse_inverse complex) X) (hAPP real complex (hAPP real (fun real complex) complex_1 (hAPP real real (hAPP real _let_0 _let_3 (hAPP complex real re X)) _let_6)) (hAPP real real (hAPP real _let_0 _let_3 (hAPP real real (uminus_uminus real) _let_5)) _let_6))) )))))))) 20.67/19.05 ( ii ) 20.67/19.05 ( (zero_zero complex) ) 20.67/19.05 ( (one_one complex) ) 20.67/19.05 ) 20.67/19.05 (instantiation (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_158930))) (let ((_let_6 (hAPP X_a X_a _let_3 BOUND_VARIABLE_158929))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_158929 $$unsorted) (BOUND_VARIABLE_158930 $$unsorted)) (or (not (division_ring X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_158930)) (= _let_0 (ti X_a BOUND_VARIABLE_158929)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_4 (hAPP X_a X_a (hAPP X_a _let_1 _let_4 _let_5) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_158930) BOUND_VARIABLE_158929))) _let_6) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 _let_5) _let_6))) )))))))) 20.67/19.06 ( nat, (one_one nat), (one_one nat) ) 20.67/19.06 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 20.67/19.06 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.67/19.06 ) 20.67/19.06 (instantiation (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (ord_less X_a))) (let ((_let_3 (zero_zero X_a))) (let ((_let_4 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_159009))) (let ((_let_5 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_159017))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_159009 $$unsorted) (BOUND_VARIABLE_159017 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (and (or (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 _let_4) _let_3)) (= _let_4 (hAPP X_a X_a _let_0 _let_4))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 _let_5) _let_3))) (= (hAPP X_a X_a _let_0 _let_5) (hAPP X_a X_a (uminus_uminus X_a) _let_5))))) ))))))) 20.67/19.06 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.67/19.06 ( 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))) ) 20.67/19.06 ( real, min_1, min_1 ) 20.67/19.06 ( 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))) ) 20.67/19.06 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 20.67/19.06 ( 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))) ) 20.67/19.06 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP 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)))))))) ) 20.67/19.06 ( nat, pls, pls ) 20.67/19.06 ( nat, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 20.67/19.06 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.67/19.06 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 20.67/19.06 ( int, pls, pls ) 20.67/19.06 ( int, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 20.67/19.06 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.67/19.06 ( 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))) ) 20.67/19.06 ( int, min_1, min_1 ) 20.67/19.06 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 20.67/19.06 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 20.67/19.06 ( complex, min_1, min_1 ) 20.67/19.06 ( quickcheck_code_int, (zero_zero int), (zero_zero int) ) 20.67/19.06 ( quickcheck_code_int, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 20.67/19.06 ( quickcheck_code_int, (one_one int), (one_one int) ) 20.67/19.06 ( code_code_numeral, pls, pls ) 20.67/19.06 ( code_code_numeral, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 20.67/19.06 ) 20.67/19.06 (instantiation (let ((_let_0 (product_prod int int))) (forall ((P_5 $$unsorted)) (= (hAPP int rat (hAPP int (fun int rat) fract (hAPP _let_0 int (product_fst int int) P_5)) (hAPP _let_0 int (product_snd int int) P_5)) (hAPP _let_0 rat frct P_5)) )) 20.67/19.06 ( (let ((_let_0 (one_one int))) (let ((_let_1 (product_prod int int))) (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) _let_0) _let_0))) ) 20.67/19.06 ) 20.67/19.06 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (forall ((A_2 $$unsorted) (Ma $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_2) Ma))) (= (one_one int) (hAPP int int (hAPP int _let_1 legacy_zgcd (hAPP _let_0 int (hAPP _let_1 (fun _let_0 int) (big_co302546470etprod int int) (combi int)) (hAPP int _let_0 (hAPP int (fun int _let_0) bnorRset A_2) Ma))) Ma))) ))) 20.67/19.06 ( (zero_zero int), (zero_zero int) ) 20.67/19.06 ( (zero_zero int), (one_one int) ) 20.67/19.06 ( (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))) ) 20.67/19.06 ( (zero_zero int), min_1 ) 20.67/19.06 ( min_1, (zero_zero int) ) 20.67/19.06 ( min_1, min_1 ) 20.67/19.06 ( 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))) ) 20.67/19.06 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 20.67/19.06 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 20.67/19.06 ( t, (zero_zero int) ) 20.67/19.06 ( t, (one_one int) ) 20.67/19.06 ( 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))) ) 20.67/19.06 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.06 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.67/19.06 ) 20.67/19.06 (instantiation (let ((_let_0 (dist_dist X_a))) (forall ((X_a $$unsorted)) (or (not (dist_norm X_a)) (= _let_0 (ti (fun X_a (fun X_a real)) _let_0))) )) 20.67/19.06 ( real ) 20.67/19.06 ( nat ) 20.67/19.06 ( int ) 20.67/19.06 ( (fun real bool) ) 20.67/19.06 ( complex ) 20.67/19.06 ( rat ) 20.67/19.06 ) 20.67/19.06 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159292 $$unsorted)) (or (not (number_semiring X_a)) (= (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_159292) (hAPP int X_a (number_number_of X_a) (hAPP nat int (semiring_1_of_nat int) BOUND_VARIABLE_159292)))) ) 20.67/19.06 ( real, (zero_zero nat) ) 20.67/19.06 ( real, (one_one nat) ) 20.67/19.06 ( nat, (zero_zero nat) ) 20.67/19.06 ( int, (zero_zero nat) ) 20.67/19.06 ( int, (hAPP nat nat suc (zero_zero nat)) ) 20.67/19.06 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.67/19.06 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.67/19.06 ( quickcheck_code_int, (zero_zero nat) ) 20.67/19.06 ( quickcheck_code_int, (hAPP nat nat suc (zero_zero nat)) ) 20.67/19.06 ( code_code_numeral, (zero_zero nat) ) 20.67/19.06 ) 20.67/19.06 (instantiation (let ((_let_0 (semiring_1_of_nat int))) (forall ((Z $$unsorted) (P_1 $$unsorted)) (or (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP int bool P_1 (hAPP nat int _let_0 N_2))) )) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP int bool P_1 (hAPP int int (uminus_uminus int) (hAPP nat int _let_0 (hAPP nat nat suc N_2))))) )) (hBOOL (hAPP int bool P_1 Z))) )) 20.67/19.06 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) pls) ) 20.67/19.06 ( (zero_zero int), nat_is_nat ) 20.67/19.06 ( (zero_zero int), (even_odd_even int) ) 20.67/19.06 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int))) ) 20.67/19.06 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) min_1) ) 20.67/19.06 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) t) ) 20.67/19.06 ( pls, (hAPP int (fun int bool) (ord_less_eq int) min_1) ) 20.67/19.06 ( (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 20.67/19.06 ( (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 20.67/19.06 ( (one_one int), nat_neg ) 20.67/19.06 ( (one_one int), nat_is_nat ) 20.67/19.06 ( (one_one int), (even_odd_even int) ) 20.67/19.06 ( (one_one int), (hAPP int (fun int bool) (ord_less int) t) ) 20.67/19.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 20.67/19.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int 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)) ) 20.67/19.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int 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) ) 20.67/19.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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)) ) 20.67/19.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 20.67/19.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int 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) ) 20.67/19.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 20.67/19.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))) ) 20.67/19.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int 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_3) ) 20.67/19.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_3)) ) 20.67/19.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 20.67/19.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int 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_9) ) 20.67/19.06 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_9)) ) 20.67/19.06 ( min_1, (hAPP int (fun int bool) (ord_less int) pls) ) 20.67/19.06 ( min_1, (hAPP int (fun int bool) (ord_less_eq int) pls) ) 20.67/19.06 ( min_1, (hAPP int (fun int bool) (ord_less int) min_1) ) 20.67/19.06 ( min_1, (hAPP int (fun int bool) (ord_less_eq int) min_1) ) 20.67/19.06 ( (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)) ) 20.67/19.06 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), zprime ) 20.67/19.06 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), nat_is_nat ) 20.67/19.06 ( (hAPP int int (number_number_of int) min_1), nat_neg ) 20.67/19.06 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) ) 20.84/19.11 ( s, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 20.84/19.11 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) ) 20.84/19.11 ( (hAPP int int (number_number_of int) pls), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 20.84/19.11 ( (hAPP int int (number_number_of int) pls), nat_neg ) 20.84/19.11 ( t, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) ) 20.84/19.11 ( (let ((_let_0 (fun int int))) (let ((_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 ) 20.84/19.11 ( (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)) ) 20.84/19.11 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), nat_is_nat ) 20.84/19.11 ( (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun int bool) (ord_less 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)))) ) 20.84/19.11 ( skv_3, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 20.84/19.11 ( skv_9, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 20.84/19.11 ) 20.84/19.11 (instantiation (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))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP complex real (norm_norm complex) (hAPP real complex (hAPP real (fun real complex) complex_1 X) Y)) (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)))) )))) 20.84/19.11 ( (zero_zero real), (zero_zero real) ) 20.84/19.11 ( (zero_zero real), (one_one real) ) 20.84/19.11 ( (one_one real), (zero_zero real) ) 20.84/19.11 ) 20.84/19.11 (instantiation (let ((_let_0 (of_real X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_159620 $$unsorted) (BOUND_VARIABLE_159621 $$unsorted)) (or (not (real_algebra_1 X_a)) (= (= (hAPP real X_a _let_0 BOUND_VARIABLE_159621) (hAPP real X_a _let_0 BOUND_VARIABLE_159620)) (= BOUND_VARIABLE_159620 BOUND_VARIABLE_159621))) )) 20.84/19.11 ( complex, pi, pi ) 20.84/19.11 ( complex, pi, (hAPP int real (number_number_of real) min_1) ) 20.84/19.11 ( complex, pi, (hAPP real real (uminus_uminus real) (one_one real)) ) 20.84/19.11 ( complex, (hAPP int real (number_number_of real) min_1), pi ) 20.84/19.11 ( complex, (hAPP real real (uminus_uminus real) (one_one real)), (hAPP int real (number_number_of real) min_1) ) 20.84/19.11 ) 20.84/19.11 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (gcd_gcd nat))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP nat nat (hAPP nat _let_0 _let_1 M) N) (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) M) N)) N)) ))) 20.84/19.11 ( (one_one nat), (one_one nat) ) 20.84/19.11 ) 20.84/19.11 (instantiation (forall ((N $$unsorted)) (= N (hAPP nat nat (size_size nat) N)) ) 20.84/19.11 ( (zero_zero nat) ) 20.84/19.11 ) 20.84/19.11 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP int bool nat_is_nat X))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (hAPP int int (fact_fact int) X)))) ) 20.84/19.11 ( (zero_zero int) ) 20.84/19.11 ( (one_one int) ) 20.84/19.11 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.84/19.11 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.84/19.11 ) 20.84/19.11 (instantiation (let ((_let_0 (fun real complex))) (forall ((Real1 $$unsorted) (Real2 $$unsorted) (Real1_2 $$unsorted) (Real2_2 $$unsorted)) (= (= (hAPP real complex (hAPP real _let_0 complex_1 Real1) Real2) (hAPP real complex (hAPP real _let_0 complex_1 Real1_2) Real2_2)) (and (= Real2 Real2_2) (= Real1 Real1_2))) )) 20.84/19.11 ( (zero_zero real), (zero_zero real), (zero_zero real), (one_one real) ) 20.84/19.11 ( (zero_zero real), (zero_zero real), (one_one real), (zero_zero real) ) 20.84/19.11 ( (zero_zero real), (one_one real), (one_one real), (zero_zero real) ) 20.84/19.11 ( (one_one real), (zero_zero real), (zero_zero real), (zero_zero real) ) 20.84/19.11 ( (one_one real), (zero_zero real), (one_one real), (zero_zero real) ) 20.84/19.11 ) 20.84/19.11 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_159718) BOUND_VARIABLE_159717))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_159717 $$unsorted) (BOUND_VARIABLE_159718 $$unsorted)) (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_159718))) (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_159718) _let_2)))) )))) 20.84/19.11 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 20.84/19.11 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 20.84/19.11 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 20.84/19.11 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 20.84/19.11 ) 20.84/19.11 (instantiation (forall ((R_4 $$unsorted)) (= (hAPP real complex (hAPP real (fun real complex) rcis R_4) (zero_zero real)) (hAPP real complex (of_real complex) R_4)) ) 20.84/19.11 ( pi ) 20.84/19.11 ( (hAPP int real (number_number_of real) min_1) ) 20.84/19.11 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 20.84/19.11 ) 20.84/19.11 (instantiation (let ((_let_0 (archim2085082626_floor X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_159746 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP X_a int _let_0 BOUND_VARIABLE_159746)) (one_one int)) (hAPP X_a int _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_159746) (one_one X_a))))) )) 20.84/19.11 ( nat, (one_one nat) ) 20.84/19.11 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 20.84/19.11 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.84/19.11 ) 20.84/19.11 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_159765 $$unsorted) (BOUND_VARIABLE_159766 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_159766))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_159766) BOUND_VARIABLE_159765)))) )) 20.84/19.11 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 20.84/19.11 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 20.84/19.11 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_8 ) 20.84/19.11 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 20.84/19.11 ) 20.84/19.11 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (norm_norm X_a))) (forall ((X_a $$unsorted)) (or (not (real_normed_algebra X_a)) (not (forall ((K_2 $$unsorted)) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (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))) )) ))) )))) 20.84/19.11 ( real ) 20.84/19.11 ( complex ) 20.84/19.11 ) 20.84/19.11 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun int bool))) (forall ((N_1 $$unsorted)) (= (hAPP _let_1 _let_0 (hAPP (fun int nat) (fun _let_1 _let_0) (image int nat) nat_1) (hAPP int _let_1 (hAPP int (fun int _let_1) (ord_atLeastAtMost int) (zero_zero int)) (hAPP nat int (semiring_1_of_nat int) N_1))) (hAPP nat _let_0 (ord_atMost nat) N_1)) ))) 20.84/19.11 ( (zero_zero nat) ) 20.84/19.11 ( (hAPP nat nat suc (zero_zero nat)) ) 20.84/19.11 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.84/19.11 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.84/19.11 ) 20.84/19.11 (instantiation (forall ((X $$unsorted)) (= (hAPP real real (sgn_sgn real) X) (hAPP real real (hAPP real (fun real real) (inverse_divide real) X) (hAPP real real (abs_abs real) X))) ) 20.84/19.11 ( (zero_zero real) ) 20.84/19.11 ( (one_one real) ) 20.84/19.11 ( pi ) 20.84/19.11 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 20.84/19.11 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 20.84/19.11 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.84/19.11 ) 20.84/19.11 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_159862 $$unsorted) (BOUND_VARIABLE_159863 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_159863) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_159862) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_159863) BOUND_VARIABLE_159862)) _let_2))) )))) 20.84/19.11 ( nat, (one_one nat), (one_one nat) ) 20.84/19.11 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 20.84/19.11 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.84/19.11 ) 20.84/19.11 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun X_b bool))) (let ((_let_2 (ord_less_eq X_b))) (let ((_let_3 (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_159956))) (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_159955 $$unsorted) (BOUND_VARIABLE_159956 $$unsorted) (BOUND_VARIABLE_159957 $$unsorted) (BOUND_VARIABLE_159958 $$unsorted)) (or (not (order X_b)) (not (order X_a)) (not (hBOOL (hAPP X_a bool _let_3 (hAPP X_b X_a BOUND_VARIABLE_159957 BOUND_VARIABLE_159958)))) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_1 _let_2 BOUND_VARIABLE_159958) BOUND_VARIABLE_159955))) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (or (not (hBOOL (hAPP X_b bool (hAPP X_b _let_1 _let_2 X_2) Y_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (hAPP X_b X_a BOUND_VARIABLE_159957 X_2)) (hAPP X_b X_a BOUND_VARIABLE_159957 Y_2)))) )) (hBOOL (hAPP X_a bool _let_3 (hAPP X_b X_a BOUND_VARIABLE_159957 BOUND_VARIABLE_159955)))) ))))) 20.84/19.11 ( real, real, pi, (zero_zero real), tan, (zero_zero real) ) 20.84/19.11 ( 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)))), (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.84/19.11 ( real, real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi, 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)))) ) 20.84/19.11 ( real, real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (sgn_sgn real), (zero_zero real) ) 20.84/19.11 ( real, real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real), sqrt, (zero_zero real) ) 20.84/19.11 ( real, real, skv_6, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), sin, (zero_zero real) ) 20.84/19.11 ( real, real, skv_11, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), arctan, (zero_zero real) ) 20.84/19.11 ( nat, int, s, (zero_zero nat), (number_number_of nat), pls ) 20.84/19.11 ( int, int, pls, skv_3, succ, min_1 ) 20.84/19.11 ( int, int, (one_one int), skv_9, pred, pls ) 20.84/19.11 ( int, int, min_1, (zero_zero int), (number_number_of int), min_1 ) 20.84/19.11 ( int, int, min_1, t, (number_number_of int), pls ) 20.84/19.11 ( int, int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), min_1, bit0, pls ) 20.84/19.11 ( int, int, (hAPP int int (number_number_of int) pls), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), bit1, pls ) 20.84/19.12 ( int, int, t, s, (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 20.84/19.12 ) 20.84/19.12 (instantiation (let ((_let_0 (fun nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_160070 $$unsorted)) (or (not (comm_monoid_add X_a)) (not (t2_space X_a)) (not (hBOOL (hAPP _let_0 bool (summable X_a) BOUND_VARIABLE_160070))) (hBOOL (hAPP X_a bool (hAPP _let_0 (fun X_a bool) (sums X_a) BOUND_VARIABLE_160070) (hAPP _let_0 X_a (suminf X_a) BOUND_VARIABLE_160070)))) )) 20.84/19.12 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))) ) 20.84/19.12 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (combc nat nat nat))) (let ((_let_4 (fun nat _let_0))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun _let_1 _let_4))) (let ((_let_7 (combb real _let_0 nat))) (hAPP _let_1 _let_1 (hAPP _let_4 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_4 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 20.84/19.12 ) 20.84/19.12 (instantiation (let ((_let_0 (ord_min X_a))) (forall ((X_a $$unsorted)) (or (not (ord X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0))) )) 20.84/19.12 ( bool ) 20.84/19.12 ( real ) 20.84/19.12 ( nat ) 20.84/19.12 ( (fun nat bool) ) 20.84/19.12 ( int ) 20.84/19.12 ( (fun int bool) ) 20.84/19.12 ( (fun real bool) ) 20.84/19.12 ( (fun real real) ) 20.84/19.12 ( complex ) 20.84/19.12 ( (fun nat real) ) 20.84/19.12 ( (fun int int) ) 20.84/19.12 ( rat ) 20.84/19.12 ( (fun int (fun int bool)) ) 20.84/19.12 ( quickcheck_code_int ) 20.84/19.12 ( (product_prod int int) ) 20.84/19.12 ( (fun (product_prod int int) bool) ) 20.84/19.12 ( code_code_numeral ) 20.84/19.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 20.84/19.12 ( (fun (product_prod int int) int) ) 20.84/19.12 ( (fun int (fun int (fun int bool))) ) 20.84/19.12 ( (fun int real) ) 20.84/19.12 ) 20.84/19.12 (instantiation (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_160117))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_160113 $$unsorted) (BOUND_VARIABLE_160114 $$unsorted) (BOUND_VARIABLE_160115 $$unsorted) (BOUND_VARIABLE_160116 $$unsorted) (BOUND_VARIABLE_160117 $$unsorted)) (or (not (topological_space X_a)) (not (real_normed_vector X_b)) (not (real_normed_vector X_c)) (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_160115) BOUND_VARIABLE_160116) _let_2))) (not (forall ((X_2 $$unsorted)) (or (= (ti X_a X_2) (ti X_a BOUND_VARIABLE_160117)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_c real (norm_norm X_c) (hAPP X_c X_c (hAPP X_c (fun X_c X_c) (minus_minus X_c) (hAPP X_a X_c BOUND_VARIABLE_160113 X_2)) BOUND_VARIABLE_160114))) (hAPP X_b real (norm_norm X_b) (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (minus_minus X_b) (hAPP X_a X_b BOUND_VARIABLE_160115 X_2)) BOUND_VARIABLE_160116))))) )) (hBOOL (hAPP _let_0 bool (hAPP X_c _let_1 (hAPP (fun X_a X_c) (fun X_c _let_1) (tendsto X_a X_c) BOUND_VARIABLE_160113) BOUND_VARIABLE_160114) _let_2))) )))) 20.84/19.12 ( real, real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.84/19.12 ) 20.84/19.12 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_160168 $$unsorted)) (or (not (real_normed_vector X_a)) (= (= _let_0 (ti X_a BOUND_VARIABLE_160168)) (= _let_0 (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_160168)))) )) 20.84/19.12 ( bool, fFalse ) 20.84/19.12 ( bool, fTrue ) 20.84/19.12 ( real, (zero_zero real) ) 20.84/19.12 ( real, pi ) 20.84/19.12 ( (fun nat bool), (even_odd_even nat) ) 20.84/19.12 ( (fun nat bool), prime ) 20.84/19.12 ( (fun nat nat), suc ) 20.84/19.12 ( (fun nat nat), (fact_fact nat) ) 20.84/19.12 ( (fun nat nat), (size_size nat) ) 20.84/19.12 ( (fun nat nat), fact ) 20.84/19.12 ( (fun nat nat), nat_size ) 20.84/19.12 ( int, pls ) 20.84/19.12 ( int, m ) 20.84/19.12 ( int, min_1 ) 20.84/19.12 ( int, s ) 20.84/19.12 ( int, s1 ) 20.84/19.12 ( int, t ) 20.84/19.12 ( (fun int bool), zprime ) 20.84/19.12 ( (fun int bool), nat_neg ) 20.84/19.12 ( (fun int bool), zEven ) 20.84/19.12 ( (fun int bool), nat_is_nat ) 20.84/19.12 ( (fun int bool), zOdd ) 20.84/19.12 ( (fun int bool), (even_odd_even int) ) 20.84/19.12 ( (fun int bool), twoSqu1091635170sum2sq ) 20.84/19.12 ( (fun int nat), nat_1 ) 20.84/19.12 ( (fun int nat), phi ) 20.84/19.12 ( (fun real real), sqrt ) 20.84/19.12 ( (fun real real), tan ) 20.84/19.12 ( (fun real real), cos ) 20.84/19.12 ( (fun real real), arccos ) 20.84/19.12 ( (fun real real), ln ) 20.84/19.12 ( (fun real real), sin ) 20.84/19.12 ( (fun real real), arctan ) 20.84/19.12 ( (fun real real), arcsin ) 20.84/19.12 ( complex, ii ) 20.84/19.12 ( (fun complex complex), cnj ) 20.84/19.12 ( (fun complex complex), expi ) 20.84/19.12 ( (fun nat real), (real_1 nat) ) 20.84/19.12 ( (fun nat real), cos_coeff ) 20.84/19.12 ( (fun nat real), sin_coeff ) 20.84/19.12 ( (fun int int), bit0 ) 20.84/19.12 ( (fun int int), bit1 ) 20.84/19.12 ( (fun int int), pred ) 20.84/19.12 ( (fun int int), succ ) 20.84/19.12 ( (fun int int), (fact_fact int) ) 20.84/19.12 ( (fun int int), zfact ) 20.84/19.12 ( rat, (zero_zero rat) ) 20.84/19.12 ( (fun bool bool), fNot ) 20.84/19.12 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 20.84/19.12 ( (fun bool (fun bool bool)), fconj ) 20.84/19.12 ( (fun bool (fun bool bool)), fdisj ) 20.84/19.12 ( (fun bool (fun bool bool)), fimplies ) 20.84/19.12 ( (fun int (fun int bool)), sRStar ) 20.84/19.12 ( (fun int (fun int bool)), quadRes ) 20.84/19.12 ( (fun int (fun int bool)), norRRset ) 20.84/19.12 ( (fun int (fun int bool)), d22set ) 20.84/19.12 ( (fun int (fun int bool)), sr ) 20.84/19.12 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 20.84/19.12 ( (fun nat (fun nat nat)), nat_gcd ) 20.84/19.12 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 20.84/19.12 ( (fun nat (fun nat nat)), nat_lcm ) 20.84/19.12 ( (fun nat (fun real real)), root ) 20.84/19.12 ( (fun real (fun real real)), log ) 20.84/19.12 ( (fun real (fun real real)), powr ) 20.84/19.12 ( (fun nat (fun nat bool)), coprime ) 20.84/19.12 ( (fun (fun int bool) int), (the int) ) 20.84/19.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 20.84/19.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 20.84/19.12 ( (fun nat (fun nat (product_prod int int))), bezw ) 20.84/19.12 ( (fun (fun int bool) bool), nat_nat_set ) 20.84/19.12 ( (filter nat), sequentially ) 20.84/19.12 ( (fun (product_prod nat nat) bool), pred_nat ) 20.84/19.12 ( (fun (product_prod int int) bool), frac_1 ) 20.84/19.12 ( (fun real complex), cis ) 20.84/19.12 ( (fun complex real), im ) 20.84/19.12 ( (fun complex real), re ) 20.84/19.12 ( (fun complex real), arg ) 20.84/19.12 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 20.84/19.12 ( (fun int (fun int int)), int_gcd ) 20.84/19.12 ( (fun int (fun int int)), multInv ) 20.84/19.12 ( (fun int (fun int int)), legacy_zgcd ) 20.84/19.12 ( (fun int (fun int int)), z3mod ) 20.84/19.12 ( (fun int (fun int int)), inv ) 20.84/19.12 ( (fun int (fun int int)), (gcd_gcd int) ) 20.84/19.12 ( (fun int (fun int int)), standardRes ) 20.84/19.12 ( (fun int (fun int int)), legendre ) 20.84/19.12 ( (fun int (fun int int)), nat_tsub ) 20.84/19.12 ( (fun int (fun int int)), z3div ) 20.84/19.12 ( (fun int (fun int int)), int_lcm ) 20.84/19.12 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 20.84/19.12 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 20.84/19.12 ( (fun int (fun (fun int bool) bool)), rsetR ) 20.84/19.12 ( (fun int (fun (fun int bool) bool)), resSet ) 20.84/19.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 20.84/19.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 20.84/19.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 20.84/19.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 20.84/19.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 20.84/19.12 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 20.84/19.12 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 20.84/19.12 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 20.84/19.12 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 20.84/19.12 ( (fun int (fun int (product_prod int int))), negDivAlg ) 20.84/19.12 ( (fun int (fun int (product_prod int int))), 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20.84/19.12 ( (fun int (fun int (fun int bool))), zcongm ) 20.84/19.12 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 20.84/19.12 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 20.84/19.12 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 20.84/19.12 ( (fun int real), (real_1 int) ) 20.84/19.12 ( (fun complex nat), (size_size complex) ) 20.84/19.12 ( (fun complex nat), complex_size ) 20.84/19.12 ( (fun int (list int)), quickc666637781d_zero ) 20.84/19.12 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 20.84/19.12 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 20.84/19.12 ( (fun (product_prod int int) rat), frct ) 20.84/19.12 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 20.84/19.12 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 20.84/19.12 ( (fun (fun nat rat) bool), vanishes ) 20.84/19.12 ( (fun int (fun int rat)), fract ) 20.84/19.12 ( (fun code_code_numeral int), code_int_of ) 20.84/19.12 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 20.84/19.12 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 20.84/19.12 ( (fun code_code_numeral nat), code_c271388182l_size ) 20.84/19.12 ( (fun real (fun real complex)), complex_1 ) 20.84/19.12 ( (fun real (fun real complex)), rcis ) 20.84/19.12 ( (fun int (fun nat nat)), nat_aux ) 20.84/19.12 ( (fun rat real), ratreal ) 20.84/19.12 ( (fun quickcheck_code_int int), quickcheck_int_of ) 20.84/19.12 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 20.84/19.12 ( (fun rat (product_prod int int)), quotient_of ) 20.84/19.12 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 20.84/19.12 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 20.84/19.12 ( (fun quickcheck_code_int nat), 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(or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_160236) BOUND_VARIABLE_160237))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_160236))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_160237))) )) 20.84/19.12 ( real, (zero_zero real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.84/19.12 ( real, (one_one real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.84/19.12 ( real, pi, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.84/19.12 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (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))) ) 20.84/19.12 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 20.84/19.12 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 20.84/19.12 ( 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)), (zero_zero real), pi ) 20.84/19.12 ( nat, (zero_zero nat), (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 20.84/19.12 ( 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))) ) 20.84/19.12 ( int, min_1, t, (zero_zero int) ) 20.84/19.12 ( int, s, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 20.84/19.12 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 20.84/19.12 ( int, t, (zero_zero int), (one_one int) ) 20.84/19.12 ( int, skv_3, (zero_zero int), (zero_zero int) ) 20.84/19.12 ( int, skv_9, min_1, (zero_zero int) ) 20.84/19.12 ) 20.84/19.12 (instantiation (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))) (forall ((X_b $$unsorted) (X_a $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (A_8 $$unsorted) (B_7 $$unsorted)) (= (and (= (ti X_a A_8) (ti X_a A_2)) (= (ti X_b B_7) (ti X_b B_1))) (= (hAPP X_b _let_0 (hAPP X_a _let_1 _let_2 A_8) B_7) (hAPP X_b _let_0 (hAPP X_a _let_1 _let_2 A_2) B_1))) )))) 20.84/19.12 ( bool, int, t, fTrue, t, fFalse ) 20.84/19.12 ( bool, (filter nat), sequentially, fFalse, sequentially, fTrue ) 20.84/19.12 ( bool, (filter 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20.84/19.14 ( (fun real real), (fun int (fun int (product_prod int int))), divmod_int, sqrt, divmod_int, ln ) 20.84/19.14 ( (fun real real), (fun int (fun int (product_prod int int))), divmod_int, ln, divmod_int, ln ) 20.84/19.14 ( (fun real real), (fun int (fun int (fun int bool))), wset, sin, wset, arcsin ) 20.84/19.14 ( (fun real real), (fun int (fun int (fun int bool))), zcong, cos, zcong, cos ) 20.84/19.14 ( (fun real real), (fun int (fun int (fun int bool))), zcong, arctan, zcong, cos ) 20.84/19.14 ( (fun real real), (fun real (fun real complex)), complex_1, cos, complex_1, arctan ) 20.84/19.14 ( complex, bool, fFalse, ii, fFalse, ii ) 20.84/19.14 ( complex, (fun nat bool), (even_odd_even nat), ii, (even_odd_even nat), ii ) 20.84/19.14 ( complex, (fun nat nat), (fact_fact nat), ii, (fact_fact nat), ii ) 20.84/19.14 ( complex, (fun nat nat), (size_size nat), ii, (size_size nat), ii ) 20.84/19.14 ( complex, (fun nat nat), fact, ii, fact, ii ) 20.84/19.14 ( complex, int, m, ii, m, 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sequentially, sin_coeff, sequentially ) 20.84/19.18 ( (filter nat), (fun int int), bit0, sequentially, bit0, sequentially ) 20.84/19.18 ( (filter nat), (fun int int), bit1, sequentially, bit1, sequentially ) 20.84/19.18 ( (filter nat), (fun int int), (fact_fact int), sequentially, (fact_fact int), sequentially ) 20.84/19.18 ( (filter nat), (fun int int), zfact, sequentially, zfact, sequentially ) 20.84/19.18 ( (filter nat), (fun bool bool), fNot, sequentially, fNot, sequentially ) 20.84/19.18 ( (filter nat), (fun bool (fun bool bool)), fconj, sequentially, fconj, sequentially ) 20.84/19.18 ( (filter nat), (fun bool (fun bool bool)), fdisj, sequentially, fdisj, sequentially ) 20.84/19.18 ( (filter nat), (fun int (fun int bool)), sRStar, sequentially, sRStar, sequentially ) 20.84/19.18 ( (filter nat), (fun int (fun int bool)), norRRset, sequentially, norRRset, sequentially ) 20.84/19.18 ( (filter nat), (fun int (fun int bool)), sr, sequentially, sr, sequentially ) 20.84/19.18 ( (filter nat), (fun int (fun int bool)), quickc1265749348ro_rel, sequentially, quickc1265749348ro_rel, sequentially ) 20.84/19.18 ( (filter nat), (fun nat (fun nat nat)), nat_gcd, sequentially, nat_gcd, sequentially ) 20.84/19.18 ( (filter nat), (fun nat (fun real real)), root, sequentially, root, sequentially ) 20.84/19.18 ( (filter nat), (fun real (fun real real)), powr, sequentially, powr, sequentially ) 20.84/19.18 ( (filter nat), (fun nat (fun nat bool)), coprime, sequentially, coprime, sequentially ) 20.84/19.18 ( (filter nat), (fun (fun int bool) int), (the int), sequentially, (the int), sequentially ) 20.84/19.18 ( (filter nat), (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, sequentially, negateSnd, sequentially ) 20.84/19.18 ( (filter nat), (fun nat (fun nat (product_prod int int))), bezw, sequentially, bezw, sequentially ) 20.84/19.18 ( (filter nat), (fun (fun int bool) bool), nat_nat_set, sequentially, nat_nat_set, sequentially ) 20.84/19.18 ( (filter nat), (filter nat), sequentially, sequentially, sequentially, sequentially ) 20.84/19.18 ( (filter nat), (fun (product_prod nat nat) bool), pred_nat, sequentially, pred_nat, sequentially ) 20.84/19.18 ( (filter nat), (fun (product_prod int int) bool), frac_1, sequentially, frac_1, sequentially ) 20.84/19.18 ( (filter nat), (fun real complex), cis, sequentially, cis, sequentially ) 20.84/19.18 ( (filter nat), (fun complex real), im, sequentially, im, sequentially ) 20.84/19.18 ( (filter nat), (fun complex real), re, sequentially, re, sequentially ) 20.84/19.18 ( (filter nat), (fun complex real), arg, sequentially, arg, sequentially ) 20.84/19.18 ( (filter nat), (fun code_code_numeral code_code_numeral), code_S1047413653umeral, sequentially, code_S1047413653umeral, sequentially ) 20.84/19.18 ( (filter nat), (fun int (fun int int)), z3mod, sequentially, z3mod, sequentially ) 20.84/19.18 ( (filter nat), (fun int (fun int int)), (gcd_gcd int), sequentially, (gcd_gcd int), sequentially ) 20.84/19.18 ( (filter nat), (fun int (fun int int)), z3div, sequentially, z3div, sequentially ) 20.84/19.18 ( (filter nat), (fun int (fun int int)), int_lcm, sequentially, int_lcm, sequentially ) 20.84/19.18 ( (filter nat), (fun int (fun (fun int bool) bool)), rsetR, sequentially, rsetR, sequentially ) 20.84/19.18 ( (filter nat), (fun int (fun (fun int bool) bool)), resSet, sequentially, resSet, sequentially ) 20.84/19.18 ( (filter nat), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, sequentially, posDivAlg_rel, sequentially ) 20.84/19.18 ( (filter nat), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, sequentially, negDivAlg_rel, sequentially ) 20.84/19.18 ( (filter nat), (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, sequentially, pair_less, sequentially ) 20.84/19.19 ( (filter nat), (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, sequentially, pair_leq, sequentially ) 20.84/19.19 ( (filter nat), (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, sequentially, divmod_int_rel, sequentially ) 20.84/19.19 ( (filter nat), (fun int (fun int (product_prod int int))), negDivAlg, sequentially, negDivAlg, sequentially ) 20.84/19.19 ( (filter nat), (fun int (fun int (product_prod int int))), divmod_int, sequentially, divmod_int, sequentially ) 20.84/19.19 ( (filter nat), (fun int (fun int (product_prod int int))), posDivAlg, sequentially, posDivAlg, sequentially ) 20.84/19.19 ( (filter nat), (fun int (fun int (product_prod int int))), pdivmod, sequentially, pdivmod, sequentially ) 20.84/19.19 ( (filter nat), (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, sequentially, adjust, sequentially ) 20.84/19.19 ( (filter nat), (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, sequentially, bolzano_bisect, sequentially ) 20.84/19.19 ( (filter nat), (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), sequentially, (ord_gr676655987ssThan nat), sequentially ) 20.84/19.19 ( (filter nat), (fun (product_prod int int) int), twoSqu1094008024sum2sq, sequentially, twoSqu1094008024sum2sq, sequentially ) 20.84/19.19 ( (filter nat), (fun real nat), natfloor, sequentially, natfloor, sequentially ) 20.84/19.19 ( (filter nat), (fun real nat), natceiling, sequentially, natceiling, sequentially ) 20.84/19.19 ( (filter nat), (fun int quickcheck_code_int), quickcheck_of_int, sequentially, quickcheck_of_int, sequentially ) 20.84/19.19 ( (filter nat), (fun int (fun int (fun int bool))), wset, sequentially, wset, sequentially ) 20.84/19.19 ( (filter nat), (fun int (fun int (fun int bool))), bnorRset, sequentially, bnorRset, sequentially ) 20.84/19.19 ( (filter nat), (fun int (fun int (fun int bool))), zcong, sequentially, zcong, sequentially ) 20.84/19.19 ( (filter nat), (fun int (fun int (fun int (fun int bool)))), multInvPair, sequentially, multInvPair, sequentially ) 20.84/19.19 ( (filter nat), (fun int (fun int (fun (fun int bool) bool))), setS, sequentially, setS, sequentially ) 20.84/19.19 ( (filter nat), (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, sequentially, code_d418564891umeral, sequentially ) 20.84/19.19 ( (filter nat), (fun int real), (real_1 int), sequentially, (real_1 int), sequentially ) 20.84/19.19 ( (filter nat), (fun complex nat), (size_size complex), sequentially, (size_size complex), sequentially ) 20.84/19.19 ( (filter nat), (fun complex nat), complex_size, sequentially, complex_size, sequentially ) 20.84/19.19 ( (filter nat), (fun int (list int)), quickc666637781d_zero, sequentially, quickc666637781d_zero, sequentially ) 20.84/19.19 ( (filter nat), (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, sequentially, divmod_nat_rel, sequentially ) 20.84/19.19 ( (filter nat), (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, sequentially, ratrel, sequentially ) 20.84/19.19 ( (filter nat), (fun (product_prod int int) rat), frct, sequentially, frct, sequentially ) 20.84/19.19 ( (filter nat), (fun code_code_numeral (fun nat nat)), code_nat_of_aux, sequentially, code_nat_of_aux, sequentially ) 20.84/19.19 ( (filter nat), (fun (fun nat rat) bool), vanishes, sequentially, vanishes, sequentially ) 20.84/19.19 ( (filter nat), (fun code_code_numeral int), code_int_of, sequentially, code_int_of, sequentially ) 20.84/19.19 ( (filter nat), (fun nat (fun nat (product_prod nat nat))), divmod_nat, sequentially, divmod_nat, sequentially ) 20.84/19.19 ( (filter nat), (fun code_code_numeral nat), (size_size code_code_numeral), sequentially, (size_size code_code_numeral), sequentially ) 20.84/19.19 ( (filter nat), (fun real (fun real complex)), complex_1, sequentially, complex_1, sequentially ) 20.84/19.19 ( (filter nat), (fun real (fun real complex)), rcis, sequentially, rcis, sequentially ) 20.84/19.19 ( (filter nat), (fun int (fun nat nat)), nat_aux, sequentially, nat_aux, sequentially ) 20.84/19.19 ( (fun (product_prod nat nat) bool), real, pi, pred_nat, pi, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun nat bool), prime, pred_nat, prime, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun nat nat), (size_size nat), pred_nat, (size_size nat), pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun nat nat), fact, pred_nat, fact, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), int, m, pred_nat, m, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), int, min_1, pred_nat, min_1, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), int, s, pred_nat, s, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), int, t, pred_nat, t, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun int bool), zprime, pred_nat, zprime, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun int bool), nat_neg, pred_nat, nat_neg, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun int bool), nat_is_nat, pred_nat, nat_is_nat, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun int bool), (even_odd_even int), pred_nat, (even_odd_even int), pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun int bool), twoSqu1091635170sum2sq, pred_nat, twoSqu1091635170sum2sq, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun int nat), phi, pred_nat, phi, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun real real), arccos, pred_nat, arccos, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun real real), ln, pred_nat, sqrt, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun real real), ln, pred_nat, ln, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun real real), sin, pred_nat, sin, pred_nat ) 20.84/19.19 ( (fun 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fNot, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun bool (fun bool bool)), fconj, pred_nat, fconj, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun bool (fun bool bool)), fdisj, pred_nat, fdisj, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun int (fun int bool)), sRStar, pred_nat, sRStar, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun int (fun int bool)), norRRset, pred_nat, norRRset, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun int (fun int bool)), sr, pred_nat, sr, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun int (fun int bool)), quickc1265749348ro_rel, pred_nat, quickc1265749348ro_rel, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun nat (fun real real)), root, pred_nat, root, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun real (fun real real)), powr, pred_nat, powr, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun nat (fun nat bool)), coprime, pred_nat, coprime, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun (fun int bool) int), (the int), pred_nat, (the int), pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, pred_nat, negateSnd, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun (fun int bool) bool), nat_nat_set, pred_nat, nat_nat_set, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun (product_prod nat nat) bool), pred_nat, pred_nat, pred_nat, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun (product_prod int int) bool), frac_1, pred_nat, frac_1, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun real complex), cis, pred_nat, cis, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun complex real), re, pred_nat, re, pred_nat ) 20.84/19.19 ( (fun (product_prod nat nat) bool), (fun complex real), arg, pred_nat, arg, pred_nat ) 20.84/19.19 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21.01/19.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun int (fun int int)), int_lcm, adjust, int_lcm, adjust ) 21.01/19.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun int (fun (fun int bool) bool)), rsetR, adjust, rsetR, adjust ) 21.01/19.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, adjust, posDivAlg_rel, adjust ) 21.01/19.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, adjust, negDivAlg_rel, adjust ) 21.01/19.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, adjust, norm_frac_rel, adjust ) 21.01/19.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (let 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adjust ) 21.01/19.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun (product_prod int int) int), twoSqu1094008024sum2sq, adjust, twoSqu1094008024sum2sq, adjust ) 21.01/19.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun real nat), natfloor, adjust, natfloor, adjust ) 21.01/19.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun real nat), natceiling, adjust, natceiling, adjust ) 21.01/19.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun int quickcheck_code_int), quickcheck_of_int, adjust, quickcheck_of_int, adjust ) 21.01/19.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun int (fun int (fun int bool))), wset, adjust, wset, adjust ) 21.01/19.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun int (fun int (fun int bool))), bnorRset, adjust, bnorRset, adjust ) 21.01/19.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun int (fun int (fun int bool))), zcong, adjust, zcong, adjust ) 21.01/19.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun int (fun int (fun int (fun int bool)))), multInvPair, adjust, multInvPair, adjust ) 21.01/19.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun int (fun int (fun (fun int bool) bool))), setS, adjust, setS, adjust ) 21.01/19.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, adjust, code_d418564891umeral, adjust ) 21.01/19.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun int real), (real_1 int), adjust, (real_1 int), adjust ) 21.01/19.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun complex nat), (size_size complex), adjust, (size_size complex), adjust ) 21.01/19.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun complex nat), complex_size, adjust, complex_size, adjust ) 21.01/19.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun int (list int)), quickc666637781d_zero, adjust, quickc666637781d_zero, adjust ) 21.01/19.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, adjust, divmod_nat_rel, adjust ) 21.01/19.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, adjust, ratrel, adjust ) 21.01/19.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun (product_prod int int) rat), frct, adjust, frct, adjust ) 21.01/19.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun code_code_numeral (fun nat nat)), code_nat_of_aux, adjust, code_nat_of_aux, adjust ) 21.01/19.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun (fun nat rat) bool), vanishes, adjust, vanishes, adjust ) 21.01/19.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun code_code_numeral int), code_int_of, adjust, code_int_of, adjust ) 21.01/19.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun nat (fun nat (product_prod nat nat))), divmod_nat, adjust, divmod_nat, adjust ) 21.01/19.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun code_code_numeral nat), (size_size code_code_numeral), adjust, (size_size code_code_numeral), adjust ) 21.01/19.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun real (fun real complex)), complex_1, adjust, complex_1, adjust ) 21.01/19.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun real (fun real complex)), rcis, adjust, rcis, adjust ) 21.01/19.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), (fun int (fun nat nat)), nat_aux, adjust, nat_aux, adjust ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), real, pi, bolzano_bisect, pi, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun nat bool), prime, bolzano_bisect, prime, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun nat nat), (size_size nat), bolzano_bisect, (size_size nat), bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun nat nat), fact, bolzano_bisect, fact, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), int, m, bolzano_bisect, m, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), int, min_1, bolzano_bisect, min_1, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), int, s, bolzano_bisect, s, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), int, t, bolzano_bisect, t, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun int bool), zprime, bolzano_bisect, zprime, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun int bool), nat_neg, bolzano_bisect, nat_neg, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun 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21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun complex complex), cnj, bolzano_bisect, cnj, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun nat real), (real_1 nat), bolzano_bisect, (real_1 nat), bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun nat real), cos_coeff, bolzano_bisect, cos_coeff, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun nat real), sin_coeff, bolzano_bisect, sin_coeff, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun int int), bit1, bolzano_bisect, bit1, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun int int), (fact_fact int), bolzano_bisect, (fact_fact int), bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun int int), zfact, bolzano_bisect, zfact, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun bool bool), fNot, bolzano_bisect, fNot, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun bool (fun bool bool)), fconj, bolzano_bisect, fconj, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun bool (fun bool bool)), fdisj, bolzano_bisect, fdisj, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real 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(fun nat _let_0))))), (fun real (fun real real)), powr, bolzano_bisect, powr, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun nat (fun nat bool)), coprime, bolzano_bisect, coprime, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun (fun int bool) int), (the int), bolzano_bisect, (the int), bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, bolzano_bisect, negateSnd, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun (fun int bool) bool), nat_nat_set, bolzano_bisect, nat_nat_set, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun (product_prod nat nat) bool), pred_nat, bolzano_bisect, pred_nat, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun (product_prod int int) bool), frac_1, bolzano_bisect, frac_1, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun real complex), cis, bolzano_bisect, cis, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun complex real), im, bolzano_bisect, im, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun complex real), re, bolzano_bisect, re, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun complex real), arg, bolzano_bisect, arg, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun code_code_numeral code_code_numeral), code_S1047413653umeral, bolzano_bisect, code_S1047413653umeral, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun int (fun int int)), z3mod, bolzano_bisect, z3mod, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun int (fun int int)), (gcd_gcd int), bolzano_bisect, (gcd_gcd int), bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun int (fun int int)), z3div, bolzano_bisect, z3div, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun int (fun int int)), int_lcm, bolzano_bisect, int_lcm, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun int (fun (fun int bool) bool)), rsetR, bolzano_bisect, rsetR, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun int (fun (fun int bool) bool)), resSet, bolzano_bisect, resSet, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, bolzano_bisect, posDivAlg_rel, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, bolzano_bisect, negDivAlg_rel, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, bolzano_bisect, pair_leq, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun int (fun int (product_prod int int))), negDivAlg, bolzano_bisect, negDivAlg, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun int (fun int (product_prod int int))), divmod_int, bolzano_bisect, divmod_int, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), (fun int (fun int (product_prod int int))), posDivAlg, bolzano_bisect, posDivAlg, bolzano_bisect ) 21.01/19.24 ( (let ((_let_0 (product_prod real real))) 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nat), code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun nat real), cos_coeff, code_d418564891umeral, cos_coeff, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun nat real), sin_coeff, code_d418564891umeral, sin_coeff, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int int), bit1, code_d418564891umeral, bit1, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int int), zfact, code_d418564891umeral, zfact, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun bool (fun bool bool)), fconj, code_d418564891umeral, fconj, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun bool (fun bool bool)), fdisj, code_d418564891umeral, fdisj, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int bool)), sRStar, code_d418564891umeral, sRStar, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int bool)), norRRset, code_d418564891umeral, norRRset, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int bool)), d22set, code_d418564891umeral, d22set, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int bool)), sr, code_d418564891umeral, sr, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int bool)), quickc1265749348ro_rel, code_d418564891umeral, quickc1265749348ro_rel, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun nat (fun real real)), root, code_d418564891umeral, root, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun real (fun real real)), powr, code_d418564891umeral, powr, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun nat (fun nat bool)), coprime, code_d418564891umeral, coprime, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, code_d418564891umeral, negateSnd, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun (fun int bool) bool), nat_nat_set, code_d418564891umeral, nat_nat_set, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun (product_prod int int) bool), frac_1, code_d418564891umeral, frac_1, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun real complex), cis, code_d418564891umeral, cis, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun complex real), re, code_d418564891umeral, re, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun complex real), arg, code_d418564891umeral, arg, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_d418564891umeral, code_S1047413653umeral, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int int)), int_gcd, code_d418564891umeral, int_gcd, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int int)), legacy_zgcd, code_d418564891umeral, legacy_zgcd, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int int)), z3mod, code_d418564891umeral, z3mod, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int int)), inv, code_d418564891umeral, legacy_zgcd, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int int)), (gcd_gcd int), code_d418564891umeral, (gcd_gcd int), code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int int)), z3div, code_d418564891umeral, z3div, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int int)), int_lcm, code_d418564891umeral, int_lcm, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun (fun int bool) bool)), rsetR, code_d418564891umeral, rsetR, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, code_d418564891umeral, posDivAlg_rel, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, code_d418564891umeral, negDivAlg_rel, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, code_d418564891umeral, norm_frac_rel, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, code_d418564891umeral, pair_leq, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int (product_prod int int))), negDivAlg, code_d418564891umeral, negDivAlg, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int (product_prod int int))), divmod_int, code_d418564891umeral, divmod_int, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int (product_prod int int))), posDivAlg, code_d418564891umeral, posDivAlg, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, code_d418564891umeral, adjust, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), code_d418564891umeral, (ord_gr676655987ssThan nat), code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun (product_prod int int) int), twoSqu1094008024sum2sq, code_d418564891umeral, twoSqu1094008024sum2sq, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun real nat), natfloor, code_d418564891umeral, natfloor, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int (fun int bool))), wset, code_d418564891umeral, wset, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int (fun int bool))), bnorRset, code_d418564891umeral, bnorRset, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int (fun int bool))), zcong, code_d418564891umeral, zcong, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int (fun int (fun int bool)))), multInvPair, code_d418564891umeral, multInvPair, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (fun int (fun (fun int bool) bool))), setS, code_d418564891umeral, setS, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral, code_d418564891umeral, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int real), (real_1 int), code_d418564891umeral, (real_1 int), code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun complex nat), (size_size complex), code_d418564891umeral, (size_size complex), code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun complex nat), complex_size, code_d418564891umeral, complex_size, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun int (list int)), quickc666637781d_zero, code_d418564891umeral, quickc666637781d_zero, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, code_d418564891umeral, divmod_nat_rel, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, code_d418564891umeral, ratrel, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun (product_prod int int) rat), frct, code_d418564891umeral, frct, code_d418564891umeral ) 21.01/19.28 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_d418564891umeral, code_nat_of_aux, code_d418564891umeral ) 21.01/19.28 ( (fun 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(fun real complex), cis, nat_gcd_rel, cis, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun int (fun int int)), int_gcd, nat_gcd_rel, int_gcd, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun int (fun int int)), legacy_zgcd, nat_gcd_rel, legacy_zgcd, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun int (fun int int)), standardRes, nat_gcd_rel, standardRes, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun int (fun int int)), nat_tsub, nat_gcd_rel, nat_tsub, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun int (fun (product_prod int int) bool)), int_ge_less_than, nat_gcd_rel, int_ge_less_than, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, nat_gcd_rel, lazy_small_lazy_rel, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, nat_gcd_rel, norm_frac_rel, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, nat_gcd_rel, xzgcd, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun int (fun int (product_prod int int))), posDivAlg, nat_gcd_rel, posDivAlg, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), nat_gcd_rel, (ord_gr676655987ssThan nat), nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun real nat), natfloor, nat_gcd_rel, natfloor, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun int (fun int (fun int bool))), zcongm, nat_gcd_rel, zcongm, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel, nat_gcd_rel, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun int (fun int rat)), fract, nat_gcd_rel, fract, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun nat (fun nat (product_prod nat nat))), divmod_nat, nat_gcd_rel, divmod_nat, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun code_code_numeral nat), code_c271388182l_size, nat_gcd_rel, code_c271388182l_size, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun real (fun real complex)), rcis, nat_gcd_rel, rcis, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun rat real), ratreal, nat_gcd_rel, ratreal, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun quickcheck_code_int int), quickcheck_int_of, nat_gcd_rel, quickcheck_int_of, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, nat_gcd_rel, quickc495462417de_int, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun rat (product_prod int int)), quotient_of, nat_gcd_rel, quotient_of, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun (fun int bool) (fun int (fun int int))), rRset2norRR, nat_gcd_rel, rRset2norRR, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun (fun real bool) real), (complete_Sup_Sup real), nat_gcd_rel, (complete_Sup_Sup real), nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), (fun quickcheck_code_int nat), quickcheck_nat_of, nat_gcd_rel, quickcheck_nat_of, nat_gcd_rel ) 21.18/19.32 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 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, nat_gcd_rel, xzgcda, nat_gcd_rel ) 21.18/19.32 ( (fun (fun nat rat) bool), bool, fFalse, vanishes, fFalse, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), real, pi, vanishes, pi, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun nat nat), (fact_fact nat), vanishes, (fact_fact nat), vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun nat nat), (size_size nat), vanishes, (size_size nat), vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun nat nat), fact, vanishes, fact, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), int, m, vanishes, m, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), int, s, vanishes, s, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), int, s1, vanishes, s1, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), int, t, vanishes, t, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun int bool), zprime, vanishes, zprime, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun int bool), zOdd, vanishes, zOdd, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun int bool), (even_odd_even int), vanishes, (even_odd_even int), vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun int bool), twoSqu1091635170sum2sq, vanishes, twoSqu1091635170sum2sq, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun int nat), phi, vanishes, phi, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun real real), cos, vanishes, cos, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun real real), ln, vanishes, ln, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun real real), arcsin, vanishes, arcsin, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), complex, ii, vanishes, ii, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun complex complex), cnj, vanishes, cnj, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun complex complex), expi, vanishes, expi, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun nat real), (real_1 nat), vanishes, (real_1 nat), vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun nat real), cos_coeff, vanishes, cos_coeff, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun nat real), sin_coeff, vanishes, sin_coeff, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun int int), pred, vanishes, pred, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun int int), zfact, vanishes, zfact, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, vanishes, is_RRset, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun bool (fun bool bool)), fconj, vanishes, fconj, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun bool (fun bool bool)), fdisj, vanishes, fdisj, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun bool (fun bool bool)), fimplies, vanishes, fimplies, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun int (fun int bool)), sRStar, vanishes, sRStar, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun int (fun int bool)), norRRset, vanishes, norRRset, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun int (fun int bool)), d22set, vanishes, d22set, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun int (fun int bool)), quickc1265749348ro_rel, vanishes, quickc1265749348ro_rel, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun nat (fun nat nat)), nat_lcm, vanishes, nat_lcm, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun nat (fun real real)), root, vanishes, root, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun real (fun real real)), log, vanishes, log, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun real (fun real real)), powr, vanishes, powr, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (fun nat (fun nat bool)), coprime, vanishes, coprime, vanishes ) 21.18/19.32 ( (fun (fun nat rat) bool), (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, vanishes, negateSnd, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun (fun int bool) bool), nat_nat_set, vanishes, nat_nat_set, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun (product_prod int int) bool), frac_1, vanishes, frac_1, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun real complex), cis, vanishes, cis, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun complex real), re, vanishes, re, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun complex real), arg, vanishes, arg, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun code_code_numeral code_code_numeral), code_S1047413653umeral, vanishes, code_S1047413653umeral, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int (fun int int)), int_gcd, vanishes, int_gcd, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int (fun int int)), legacy_zgcd, vanishes, legacy_zgcd, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int (fun int int)), (gcd_gcd int), vanishes, (gcd_gcd int), vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int (fun int int)), legendre, vanishes, nat_tsub, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int (fun int int)), nat_tsub, vanishes, nat_tsub, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int (fun int int)), int_lcm, vanishes, int_lcm, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int (fun (product_prod int int) bool)), int_ge_less_than, vanishes, int_ge_less_than, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int (fun (fun int bool) bool)), rsetR, vanishes, rsetR, vanishes ) 21.18/19.36 ( (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 ) 21.18/19.36 ( (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 ) 21.18/19.36 ( (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 ) 21.18/19.36 ( (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 ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int (fun int (product_prod int int))), negDivAlg, vanishes, negDivAlg, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int (fun int (product_prod int int))), divmod_int, vanishes, divmod_int, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int (fun int (product_prod int int))), posDivAlg, vanishes, posDivAlg, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), vanishes, (ord_gr676655987ssThan nat), vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun (product_prod int int) int), twoSqu1094008024sum2sq, vanishes, twoSqu1094008024sum2sq, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun real nat), natfloor, vanishes, natfloor, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int (fun int (fun int bool))), bnorRset, vanishes, bnorRset, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int (fun int (fun int bool))), zcong, vanishes, zcong, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int (fun int (fun int bool))), zcongm, vanishes, zcongm, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int real), (real_1 int), vanishes, (real_1 int), vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun complex nat), (size_size complex), vanishes, (size_size complex), vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun complex nat), complex_size, vanishes, complex_size, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int (list int)), quickc666637781d_zero, vanishes, quickc666637781d_zero, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, vanishes, divmod_nat_rel, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, vanishes, ratrel, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun (product_prod int int) rat), frct, vanishes, frct, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun code_code_numeral (fun nat nat)), code_nat_of_aux, vanishes, code_nat_of_aux, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun (fun nat rat) bool), vanishes, vanishes, vanishes, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int (fun int rat)), fract, vanishes, fract, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun code_code_numeral int), code_int_of, vanishes, code_int_of, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun nat (fun nat (product_prod nat nat))), divmod_nat, vanishes, divmod_nat, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun code_code_numeral nat), (size_size code_code_numeral), vanishes, (size_size code_code_numeral), vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun real (fun real complex)), complex_1, vanishes, complex_1, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun real (fun real complex)), rcis, vanishes, rcis, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun int (fun nat nat)), nat_aux, vanishes, nat_aux, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun rat real), ratreal, vanishes, ratreal, vanishes ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun quickcheck_code_int int), quickcheck_int_of, vanishes, quickcheck_int_of, vanishes ) 21.18/19.36 ( (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 ) 21.18/19.36 ( (fun (fun nat rat) bool), (fun rat (product_prod int int)), quotient_of, vanishes, quotient_of, vanishes ) 21.18/19.36 ( (fun int (fun int rat)), bool, fFalse, fract, fFalse, fract ) 21.18/19.36 ( (fun int (fun int rat)), (fun nat bool), (even_odd_even nat), fract, (even_odd_even nat), fract ) 21.18/19.36 ( (fun int (fun int rat)), (fun nat nat), (fact_fact nat), fract, (fact_fact nat), fract ) 21.18/19.36 ( (fun int (fun int rat)), int, m, fract, m, fract ) 21.18/19.36 ( (fun int (fun int rat)), int, s1, fract, s1, fract ) 21.18/19.36 ( (fun int (fun int rat)), int, t, fract, t, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int bool), zprime, fract, zprime, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int bool), zOdd, fract, zOdd, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int bool), (even_odd_even int), fract, (even_odd_even int), fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int nat), nat_1, fract, nat_1, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int nat), phi, fract, phi, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun real real), cos, fract, cos, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun real real), ln, fract, ln, fract ) 21.18/19.37 ( (fun int (fun int rat)), complex, ii, fract, ii, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun complex complex), cnj, fract, cnj, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun complex complex), expi, fract, expi, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun nat real), cos_coeff, fract, cos_coeff, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int int), pred, fract, pred, fract ) 21.18/19.37 ( (fun int (fun int rat)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, fract, is_RRset, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun bool (fun bool bool)), fconj, fract, fconj, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun bool (fun bool bool)), fimplies, fract, fimplies, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int (fun int bool)), sRStar, fract, sRStar, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int (fun int bool)), d22set, fract, d22set, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun nat (fun nat nat)), nat_lcm, fract, nat_lcm, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun real (fun real real)), log, fract, log, fract ) 21.18/19.37 ( (fun int (fun int rat)), (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, fract, normalize, fract ) 21.18/19.37 ( (fun int (fun int rat)), (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, fract, negateSnd, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun (fun int bool) bool), nat_nat_set, fract, nat_nat_set, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun (product_prod int int) bool), frac_1, fract, frac_1, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun real complex), cis, fract, cis, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun complex real), arg, fract, arg, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int (fun int int)), int_gcd, fract, int_gcd, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int (fun int int)), legacy_zgcd, fract, legacy_zgcd, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int (fun int int)), standardRes, fract, standardRes, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int (fun int int)), nat_tsub, fract, nat_tsub, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int (fun int int)), int_lcm, fract, int_lcm, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int (fun (product_prod int int) bool)), int_ge_less_than, fract, int_ge_less_than, fract ) 21.18/19.37 ( (fun int (fun int rat)), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, fract, lazy_small_lazy_rel, fract ) 21.18/19.37 ( (fun int (fun int rat)), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, fract, negDivAlg_rel, fract ) 21.18/19.37 ( (fun int (fun int rat)), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, fract, norm_frac_rel, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, fract, xzgcd, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int (fun int (product_prod int int))), posDivAlg, fract, posDivAlg, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), fract, (ord_gr676655987ssThan nat), fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun real nat), natfloor, fract, natfloor, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int (fun int (fun int bool))), zcong, fract, zcong, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int (fun int (fun int bool))), zcongm, fract, zcongm, fract ) 21.18/19.37 ( (fun int (fun int rat)), (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, fract, nat_gcd_rel, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int (fun int rat)), fract, fract, fract, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun nat (fun nat (product_prod nat nat))), divmod_nat, fract, divmod_nat, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun code_code_numeral nat), code_c271388182l_size, fract, code_c271388182l_size, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun real (fun real complex)), complex_1, fract, complex_1, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun real (fun real complex)), rcis, fract, rcis, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int (fun nat nat)), nat_aux, fract, nat_aux, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun rat real), ratreal, fract, ratreal, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun quickcheck_code_int int), quickcheck_int_of, fract, quickcheck_int_of, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, fract, quickc495462417de_int, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun rat (product_prod int int)), quotient_of, fract, quotient_of, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun (fun int bool) (fun int (fun int int))), rRset2norRR, fract, rRset2norRR, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun (fun real bool) real), (complete_Sup_Sup real), fract, (complete_Sup_Sup real), fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun quickcheck_code_int nat), quickcheck_nat_of, fract, quickcheck_nat_of, fract ) 21.18/19.37 ( (fun int (fun int rat)), (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda, fract, xzgcda, fract ) 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(even_odd_even int), quickcheck_int_of ) 21.18/19.38 ( (fun quickcheck_code_int int), (fun int nat), nat_1, quickcheck_int_of, nat_1, quickcheck_int_of ) 21.18/19.38 ( (fun quickcheck_code_int int), (fun int nat), phi, quickcheck_int_of, phi, quickcheck_int_of ) 21.18/19.38 ( (fun quickcheck_code_int int), (fun real real), cos, quickcheck_int_of, cos, quickcheck_int_of ) 21.18/19.38 ( (fun quickcheck_code_int int), (fun real real), ln, quickcheck_int_of, ln, quickcheck_int_of ) 21.18/19.38 ( (fun quickcheck_code_int int), complex, ii, quickcheck_int_of, ii, quickcheck_int_of ) 21.18/19.38 ( (fun quickcheck_code_int int), (fun complex complex), expi, quickcheck_int_of, expi, quickcheck_int_of ) 21.18/19.38 ( (fun quickcheck_code_int int), (fun nat real), cos_coeff, quickcheck_int_of, cos_coeff, quickcheck_int_of ) 21.18/19.38 ( (fun quickcheck_code_int int), (fun int int), pred, quickcheck_int_of, pred, quickcheck_int_of ) 21.18/19.38 ( (fun quickcheck_code_int int), (let ((_let_0 (fun 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(hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 21.34/19.41 ) 21.34/19.41 (instantiation (let ((_let_0 (ord_gr676655987ssThan X_a))) (forall ((X_a $$unsorted)) (or (not (dense_linorder X_a)) (= _let_0 (ti (fun X_a (fun X_a (fun X_a bool))) _let_0))) )) 21.34/19.41 ( bool ) 21.34/19.41 ( real ) 21.34/19.41 ( nat ) 21.34/19.41 ( (fun nat bool) ) 21.34/19.41 ( int ) 21.34/19.41 ( (fun int bool) ) 21.34/19.41 ( rat ) 21.34/19.41 ( (product_prod real real) ) 21.34/19.41 ( (product_prod int int) ) 21.34/19.41 ( (filter real) ) 21.34/19.41 ( (filter nat) ) 21.34/19.41 ( (product_prod nat nat) ) 21.34/19.41 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 21.34/19.41 ( (fun nat rat) ) 21.34/19.41 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 21.34/19.41 ) 21.34/19.41 (instantiation (let ((_let_0 (nat_rec X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun X_a (fun (fun nat (fun X_a X_a)) (fun nat X_a))) _let_0)) )) 21.34/19.41 ( bool ) 21.34/19.41 ( real ) 21.34/19.41 ( nat ) 21.34/19.41 ( (fun nat bool) ) 21.34/19.41 ( int ) 21.34/19.41 ( (fun int bool) ) 21.34/19.41 ( (fun real bool) ) 21.34/19.41 ( (fun real real) ) 21.34/19.41 ( complex ) 21.34/19.41 ( (fun nat real) ) 21.34/19.41 ( (fun int int) ) 21.34/19.41 ( (fun int (fun int bool)) ) 21.34/19.41 ( (product_prod int int) ) 21.34/19.41 ( (fun (product_prod int int) bool) ) 21.34/19.41 ( code_code_numeral ) 21.34/19.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 21.34/19.41 ( (fun (product_prod int int) int) ) 21.34/19.41 ( (fun int (fun int (fun int bool))) ) 21.34/19.41 ( (fun int real) ) 21.34/19.41 ) 21.34/19.41 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun nat real))) (let ((_let_3 (fun (filter nat) bool))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less_eq real) _let_0) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) X_1) (one_one real)))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_3 (hAPP _let_2 (fun real _let_3) (tendsto nat real) (hAPP real _let_2 (power_power real) X_1)) _let_0) sequentially))) ))))) 21.34/19.41 ( (zero_zero real) ) 21.34/19.41 ( (one_one real) ) 21.34/19.41 ( pi ) 21.34/19.41 ( (hAPP int real (number_number_of real) min_1) ) 21.34/19.41 ( (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)))) ) 21.34/19.41 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.34/19.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.41 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.41 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.41 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 21.34/19.41 ( skv_6 ) 21.34/19.41 ( skv_11 ) 21.34/19.41 ( skv_12 ) 21.34/19.41 ( skv_14 ) 21.34/19.41 ) 21.34/19.41 (instantiation (let ((_let_0 (hAPP real (fun real complex) complex_1 A_1))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (hAPP real complex _let_0 (hAPP real real (uminus_uminus real) B)) (hAPP complex complex cnj (hAPP real complex _let_0 B))) )) 21.34/19.41 ( (zero_zero real), (zero_zero real) ) 21.34/19.41 ( (zero_zero real), (one_one real) ) 21.34/19.41 ( (one_one real), (zero_zero real) ) 21.34/19.41 ) 21.34/19.41 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_160494 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_160494) _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_160494)) _let_2))) )))) 21.34/19.41 ( real, (zero_zero real) ) 21.34/19.41 ( real, pi ) 21.34/19.41 ( 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))))) ) 21.34/19.41 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.41 ( int, (zero_zero int) ) 21.34/19.41 ( int, min_1 ) 21.34/19.41 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 21.34/19.41 ( int, t ) 21.34/19.41 ( complex, ii ) 21.34/19.41 ) 21.34/19.41 (instantiation (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_160516))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_160516 $$unsorted) (BOUND_VARIABLE_160517 $$unsorted) (BOUND_VARIABLE_160518 $$unsorted)) (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_160517)) BOUND_VARIABLE_160518) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_160518)) BOUND_VARIABLE_160517))) )))) 21.34/19.41 ( 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) ) 21.34/19.41 ( 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 ) 21.34/19.41 ) 21.34/19.41 (instantiation (let ((_let_0 (hAPP nat real (real_1 nat) A_1))) (forall ((A_1 $$unsorted) (X $$unsorted)) (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)))) )) 21.34/19.41 ( (zero_zero nat), pi ) 21.34/19.41 ( (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)))) ) 21.34/19.41 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.41 ( (zero_zero nat), skv_6 ) 21.34/19.41 ( (zero_zero nat), skv_11 ) 21.34/19.41 ( (zero_zero nat), skv_12 ) 21.34/19.41 ( (zero_zero nat), skv_14 ) 21.34/19.41 ) 21.34/19.41 (instantiation (let ((_let_0 (fun int int))) (forall ((N $$unsorted) (K_4 $$unsorted)) (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)))) )) 21.34/19.41 ( (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))) ) 21.34/19.41 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.41 ( 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))) ) 21.34/19.41 ( skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.34/19.41 ) 21.34/19.41 (instantiation (let ((_let_0 (fun nat real))) (let ((_let_1 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (forall ((F $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (summable real) F))) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool _let_1 (hAPP nat real F N_2))) )) (hBOOL (hAPP real bool _let_1 (hAPP _let_0 real (suminf real) F)))) ))) 21.34/19.41 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (combc nat nat nat))) (let ((_let_4 (fun nat _let_0))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun _let_1 _let_4))) (let ((_let_7 (combb real _let_0 nat))) (hAPP _let_1 _let_1 (hAPP _let_4 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_4 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_4 (hAPP _let_5 _let_6 _let_7 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_3 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 21.34/19.41 ) 21.34/19.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160673 $$unsorted)) (or (not (monoid_mult X_a)) (= (ti X_a BOUND_VARIABLE_160673) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_160673) (one_one X_a)))) ) 21.34/19.41 ( bool, fFalse ) 21.34/19.41 ( bool, fTrue ) 21.34/19.41 ( real, pi ) 21.34/19.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.41 ( 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))))) ) 21.34/19.41 ( (fun nat bool), (even_odd_even nat) ) 21.34/19.41 ( (fun nat bool), prime ) 21.34/19.41 ( (fun nat nat), suc ) 21.34/19.41 ( (fun nat nat), (fact_fact nat) ) 21.34/19.41 ( (fun nat nat), (size_size nat) ) 21.34/19.41 ( (fun nat nat), fact ) 21.34/19.41 ( (fun nat nat), nat_size ) 21.34/19.41 ( int, pls ) 21.34/19.41 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.41 ( int, m ) 21.34/19.41 ( 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))) ) 21.34/19.41 ( int, min_1 ) 21.34/19.41 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.41 ( int, s ) 21.34/19.41 ( int, s1 ) 21.34/19.41 ( int, t ) 21.34/19.41 ( (fun int bool), zprime ) 21.34/19.41 ( (fun int bool), nat_neg ) 21.34/19.41 ( (fun int bool), zEven ) 21.34/19.41 ( (fun int bool), nat_is_nat ) 21.34/19.41 ( (fun int bool), zOdd ) 21.34/19.41 ( (fun int bool), (even_odd_even int) ) 21.34/19.41 ( (fun int bool), twoSqu1091635170sum2sq ) 21.34/19.41 ( (fun int nat), nat_1 ) 21.34/19.41 ( (fun int nat), phi ) 21.34/19.41 ( (fun real real), sqrt ) 21.34/19.41 ( (fun real real), tan ) 21.34/19.41 ( (fun real real), cos ) 21.34/19.41 ( (fun real real), arccos ) 21.34/19.41 ( (fun real real), ln ) 21.34/19.41 ( (fun real real), sin ) 21.34/19.41 ( (fun real real), arctan ) 21.34/19.41 ( (fun real real), arcsin ) 21.34/19.41 ( complex, ii ) 21.34/19.41 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.41 ( 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)) ) 21.34/19.41 ( (fun complex complex), cnj ) 21.34/19.41 ( (fun complex complex), expi ) 21.34/19.41 ( (fun nat real), (real_1 nat) ) 21.34/19.41 ( (fun nat real), cos_coeff ) 21.34/19.41 ( (fun nat real), sin_coeff ) 21.34/19.41 ( (fun int int), bit0 ) 21.34/19.41 ( (fun int int), bit1 ) 21.34/19.41 ( (fun int int), pred ) 21.34/19.41 ( (fun int int), succ ) 21.34/19.41 ( (fun int int), (fact_fact int) ) 21.34/19.41 ( (fun int int), zfact ) 21.34/19.41 ( (fun bool bool), fNot ) 21.34/19.41 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.34/19.41 ( (fun bool (fun bool bool)), fconj ) 21.34/19.41 ( (fun bool (fun bool bool)), fdisj ) 21.34/19.41 ( (fun bool (fun bool bool)), fimplies ) 21.34/19.41 ( (fun int (fun int bool)), sRStar ) 21.34/19.41 ( (fun int (fun int bool)), quadRes ) 21.34/19.41 ( (fun int (fun int bool)), norRRset ) 21.34/19.41 ( (fun int (fun int bool)), d22set ) 21.34/19.41 ( (fun int (fun int bool)), sr ) 21.34/19.41 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.34/19.41 ( (fun nat (fun nat nat)), nat_gcd ) 21.34/19.41 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.34/19.41 ( (fun nat (fun nat nat)), nat_lcm ) 21.34/19.41 ( (fun nat (fun real real)), root ) 21.34/19.41 ( (fun real (fun real real)), log ) 21.34/19.41 ( (fun real (fun real real)), powr ) 21.34/19.41 ( (fun nat (fun nat bool)), coprime ) 21.34/19.41 ( (fun (fun int bool) int), (the int) ) 21.34/19.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.34/19.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.34/19.41 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.34/19.41 ( (fun (fun int bool) bool), nat_nat_set ) 21.34/19.41 ( (filter nat), sequentially ) 21.34/19.41 ( (fun (product_prod nat nat) bool), pred_nat ) 21.34/19.41 ( (fun (product_prod int int) bool), frac_1 ) 21.34/19.41 ( (fun real complex), cis ) 21.34/19.41 ( (fun complex real), im ) 21.34/19.41 ( (fun complex real), re ) 21.34/19.41 ( (fun complex real), arg ) 21.34/19.41 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.34/19.41 ( (fun int (fun int int)), int_gcd ) 21.34/19.41 ( (fun int (fun int int)), multInv ) 21.34/19.41 ( (fun int (fun int int)), legacy_zgcd ) 21.34/19.41 ( (fun int (fun int int)), z3mod ) 21.34/19.41 ( (fun int (fun int int)), inv ) 21.34/19.41 ( (fun int (fun int int)), (gcd_gcd int) ) 21.34/19.41 ( (fun int (fun int int)), standardRes ) 21.34/19.41 ( (fun int (fun int int)), legendre ) 21.34/19.41 ( (fun int (fun int int)), nat_tsub ) 21.34/19.41 ( (fun int (fun int int)), z3div ) 21.34/19.41 ( (fun int (fun int int)), int_lcm ) 21.34/19.42 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.34/19.42 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.34/19.42 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.34/19.42 ( (fun int (fun (fun int bool) bool)), resSet ) 21.34/19.42 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.34/19.42 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.34/19.42 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.34/19.42 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.34/19.42 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.34/19.42 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.34/19.42 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.34/19.42 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.34/19.42 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.34/19.42 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.34/19.42 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.34/19.42 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.34/19.42 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.34/19.42 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.34/19.42 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.34/19.42 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.34/19.42 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.34/19.42 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.34/19.42 ( (fun real nat), natfloor ) 21.34/19.42 ( (fun real nat), natceiling ) 21.34/19.42 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.34/19.42 ( (fun int (fun int (fun int bool))), wset ) 21.34/19.42 ( (fun int (fun int (fun int bool))), bnorRset ) 21.34/19.42 ( (fun int (fun int (fun int bool))), zcong ) 21.34/19.42 ( (fun int (fun int (fun int bool))), noXRRset ) 21.34/19.42 ( (fun int (fun int (fun int bool))), zcongm ) 21.34/19.42 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.34/19.42 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.34/19.42 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.34/19.42 ( (fun int real), (real_1 int) ) 21.34/19.42 ( (fun complex nat), (size_size complex) ) 21.34/19.42 ( (fun complex nat), complex_size ) 21.34/19.42 ( (fun int (list int)), quickc666637781d_zero ) 21.34/19.42 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.34/19.42 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.34/19.42 ( (fun (product_prod int int) rat), frct ) 21.34/19.42 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.34/19.42 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.34/19.42 ( (fun (fun nat rat) bool), vanishes ) 21.34/19.42 ( (fun int (fun int rat)), fract ) 21.34/19.42 ( (fun code_code_numeral int), code_int_of ) 21.34/19.42 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.34/19.42 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.34/19.42 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.34/19.42 ( (fun real (fun real complex)), complex_1 ) 21.34/19.42 ( (fun real (fun real complex)), rcis ) 21.34/19.42 ( (fun int (fun nat nat)), nat_aux ) 21.34/19.42 ( (fun rat real), ratreal ) 21.34/19.42 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.34/19.42 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.34/19.42 ( (fun rat (product_prod int int)), quotient_of ) 21.34/19.42 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.34/19.42 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.34/19.42 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.34/19.42 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.34/19.42 ) 21.34/19.42 (instantiation (let ((_let_0 (semiring_1_of_nat int))) (forall ((M $$unsorted)) (= (hAPP nat int _let_0 (hAPP nat nat suc M)) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int _let_0 M))) )) 21.34/19.42 ( (zero_zero nat) ) 21.34/19.42 ( (hAPP nat nat suc (zero_zero nat)) ) 21.34/19.42 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.34/19.42 ) 21.34/19.42 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_160697 $$unsorted) (BOUND_VARIABLE_160698 $$unsorted)) (or (not (linorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_160697) BOUND_VARIABLE_160698))) (= (= (ti X_a BOUND_VARIABLE_160697) (ti X_a BOUND_VARIABLE_160698)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_160697) BOUND_VARIABLE_160698))))) )) 21.34/19.42 ( real, (zero_zero real), pi ) 21.34/19.42 ( 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)))) ) 21.34/19.42 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.42 ( real, (zero_zero real), skv_2 ) 21.34/19.42 ( real, (zero_zero real), skv_6 ) 21.34/19.42 ( real, (zero_zero real), skv_10 ) 21.34/19.42 ( real, (zero_zero real), skv_11 ) 21.34/19.42 ( real, (zero_zero real), skv_12 ) 21.34/19.42 ( real, (zero_zero real), skv_13 ) 21.34/19.42 ( real, (zero_zero real), skv_14 ) 21.34/19.42 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.42 ( real, pi, (zero_zero real) ) 21.34/19.42 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.42 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.34/19.42 ( real, (hAPP real real (hAPP real (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))) ) 21.34/19.42 ( 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) ) 21.34/19.42 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.34/19.42 ( 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 ) 21.34/19.42 ( real, skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.42 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.42 ( int, (zero_zero int), (zero_zero int) ) 21.34/19.42 ( int, (zero_zero int), (one_one int) ) 21.34/19.42 ( 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))) ) 21.34/19.42 ( int, (zero_zero int), min_1 ) 21.34/19.42 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.42 ( int, (zero_zero int), s ) 21.34/19.42 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 21.34/19.42 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.34/19.42 ( int, (zero_zero int), skv_3 ) 21.34/19.42 ( int, (zero_zero int), skv_9 ) 21.34/19.42 ( int, (one_one int), t ) 21.34/19.42 ( int, min_1, (zero_zero int) ) 21.34/19.42 ( int, min_1, pls ) 21.34/19.42 ( int, min_1, min_1 ) 21.34/19.42 ( 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))) ) 21.34/19.42 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 21.34/19.42 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 21.34/19.42 ( int, t, (zero_zero int) ) 21.34/19.42 ( int, t, (one_one int) ) 21.34/19.42 ( 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))) ) 21.34/19.42 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.34/19.42 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.34/19.42 ) 21.34/19.42 (instantiation (let ((_let_0 (inverse_divide real))) (let ((_let_1 (hAPP nat (fun real real) root N))) (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (let ((_let_0 (fun real real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (hAPP real real _let_1 (hAPP real real (hAPP real _let_0 _let_0 X) Y)) (hAPP real real (hAPP real _let_0 _let_0 (hAPP real real _let_1 X)) (hAPP real real _let_1 Y))))) ))) 21.34/19.42 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.42 ) 21.34/19.42 (instantiation (let ((_let_0 (one_one X_a))) (forall ((X_a $$unsorted)) (or (not (division_ring X_a)) (= _let_0 (hAPP X_a X_a (inverse_inverse X_a) _let_0))) )) 21.34/19.42 ( real ) 21.34/19.42 ( nat ) 21.34/19.42 ( int ) 21.34/19.42 ( complex ) 21.34/19.42 ( rat ) 21.34/19.42 ( quickcheck_code_int ) 21.34/19.42 ( code_code_numeral ) 21.34/19.42 ) 21.34/19.42 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (forall ((X $$unsorted) (Y $$unsorted)) (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))) ))) 21.34/19.42 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.42 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 21.34/19.42 ) 21.34/19.42 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (hAPP int (fun int int) inv P_5))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (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))) (= (hAPP int int _let_2 (hAPP int int _let_2 A_1)) (ti int A_1))) )))) 21.34/19.42 ( (zero_zero int), (zero_zero int) ) 21.34/19.42 ( (zero_zero int), (one_one int) ) 21.34/19.42 ( (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))) ) 21.34/19.42 ( (zero_zero int), min_1 ) 21.34/19.42 ( min_1, (zero_zero int) ) 21.34/19.42 ( min_1, min_1 ) 21.34/19.42 ( 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))) ) 21.34/19.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 21.34/19.