0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.14 % Command : do_CVC4 %s %d 0.14/0.35 % Computer : n008.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 960 0.14/0.35 % WCLimit : 120 0.14/0.35 % DateTime : Thu Jul 2 07:58:29 EDT 2020 0.14/0.35 % CPUTime : 0.21/0.58 %----Proving TF0_NAR, FOF, or CNF 0.21/0.59 ------- cvc4-fof casc j10 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 960... 0.21/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20... 1.14/1.32 % SZS status Theorem for theBenchmark 1.14/1.33 % SZS output start Proof for theBenchmark 1.14/1.33 (skolem (forall ((X $$unsorted)) (let ((_let_0 (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))))) (let ((_let_1 (plus_plus_int (hAPP_int_int _let_0 m)))) (let ((_let_2 (hAPP_int_int _let_1 one_one_int))) (or (not (is_int X)) (not (forall ((Y $$unsorted)) (or (not (is_int Y)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Y))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Y) _let_2))) (not (hBOOL (hAPP_int_bool (zcong s1 Y) _let_2))) (= X Y)) )) (not (hBOOL (hAPP_int_bool (zcong s1 X) _let_2))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X) _let_2))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X))))))) ) 1.14/1.33 ( skv_1 ) 1.14/1.33 ) 1.14/1.33 (skolem (forall ((S_1 $$unsorted)) (let ((_let_0 (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))))) (let ((_let_1 (plus_plus_int (hAPP_int_int _let_0 m)))) (let ((_let_2 (hAPP_int_int _let_1 one_one_int))) (or (not (is_int S_1)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int S_1) _let_2))) (not (hBOOL (hAPP_int_bool (zcong s1 S_1) _let_2))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) S_1))))))) ) 1.14/1.33 ( skv_2 ) 1.14/1.33 ) 1.14/1.33 (skolem (forall ((T_1 $$unsorted)) (let ((_let_0 (bit0 (bit1 pls)))) (or (not (is_int T_1)) (not (= (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int s) (number_number_of_nat _let_0))) one_one_int) (hAPP_int_int (times_times_int (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 _let_0))) m)) one_one_int)) T_1))))) ) 1.14/1.33 ( skv_3 ) 1.14/1.33 ) 1.14/1.33 (skolem (forall ((S1 $$unsorted)) (let ((_let_0 (bit0 (bit1 pls)))) (or (not (is_int S1)) (not (hBOOL (hAPP_int_bool (zcong (hAPP_nat_int (power_power_int S1) (number_number_of_nat _let_0)) (number_number_of_int min)) (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 _let_0))) m)) one_one_int)))))) ) 1.14/1.33 ( skv_4 ) 1.14/1.33 ) 1.14/1.33 (skolem (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (or (not (is_int X)) (not (= (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int X) _let_0)) (hAPP_nat_int (power_power_int Y) _let_0)))) (not (is_int Y)))) ) 1.14/1.33 ( skv_5 skv_6 ) 1.14/1.33 ) 1.14/1.33 (skolem (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (or (not (= (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int X) _let_0)) (hAPP_nat_int (power_power_int Y) _let_0)))) (not (is_int Y)) (not (is_int X)))) ) 1.14/1.33 ( skv_7 skv_8 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K) min)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (bit1 K)) min))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (number_number_of_int X_2)) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_2) pls))) ) 1.14/1.33 ( min ) 1.14/1.33 ( zero_zero_int ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ( (bit0 (bit0 (bit1 pls))) ) 1.14/1.33 ( (bit1 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_12 $$unsorted) (Y_9 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real (plus_plus_real (hAPP_nat_real (power_power_real X_12) _let_0)) (hAPP_nat_real (power_power_real Y_9) _let_0))))) ) 1.14/1.33 ( one_one_real, one_one_real ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K) pls)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (bit1 K)) pls))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (= (hBOOL (hAPP_nat_bool _let_0 (hAPP_nat_nat (power_power_nat X_2) N))) (or (hBOOL (hAPP_nat_bool _let_0 X_2)) (= zero_zero_nat N)))) ) 1.14/1.33 ( zero_zero_nat, zero_zero_nat ) 1.14/1.33 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ( one_one_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP_n1699378549t_bool dvd_dvd_nat K))) (= (hBOOL (hAPP_nat_bool _let_0 N)) (hBOOL (hAPP_nat_bool _let_0 (hAPP_nat_nat (plus_plus_nat N) K))))) ) 1.14/1.33 ( one_one_nat, one_one_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_1) (hAPP_nat_int (power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls)))))) ) 1.14/1.33 ( min ) 1.14/1.33 ( zero_zero_int ) 1.14/1.33 ( pls ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( s1 ) 1.14/1.33 ( s ) 1.14/1.33 ( skv_4 ) 1.14/1.33 ( skv_5 ) 1.14/1.33 ( skv_6 ) 1.14/1.33 ( skv_7 ) 1.14/1.33 ( skv_8 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (= M (hAPP_nat_nat (minus_minus_nat (hAPP_nat_nat (plus_plus_nat N_1) M)) N_1)) ) 1.14/1.33 ( one_one_nat, one_one_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_2) (bit1 pls))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (number267125858f_real X_2)) one_one_real))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( t ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ( s ) 1.14/1.33 ( skv_1 ) 1.14/1.33 ( skv_2 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_94 $$unsorted)) (= A_94 (hAPP_real_real (plus_plus_real A_94) (number267125858f_real pls))) ) 1.14/1.33 ( one_one_real ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (bit1 K1)) (bit1 K2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K1) K2))) ) 1.14/1.33 ( min, min ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_2 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int Ma) (hAPP_int_int (minus_minus_int A_2) B_2))) (hBOOL (hAPP_int_bool (zcong A_2 B_2) Ma))) ) 1.14/1.33 ( s1, s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( s1, skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( s1, skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int skv_4) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted) (L_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K) L_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (number_number_of_int K)) (number_number_of_int L_1)))) ) 1.14/1.33 ( pls, pls ) 1.14/1.33 ( pls, (bit1 pls) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((J_1 $$unsorted) (I_1 $$unsorted)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (plus_plus_nat J_1) I_1)) I_1))) ) 1.14/1.33 ( one_one_nat, one_one_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_68 $$unsorted)) (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real (power_power_real A_68) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real))) ) 1.14/1.33 ( one_one_real ) 1.14/1.33 ( zero_zero_real ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (= (not (= Ma N)) (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) Ma)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N)))) ) 1.14/1.33 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted) (L_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K) L_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (number_number_of_int K)) (number_number_of_int L_1)))) ) 1.14/1.33 ( pls, pls ) 1.14/1.33 ( pls, (bit1 pls) ) 1.14/1.33 ( pls, (bit0 (bit1 pls)) ) 1.14/1.33 ( pls, (bit1 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (bit0 K1)) (bit0 K2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K1) K2))) ) 1.14/1.33 ( pls, pls ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((L $$unsorted)) (not (= pls (bit1 L))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int min) (bit0 K))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int min) K))) ) 1.14/1.33 ( min ) 1.14/1.33 ( zero_zero_int ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_2 $$unsorted)) (= (not (= zero_zero_real A_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_nat_real (power_power_real A_2) (number_number_of_nat (bit0 (bit1 pls))))))) ) 1.14/1.33 ( one_one_real ) 1.14/1.33 ( zero_zero_real ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int one_one_int) (number_number_of_int Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (bit1 pls)) Y_2))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ( (bit0 (bit0 (bit1 pls))) ) 1.14/1.33 ( (bit1 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (bit1 pls)) Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) (number267125858f_real Y_2)))) ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted) (L_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (bit1 K)) (bit0 L_1))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K) L_1))) ) 1.14/1.33 ( min, min ) 1.14/1.33 ( min, zero_zero_int ) 1.14/1.33 ( min, pls ) 1.14/1.33 ( pls, min ) 1.14/1.33 ( pls, zero_zero_int ) 1.14/1.33 ( pls, one_one_int ) 1.14/1.33 ( pls, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( one_one_int, t ) 1.14/1.33 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_57 $$unsorted)) (= one_one_int (hAPP_nat_int (power_power_int A_57) zero_zero_nat)) ) 1.14/1.33 ( zero_zero_int ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( s1 ) 1.14/1.33 ( s ) 1.14/1.33 ( skv_4 ) 1.14/1.33 ( skv_5 ) 1.14/1.33 ( skv_6 ) 1.14/1.33 ( skv_7 ) 1.14/1.33 ( skv_8 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (bit1 K1)) (bit0 K2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K1) K2))) ) 1.14/1.33 ( min, pls ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((N $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (not (= zero_zero_nat N))) ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((I_1 $$unsorted) (J_1 $$unsorted)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (plus_plus_nat I_1) J_1)) I_1))) ) 1.14/1.33 ( one_one_nat, one_one_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K) pls)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (bit1 K)) pls))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( t ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( s ) 1.14/1.33 ( skv_1 ) 1.14/1.33 ( skv_2 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((V_7 $$unsorted) (W_1 $$unsorted)) (let ((_let_0 (number_number_of_nat V_7))) (let ((_let_1 (number_number_of_nat W_1))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat _let_0) _let_1)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat _let_1) _let_0)))))) ) 1.14/1.33 ( (bit0 (bit1 pls)), pls ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Z_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Z_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int one_one_int) Z_1))) ) 1.14/1.33 ( min ) 1.14/1.33 ( zero_zero_int ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( t ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) (number_number_of_int Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (bit1 pls)) Y_2))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ( (bit0 (bit0 (bit1 pls))) ) 1.14/1.33 ( (bit1 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (= (hBOOL (hAPP_int_bool _let_0 K)) (hBOOL (hAPP_int_bool _let_0 (bit1 K))))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int pls) Y_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (number_number_of_int Y_2)))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ( (bit0 (bit0 (bit1 pls))) ) 1.14/1.33 ( (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.33 ( (bit1 (bit1 pls)) ) 1.14/1.33 ( (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.33 ( (number_number_of_int pls) ) 1.14/1.33 ( s ) 1.14/1.33 ( skv_1 ) 1.14/1.33 ( skv_2 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_int min))) (= (hBOOL (hAPP_int_bool _let_0 K)) (hBOOL (hAPP_int_bool _let_0 (bit1 K))))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (plus_plus_int A_2) A_2)) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_2) zero_zero_int))) ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_int min))) (= (hBOOL (hAPP_int_bool _let_0 K)) (hBOOL (hAPP_int_bool _let_0 (bit0 K))))) ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_2) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (plus_plus_real A_2) A_2)) zero_zero_real))) ) 1.14/1.33 ( one_one_real ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_2 $$unsorted) (P_3 $$unsorted)) (= (hBOOL (hAPP_int_bool (zcong X_2 zero_zero_int) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int P_3) X_2))) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((W_1 $$unsorted) (Z_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W_1) Z_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (plus_plus_int W_1) one_one_int)) Z_1))) ) 1.14/1.33 ( min, min ) 1.14/1.33 ( min, zero_zero_int ) 1.14/1.33 ( pls, min ) 1.14/1.33 ( pls, zero_zero_int ) 1.14/1.33 ( pls, one_one_int ) 1.14/1.33 ( pls, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( one_one_int, t ) 1.14/1.33 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K1) K2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (bit0 K1)) (bit1 K2)))) ) 1.14/1.33 ( min, min ) 1.14/1.33 ( min, pls ) 1.14/1.33 ( pls, min ) 1.14/1.33 ( pls, one_one_int ) 1.14/1.33 ( pls, (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.33 ( pls, (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.33 ( pls, (number_number_of_int pls) ) 1.14/1.33 ( pls, s ) 1.14/1.33 ( pls, skv_1 ) 1.14/1.33 ( pls, skv_2 ) 1.14/1.33 ( one_one_int, t ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_5 $$unsorted)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (times_times_int A_5) A_5)) zero_zero_int))) ) 1.14/1.33 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((N_1 $$unsorted)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_1) zero_zero_nat))) ) 1.14/1.33 ( zero_zero_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A $$unsorted) (B $$unsorted)) (hBOOL (hAPP_int_bool (zcong A B) one_one_int)) ) 1.14/1.33 ( s1, s ) 1.14/1.33 ( s1, skv_1 ) 1.14/1.33 ( s1, skv_2 ) 1.14/1.33 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int skv_4) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted) (L_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (minus_minus_int K) L_1)) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K) L_1))) ) 1.14/1.33 ( min, min ) 1.14/1.33 ( min, zero_zero_int ) 1.14/1.33 ( pls, min ) 1.14/1.33 ( pls, zero_zero_int ) 1.14/1.33 ( pls, one_one_int ) 1.14/1.33 ( pls, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( one_one_int, t ) 1.14/1.33 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min) ) 1.14/1.33 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (bit0 K)) min)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K) min))) ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((B_1_1 $$unsorted)) (is_int (twoSqu1241645765sum2sq B_1_1)) ) 1.14/1.33 ( (product_Pair_int_int s one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int min))) (= (hBOOL (hAPP_int_bool _let_0 (bit1 K))) (hBOOL (hAPP_int_bool _let_0 K)))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K) pls)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (bit0 K)) pls))) ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_1) (hAPP_nat_nat (plus_plus_nat N_1) M))) ) 1.14/1.33 ( one_one_nat, one_one_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_2 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (= (or (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_2) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_2) zero_zero_int))) (and (hBOOL (hAPP_int_bool _let_0 A_2)) (hBOOL (hAPP_int_bool _let_0 B_2)))) (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (times_times_int A_2) B_2))))) ) 1.14/1.33 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_3 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_11 $$unsorted) (Y_8 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int X_11) _let_0)) (hAPP_nat_int (power_power_int Y_8) _let_0))) zero_zero_int)))) ) 1.14/1.33 ( one_one_int, one_one_int ) 1.14/1.33 ( s, one_one_int ) 1.14/1.33 ( skv_5, skv_6 ) 1.14/1.33 ( skv_7, skv_8 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_int pls))) (= (hBOOL (hAPP_int_bool _let_0 K)) (hBOOL (hAPP_int_bool _let_0 (bit0 K))))) ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_2) pls)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (number_number_of_int X_2)) zero_zero_int))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ( (bit0 (bit0 (bit1 pls))) ) 1.14/1.33 ( (bit1 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (= (and (= zero_zero_nat N) (= zero_zero_nat Ma)) (= zero_zero_nat (hAPP_nat_nat (plus_plus_nat Ma) N))) ) 1.14/1.33 ( one_one_nat, one_one_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((V_7 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) V_7)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) (number_number_of_nat V_7)))) ) 1.14/1.33 ( min ) 1.14/1.33 ( zero_zero_int ) 1.14/1.33 ( pls ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_11 $$unsorted) (Y_8 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (plus_plus_real (hAPP_nat_real (power_power_real X_11) _let_0)) (hAPP_nat_real (power_power_real Y_8) _let_0))) zero_zero_real)))) ) 1.14/1.33 ( one_one_real, one_one_real ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Z_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (plus_plus_int (hAPP_int_int (plus_plus_int one_one_int) Z_1)) Z_1)) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Z_1) zero_zero_int))) ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_12 $$unsorted) (Y_9 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int X_12) _let_0)) (hAPP_nat_int (power_power_int Y_9) _let_0))))) ) 1.14/1.33 ( one_one_int, one_one_int ) 1.14/1.33 ( s, one_one_int ) 1.14/1.33 ( skv_5, skv_6 ) 1.14/1.33 ( skv_7, skv_8 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) (hAPP_nat_nat (minus_minus_nat N) Ma)))) ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K1) K2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (bit0 K1)) (bit0 K2)))) ) 1.14/1.33 ( pls, pls ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted) (L_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K) L_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (bit0 K)) (bit1 L_1)))) ) 1.14/1.33 ( pls, min ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_52 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A_52) A_52)) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted) (L_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K) L_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (bit1 K)) (bit1 L_1)))) ) 1.14/1.33 ( min, min ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_69 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_nat_int (power_power_int A_69) (number_number_of_nat (bit0 (bit1 pls)))))) ) 1.14/1.33 ( zero_zero_int ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( s1 ) 1.14/1.33 ( s ) 1.14/1.33 ( skv_4 ) 1.14/1.33 ( skv_5 ) 1.14/1.33 ( skv_6 ) 1.14/1.33 ( skv_7 ) 1.14/1.33 ( skv_8 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_1) (hAPP_nat_nat (plus_plus_nat M) N_1))) ) 1.14/1.33 ( one_one_nat, one_one_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((W $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int W) W)) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((W_1 $$unsorted) (Z_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W_1) Z_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int W_1) (hAPP_int_int (minus_minus_int Z_1) one_one_int)))) ) 1.14/1.33 ( min, min ) 1.14/1.33 ( min, zero_zero_int ) 1.14/1.33 ( pls, min ) 1.14/1.33 ( pls, zero_zero_int ) 1.14/1.33 ( pls, one_one_int ) 1.14/1.33 ( pls, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( one_one_int, t ) 1.14/1.33 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (= (hBOOL (hAPP_int_bool _let_0 (bit0 K))) (hBOOL (hAPP_int_bool _let_0 K)))) ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((W_1 $$unsorted) (Z_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W_1) (hAPP_int_int (plus_plus_int Z_1) one_one_int))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int W_1) Z_1))) ) 1.14/1.33 ( min, min ) 1.14/1.33 ( min, pls ) 1.14/1.33 ( pls, min ) 1.14/1.33 ( pls, one_one_int ) 1.14/1.33 ( pls, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.33 ( pls, (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.33 ( pls, (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.33 ( pls, (number_number_of_int pls) ) 1.14/1.33 ( pls, s ) 1.14/1.33 ( pls, skv_1 ) 1.14/1.33 ( pls, skv_2 ) 1.14/1.33 ( one_one_int, t ) 1.14/1.33 ( t, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.33 ( s, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.33 ( skv_1, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.33 ( skv_2, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (number267125858f_real Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) Y_2))) ) 1.14/1.33 ( min ) 1.14/1.33 ( zero_zero_int ) 1.14/1.33 ( pls ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (= (or (hBOOL (hAPP_nat_bool _let_0 N)) (hBOOL (hAPP_nat_bool _let_0 Ma))) (hBOOL (hAPP_nat_bool _let_0 (hAPP_nat_nat (plus_plus_nat Ma) N))))) ) 1.14/1.33 ( one_one_nat, one_one_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Z $$unsorted) (W $$unsorted)) (or (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Z) W)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int W) Z))) ) 1.14/1.33 ( min, min ) 1.14/1.33 ( min, pls ) 1.14/1.33 ( pls, min ) 1.14/1.33 ( pls, one_one_int ) 1.14/1.33 ( pls, (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.33 ( pls, (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.33 ( pls, (number_number_of_int pls) ) 1.14/1.33 ( pls, s ) 1.14/1.33 ( pls, skv_1 ) 1.14/1.33 ( pls, skv_2 ) 1.14/1.33 ( one_one_int, pls ) 1.14/1.33 ( one_one_int, t ) 1.14/1.33 ( t, one_one_int ) 1.14/1.33 ( (number_number_of_int (bit0 (bit1 pls))), pls ) 1.14/1.33 ( (number_number_of_int (bit1 (bit1 pls))), pls ) 1.14/1.33 ( (number_number_of_int pls), pls ) 1.14/1.33 ( s, pls ) 1.14/1.33 ( skv_1, pls ) 1.14/1.33 ( skv_2, pls ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (bit0 K)) pls)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K) pls))) ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (number267125858f_real X_2)) one_one_real)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_2) (bit1 pls)))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_2 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_int_bool (zcong A_2 B_2) Ma)) (hBOOL (hAPP_int_bool (zcong B_2 A_2) Ma))) ) 1.14/1.33 ( (number_number_of_int min), (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( (number_number_of_int min), (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( (number_number_of_int min), (hAPP_nat_int (power_power_int skv_4) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( s1, s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( s1, skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( s1, skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( s, s1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_1, s1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_2, s1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int skv_4) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_2 $$unsorted)) (= (= zero_zero_real (hAPP_real_real (plus_plus_real A_2) A_2)) (= zero_zero_real A_2)) ) 1.14/1.33 ( one_one_real ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K) min)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (bit1 K)) min))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (number_number_of_int X_2)) one_one_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_2) (bit1 pls)))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ( (bit0 (bit0 (bit1 pls))) ) 1.14/1.33 ( (bit1 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_2) pls)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (number267125858f_real X_2)) zero_zero_real))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (bit1 pls)) Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real one_one_real) (number267125858f_real Y_2)))) ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (number267125858f_real X_2)) (number267125858f_real Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_2) Y_2))) ) 1.14/1.33 ( min, min ) 1.14/1.33 ( min, pls ) 1.14/1.33 ( pls, min ) 1.14/1.33 ( pls, one_one_int ) 1.14/1.33 ( pls, (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.33 ( pls, (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.33 ( pls, (number_number_of_int pls) ) 1.14/1.33 ( pls, s ) 1.14/1.33 ( pls, skv_1 ) 1.14/1.33 ( pls, skv_2 ) 1.14/1.33 ( one_one_int, t ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_nat_bool B_1_1 B_2_1)) ) 1.14/1.33 ( (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_2) (bit1 pls))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (number_number_of_int X_2)) one_one_int))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ( (bit0 (bit0 (bit1 pls))) ) 1.14/1.33 ( (bit1 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) Y_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) (number_number_of_int Y_2)))) ) 1.14/1.33 ( min ) 1.14/1.33 ( zero_zero_int ) 1.14/1.33 ( pls ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ( (bit0 (bit0 (bit1 pls))) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( (bit1 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_18 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int (times_times_int A_18) A_18))) ) 1.14/1.33 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int pls) K)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) (bit1 K)))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.33 ( (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.33 ( (number_number_of_int pls) ) 1.14/1.33 ( s ) 1.14/1.33 ( skv_1 ) 1.14/1.33 ( skv_2 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_53 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A_53) zero_zero_int)) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((V_7 $$unsorted) (W_1 $$unsorted)) (let ((_let_0 (number_number_of_int V_7))) (let ((_let_1 (number_number_of_int W_1))) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int _let_0) _let_1)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_1) _let_0)))))) ) 1.14/1.33 ( pls, pls ) 1.14/1.33 ( pls, (bit1 pls) ) 1.14/1.33 ( pls, (bit0 (bit1 pls)) ) 1.14/1.33 ( pls, (bit1 (bit1 pls)) ) 1.14/1.33 ( (bit1 pls), pls ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_69 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_nat_real (power_power_real A_69) (number_number_of_nat (bit0 (bit1 pls)))))) ) 1.14/1.33 ( one_one_real ) 1.14/1.33 ( zero_zero_real ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_2) pls)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (number267125858f_real X_2)) zero_zero_real))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( t ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ( s ) 1.14/1.33 ( skv_1 ) 1.14/1.33 ( skv_2 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_2 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (times_times_int A_2) B_2)) zero_zero_int)) (or (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_2) zero_zero_int)) (hBOOL (hAPP_int_bool _let_0 B_2))) (and (hBOOL (hAPP_int_bool _let_0 A_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_2) zero_zero_int)))))) ) 1.14/1.33 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_3 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (number267125858f_real Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int pls) Y_2))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ( (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.33 ( (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.33 ( (number_number_of_int pls) ) 1.14/1.33 ( s ) 1.14/1.33 ( skv_1 ) 1.14/1.33 ( skv_2 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_2 $$unsorted) (A_109 $$unsorted)) (= (hBOOL (hAPP_int_bool A_109 X_2)) (hBOOL (member_int X_2 A_109))) ) 1.14/1.33 ( min, (hAPP_i1948725293t_bool ord_less_int min) ) 1.14/1.33 ( min, (hAPP_i1948725293t_bool ord_less_eq_int pls) ) 1.14/1.33 ( min, (hAPP_i1948725293t_bool ord_less_eq_int min) ) 1.14/1.33 ( min, (hAPP_i1948725293t_bool ord_less_int pls) ) 1.14/1.33 ( zero_zero_int, (hAPP_i1948725293t_bool ord_less_int min) ) 1.14/1.33 ( zero_zero_int, (hAPP_i1948725293t_bool ord_less_int pls) ) 1.14/1.33 ( pls, (hAPP_i1948725293t_bool ord_less_eq_int min) ) 1.14/1.33 ( one_one_int, (hAPP_i1948725293t_bool ord_less_int zero_zero_int) ) 1.14/1.33 ( one_one_int, (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) ) 1.14/1.33 ( t, (hAPP_i1948725293t_bool ord_less_int one_one_int) ) 1.14/1.33 ( t, (hAPP_i1948725293t_bool ord_less_eq_int one_one_int) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), zprime ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_i1948725293t_bool ord_less_int t) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_i1948725293t_bool ord_less_int zero_zero_int) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_i1948725293t_bool ord_less_int s) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (zcong s1 s) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (zcong (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) (number_number_of_int min)) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (zcong (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))) (number_number_of_int min)) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (zcong (hAPP_nat_int (power_power_int s) _let_0) (hAPP_nat_int (power_power_int s1) _let_0))) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (zcong s1 skv_1) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_i1948725293t_bool ord_less_int skv_1) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_i1948725293t_bool ord_less_int skv_2) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (zcong s1 skv_2) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (zcong (hAPP_nat_int (power_power_int skv_4) (number_number_of_nat (bit0 (bit1 pls)))) (number_number_of_int min)) ) 1.14/1.33 ( (number_number_of_int min), (quadRes (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ) 1.14/1.33 ( (number_number_of_int (bit0 (bit1 pls))), zprime ) 1.14/1.33 ( (number_number_of_int (bit0 (bit1 pls))), (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) ) 1.14/1.33 ( (number_number_of_int (bit1 (bit1 pls))), (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) ) 1.14/1.33 ( (number_number_of_int pls), (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) ) 1.14/1.33 ( s, (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) ) 1.14/1.33 ( (hAPP_int_int (times_times_int (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t), twoSqu1154269391sum2sq ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int), (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ) 1.14/1.33 ( skv_1, (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) ) 1.14/1.33 ( skv_2, (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K) min)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (bit0 K)) min))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_36 $$unsorted) (B_33 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A_36) (hAPP_int_int (times_times_int B_33) A_36))) ) 1.14/1.33 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( m, (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.33 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (= M (hAPP_nat_nat (minus_minus_nat (hAPP_nat_nat (plus_plus_nat M) N_1)) N_1)) ) 1.14/1.33 ( one_one_nat, one_one_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (number267125858f_real X_2)) (number267125858f_real Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_2) Y_2))) ) 1.14/1.33 ( min, min ) 1.14/1.33 ( min, zero_zero_int ) 1.14/1.33 ( pls, min ) 1.14/1.33 ( pls, zero_zero_int ) 1.14/1.33 ( pls, one_one_int ) 1.14/1.33 ( pls, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( one_one_int, t ) 1.14/1.33 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_int (hAPP_nat_int B_1_1 B_2_1)) ) 1.14/1.33 ( (power_power_int zero_zero_int), zero_zero_nat ) 1.14/1.33 ( (power_power_int zero_zero_int), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ( (power_power_int one_one_int), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ( (power_power_int s), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ( (power_power_int s1), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ( (power_power_int skv_4), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ( (power_power_int skv_5), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ( (power_power_int skv_6), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ( (power_power_int skv_7), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ( (power_power_int skv_8), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_68 $$unsorted)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int (power_power_int A_68) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int))) ) 1.14/1.33 ( zero_zero_int ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( s1 ) 1.14/1.33 ( s ) 1.14/1.33 ( skv_4 ) 1.14/1.33 ( skv_5 ) 1.14/1.33 ( skv_6 ) 1.14/1.33 ( skv_7 ) 1.14/1.33 ( skv_8 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((W_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W_1) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (bit0 W_1)) zero_zero_int))) ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((W_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (bit1 W_1)) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W_1) zero_zero_int))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_102 $$unsorted) (M_13 $$unsorted) (B_59 $$unsorted)) (= (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int A_102) M_13)) (hAPP_int_int (times_times_int B_59) M_13)) (hAPP_int_int (times_times_int (hAPP_int_int (plus_plus_int A_102) B_59)) M_13)) ) 1.14/1.33 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m), t, one_one_int ) 1.14/1.33 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m), skv_3, one_one_int ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((B_43 $$unsorted) (A_49 $$unsorted)) (or (not (is_int A_49)) (not (is_int B_43)) (= zero_zero_int A_49) (= zero_zero_int B_43) (not (= zero_zero_int (hAPP_int_int (times_times_int A_49) B_43)))) ) 1.14/1.33 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( m, (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.33 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (or (not (is_int Y_2)) (not (is_int X_2)) (= (= (number267125858f_real X_2) (number267125858f_real Y_2)) (= X_2 Y_2))) ) 1.14/1.33 ( min, min ) 1.14/1.33 ( min, zero_zero_int ) 1.14/1.33 ( zero_zero_int, min ) 1.14/1.33 ( pls, (undefined_int int) ) 1.14/1.33 ( one_one_int, one_one_int ) 1.14/1.33 ( one_one_int, m ) 1.14/1.33 ( t, t ) 1.14/1.33 ( t, s ) 1.14/1.33 ( m, one_one_int ) 1.14/1.33 ( s1, s1 ) 1.14/1.33 ( s1, skv_1 ) 1.14/1.33 ( s, t ) 1.14/1.33 ( (undefined_int int), pls ) 1.14/1.33 ( (undefined_int int), (undefined_int int) ) 1.14/1.33 ( skv_1, s1 ) 1.14/1.33 ( skv_2, skv_2 ) 1.14/1.33 ( skv_2, skv_3 ) 1.14/1.33 ( skv_3, skv_2 ) 1.14/1.33 ( skv_4, skv_4 ) 1.14/1.33 ( skv_4, skv_5 ) 1.14/1.33 ( skv_5, skv_4 ) 1.14/1.33 ( skv_6, skv_6 ) 1.14/1.33 ( skv_6, skv_8 ) 1.14/1.33 ( skv_7, skv_7 ) 1.14/1.33 ( skv_8, skv_6 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Z_2 $$unsorted) (X_3 $$unsorted) (Y_3 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool dvd_dvd_int X_3))) (or (not (hBOOL (hAPP_int_bool _let_0 Y_3))) (not (hBOOL (hAPP_int_bool _let_0 Z_2))) (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (minus_minus_int Y_3) Z_2))))) ) 1.14/1.33 ( (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (or (not (= M (hAPP_nat_nat (plus_plus_nat M) N_1))) (= zero_zero_nat N_1)) ) 1.14/1.33 ( one_one_nat, one_one_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((V_7 $$unsorted)) (= (= zero_zero_nat (number_number_of_nat V_7)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int V_7) pls))) ) 1.14/1.33 ( min ) 1.14/1.33 ( pls ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_13 $$unsorted) (Y_10 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int (power_power_int X_13) _let_0)) (hAPP_nat_int (power_power_int Y_10) _let_0)))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Y_10))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_13) Y_10)))) ) 1.14/1.33 ( zero_zero_int, zero_zero_int ) 1.14/1.33 ( zero_zero_int, one_one_int ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((N_1 $$unsorted) (P_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool dvd_dvd_int P_1))) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) M))) (not (hBOOL (hAPP_int_bool zprime P_1))) (not (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (times_times_int M) N_1)))) (hBOOL (hAPP_int_bool _let_0 M)) (hBOOL (hAPP_int_bool _let_0 N_1)))) ) 1.14/1.33 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (or (not (is_int M)) (not (= one_one_int (hAPP_int_int (times_times_int M) N_1))) (= one_one_int M) (= M (number_number_of_int min))) ) 1.14/1.33 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_3 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (= (hAPP_nat_nat (plus_plus_nat (hAPP_nat_nat (plus_plus_nat (hAPP_nat_nat (power_power_nat X_2) _let_0)) (hAPP_nat_nat (power_power_nat Y_2) _let_0))) (hAPP_nat_nat (times_times_nat (hAPP_nat_nat (times_times_nat _let_0) X_2)) Y_2)) (hAPP_nat_nat (power_power_nat (hAPP_nat_nat (plus_plus_nat X_2) Y_2)) _let_0))) ) 1.14/1.33 ( one_one_nat, one_one_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_2 $$unsorted) (P_2 $$unsorted)) (or (not (forall ((A_3 $$unsorted)) (or (not (is_int A_3)) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A_3)) (not (hBOOL (hAPP_int_bool P_2 (hAPP_int_int (minus_minus_int A_3) one_one_int))))) (hBOOL (hAPP_int_bool P_2 A_3))) )) (hBOOL (hAPP_int_bool P_2 X_2))) ) 1.14/1.33 ( min, (hAPP_i1948725293t_bool ord_less_int min) ) 1.14/1.33 ( min, (hAPP_i1948725293t_bool ord_less_eq_int pls) ) 1.14/1.33 ( min, (hAPP_i1948725293t_bool ord_less_eq_int min) ) 1.14/1.33 ( min, (hAPP_i1948725293t_bool ord_less_int pls) ) 1.14/1.33 ( zero_zero_int, (hAPP_i1948725293t_bool ord_less_int min) ) 1.14/1.33 ( zero_zero_int, (hAPP_i1948725293t_bool ord_less_int pls) ) 1.14/1.33 ( pls, (hAPP_i1948725293t_bool ord_less_eq_int min) ) 1.14/1.33 ( one_one_int, (hAPP_i1948725293t_bool ord_less_int zero_zero_int) ) 1.14/1.33 ( one_one_int, (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) ) 1.14/1.33 ( t, (hAPP_i1948725293t_bool ord_less_int one_one_int) ) 1.14/1.33 ( t, (hAPP_i1948725293t_bool ord_less_eq_int one_one_int) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), zprime ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_i1948725293t_bool ord_less_int t) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_i1948725293t_bool ord_less_int zero_zero_int) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_i1948725293t_bool ord_less_int s) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (zcong s1 s) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (zcong (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) (number_number_of_int min)) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (zcong (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))) (number_number_of_int min)) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (zcong (hAPP_nat_int (power_power_int s) _let_0) (hAPP_nat_int (power_power_int s1) _let_0))) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (zcong s1 skv_1) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_i1948725293t_bool ord_less_int skv_1) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_i1948725293t_bool ord_less_int skv_2) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (zcong s1 skv_2) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (zcong (hAPP_nat_int (power_power_int skv_4) (number_number_of_nat (bit0 (bit1 pls)))) (number_number_of_int min)) ) 1.14/1.33 ( (number_number_of_int min), (quadRes (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ) 1.14/1.33 ( (number_number_of_int (bit0 (bit1 pls))), zprime ) 1.14/1.33 ( (number_number_of_int (bit0 (bit1 pls))), (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) ) 1.14/1.33 ( (number_number_of_int (bit1 (bit1 pls))), (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) ) 1.14/1.33 ( (number_number_of_int pls), (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) ) 1.14/1.33 ( s, (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) ) 1.14/1.33 ( (hAPP_int_int (times_times_int (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t), twoSqu1154269391sum2sq ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int), (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ) 1.14/1.33 ( skv_1, (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) ) 1.14/1.33 ( skv_2, (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((B_2 $$unsorted) (A_2 $$unsorted)) (or (not (is_int A_2)) (not (is_int B_2)) (= (= B_2 (hAPP_int_int (plus_plus_int B_2) A_2)) (= zero_zero_int A_2))) ) 1.14/1.33 ( one_one_int, one_one_int ) 1.14/1.33 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m), one_one_int ) 1.14/1.33 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), one_one_int ) 1.14/1.33 ( (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_6) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_8) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (or (not (is_int B_2_1)) (is_int (hAPP_int_int B_1_1 B_2_1))) ) 1.14/1.33 ( (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))), m ) 1.14/1.33 ( (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)), one_one_int ) 1.14/1.33 ( (plus_plus_int one_one_int), one_one_int ) 1.14/1.33 ( (times_times_int (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)), t ) 1.14/1.33 ( (times_times_int (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)), skv_3 ) 1.14/1.33 ( (plus_plus_int (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))), one_one_int ) 1.14/1.33 ( (minus_minus_int (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))), (number_number_of_int min) ) 1.14/1.33 ( (plus_plus_int (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls))))), (hAPP_nat_int (power_power_int skv_6) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.33 ( (plus_plus_int (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls))))), (hAPP_nat_int (power_power_int skv_8) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_97 $$unsorted) (M_12 $$unsorted)) (= (hAPP_int_int (times_times_int (hAPP_int_int (plus_plus_int A_97) one_one_int)) M_12) (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int A_97) M_12)) M_12)) ) 1.14/1.33 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m ) 1.14/1.33 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m), t ) 1.14/1.33 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m), skv_3 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_2 $$unsorted) (W_1 $$unsorted)) (let ((_let_0 (number_number_of_nat W_1))) (or (not (is_int A_2)) (= (= zero_zero_int (hAPP_nat_int (power_power_int A_2) _let_0)) (and (not (= zero_zero_nat _let_0)) (= zero_zero_int A_2))))) ) 1.14/1.33 ( zero_zero_int, pls ) 1.14/1.33 ( zero_zero_int, (bit0 (bit1 pls)) ) 1.14/1.33 ( one_one_int, (bit0 (bit1 pls)) ) 1.14/1.33 ( s1, (bit0 (bit1 pls)) ) 1.14/1.33 ( s, (bit0 (bit1 pls)) ) 1.14/1.33 ( skv_4, (bit0 (bit1 pls)) ) 1.14/1.33 ( skv_5, (bit0 (bit1 pls)) ) 1.14/1.33 ( skv_6, (bit0 (bit1 pls)) ) 1.14/1.33 ( skv_7, (bit0 (bit1 pls)) ) 1.14/1.33 ( skv_8, (bit0 (bit1 pls)) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_24 $$unsorted) (P_7 $$unsorted) (Q_7 $$unsorted)) (let ((_let_0 (power_power_int X_24))) (= (hAPP_nat_int _let_0 (hAPP_nat_nat (times_times_nat P_7) Q_7)) (hAPP_nat_int (power_power_int (hAPP_nat_int _let_0 P_7)) Q_7))) ) 1.14/1.33 ( zero_zero_int, (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.33 ( zero_zero_int, (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ( one_one_int, (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((V_7 $$unsorted) (V_8 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int V_7))) (= (or (hBOOL (hAPP_int_bool _let_0 V_8)) (hBOOL (hAPP_int_bool _let_0 pls))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (number_number_of_nat V_7)) (number_number_of_nat V_8))))) ) 1.14/1.33 ( min, min ) 1.14/1.33 ( min, pls ) 1.14/1.33 ( pls, min ) 1.14/1.33 ( pls, one_one_int ) 1.14/1.33 ( pls, (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.33 ( pls, (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.33 ( pls, (number_number_of_int pls) ) 1.14/1.33 ( pls, s ) 1.14/1.33 ( pls, skv_1 ) 1.14/1.33 ( pls, skv_2 ) 1.14/1.33 ( one_one_int, t ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A $$unsorted) (P_1 $$unsorted)) (or (not (hBOOL (hAPP_int_bool zprime P_1))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) P_1))) (hBOOL (hAPP_int_bool (zcong (hAPP_int_int (times_times_int A) (inv P_1 A)) one_one_int) P_1))) ) 1.14/1.33 ( min, min ) 1.14/1.33 ( min, zero_zero_int ) 1.14/1.33 ( pls, min ) 1.14/1.33 ( pls, zero_zero_int ) 1.14/1.33 ( pls, one_one_int ) 1.14/1.33 ( pls, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( one_one_int, t ) 1.14/1.33 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (= X_1 Y_1) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_1) Y_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Y_1) X_1))) ) 1.14/1.33 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A $$unsorted) (B $$unsorted)) (or (not (is_int A)) (= A (hAPP_int_int (plus_plus_int (hAPP_int_int (minus_minus_int A) B)) B))) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Ma $$unsorted) (N $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (power_power_nat A_2))) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) A_2))) (= (= Ma N) (= (hAPP_nat_nat _let_0 Ma) (hAPP_nat_nat _let_0 N))))) ) 1.14/1.33 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat, zero_zero_nat ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))), one_one_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((V_18 $$unsorted) (V_17 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (or (not (hBOOL (hAPP_int_bool _let_0 V_17))) (not (hBOOL (hAPP_int_bool _let_0 V_18))) (= (hAPP_int_int (plus_plus_int (number_number_of_int V_17)) (number_number_of_int V_18)) (number_number_of_int (hAPP_int_int (plus_plus_int V_17) V_18))))) ) 1.14/1.33 ( (bit1 pls), (bit1 pls) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Ma $$unsorted) (K $$unsorted) (F_1 $$unsorted)) (or (not (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_2) N_2))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat F_1 M_2)) (hAPP_nat_nat F_1 N_2)))) )) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (plus_plus_nat (hAPP_nat_nat F_1 Ma)) K)) (hAPP_nat_nat F_1 (hAPP_nat_nat (plus_plus_nat Ma) K))))) ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_nat, (power_power_nat one_one_nat) ) 1.14/1.33 ( one_one_nat, one_one_nat, (power_power_nat zero_zero_nat) ) 1.14/1.33 ( one_one_nat, one_one_nat, (power_power_nat one_one_nat) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((Z_4 $$unsorted)) (= (hAPP_int_int (times_times_int Z_4) (number_number_of_int (bit0 (bit1 pls)))) (hAPP_int_int (plus_plus_int Z_4) Z_4)) ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.33 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_2 $$unsorted)) (or (not (is_int A_2)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) (hAPP_nat_int (power_power_int A_2) (number_number_of_nat (bit0 (bit1 pls)))))) (not (= zero_zero_int A_2)))) ) 1.14/1.33 ( min ) 1.14/1.33 ( zero_zero_int ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( t ) 1.14/1.33 ( m ) 1.14/1.33 ( s1 ) 1.14/1.33 ( s ) 1.14/1.33 ( (undefined_int int) ) 1.14/1.33 ( skv_1 ) 1.14/1.33 ( skv_2 ) 1.14/1.33 ( skv_3 ) 1.14/1.33 ( skv_4 ) 1.14/1.33 ( skv_5 ) 1.14/1.33 ( skv_6 ) 1.14/1.33 ( skv_7 ) 1.14/1.33 ( skv_8 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((N_27 $$unsorted) (A_78 $$unsorted)) (let ((_let_0 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (or (not (hBOOL (hAPP_real_bool _let_0 A_78))) (hBOOL (hAPP_real_bool _let_0 (hAPP_nat_real (power_power_real A_78) N_27))))) ) 1.14/1.33 ( zero_zero_nat, zero_zero_real ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_real ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_real ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_5 $$unsorted) (Y_4 $$unsorted)) (or (not (is_int Y_4)) (not (is_int X_5)) (= X_5 Y_4) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_5) Y_4)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Y_4) X_5))) ) 1.14/1.33 ( min, min ) 1.14/1.33 ( min, zero_zero_int ) 1.14/1.33 ( min, pls ) 1.14/1.33 ( zero_zero_int, min ) 1.14/1.33 ( zero_zero_int, pls ) 1.14/1.33 ( pls, min ) 1.14/1.33 ( pls, zero_zero_int ) 1.14/1.33 ( pls, one_one_int ) 1.14/1.33 ( pls, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( one_one_int, pls ) 1.14/1.33 ( one_one_int, t ) 1.14/1.33 ( t, one_one_int ) 1.14/1.33 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), pls ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), s ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_1 ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_2 ) 1.14/1.33 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (or (not (hBOOL (hAPP_int_bool _let_0 X_1))) (hBOOL (hAPP_int_bool _let_0 (hAPP_nat_int (power_power_int X_1) N_1))))) ) 1.14/1.33 ( zero_zero_nat, zero_zero_int ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_int ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), s1 ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), s ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), skv_4 ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), skv_5 ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), skv_6 ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), skv_7 ) 1.14/1.33 ( (number_number_of_nat (bit0 (bit1 pls))), skv_8 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N_1)) (= (hAPP_nat_nat (div_mod_nat M) N_1) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (minus_minus_nat M) N_1)) N_1))) ) 1.14/1.33 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_64 $$unsorted) (M_4 $$unsorted) (N_14 $$unsorted)) (let ((_let_0 (power_power_real A_64))) (= (hAPP_nat_real _let_0 (hAPP_nat_nat (times_times_nat M_4) N_14)) (hAPP_nat_real (power_power_real (hAPP_nat_real _let_0 M_4)) N_14))) ) 1.14/1.33 ( zero_zero_real, zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ( zero_zero_real, (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.33 ( zero_zero_real, (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_65 $$unsorted) (M_5 $$unsorted) (N_16 $$unsorted)) (let ((_let_0 (power_power_int A_65))) (= (hAPP_nat_int _let_0 (hAPP_nat_nat (plus_plus_nat M_5) N_16)) (hAPP_int_int (times_times_int (hAPP_nat_int _let_0 M_5)) (hAPP_nat_int _let_0 N_16)))) ) 1.14/1.33 ( zero_zero_int, one_one_nat, one_one_nat ) 1.14/1.33 ( one_one_int, one_one_nat, one_one_nat ) 1.14/1.33 ( s1, one_one_nat, one_one_nat ) 1.14/1.33 ( s, one_one_nat, one_one_nat ) 1.14/1.33 ( skv_4, one_one_nat, one_one_nat ) 1.14/1.33 ( skv_5, one_one_nat, one_one_nat ) 1.14/1.33 ( skv_6, one_one_nat, one_one_nat ) 1.14/1.33 ( skv_7, one_one_nat, one_one_nat ) 1.14/1.33 ( skv_8, one_one_nat, one_one_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_2 $$unsorted)) (= (= zero_zero_real (hAPP_nat_real (power_power_real A_2) (number_number_of_nat (bit0 (bit1 pls))))) (= zero_zero_real A_2)) ) 1.14/1.33 ( one_one_real ) 1.14/1.33 ( zero_zero_real ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_99 $$unsorted)) (or (not (is_int A_99)) (= A_99 (hAPP_int_int (times_times_int one_one_int) A_99))) ) 1.14/1.33 ( min ) 1.14/1.33 ( zero_zero_int ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( t ) 1.14/1.33 ( m ) 1.14/1.33 ( s1 ) 1.14/1.33 ( s ) 1.14/1.33 ( (undefined_int int) ) 1.14/1.33 ( skv_1 ) 1.14/1.33 ( skv_2 ) 1.14/1.33 ( skv_3 ) 1.14/1.33 ( skv_4 ) 1.14/1.33 ( skv_5 ) 1.14/1.33 ( skv_6 ) 1.14/1.33 ( skv_7 ) 1.14/1.33 ( skv_8 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((M $$unsorted)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) M))) ) 1.14/1.33 ( zero_zero_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((BOUND_VARIABLE_17857 $$unsorted) (BOUND_VARIABLE_17858 $$unsorted)) (let ((_let_0 (quadRes BOUND_VARIABLE_17858))) (let ((_let_1 (hBOOL (hAPP_int_bool _let_0 BOUND_VARIABLE_17857)))) (let ((_let_2 (legendre BOUND_VARIABLE_17857 BOUND_VARIABLE_17858))) (or (hBOOL (hAPP_int_bool (zcong BOUND_VARIABLE_17857 zero_zero_int) BOUND_VARIABLE_17858)) (and (or _let_1 (= (number_number_of_int min) _let_2)) (or (not _let_1) (= one_one_int _let_2))))))) ) 1.14/1.33 ( (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((BOUND_VARIABLE_17875 $$unsorted) (BOUND_VARIABLE_17876 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (zcong BOUND_VARIABLE_17875 zero_zero_int) BOUND_VARIABLE_17876))) (= zero_zero_int (legendre BOUND_VARIABLE_17875 BOUND_VARIABLE_17876))) ) 1.14/1.33 ( (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_2 $$unsorted) (N $$unsorted)) (= (and (not (= zero_zero_nat N)) (= zero_zero_real A_2)) (= zero_zero_real (hAPP_nat_real (power_power_real A_2) N))) ) 1.14/1.33 ( one_one_real, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ( zero_zero_real, zero_zero_nat ) 1.14/1.33 ( zero_zero_real, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_23 $$unsorted)) (or (not (is_int X_23)) (= X_23 (hAPP_nat_int (power_power_int X_23) one_one_nat))) ) 1.14/1.33 ( min ) 1.14/1.33 ( zero_zero_int ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( t ) 1.14/1.33 ( m ) 1.14/1.33 ( s1 ) 1.14/1.33 ( s ) 1.14/1.33 ( (undefined_int int) ) 1.14/1.33 ( skv_1 ) 1.14/1.33 ( skv_2 ) 1.14/1.33 ( skv_3 ) 1.14/1.33 ( skv_4 ) 1.14/1.33 ( skv_5 ) 1.14/1.33 ( skv_6 ) 1.14/1.33 ( skv_7 ) 1.14/1.33 ( skv_8 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((X_8 $$unsorted) (Y_7 $$unsorted)) (or (not (is_int X_8)) (not (is_int Y_7)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_8) Y_7))) (= X_8 Y_7) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_8) Y_7))) ) 1.14/1.33 ( min, min ) 1.14/1.33 ( min, zero_zero_int ) 1.14/1.33 ( min, pls ) 1.14/1.33 ( pls, min ) 1.14/1.33 ( pls, zero_zero_int ) 1.14/1.33 ( pls, one_one_int ) 1.14/1.33 ( pls, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( pls, (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.33 ( pls, (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.33 ( pls, (number_number_of_int pls) ) 1.14/1.33 ( pls, s ) 1.14/1.33 ( pls, skv_1 ) 1.14/1.33 ( pls, skv_2 ) 1.14/1.33 ( one_one_int, t ) 1.14/1.33 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((A_91 $$unsorted)) (= (hAPP_nat_nat (power_power_nat A_91) (number_number_of_nat (bit1 (bit1 pls)))) (hAPP_nat_nat (times_times_nat (hAPP_nat_nat (times_times_nat A_91) A_91)) A_91)) ) 1.14/1.33 ( zero_zero_nat ) 1.14/1.33 ( one_one_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((K_1 $$unsorted)) (or (not (is_int K_1)) (= K_1 (number_number_of_int K_1))) ) 1.14/1.33 ( min ) 1.14/1.33 ( zero_zero_int ) 1.14/1.33 ( pls ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( t ) 1.14/1.33 ( (bit1 pls) ) 1.14/1.33 ( (bit0 (bit1 pls)) ) 1.14/1.33 ( (bit0 (bit0 (bit1 pls))) ) 1.14/1.33 ( m ) 1.14/1.33 ( s1 ) 1.14/1.33 ( (bit1 (bit1 pls)) ) 1.14/1.33 ( s ) 1.14/1.33 ( (undefined_int int) ) 1.14/1.33 ( skv_1 ) 1.14/1.33 ( skv_2 ) 1.14/1.33 ( skv_3 ) 1.14/1.33 ( skv_4 ) 1.14/1.33 ( skv_5 ) 1.14/1.33 ( skv_6 ) 1.14/1.33 ( skv_7 ) 1.14/1.33 ( skv_8 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((BOUND_VARIABLE_17949 $$unsorted)) (= one_one_nat (hAPP_nat_nat (power_power_nat BOUND_VARIABLE_17949) zero_zero_nat)) ) 1.14/1.33 ( zero_zero_nat ) 1.14/1.33 ( one_one_nat ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((B_37 $$unsorted) (K_3 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int B_37) (hAPP_int_int (times_times_int B_37) K_3))) ) 1.14/1.33 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.33 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_3 ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N_1))) ) 1.14/1.33 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.33 ) 1.14/1.33 (instantiation (forall ((M_10 $$unsorted)) (= (hAPP_int_int (times_times_int (hAPP_int_int (plus_plus_int one_one_int) one_one_int)) M_10) (hAPP_int_int (plus_plus_int M_10) M_10)) ) 1.14/1.33 ( one_one_int ) 1.14/1.33 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.33 ( (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.33 ) 1.14/1.34 (instantiation (forall ((A $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A))) (not (forall ((P_4 $$unsorted)) (or (not (is_int P_4)) (not (hBOOL (hAPP_int_bool zprime P_4))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int P_4) A)))) ))) ) 1.14/1.34 ( t ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_57 $$unsorted)) (= one_one_real (hAPP_nat_real (power_power_real A_57) zero_zero_nat)) ) 1.14/1.34 ( one_one_real ) 1.14/1.34 ( zero_zero_real ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((W_16 $$unsorted)) (let ((_let_0 (number_number_of_int W_16))) (= (hAPP_nat_int (power_power_int _let_0) (number_number_of_nat (bit0 (bit1 pls)))) (hAPP_int_int (times_times_int _let_0) _let_0))) ) 1.14/1.34 ( min ) 1.14/1.34 ( pls ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ( (bit0 (bit1 pls)) ) 1.14/1.34 ( (bit0 (bit0 (bit1 pls))) ) 1.14/1.34 ( (bit1 (bit1 pls)) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((K_1 $$unsorted)) (= (hAPP_int_int (plus_plus_int K_1) K_1) (bit0 K_1)) ) 1.14/1.34 ( pls ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ( (bit0 (bit1 pls)) ) 1.14/1.34 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((K_1 $$unsorted) (L $$unsorted)) (not (= (bit0 L) (bit1 K_1))) ) 1.14/1.34 ( min, (bit0 (bit1 pls)) ) 1.14/1.34 ( pls, (bit1 pls) ) 1.14/1.34 ( (bit1 pls), pls ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((V_10 $$unsorted) (W_9 $$unsorted)) (= (number_number_of_int (hAPP_int_int (plus_plus_int V_10) W_9)) (hAPP_int_int (plus_plus_int (number_number_of_int V_10)) (number_number_of_int W_9))) ) 1.14/1.34 ( (bit1 pls), (bit1 pls) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((C_15 $$unsorted) (A_34 $$unsorted) (B_31 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool dvd_dvd_int A_34))) (or (not (hBOOL (hAPP_int_bool _let_0 B_31))) (not (hBOOL (hAPP_int_bool _let_0 C_15))) (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (plus_plus_int B_31) C_15))))) ) 1.14/1.34 ( one_one_int, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_26 $$unsorted)) (= (hAPP_nat_nat (times_times_nat X_26) X_26) (hAPP_nat_nat (power_power_nat X_26) (number_number_of_nat (bit0 (bit1 pls))))) ) 1.14/1.34 ( zero_zero_nat ) 1.14/1.34 ( one_one_nat ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) M))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int M) N_1))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int N_1) M)))) ) 1.14/1.34 ( min, min ) 1.14/1.34 ( min, pls ) 1.14/1.34 ( zero_zero_int, min ) 1.14/1.34 ( zero_zero_int, pls ) 1.14/1.34 ( one_one_int, pls ) 1.14/1.34 ( t, one_one_int ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), pls ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), s ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int) ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_1 ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_2 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_75 $$unsorted) (N_24 $$unsorted) (B_51 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int (power_power_int A_75) N_24)) (hAPP_nat_int (power_power_int B_51) N_24)))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) B_51))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_75) B_51))) ) 1.14/1.34 ( zero_zero_int, (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int ) 1.14/1.34 ( zero_zero_int, (number_number_of_nat (bit0 (bit1 pls))), one_one_int ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((BOUND_VARIABLE_18096 $$unsorted)) (let ((_let_0 (number_number_of_nat BOUND_VARIABLE_18096))) (or (= zero_zero_nat _let_0) (= zero_zero_real (hAPP_nat_real (power_power_real zero_zero_real) _let_0)))) ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ( (bit0 (bit1 pls)) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((BOUND_VARIABLE_18104 $$unsorted)) (let ((_let_0 (number_number_of_nat BOUND_VARIABLE_18104))) (or (not (= zero_zero_nat _let_0)) (= one_one_real (hAPP_nat_real (power_power_real zero_zero_real) _let_0)))) ) 1.14/1.34 ( pls ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ( (bit0 (bit1 pls)) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_26 $$unsorted)) (= (hAPP_int_int (times_times_int X_26) X_26) (hAPP_nat_int (power_power_int X_26) (number_number_of_nat (bit0 (bit1 pls))))) ) 1.14/1.34 ( zero_zero_int ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( s1 ) 1.14/1.34 ( s ) 1.14/1.34 ( skv_4 ) 1.14/1.34 ( skv_5 ) 1.14/1.34 ( skv_6 ) 1.14/1.34 ( skv_7 ) 1.14/1.34 ( skv_8 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((P_5 $$unsorted) (P_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (let ((_let_1 (hBOOL (hAPP_int_bool _let_0 X_2)))) (let ((_let_2 (hBOOL P_2))) (let ((_let_3 (hBOOL P_5))) (or (and _let_1 (= (not _let_2) _let_3)) (= (and _let_2 _let_1) (and _let_1 _let_3))))))) ) 1.14/1.34 ( (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int t) (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)), (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int t) (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)), min ) 1.14/1.34 ( (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int min) min), (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int min) min), (number_number_of_int pls) ) 1.14/1.34 ( (hAPP_int_bool zprime (number_number_of_int (bit0 (bit1 pls)))), (hAPP_int_bool zprime (number_number_of_int (bit0 (bit1 pls)))), s ) 1.14/1.34 ( (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int pls) min), (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int pls) min), (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.34 ( (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (number_number_of_int pls)), (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (number_number_of_int pls)), (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.34 ( (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) zero_zero_int), (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) zero_zero_int), one_one_int ) 1.14/1.34 ( (hAPP_int_bool (quadRes (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) (number_number_of_int min)), (hAPP_int_bool (quadRes (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) (number_number_of_int min)), skv_1 ) 1.14/1.34 ( (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls)))), skv_2 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (= (and (not (= Ma N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N))) ) 1.14/1.34 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((L $$unsorted)) (not (= min (bit0 L))) ) 1.14/1.34 ( pls ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ( (bit0 (bit1 pls)) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((M_9 $$unsorted) (N_36 $$unsorted) (A_88 $$unsorted)) (let ((_let_0 (power_power_int A_88))) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A_88))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int _let_0 M_9)) (hAPP_nat_int _let_0 N_36)))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_9) N_36)))) ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat, zero_zero_int ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((M $$unsorted)) (let ((_let_0 (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))))) (let ((_let_1 (plus_plus_int (hAPP_int_int _let_0 M)))) (let ((_let_2 (hAPP_int_int _let_1 one_one_int))) (or (not (hBOOL (hAPP_int_bool zprime _let_2))) (= one_one_int (legendre (number_number_of_int min) _let_2)))))) ) 1.14/1.34 ( m ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int I_1))) (or (not (hBOOL (hAPP_int_bool _let_0 J_1))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int J_1) K_1))) (hBOOL (hAPP_int_bool _let_0 K_1)))) ) 1.14/1.34 ( min, pls, min ) 1.14/1.34 ( min, pls, (number_number_of_int pls) ) 1.14/1.34 ( pls, min, min ) 1.14/1.34 ( t, pls, one_one_int ) 1.14/1.34 ( (number_number_of_int pls), min, pls ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((BOUND_VARIABLE_18211 $$unsorted) (BOUND_VARIABLE_18212 $$unsorted)) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) BOUND_VARIABLE_18212))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat BOUND_VARIABLE_18211) (hAPP_nat_nat (power_power_nat BOUND_VARIABLE_18211) BOUND_VARIABLE_18212)))) ) 1.14/1.34 ( zero_zero_nat, zero_zero_nat ) 1.14/1.34 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ( one_one_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((BOUND_VARIABLE_18200 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat one_one_nat) (hAPP_nat_nat (power_power_nat one_one_nat) BOUND_VARIABLE_18200))) ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_22 $$unsorted) (P_6 $$unsorted) (Q_6 $$unsorted)) (let ((_let_0 (power_power_nat X_22))) (= (hAPP_nat_nat (times_times_nat (hAPP_nat_nat _let_0 P_6)) (hAPP_nat_nat _let_0 Q_6)) (hAPP_nat_nat _let_0 (hAPP_nat_nat (plus_plus_nat P_6) Q_6)))) ) 1.14/1.34 ( zero_zero_nat, one_one_nat, one_one_nat ) 1.14/1.34 ( one_one_nat, one_one_nat, one_one_nat ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((Z $$unsorted)) (not (= zero_zero_int (hAPP_int_int (plus_plus_int (hAPP_int_int (plus_plus_int one_one_int) Z)) Z))) ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (= (= zero_zero_nat (hAPP_nat_nat (power_power_nat Ma) N)) (and (not (= zero_zero_nat N)) (= zero_zero_nat Ma))) ) 1.14/1.34 ( zero_zero_nat, zero_zero_nat ) 1.14/1.34 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ( one_one_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((B_30 $$unsorted) (A_32 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (or (and (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_30) zero_zero_int))) (not (hBOOL (hAPP_int_bool _let_0 A_32)))) (or (not (hBOOL (hAPP_int_bool _let_0 B_30))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_32) zero_zero_int))))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (times_times_int A_32) B_30)) zero_zero_int)))) ) 1.14/1.34 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( m, (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.34 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((W_5 $$unsorted)) (let ((_let_0 (number267125858f_real W_5))) (= (number267125858f_real (bit0 W_5)) (hAPP_real_real (plus_plus_real (hAPP_real_real (plus_plus_real zero_zero_real) _let_0)) _let_0))) ) 1.14/1.34 ( pls ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ( (bit0 (bit1 pls)) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((BOUND_VARIABLE_18350 $$unsorted) (BOUND_VARIABLE_18351 $$unsorted)) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat BOUND_VARIABLE_18350) BOUND_VARIABLE_18351))) (= BOUND_VARIABLE_18350 (hAPP_nat_nat (div_mod_nat BOUND_VARIABLE_18350) BOUND_VARIABLE_18351))) ) 1.14/1.34 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_2 $$unsorted) (B_2 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_2) B_2))) (not (hBOOL (member_int B_2 (d22set A_2))))) ) 1.14/1.34 ( min, min ) 1.14/1.34 ( min, zero_zero_int ) 1.14/1.34 ( pls, min ) 1.14/1.34 ( pls, zero_zero_int ) 1.14/1.34 ( pls, one_one_int ) 1.14/1.34 ( pls, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( one_one_int, t ) 1.14/1.34 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_7 $$unsorted) (Y_6 $$unsorted)) (let ((_let_0 (bit0 (bit1 pls)))) (let ((_let_1 (number_number_of_nat _let_0))) (= (hAPP_nat_real (power_power_real (hAPP_real_real (minus_minus_real X_7) Y_6)) _let_1) (hAPP_real_real (minus_minus_real (hAPP_real_real (plus_plus_real (hAPP_nat_real (power_power_real X_7) _let_1)) (hAPP_nat_real (power_power_real Y_6) _let_1))) (hAPP_real_real (times_times_real (hAPP_real_real (times_times_real (number267125858f_real _let_0)) X_7)) Y_6))))) ) 1.14/1.34 ( one_one_real, one_one_real ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((Z_4 $$unsorted)) (= (hAPP_nat_nat (plus_plus_nat Z_4) Z_4) (hAPP_nat_nat (times_times_nat Z_4) (number_number_of_nat (bit0 (bit1 pls))))) ) 1.14/1.34 ( one_one_nat ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_14 $$unsorted) (Y_11 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat))) (or (not (= (hAPP_nat_nat (power_power_nat X_14) _let_0) (hAPP_nat_nat (power_power_nat Y_11) _let_0))) (not (hBOOL (hAPP_nat_bool _let_1 X_14))) (not (hBOOL (hAPP_nat_bool _let_1 Y_11))) (= X_14 Y_11)))) ) 1.14/1.34 ( zero_zero_nat, zero_zero_nat ) 1.14/1.34 ( zero_zero_nat, one_one_nat ) 1.14/1.34 ( one_one_nat, zero_zero_nat ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((B_19 $$unsorted) (A_21 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_21))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_19) zero_zero_int))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (times_times_int