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 21.34/19.42 ( t, (zero_zero int) ) 21.34/19.42 ( t, (one_one int) ) 21.34/19.42 ( 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))) ) 21.34/19.42 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.34/19.42 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.34/19.42 ) 21.34/19.42 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (let ((_let_4 (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_161008)))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_161008) _let_2)))) (let ((_let_6 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_161009) BOUND_VARIABLE_161008))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_161007 $$unsorted) (BOUND_VARIABLE_161008 $$unsorted) (BOUND_VARIABLE_161009 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_161007) BOUND_VARIABLE_161008)) BOUND_VARIABLE_161009)) (and (or _let_4 (and (or _let_5 (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_161009))) (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_6) BOUND_VARIABLE_161007))))) (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_161007) _let_6)))))) )))))))) 21.34/19.42 ( real, (zero_zero real), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.42 ( 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))) ) 21.34/19.42 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.42 ( 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 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.43 ( int, (zero_zero int), skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.34/19.43 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (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))) ) 21.34/19.43 ( 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))) (zero_zero int)))), skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.34/19.43 ) 21.34/19.43 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP complex real (norm_norm complex) Z_1) (hAPP real real sqrt (hAPP complex real re (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) Z_1) (hAPP complex complex cnj Z_1))))) ) 21.34/19.43 ( ii ) 21.34/19.43 ( (zero_zero complex) ) 21.34/19.43 ( (one_one complex) ) 21.34/19.43 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.43 ( (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 21.34/19.43 ) 21.34/19.43 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (let ((_let_3 (filter X_a))) (let ((_let_4 (fun _let_3 bool))) (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_161085 $$unsorted) (BOUND_VARIABLE_161086 $$unsorted) (BOUND_VARIABLE_161087 $$unsorted) (BOUND_VARIABLE_161088 $$unsorted)) (or (not (metric_space X_b)) (not (metric_space X_a)) (not (hBOOL (hAPP _let_3 bool (hAPP X_b _let_4 (hAPP (fun X_a X_b) (fun X_b _let_4) (tendsto X_a X_b) BOUND_VARIABLE_161086) BOUND_VARIABLE_161087) (hAPP X_a _let_3 (at X_a) BOUND_VARIABLE_161088)))) (not (hBOOL (hAPP real bool _let_2 BOUND_VARIABLE_161085))) (not (forall ((S_1 $$unsorted)) (or (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) X_2) BOUND_VARIABLE_161088)) S_1))) (= (ti X_a X_2) (ti X_a BOUND_VARIABLE_161088)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_b real (hAPP X_b (fun X_b real) (dist_dist X_b) (hAPP X_a X_b BOUND_VARIABLE_161086 X_2)) BOUND_VARIABLE_161087)) BOUND_VARIABLE_161085))) )) (not (hBOOL (hAPP real bool _let_2 S_1)))) ))) )))))) 21.34/19.43 ( real, real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.43 ) 21.34/19.43 (instantiation (let ((_let_0 (archimedean_ceiling X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_161138 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP X_a int _let_0 BOUND_VARIABLE_161138)) (one_one int)) (hAPP X_a int _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_161138) (one_one X_a))))) )) 21.34/19.43 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 21.34/19.43 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.43 ( code_code_numeral, (zero_zero code_code_numeral) ) 21.34/19.43 ) 21.34/19.43 (instantiation (let ((_let_0 (times_times X_a))) (forall ((X_a $$unsorted)) (or (not (no_zero_divisors X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0))) )) 21.34/19.43 ( bool ) 21.34/19.43 ( real ) 21.34/19.43 ( nat ) 21.34/19.43 ( (fun nat bool) ) 21.34/19.43 ( int ) 21.34/19.43 ( (fun int bool) ) 21.34/19.43 ( (fun real bool) ) 21.34/19.43 ( (fun real real) ) 21.34/19.43 ( complex ) 21.34/19.43 ( (fun nat real) ) 21.34/19.43 ( (fun int int) ) 21.34/19.43 ( rat ) 21.34/19.43 ( (fun int (fun int bool)) ) 21.34/19.43 ( quickcheck_code_int ) 21.34/19.43 ( (product_prod int int) ) 21.34/19.43 ( (fun (product_prod int int) bool) ) 21.34/19.43 ( code_code_numeral ) 21.34/19.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 21.34/19.43 ( (fun (product_prod int int) int) ) 21.34/19.43 ( (fun int (fun int (fun int bool))) ) 21.34/19.43 ( (fun int real) ) 21.34/19.43 ) 21.34/19.43 (instantiation (forall ((X_a $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (one_one int) (hAPP X_a int (archim2085082626_floor X_a) (one_one X_a)))) ) 21.34/19.43 ( real ) 21.34/19.43 ( nat ) 21.34/19.43 ( int ) 21.34/19.43 ( complex ) 21.34/19.43 ( rat ) 21.34/19.43 ( quickcheck_code_int ) 21.34/19.43 ( code_code_numeral ) 21.34/19.43 ) 21.34/19.43 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_161209 $$unsorted) (BOUND_VARIABLE_161210 $$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 _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_161209) BOUND_VARIABLE_161210))) (or (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_161209) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_161210) _let_2))) (and (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_161209)) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_161210))))))))) )) 21.34/19.43 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.43 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.34/19.43 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.43 ( 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))))))))) ) 21.34/19.43 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.43 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.43 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.34/19.43 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.34/19.43 ( 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))) ) 21.34/19.43 ( 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))) ) 21.34/19.43 ( 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))) ) 21.34/19.43 ) 21.34/19.43 (instantiation (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_161259))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_161255 $$unsorted) (BOUND_VARIABLE_161256 $$unsorted) (BOUND_VARIABLE_161257 $$unsorted) (BOUND_VARIABLE_161258 $$unsorted) (BOUND_VARIABLE_161259 $$unsorted)) (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_161257) BOUND_VARIABLE_161258) _let_2))) (not (forall ((X_2 $$unsorted)) (or (= (ti X_a X_2) (ti X_a BOUND_VARIABLE_161259)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_c real (hAPP X_c (fun X_c real) (dist_dist X_c) (hAPP X_a X_c BOUND_VARIABLE_161255 X_2)) BOUND_VARIABLE_161256)) (hAPP X_b real (hAPP X_b (fun X_b real) (dist_dist X_b) (hAPP X_a X_b BOUND_VARIABLE_161257 X_2)) BOUND_VARIABLE_161258)))) )) (hBOOL (hAPP _let_0 bool (hAPP X_c _let_1 (hAPP (fun X_a X_c) (fun X_c _let_1) (tendsto X_a X_c) BOUND_VARIABLE_161255) BOUND_VARIABLE_161256) _let_2))) )))) 21.34/19.43 ( real, real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.43 ) 21.34/19.43 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (ord_less_eq X_a))) (let ((_let_3 (zero_zero X_a))) (let ((_let_4 (fun X_a X_a))) (let ((_let_5 (times_times X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_161310 $$unsorted) (BOUND_VARIABLE_161311 $$unsorted) (BOUND_VARIABLE_161312 $$unsorted) (BOUND_VARIABLE_161313 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_161312) BOUND_VARIABLE_161313))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_161310) BOUND_VARIABLE_161311))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_3) BOUND_VARIABLE_161312))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_3) BOUND_VARIABLE_161310))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_161312) BOUND_VARIABLE_161310)) (hAPP X_a X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_161313) BOUND_VARIABLE_161311)))) ))))))) 21.34/19.43 ( int, skv_1, (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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.34/19.43 ) 21.34/19.43 (instantiation (let ((_let_0 (fun int bool))) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool nat_nat_set A_3))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_1) A_3))) (hBOOL (hAPP int bool nat_is_nat X_1))) )) 21.34/19.43 ( (one_one int), zEven ) 21.34/19.43 ) 21.34/19.43 (instantiation (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (the _let_0))) (let ((_let_3 (fun _let_0 X_b))) (let ((_let_4 (fun X_b bool))) (let ((_let_5 (fun _let_0 _let_4))) (let ((_let_6 (fun _let_0 X_a))) (let ((_let_7 (fun X_a _let_4))) (forall ((X_a $$unsorted) (X_b $$unsorted) (P_1 $$unsorted)) (= (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)))) ))))))))) 21.34/19.43 ( 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))) ) 21.34/19.43 ( int, int, (fequal int) ) 21.34/19.43 ( int, int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun 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_5 _let_5))) (let ((_let_7 (fun _let_1 _let_5))) (let ((_let_8 (fun int _let_1))) (let ((_let_9 (fun int _let_5))) (hAPP _let_5 _let_5 (hAPP _let_4 _let_6 (combb _let_0 _let_0 int) (hAPP _let_3 _let_4 (combs int bool bool) (hAPP _let_0 _let_3 (hAPP (fun bool _let_2) (fun _let_0 _let_3) (combb bool _let_2 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int))))) (hAPP int _let_5 (hAPP _let_9 _let_9 (combc int int _let_0) (hAPP _let_9 _let_9 (hAPP _let_6 (fun _let_9 _let_9) (combb _let_5 _let_5 int) (combc int int bool)) (hAPP _let_8 _let_9 (hAPP _let_7 (fun _let_8 _let_9) (combb _let_1 _let_5 int) (hAPP _let_5 _let_7 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int))))))))))))) ) 21.34/19.43 ( (product_prod int int), (product_prod int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (product_prod int int))) (let ((_let_4 (product_snd int int))) (let ((_let_5 (fun _let_3 (fun _let_3 bool)))) (let ((_let_6 (fun _let_3 int))) (let ((_let_7 (fun _let_3 _let_2))) (let ((_let_8 (fun (fun _let_3 bool) (fun _let_3 bool)))) (let ((_let_9 (fun _let_6 (fun _let_3 bool)))) (let ((_let_10 (fun _let_3 _let_0))) (let ((_let_11 (fun _let_6 _let_10))) (let ((_let_12 (hAPP (fun int _let_0) _let_11 (combb int _let_0 _let_3) (fequal int)))) (let ((_let_13 (fun _let_3 _let_1))) (let ((_let_14 (fun _let_6 _let_6))) (let ((_let_15 (fun _let_3 _let_8))) (let ((_let_16 (fun _let_5 _let_5))) (let ((_let_17 (hAPP (fun _let_3 bool) _let_7 (hAPP (fun bool _let_2) (fun (fun _let_3 bool) _let_7) (combb bool _let_2 _let_3) fconj) (hAPP (fun _let_3 bool) (fun _let_3 bool) (hAPP _let_2 _let_8 (combb bool bool _let_3) fNot) (hAPP int (fun _let_3 bool) (hAPP _let_10 (fun int (fun _let_3 bool)) (combc _let_3 int bool) (hAPP _let_6 _let_10 _let_12 _let_4)) (zero_zero int)))))) (let ((_let_18 (fun _let_3 _let_6))) (let ((_let_19 (fun _let_3 _let_9))) (let ((_let_20 (fun _let_3 _let_10))) (let ((_let_21 (fun _let_3 _let_14))) (let ((_let_22 (fun _let_6 _let_18))) (let ((_let_23 (hAPP _let_6 _let_13 (hAPP (fun int _let_1) (fun _let_6 _let_13) (combb int _let_1 _let_3) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_6))) (hAPP _let_5 _let_5 (hAPP _let_15 _let_16 (combs _let_3 (fun _let_3 bool) (fun _let_3 bool)) (hAPP _let_7 _let_15 (hAPP (fun _let_2 _let_8) (fun _let_7 _let_15) (combb _let_2 _let_8 _let_3) (combb bool bool _let_3)) _let_17)) (hAPP _let_5 _let_5 (hAPP _let_8 _let_16 (combb (fun _let_3 bool) (fun _let_3 bool) _let_3) (hAPP _let_7 _let_8 (combs _let_3 bool bool) _let_17)) (hAPP _let_18 _let_5 (hAPP _let_19 (fun _let_18 _let_5) (combs _let_3 _let_6 (fun _let_3 bool)) (hAPP _let_20 _let_19 (hAPP (fun _let_10 _let_9) (fun _let_20 _let_19) (combb _let_10 _let_9 _let_3) (combs _let_3 int bool)) (hAPP _let_18 _let_20 (hAPP _let_11 (fun _let_18 _let_20) (combb _let_6 _let_10 _let_3) _let_12) (hAPP _let_6 _let_18 (hAPP _let_21 _let_22 (combc _let_3 _let_6 _let_6) (hAPP _let_13 _let_21 (hAPP (fun _let_1 _let_14) (fun _let_13 _let_21) (combb _let_1 _let_14 _let_3) (combb int int _let_3)) _let_23)) _let_4)))) (hAPP _let_6 _let_18 (hAPP _let_24 _let_22 (combb int _let_6 _let_3) (hAPP _let_13 _let_24 (combc _let_3 int int) _let_23)) _let_4))))))))))))))))))))))))))))) ) 21.34/19.43 ) 21.34/19.43 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (ord_less real))) (let ((_let_4 (hAPP real _let_0 _let_3 A_2))) (let ((_let_5 (hAPP real _let_0 _let_1 A_2))) (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (BOUND_VARIABLE_161566 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_4 B_1))) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_5 X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) B_1))) (hBOOL (hAPP real bool (hAPP _let_2 _let_0 (isCont real real) F) X_2))) )) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_3 X_2) B_1))) (not (hBOOL (hAPP real bool _let_4 X_2))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (deriv real) F) X_2) (zero_zero real)))) )) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 BOUND_VARIABLE_161566) B_1))) (not (hBOOL (hAPP real bool _let_5 BOUND_VARIABLE_161566))) (= (hAPP real real F A_2) (hAPP real real F BOUND_VARIABLE_161566))) ))))))) 21.34/19.44 ( sqrt, (zero_zero real), pi, skv_14 ) 21.34/19.44 ( (uminus_uminus real), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.44 ( tan, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.44 ( sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 21.34/19.44 ( (sgn_sgn real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.44 ) 21.34/19.44 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (ring_1_Ints X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_161627 $$unsorted) (BOUND_VARIABLE_161628 $$unsorted)) (or (not (ring_1 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_161628) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_161627) _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_161628) BOUND_VARIABLE_161627)) _let_3))) ))))) 21.34/19.44 ( nat, (one_one nat), (one_one nat) ) 21.34/19.44 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 21.34/19.44 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.44 ) 21.34/19.44 (instantiation (let ((_let_0 (real_1 nat))) (forall ((M $$unsorted) (N $$unsorted)) (= (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))) )) 21.34/19.44 ( (one_one nat), (one_one nat) ) 21.34/19.44 ) 21.34/19.44 (instantiation (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))))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP int bool (even_odd_even int) X))) (= (hAPP int int (hAPP int _let_0 (times_times int) _let_1) (hAPP int int (hAPP int _let_0 (div_div int) X) _let_1)) (ti int X))) ))) 21.34/19.44 ( (zero_zero int) ) 21.34/19.44 ( pls ) 21.34/19.44 ( m ) 21.34/19.44 ( (one_one int) ) 21.34/19.44 ( min_1 ) 21.34/19.44 ( s ) 21.34/19.44 ( s1 ) 21.34/19.44 ( t ) 21.34/19.44 ) 21.34/19.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161693 $$unsorted)) (or (not (number_ring X_a)) (not (real_algebra_1 X_a)) (= (hAPP real X_a (of_real X_a) (hAPP int real (number_number_of real) BOUND_VARIABLE_161693)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_161693))) ) 21.34/19.44 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.34/19.44 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.44 ( real, min_1 ) 21.34/19.44 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.44 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.34/19.44 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.34/19.44 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 21.34/19.44 ( nat, pls ) 21.34/19.44 ( nat, (hAPP int int bit1 pls) ) 21.34/19.44 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.34/19.44 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.34/19.44 ( int, pls ) 21.34/19.44 ( int, (hAPP int int bit1 pls) ) 21.34/19.44 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.34/19.44 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.44 ( int, min_1 ) 21.34/19.44 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.34/19.44 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.34/19.44 ( complex, min_1 ) 21.34/19.44 ( quickcheck_code_int, (zero_zero int) ) 21.34/19.44 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 21.34/19.44 ( quickcheck_code_int, (one_one int) ) 21.34/19.44 ( code_code_numeral, pls ) 21.34/19.44 ( code_code_numeral, (hAPP int int bit1 pls) ) 21.34/19.44 ) 21.34/19.44 (instantiation (forall ((N_1 $$unsorted)) (= (not (forall ((M_2 $$unsorted)) (not (= N_1 (hAPP nat nat suc M_2))) )) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) ) 21.34/19.44 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.44 ) 21.34/19.44 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (let ((_let_2 (times_times X_a))) (let ((_let_3 (one_one X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_161739 $$unsorted)) (or (not (ring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_161739) _let_3)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_161739) _let_3)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_161739) BOUND_VARIABLE_161739)) _let_3))) ))))) 21.34/19.44 ( nat, (one_one nat) ) 21.34/19.44 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 21.34/19.44 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.44 ( complex, ii ) 21.34/19.44 ) 21.34/19.44 (instantiation (let ((_let_0 (zero_zero int))) (forall ((Z_1 $$unsorted)) (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)))) )) 21.34/19.44 ( (zero_zero int) ) 21.34/19.44 ( (one_one int) ) 21.34/19.44 ( min_1 ) 21.34/19.44 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.44 ( s ) 21.34/19.44 ( (hAPP int int (number_number_of int) pls) ) 21.34/19.44 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.34/19.44 ( skv_3 ) 21.34/19.44 ( skv_9 ) 21.34/19.44 ) 21.34/19.44 (instantiation (let ((_let_0 (div_div X_a))) (forall ((X_a $$unsorted)) (or (not (semiring_div X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0))) )) 21.34/19.44 ( bool ) 21.34/19.44 ( real ) 21.34/19.44 ( nat ) 21.34/19.44 ( (fun nat bool) ) 21.34/19.44 ( int ) 21.34/19.44 ( (fun int bool) ) 21.34/19.44 ( (fun real bool) ) 21.34/19.44 ( (fun real real) ) 21.34/19.44 ( complex ) 21.34/19.44 ( (fun nat real) ) 21.34/19.44 ( (fun int int) ) 21.34/19.44 ( (fun int (fun int bool)) ) 21.34/19.44 ( quickcheck_code_int ) 21.34/19.44 ( (product_prod int int) ) 21.34/19.44 ( (fun (product_prod int int) bool) ) 21.34/19.44 ( code_code_numeral ) 21.34/19.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 21.34/19.44 ( (fun (product_prod int int) int) ) 21.34/19.44 ( (fun int (fun int (fun int bool))) ) 21.34/19.44 ( (fun int real) ) 21.34/19.44 ) 21.34/19.44 (instantiation (forall ((A_1 $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) A_1) (hAPP real int (archim2085082626_floor real) X)))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (real_1 int) A_1)) X))) ) 21.34/19.44 ( (zero_zero int), pi ) 21.34/19.44 ( (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.44 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.44 ( (zero_zero int), skv_6 ) 21.34/19.44 ( (zero_zero int), skv_11 ) 21.34/19.44 ( (zero_zero int), skv_12 ) 21.34/19.44 ( (zero_zero int), skv_14 ) 21.34/19.44 ) 21.34/19.44 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (hAPP nat (fun real real) root N))) (forall ((X $$unsorted) (Y $$unsorted) (N $$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 _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)))) )))) 21.34/19.44 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.44 ) 21.34/19.44 (instantiation (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_1)))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_1 X_1))) (not (hBOOL (hAPP int bool _let_1 Y_1))) (= (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_3 Y_1) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_3 X_1) zEven))) (= (hAPP nat int _let_4 (hAPP int nat nat_1 Y_1)) (hAPP nat int _let_4 (hAPP int nat nat_1 X_1)))) )))))) 21.34/19.44 ( (one_one int), (one_one int) ) 21.34/19.44 ( (one_one int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.34/19.44 ( min_1, (hAPP int int (number_number_of int) pls) ) 21.34/19.44 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 21.34/19.44 ( s, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.44 ( s, s ) 21.34/19.44 ( (hAPP int int (number_number_of int) pls), min_1 ) 21.34/19.44 ( (hAPP int int (number_number_of int) pls), (hAPP int int (number_number_of int) pls) ) 21.34/19.44 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (one_one int) ) 21.34/19.44 ( skv_3, skv_3 ) 21.34/19.44 ( skv_3, skv_9 ) 21.34/19.44 ( skv_9, skv_3 ) 21.34/19.44 ) 21.34/19.44 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (div_div nat))) (let ((_let_2 (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))))) (forall ((X $$unsorted)) (or (hBOOL (hAPP nat bool (even_odd_even nat) X)) (= (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_1 X) _let_2)) (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat suc X)) _let_2))) )))) 21.34/19.44 ( (zero_zero nat) ) 21.34/19.44 ( (one_one nat) ) 21.34/19.44 ) 21.34/19.44 (instantiation (let ((_let_0 (plus_plus X_a))) (forall ((X_a $$unsorted)) (or (not (monoid_add X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0))) )) 21.34/19.44 ( bool ) 21.34/19.44 ( real ) 21.34/19.44 ( nat ) 21.34/19.44 ( (fun nat bool) ) 21.34/19.44 ( int ) 21.34/19.44 ( (fun int bool) ) 21.34/19.44 ( (fun real bool) ) 21.34/19.44 ( (fun real real) ) 21.34/19.44 ( complex ) 21.34/19.44 ( (fun nat real) ) 21.34/19.44 ( (fun int int) ) 21.34/19.44 ( rat ) 21.34/19.44 ( (fun int (fun int bool)) ) 21.34/19.44 ( quickcheck_code_int ) 21.34/19.44 ( (product_prod int int) ) 21.34/19.44 ( (fun (product_prod int int) bool) ) 21.34/19.44 ( code_code_numeral ) 21.34/19.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 21.34/19.44 ( (fun (product_prod int int) int) ) 21.34/19.44 ( (fun int (fun int (fun int bool))) ) 21.34/19.44 ( (fun int real) ) 21.34/19.44 ) 21.34/19.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161882 $$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_161882) (zero_zero X_a)) (ti X_a BOUND_VARIABLE_161882))) ) 21.34/19.44 ( bool, fFalse ) 21.34/19.44 ( bool, fTrue ) 21.34/19.44 ( real, pi ) 21.34/19.44 ( (fun nat bool), (even_odd_even nat) ) 21.34/19.44 ( (fun nat bool), prime ) 21.34/19.44 ( (fun nat nat), suc ) 21.34/19.44 ( (fun nat nat), (fact_fact nat) ) 21.34/19.44 ( (fun nat nat), (size_size nat) ) 21.34/19.44 ( (fun nat nat), fact ) 21.34/19.44 ( (fun nat nat), nat_size ) 21.34/19.44 ( int, pls ) 21.34/19.44 ( int, m ) 21.34/19.44 ( int, min_1 ) 21.34/19.44 ( int, s ) 21.34/19.44 ( int, s1 ) 21.34/19.44 ( int, t ) 21.34/19.44 ( (fun int bool), zprime ) 21.34/19.44 ( (fun int bool), nat_neg ) 21.34/19.44 ( (fun int bool), zEven ) 21.34/19.44 ( (fun int bool), nat_is_nat ) 21.34/19.44 ( (fun int bool), zOdd ) 21.34/19.44 ( (fun int bool), (even_odd_even int) ) 21.34/19.44 ( (fun int bool), twoSqu1091635170sum2sq ) 21.34/19.44 ( (fun int nat), nat_1 ) 21.34/19.44 ( (fun int nat), phi ) 21.34/19.44 ( (fun real real), sqrt ) 21.34/19.44 ( (fun real real), tan ) 21.34/19.44 ( (fun real real), cos ) 21.34/19.44 ( (fun real real), arccos ) 21.34/19.44 ( (fun real real), ln ) 21.34/19.44 ( (fun real real), sin ) 21.34/19.44 ( (fun real real), arctan ) 21.34/19.44 ( (fun real real), arcsin ) 21.34/19.44 ( complex, ii ) 21.34/19.44 ( (fun complex complex), cnj ) 21.34/19.44 ( (fun complex complex), expi ) 21.34/19.44 ( (fun nat real), (real_1 nat) ) 21.34/19.44 ( (fun nat real), cos_coeff ) 21.34/19.44 ( (fun nat real), sin_coeff ) 21.34/19.44 ( (fun int int), bit0 ) 21.34/19.44 ( (fun int int), bit1 ) 21.34/19.44 ( (fun int int), pred ) 21.34/19.44 ( (fun int int), succ ) 21.34/19.44 ( (fun int int), (fact_fact int) ) 21.34/19.44 ( (fun int int), zfact ) 21.34/19.44 ( (fun bool bool), fNot ) 21.34/19.44 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.34/19.44 ( (fun bool (fun bool bool)), fconj ) 21.34/19.44 ( (fun bool (fun bool bool)), fdisj ) 21.34/19.44 ( (fun bool (fun bool bool)), fimplies ) 21.34/19.44 ( (fun int (fun int bool)), sRStar ) 21.34/19.44 ( (fun int (fun int bool)), quadRes ) 21.34/19.44 ( (fun int (fun int bool)), norRRset ) 21.34/19.44 ( (fun int (fun int bool)), d22set ) 21.34/19.44 ( (fun int (fun int bool)), sr ) 21.34/19.44 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.34/19.44 ( (fun nat (fun nat nat)), nat_gcd ) 21.34/19.44 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.34/19.44 ( (fun nat (fun nat nat)), nat_lcm ) 21.34/19.44 ( (fun nat (fun real real)), root ) 21.34/19.44 ( (fun real (fun real real)), log ) 21.34/19.44 ( (fun real (fun real real)), powr ) 21.34/19.44 ( (fun nat (fun nat bool)), coprime ) 21.34/19.44 ( (fun (fun int bool) int), (the int) ) 21.34/19.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.34/19.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.34/19.44 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.34/19.44 ( (fun (fun int bool) bool), nat_nat_set ) 21.34/19.44 ( (filter nat), sequentially ) 21.34/19.44 ( (fun (product_prod nat nat) bool), pred_nat ) 21.34/19.44 ( (fun (product_prod int int) bool), frac_1 ) 21.34/19.44 ( (fun real complex), cis ) 21.34/19.44 ( (fun complex real), im ) 21.34/19.44 ( (fun complex real), re ) 21.34/19.44 ( (fun complex real), arg ) 21.34/19.44 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.34/19.44 ( (fun int (fun int int)), int_gcd ) 21.34/19.44 ( (fun int (fun int int)), multInv ) 21.34/19.44 ( (fun int (fun int int)), legacy_zgcd ) 21.34/19.44 ( (fun int (fun int int)), z3mod ) 21.34/19.44 ( (fun int (fun int int)), inv ) 21.34/19.44 ( (fun int (fun int int)), (gcd_gcd int) ) 21.34/19.44 ( (fun int (fun int int)), standardRes ) 21.34/19.44 ( (fun int (fun int int)), legendre ) 21.34/19.44 ( (fun int (fun int int)), nat_tsub ) 21.34/19.44 ( (fun int (fun int int)), z3div ) 21.34/19.44 ( (fun int (fun int int)), int_lcm ) 21.34/19.44 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.34/19.44 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.34/19.44 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.34/19.44 ( (fun int (fun (fun int bool) bool)), resSet ) 21.34/19.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.34/19.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.34/19.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.34/19.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.34/19.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.34/19.44 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.34/19.44 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.34/19.44 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.34/19.44 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.34/19.44 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.34/19.44 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.34/19.44 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.34/19.44 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.34/19.44 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.34/19.44 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.34/19.44 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.34/19.44 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.34/19.44 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.34/19.44 ( (fun real nat), natfloor ) 21.34/19.44 ( (fun real nat), natceiling ) 21.34/19.44 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.34/19.44 ( (fun int (fun int (fun int bool))), wset ) 21.34/19.44 ( (fun int (fun int (fun int bool))), bnorRset ) 21.34/19.44 ( (fun int (fun int (fun int bool))), zcong ) 21.34/19.44 ( (fun int (fun int (fun int bool))), noXRRset ) 21.34/19.44 ( (fun int (fun int (fun int bool))), zcongm ) 21.34/19.44 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.34/19.44 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.34/19.44 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.34/19.44 ( (fun int real), (real_1 int) ) 21.34/19.44 ( (fun complex nat), (size_size complex) ) 21.34/19.44 ( (fun complex nat), complex_size ) 21.34/19.44 ( (fun int (list int)), quickc666637781d_zero ) 21.34/19.44 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.34/19.44 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.34/19.44 ( (fun (product_prod int int) rat), frct ) 21.34/19.45 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.34/19.45 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.34/19.45 ( (fun (fun nat rat) bool), vanishes ) 21.34/19.45 ( (fun int (fun int rat)), fract ) 21.34/19.45 ( (fun code_code_numeral int), code_int_of ) 21.34/19.45 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.34/19.45 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.34/19.45 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.34/19.45 ( (fun real (fun real complex)), complex_1 ) 21.34/19.45 ( (fun real (fun real complex)), rcis ) 21.34/19.45 ( (fun int (fun nat nat)), nat_aux ) 21.34/19.45 ( (fun rat real), ratreal ) 21.34/19.45 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.34/19.45 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.34/19.45 ( (fun rat (product_prod int int)), quotient_of ) 21.34/19.45 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.34/19.45 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.34/19.45 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.34/19.45 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.34/19.45 ) 21.34/19.45 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat real))) (let ((_let_4 (inverse_divide real))) (let ((_let_5 (fun nat _let_2))) (let ((_let_6 (fun _let_3 _let_3))) (let ((_let_7 (combs nat real real))) (let ((_let_8 (fun real _let_2))) (let ((_let_9 (fun _let_3 _let_5))) (let ((_let_10 (combb real _let_2 nat))) (let ((_let_11 (real_1 nat))) (let ((_let_12 (fact_fact nat))) (let ((_let_13 (zero_zero nat))) (let ((_let_14 (times_times real))) (let ((_let_15 (hAPP real _let_3 (power_power real) (zero_zero real)))) (let ((_let_16 (fun X_a real))) (let ((_let_17 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_161908 $$unsorted) (BOUND_VARIABLE_161909 $$unsorted)) (or (not (zero X_a)) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) _let_13) BOUND_VARIABLE_161909))) (= (hAPP X_a real (hAPP nat _let_16 BOUND_VARIABLE_161908 _let_13) _let_17) (hAPP real real (hAPP real _let_2 (plus_plus real) (hAPP _let_0 real (hAPP _let_3 (fun _let_0 real) (big_co1399186613setsum nat real) (hAPP _let_3 _let_3 (hAPP _let_5 _let_6 _let_7 (hAPP _let_3 _let_5 (hAPP _let_8 _let_9 _let_10 _let_4) (hAPP _let_3 _let_3 (hAPP _let_5 _let_6 _let_7 (hAPP _let_3 _let_5 (hAPP _let_8 _let_9 _let_10 _let_14) (hAPP X_a _let_3 (hAPP (fun nat _let_16) (fun X_a _let_3) (combc nat X_a real) BOUND_VARIABLE_161908) _let_17))) _let_15))) (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb nat real nat) _let_11) _let_12))) (hAPP nat _let_0 (hAPP nat (fun nat _let_0) (ord_atLeastLessThan nat) _let_13) BOUND_VARIABLE_161909))) (hAPP real real (hAPP real _let_2 _let_4 (hAPP real real (hAPP real _let_2 _let_14 (hAPP X_a real (hAPP nat _let_16 BOUND_VARIABLE_161908 BOUND_VARIABLE_161909) _let_17)) (hAPP nat real _let_15 BOUND_VARIABLE_161909))) (hAPP nat real _let_11 (hAPP nat nat _let_12 BOUND_VARIABLE_161909)))))) ))))))))))))))))))) 21.34/19.45 ( real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.45 ) 21.34/19.45 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Xa_2 $$unsorted)) (= (= (hAPP real complex (of_real complex) Xa_2) (hAPP real complex (hAPP real (fun real complex) complex_1 X_1) Y_1)) (and (= X_1 Xa_2) (= (zero_zero real) Y_1))) ) 21.34/19.45 ( (zero_zero real), (zero_zero real), (hAPP int real (number_number_of real) min_1) ) 21.34/19.45 ( (zero_zero real), (one_one real), (hAPP real real (uminus_uminus real) (one_one real)) ) 21.34/19.45 ( (one_one real), (zero_zero real), pi ) 21.34/19.45 ) 21.34/19.45 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP complex real im (hAPP complex complex (sgn_sgn complex) Z_1)) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP complex real im Z_1)) (hAPP complex real (norm_norm complex) Z_1))) ) 21.34/19.45 ( ii ) 21.34/19.45 ) 21.34/19.45 (instantiation (let ((_let_0 (fun nat bool))) (forall ((M $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M) N))) (= M N) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) N))) )) 21.34/19.45 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.45 ) 21.34/19.45 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (uminus_uminus real))) (forall ((X $$unsorted)) (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)))) )))) 21.34/19.45 ( (zero_zero real) ) 21.34/19.45 ( (one_one real) ) 21.34/19.45 ( pi ) 21.34/19.45 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.45 ( (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)))) ) 21.34/19.45 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.34/19.45 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.34/19.45 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 21.34/19.45 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.45 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.34/19.45 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.34/19.45 ( skv_14 ) 21.34/19.45 ) 21.34/19.45 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (member int))) (let ((_let_4 (ti int Ta))) (let ((_let_5 (ti int BOUND_VARIABLE_162109))) (forall ((Ta $$unsorted) (B_2 $$unsorted) (D_2 $$unsorted) (BOUND_VARIABLE_162109 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) D_2))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_3 Ta) B_2))) (not (forall ((Xa $$unsorted) (BOUND_VARIABLE_162072 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_3 Xa) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastAtMost int) (one_one int)) D_2)))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_3 BOUND_VARIABLE_162072) B_2))) (not (= (hAPP int int (hAPP int _let_1 (plus_plus int) BOUND_VARIABLE_162072) Xa) _let_5))) )) (= _let_4 _let_5) (not (= _let_4 (hAPP int int (hAPP int _let_1 (minus_minus int) BOUND_VARIABLE_162109) D_2)))) ))))))) 21.34/19.45 ( (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))), min_1 ) 21.34/19.45 ) 21.34/19.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162141 $$unsorted)) (or (not (ring_1 X_a)) (= (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_162141) (hAPP int X_a (ring_1_of_int X_a) (hAPP nat int (semiring_1_of_nat int) BOUND_VARIABLE_162141)))) ) 21.34/19.45 ( real, (zero_zero nat) ) 21.34/19.45 ( real, (hAPP nat nat suc (zero_zero nat)) ) 21.34/19.45 ( real, (one_one nat) ) 21.34/19.45 ( int, (zero_zero nat) ) 21.34/19.45 ( int, (hAPP nat nat suc (zero_zero nat)) ) 21.34/19.45 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.45 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.34/19.45 ) 21.34/19.45 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (ord_less real))) (let ((_let_3 (one_one real))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP int real (number_number_of real) min_1)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X_1) _let_3))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) arccos) X_1) (hAPP real real (inverse_inverse real) (hAPP real real (uminus_uminus real) (hAPP real real sqrt (hAPP real real (hAPP real _let_1 (minus_minus real) _let_3) (hAPP nat real (hAPP real (fun nat real) (power_power real) X_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))) ))))) 21.34/19.45 ( (zero_zero real) ) 21.34/19.45 ( (one_one real) ) 21.34/19.45 ( pi ) 21.34/19.45 ( (hAPP int real (number_number_of real) min_1) ) 21.34/19.45 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.45 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.34/19.45 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.45 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.45 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 21.34/19.45 ) 21.34/19.45 (instantiation (forall ((Z_1 $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg Z_1))) (= (zero_zero nat) (hAPP int nat nat_1 Z_1))) ) 21.34/19.45 ( (one_one int) ) 21.34/19.45 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.45 ( (hAPP int int (number_number_of int) min_1) ) 21.34/19.45 ( (hAPP int int (number_number_of int) pls) ) 21.34/19.45 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.34/19.45 ) 21.34/19.45 (instantiation (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP int bool (even_odd_even int) X_1)) (= (zero_zero int) (hAPP int int (hAPP int (fun int int) (div_mod int) X_1) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.34/19.45 ( (zero_zero int) ) 21.34/19.45 ( (one_one int) ) 21.34/19.45 ) 21.34/19.45 (instantiation (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (forall ((X $$unsorted)) (= (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))) )))) 21.34/19.45 ( (zero_zero real) ) 21.34/19.45 ( pi ) 21.34/19.45 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.45 ( (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)))) ) 21.34/19.45 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.34/19.45 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.34/19.45 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 21.34/19.45 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.34/19.45 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.34/19.45 ( skv_14 ) 21.34/19.45 ) 21.34/19.45 (instantiation (let ((_let_0 (fun int (fun int bool)))) (forall ((I $$unsorted)) (let ((_let_0 (fun int bool))) (or (= (zero_zero int) (ti int I)) (hBOOL (hAPP _let_0 bool (finite_finite_1 int) (hAPP _let_0 _let_0 (collect int) (hAPP int _let_0 (hAPP _let_0 _let_0 (combc int int bool) (dvd_dvd int)) I)))))) )) 21.34/19.45 ( m ) 21.34/19.45 ( min_1 ) 21.34/19.45 ( s ) 21.34/19.45 ( s1 ) 21.34/19.45 ( t ) 21.34/19.45 ) 21.34/19.45 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (div_div int) A_1) B) (hAPP rat int (archim2085082626_floor rat) (hAPP int rat (hAPP int (fun int rat) fract A_1) B))) ) 21.34/19.45 ( (zero_zero int), (one_one int) ) 21.34/19.45 ( (one_one int), (one_one int) ) 21.34/19.45 ) 21.34/19.45 (instantiation (let ((_let_0 (scaleR_scaleR X_a))) (forall ((X_a $$unsorted)) (or (not (sgn_div_norm X_a)) (= _let_0 (ti (fun real (fun X_a X_a)) _let_0))) )) 21.34/19.45 ( bool ) 21.34/19.45 ( real ) 21.34/19.45 ( nat ) 21.34/19.45 ( (fun nat bool) ) 21.34/19.45 ( int ) 21.34/19.45 ( (fun int bool) ) 21.34/19.45 ( (fun real bool) ) 21.34/19.45 ( (fun real real) ) 21.34/19.45 ( complex ) 21.34/19.45 ( (fun nat real) ) 21.34/19.45 ( (fun int int) ) 21.34/19.45 ( (fun int (fun int bool)) ) 21.34/19.45 ( (product_prod int int) ) 21.34/19.45 ( (fun (product_prod int int) bool) ) 21.34/19.45 ( code_code_numeral ) 21.34/19.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 21.34/19.45 ( (fun (product_prod int int) int) ) 21.34/19.45 ( (fun int (fun int (fun int bool))) ) 21.34/19.45 ( (fun int real) ) 21.34/19.45 ) 21.34/19.45 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (preorder T_1)) (preorder (fun T_2 T_1))) ) 21.34/19.45 ( bool, bool ) 21.34/19.45 ( bool, (fun bool bool) ) 21.34/19.45 ( real, bool ) 21.34/19.45 ( real, real ) 21.34/19.45 ( real, nat ) 21.34/19.45 ( real, (fun int bool) ) 21.34/19.45 ( real, (fun real bool) ) 21.34/19.45 ( real, (fun real real) ) 21.34/19.45 ( real, complex ) 21.34/19.45 ( real, (fun nat real) ) 21.34/19.45 ( real, (fun bool bool) ) 21.34/19.45 ( real, (fun int (fun int bool)) ) 21.34/19.45 ( real, (fun (filter real) bool) ) 21.34/19.45 ( real, (fun (filter nat) bool) ) 21.34/19.45 ( real, (fun real complex) ) 21.34/19.45 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 21.34/19.45 ( real, (fun nat (product_prod real real)) ) 21.34/19.45 ( real, (fun real (fun nat (product_prod real real))) ) 21.34/19.45 ( real, 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real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.34/19.46 ( skv_14 ) 21.34/19.46 ) 21.34/19.46 (instantiation (let ((_let_0 (fun real X_a))) (forall ((X_a $$unsorted) (F1 $$unsorted) (Real1 $$unsorted) (Real2 $$unsorted)) (= (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))) )) 21.34/19.46 ( bool, (ord_less_eq real), (zero_zero real), pi ) 21.34/19.46 ( 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)))) ) 21.34/19.46 ( 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)))) ) 21.34/19.46 ( bool, (ord_less_eq real), (zero_zero real), skv_6 ) 21.34/19.46 ( bool, (ord_less_eq real), (zero_zero real), skv_11 ) 21.34/19.46 ( bool, (ord_less_eq real), (zero_zero real), skv_12 ) 21.34/19.46 ( bool, (ord_less_eq real), (zero_zero real), skv_14 ) 21.34/19.46 ( bool, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.34/19.46 ( 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))) ) 21.34/19.46 ( 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) ) 21.34/19.46 ( bool, (ord_less_eq real), skv_14, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.46 ( bool, (ord_less real), (zero_zero real), pi ) 21.34/19.46 ( 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)))) ) 21.34/19.46 ( 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)))) ) 21.34/19.46 ( bool, (ord_less real), (zero_zero real), skv_2 ) 21.34/19.46 ( bool, (ord_less real), (zero_zero real), skv_10 ) 21.34/19.46 ( bool, (ord_less real), (zero_zero real), skv_13 ) 21.34/19.46 ( 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)))) ) 21.34/19.46 ( bool, (ord_less real), pi, (zero_zero real) ) 21.34/19.46 ( 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)))) ) 21.34/19.46 ( 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))) ) 21.34/19.46 ( 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) ) 21.34/19.46 ( 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) ) 21.34/19.46 ( 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 ) 21.34/19.46 ( real, (minus_minus real), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 21.34/19.46 ( real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.46 ( 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)))) ) 21.34/19.46 ( 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)))) ) 21.34/19.46 ( 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))))))))) ) 21.34/19.46 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.46 ( 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)))) ) 21.34/19.46 ( 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)))) ) 21.34/19.46 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.34/19.46 ( 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))) ) 21.34/19.46 ( 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))) ) 21.34/19.46 ( 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))) ) 21.34/19.46 ( real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.34/19.46 ( real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 21.34/19.47 ( real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.34/19.47 ( real, (times_times real), (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 21.34/19.47 ( complex, complex_1, (zero_zero real), (zero_zero real) ) 21.34/19.47 ( complex, complex_1, (zero_zero real), (one_one real) ) 21.34/19.47 ( complex, complex_1, (one_one real), (zero_zero real) ) 21.34/19.47 ) 21.34/19.47 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_162548 $$unsorted) (BOUND_VARIABLE_162549 $$unsorted)) (or (not (linorder X_a)) (= (not (= (ti X_a BOUND_VARIABLE_162548) (ti X_a BOUND_VARIABLE_162549))) (or (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_162549) BOUND_VARIABLE_162548)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_162548) BOUND_VARIABLE_162549))))) ))) 21.34/19.47 ( real, (zero_zero real), pi ) 21.34/19.47 ( 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)))) ) 21.34/19.47 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.34/19.47 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.47 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.47 ( real, (zero_zero real), skv_2 ) 21.34/19.47 ( real, (zero_zero real), skv_10 ) 21.34/19.47 ( real, (zero_zero real), skv_13 ) 21.34/19.47 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.47 ( real, pi, (zero_zero real) ) 21.34/19.47 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.47 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 21.34/19.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.47 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.34/19.47 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 21.34/19.47 ( 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))))), (zero_zero real) ) 21.34/19.47 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.34/19.47 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.34/19.47 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 21.34/19.47 ( 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)), pi ) 21.34/19.47 ( real, skv_2, (zero_zero real) ) 21.34/19.47 ( real, skv_10, (zero_zero real) ) 21.34/19.47 ( real, skv_13, (zero_zero real) ) 21.34/19.47 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.47 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 21.34/19.47 ( int, (zero_zero int), (zero_zero int) ) 21.34/19.47 ( int, (zero_zero int), (one_one int) ) 21.34/19.47 ( 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))) ) 21.34/19.47 ( int, (zero_zero int), min_1 ) 21.34/19.47 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 21.34/19.47 ( int, (zero_zero int), t ) 21.34/19.47 ( int, (one_one int), (zero_zero int) ) 21.34/19.47 ( int, (one_one int), t ) 21.34/19.47 ( 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))), (zero_zero int) ) 21.34/19.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 21.34/19.47 ( 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 ) 21.34/19.47 ( 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_3 ) 21.34/19.47 ( 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_9 ) 21.34/19.47 ( int, min_1, (zero_zero int) ) 21.34/19.47 ( int, min_1, min_1 ) 21.34/19.47 ( 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))) ) 21.34/19.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 21.34/19.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 21.34/19.47 ( int, t, (zero_zero int) ) 21.34/19.47 ( int, t, (one_one int) ) 21.34/19.47 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.34/19.47 ( 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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 21.34/19.47 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.34/19.47 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.34/19.47 ) 21.34/19.47 (instantiation (forall ((Nat $$unsorted) (Nat_5 $$unsorted)) (= (= (hAPP nat nat suc Nat) (hAPP nat nat suc Nat_5)) (= Nat Nat_5)) ) 21.34/19.47 ( (zero_zero nat), (zero_zero nat) ) 21.34/19.47 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 21.34/19.47 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 21.34/19.47 ( (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.34/19.47 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (zero_zero nat) ) 21.34/19.47 ) 21.34/19.47 (instantiation (let ((_let_0 (one_one int))) (let ((_let_1 (uminus_uminus int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (hAPP int int (number_number_of int) W))) (forall ((W $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_3) (zero_zero int)))) (= (hAPP int int (hAPP int (fun int int) (div_div int) _let_0) _let_3) (hAPP _let_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_1 _let_0)) (hAPP int int _let_1 _let_3)))))) ))))) 21.34/19.47 ( pls ) 21.34/19.47 ( (hAPP int int bit1 pls) ) 21.34/19.47 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.34/19.47 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.47 ( min_1 ) 21.34/19.47 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.34/19.47 ) 21.34/19.47 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) min_1) K_4) (hAPP int int pred K_4)) ) 21.34/19.47 ( pls ) 21.34/19.47 ( min_1 ) 21.34/19.47 ) 21.34/19.47 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (forall ((I_1 $$unsorted) (J_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 I_1) J_2))) (not (forall ((K_1 $$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 _let_0 _let_1 (zero_zero nat)) K_1)))) ))) ))) 21.34/19.47 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.47 ) 21.34/19.47 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int bit1 (hAPP int int pred K_4)) (hAPP int int pred (hAPP int int bit0 K_4))) ) 21.34/19.47 ( pls ) 21.34/19.47 ( (hAPP int int bit1 pls) ) 21.34/19.47 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.34/19.47 ( min_1 ) 21.34/19.47 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.34/19.47 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.34/19.47 ) 21.34/19.47 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (filter X_a))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun X_a X_b))) (let ((_let_5 (fun X_a X_c))) (let ((_let_6 (fun X_b X_c))) (let ((_let_7 (filter X_b))) (let ((_let_8 (fun _let_7 bool))) (let ((_let_9 (hAPP X_a _let_2 (at X_a) BOUND_VARIABLE_162720))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_162716 $$unsorted) (BOUND_VARIABLE_162717 $$unsorted) (BOUND_VARIABLE_162718 $$unsorted) (BOUND_VARIABLE_162719 $$unsorted) (BOUND_VARIABLE_162720 $$unsorted) (BOUND_VARIABLE_162721 $$unsorted)) (or (not (topological_space X_b)) (not (topological_space X_c)) (not (real_normed_vector X_a)) (not (hBOOL (hAPP _let_2 bool (hAPP X_b _let_3 (hAPP _let_4 (fun X_b _let_3) (tendsto X_a X_b) BOUND_VARIABLE_162718) BOUND_VARIABLE_162719) _let_9))) (not (hBOOL (hAPP _let_7 bool (hAPP X_c _let_8 (hAPP _let_6 (fun X_c _let_8) (tendsto X_b X_c) BOUND_VARIABLE_162716) BOUND_VARIABLE_162717) (hAPP X_b _let_7 (at X_b) BOUND_VARIABLE_162719)))) (hBOOL (hAPP _let_2 bool (hAPP X_c _let_3 (hAPP _let_5 (fun X_c _let_3) (tendsto X_a X_c) (hAPP _let_4 _let_5 (hAPP _let_6 (fun _let_4 _let_5) (combb X_b X_c X_a) BOUND_VARIABLE_162716) BOUND_VARIABLE_162718)) BOUND_VARIABLE_162717) _let_9)) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) BOUND_VARIABLE_162721))) (not (forall ((X_2 $$unsorted)) (or (= (ti X_a X_2) (ti X_a BOUND_VARIABLE_162720)) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (norm_norm X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) X_2) BOUND_VARIABLE_162720))) BOUND_VARIABLE_162721))) (not (= (ti X_b BOUND_VARIABLE_162719) (hAPP X_a X_b BOUND_VARIABLE_162718 X_2)))) ))) ))))))))))) 21.34/19.47 ( real, real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.47 ) 21.34/19.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162779 $$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_162779) (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 pls))) (ti X_a BOUND_VARIABLE_162779))) ) 21.34/19.47 ( bool, fFalse ) 21.34/19.47 ( bool, fTrue ) 21.34/19.47 ( real, pi ) 21.34/19.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.47 ( 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))))) ) 21.34/19.47 ( (fun nat bool), (even_odd_even nat) ) 21.34/19.47 ( (fun nat bool), prime ) 21.34/19.47 ( (fun nat nat), suc ) 21.34/19.47 ( (fun nat nat), (fact_fact nat) ) 21.34/19.47 ( (fun nat nat), (size_size nat) ) 21.34/19.47 ( (fun nat nat), fact ) 21.34/19.47 ( (fun nat nat), nat_size ) 21.34/19.47 ( int, pls ) 21.34/19.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.47 ( int, m ) 21.34/19.47 ( 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))) ) 21.34/19.47 ( int, min_1 ) 21.34/19.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.47 ( int, s ) 21.34/19.47 ( int, s1 ) 21.34/19.47 ( int, t ) 21.34/19.47 ( (fun int bool), zprime ) 21.34/19.47 ( (fun int bool), nat_neg ) 21.34/19.47 ( (fun int bool), zEven ) 21.34/19.47 ( (fun int bool), nat_is_nat ) 21.34/19.47 ( (fun int bool), zOdd ) 21.34/19.47 ( (fun int bool), (even_odd_even int) ) 21.34/19.47 ( (fun int bool), twoSqu1091635170sum2sq ) 21.34/19.47 ( (fun int nat), nat_1 ) 21.34/19.47 ( (fun int nat), phi ) 21.34/19.47 ( (fun real real), sqrt ) 21.34/19.47 ( (fun real real), tan ) 21.34/19.47 ( (fun real real), cos ) 21.34/19.47 ( (fun real real), arccos ) 21.34/19.47 ( (fun real real), ln ) 21.34/19.47 ( (fun real real), sin ) 21.34/19.47 ( (fun real real), arctan ) 21.34/19.47 ( (fun real real), arcsin ) 21.34/19.47 ( complex, ii ) 21.34/19.47 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.48 ( 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)) ) 21.34/19.48 ( (fun complex complex), cnj ) 21.34/19.48 ( (fun complex complex), expi ) 21.34/19.48 ( (fun nat real), (real_1 nat) ) 21.34/19.48 ( (fun nat real), cos_coeff ) 21.34/19.48 ( (fun nat real), sin_coeff ) 21.34/19.48 ( (fun int int), bit0 ) 21.34/19.48 ( (fun int int), bit1 ) 21.34/19.48 ( (fun int int), pred ) 21.34/19.48 ( (fun int int), succ ) 21.34/19.48 ( (fun int int), (fact_fact int) ) 21.34/19.48 ( (fun int int), zfact ) 21.34/19.48 ( (fun bool bool), fNot ) 21.34/19.48 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.34/19.48 ( (fun bool (fun bool bool)), fconj ) 21.34/19.48 ( (fun bool (fun bool bool)), fdisj ) 21.34/19.48 ( (fun bool (fun bool bool)), fimplies ) 21.34/19.48 ( (fun int (fun int bool)), sRStar ) 21.34/19.48 ( (fun int (fun int bool)), quadRes ) 21.34/19.48 ( (fun int (fun int bool)), norRRset ) 21.34/19.48 ( (fun int (fun int bool)), d22set ) 21.34/19.48 ( (fun int (fun int bool)), sr ) 21.34/19.48 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.34/19.48 ( (fun nat (fun nat nat)), nat_gcd ) 21.34/19.48 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.34/19.48 ( (fun nat (fun nat nat)), nat_lcm ) 21.34/19.48 ( (fun nat (fun real real)), root ) 21.34/19.48 ( (fun real (fun real real)), log ) 21.34/19.48 ( (fun real (fun real real)), powr ) 21.34/19.48 ( (fun nat (fun nat bool)), coprime ) 21.34/19.48 ( (fun (fun int bool) int), (the int) ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.34/19.48 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.34/19.48 ( (fun (fun int bool) bool), nat_nat_set ) 21.34/19.48 ( (filter nat), sequentially ) 21.34/19.48 ( (fun (product_prod nat nat) bool), pred_nat ) 21.34/19.48 ( (fun (product_prod int int) bool), frac_1 ) 21.34/19.48 ( (fun real complex), cis ) 21.34/19.48 ( (fun complex real), im ) 21.34/19.48 ( (fun complex real), re ) 21.34/19.48 ( (fun complex real), arg ) 21.34/19.48 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.34/19.48 ( (fun int (fun int int)), int_gcd ) 21.34/19.48 ( (fun int (fun int int)), multInv ) 21.34/19.48 ( (fun int (fun int int)), legacy_zgcd ) 21.34/19.48 ( (fun int (fun int int)), z3mod ) 21.34/19.48 ( (fun int (fun int int)), inv ) 21.34/19.48 ( (fun int (fun int int)), (gcd_gcd int) ) 21.34/19.48 ( (fun int (fun int int)), standardRes ) 21.34/19.48 ( (fun int (fun int int)), legendre ) 21.34/19.48 ( (fun int (fun int int)), nat_tsub ) 21.34/19.48 ( (fun int (fun int int)), z3div ) 21.34/19.48 ( (fun int (fun int int)), int_lcm ) 21.34/19.48 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.34/19.48 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.34/19.48 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.34/19.48 ( (fun int (fun (fun int bool) bool)), resSet ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.34/19.48 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.34/19.48 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.34/19.48 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.34/19.48 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.34/19.48 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.34/19.48 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.34/19.48 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.34/19.48 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.34/19.48 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.34/19.48 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.34/19.48 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.34/19.48 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.34/19.48 ( (fun real nat), natfloor ) 21.34/19.48 ( (fun real nat), natceiling ) 21.34/19.48 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.34/19.48 ( (fun int (fun int (fun int bool))), wset ) 21.34/19.48 ( (fun int (fun int (fun int bool))), bnorRset ) 21.34/19.48 ( (fun int (fun int (fun int bool))), zcong ) 21.34/19.48 ( (fun int (fun int (fun int bool))), noXRRset ) 21.34/19.48 ( (fun int (fun int (fun int bool))), zcongm ) 21.34/19.48 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.34/19.48 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.34/19.48 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.34/19.48 ( (fun int real), (real_1 int) ) 21.34/19.48 ( (fun complex nat), (size_size complex) ) 21.34/19.48 ( (fun complex nat), complex_size ) 21.34/19.48 ( (fun int (list int)), quickc666637781d_zero ) 21.34/19.48 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.34/19.48 ( (fun (product_prod int int) rat), frct ) 21.34/19.48 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.34/19.48 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.34/19.48 ( (fun (fun nat rat) bool), vanishes ) 21.34/19.48 ( (fun int (fun int rat)), fract ) 21.34/19.48 ( (fun code_code_numeral int), code_int_of ) 21.34/19.48 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.34/19.48 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.34/19.48 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.34/19.48 ( (fun real (fun real complex)), complex_1 ) 21.34/19.48 ( (fun real (fun real complex)), rcis ) 21.34/19.48 ( (fun int (fun nat nat)), nat_aux ) 21.34/19.48 ( (fun rat real), ratreal ) 21.34/19.48 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.34/19.48 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.34/19.48 ( (fun rat (product_prod int int)), quotient_of ) 21.34/19.48 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.34/19.48 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.34/19.48 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.34/19.48 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.34/19.48 ) 21.34/19.48 (instantiation (let ((_let_0 (mono nat X_a))) (forall ((X_a $$unsorted)) (or (not (order X_a)) (= _let_0 (ti (fun (fun nat (fun nat bool)) (fun (fun nat X_a) bool)) _let_0))) )) 21.34/19.48 ( bool ) 21.34/19.48 ( real ) 21.34/19.48 ( nat ) 21.34/19.48 ( (fun nat bool) ) 21.34/19.48 ( (fun nat nat) ) 21.34/19.48 ( int ) 21.34/19.48 ( (fun real real) ) 21.34/19.48 ( complex ) 21.34/19.48 ( (fun int int) ) 21.34/19.48 ( rat ) 21.34/19.48 ( (fun bool bool) ) 21.34/19.48 ( quickcheck_code_int ) 21.34/19.48 ( (fun nat (fun nat bool)) ) 21.34/19.48 ( (product_prod real real) ) 21.34/19.48 ( (product_prod int int) ) 21.34/19.48 ( (fun nat (product_prod int int)) ) 21.34/19.48 ( (product_prod nat nat) ) 21.34/19.48 ( (fun (product_prod nat nat) bool) ) 21.34/19.48 ( (fun nat (fun (product_prod nat nat) bool)) ) 21.34/19.48 ( (fun nat (product_prod nat nat)) ) 21.34/19.48 ( code_code_numeral ) 21.34/19.48 ) 21.34/19.48 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (hBOOL (hAPP X_a bool (iszero X_a) (hAPP int X_a (number_number_of X_a) pls)))) ) 21.34/19.48 ( real ) 21.34/19.48 ( nat ) 21.34/19.48 ( int ) 21.34/19.48 ( complex ) 21.34/19.48 ( rat ) 21.34/19.48 ( quickcheck_code_int ) 21.34/19.48 ( code_code_numeral ) 21.34/19.48 ) 21.34/19.48 (instantiation (let ((_let_0 (ti T A))) (forall ((T $$unsorted) (A $$unsorted)) (= _let_0 (ti T _let_0)) )) 21.34/19.48 ( bool, fFalse ) 21.34/19.48 ( bool, fTrue ) 21.34/19.48 ( real, pi ) 21.34/19.48 ( (fun nat bool), (even_odd_even nat) ) 21.34/19.48 ( (fun nat bool), prime ) 21.34/19.48 ( (fun nat nat), suc ) 21.34/19.48 ( (fun nat nat), (fact_fact nat) ) 21.34/19.48 ( (fun nat nat), (size_size nat) ) 21.34/19.48 ( (fun nat nat), fact ) 21.34/19.48 ( (fun nat nat), nat_size ) 21.34/19.48 ( int, pls ) 21.34/19.48 ( int, m ) 21.34/19.48 ( int, min_1 ) 21.34/19.48 ( int, s ) 21.34/19.48 ( int, s1 ) 21.34/19.48 ( int, t ) 21.34/19.48 ( (fun int bool), zprime ) 21.34/19.48 ( (fun int bool), nat_neg ) 21.34/19.48 ( (fun int bool), zEven ) 21.34/19.48 ( (fun int bool), nat_is_nat ) 21.34/19.48 ( (fun int bool), zOdd ) 21.34/19.48 ( (fun int bool), (even_odd_even int) ) 21.34/19.48 ( (fun int bool), twoSqu1091635170sum2sq ) 21.34/19.48 ( (fun int nat), nat_1 ) 21.34/19.48 ( (fun int nat), phi ) 21.34/19.48 ( (fun real real), sqrt ) 21.34/19.48 ( (fun real real), tan ) 21.34/19.48 ( (fun real real), cos ) 21.34/19.48 ( (fun real real), arccos ) 21.34/19.48 ( (fun real real), ln ) 21.34/19.48 ( (fun real real), sin ) 21.34/19.48 ( (fun real real), arctan ) 21.34/19.48 ( (fun real real), arcsin ) 21.34/19.48 ( complex, ii ) 21.34/19.48 ( (fun complex complex), cnj ) 21.34/19.48 ( (fun complex complex), expi ) 21.34/19.48 ( (fun nat real), (real_1 nat) ) 21.34/19.48 ( (fun nat real), cos_coeff ) 21.34/19.48 ( (fun nat real), sin_coeff ) 21.34/19.48 ( (fun int int), bit0 ) 21.34/19.48 ( (fun int int), bit1 ) 21.34/19.48 ( (fun int int), pred ) 21.34/19.48 ( (fun int int), succ ) 21.34/19.48 ( (fun int int), (fact_fact int) ) 21.34/19.48 ( (fun int int), zfact ) 21.34/19.48 ( (fun bool bool), fNot ) 21.34/19.48 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.34/19.48 ( (fun bool (fun bool bool)), fconj ) 21.34/19.48 ( (fun bool (fun bool bool)), fdisj ) 21.34/19.48 ( (fun bool (fun bool bool)), fimplies ) 21.34/19.48 ( (fun int (fun int bool)), sRStar ) 21.34/19.48 ( (fun int (fun int bool)), quadRes ) 21.34/19.48 ( (fun int (fun int bool)), norRRset ) 21.34/19.48 ( (fun int (fun int bool)), d22set ) 21.34/19.48 ( (fun int (fun int bool)), sr ) 21.34/19.48 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.34/19.48 ( (fun nat (fun nat nat)), nat_gcd ) 21.34/19.48 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.34/19.48 ( (fun nat (fun nat nat)), nat_lcm ) 21.34/19.48 ( (fun nat (fun real real)), root ) 21.34/19.48 ( (fun real (fun real real)), log ) 21.34/19.48 ( (fun real (fun real real)), powr ) 21.34/19.48 ( (fun nat (fun nat bool)), coprime ) 21.34/19.48 ( (fun (fun int bool) int), (the int) ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.34/19.48 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.34/19.48 ( (fun (fun int bool) bool), nat_nat_set ) 21.34/19.48 ( (filter nat), sequentially ) 21.34/19.48 ( (fun (product_prod nat nat) bool), pred_nat ) 21.34/19.48 ( (fun (product_prod int int) bool), frac_1 ) 21.34/19.48 ( (fun real complex), cis ) 21.34/19.48 ( (fun complex real), im ) 21.34/19.48 ( (fun complex real), re ) 21.34/19.48 ( (fun complex real), arg ) 21.34/19.48 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.34/19.48 ( (fun int (fun int int)), int_gcd ) 21.34/19.48 ( (fun int (fun int int)), multInv ) 21.34/19.48 ( (fun int (fun int int)), legacy_zgcd ) 21.34/19.48 ( (fun int (fun int int)), z3mod ) 21.34/19.48 ( (fun int (fun int int)), inv ) 21.34/19.48 ( (fun int (fun int int)), (gcd_gcd int) ) 21.34/19.48 ( (fun int (fun int int)), standardRes ) 21.34/19.48 ( (fun int (fun int int)), legendre ) 21.34/19.48 ( (fun int (fun int int)), nat_tsub ) 21.34/19.48 ( (fun int (fun int int)), z3div ) 21.34/19.48 ( (fun int (fun int int)), int_lcm ) 21.34/19.48 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.34/19.48 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.34/19.48 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.34/19.48 ( (fun int (fun (fun int bool) bool)), resSet ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.34/19.48 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.34/19.48 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.34/19.48 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.34/19.48 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.34/19.48 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.34/19.48 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.34/19.48 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.34/19.48 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.34/19.48 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.34/19.48 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.34/19.48 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.34/19.48 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.34/19.48 ( (fun real nat), natfloor ) 21.34/19.48 ( (fun real nat), natceiling ) 21.34/19.48 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.34/19.48 ( (fun int (fun int (fun int bool))), wset ) 21.34/19.48 ( (fun int (fun int (fun int bool))), bnorRset ) 21.34/19.48 ( (fun int (fun int (fun int bool))), zcong ) 21.34/19.48 ( (fun int (fun int (fun int bool))), noXRRset ) 21.34/19.48 ( (fun int (fun int (fun int bool))), zcongm ) 21.34/19.48 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.34/19.48 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.34/19.48 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.34/19.48 ( (fun int real), (real_1 int) ) 21.34/19.48 ( (fun complex nat), (size_size complex) ) 21.34/19.48 ( (fun complex nat), complex_size ) 21.34/19.48 ( (fun int (list int)), quickc666637781d_zero ) 21.34/19.48 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.34/19.48 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.34/19.48 ( (fun (product_prod int int) rat), frct ) 21.34/19.48 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.34/19.48 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.34/19.48 ( (fun (fun nat rat) bool), vanishes ) 21.34/19.48 ( (fun int (fun int rat)), fract ) 21.34/19.48 ( (fun code_code_numeral int), code_int_of ) 21.34/19.48 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.34/19.48 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.34/19.48 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.34/19.48 ( (fun real (fun real complex)), complex_1 ) 21.34/19.48 ( (fun real (fun real complex)), rcis ) 21.34/19.48 ( (fun int (fun nat nat)), nat_aux ) 21.34/19.48 ( (fun rat real), ratreal ) 21.34/19.48 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.34/19.48 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.34/19.48 ( (fun rat (product_prod int int)), quotient_of ) 21.34/19.48 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.34/19.48 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.34/19.48 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.34/19.48 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.34/19.48 ) 21.34/19.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162828 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_162828) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_162828)) (one_one int))))) ) 21.34/19.48 ( real, (zero_zero real) ) 21.34/19.48 ( real, (one_one real) ) 21.34/19.48 ( real, pi ) 21.34/19.48 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.48 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.34/19.48 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.48 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 21.34/19.48 ( nat, (zero_zero nat) ) 21.34/19.48 ( int, (zero_zero int) ) 21.34/19.48 ( int, min_1 ) 21.34/19.48 ( int, s ) 21.34/19.48 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 21.34/19.48 ( int, t ) 21.34/19.48 ( int, skv_3 ) 21.34/19.48 ( int, skv_9 ) 21.34/19.48 ) 21.34/19.48 (instantiation (let ((_let_0 (fun int bool))) (forall ((Z_1 $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) Z_1) N))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) N))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) Z_1) N))) )) 21.34/19.48 ( (zero_zero int), (one_one int) ) 21.34/19.48 ( (zero_zero int), min_1 ) 21.34/19.48 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.48 ( (zero_zero int), s ) 21.34/19.48 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 21.34/19.48 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.34/19.48 ( (zero_zero int), skv_3 ) 21.34/19.48 ( (zero_zero int), skv_9 ) 21.34/19.48 ( (one_one int), t ) 21.34/19.48 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 21.34/19.48 ( min_1, pls ) 21.34/19.48 ( min_1, min_1 ) 21.34/19.48 ) 21.34/19.48 (instantiation (let ((_let_0 (fun nat X_a))) (let ((_let_1 (power_power X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_162856 $$unsorted) (BOUND_VARIABLE_162857 $$unsorted)) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_162857))) (= (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_162856) BOUND_VARIABLE_162857) (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_162856)) BOUND_VARIABLE_162857))) ))) 21.34/19.48 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.48 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.48 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.48 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.49 ) 21.34/19.49 (instantiation (forall ((N $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) N) (zero_zero int)))) (= (one_one int) (hAPP int int zfact N))) ) 21.34/19.49 ( (zero_zero int) ) 21.34/19.49 ( (one_one int) ) 21.34/19.49 ( min_1 ) 21.34/19.49 ) 21.34/19.49 (instantiation (let ((_let_0 (fun int int))) (forall ((N $$unsorted)) (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)))))) )) 21.34/19.49 ( (zero_zero int) ) 21.34/19.49 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.49 ( (one_one int) ) 21.34/19.49 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.34/19.49 ( min_1 ) 21.34/19.49 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.49 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.49 ) 21.34/19.49 (instantiation (let ((_let_0 (inverse_inverse X_a))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (ti X_a BOUND_VARIABLE_162927))) (let ((_let_3 (ti X_a BOUND_VARIABLE_162928))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_162927 $$unsorted) (BOUND_VARIABLE_162928 $$unsorted)) (or (not (division_ring X_a)) (not (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_162928) (hAPP X_a X_a _let_0 BOUND_VARIABLE_162927))) (= _let_1 _let_2) (= _let_1 _let_3) (= _let_2 _let_3)) ))))) 21.34/19.49 ( real, (zero_zero real), (zero_zero real) ) 21.34/19.49 ( complex, ii, ii ) 21.34/19.49 ) 21.34/19.49 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_162956 $$unsorted) (BOUND_VARIABLE_162957 $$unsorted)) (or (not (ordered_ring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_162957) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_162956) _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_162957) BOUND_VARIABLE_162956)))) )))) 21.34/19.49 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.49 ( 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))))) ) 21.34/19.49 ( real, (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.49 ( 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 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)))) ) 21.34/19.49 ( 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))) ) 21.34/19.49 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.49 ( 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))) ) 21.34/19.49 ( int, skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.34/19.49 ( complex, ii, ii ) 21.34/19.49 ( 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)) ) 21.34/19.49 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.49 ) 21.34/19.49 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP int real (real_1 int) N))) (forall ((N $$unsorted) (X $$unsorted)) (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))) )))) 21.34/19.49 ( (zero_zero int), pi ) 21.34/19.49 ( (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)))) ) 21.34/19.49 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.49 ( (zero_zero int), skv_2 ) 21.34/19.49 ( (zero_zero int), skv_10 ) 21.34/19.49 ( (zero_zero int), skv_13 ) 21.34/19.49 ( (one_one int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.49 ) 21.34/19.49 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_162996 $$unsorted)) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_162996)) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_162996)))) )))) 21.34/19.49 ( real, (one_one real) ) 21.34/19.49 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.49 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.34/19.49 ( int, pls ) 21.34/19.49 ( int, (one_one int) ) 21.34/19.49 ( int, min_1 ) 21.34/19.49 ( complex, ii ) 21.34/19.49 ( complex, (one_one complex) ) 21.34/19.49 ) 21.34/19.49 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_163037 $$unsorted) (BOUND_VARIABLE_163038 $$unsorted)) (or (not (linordered_idom X_a)) (= (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_163037) _let_2)) (not (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_163038)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_163037) BOUND_VARIABLE_163038)) _let_2)))) )))) 21.34/19.49 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.49 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.49 ( int, skv_8, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.49 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.49 ) 21.34/19.49 (instantiation (let ((_let_0 (fun nat X_a))) (let ((_let_1 (zero_zero X_a))) (forall ((X_a $$unsorted)) (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))) ))) 21.34/19.49 ( bool ) 21.34/19.49 ( real ) 21.34/19.49 ( nat ) 21.34/19.49 ( (fun nat bool) ) 21.34/19.49 ( (fun nat nat) ) 21.34/19.49 ( int ) 21.34/19.49 ( (fun int bool) ) 21.34/19.49 ( (fun real real) ) 21.34/19.49 ( complex ) 21.34/19.49 ( (fun int int) ) 21.34/19.49 ( rat ) 21.34/19.49 ( (fun bool bool) ) 21.34/19.49 ( quickcheck_code_int ) 21.34/19.49 ( (fun nat (fun nat bool)) ) 21.34/19.49 ( (product_prod real real) ) 21.34/19.49 ( (product_prod int int) ) 21.34/19.49 ( (fun nat (product_prod int int)) ) 21.34/19.49 ( (filter real) ) 21.34/19.49 ( (filter nat) ) 21.34/19.49 ( (product_prod nat nat) ) 21.34/19.49 ( (fun (product_prod nat nat) bool) ) 21.34/19.49 ( (fun nat (fun (product_prod nat nat) bool)) ) 21.34/19.49 ( (fun nat (product_prod nat nat)) ) 21.34/19.49 ( code_code_numeral ) 21.34/19.49 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 21.34/19.49 ( (fun nat rat) ) 21.34/19.49 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 21.34/19.49 ) 21.34/19.49 (instantiation (let ((_let_0 (isCont X_a X_b))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (or (not (topological_space X_a)) (not (topological_space X_b)) (= _let_0 (ti (fun (fun X_a X_b) (fun X_a bool)) _let_0))) )) 21.34/19.49 ( bool, real ) 21.34/19.49 ( bool, nat ) 21.34/19.49 ( bool, int ) 21.34/19.49 ( bool, (product_prod int int) ) 21.34/19.49 ( real, nat ) 21.34/19.49 ( real, int ) 21.34/19.49 ( (fun nat bool), int ) 21.34/19.49 ( int, int ) 21.34/19.49 ( int, (product_prod int int) ) 21.34/19.49 ( (fun int bool), real ) 21.34/19.49 ( (fun int bool), int ) 21.34/19.49 ) 21.34/19.49 (instantiation (let ((_let_0 (zero_zero int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (forall ((B $$unsorted)) (or (= _let_0 (ti int B)) (hBOOL (hAPP _let_1 bool (hAPP int _let_2 (hAPP int (fun int _let_2) divmod_int_rel _let_0) B) (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) _let_0) _let_0)))) )))) 21.34/19.49 ( m ) 21.34/19.49 ( min_1 ) 21.34/19.49 ( s ) 21.34/19.49 ( s1 ) 21.34/19.49 ( t ) 21.34/19.49 ) 21.34/19.49 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (one_one int))) (let ((_let_3 (dvd_dvd int))) (let ((_let_4 (gcd_gcd int))) (forall ((E_1 $$unsorted) (B $$unsorted) (D $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 D) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 E_1) B))) (not (= _let_2 (hAPP int int (hAPP int _let_1 _let_4 A_1) B))) (= _let_2 (hAPP int int (hAPP int _let_1 _let_4 D) E_1))) )))))) 21.34/19.49 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 21.34/19.49 ) 21.34/19.49 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) B_1))) (= (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less rat) (one_one rat)) (hAPP int rat (hAPP int (fun int rat) fract A_2) B_1))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B_1) A_2)))) ))) 21.34/19.49 ( (zero_zero int), (zero_zero int) ) 21.34/19.49 ( (zero_zero int), (one_one int) ) 21.34/19.49 ( (zero_zero int), min_1 ) 21.34/19.49 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 21.34/19.49 ( (zero_zero int), t ) 21.34/19.49 ( (one_one int), (zero_zero int) ) 21.34/19.49 ( (one_one int), (one_one int) ) 21.34/19.49 ( (one_one int), t ) 21.34/19.49 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 21.34/19.49 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 21.34/19.49 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 21.34/19.49 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_3 ) 21.34/19.49 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_9 ) 21.34/19.49 ( min_1, (zero_zero int) ) 21.34/19.49 ( min_1, min_1 ) 21.34/19.49 ( (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 21.34/19.49 ) 21.34/19.49 (instantiation (forall ((X_a $$unsorted)) (or (not (ring_1 X_a)) (= (hAPP int X_a (ring_1_of_int X_a) (zero_zero int)) (zero_zero X_a))) ) 21.34/19.49 ( real ) 21.34/19.49 ( nat ) 21.34/19.49 ( int ) 21.34/19.49 ( complex ) 21.34/19.49 ( rat ) 21.34/19.49 ( quickcheck_code_int ) 21.34/19.49 ( code_code_numeral ) 21.34/19.49 ) 21.34/19.49 (instantiation (forall ((M $$unsorted)) (= M (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) (zero_zero nat))) ) 21.34/19.49 ( (one_one nat) ) 21.34/19.49 ) 21.34/19.49 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_163432))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_163432 $$unsorted) (BOUND_VARIABLE_163433 $$unsorted)) (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_163433))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_163433) (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_163433) (ti int BOUND_VARIABLE_163432))) ))) 21.34/19.49 ( real, (zero_zero int), pi ) 21.34/19.49 ( 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)))) ) 21.34/19.49 ( real, (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.49 ( real, (zero_zero int), skv_6 ) 21.34/19.49 ( real, (zero_zero int), skv_11 ) 21.34/19.49 ( real, (zero_zero int), skv_12 ) 21.34/19.49 ( real, (zero_zero int), skv_14 ) 21.34/19.49 ) 21.34/19.49 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_163478 $$unsorted) (BOUND_VARIABLE_163479 $$unsorted)) (or (not (linorder X_a)) (= (ti X_a BOUND_VARIABLE_163478) (ti X_a BOUND_VARIABLE_163479)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_163478) BOUND_VARIABLE_163479)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_163479) BOUND_VARIABLE_163478))) ))) 21.34/19.49 ( real, (zero_zero real), pi ) 21.34/19.49 ( 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)))) ) 21.34/19.49 ( 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))))) ) 21.34/19.49 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.49 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.50 ( real, (zero_zero real), skv_2 ) 21.34/19.50 ( real, (zero_zero real), skv_10 ) 21.34/19.50 ( real, (zero_zero real), skv_13 ) 21.34/19.50 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.50 ( real, pi, (zero_zero real) ) 21.34/19.50 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.34/19.50 ( 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)) ) 21.34/19.50 ( 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)))) ) 21.34/19.50 ( real, (hAPP real real (hAPP 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) ) 21.34/19.50 ( real, (hAPP real real (hAPP real (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))) ) 21.34/19.50 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 21.34/19.50 ( 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) ) 21.34/19.50 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.34/19.50 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.34/19.50 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 21.34/19.50 ( 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 ) 21.34/19.50 ( real, skv_2, (zero_zero real) ) 21.34/19.50 ( real, skv_10, (zero_zero real) ) 21.34/19.50 ( real, skv_13, (zero_zero real) ) 21.34/19.50 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.34/19.50 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 21.34/19.50 ( int, (zero_zero int), (zero_zero int) ) 21.34/19.50 ( int, (zero_zero int), (one_one int) ) 21.34/19.50 ( 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))) ) 21.34/19.50 ( int, (zero_zero int), min_1 ) 21.34/19.50 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 21.34/19.50 ( int, (zero_zero int), t ) 21.34/19.50 ( int, (one_one int), (zero_zero int) ) 21.34/19.50 ( int, (one_one int), t ) 21.34/19.50 ( 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))), (zero_zero int) ) 21.34/19.50 ( 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))), s ) 21.34/19.50 ( 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 ) 21.34/19.50 ( 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_3 ) 21.51/19.50 ( 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_9 ) 21.51/19.50 ( int, min_1, (zero_zero int) ) 21.51/19.50 ( int, min_1, min_1 ) 21.51/19.50 ( 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))) ) 21.51/19.50 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 21.51/19.50 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 21.51/19.50 ( int, t, (zero_zero int) ) 21.51/19.50 ( int, t, (one_one int) ) 21.51/19.50 ( 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))) ) 21.51/19.50 ( 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) (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))) (zero_zero int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 21.51/19.50 ( int, skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.51/19.50 ( int, skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.51/19.50 ) 21.51/19.50 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163498 $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP nat X_a (semiring_1_of_nat X_a) (hAPP nat nat (fact_fact nat) BOUND_VARIABLE_163498))))) ) 21.51/19.50 ( real, (hAPP nat nat suc (zero_zero nat)) ) 21.51/19.50 ( int, (hAPP nat nat suc (zero_zero nat)) ) 21.51/19.50 ) 21.51/19.50 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (minus_minus int) K_4) pls) (ti int K_4)) ) 21.51/19.50 ( pls ) 21.51/19.50 ( m ) 21.51/19.50 ( min_1 ) 21.51/19.50 ( s ) 21.51/19.50 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.50 ( s1 ) 21.51/19.50 ( t ) 21.51/19.50 ) 21.51/19.50 (instantiation (forall ((X $$unsorted)) (= (hAPP int real (ring_1_of_int real) X) (hAPP int real (number_number_of real) X)) ) 21.51/19.50 ( (zero_zero int) ) 21.51/19.50 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.51/19.50 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.50 ( (one_one int) ) 21.51/19.50 ( min_1 ) 21.51/19.50 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.50 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.51/19.50 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.51/19.50 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 21.51/19.50 ) 21.51/19.50 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (one_one X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_163537 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (= (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_163537)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_163537) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_163537))))) )))) 21.51/19.50 ( real, (zero_zero real) ) 21.51/19.50 ( real, pi ) 21.51/19.50 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.50 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.50 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.50 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.50 ( real, skv_2 ) 21.51/19.50 ( real, skv_10 ) 21.51/19.50 ( real, skv_13 ) 21.51/19.50 ( real, skv_14 ) 21.51/19.50 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.50 ( int, (zero_zero int) ) 21.51/19.50 ( int, (one_one int) ) 21.51/19.50 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.51/19.50 ( int, min_1 ) 21.51/19.50 ( complex, ii ) 21.51/19.50 ) 21.51/19.50 (instantiation (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_163650))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_163650 $$unsorted) (BOUND_VARIABLE_163651 $$unsorted) (BOUND_VARIABLE_163652 $$unsorted)) (or (not (monoid_mult X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_163651)) (hAPP nat X_a _let_0 BOUND_VARIABLE_163652)) (hAPP nat X_a _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) BOUND_VARIABLE_163651) BOUND_VARIABLE_163652)))) )) 21.51/19.50 ( int, s, (one_one nat), (one_one nat) ) 21.51/19.50 ( int, s1, (one_one nat), (one_one nat) ) 21.51/19.50 ( int, skv_8, (one_one nat), (one_one nat) ) 21.51/19.50 ( complex, ii, (one_one nat), (one_one nat) ) 21.51/19.50 ) 21.51/19.50 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)))) (let ((_let_1 (archim2085082626_floor real))) (forall ((B $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_0 A_1))) (not (hBOOL (hAPP real bool _let_0 B))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP real int _let_1 A_1)) (hAPP real int _let_1 B))) (hAPP real int _let_1 (hAPP real real (hAPP real (fun real real) (times_times real) A_1) B))))) ))) 21.51/19.50 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.50 ( 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))))) ) 21.51/19.50 ( (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.50 ( (hAPP real real arctan (hAPP real real (hAPP 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)))) ) 21.51/19.50 ) 21.51/19.50 (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)))) ) 21.51/19.50 ( ii ) 21.51/19.50 ( (zero_zero complex) ) 21.51/19.50 ( (one_one complex) ) 21.51/19.50 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.50 ( (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)) ) 21.51/19.50 ) 21.51/19.50 (instantiation (forall ((N $$unsorted)) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP nat nat suc (hAPP nat nat suc N))) ) 21.51/19.50 ( (zero_zero nat) ) 21.51/19.50 ( (hAPP nat nat suc (zero_zero nat)) ) 21.51/19.50 ( (one_one nat) ) 21.51/19.50 ) 21.51/19.50 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163779 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls)))) BOUND_VARIABLE_163779)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (one_one int)) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_163779))))) ) 21.51/19.50 ( real, pi ) 21.51/19.50 ) 21.51/19.50 (instantiation (forall ((Z_1 $$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))) ) 21.51/19.50 ( (zero_zero int) ) 21.51/19.50 ( (one_one int) ) 21.51/19.50 ( min_1 ) 21.51/19.50 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.50 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.51/19.50 ) 21.51/19.50 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (one_one nat))) (forall ((P_4 $$unsorted)) (= (and (forall ((M_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (dvd_dvd nat) M_2) P_4))) (= _let_1 M_2) (= P_4 M_2)) ) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) _let_1) P_4))) (hBOOL (hAPP nat bool prime P_4))) ))) 21.51/19.50 ( (zero_zero nat) ) 21.51/19.50 ( (one_one nat) ) 21.51/19.50 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.50 ) 21.51/19.50 (instantiation (let ((_let_0 (hAPP int (fun nat int) (power_power int) A_1))) (let ((_let_1 (hAPP int nat nat_1 P_5))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (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))) ))) 21.51/19.50 ( s, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.50 ( s1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.50 ( skv_8, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.50 ) 21.51/19.50 (instantiation (let ((_let_0 (even_odd_even int))) (forall ((Y $$unsorted) (X $$unsorted)) (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)))) )) 21.51/19.50 ( (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) ) 21.51/19.50 ( (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)))) ) 21.51/19.50 ) 21.51/19.50 (instantiation (let ((_let_0 (fun int bool))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_2) B_1))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) B_1) (hAPP int _let_0 d22set A_2))))) )) 21.51/19.50 ( (zero_zero int), (zero_zero int) ) 21.51/19.50 ( (zero_zero int), (one_one int) ) 21.51/19.50 ( (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))) ) 21.51/19.51 ( (zero_zero int), min_1 ) 21.51/19.51 ( min_1, (zero_zero int) ) 21.51/19.51 ( min_1, min_1 ) 21.51/19.51 ( 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))) ) 21.51/19.51 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 21.51/19.51 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 21.51/19.51 ( t, (zero_zero int) ) 21.51/19.51 ( t, (one_one int) ) 21.51/19.51 ( 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))) ) 21.51/19.51 ( skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.51/19.51 ( skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.51/19.51 ) 21.51/19.51 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (ord_less int))) (let ((_let_3 (ring_1_of_int X_a))) (let ((_let_4 (semiring_1_of_nat X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_163925 $$unsorted) (BOUND_VARIABLE_163937 $$unsorted)) (or (not (ring_1 X_a)) (and (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 BOUND_VARIABLE_163925) _let_1))) (= (hAPP X_a X_a (uminus_uminus X_a) (hAPP nat X_a _let_4 (hAPP int nat nat_1 (hAPP int int (uminus_uminus int) BOUND_VARIABLE_163925)))) (hAPP int X_a _let_3 BOUND_VARIABLE_163925))) (or (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 BOUND_VARIABLE_163937) _let_1)) (= (hAPP int X_a _let_3 BOUND_VARIABLE_163937) (hAPP nat X_a _let_4 (hAPP int nat nat_1 BOUND_VARIABLE_163937)))))) )))))) 21.51/19.51 ( real, t, t ) 21.51/19.51 ( int, (zero_zero int), (zero_zero int) ) 21.51/19.51 ( complex, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 21.51/19.51 ( rat, s, s ) 21.51/19.51 ) 21.51/19.51 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_163959))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_163959 $$unsorted)) (or (not (linordered_idom X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 _let_2) _let_2) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_163959) BOUND_VARIABLE_163959))) )))) 21.51/19.51 ( complex, ii ) 21.51/19.51 ) 21.51/19.51 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_idom X_a)) (not (number_ring X_a)) (= (hAPP X_a X_a (abs_abs X_a) (hAPP int X_a (number_number_of X_a) min_1)) (one_one X_a))) ) 21.51/19.51 ( real ) 21.51/19.51 ( nat ) 21.51/19.51 ( int ) 21.51/19.51 ( complex ) 21.51/19.51 ( rat ) 21.51/19.51 ( quickcheck_code_int ) 21.51/19.51 ( code_code_numeral ) 21.51/19.51 ) 21.51/19.51 (instantiation (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int (fun int bool) (dvd_dvd int) K_4))) (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (or (not (= (one_one int) (hAPP int int (hAPP int _let_0 legacy_zgcd N) K_4))) (not (hBOOL (hAPP int bool _let_1 (hAPP int int (hAPP int _let_0 (times_times int) M) N)))) (hBOOL (hAPP int bool _let_1 M))) ))) 21.51/19.51 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.51/19.51 ) 21.51/19.51 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int succ K_4) (hAPP int int (hAPP int (fun int int) (plus_plus int) K_4) (one_one int))) ) 21.51/19.51 ( pls ) 21.51/19.51 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 21.51/19.51 ( min_1 ) 21.51/19.51 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.51 ) 21.51/19.51 (instantiation (let ((_let_0 (one_one int))) (let ((_let_1 (hAPP int (fun int int) (minus_minus int) M))) (forall ((M $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_0) M))) (= (hAPP nat nat suc (hAPP int nat nat_1 (hAPP int int _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP int nat nat_1 (hAPP int int _let_1 _let_0)))) ))) 21.51/19.51 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.51 ) 21.51/19.51 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (fun X_a bool))) (let ((_let_3 (sums X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_164191 $$unsorted) (BOUND_VARIABLE_164192 $$unsorted)) (or (not (comm_monoid_add X_a)) (not (topological_space X_a)) (not (= (zero_zero X_a) (hAPP nat X_a BOUND_VARIABLE_164192 (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_164192) suc)) BOUND_VARIABLE_164191))) (hBOOL (hAPP X_a bool (hAPP _let_1 _let_2 _let_3 BOUND_VARIABLE_164192) BOUND_VARIABLE_164191))) ))))) 21.51/19.51 ( 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))))) ) 21.51/19.51 ) 21.51/19.51 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164221 $$unsorted)) (or (not (field_inverse_zero X_a)) (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_164221) (hAPP int X_a (number_number_of X_a) min_1)) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_164221))) ) 21.51/19.51 ( real, (one_one real) ) 21.51/19.51 ( real, pi ) 21.51/19.51 ( 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)))) ) 21.51/19.51 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.51/19.51 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.51/19.51 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.51/19.51 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.51 ( int, pls ) 21.51/19.51 ( int, (one_one int) ) 21.51/19.51 ( int, min_1 ) 21.51/19.51 ( complex, ii ) 21.51/19.51 ( complex, (one_one complex) ) 21.51/19.51 ) 21.51/19.51 (instantiation (let ((_let_0 (inverse_inverse real))) (forall ((X $$unsorted)) (= (hAPP real real _let_0 (hAPP real real sqrt X)) (hAPP real real sqrt (hAPP real real _let_0 X))) )) 21.51/19.51 ( (zero_zero real) ) 21.51/19.51 ) 21.51/19.51 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) B_1))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) A_2) _let_1)) (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less_eq rat) (hAPP int rat (hAPP int (fun int rat) fract A_2) B_1)) (zero_zero rat))))) ))) 21.51/19.51 ( (zero_zero int), (one_one int) ) 21.51/19.51 ( (one_one int), (one_one int) ) 21.51/19.51 ) 21.51/19.51 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (real_1 nat))) (let ((_let_2 (times_times real))) (let ((_let_3 (even_odd_even nat))) (let ((_let_4 (hAPP real real (hAPP real _let_0 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (forall ((X_1 $$unsorted)) (= (or (not (forall ((N_2 $$unsorted)) (or (not (= X_1 (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real _let_0 _let_2 (hAPP nat real _let_1 N_2)) _let_4)))) (not (hBOOL (hAPP nat bool _let_3 N_2)))) )) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool _let_3 N_2))) (not (= X_1 (hAPP real real (hAPP real _let_0 _let_2 (hAPP nat real _let_1 N_2)) _let_4)))) ))) (= (zero_zero real) (hAPP real real sin X_1))) )))))) 21.51/19.51 ( (zero_zero real) ) 21.51/19.51 ( pi ) 21.51/19.51 ( (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)))) ) 21.51/19.51 ( (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) ) 21.51/19.51 ( (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))))) ) 21.51/19.51 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 21.51/19.51 ( (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))))) ) 21.51/19.51 ( (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)))) ) 21.51/19.51 ) 21.51/19.51 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) _let_2)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) _let_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) (hAPP real real cos X)))) )))) 21.51/19.51 ( (zero_zero real) ) 21.51/19.51 ( pi ) 21.51/19.51 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.51 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.51 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.51/19.51 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.51/19.51 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 21.51/19.51 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.51 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.51/19.51 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.51/19.51 ( skv_14 ) 21.51/19.51 ) 21.51/19.51 (instantiation (let ((_let_0 (hAPP int nat (number_number_of nat) W))) (forall ((W $$unsorted)) (= (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)) )) 21.51/19.51 ( pls ) 21.51/19.51 ( (hAPP int int bit1 pls) ) 21.51/19.51 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.51/19.51 ( min_1 ) 21.51/19.51 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.51/19.51 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.51/19.51 ) 21.51/19.51 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X))) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natfloor X)) (one_one nat)) (hAPP real nat natfloor (hAPP real real (hAPP real (fun real real) (plus_plus real) X) (one_one real))))) ) 21.51/19.51 ( (one_one real) ) 21.51/19.51 ( pi ) 21.51/19.51 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.51 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.51 ( skv_6 ) 21.51/19.51 ( skv_11 ) 21.51/19.51 ( skv_12 ) 21.51/19.51 ( skv_14 ) 21.51/19.51 ) 21.51/19.51 (instantiation (let ((_let_0 (zero_zero nat))) (forall ((N $$unsorted)) (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)) )) 21.51/19.51 ( (zero_zero nat) ) 21.51/19.51 ) 21.51/19.51 (instantiation (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))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_164372 $$unsorted) (BOUND_VARIABLE_164373 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (= (or (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_164373) _let_2)) (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_164372))) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_164372) _let_2)) (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_164373)))) (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_164372) BOUND_VARIABLE_164373)) _let_2)))) ))))) 21.51/19.51 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.51 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.51/19.51 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.51 ( 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))))))))) ) 21.51/19.51 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.51 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.51 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.51/19.51 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.51/19.51 ( 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))) ) 21.51/19.51 ( 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))) ) 21.51/19.51 ( 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))) ) 21.51/19.51 ) 21.51/19.51 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_164410 $$unsorted) (BOUND_VARIABLE_164411 $$unsorted) (BOUND_VARIABLE_164412 $$unsorted)) (or (not (cancel_semigroup_add X_a)) (= (= (ti X_a BOUND_VARIABLE_164410) (ti X_a BOUND_VARIABLE_164412)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_164410) BOUND_VARIABLE_164411) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_164412) BOUND_VARIABLE_164411)))) ))) 21.51/19.52 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), min_1 ) 21.51/19.52 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int), s ) 21.51/19.52 ) 21.51/19.52 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (pow X_a))) (forall ((X_a $$unsorted)) (= _let_1 (ti (fun _let_0 (fun _let_0 bool)) _let_1)) ))) 21.51/19.52 ( nat ) 21.51/19.52 ( int ) 21.51/19.52 ) 21.51/19.52 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat real))) (let ((_let_4 (fun nat _let_1))) (let ((_let_5 (fun _let_0 real))) (let ((_let_6 (fun nat _let_2))) (let ((_let_7 (fun nat _let_0))) (let ((_let_8 (fun (filter nat) bool))) (let ((_let_9 (fun real _let_8))) (let ((_let_10 (tendsto nat real))) (let ((_let_11 (hAPP _let_3 _let_3 (hAPP _let_6 (fun _let_3 _let_3) (combs nat real real) (hAPP _let_3 _let_6 (hAPP (fun real _let_2) (fun _let_3 _let_6) (combb real _let_2 nat) (times_times real)) (hAPP real _let_3 (power_power real) (hAPP int real (number_number_of real) min_1)))) A_2))) (forall ((A_2 $$unsorted)) (let ((_let_0 (filter nat))) (or (not (hBOOL (hAPP _let_0 bool (hAPP real _let_8 (hAPP _let_3 _let_9 _let_10 A_2) (zero_zero real)) sequentially))) (not (hBOOL (hAPP _let_3 bool (monoseq real) A_2))) (hBOOL (hAPP _let_0 bool (hAPP real _let_8 (hAPP _let_3 _let_9 _let_10 (hAPP _let_7 _let_3 (hAPP _let_5 (fun _let_7 _let_3) (combb _let_0 real nat) (hAPP _let_3 _let_5 (big_co1399186613setsum nat real) _let_11)) (hAPP _let_1 _let_7 (hAPP _let_7 (fun _let_1 _let_7) (combb nat _let_0 nat) (hAPP nat _let_7 (ord_atLeastLessThan nat) (zero_zero nat))) (hAPP nat _let_1 (hAPP _let_4 _let_4 (combc nat nat nat) (hAPP _let_1 _let_4 (hAPP _let_4 (fun _let_1 _let_4) (combb nat _let_1 nat) (plus_plus nat)) (hAPP nat _let_1 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat))))) (hAPP _let_3 real (suminf real) _let_11)) sequentially)))) ))))))))))))) 21.51/19.56 ( (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 21.51/19.56 ) 21.51/19.56 (instantiation (let ((_let_0 (product_prod nat nat))) (let ((_let_1 (fun nat _let_0))) (forall ((M $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N))) (= (hAPP nat _let_0 (hAPP nat _let_1 divmod_nat M) N) (hAPP nat _let_0 (hAPP nat _let_1 (product_Pair nat nat) (zero_zero nat)) M))) ))) 21.51/19.56 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.56 ) 21.51/19.56 (instantiation (let ((_let_0 (hAPP nat nat suc N))) (forall ((N $$unsorted)) (= (hAPP nat nat fact _let_0) (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) _let_0) (hAPP nat nat fact N))) )) 21.51/19.56 ( (zero_zero nat) ) 21.51/19.56 ( (hAPP nat nat suc (zero_zero nat)) ) 21.51/19.56 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.51/19.56 ) 21.51/19.56 (instantiation (let ((_let_0 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_164616 $$unsorted)) (or (not (comm_ring_1 X_a)) (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_164616) (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_164616))) )) 21.51/19.56 ( real, (one_one real) ) 21.51/19.56 ( 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)))) ) 21.51/19.56 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.51/19.56 ( int, pls ) 21.51/19.56 ( int, (one_one int) ) 21.51/19.56 ( int, min_1 ) 21.51/19.56 ( complex, ii ) 21.51/19.56 ( complex, (one_one complex) ) 21.51/19.56 ) 21.51/19.56 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun nat real))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (one_one real)))) (hBOOL (hAPP _let_2 bool (bseq real) (hAPP real _let_2 (power_power real) X_1)))) )))) 21.51/19.56 ( (zero_zero real) ) 21.51/19.56 ( pi ) 21.51/19.56 ( (hAPP int real (number_number_of real) min_1) ) 21.51/19.56 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.56 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.56 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.56 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.56 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.56 ( skv_6 ) 21.51/19.56 ( skv_11 ) 21.51/19.56 ( skv_12 ) 21.51/19.56 ( skv_14 ) 21.51/19.56 ) 21.51/19.56 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (power_power real))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_4 (hAPP int nat (number_number_of nat) _let_3))) (forall ((X $$unsorted)) (= (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP nat real (hAPP real _let_1 _let_2 (hAPP real real cos X)) _let_4)) (hAPP nat real (hAPP real _let_1 _let_2 (hAPP real real sin X)) _let_4)) (hAPP real real cos (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real (number_number_of real) _let_3)) X))) )))))) 21.51/19.56 ( (zero_zero real) ) 21.51/19.56 ( pi ) 21.51/19.56 ( (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)))) ) 21.51/19.56 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.51/19.56 ( (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 21.51/19.56 ( (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 (hAPP int int bit1 pls))))) ) 21.51/19.56 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 21.51/19.56 ( (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 bit0 (hAPP int int bit1 pls))))) ) 21.51/19.56 ( (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)))) ) 21.51/19.56 ) 21.51/19.56 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real real))) (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) _let_0) X))) (not (= _let_0 (hAPP real real sin X))) (not (forall ((N_2 $$unsorted)) (or (not (= X (hAPP real real (hAPP real _let_1 (times_times real) (hAPP nat real (real_1 nat) N_2)) (hAPP real real (hAPP real _let_1 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (not (hBOOL (hAPP nat bool (even_odd_even nat) N_2)))) ))) ))) 21.51/19.56 ( (zero_zero real) ) 21.51/19.56 ( pi ) 21.51/19.56 ( (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)))) ) 21.51/19.56 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.51/19.56 ( (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 (hAPP int int bit1 pls))))) ) 21.51/19.56 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 21.51/19.56 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.56 ( (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 bit0 (hAPP int int bit1 pls))))) ) 21.51/19.56 ( (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)))) ) 21.51/19.56 ( skv_6 ) 21.51/19.56 ( skv_11 ) 21.51/19.56 ( skv_12 ) 21.51/19.56 ( skv_14 ) 21.51/19.56 ) 21.51/19.56 (instantiation (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))) (forall ((A_1 $$unsorted) (B $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (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))) (= (hAPP int rat (hAPP int _let_0 fract P_5) Q_3) _let_2)) )))) 21.51/19.56 ( (zero_zero int), (one_one int), (zero_zero int), (one_one int) ) 21.51/19.56 ( (zero_zero int), (one_one int), (one_one int), (one_one int) ) 21.51/19.56 ( (one_one int), (one_one int), (zero_zero int), (one_one int) ) 21.51/19.56 ) 21.51/19.56 (instantiation (forall ((Z_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Z_1))) (= (hAPP nat nat suc (hAPP int nat nat_1 Z_1)) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) Z_1)))) ) 21.51/19.56 ( (zero_zero int) ) 21.51/19.56 ( (one_one int) ) 21.51/19.56 ( min_1 ) 21.51/19.56 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.56 ( s ) 21.51/19.56 ( (hAPP int int (number_number_of int) pls) ) 21.51/19.56 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.51/19.56 ( skv_3 ) 21.51/19.56 ( skv_9 ) 21.51/19.56 ) 21.51/19.56 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_164821 $$unsorted) (BOUND_VARIABLE_164822 $$unsorted) (BOUND_VARIABLE_164823 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_164823))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_164821) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_164822) BOUND_VARIABLE_164823))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_164821) BOUND_VARIABLE_164823)) BOUND_VARIABLE_164822)))) )))) 21.51/19.56 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.56 ) 21.51/19.56 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) 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)))) ))) 21.51/19.57 ( (zero_zero real) ) 21.51/19.57 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.57 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.57 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.57 ( skv_14 ) 21.51/19.57 ) 21.51/19.57 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164852 $$unsorted) (BOUND_VARIABLE_164853 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_164852) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_164853))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_164852)) BOUND_VARIABLE_164853)))) ) 21.51/19.57 ( real, (zero_zero int), pi ) 21.51/19.57 ( real, (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.57 ( real, (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.57 ( real, (zero_zero int), skv_6 ) 21.51/19.57 ( real, (zero_zero int), skv_11 ) 21.51/19.57 ( real, (zero_zero int), skv_12 ) 21.51/19.57 ( real, (zero_zero int), skv_14 ) 21.51/19.57 ) 21.51/19.57 (instantiation (forall ((K_4 $$unsorted)) (= (zero_zero rat) (hAPP int rat (hAPP int (fun int rat) fract K_4) (zero_zero int))) ) 21.51/19.57 ( (zero_zero int) ) 21.51/19.57 ( (one_one int) ) 21.51/19.57 ) 21.51/19.57 (instantiation (let ((_let_0 (inverse_inverse X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_164880 $$unsorted) (BOUND_VARIABLE_164881 $$unsorted)) (or (not (divisi14063676e_zero X_a)) (not (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_164880) (hAPP X_a X_a _let_0 BOUND_VARIABLE_164881))) (= (ti X_a BOUND_VARIABLE_164881) (ti X_a BOUND_VARIABLE_164880))) )) 21.51/19.57 ( real, (zero_zero real), (zero_zero real) ) 21.51/19.57 ( complex, ii, ii ) 21.51/19.57 ) 21.51/19.57 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164936 $$unsorted) (BOUND_VARIABLE_164937 $$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_164936) BOUND_VARIABLE_164937)) (= (ti X_a BOUND_VARIABLE_164936) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_164937)))) ) 21.51/19.57 ( nat, (one_one nat), (one_one nat) ) 21.51/19.57 ( 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) ) 21.51/19.57 ( 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) ) 21.51/19.57 ) 21.51/19.57 (instantiation (let ((_let_0 (ord_atLeastAtMost X_a))) (forall ((X_a $$unsorted)) (or (not (order X_a)) (= _let_0 (ti (fun X_a (fun X_a (fun X_a bool))) _let_0))) )) 21.51/19.57 ( bool ) 21.51/19.57 ( real ) 21.51/19.57 ( nat ) 21.51/19.57 ( (fun nat bool) ) 21.51/19.57 ( int ) 21.51/19.57 ( (fun int bool) ) 21.51/19.57 ( rat ) 21.51/19.57 ( quickcheck_code_int ) 21.51/19.57 ( (product_prod real real) ) 21.51/19.57 ( (product_prod int int) ) 21.51/19.57 ( (filter real) ) 21.51/19.57 ( (filter nat) ) 21.51/19.57 ( (product_prod nat nat) ) 21.51/19.57 ( code_code_numeral ) 21.51/19.57 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 21.51/19.57 ( (fun nat rat) ) 21.51/19.57 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 21.51/19.57 ) 21.51/19.57 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP (fun X_a _let_0) _let_0 (accp X_a) R_1))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (R_1 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP X_a bool _let_1 B_1))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 R_1 A_2) B_1))) (hBOOL (hAPP X_a bool _let_1 A_2))) ))) 21.51/19.57 ( real, (zero_zero real), (ord_less_eq real), pi ) 21.51/19.57 ( 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)))) ) 21.51/19.57 ( 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)))) ) 21.51/19.57 ( real, (zero_zero real), (ord_less_eq real), skv_6 ) 21.51/19.57 ( real, (zero_zero real), (ord_less_eq real), skv_11 ) 21.51/19.57 ( real, (zero_zero real), (ord_less_eq real), skv_12 ) 21.51/19.57 ( real, (zero_zero real), (ord_less_eq real), skv_14 ) 21.51/19.57 ( real, (zero_zero real), (ord_less real), pi ) 21.51/19.57 ( 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)))) ) 21.51/19.57 ( 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)))) ) 21.51/19.57 ( real, (zero_zero real), (ord_less real), skv_2 ) 21.51/19.57 ( real, (zero_zero real), (ord_less real), skv_10 ) 21.51/19.57 ( real, (zero_zero real), (ord_less real), skv_13 ) 21.51/19.57 ( 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)))) ) 21.51/19.57 ( real, pi, (ord_less real), (zero_zero real) ) 21.51/19.57 ( 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)))) ) 21.51/19.57 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (ord_less_eq real), pi ) 21.51/19.57 ( real, (hAPP real real (hAPP 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))) ) 21.51/19.57 ( real, (hAPP real real (hAPP 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))) ) 21.51/19.57 ( 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) ) 21.51/19.57 ( 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) ) 21.51/19.57 ( 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) ) 21.51/19.57 ( 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 ) 21.51/19.57 ( real, skv_14, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.57 ( nat, (zero_zero nat), (ord_less nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.57 ( int, (zero_zero int), (ord_less_eq int), (one_one int) ) 21.51/19.57 ( int, (zero_zero int), (ord_less_eq int), min_1 ) 21.51/19.57 ( int, (zero_zero int), (ord_less_eq int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.57 ( int, (zero_zero int), (ord_less_eq int), s ) 21.51/19.57 ( int, (zero_zero int), (ord_less_eq int), (hAPP int int (number_number_of int) pls) ) 21.51/19.57 ( int, (zero_zero int), (ord_less_eq int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.51/19.57 ( int, (zero_zero int), (ord_less_eq int), skv_3 ) 21.51/19.57 ( int, (zero_zero int), (ord_less_eq int), skv_9 ) 21.51/19.57 ( int, (zero_zero int), (ord_less int), (zero_zero int) ) 21.51/19.57 ( int, (zero_zero int), (ord_less int), (one_one int) ) 21.51/19.57 ( 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))) ) 21.51/19.57 ( int, (zero_zero int), (ord_less int), min_1 ) 21.51/19.57 ( int, (one_one int), (ord_less_eq int), t ) 21.51/19.57 ( 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))), (dvd_dvd int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 21.51/19.57 ( 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))), quadRes, (hAPP int int (number_number_of int) min_1) ) 21.51/19.57 ( int, min_1, (ord_less_eq int), pls ) 21.51/19.57 ( int, min_1, (ord_less_eq int), min_1 ) 21.51/19.57 ( int, min_1, (ord_less int), (zero_zero int) ) 21.51/19.57 ( int, min_1, (ord_less int), min_1 ) 21.51/19.57 ( int, (hAPP int int (number_number_of int) min_1), (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.51/19.57 ( int, (hAPP int int (number_number_of int) min_1), (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.51/19.57 ( int, (hAPP int int (number_number_of int) min_1), (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (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))) ) 21.51/19.57 ( 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))) ) 21.51/19.57 ( 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))) ) 21.51/19.57 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (ord_less int), (zero_zero int) ) 21.51/19.57 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (ord_less 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))) (zero_zero int)))) ) 21.51/19.57 ( int, t, (ord_less int), (zero_zero int) ) 21.51/19.57 ( int, t, (ord_less int), (one_one int) ) 21.51/19.57 ( 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))) ) 21.51/19.57 ( 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))) ) 21.51/19.57 ( int, skv_3, (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))) ) 21.51/19.57 ( int, skv_3, (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))) ) 21.51/19.57 ( int, skv_9, (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))) ) 21.51/19.57 ( int, skv_9, (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))) ) 21.51/19.57 ) 21.51/19.57 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_165142 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (one_one X_a)) BOUND_VARIABLE_165142)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_165142))))) ) 21.51/19.57 ( int, t ) 21.51/19.57 ) 21.51/19.57 (instantiation (let ((_let_0 (member X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun X_a (fun (fun X_a bool) bool)) _let_0)) )) 21.51/19.57 ( nat ) 21.51/19.57 ( int ) 21.51/19.57 ) 21.51/19.57 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_165197 $$unsorted) (BOUND_VARIABLE_165198 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_165198))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_165197))) (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_165198) BOUND_VARIABLE_165197)))) )) 21.51/19.57 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 21.51/19.57 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.51/19.57 ( 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))) ) 21.51/19.57 ( 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)))) ) 21.51/19.57 ( 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)))) ) 21.51/19.57 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 21.51/19.57 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 21.51/19.57 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 21.51/19.57 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 21.51/19.57 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 21.51/19.57 ( 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) ) 21.51/19.57 ) 21.51/19.57 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_165239 $$unsorted) (BOUND_VARIABLE_165240 $$unsorted)) (or (not (ab_group_add X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_165240) BOUND_VARIABLE_165239) (hAPP X_a X_a (uminus_uminus X_a) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_165239) BOUND_VARIABLE_165240)))) ))) 21.51/19.57 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP 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))))))))))) ) 21.51/19.58 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 21.51/19.58 ( int, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.58 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 21.51/19.58 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 21.51/19.58 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 21.51/19.58 ) 21.51/19.58 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_165322))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_165321 $$unsorted) (BOUND_VARIABLE_165322 $$unsorted) (BOUND_VARIABLE_165323 $$unsorted)) (or (not (comm_semiring_1 X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_165323))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_165321))) (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_165323) BOUND_VARIABLE_165321)))) )) 21.51/19.58 ( 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)))) ) 21.51/19.58 ) 21.51/19.58 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) (one_one real)))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) (hAPP real real arccos Y)))) ))) 21.51/19.58 ( (zero_zero real) ) 21.51/19.58 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.58 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.58 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.58 ( skv_14 ) 21.51/19.58 ) 21.51/19.58 (instantiation (let ((_let_0 (zero_zero real))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (and (= _let_0 A_2) (= _let_0 B_1)) (= (zero_zero complex) (hAPP real complex (hAPP real (fun real complex) complex_1 A_2) B_1))) )) 21.51/19.58 ( (zero_zero real), (zero_zero real) ) 21.51/19.58 ( (zero_zero real), (one_one real) ) 21.51/19.58 ( (one_one real), (zero_zero real) ) 21.51/19.58 ) 21.51/19.58 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_165387))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_165387 $$unsorted) (BOUND_VARIABLE_165388 $$unsorted) (BOUND_VARIABLE_165389 $$unsorted)) (or (not (linordered_semiring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_165388)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_165389)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_165387))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_165388) BOUND_VARIABLE_165389))) )))) 21.51/19.58 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_1, (zero_zero int) ) 21.51/19.58 ) 21.51/19.58 (instantiation (let ((_let_0 (fun nat X_a))) (let ((_let_1 (zero_zero X_a))) (forall ((X_a $$unsorted)) (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)))) ))) 21.51/19.58 ( bool ) 21.51/19.58 ( real ) 21.51/19.58 ( nat ) 21.51/19.58 ( (fun nat bool) ) 21.51/19.58 ( (fun nat nat) ) 21.51/19.58 ( int ) 21.51/19.58 ( (fun real real) ) 21.51/19.58 ( complex ) 21.51/19.58 ( (fun int int) ) 21.51/19.58 ( rat ) 21.51/19.58 ( (fun bool bool) ) 21.51/19.58 ( quickcheck_code_int ) 21.51/19.58 ( (fun nat (fun nat bool)) ) 21.51/19.58 ( (product_prod real real) ) 21.51/19.58 ( (product_prod int int) ) 21.51/19.58 ( (fun nat (product_prod int int)) ) 21.51/19.58 ( (product_prod nat nat) ) 21.51/19.58 ( (fun (product_prod nat nat) bool) ) 21.51/19.58 ( (fun nat (fun (product_prod nat nat) bool)) ) 21.51/19.58 ( (fun nat (product_prod nat nat)) ) 21.51/19.58 ( code_code_numeral ) 21.51/19.58 ) 21.51/19.58 (instantiation (let ((_let_0 (even_odd_even nat))) (let ((_let_1 (uminus_uminus X_a))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (power_power X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_165437 $$unsorted) (BOUND_VARIABLE_165438 $$unsorted) (BOUND_VARIABLE_165449 $$unsorted) (BOUND_VARIABLE_165450 $$unsorted)) (or (not (comm_ring_1 X_a)) (and (or (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_165438)) (= (hAPP nat X_a (hAPP X_a _let_2 _let_3 (hAPP X_a X_a _let_1 BOUND_VARIABLE_165437)) BOUND_VARIABLE_165438) (hAPP X_a X_a _let_1 (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_165437) BOUND_VARIABLE_165438)))) (or (not (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_165450))) (= (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_165449) BOUND_VARIABLE_165450) (hAPP nat X_a (hAPP X_a _let_2 _let_3 (hAPP X_a X_a _let_1 BOUND_VARIABLE_165449)) BOUND_VARIABLE_165450))))) ))))) 21.51/19.58 ( int, (one_one int), (one_one nat), s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.58 ( complex, (one_one complex), (zero_zero nat), ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.58 ) 21.51/19.58 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_165475 $$unsorted) (BOUND_VARIABLE_165476 $$unsorted) (BOUND_VARIABLE_165477 $$unsorted)) (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_165477))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_165475) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_165476) BOUND_VARIABLE_165477))) (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_165475) BOUND_VARIABLE_165477)) BOUND_VARIABLE_165476)))) )))) 21.51/19.58 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 21.51/19.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_1 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_1 real (the real) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 _let_2 _let_0))) (hAPP _let_1 _let_1 (hAPP _let_6 _let_7 _let_8 (hAPP _let_1 _let_6 _let_9 (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 _let_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_1 (hAPP _let_5 _let_5 _let_10 (hAPP _let_3 _let_5 (hAPP _let_5 (fun _let_3 _let_5) (combb real _let_1 real) (fequal real)) cos)) _let_0))))))))))))))) ) 21.51/19.58 ( 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))), (zero_zero int), skv_1 ) 21.51/19.58 ( 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))), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))), skv_1 ) 21.51/19.58 ) 21.51/19.58 (instantiation (let ((_let_0 (fun int bool))) (forall ((U_1 $$unsorted)) (= (hAPP int nat nat_1 U_1) (hAPP _let_0 nat (finite_card int) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastLessThan int) (zero_zero int)) U_1))) )) 21.51/19.58 ( (zero_zero int) ) 21.51/19.58 ( (one_one int) ) 21.51/19.58 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.58 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.51/19.58 ) 21.51/19.58 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int (fun int _let_0) zcong C_1))) (let ((_let_2 (hAPP int (fun int int) (times_times int) D_1))) (forall ((C_1 $$unsorted) (D_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_2) B_1) Ma))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int _let_2 A_2)) Ma)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int _let_2 B_1)) Ma)))) )))) 21.51/19.58 ( (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)))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.51/19.58 ( s1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), s1, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.51/19.58 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.51/19.58 ) 21.51/19.58 (instantiation (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (power_power real))) (let ((_let_3 (one_one real))) (let ((_let_4 (combc nat nat nat))) (let ((_let_5 (fun nat _let_0))) (let ((_let_6 (fun _let_1 _let_1))) (let ((_let_7 (combs nat real real))) (let ((_let_8 (fun (fun nat nat) _let_1))) (let ((_let_9 (combb nat real nat))) (let ((_let_10 (hAPP (fun real _let_0) (fun _let_1 _let_5) (combb real _let_0 nat) (times_times real)))) (let ((_let_11 (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) _let_4 (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_4 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) X_1)) _let_3))) (hBOOL (hAPP _let_1 bool (summable real) (hAPP _let_1 _let_1 (hAPP _let_5 _let_6 _let_7 (hAPP _let_1 _let_5 _let_10 (hAPP real _let_1 _let_2 (hAPP int real (number_number_of real) min_1)))) (hAPP _let_1 _let_1 (hAPP _let_5 _let_6 _let_7 (hAPP _let_1 _let_5 _let_10 (hAPP _let_1 _let_1 (hAPP _let_0 _let_6 (combb real real nat) (hAPP real _let_0 (inverse_divide real) _let_3)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_8 _let_9 (real_1 nat)) _let_11)))) (hAPP _let_0 _let_1 (hAPP _let_1 _let_8 _let_9 (hAPP real _let_1 _let_2 X_1)) _let_11))))))) ))))))))))))) 21.51/19.58 ( (hAPP int real (number_number_of real) min_1) ) 21.51/19.58 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.58 ) 21.51/19.58 (instantiation (let ((_let_0 (sgn_sgn X_a))) (let ((_let_1 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_165555 $$unsorted)) (or (not (real_normed_vector X_a)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_165555)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_165555)))) ))) 21.51/19.58 ( real, (zero_zero real) ) 21.51/19.58 ( real, (one_one real) ) 21.51/19.58 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.58 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.51/19.58 ( int, pls ) 21.51/19.58 ( int, (one_one int) ) 21.51/19.58 ( int, min_1 ) 21.51/19.58 ( complex, ii ) 21.51/19.58 ( complex, (one_one complex) ) 21.51/19.58 ( rat, (zero_zero rat) ) 21.51/19.58 ) 21.51/19.58 (instantiation (let ((_let_0 (archimedean_ceiling X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_165595 $$unsorted) (BOUND_VARIABLE_165596 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_165595) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_165596))) (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP X_a int _let_0 BOUND_VARIABLE_165595)) (hAPP int int (number_number_of int) BOUND_VARIABLE_165596)))) )) 21.51/19.58 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), min_1 ) 21.51/19.58 ( code_code_numeral, (zero_zero code_code_numeral), (hAPP int int bit1 pls) ) 21.51/19.58 ) 21.51/19.58 (instantiation (let ((_let_0 (fun nat nat))) (forall ((N $$unsorted) (M $$unsorted)) (= M (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N) M)) N)) )) 21.51/19.58 ( (one_one nat), (one_one nat) ) 21.51/19.58 ) 21.51/19.58 (instantiation (let ((_let_0 (zero_zero nat))) (forall ((N $$unsorted)) (or (= _let_0 N) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) N))) )) 21.51/19.59 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.59 ) 21.51/19.59 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_165663))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_165663 $$unsorted) (BOUND_VARIABLE_165664 $$unsorted) (BOUND_VARIABLE_165665 $$unsorted)) (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_165664) BOUND_VARIABLE_165665))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_165664))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_165665))) )) 21.51/19.59 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.59 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.51/19.59 ( real, pi, (zero_zero real), pi ) 21.51/19.59 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.59 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real), skv_6 ) 21.51/19.59 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.51/19.59 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.51/19.59 ( int, (zero_zero int), (zero_zero int), s ) 21.51/19.59 ( int, min_1, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.51/19.59 ( int, s, (zero_zero int), min_1 ) 21.51/19.59 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 21.51/19.59 ( int, t, min_1, min_1 ) 21.51/19.59 ( int, skv_3, (zero_zero int), (one_one int) ) 21.51/19.59 ( int, skv_9, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.51/19.59 ) 21.51/19.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_165717 $$unsorted)) (or (not (monoid_mult X_a)) (= (ti X_a BOUND_VARIABLE_165717) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (one_one X_a)) BOUND_VARIABLE_165717))) ) 21.51/19.59 ( bool, fFalse ) 21.51/19.59 ( bool, fTrue ) 21.51/19.59 ( real, pi ) 21.51/19.59 ( (fun nat bool), (even_odd_even nat) ) 21.51/19.59 ( (fun nat bool), prime ) 21.51/19.59 ( (fun nat nat), suc ) 21.51/19.59 ( (fun nat nat), (fact_fact nat) ) 21.51/19.59 ( (fun nat nat), (size_size nat) ) 21.51/19.59 ( (fun nat nat), fact ) 21.51/19.59 ( (fun nat nat), nat_size ) 21.64/19.59 ( int, pls ) 21.64/19.59 ( int, m ) 21.64/19.59 ( int, min_1 ) 21.64/19.59 ( int, s ) 21.64/19.59 ( int, s1 ) 21.64/19.59 ( int, t ) 21.64/19.59 ( (fun int bool), zprime ) 21.64/19.59 ( (fun int bool), nat_neg ) 21.64/19.59 ( (fun int bool), zEven ) 21.64/19.59 ( (fun int bool), nat_is_nat ) 21.64/19.59 ( (fun int bool), zOdd ) 21.64/19.59 ( (fun int bool), (even_odd_even int) ) 21.64/19.59 ( (fun int bool), twoSqu1091635170sum2sq ) 21.64/19.59 ( (fun int nat), nat_1 ) 21.64/19.59 ( (fun int nat), phi ) 21.64/19.59 ( (fun real real), sqrt ) 21.64/19.59 ( (fun real real), tan ) 21.64/19.59 ( (fun real real), cos ) 21.64/19.59 ( (fun real real), arccos ) 21.64/19.59 ( (fun real real), ln ) 21.64/19.59 ( (fun real real), sin ) 21.64/19.59 ( (fun real real), arctan ) 21.64/19.59 ( (fun real real), arcsin ) 21.64/19.59 ( complex, ii ) 21.64/19.59 ( (fun complex complex), cnj ) 21.64/19.59 ( (fun complex complex), expi ) 21.64/19.59 ( (fun nat real), (real_1 nat) ) 21.64/19.59 ( (fun nat real), cos_coeff ) 21.64/19.59 ( (fun nat real), sin_coeff ) 21.64/19.59 ( (fun int int), bit0 ) 21.64/19.59 ( (fun int int), bit1 ) 21.64/19.59 ( (fun int int), pred ) 21.64/19.59 ( (fun int int), succ ) 21.64/19.59 ( (fun int int), (fact_fact int) ) 21.64/19.59 ( (fun int int), zfact ) 21.64/19.59 ( (fun bool bool), fNot ) 21.64/19.59 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.64/19.59 ( (fun bool (fun bool bool)), fconj ) 21.64/19.59 ( (fun bool (fun bool bool)), fdisj ) 21.64/19.59 ( (fun bool (fun bool bool)), fimplies ) 21.64/19.59 ( (fun int (fun int bool)), sRStar ) 21.64/19.59 ( (fun int (fun int bool)), quadRes ) 21.64/19.59 ( (fun int (fun int bool)), norRRset ) 21.64/19.59 ( (fun int (fun int bool)), d22set ) 21.64/19.59 ( (fun int (fun int bool)), sr ) 21.64/19.59 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.64/19.59 ( (fun nat (fun nat nat)), nat_gcd ) 21.64/19.59 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.64/19.59 ( (fun nat (fun nat nat)), nat_lcm ) 21.64/19.59 ( (fun nat (fun real real)), root ) 21.64/19.59 ( (fun real (fun real real)), log ) 21.64/19.59 ( (fun real (fun real real)), powr ) 21.64/19.59 ( (fun nat (fun nat bool)), coprime ) 21.64/19.59 ( (fun (fun int bool) int), (the int) ) 21.64/19.59 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.64/19.59 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.64/19.59 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.64/19.59 ( (fun (fun int bool) bool), nat_nat_set ) 21.64/19.59 ( (filter nat), sequentially ) 21.64/19.59 ( (fun (product_prod nat nat) bool), pred_nat ) 21.64/19.59 ( (fun (product_prod int int) bool), frac_1 ) 21.64/19.59 ( (fun real complex), cis ) 21.64/19.59 ( (fun complex real), im ) 21.64/19.59 ( (fun complex real), re ) 21.64/19.59 ( (fun complex real), arg ) 21.64/19.59 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.64/19.59 ( (fun int (fun int int)), int_gcd ) 21.64/19.59 ( (fun int (fun int int)), multInv ) 21.64/19.59 ( (fun int (fun int int)), legacy_zgcd ) 21.64/19.59 ( (fun int (fun int int)), z3mod ) 21.64/19.59 ( (fun int (fun int int)), inv ) 21.64/19.59 ( (fun int (fun int int)), (gcd_gcd int) ) 21.64/19.59 ( (fun int (fun int int)), standardRes ) 21.64/19.59 ( (fun int (fun int int)), legendre ) 21.64/19.59 ( (fun int (fun int int)), nat_tsub ) 21.64/19.59 ( (fun int (fun int int)), z3div ) 21.64/19.59 ( (fun int (fun int int)), int_lcm ) 21.64/19.59 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.64/19.59 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.64/19.59 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.64/19.59 ( (fun int (fun (fun int bool) bool)), resSet ) 21.64/19.59 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.64/19.59 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.64/19.59 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.64/19.59 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.64/19.59 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.64/19.59 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.64/19.59 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.64/19.59 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.64/19.59 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.64/19.59 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.64/19.59 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.64/19.59 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.64/19.59 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.64/19.59 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.64/19.59 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.64/19.59 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.64/19.59 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.64/19.59 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.64/19.59 ( (fun real nat), natfloor ) 21.64/19.59 ( (fun real nat), natceiling ) 21.64/19.59 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.64/19.59 ( (fun int (fun int (fun int bool))), wset ) 21.64/19.59 ( (fun int (fun int (fun int bool))), bnorRset ) 21.64/19.59 ( (fun int (fun int (fun int bool))), zcong ) 21.64/19.59 ( (fun int (fun int (fun int bool))), noXRRset ) 21.64/19.59 ( (fun int (fun int (fun int bool))), zcongm ) 21.64/19.59 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.64/19.59 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.64/19.59 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.64/19.59 ( (fun int real), (real_1 int) ) 21.64/19.59 ( (fun complex nat), (size_size complex) ) 21.64/19.59 ( (fun complex nat), complex_size ) 21.64/19.59 ( (fun int (list int)), quickc666637781d_zero ) 21.64/19.59 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.64/19.59 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.64/19.59 ( (fun (product_prod int int) rat), frct ) 21.64/19.59 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.64/19.59 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.64/19.59 ( (fun (fun nat rat) bool), vanishes ) 21.64/19.59 ( (fun int (fun int rat)), fract ) 21.64/19.59 ( (fun code_code_numeral int), code_int_of ) 21.64/19.59 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.64/19.59 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.64/19.59 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.64/19.59 ( (fun real (fun real complex)), complex_1 ) 21.64/19.59 ( (fun real (fun real complex)), rcis ) 21.64/19.59 ( (fun int (fun nat nat)), nat_aux ) 21.64/19.59 ( (fun rat real), ratreal ) 21.64/19.59 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.64/19.59 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.64/19.59 ( (fun rat (product_prod int int)), quotient_of ) 21.64/19.59 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.64/19.59 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.64/19.59 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.64/19.59 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.64/19.59 ) 21.64/19.59 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 X_1))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_2 Y_1))) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) Y_1))) (not (hBOOL (hAPP real bool _let_2 X_2))) (not (hBOOL (hAPP _let_0 bool (hAPP real (fun _let_0 bool) (member real) X_2) (field_char_0_Rats real))))) ))) )))) 21.64/19.59 ( (zero_zero real), pi ) 21.64/19.59 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.64/19.59 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.64/19.59 ( (zero_zero real), skv_2 ) 21.64/19.59 ( (zero_zero real), skv_10 ) 21.64/19.59 ( (zero_zero real), skv_13 ) 21.64/19.59 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.64/19.59 ( pi, (zero_zero real) ) 21.64/19.59 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.64/19.59 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.64/19.59 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 21.64/19.59 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.64/19.59 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 21.64/19.59 ) 21.64/19.59 (instantiation (forall ((V $$unsorted)) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V))) (= (hAPP int real (number_number_of real) V) (hAPP nat real (real_1 nat) (hAPP int nat (number_number_of nat) V)))) ) 21.64/19.59 ( pls ) 21.64/19.59 ( (hAPP int int bit1 pls) ) 21.64/19.59 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.64/19.59 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.64/19.59 ( min_1 ) 21.64/19.59 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.64/19.59 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.64/19.59 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.64/19.59 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 21.64/19.59 ) 21.64/19.59 (instantiation (forall ((V $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V)))) (= (zero_zero real) (hAPP nat real (real_1 nat) (hAPP int nat (number_number_of nat) V)))) ) 21.64/19.59 ( pls ) 21.64/19.59 ( (hAPP int int bit1 pls) ) 21.64/19.59 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.64/19.59 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.64/19.59 ( min_1 ) 21.64/19.59 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.64/19.59 ) 21.64/19.59 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_165807 $$unsorted)) (or (not (mult_zero X_a)) (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_165807) _let_0))) )) 21.64/19.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.64/19.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.64/19.59 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 21.64/19.59 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.64/19.59 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.64/19.59 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.64/19.59 ( complex, ii ) 21.64/19.59 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.64/19.59 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 21.64/19.59 ) 21.64/19.59 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP X_a _let_0 (ord_less_eq X_a) (zero_zero X_a)))) (let ((_let_2 (ord_less X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (times_times X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_165828 $$unsorted) (BOUND_VARIABLE_165829 $$unsorted) (BOUND_VARIABLE_165830 $$unsorted) (BOUND_VARIABLE_165831 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_165830) BOUND_VARIABLE_165831))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_165828) BOUND_VARIABLE_165829))) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_165830))) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_165828))) (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_165830) BOUND_VARIABLE_165828)) (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_165831) BOUND_VARIABLE_165829)))) )))))) 21.64/19.59 ( int, skv_1, (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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.64/19.59 ) 21.64/19.59 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (fun (filter nat) bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_165923 $$unsorted) (BOUND_VARIABLE_165924 $$unsorted) (BOUND_VARIABLE_165925 $$unsorted)) (or (not (real_normed_vector X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_2 (hAPP (fun nat X_a) (fun X_a _let_2) (tendsto nat X_a) BOUND_VARIABLE_165924) BOUND_VARIABLE_165925) sequentially))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) BOUND_VARIABLE_165923))) (not (forall ((No $$unsorted)) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_2))) (hBOOL (hAPP real bool (hAPP real _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) (hAPP nat X_a BOUND_VARIABLE_165924 N_2)) BOUND_VARIABLE_165925))) BOUND_VARIABLE_165923))) )) ))) )))) 21.64/19.59 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 21.64/19.59 ) 21.64/19.59 (instantiation (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (let ((_let_1 (hAPP real (fun real bool) (ord_less real) E))) (forall ((D2 $$unsorted) (D1 $$unsorted)) (or (not (hBOOL (hAPP real bool _let_0 D1))) (not (hBOOL (hAPP real bool _let_0 D2))) (not (forall ((E $$unsorted)) (or (not (hBOOL (hAPP real bool _let_0 E))) (not (hBOOL (hAPP real bool _let_1 D1))) (not (hBOOL (hAPP real bool _let_1 D2)))) ))) ))) 21.64/19.60 ( pi, pi ) 21.64/19.60 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.64/19.60 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.64/19.60 ( skv_2, skv_2 ) 21.64/19.60 ( skv_10, skv_10 ) 21.64/19.60 ( skv_13, skv_13 ) 21.64/19.60 ) 21.64/19.60 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_165976 $$unsorted) (BOUND_VARIABLE_165977 $$unsorted)) (or (not (group_add X_a)) (= (ti X_a BOUND_VARIABLE_165977) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_165976)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_165976) BOUND_VARIABLE_165977)))) ))) 21.64/19.60 ( nat, (one_one nat), (one_one nat) ) 21.64/19.60 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 21.64/19.60 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 21.64/19.60 ) 21.64/19.60 (instantiation (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (uminus_uminus X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_166019 $$unsorted) (BOUND_VARIABLE_166020 $$unsorted)) (or (not (group_add X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_166019) BOUND_VARIABLE_166020)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_166020)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_166019)))) )))) 21.64/19.60 ( nat, (one_one nat), (one_one nat) ) 21.64/19.60 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 21.64/19.60 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 21.64/19.60 ) 21.64/19.60 (instantiation (let ((_let_0 (monoseq X_a))) (forall ((X_a $$unsorted)) (or (not (order X_a)) (= _let_0 (ti (fun (fun nat X_a) bool) _let_0))) )) 21.64/19.60 ( bool ) 21.64/19.60 ( real ) 21.64/19.60 ( nat ) 21.64/19.60 ( (fun nat bool) ) 21.64/19.60 ( (fun nat nat) ) 21.64/19.60 ( int ) 21.64/19.60 ( (fun real real) ) 21.64/19.60 ( complex ) 21.64/19.60 ( (fun int int) ) 21.64/19.60 ( rat ) 21.64/19.60 ( (fun bool bool) ) 21.64/19.60 ( quickcheck_code_int ) 21.64/19.60 ( (fun nat (fun nat bool)) ) 21.64/19.60 ( (product_prod real real) ) 21.64/19.60 ( (product_prod int int) ) 21.64/19.60 ( (fun nat (product_prod int int)) ) 21.64/19.60 ( (product_prod nat nat) ) 21.64/19.60 ( (fun (product_prod nat nat) bool) ) 21.64/19.60 ( (fun nat (fun (product_prod nat nat) bool)) ) 21.64/19.60 ( (fun nat (product_prod nat nat)) ) 21.64/19.60 ( code_code_numeral ) 21.64/19.60 ) 21.64/19.60 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (uminus_uminus 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 (fun _let_2 bool))) (let ((_let_6 (hAPP (fun _let_2 _let_5) _let_5 (accp _let_2) norm_frac_rel))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (or (not (hBOOL (hAPP _let_2 bool _let_6 (hAPP int _let_2 (hAPP int _let_3 _let_4 A0) A1)))) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (or (not (hBOOL (hAPP _let_2 bool _let_6 (hAPP int _let_2 (hAPP int _let_3 _let_4 A_4) B_4)))) (and (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) B_4) (zero_zero int))) (not (hBOOL (hAPP int bool (hAPP int _let_0 P_1 (hAPP int int _let_1 A_4)) (hAPP int int _let_1 B_4))))) (hBOOL (hAPP int bool (hAPP int _let_0 P_1 A_4) B_4))) )) (hBOOL (hAPP int bool (hAPP int _let_0 P_1 A0) A1))) )))))))) 21.64/19.60 ( (ord_less_eq int), (zero_zero int), (one_one int) ) 21.64/19.60 ( (ord_less_eq int), (zero_zero int), min_1 ) 21.64/19.60 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.64/19.60 ( (ord_less_eq int), (zero_zero int), s ) 21.64/19.60 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 21.64/19.60 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.64/19.60 ( (ord_less_eq int), (zero_zero int), skv_3 ) 21.64/19.60 ( (ord_less_eq int), (zero_zero int), skv_9 ) 21.64/19.60 ( (ord_less_eq int), (one_one int), t ) 21.64/19.60 ( (ord_less_eq int), min_1, pls ) 21.64/19.60 ( (ord_less_eq int), min_1, min_1 ) 21.64/19.60 ( (ord_less int), (zero_zero int), (zero_zero int) ) 21.64/19.60 ( (ord_less int), (zero_zero int), (one_one int) ) 21.64/19.60 ( (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))) ) 21.64/19.60 ( (ord_less int), (zero_zero int), min_1 ) 21.64/19.60 ( (ord_less int), min_1, (zero_zero int) ) 21.64/19.60 ( (ord_less int), min_1, min_1 ) 21.64/19.60 ( (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))) ) 21.64/19.60 ( (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (zero_zero int) ) 21.64/19.60 ( (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (let ((_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))) (zero_zero int)))) ) 21.64/19.60 ( (ord_less int), t, (zero_zero int) ) 21.64/19.60 ( (ord_less int), t, (one_one int) ) 21.64/19.60 ( (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))) ) 21.64/19.60 ( (ord_less int), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.64/19.60 ( (ord_less int), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.64/19.60 ( (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 21.64/19.60 ( quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 21.64/19.60 ( (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))) ) 21.64/19.60 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_3, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.64/19.60 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_9, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.64/19.60 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.64/19.60 ( (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))) ) 21.64/19.60 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.64/19.60 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_8) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.64/19.60 ) 21.64/19.60 (instantiation (let ((_let_0 (hAPP nat (fun real real) root N_1))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (= (hAPP real real _let_0 Y_1) (hAPP real real _let_0 X_1)) (= X_1 Y_1))) )) 21.64/19.60 ( (zero_zero real), (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.64/19.60 ( (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))) ) 21.64/19.60 ( (hAPP int 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))) ) 21.64/19.60 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.64/19.60 ( (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))) ) 21.64/19.60 ( (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 int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.64/19.60 ) 21.64/19.60 (instantiation (let ((_let_0 (fun int bool))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_1) zEven))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) X_1))) (= (one_one int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (number_number_of int) min_1)) (hAPP int nat nat_1 X_1)))) )) 21.64/19.60 ( (zero_zero int) ) 21.64/19.60 ( (one_one int) ) 21.64/19.60 ( min_1 ) 21.64/19.60 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.64/19.60 ( s ) 21.64/19.60 ( (hAPP int int (number_number_of int) pls) ) 21.64/19.60 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.64/19.60 ( skv_3 ) 21.64/19.60 ( skv_9 ) 21.64/19.60 ) 21.64/19.60 (instantiation (let ((_let_0 (fun nat bool))) (forall ((S $$unsorted)) (= (forall ((M_2 $$unsorted)) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M_2) N_2))) (not (hBOOL (hAPP _let_0 bool (hAPP nat (fun _let_0 bool) (member nat) N_2) S)))) )) ) (not (hBOOL (hAPP _let_0 bool (finite_finite_1 nat) S)))) )) 21.64/19.60 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 21.64/19.60 ) 21.64/19.60 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (forall ((I $$unsorted) (P_1 $$unsorted) (P_4 $$unsorted)) (or (not (forall ((I_2 $$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))) (hBOOL (hAPP nat bool P_1 (zero_zero nat)))) ))) 21.64/19.60 ( (zero_zero nat), (even_odd_even nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.64/19.60 ) 21.64/19.60 (instantiation (let ((_let_0 (zero_zero nat))) (forall ((N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) N))) (= N (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N) (hAPP nat nat suc _let_0))))) )) 21.64/19.60 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.64/19.60 ) 21.64/19.60 (instantiation (let ((_let_0 (fun int rat))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (product_Pair int int))) (forall ((A_1 $$unsorted) (B $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (or (not (= (hAPP _let_1 _let_1 normalize (hAPP int _let_1 (hAPP int _let_2 _let_3 A_1) B)) (hAPP int _let_1 (hAPP int _let_2 _let_3 P_5) Q_3))) (= (hAPP int rat (hAPP int _let_0 fract A_1) B) (hAPP int rat (hAPP int _let_0 fract P_5) Q_3))) ))))) 21.64/19.60 ( (zero_zero int), (one_one int), (zero_zero int), (one_one int) ) 21.64/19.60 ( (zero_zero int), (one_one int), (one_one int), (one_one int) ) 21.64/19.60 ( (one_one int), (one_one int), (zero_zero int), (one_one int) ) 21.64/19.60 ( s, (one_one int), s, (one_one int) ) 21.64/19.60 ) 21.64/19.60 (instantiation (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (minus_minus real))) (let ((_let_4 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_5 (one_one real))) (let ((_let_6 (hAPP int real (number_number_of real) _let_4))) (forall ((X $$unsorted)) (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) (hAPP real real (hAPP real _let_2 (inverse_divide real) _let_5) _let_6)))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_2 _let_3 (hAPP real real (uminus_uminus real) X)) (hAPP real real (hAPP real _let_2 (times_times real) _let_6) (hAPP nat real (hAPP real (fun nat real) (power_power real) X) (hAPP int nat (number_number_of nat) _let_4))))) (hAPP real real ln (hAPP real real (hAPP real _let_2 _let_3 _let_5) X))))) )))))))) 21.64/19.61 ( (one_one real) ) 21.64/19.61 ( pi ) 21.64/19.61 ( (hAPP int real (number_number_of real) min_1) ) 21.64/19.61 ( (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)))) ) 21.64/19.61 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.64/19.61 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.64/19.61 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.64/19.61 ( skv_6 ) 21.64/19.61 ( skv_11 ) 21.64/19.61 ( skv_12 ) 21.64/19.61 ( skv_14 ) 21.64/19.61 ) 21.64/19.61 (instantiation (let ((_let_0 (inverse_inverse X_a))) (let ((_let_1 (ti X_a BOUND_VARIABLE_166280))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_166280 $$unsorted)) (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_166280)))) ))) 21.64/19.61 ( bool, fFalse ) 21.64/19.61 ( bool, fTrue ) 21.64/19.61 ( real, (zero_zero real) ) 21.64/19.61 ( real, pi ) 21.64/19.61 ( (fun nat bool), (even_odd_even nat) ) 21.64/19.61 ( (fun nat bool), prime ) 21.64/19.61 ( (fun nat nat), suc ) 21.64/19.61 ( (fun nat nat), (fact_fact nat) ) 21.64/19.61 ( (fun nat nat), (size_size nat) ) 21.64/19.61 ( (fun nat nat), fact ) 21.64/19.61 ( (fun nat nat), nat_size ) 21.64/19.61 ( int, pls ) 21.64/19.61 ( int, m ) 21.64/19.61 ( int, min_1 ) 21.64/19.61 ( int, s ) 21.64/19.61 ( int, s1 ) 21.64/19.61 ( int, t ) 21.64/19.61 ( (fun int bool), zprime ) 21.64/19.61 ( (fun int bool), nat_neg ) 21.64/19.61 ( (fun int bool), zEven ) 21.64/19.61 ( (fun int bool), nat_is_nat ) 21.64/19.61 ( (fun int bool), zOdd ) 21.64/19.61 ( (fun int bool), (even_odd_even int) ) 21.64/19.61 ( (fun int bool), twoSqu1091635170sum2sq ) 21.64/19.61 ( (fun int nat), nat_1 ) 21.64/19.61 ( (fun int nat), phi ) 21.64/19.61 ( (fun real real), sqrt ) 21.64/19.61 ( (fun real real), tan ) 21.64/19.61 ( (fun real real), cos ) 21.64/19.61 ( (fun real real), arccos ) 21.64/19.61 ( (fun real real), ln ) 21.64/19.61 ( (fun real real), sin ) 21.64/19.61 ( (fun real real), arctan ) 21.64/19.61 ( (fun real real), arcsin ) 21.64/19.61 ( complex, ii ) 21.64/19.61 ( (fun complex complex), cnj ) 21.64/19.61 ( (fun complex complex), expi ) 21.64/19.61 ( (fun nat real), (real_1 nat) ) 21.64/19.61 ( (fun nat real), cos_coeff ) 21.64/19.61 ( (fun nat real), sin_coeff ) 21.64/19.61 ( (fun int int), bit0 ) 21.64/19.61 ( (fun int int), bit1 ) 21.64/19.61 ( (fun int int), pred ) 21.64/19.61 ( (fun int int), succ ) 21.64/19.61 ( (fun int int), (fact_fact int) ) 21.64/19.61 ( (fun int int), zfact ) 21.64/19.61 ( (fun bool bool), fNot ) 21.64/19.61 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.64/19.61 ( (fun bool (fun bool bool)), fconj ) 21.64/19.61 ( (fun bool (fun bool bool)), fdisj ) 21.64/19.61 ( (fun bool (fun bool bool)), fimplies ) 21.64/19.61 ( (fun int (fun int bool)), sRStar ) 21.64/19.61 ( (fun int (fun int bool)), quadRes ) 21.64/19.61 ( (fun int (fun int bool)), norRRset ) 21.64/19.61 ( (fun int (fun int bool)), d22set ) 21.64/19.61 ( (fun int (fun int bool)), sr ) 21.64/19.61 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.64/19.61 ( (fun nat (fun nat nat)), nat_gcd ) 21.64/19.61 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.64/19.61 ( (fun nat (fun nat nat)), nat_lcm ) 21.64/19.61 ( (fun nat (fun real real)), root ) 21.64/19.61 ( (fun real (fun real real)), log ) 21.64/19.61 ( (fun real (fun real real)), powr ) 21.64/19.61 ( (fun nat (fun nat bool)), coprime ) 21.64/19.61 ( (fun (fun int bool) int), (the int) ) 21.64/19.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.64/19.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.64/19.61 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.64/19.61 ( (fun (fun int bool) bool), nat_nat_set ) 21.64/19.61 ( (filter nat), sequentially ) 21.64/19.61 ( (fun (product_prod nat nat) bool), pred_nat ) 21.64/19.61 ( (fun (product_prod int int) bool), frac_1 ) 21.64/19.61 ( (fun real complex), cis ) 21.64/19.61 ( (fun complex real), im ) 21.64/19.61 ( (fun complex real), re ) 21.64/19.61 ( (fun complex real), arg ) 21.64/19.61 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.64/19.61 ( (fun int (fun int int)), int_gcd ) 21.64/19.61 ( (fun int (fun int int)), multInv ) 21.64/19.61 ( (fun int (fun int int)), legacy_zgcd ) 21.64/19.61 ( (fun int (fun int int)), z3mod ) 21.64/19.61 ( (fun int (fun int int)), inv ) 21.64/19.61 ( (fun int (fun int int)), (gcd_gcd int) ) 21.64/19.61 ( (fun int (fun int int)), standardRes ) 21.64/19.61 ( (fun int (fun int int)), legendre ) 21.64/19.61 ( (fun int (fun int int)), nat_tsub ) 21.64/19.61 ( (fun int (fun int int)), z3div ) 21.64/19.61 ( (fun int (fun int int)), int_lcm ) 21.64/19.61 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.64/19.61 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.64/19.61 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.64/19.61 ( (fun int (fun (fun int bool) bool)), resSet ) 21.64/19.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.64/19.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.64/19.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.64/19.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.64/19.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.64/19.61 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.64/19.61 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.64/19.61 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.64/19.61 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.64/19.61 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.64/19.61 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.64/19.61 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.64/19.61 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.64/19.61 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.64/19.61 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.64/19.61 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.64/19.61 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.64/19.61 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.64/19.61 ( (fun real nat), natfloor ) 21.64/19.61 ( (fun real nat), natceiling ) 21.64/19.61 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.64/19.61 ( (fun int (fun int (fun int bool))), wset ) 21.64/19.61 ( (fun int (fun int (fun int bool))), bnorRset ) 21.64/19.61 ( (fun int (fun int (fun int bool))), zcong ) 21.64/19.61 ( (fun int (fun int (fun int bool))), noXRRset ) 21.64/19.61 ( (fun int (fun int (fun int bool))), zcongm ) 21.64/19.61 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.64/19.61 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.64/19.61 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.64/19.61 ( (fun int real), (real_1 int) ) 21.64/19.61 ( (fun complex nat), (size_size complex) ) 21.64/19.61 ( (fun complex nat), complex_size ) 21.64/19.61 ( (fun int (list int)), quickc666637781d_zero ) 21.64/19.61 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.64/19.61 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.64/19.61 ( (fun (product_prod int int) rat), frct ) 21.64/19.61 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.64/19.61 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.64/19.61 ( (fun (fun nat rat) bool), vanishes ) 21.64/19.61 ( (fun int (fun int rat)), fract ) 21.64/19.61 ( (fun code_code_numeral int), code_int_of ) 21.64/19.61 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.64/19.61 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.64/19.61 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.64/19.61 ( (fun real (fun real complex)), complex_1 ) 21.64/19.61 ( (fun real (fun real complex)), rcis ) 21.64/19.61 ( (fun int (fun nat nat)), nat_aux ) 21.64/19.61 ( (fun rat real), ratreal ) 21.64/19.61 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.64/19.61 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.64/19.61 ( (fun rat (product_prod int int)), quotient_of ) 21.64/19.61 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.64/19.61 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.64/19.61 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.64/19.61 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.64/19.61 ) 21.64/19.61 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_166332 $$unsorted)) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_166332))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_166332)))) )) 21.64/19.61 ( real, (zero_zero real) ) 21.64/19.61 ( complex, ii ) 21.64/19.61 ) 21.64/19.61 (instantiation (forall ((X_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real im X_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_2)) skv_2))) ) 21.64/19.61 ( ii ) 21.64/19.61 ( (zero_zero complex) ) 21.64/19.61 ( (one_one complex) ) 21.64/19.61 ) 21.64/19.61 (instantiation (forall ((X_2 $$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_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_2)) skv_4))) ) 21.64/19.61 ( ii ) 21.64/19.61 ( (zero_zero complex) ) 21.64/19.61 ( (one_one complex) ) 21.64/19.61 ) 21.64/19.61 (instantiation (let ((_let_0 (norm_norm complex))) (forall ((X_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP complex real _let_0 (hAPP complex complex cnj X_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_0 X_2)) skv_5))) )) 21.64/19.61 ( ii ) 21.64/19.61 ( (zero_zero complex) ) 21.64/19.61 ( (one_one complex) ) 21.64/19.61 ) 21.64/19.61 (instantiation (let ((_let_0 (norm_norm complex))) (forall ((X_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP complex real _let_0 (hAPP complex complex cnj X_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_0 X_2)) skv_6))) )) 21.64/19.61 ( ii ) 21.64/19.61 ( (zero_zero complex) ) 21.64/19.61 ( (one_one complex) ) 21.64/19.61 ) 21.64/19.61 (instantiation (forall ((X_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real re X_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_2)) skv_7))) ) 21.64/19.61 ( ii ) 21.64/19.61 ( (zero_zero complex) ) 21.64/19.61 ( (one_one complex) ) 21.64/19.61 ) 21.64/19.61 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) (forall ((Y_2 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) Y_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) Y_2) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) Y_2) _let_2))) (= (ti int Y_2) (ti int skv_9))) )))) 21.64/19.61 ( (zero_zero int) ) 21.64/19.61 ( pls ) 21.64/19.61 ( m ) 21.64/19.61 ( (one_one int) ) 21.64/19.61 ( min_1 ) 21.64/19.61 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.64/19.61 ( s ) 21.64/19.61 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 21.64/19.61 ( (hAPP int int (number_number_of int) pls) ) 21.64/19.61 ( s1 ) 21.64/19.61 ( t ) 21.64/19.61 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.64/19.61 ( skv_3 ) 21.64/19.61 ( skv_9 ) 21.64/19.61 ) 21.64/19.61 (instantiation (forall ((X_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real re X_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_2)) skv_10))) ) 21.64/19.61 ( ii ) 21.64/19.61 ( (zero_zero complex) ) 21.64/19.61 ( (one_one complex) ) 21.64/19.61 ) 21.64/19.61 (instantiation (forall ((X_2 $$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_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_2)) skv_11))) ) 21.64/19.61 ( ii ) 21.64/19.61 ( (zero_zero complex) ) 21.64/19.61 ( (one_one complex) ) 21.64/19.61 ) 21.64/19.61 (instantiation (forall ((X_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real im X_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_2)) skv_12))) ) 21.64/19.61 ( ii ) 21.64/19.61 ( (zero_zero complex) ) 21.64/19.61 ( (one_one complex) ) 21.64/19.61 ) 21.64/19.61 (instantiation (let ((_let_0 (norm_norm complex))) (forall ((X_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP complex real _let_0 (hAPP complex complex cnj X_2))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_0 X_2)) skv_13))) )) 21.64/19.61 ( ii ) 21.64/19.61 ( (zero_zero complex) ) 21.64/19.61 ( (one_one complex) ) 21.64/19.61 ) 21.64/19.61 (instantiation (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (forall ((Y_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 _let_0) Y_2))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Y_2) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (not (= _let_0 (hAPP real real cos Y_2))) (= Y_2 skv_14)) )))) 21.64/19.61 ( (zero_zero real) ) 21.64/19.61 ( pi ) 21.64/19.61 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.64/19.61 ( (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)))) ) 21.64/19.61 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.64/19.61 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.64/19.61 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 21.64/19.61 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.64/19.61 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.64/19.61 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.64/19.61 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.64/19.61 ( skv_6 ) 21.64/19.61 ( skv_11 ) 21.64/19.61 ( skv_12 ) 21.64/19.61 ( skv_14 ) 21.64/19.61 ) 21.64/19.61 % SZS output end Proof for theBenchmark 21.64/19.65 EOF