B_19) A_21)) zero_zero_int))) ) 1.14/1.34 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_3 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_95 $$unsorted)) (or (not (is_int A_95)) (= A_95 (hAPP_int_int (plus_plus_int (number_number_of_int pls)) A_95))) ) 1.14/1.34 ( min ) 1.14/1.34 ( zero_zero_int ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ( t ) 1.14/1.34 ( m ) 1.14/1.34 ( s1 ) 1.14/1.34 ( s ) 1.14/1.34 ( (undefined_int int) ) 1.14/1.34 ( skv_1 ) 1.14/1.34 ( skv_2 ) 1.14/1.34 ( skv_3 ) 1.14/1.34 ( skv_4 ) 1.14/1.34 ( skv_5 ) 1.14/1.34 ( skv_6 ) 1.14/1.34 ( skv_7 ) 1.14/1.34 ( skv_8 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_80 $$unsorted)) (or (not (is_int A_80)) (= A_80 (hAPP_int_int (plus_plus_int zero_zero_int) A_80))) ) 1.14/1.34 ( min ) 1.14/1.34 ( zero_zero_int ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ( t ) 1.14/1.34 ( m ) 1.14/1.34 ( s1 ) 1.14/1.34 ( s ) 1.14/1.34 ( (undefined_int int) ) 1.14/1.34 ( skv_1 ) 1.14/1.34 ( skv_2 ) 1.14/1.34 ( skv_3 ) 1.14/1.34 ( skv_4 ) 1.14/1.34 ( skv_5 ) 1.14/1.34 ( skv_6 ) 1.14/1.34 ( skv_7 ) 1.14/1.34 ( skv_8 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((Z $$unsorted) (W $$unsorted)) (or (not (is_int Z)) (not (is_int W)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Z) W))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int W) Z))) (= Z W)) ) 1.14/1.34 ( min, min ) 1.14/1.34 ( min, pls ) 1.14/1.34 ( pls, min ) 1.14/1.34 ( pls, one_one_int ) 1.14/1.34 ( pls, (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.34 ( pls, (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.34 ( pls, (number_number_of_int pls) ) 1.14/1.34 ( pls, s ) 1.14/1.34 ( pls, skv_1 ) 1.14/1.34 ( pls, skv_2 ) 1.14/1.34 ( one_one_int, pls ) 1.14/1.34 ( one_one_int, t ) 1.14/1.34 ( t, one_one_int ) 1.14/1.34 ( (number_number_of_int (bit0 (bit1 pls))), pls ) 1.14/1.34 ( (number_number_of_int (bit1 (bit1 pls))), pls ) 1.14/1.34 ( (number_number_of_int pls), pls ) 1.14/1.34 ( s, pls ) 1.14/1.34 ( skv_1, pls ) 1.14/1.34 ( skv_2, pls ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((N_37 $$unsorted) (A_89 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_int one_one_int))) (or (not (hBOOL (hAPP_int_bool _let_0 A_89))) (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (times_times_int A_89) (hAPP_nat_int (power_power_int A_89) N_37)))))) ) 1.14/1.34 ( zero_zero_nat, zero_zero_int ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_int ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), s1 ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), s ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), skv_4 ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), skv_5 ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), skv_6 ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), skv_7 ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), skv_8 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_79 $$unsorted)) (or (not (is_int A_79)) (= A_79 (hAPP_int_int (plus_plus_int A_79) zero_zero_int))) ) 1.14/1.34 ( min ) 1.14/1.34 ( zero_zero_int ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ( t ) 1.14/1.34 ( m ) 1.14/1.34 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.34 ( s1 ) 1.14/1.34 ( s ) 1.14/1.34 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (undefined_int int) ) 1.14/1.34 ( skv_1 ) 1.14/1.34 ( skv_2 ) 1.14/1.34 ( skv_3 ) 1.14/1.34 ( skv_4 ) 1.14/1.34 ( skv_5 ) 1.14/1.34 ( skv_6 ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( skv_7 ) 1.14/1.34 ( skv_8 ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (= (= zero_zero_real (hAPP_real_real (plus_plus_real (hAPP_nat_real (power_power_real X_2) _let_0)) (hAPP_nat_real (power_power_real Y_2) _let_0))) (and (= zero_zero_real X_2) (= zero_zero_real Y_2)))) ) 1.14/1.34 ( one_one_real, one_one_real ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((B_21 $$unsorted) (A_23 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_23) zero_zero_int))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_21) zero_zero_int))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int (times_times_int A_23) B_21)))) ) 1.14/1.34 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( m, (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.34 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((P_1 $$unsorted)) (let ((_let_0 (bit1 pls))) (let ((_let_1 (bit0 _let_0))) (or (not (is_int P_1)) (not (hBOOL (hAPP_int_bool zprime P_1))) (= (number_number_of_int _let_1) P_1) (= (number_number_of_int (bit1 _let_0)) P_1) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (number_number_of_int (bit1 _let_1))) P_1))))) ) 1.14/1.34 ( min ) 1.14/1.34 ( zero_zero_int ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ( t ) 1.14/1.34 ( m ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( s1 ) 1.14/1.34 ( (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.34 ( s ) 1.14/1.34 ( (undefined_int int) ) 1.14/1.34 ( skv_1 ) 1.14/1.34 ( skv_2 ) 1.14/1.34 ( skv_3 ) 1.14/1.34 ( skv_4 ) 1.14/1.34 ( skv_5 ) 1.14/1.34 ( skv_6 ) 1.14/1.34 ( skv_7 ) 1.14/1.34 ( skv_8 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_81 $$unsorted)) (= zero_zero_int (hAPP_int_int (times_times_int A_81) zero_zero_int)) ) 1.14/1.34 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((B_48 $$unsorted) (Q_4 $$unsorted) (R_3 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int B_48) Q_4)) R_3)) zero_zero_int))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) R_3))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_48))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Q_4) zero_zero_int))) ) 1.14/1.34 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m, one_one_int ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_2 $$unsorted)) (or (not (is_int A_2)) (= (= zero_zero_int A_2) (= zero_zero_int (hAPP_nat_int (power_power_int A_2) (number_number_of_nat (bit0 (bit1 pls))))))) ) 1.14/1.34 ( min ) 1.14/1.34 ( zero_zero_int ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ( t ) 1.14/1.34 ( m ) 1.14/1.34 ( s1 ) 1.14/1.34 ( s ) 1.14/1.34 ( (undefined_int int) ) 1.14/1.34 ( skv_1 ) 1.14/1.34 ( skv_2 ) 1.14/1.34 ( skv_3 ) 1.14/1.34 ( skv_4 ) 1.14/1.34 ( skv_5 ) 1.14/1.34 ( skv_6 ) 1.14/1.34 ( skv_7 ) 1.14/1.34 ( skv_8 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((B_2 $$unsorted) (A_2 $$unsorted)) (or (not (hBOOL (member_int B_2 (d22set A_2)))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_2) A_2))) ) 1.14/1.34 ( min, min ) 1.14/1.34 ( min, pls ) 1.14/1.34 ( pls, min ) 1.14/1.34 ( pls, one_one_int ) 1.14/1.34 ( pls, (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.34 ( pls, (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.34 ( pls, (number_number_of_int pls) ) 1.14/1.34 ( pls, s ) 1.14/1.34 ( pls, skv_1 ) 1.14/1.34 ( pls, skv_2 ) 1.14/1.34 ( one_one_int, t ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_112 $$unsorted)) (= (hAPP_real_real (times_times_real A_112) A_112) (hAPP_nat_real (power_power_real A_112) (number_number_of_nat (bit0 (bit1 pls))))) ) 1.14/1.34 ( one_one_real ) 1.14/1.34 ( zero_zero_real ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((W_15 $$unsorted)) (= (number_number_of_int (hAPP_int_int (plus_plus_int (bit1 pls)) W_15)) (hAPP_int_int (plus_plus_int one_one_int) (number_number_of_int W_15))) ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_85 $$unsorted) (N_32 $$unsorted) (B_54 $$unsorted)) (let ((_let_0 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (or (not (= (hAPP_nat_real (power_power_real B_54) N_32) (hAPP_nat_real (power_power_real A_85) N_32))) (not (hBOOL (hAPP_real_bool _let_0 A_85))) (not (hBOOL (hAPP_real_bool _let_0 B_54))) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_32))) (= A_85 B_54))) ) 1.14/1.34 ( one_one_real, (number_number_of_nat (bit0 (bit1 pls))), one_one_real ) 1.14/1.34 ( one_one_real, (number_number_of_nat (bit0 (bit1 pls))), zero_zero_real ) 1.14/1.34 ( zero_zero_real, (number_number_of_nat (bit0 (bit1 pls))), one_one_real ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((M $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_0 (hAPP_n1699378549t_bool ord_less_nat I_1))) (or (not (hBOOL (hAPP_nat_bool _let_0 J_1))) (hBOOL (hAPP_nat_bool _let_0 (hAPP_nat_nat (plus_plus_nat J_1) M))))) ) 1.14/1.34 ( one_one_nat, zero_zero_nat, one_one_nat ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((K_1 $$unsorted)) (or (not (is_int K_1)) (= K_1 (hAPP_int_int (plus_plus_int pls) K_1))) ) 1.14/1.34 ( min ) 1.14/1.34 ( zero_zero_int ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ( t ) 1.14/1.34 ( m ) 1.14/1.34 ( s1 ) 1.14/1.34 ( s ) 1.14/1.34 ( (undefined_int int) ) 1.14/1.34 ( skv_1 ) 1.14/1.34 ( skv_2 ) 1.14/1.34 ( skv_3 ) 1.14/1.34 ( skv_4 ) 1.14/1.34 ( skv_5 ) 1.14/1.34 ( skv_6 ) 1.14/1.34 ( skv_7 ) 1.14/1.34 ( skv_8 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((I_1 $$unsorted) (J_1 $$unsorted)) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I_1) J_1))) (not (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) K_2))) (not (= J_1 (hAPP_nat_nat (plus_plus_nat I_1) K_2)))) ))) ) 1.14/1.34 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((M $$unsorted)) (= M (hAPP_nat_nat (plus_plus_nat M) zero_zero_nat)) ) 1.14/1.34 ( one_one_nat ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((P_2 $$unsorted) (K $$unsorted) (I_2 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K) I_2))) (not (hBOOL (hAPP_int_bool P_2 K))) (not (forall ((I $$unsorted)) (or (not (is_int I)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K) I))) (not (hBOOL (hAPP_int_bool P_2 I))) (hBOOL (hAPP_int_bool P_2 (hAPP_int_int (plus_plus_int I) one_one_int)))) )) (hBOOL (hAPP_int_bool P_2 I_2))) ) 1.14/1.34 ( (hAPP_i1948725293t_bool ord_less_int zero_zero_int), one_one_int, t ) 1.14/1.34 ( (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int), pls, min ) 1.14/1.34 ( (hAPP_i1948725293t_bool ord_less_int min), min, min ) 1.14/1.34 ( (hAPP_i1948725293t_bool ord_less_int min), pls, s ) 1.14/1.34 ( (hAPP_i1948725293t_bool ord_less_eq_int pls), min, pls ) 1.14/1.34 ( (hAPP_i1948725293t_bool ord_less_eq_int min), pls, (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.34 ( (hAPP_i1948725293t_bool ord_less_int pls), pls, (number_number_of_int pls) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_1 $$unsorted) (M $$unsorted) (Y_1 $$unsorted)) (or (not (= (hAPP_int_int (div_mod_int X_1) M) (hAPP_int_int (div_mod_int Y_1) M))) (hBOOL (hAPP_int_bool (zcong X_1 Y_1) M))) ) 1.14/1.34 ( s1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), s ) 1.14/1.34 ( s1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_1 ) 1.14/1.34 ( s1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_2 ) 1.14/1.34 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (number_number_of_int min) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (number_number_of_int min) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_4) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (number_number_of_int min) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((K_1 $$unsorted)) (or (not (is_int K_1)) (= K_1 (hAPP_int_int (plus_plus_int K_1) pls))) ) 1.14/1.34 ( min ) 1.14/1.34 ( zero_zero_int ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ( t ) 1.14/1.34 ( m ) 1.14/1.34 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.34 ( s1 ) 1.14/1.34 ( s ) 1.14/1.34 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (undefined_int int) ) 1.14/1.34 ( skv_1 ) 1.14/1.34 ( skv_2 ) 1.14/1.34 ( skv_3 ) 1.14/1.34 ( skv_4 ) 1.14/1.34 ( skv_5 ) 1.14/1.34 ( skv_6 ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( skv_7 ) 1.14/1.34 ( skv_8 ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((V_21 $$unsorted)) (= (number267125858f_real (hAPP_int_int (plus_plus_int V_21) (bit1 pls))) (hAPP_real_real (plus_plus_real (number267125858f_real V_21)) one_one_real)) ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((W_6 $$unsorted)) (= (hAPP_int_int (times_times_int (hAPP_int_int (plus_plus_int one_one_int) one_one_int)) (number_number_of_int W_6)) (number_number_of_int (bit0 W_6))) ) 1.14/1.34 ( pls ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ( (bit0 (bit1 pls)) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((B_1_1 $$unsorted)) (or (not (is_int B_1_1)) (is_int (number_number_of_int B_1_1))) ) 1.14/1.34 ( min ) 1.14/1.34 ( pls ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ( (bit0 (bit1 pls)) ) 1.14/1.34 ( (bit0 (bit0 (bit1 pls))) ) 1.14/1.34 ( (bit1 (bit1 pls)) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((K_1 $$unsorted)) (or (not (is_int K_1)) (= K_1 (hAPP_int_int (minus_minus_int K_1) pls))) ) 1.14/1.34 ( min ) 1.14/1.34 ( zero_zero_int ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ( t ) 1.14/1.34 ( m ) 1.14/1.34 ( s1 ) 1.14/1.34 ( s ) 1.14/1.34 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (undefined_int int) ) 1.14/1.34 ( skv_1 ) 1.14/1.34 ( skv_2 ) 1.14/1.34 ( skv_3 ) 1.14/1.34 ( skv_4 ) 1.14/1.34 ( skv_5 ) 1.14/1.34 ( skv_6 ) 1.14/1.34 ( skv_7 ) 1.14/1.34 ( skv_8 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((B $$unsorted) (Q_1 $$unsorted) (R_1 $$unsorted) (B_48 $$unsorted) (Q_4 $$unsorted) (R_3 $$unsorted)) (let ((_let_0 (times_times_int B_48))) (let ((_let_1 (plus_plus_int (hAPP_int_int _let_0 Q_4)))) (let ((_let_2 (hAPP_int_int _let_1 R_3))) (or (not (= _let_2 (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int B) Q_1)) R_1))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_2) zero_zero_int))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int R_1) B))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) R_3))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_48))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_48) B))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Q_4) Q_1)))))) ) 1.14/1.34 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m, one_one_int, (number_number_of_int (bit0 (bit0 (bit1 pls)))), m, one_one_int ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((N_25 $$unsorted) (A_76 $$unsorted)) (let ((_let_0 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (or (not (hBOOL (hAPP_real_bool _let_0 A_76))) (hBOOL (hAPP_real_bool _let_0 (hAPP_nat_real (power_power_real A_76) N_25))))) ) 1.14/1.34 ( zero_zero_nat, zero_zero_real ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_real ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_real ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((B_29 $$unsorted) (A_31 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (or (and (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_29) zero_zero_int))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_31) zero_zero_int)))) (or (not (hBOOL (hAPP_int_bool _let_0 B_29))) (not (hBOOL (hAPP_int_bool _let_0 A_31))))) (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (times_times_int A_31) B_29))))) ) 1.14/1.34 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( m, (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.34 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((N_19 $$unsorted) (A_71 $$unsorted)) (let ((_let_0 (power_power_nat A_71))) (let ((_let_1 (hAPP_nat_nat _let_0 N_19))) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) A_71))) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_71) one_one_nat))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (times_times_nat A_71) _let_1)) _let_1))))) ) 1.14/1.34 ( zero_zero_nat, zero_zero_nat ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_nat ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (power_power_int B_2))) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) B_2))) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int _let_0 X_2)) (hAPP_nat_int _let_0 Y_2))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat X_2) Y_2))))) ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat, zero_zero_int ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (or (not (hBOOL (hAPP_int_bool _let_0 X_1))) (not (hBOOL (hAPP_int_bool _let_0 Y_1))) (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (times_times_int X_1) Y_1))))) ) 1.14/1.34 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( m, (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.34 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((N_1 $$unsorted)) (or (= zero_zero_nat N_1) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1))) ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_93 $$unsorted)) (or (not (is_int A_93)) (= A_93 (hAPP_int_int (times_times_int (number_number_of_int (bit1 pls))) A_93))) ) 1.14/1.34 ( min ) 1.14/1.34 ( zero_zero_int ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ( t ) 1.14/1.34 ( m ) 1.14/1.34 ( s1 ) 1.14/1.34 ( s ) 1.14/1.34 ( (undefined_int int) ) 1.14/1.34 ( skv_1 ) 1.14/1.34 ( skv_2 ) 1.14/1.34 ( skv_3 ) 1.14/1.34 ( skv_4 ) 1.14/1.34 ( skv_5 ) 1.14/1.34 ( skv_6 ) 1.14/1.34 ( skv_7 ) 1.14/1.34 ( skv_8 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_2 $$unsorted)) (or (not (is_int A_2)) (= (= zero_zero_int A_2) (= zero_zero_int (hAPP_int_int (plus_plus_int A_2) A_2)))) ) 1.14/1.34 ( min ) 1.14/1.34 ( zero_zero_int ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ( t ) 1.14/1.34 ( m ) 1.14/1.34 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.34 ( s1 ) 1.14/1.34 ( s ) 1.14/1.34 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (undefined_int int) ) 1.14/1.34 ( skv_1 ) 1.14/1.34 ( skv_2 ) 1.14/1.34 ( skv_3 ) 1.14/1.34 ( skv_4 ) 1.14/1.34 ( skv_5 ) 1.14/1.34 ( skv_6 ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( skv_7 ) 1.14/1.34 ( skv_8 ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A $$unsorted)) (let ((_let_0 (bit1 pls))) (let ((_let_1 (power_power_int A))) (= (hAPP_int_int (times_times_int A) (hAPP_nat_int _let_1 (number_number_of_nat (bit0 _let_0)))) (hAPP_nat_int _let_1 (number_number_of_nat (bit1 _let_0)))))) ) 1.14/1.34 ( zero_zero_int ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( s1 ) 1.14/1.34 ( s ) 1.14/1.34 ( skv_4 ) 1.14/1.34 ( skv_5 ) 1.14/1.34 ( skv_6 ) 1.14/1.34 ( skv_7 ) 1.14/1.34 ( skv_8 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_70 $$unsorted)) (= A_70 (hAPP_nat_real (power_power_real A_70) one_one_nat)) ) 1.14/1.34 ( one_one_real ) 1.14/1.34 ( zero_zero_real ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (= (or (not (= zero_zero_real Y_2)) (not (= zero_zero_real X_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_real_real (plus_plus_real (hAPP_nat_real (power_power_real X_2) _let_0)) (hAPP_nat_real (power_power_real Y_2) _let_0)))))) ) 1.14/1.34 ( one_one_real, one_one_real ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((N_27 $$unsorted) (A_78 $$unsorted)) (let ((_let_0 (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat))) (or (not (hBOOL (hAPP_nat_bool _let_0 A_78))) (hBOOL (hAPP_nat_bool _let_0 (hAPP_nat_nat (power_power_nat A_78) N_27))))) ) 1.14/1.34 ( zero_zero_nat, zero_zero_nat ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_nat ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (or (not (is_int Y_2)) (not (is_int X_2)) (= (= zero_zero_int (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int X_2) _let_0)) (hAPP_nat_int (power_power_int Y_2) _let_0))) (and (= zero_zero_int X_2) (= zero_zero_int Y_2))))) ) 1.14/1.34 ( one_one_int, one_one_int ) 1.14/1.34 ( s, one_one_int ) 1.14/1.34 ( skv_5, skv_6 ) 1.14/1.34 ( skv_7, skv_8 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((K $$unsorted) (L_1 $$unsorted)) (or (not (is_int K)) (not (is_int L_1)) (= (= (bit1 L_1) (bit1 K)) (= K L_1))) ) 1.14/1.34 ( min, min ) 1.14/1.34 ( min, zero_zero_int ) 1.14/1.34 ( zero_zero_int, min ) 1.14/1.34 ( pls, (undefined_int int) ) 1.14/1.34 ( one_one_int, one_one_int ) 1.14/1.34 ( one_one_int, m ) 1.14/1.34 ( t, t ) 1.14/1.34 ( t, s ) 1.14/1.34 ( m, one_one_int ) 1.14/1.34 ( s1, s1 ) 1.14/1.34 ( s1, skv_1 ) 1.14/1.34 ( s, t ) 1.14/1.34 ( (undefined_int int), pls ) 1.14/1.34 ( (undefined_int int), (undefined_int int) ) 1.14/1.34 ( skv_1, s1 ) 1.14/1.34 ( skv_2, skv_2 ) 1.14/1.34 ( skv_2, skv_3 ) 1.14/1.34 ( skv_3, skv_2 ) 1.14/1.34 ( skv_4, skv_4 ) 1.14/1.34 ( skv_4, skv_5 ) 1.14/1.34 ( skv_5, skv_4 ) 1.14/1.34 ( skv_6, skv_6 ) 1.14/1.34 ( skv_6, skv_8 ) 1.14/1.34 ( skv_7, skv_7 ) 1.14/1.34 ( skv_8, skv_6 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((P_1 $$unsorted)) (or (not (hBOOL (hAPP_int_bool zprime P_1))) (hBOOL (hAPP_int_bool (zcong (zfact (hAPP_int_int (minus_minus_int P_1) one_one_int)) (number_number_of_int min)) P_1))) ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((V_7 $$unsorted) (V_8 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_int V_7))) (let ((_let_1 (hBOOL (hAPP_int_bool _let_0 V_8)))) (= (and (or (not _let_1) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) V_8))) _let_1) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (number_number_of_nat V_7)) (number_number_of_nat V_8)))))) ) 1.14/1.34 ( min, min ) 1.14/1.34 ( min, zero_zero_int ) 1.14/1.34 ( pls, min ) 1.14/1.34 ( pls, zero_zero_int ) 1.14/1.34 ( pls, one_one_int ) 1.14/1.34 ( pls, (bit0 (bit1 pls)) ) 1.14/1.34 ( pls, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( one_one_int, t ) 1.14/1.34 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (bit0 (bit1 pls)))) (let ((_let_1 (number_number_of_nat _let_0))) (let ((_let_2 (power_power_int X_1))) (= (hAPP_nat_int (power_power_int (hAPP_nat_int _let_2 _let_1)) _let_1) (hAPP_nat_int _let_2 (number_number_of_nat (bit0 _let_0))))))) ) 1.14/1.34 ( zero_zero_int ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (or (not (is_int M)) (not (is_int N_1)) (not (hBOOL (hAPP_int_bool _let_0 M))) (not (hBOOL (hAPP_int_bool _let_0 N_1))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int M) N_1))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int N_1) M))) (= N_1 M))) ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int) ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((B $$unsorted) (A $$unsorted) (C $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) C))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B) C))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A) B)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B) A))) ) 1.14/1.34 ( min, min, min ) 1.14/1.34 ( pls, pls, zero_zero_int ) 1.14/1.34 ( one_one_int, pls, one_one_int ) 1.14/1.34 ( t, t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( s, min, zero_zero_int ) 1.14/1.34 ( skv_1, s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( skv_2, pls, min ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((N_38 $$unsorted) (A_90 $$unsorted)) (let ((_let_0 (power_power_real A_90))) (let ((_let_1 (hAPP_nat_real _let_0 N_38))) (or (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) A_90))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_1) (hAPP_real_real (times_times_real A_90) _let_1)))))) ) 1.14/1.34 ( zero_zero_nat, zero_zero_real ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_real ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_real ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((BOUND_VARIABLE_19082 $$unsorted) (BOUND_VARIABLE_19083 $$unsorted)) (or (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int BOUND_VARIABLE_19083) pls)) (= (hAPP_nat_nat (times_times_nat (number_number_of_nat BOUND_VARIABLE_19083)) (number_number_of_nat BOUND_VARIABLE_19082)) (number_number_of_nat (hAPP_int_int (times_times_int BOUND_VARIABLE_19083) BOUND_VARIABLE_19082)))) ) 1.14/1.34 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( m, (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.34 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((M_10 $$unsorted)) (= (hAPP_nat_nat (times_times_nat (hAPP_nat_nat (plus_plus_nat one_one_nat) one_one_nat)) M_10) (hAPP_nat_nat (plus_plus_nat M_10) M_10)) ) 1.14/1.34 ( one_one_nat ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((N_6 $$unsorted) (A_56 $$unsorted)) (let ((_let_0 (hAPP_n1699378549t_bool ord_less_nat one_one_nat))) (or (not (hBOOL (hAPP_nat_bool _let_0 A_56))) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_6))) (hBOOL (hAPP_nat_bool _let_0 (hAPP_nat_nat (power_power_nat A_56) N_6))))) ) 1.14/1.34 ( zero_zero_nat, zero_zero_nat ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_nat ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP_int_bool twoSqu1154269391sum2sq X_1))) (not (hBOOL (hAPP_int_bool twoSqu1154269391sum2sq Y_1))) (hBOOL (hAPP_int_bool twoSqu1154269391sum2sq (hAPP_int_int (times_times_int X_1) Y_1)))) ) 1.14/1.34 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( m, (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.34 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (or (not (hBOOL (hAPP_int_bool _let_0 X_1))) (not (hBOOL (hAPP_int_bool _let_0 Y_1))) (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (plus_plus_int X_1) Y_1))))) ) 1.14/1.34 ( one_one_int, one_one_int ) 1.14/1.34 ( one_one_int, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.34 ( one_one_int, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_6) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_8) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((B_2 $$unsorted) (A_2 $$unsorted)) (= (= B_2 (hAPP_nat_nat (plus_plus_nat B_2) A_2)) (= zero_zero_nat A_2)) ) 1.14/1.34 ( one_one_nat, one_one_nat ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((K $$unsorted) (L_1 $$unsorted)) (or (not (is_int L_1)) (not (is_int K)) (= (= (bit0 L_1) (bit0 K)) (= K L_1))) ) 1.14/1.34 ( min, min ) 1.14/1.34 ( min, zero_zero_int ) 1.14/1.34 ( zero_zero_int, min ) 1.14/1.34 ( pls, (undefined_int int) ) 1.14/1.34 ( one_one_int, one_one_int ) 1.14/1.34 ( one_one_int, m ) 1.14/1.34 ( t, t ) 1.14/1.34 ( t, s ) 1.14/1.34 ( m, one_one_int ) 1.14/1.34 ( s1, s1 ) 1.14/1.34 ( s1, skv_1 ) 1.14/1.34 ( s, t ) 1.14/1.34 ( (undefined_int int), pls ) 1.14/1.34 ( (undefined_int int), (undefined_int int) ) 1.14/1.34 ( skv_1, s1 ) 1.14/1.34 ( skv_2, skv_2 ) 1.14/1.34 ( skv_2, skv_3 ) 1.14/1.34 ( skv_3, skv_2 ) 1.14/1.34 ( skv_4, skv_4 ) 1.14/1.34 ( skv_4, skv_5 ) 1.14/1.34 ( skv_5, skv_4 ) 1.14/1.34 ( skv_6, skv_6 ) 1.14/1.34 ( skv_6, skv_8 ) 1.14/1.34 ( skv_7, skv_7 ) 1.14/1.34 ( skv_8, skv_6 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((BOUND_VARIABLE_19369 $$unsorted)) (or (= zero_zero_nat BOUND_VARIABLE_19369) (= zero_zero_int (hAPP_nat_int (power_power_int zero_zero_int) BOUND_VARIABLE_19369))) ) 1.14/1.34 ( zero_zero_nat ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((B_10 $$unsorted) (A_11 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_11) zero_zero_int))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_10))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (times_times_int A_11) B_10)) zero_zero_int))) ) 1.14/1.34 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( m, (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.34 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((N_12 $$unsorted) (A_62 $$unsorted)) (let ((_let_0 (hAPP_n1699378549t_bool ord_less_eq_nat one_one_nat))) (or (not (hBOOL (hAPP_nat_bool _let_0 A_62))) (hBOOL (hAPP_nat_bool _let_0 (hAPP_nat_nat (power_power_nat A_62) N_12))))) ) 1.14/1.34 ( zero_zero_nat, zero_zero_nat ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_nat ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_9 $$unsorted) (B_8 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (or (not (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (times_times_int A_9) B_8)))) (not (hBOOL (hAPP_int_bool _let_0 A_9))) (hBOOL (hAPP_int_bool _let_0 B_8)))) ) 1.14/1.34 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_3 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((BOUND_VARIABLE_19466 $$unsorted)) (let ((_let_0 (number_number_of_nat BOUND_VARIABLE_19466))) (or (not (= zero_zero_nat _let_0)) (= one_one_int (hAPP_nat_int (power_power_int zero_zero_int) _let_0)))) ) 1.14/1.34 ( pls ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ( (bit0 (bit1 pls)) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((BOUND_VARIABLE_19475 $$unsorted)) (let ((_let_0 (number_number_of_nat BOUND_VARIABLE_19475))) (or (= zero_zero_nat _let_0) (= zero_zero_int (hAPP_nat_int (power_power_int zero_zero_int) _let_0)))) ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ( (bit0 (bit1 pls)) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_100 $$unsorted)) (or (not (is_int A_100)) (= A_100 (hAPP_int_int (times_times_int A_100) one_one_int))) ) 1.14/1.34 ( min ) 1.14/1.34 ( zero_zero_int ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ( t ) 1.14/1.34 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.34 ( m ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( s1 ) 1.14/1.34 ( s ) 1.14/1.34 ( (undefined_int int) ) 1.14/1.34 ( skv_1 ) 1.14/1.34 ( skv_2 ) 1.14/1.34 ( skv_3 ) 1.14/1.34 ( skv_4 ) 1.14/1.34 ( skv_5 ) 1.14/1.34 ( skv_6 ) 1.14/1.34 ( skv_7 ) 1.14/1.34 ( skv_8 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((W_7 $$unsorted)) (let ((_let_0 (number_number_of_int W_7))) (= (hAPP_int_int (plus_plus_int (hAPP_int_int (plus_plus_int one_one_int) _let_0)) _let_0) (number_number_of_int (bit1 W_7)))) ) 1.14/1.34 ( min ) 1.14/1.34 ( pls ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (bit0 (bit1 pls)))) (let ((_let_1 (number_number_of_nat _let_0))) (= (hAPP_nat_int (power_power_int (hAPP_int_int (plus_plus_int X_2) Y_2)) _let_1) (hAPP_int_int (plus_plus_int (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int X_2) _let_1)) (hAPP_nat_int (power_power_int Y_2) _let_1))) (hAPP_int_int (times_times_int (hAPP_int_int (times_times_int (number_number_of_int _let_0)) X_2)) Y_2))))) ) 1.14/1.34 ( one_one_int, one_one_int ) 1.14/1.34 ( s, one_one_int ) 1.14/1.34 ( skv_5, skv_6 ) 1.14/1.34 ( skv_7, skv_8 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (= (hAPP_nat_nat (plus_plus_nat N_1) M) (hAPP_nat_nat (plus_plus_nat M) N_1)) ) 1.14/1.34 ( one_one_nat, one_one_nat ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_2 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (or (not (is_int B_2)) (= (hBOOL (hAPP_int_bool (zcong A_2 B_2) Ma)) (not (forall ((K_2 $$unsorted)) (or (not (= B_2 (hAPP_int_int (plus_plus_int A_2) (hAPP_int_int (times_times_int Ma) K_2)))) (not (is_int K_2))) )))) ) 1.14/1.34 ( s1, s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( s1, skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( s1, skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_4) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_22 $$unsorted) (P_6 $$unsorted) (Q_6 $$unsorted)) (let ((_let_0 (power_power_real X_22))) (= (hAPP_real_real (times_times_real (hAPP_nat_real _let_0 P_6)) (hAPP_nat_real _let_0 Q_6)) (hAPP_nat_real _let_0 (hAPP_nat_nat (plus_plus_nat P_6) Q_6)))) ) 1.14/1.34 ( one_one_real, one_one_nat, one_one_nat ) 1.14/1.34 ( zero_zero_real, one_one_nat, one_one_nat ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_8 $$unsorted) (Y_7 $$unsorted)) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat X_8) Y_7))) (= X_8 Y_7) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_8) Y_7))) ) 1.14/1.34 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_94 $$unsorted)) (or (not (is_int A_94)) (= A_94 (hAPP_int_int (plus_plus_int A_94) (number_number_of_int pls)))) ) 1.14/1.34 ( min ) 1.14/1.34 ( zero_zero_int ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ( t ) 1.14/1.34 ( m ) 1.14/1.34 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.34 ( s1 ) 1.14/1.34 ( s ) 1.14/1.34 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (undefined_int int) ) 1.14/1.34 ( skv_1 ) 1.14/1.34 ( skv_2 ) 1.14/1.34 ( skv_3 ) 1.14/1.34 ( skv_4 ) 1.14/1.34 ( skv_5 ) 1.14/1.34 ( skv_6 ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( skv_7 ) 1.14/1.34 ( skv_8 ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((B $$unsorted) (A $$unsorted)) (or (not (is_int A)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) B))) (= A (hAPP_int_int (div_mod_int A) B))) ) 1.14/1.34 ( min, min ) 1.14/1.34 ( min, pls ) 1.14/1.34 ( zero_zero_int, min ) 1.14/1.34 ( zero_zero_int, pls ) 1.14/1.34 ( one_one_int, pls ) 1.14/1.34 ( t, one_one_int ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), pls ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), s ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_1 ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_2 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((V_13 $$unsorted) (W_12 $$unsorted)) (= (hAPP_real_real (times_times_real (number267125858f_real V_13)) (number267125858f_real W_12)) (number267125858f_real (hAPP_int_int (times_times_int V_13) W_12))) ) 1.14/1.34 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_3 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((K_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool dvd_dvd_int K_1))) (or (not (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (minus_minus_int M) N_1)))) (not (hBOOL (hAPP_int_bool _let_0 N_1))) (hBOOL (hAPP_int_bool _let_0 M)))) ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_74 $$unsorted) (N_23 $$unsorted) (N_22 $$unsorted)) (let ((_let_0 (power_power_int A_74))) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_23) N_22))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_74))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_74) one_one_int))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int _let_0 N_22)) (hAPP_nat_int _let_0 N_23))))) ) 1.14/1.34 ( zero_zero_int, zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ( zero_zero_int, (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_2 $$unsorted) (B_2 $$unsorted)) (or (not (is_int B_2)) (not (is_int A_2)) (= (= zero_zero_int (hAPP_int_int (times_times_int A_2) B_2)) (or (= zero_zero_int B_2) (= zero_zero_int A_2)))) ) 1.14/1.34 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.34 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_3 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_2 $$unsorted) (N $$unsorted)) (or (not (is_int A_2)) (= (and (= zero_zero_int A_2) (not (= zero_zero_nat N))) (= zero_zero_int (hAPP_nat_int (power_power_int A_2) N)))) ) 1.14/1.34 ( zero_zero_int, zero_zero_nat ) 1.14/1.34 ( zero_zero_int, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ( one_one_int, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ( s1, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ( s, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ( skv_4, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ( skv_5, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ( skv_6, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ( skv_7, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ( skv_8, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_73 $$unsorted) (N_21 $$unsorted) (N_20 $$unsorted)) (let ((_let_0 (power_power_int A_73))) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_21) N_20))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_73))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_73) one_one_int))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int _let_0 N_20)) (hAPP_nat_int _let_0 N_21))))) ) 1.14/1.34 ( zero_zero_int, zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ( zero_zero_int, (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((V_5 $$unsorted) (W_3 $$unsorted)) (= (number267125858f_real (hAPP_int_int (minus_minus_int V_5) W_3)) (hAPP_real_real (minus_minus_real (number267125858f_real V_5)) (number267125858f_real W_3))) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((K $$unsorted)) (or (not (is_int K)) (= (= pls K) (= pls (bit0 K)))) ) 1.14/1.34 ( min ) 1.14/1.34 ( zero_zero_int ) 1.14/1.34 ( pls ) 1.14/1.34 ( one_one_int ) 1.14/1.34 ( t ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ( (bit0 (bit1 pls)) ) 1.14/1.34 ( m ) 1.14/1.34 ( s1 ) 1.14/1.34 ( s ) 1.14/1.34 ( (undefined_int int) ) 1.14/1.34 ( skv_1 ) 1.14/1.34 ( skv_2 ) 1.14/1.34 ( skv_3 ) 1.14/1.34 ( skv_4 ) 1.14/1.34 ( skv_5 ) 1.14/1.34 ( skv_6 ) 1.14/1.34 ( skv_7 ) 1.14/1.34 ( skv_8 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (plus_plus_real (hAPP_nat_real (power_power_real X_2) _let_0)) (hAPP_nat_real (power_power_real Y_2) _let_0))) zero_zero_real)) (and (= zero_zero_real X_2) (= zero_zero_real Y_2)))) ) 1.14/1.34 ( one_one_real, one_one_real ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((Z_5 $$unsorted)) (= (hAPP_real_real (times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_5) (hAPP_real_real (plus_plus_real Z_5) Z_5)) ) 1.14/1.34 ( one_one_real ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (or (not (is_int Y_2)) (not (is_int X_2)) (= (or (not (= zero_zero_int X_2)) (not (= zero_zero_int Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int X_2) _let_0)) (hAPP_nat_int (power_power_int Y_2) _let_0))))))) ) 1.14/1.34 ( one_one_int, one_one_int ) 1.14/1.34 ( s, one_one_int ) 1.14/1.34 ( skv_5, skv_6 ) 1.14/1.34 ( skv_7, skv_8 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((BOUND_VARIABLE_19748 $$unsorted)) (let ((_let_0 (number_number_of_nat BOUND_VARIABLE_19748))) (or (not (= zero_zero_nat _let_0)) (= one_one_nat (hAPP_nat_nat (power_power_nat zero_zero_nat) _let_0)))) ) 1.14/1.34 ( pls ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ( (bit0 (bit1 pls)) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((BOUND_VARIABLE_19757 $$unsorted)) (let ((_let_0 (number_number_of_nat BOUND_VARIABLE_19757))) (or (= zero_zero_nat _let_0) (= zero_zero_nat (hAPP_nat_nat (power_power_nat zero_zero_nat) _let_0)))) ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ( (bit0 (bit1 pls)) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((B $$unsorted) (M $$unsorted) (A $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (or (not (is_int B)) (not (is_int A)) (not (hBOOL (hAPP_int_bool _let_0 A))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) M))) (not (hBOOL (hAPP_int_bool _let_0 B))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B) M))) (not (hBOOL (hAPP_int_bool (zcong A B) M))) (= B A))) ) 1.14/1.34 ( (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_nat_int (power_power_int skv_4) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), s1 ) 1.14/1.34 ( (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), s1 ) 1.14/1.34 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), s1 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((BOUND_VARIABLE_19829 $$unsorted) (BOUND_VARIABLE_19830 $$unsorted)) (let ((_let_0 (number_number_of_nat BOUND_VARIABLE_19829))) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int BOUND_VARIABLE_19830) pls))) (= _let_0 (hAPP_nat_nat (plus_plus_nat (number_number_of_nat BOUND_VARIABLE_19830)) _let_0)))) ) 1.14/1.34 ( (bit1 pls), (bit1 pls) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((BOUND_VARIABLE_19843 $$unsorted) (BOUND_VARIABLE_19844 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_int BOUND_VARIABLE_19843))) (let ((_let_1 (hBOOL (hAPP_int_bool _let_0 pls)))) (let ((_let_2 (plus_plus_nat (number_number_of_nat BOUND_VARIABLE_19844)))) (let ((_let_3 (number_number_of_nat BOUND_VARIABLE_19843))) (let ((_let_4 (hAPP_nat_nat _let_2 _let_3))) (or (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int BOUND_VARIABLE_19844) pls)) (and (or (not _let_1) (= (number_number_of_nat BOUND_VARIABLE_19844) _let_4)) (or _let_1 (= _let_4 (number_number_of_nat (hAPP_int_int (plus_plus_int BOUND_VARIABLE_19844) BOUND_VARIABLE_19843))))))))))) ) 1.14/1.34 ( one_one_int, one_one_int ) 1.14/1.34 ( one_one_int, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.34 ( one_one_int, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (bit1 pls), (bit1 pls) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_6) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_8) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_7 $$unsorted) (Y_6 $$unsorted)) (let ((_let_0 (bit0 (bit1 pls)))) (let ((_let_1 (number_number_of_nat _let_0))) (= (hAPP_nat_int (power_power_int (hAPP_int_int (minus_minus_int X_7) Y_6)) _let_1) (hAPP_int_int (minus_minus_int (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int X_7) _let_1)) (hAPP_nat_int (power_power_int Y_6) _let_1))) (hAPP_int_int (times_times_int (hAPP_int_int (times_times_int (number_number_of_int _let_0)) X_7)) Y_6))))) ) 1.14/1.34 ( one_one_int, one_one_int ) 1.14/1.34 ( s, one_one_int ) 1.14/1.34 ( skv_5, skv_6 ) 1.14/1.34 ( skv_7, skv_8 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((N_37 $$unsorted) (A_89 $$unsorted)) (let ((_let_0 (hAPP_r1134773055l_bool ord_less_real one_one_real))) (or (not (hBOOL (hAPP_real_bool _let_0 A_89))) (hBOOL (hAPP_real_bool _let_0 (hAPP_real_real (times_times_real A_89) (hAPP_nat_real (power_power_real A_89) N_37)))))) ) 1.14/1.34 ( zero_zero_nat, zero_zero_real ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_real ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_real ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP_int_bool (zcong A B) M))) (not (hBOOL (hAPP_int_bool (zcong B C) M))) (hBOOL (hAPP_int_bool (zcong A C) M))) ) 1.14/1.34 ( (number_number_of_int min), (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((Z_1 $$unsorted) (W_1 $$unsorted)) (or (not (is_int W_1)) (not (is_int Z_1)) (= (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Z_1) W_1)) (not (= Z_1 W_1))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Z_1) W_1)))) ) 1.14/1.34 ( min, min ) 1.14/1.34 ( min, zero_zero_int ) 1.14/1.34 ( min, pls ) 1.14/1.34 ( pls, min ) 1.14/1.34 ( pls, zero_zero_int ) 1.14/1.34 ( pls, one_one_int ) 1.14/1.34 ( pls, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( pls, (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.34 ( pls, (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.34 ( pls, (number_number_of_int pls) ) 1.14/1.34 ( pls, s ) 1.14/1.34 ( pls, skv_1 ) 1.14/1.34 ( pls, skv_2 ) 1.14/1.34 ( one_one_int, t ) 1.14/1.34 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (or (not (is_int Y_2)) (not (is_int X_2)) (= (and (= zero_zero_int X_2) (= zero_zero_int Y_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int X_2) _let_0)) (hAPP_nat_int (power_power_int Y_2) _let_0))) zero_zero_int))))) ) 1.14/1.34 ( one_one_int, one_one_int ) 1.14/1.34 ( s, one_one_int ) 1.14/1.34 ( skv_5, skv_6 ) 1.14/1.34 ( skv_7, skv_8 ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((M_11 $$unsorted) (A_96 $$unsorted)) (= (hAPP_int_int (times_times_int (hAPP_int_int (plus_plus_int A_96) one_one_int)) M_11) (hAPP_int_int (plus_plus_int M_11) (hAPP_int_int (times_times_int A_96) M_11))) ) 1.14/1.34 ( t, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.34 ( skv_3, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((W_16 $$unsorted)) (let ((_let_0 (number267125858f_real W_16))) (= (hAPP_nat_real (power_power_real _let_0) (number_number_of_nat (bit0 (bit1 pls)))) (hAPP_real_real (times_times_real _let_0) _let_0))) ) 1.14/1.34 ( pls ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ( (bit0 (bit1 pls)) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((N_38 $$unsorted) (A_90 $$unsorted)) (let ((_let_0 (power_power_nat A_90))) (let ((_let_1 (hAPP_nat_nat _let_0 N_38))) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) A_90))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat _let_1) (hAPP_nat_nat (times_times_nat A_90) _let_1)))))) ) 1.14/1.34 ( zero_zero_nat, zero_zero_nat ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.34 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_nat ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_103 $$unsorted) (N_39 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (let ((_let_1 (power_power_real A_103))) (= (hAPP_nat_real _let_1 (hAPP_nat_nat (times_times_nat _let_0) N_39)) (hAPP_nat_real (power_power_real (hAPP_nat_real _let_1 N_39)) _let_0)))) ) 1.14/1.34 ( zero_zero_real, zero_zero_nat ) 1.14/1.34 ( zero_zero_real, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((V_18 $$unsorted) (V_17 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (or (not (hBOOL (hAPP_int_bool _let_0 V_17))) (not (hBOOL (hAPP_int_bool _let_0 V_18))) (= (hAPP_nat_nat (plus_plus_nat (number_number_of_nat V_17)) (number_number_of_nat V_18)) (number_number_of_nat (hAPP_int_int (plus_plus_int V_17) V_18))))) ) 1.14/1.34 ( one_one_int, one_one_int ) 1.14/1.34 ( one_one_int, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.34 ( one_one_int, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (bit1 pls), (bit1 pls) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_6) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_8) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_bool (hAPP_i1948725293t_bool P R) Q) (hAPP_int_bool (cOMBC_int_int_bool P Q) R)) ) 1.14/1.34 ( ord_less_eq_int, min, min ) 1.14/1.34 ( ord_less_eq_int, min, pls ) 1.14/1.34 ( ord_less_eq_int, pls, min ) 1.14/1.34 ( ord_less_eq_int, one_one_int, pls ) 1.14/1.34 ( ord_less_eq_int, t, one_one_int ) 1.14/1.34 ( ord_less_eq_int, (number_number_of_int (bit0 (bit1 pls))), pls ) 1.14/1.34 ( ord_less_eq_int, (number_number_of_int (bit1 (bit1 pls))), pls ) 1.14/1.34 ( ord_less_eq_int, (number_number_of_int pls), pls ) 1.14/1.34 ( ord_less_eq_int, s, pls ) 1.14/1.34 ( ord_less_eq_int, skv_1, pls ) 1.14/1.34 ( ord_less_eq_int, skv_2, pls ) 1.14/1.34 ( ord_less_int, min, min ) 1.14/1.34 ( ord_less_int, min, pls ) 1.14/1.34 ( ord_less_int, zero_zero_int, min ) 1.14/1.34 ( ord_less_int, zero_zero_int, pls ) 1.14/1.34 ( ord_less_int, one_one_int, pls ) 1.14/1.34 ( ord_less_int, t, one_one_int ) 1.14/1.34 ( ord_less_int, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), pls ) 1.14/1.34 ( ord_less_int, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.34 ( ord_less_int, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), s ) 1.14/1.34 ( ord_less_int, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_1 ) 1.14/1.34 ( ord_less_int, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_2 ) 1.14/1.34 ( dvd_dvd_int, (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((B $$unsorted) (A $$unsorted)) (let ((_let_0 (plus_plus_int A))) (let ((_let_1 (hAPP_int_int _let_0 B))) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int _let_1) zero_zero_int))) (= _let_1 (hAPP_int_int (div_mod_int A) B))))) ) 1.14/1.34 ( one_one_int, one_one_int ) 1.14/1.34 ( one_one_int, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.34 ( one_one_int, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_6) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ( (hAPP_nat_int (power_power_int skv_8) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((B_18 $$unsorted) (A_20 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_20))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_18) zero_zero_int))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (times_times_int A_20) B_18)) zero_zero_int))) ) 1.14/1.34 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ( m, (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.34 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((A_61 $$unsorted) (N_11 $$unsorted) (N_10 $$unsorted)) (let ((_let_0 (power_power_int A_61))) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_11) N_10))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int one_one_int) A_61))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int _let_0 N_11)) (hAPP_nat_int _let_0 N_10))))) ) 1.14/1.34 ( zero_zero_int, (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.34 ( zero_zero_int, (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((W_15 $$unsorted)) (= (number267125858f_real (hAPP_int_int (plus_plus_int (bit1 pls)) W_15)) (hAPP_real_real (plus_plus_real one_one_real) (number267125858f_real W_15))) ) 1.14/1.34 ( (bit1 pls) ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((M $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_0 (hAPP_n1699378549t_bool ord_less_nat I_1))) (or (not (hBOOL (hAPP_nat_bool _let_0 J_1))) (hBOOL (hAPP_nat_bool _let_0 (hAPP_nat_nat (plus_plus_nat M) J_1))))) ) 1.14/1.34 ( one_one_nat, zero_zero_nat, one_one_nat ) 1.14/1.34 ) 1.14/1.34 (instantiation (forall ((N $$unsorted) (P_2 $$unsorted)) (or (hBOOL (hAPP_nat_bool P_2 zero_zero_nat)) (not (hBOOL (hAPP_nat_bool P_2 N))) (not (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat K_2) N))) (not (forall ((I $$unsorted)) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I) K_2))) (not (hBOOL (hAPP_nat_bool P_2 I)))) )) (not (hBOOL (hAPP_nat_bool P_2 (hAPP_nat_nat (plus_plus_nat K_2) one_one_nat))))) ))) ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((L_1 $$unsorted)) (or (not (is_int L_1)) (= (= min L_1) (= min (bit1 L_1)))) ) 1.14/1.35 ( min ) 1.14/1.35 ( zero_zero_int ) 1.14/1.35 ( pls ) 1.14/1.35 ( one_one_int ) 1.14/1.35 ( t ) 1.14/1.35 ( (bit1 pls) ) 1.14/1.35 ( m ) 1.14/1.35 ( s1 ) 1.14/1.35 ( s ) 1.14/1.35 ( (undefined_int int) ) 1.14/1.35 ( skv_1 ) 1.14/1.35 ( skv_2 ) 1.14/1.35 ( skv_3 ) 1.14/1.35 ( skv_4 ) 1.14/1.35 ( skv_5 ) 1.14/1.35 ( skv_6 ) 1.14/1.35 ( skv_7 ) 1.14/1.35 ( skv_8 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (power_power_int B_2))) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) B_2))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_2) Y_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int _let_0 X_2)) (hAPP_nat_int _let_0 Y_2)))))) ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat, zero_zero_int ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) M))) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N_1))) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat N_1) M)))) ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((V_10 $$unsorted) (W_9 $$unsorted)) (= (number267125858f_real (hAPP_int_int (plus_plus_int V_10) W_9)) (hAPP_real_real (plus_plus_real (number267125858f_real V_10)) (number267125858f_real W_9))) ) 1.14/1.35 ( one_one_int, one_one_int ) 1.14/1.35 ( (bit1 pls), (bit1 pls) ) 1.14/1.35 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m), one_one_int ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), one_one_int ) 1.14/1.35 ( (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_6) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_8) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((Z_6 $$unsorted)) (= (hAPP_nat_nat (times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z_6) (hAPP_nat_nat (plus_plus_nat Z_6) Z_6)) ) 1.14/1.35 ( one_one_nat ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A_92 $$unsorted)) (or (not (is_int A_92)) (= A_92 (hAPP_int_int (times_times_int A_92) (number_number_of_int (bit1 pls))))) ) 1.14/1.35 ( min ) 1.14/1.35 ( zero_zero_int ) 1.14/1.35 ( one_one_int ) 1.14/1.35 ( t ) 1.14/1.35 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.35 ( m ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( s1 ) 1.14/1.35 ( s ) 1.14/1.35 ( (undefined_int int) ) 1.14/1.35 ( skv_1 ) 1.14/1.35 ( skv_2 ) 1.14/1.35 ( skv_3 ) 1.14/1.35 ( skv_4 ) 1.14/1.35 ( skv_5 ) 1.14/1.35 ( skv_6 ) 1.14/1.35 ( skv_7 ) 1.14/1.35 ( skv_8 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((BOUND_VARIABLE_20277 $$unsorted)) (or (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int BOUND_VARIABLE_20277) zero_zero_int)) (= (hAPP_int_int (times_times_int BOUND_VARIABLE_20277) (zfact (hAPP_int_int (minus_minus_int BOUND_VARIABLE_20277) one_one_int))) (zfact BOUND_VARIABLE_20277))) ) 1.14/1.35 ( min ) 1.14/1.35 ( pls ) 1.14/1.35 ( one_one_int ) 1.14/1.35 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((BOUND_VARIABLE_20291 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int BOUND_VARIABLE_20291) zero_zero_int))) (= one_one_int (zfact BOUND_VARIABLE_20291))) ) 1.14/1.35 ( min ) 1.14/1.35 ( pls ) 1.14/1.35 ( one_one_int ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((V_18 $$unsorted) (V_17 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (or (not (hBOOL (hAPP_int_bool _let_0 V_17))) (not (hBOOL (hAPP_int_bool _let_0 V_18))) (= (number267125858f_real (hAPP_int_int (plus_plus_int V_17) V_18)) (hAPP_real_real (plus_plus_real (number267125858f_real V_17)) (number267125858f_real V_18))))) ) 1.14/1.35 ( one_one_int, one_one_int ) 1.14/1.35 ( one_one_int, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.35 ( one_one_int, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( (bit1 pls), (bit1 pls) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int skv_6) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int skv_8) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((N $$unsorted) (P_2 $$unsorted)) (or (hBOOL (hAPP_nat_bool P_2 zero_zero_nat)) (not (hBOOL (hAPP_nat_bool P_2 N))) (not (forall ((K_2 $$unsorted)) (or (not (forall ((I $$unsorted)) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I) K_2))) (not (hBOOL (hAPP_nat_bool P_2 I)))) )) (not (hBOOL (hAPP_nat_bool P_2 K_2))) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K_2) N)))) ))) ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A_104 $$unsorted) (C_30 $$unsorted)) (= (hAPP_real_real (plus_plus_real A_104) C_30) (hAPP_real_real (plus_plus_real C_30) A_104)) ) 1.14/1.35 ( one_one_real, one_one_real ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((Z $$unsorted) (W $$unsorted)) (= (hAPP_int_int (times_times_int Z) W) (hAPP_int_int (times_times_int W) Z)) ) 1.14/1.35 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m ) 1.14/1.35 ( m, (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_3 ) 1.14/1.35 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((B_5 $$unsorted) (A_6 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (or (not (hBOOL (hAPP_int_bool _let_0 A_6))) (not (hBOOL (hAPP_int_bool _let_0 B_5))) (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (times_times_int A_6) B_5))))) ) 1.14/1.35 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( m, (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.35 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((M $$unsorted) (A $$unsorted)) (or (not (is_int A)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) M))) (not (hBOOL (hAPP_int_bool (zcong A zero_zero_int) M))) (= zero_zero_int A)) ) 1.14/1.35 ( min, min ) 1.14/1.35 ( min, pls ) 1.14/1.35 ( zero_zero_int, min ) 1.14/1.35 ( zero_zero_int, pls ) 1.14/1.35 ( one_one_int, pls ) 1.14/1.35 ( t, one_one_int ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), pls ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), s ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_1 ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_2 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((Z $$unsorted) (W $$unsorted)) (= (hAPP_int_int (plus_plus_int W) Z) (hAPP_int_int (plus_plus_int Z) W)) ) 1.14/1.35 ( one_one_int, one_one_int ) 1.14/1.35 ( one_one_int, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.35 ( one_one_int, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m), one_one_int ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), one_one_int ) 1.14/1.35 ( (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_6) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int skv_6) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_8) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int skv_8) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((X1 $$unsorted) (X2 $$unsorted) (Ma $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Ma))) (= (hBOOL (hAPP_int_bool (zcong X1 X2) Ma)) (= (standardRes Ma X2) (standardRes Ma X1)))) ) 1.14/1.35 ( s1, s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( s1, skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( s1, skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int skv_4) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((K $$unsorted) (Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (plus_plus_nat K))) (= (= (hAPP_nat_nat _let_0 Ma) (hAPP_nat_nat _let_0 N)) (= Ma N))) ) 1.14/1.35 ( one_one_nat, one_one_nat, one_one_nat ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((B_6 $$unsorted) (A_7 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_7))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_6) zero_zero_int))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (times_times_int A_7) B_6)) zero_zero_int))) ) 1.14/1.35 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( m, (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.35 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((M $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) X_1))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_1) M))) (not (hBOOL (hAPP_int_bool (zcong X_1 zero_zero_int) M)))) ) 1.14/1.35 ( min, min ) 1.14/1.35 ( min, pls ) 1.14/1.35 ( zero_zero_int, min ) 1.14/1.35 ( zero_zero_int, pls ) 1.14/1.35 ( one_one_int, pls ) 1.14/1.35 ( t, one_one_int ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), pls ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), s ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_1 ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_2 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A_44 $$unsorted)) (or (not (is_int A_44)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int zero_zero_int) A_44))) (= zero_zero_int A_44)) ) 1.14/1.35 ( min ) 1.14/1.35 ( zero_zero_int ) 1.14/1.35 ( one_one_int ) 1.14/1.35 ( t ) 1.14/1.35 ( m ) 1.14/1.35 ( s1 ) 1.14/1.35 ( s ) 1.14/1.35 ( (undefined_int int) ) 1.14/1.35 ( skv_1 ) 1.14/1.35 ( skv_2 ) 1.14/1.35 ( skv_3 ) 1.14/1.35 ( skv_4 ) 1.14/1.35 ( skv_5 ) 1.14/1.35 ( skv_6 ) 1.14/1.35 ( skv_7 ) 1.14/1.35 ( skv_8 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((W_6 $$unsorted)) (= (number267125858f_real (bit0 W_6)) (hAPP_real_real (times_times_real (hAPP_real_real (plus_plus_real one_one_real) one_one_real)) (number267125858f_real W_6))) ) 1.14/1.35 ( pls ) 1.14/1.35 ( (bit1 pls) ) 1.14/1.35 ( (bit0 (bit1 pls)) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A_59 $$unsorted) (N_8 $$unsorted) (N_7 $$unsorted)) (let ((_let_0 (power_power_int A_59))) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_8) N_7))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A_59))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int _let_0 N_8)) (hAPP_nat_int _let_0 N_7))))) ) 1.14/1.35 ( zero_zero_int, (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.35 ( zero_zero_int, (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A_70 $$unsorted)) (= A_70 (hAPP_nat_nat (power_power_nat A_70) one_one_nat)) ) 1.14/1.35 ( zero_zero_nat ) 1.14/1.35 ( one_one_nat ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((X_14 $$unsorted) (Y_11 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (or (not (is_int Y_11)) (not (is_int X_14)) (not (= (hAPP_nat_int (power_power_int Y_11) _let_0) (hAPP_nat_int (power_power_int X_14) _let_0))) (not (hBOOL (hAPP_int_bool _let_1 X_14))) (not (hBOOL (hAPP_int_bool _let_1 Y_11))) (= X_14 Y_11)))) ) 1.14/1.35 ( min, min ) 1.14/1.35 ( min, zero_zero_int ) 1.14/1.35 ( zero_zero_int, min ) 1.14/1.35 ( pls, (undefined_int int) ) 1.14/1.35 ( one_one_int, one_one_int ) 1.14/1.35 ( one_one_int, m ) 1.14/1.35 ( t, t ) 1.14/1.35 ( t, s ) 1.14/1.35 ( m, one_one_int ) 1.14/1.35 ( s1, s1 ) 1.14/1.35 ( s1, skv_1 ) 1.14/1.35 ( s, t ) 1.14/1.35 ( (undefined_int int), pls ) 1.14/1.35 ( (undefined_int int), (undefined_int int) ) 1.14/1.35 ( skv_1, s1 ) 1.14/1.35 ( skv_2, skv_2 ) 1.14/1.35 ( skv_2, skv_3 ) 1.14/1.35 ( skv_3, skv_2 ) 1.14/1.35 ( skv_4, skv_4 ) 1.14/1.35 ( skv_4, skv_5 ) 1.14/1.35 ( skv_5, skv_4 ) 1.14/1.35 ( skv_6, skv_6 ) 1.14/1.35 ( skv_6, skv_8 ) 1.14/1.35 ( skv_7, skv_7 ) 1.14/1.35 ( skv_8, skv_6 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((BOUND_VARIABLE_20651 $$unsorted)) (or (= zero_zero_nat BOUND_VARIABLE_20651) (= zero_zero_nat (hAPP_nat_nat (power_power_nat zero_zero_nat) BOUND_VARIABLE_20651))) ) 1.14/1.35 ( zero_zero_nat ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((N_19 $$unsorted) (A_71 $$unsorted)) (let ((_let_0 (power_power_real A_71))) (let ((_let_1 (hAPP_nat_real _let_0 N_19))) (or (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) A_71))) (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_71) one_one_real))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (times_times_real A_71) _let_1)) _let_1))))) ) 1.14/1.35 ( zero_zero_nat, zero_zero_real ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_real ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_real ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((B $$unsorted) (M $$unsorted) (A $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (or (not (hBOOL (hAPP_int_bool _let_0 A))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) M))) (not (hBOOL (hAPP_int_bool _let_0 B))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B) A))) (not (hBOOL (hAPP_int_bool (zcong A B) M))))) ) 1.14/1.35 ( (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_nat_int (power_power_int skv_4) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), s1 ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), s1 ) 1.14/1.35 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), s1 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((Z_5 $$unsorted)) (= (hAPP_int_int (plus_plus_int Z_5) Z_5) (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_5)) ) 1.14/1.35 ( one_one_int ) 1.14/1.35 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((M $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (or (not (is_int X_1)) (not (is_int Y_1)) (not (hBOOL (hAPP_int_bool _let_0 X_1))) (not (hBOOL (hAPP_int_bool _let_0 Y_1))) (not (hBOOL (hAPP_int_bool _let_0 M))) (not (hBOOL (hAPP_int_bool (zcong X_1 Y_1) M))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_1) M))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Y_1) M))) (= Y_1 X_1))) ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (number_number_of_int min), (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (number_number_of_int min), (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (number_number_of_int min), (hAPP_nat_int (power_power_int skv_4) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), s, s1 ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_1, s1 ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_2, s1 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((B $$unsorted) (A $$unsorted)) (or (not (is_int A)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A) zero_zero_int))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B) A))) (= A (hAPP_int_int (div_mod_int A) B))) ) 1.14/1.35 ( min, min ) 1.14/1.35 ( min, zero_zero_int ) 1.14/1.35 ( pls, min ) 1.14/1.35 ( pls, zero_zero_int ) 1.14/1.35 ( pls, one_one_int ) 1.14/1.35 ( pls, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( one_one_int, t ) 1.14/1.35 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((B_1_1 $$unsorted)) (or (not (is_int B_1_1)) (is_int (bit0 B_1_1))) ) 1.14/1.35 ( pls ) 1.14/1.35 ( (bit1 pls) ) 1.14/1.35 ( (bit0 (bit1 pls)) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted)) (= (or (= zero_zero_nat N) (= one_one_nat X_2)) (= one_one_nat (hAPP_nat_nat (power_power_nat X_2) N))) ) 1.14/1.35 ( zero_zero_nat, zero_zero_nat ) 1.14/1.35 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( one_one_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((W_1 $$unsorted) (Z_1 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_int W_1))) (or (not (is_int Z_1)) (not (is_int W_1)) (= (or (= W_1 Z_1) (hBOOL (hAPP_int_bool _let_0 Z_1))) (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (plus_plus_int Z_1) one_one_int)))))) ) 1.14/1.35 ( pls, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.35 ( t, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.35 ( s, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.35 ( skv_1, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.35 ( skv_2, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((N_6 $$unsorted) (A_56 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_int one_one_int))) (or (not (hBOOL (hAPP_int_bool _let_0 A_56))) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_6))) (hBOOL (hAPP_int_bool _let_0 (hAPP_nat_int (power_power_int A_56) N_6))))) ) 1.14/1.35 ( zero_zero_nat, zero_zero_int ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_int ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), s1 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), s ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_4 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_5 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_6 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_7 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_8 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((N_38 $$unsorted) (A_90 $$unsorted)) (let ((_let_0 (power_power_int A_90))) (let ((_let_1 (hAPP_nat_int _let_0 N_38))) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A_90))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_1) (hAPP_int_int (times_times_int A_90) _let_1)))))) ) 1.14/1.35 ( zero_zero_nat, zero_zero_int ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_int ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), s1 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), s ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_4 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_5 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_6 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_7 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_8 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted) (P_1 $$unsorted)) (or (hBOOL (hAPP_int_bool (zcong X_1 zero_zero_int) P_1)) (not (hBOOL (hAPP_int_bool (zcong (hAPP_nat_int (power_power_int Y_1) (number_number_of_nat (bit0 (bit1 pls)))) X_1) P_1))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int P_1) Y_1)))) ) 1.14/1.35 ( s1, (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( s, (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( s, (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( skv_4, (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A_91 $$unsorted)) (= (hAPP_real_real (times_times_real (hAPP_real_real (times_times_real A_91) A_91)) A_91) (hAPP_nat_real (power_power_real A_91) (number_number_of_nat (bit1 (bit1 pls))))) ) 1.14/1.35 ( one_one_real ) 1.14/1.35 ( zero_zero_real ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((N_12 $$unsorted) (A_62 $$unsorted)) (let ((_let_0 (hAPP_r1134773055l_bool ord_less_eq_real one_one_real))) (or (not (hBOOL (hAPP_real_bool _let_0 A_62))) (hBOOL (hAPP_real_bool _let_0 (hAPP_nat_real (power_power_real A_62) N_12))))) ) 1.14/1.35 ( zero_zero_nat, zero_zero_real ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_real ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_real ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((P_3 $$unsorted)) (let ((_let_0 (number_number_of_int (bit0 (bit1 pls))))) (let ((_let_1 (minus_minus_int P_3))) (let ((_let_2 (hAPP_int_int _let_1 _let_0))) (or (not (hBOOL (hAPP_int_bool zprime P_3))) (= (d22set _let_2) (wset _let_2 P_3)))))) ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((N_25 $$unsorted) (A_76 $$unsorted)) (let ((_let_0 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (or (not (hBOOL (hAPP_nat_bool _let_0 A_76))) (hBOOL (hAPP_nat_bool _let_0 (hAPP_nat_nat (power_power_nat A_76) N_25))))) ) 1.14/1.35 ( zero_zero_nat, zero_zero_nat ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_nat ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((Z_3 $$unsorted)) (= (hAPP_real_real (times_times_real Z_3) (number267125858f_real (bit0 (bit1 pls)))) (hAPP_real_real (plus_plus_real Z_3) Z_3)) ) 1.14/1.35 ( one_one_real ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A_50 $$unsorted) (B_44 $$unsorted)) (or (not (is_int B_44)) (not (is_int A_50)) (not (= zero_zero_int (hAPP_int_int (times_times_int A_50) B_44))) (= zero_zero_int B_44) (= zero_zero_int A_50)) ) 1.14/1.35 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_3 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A_2 $$unsorted) (W_1 $$unsorted)) (let ((_let_0 (number_number_of_nat W_1))) (= (= zero_zero_real (hAPP_nat_real (power_power_real A_2) _let_0)) (and (not (= zero_zero_nat _let_0)) (= zero_zero_real A_2)))) ) 1.14/1.35 ( one_one_real, (bit0 (bit1 pls)) ) 1.14/1.35 ( zero_zero_real, pls ) 1.14/1.35 ( zero_zero_real, (bit0 (bit1 pls)) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((K_1 $$unsorted)) (= (bit1 K_1) (hAPP_int_int (plus_plus_int (hAPP_int_int (plus_plus_int one_one_int) K_1)) K_1)) ) 1.14/1.35 ( min ) 1.14/1.35 ( pls ) 1.14/1.35 ( one_one_int ) 1.14/1.35 ( (bit1 pls) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A_67 $$unsorted) (N_18 $$unsorted)) (let ((_let_0 (power_power_int A_67))) (let ((_let_1 (hAPP_nat_int _let_0 N_18))) (= (hAPP_int_int (times_times_int A_67) _let_1) (hAPP_int_int (times_times_int _let_1) A_67)))) ) 1.14/1.35 ( zero_zero_int, zero_zero_nat ) 1.14/1.35 ( zero_zero_int, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( one_one_int, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( s1, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( s, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( skv_4, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( skv_5, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( skv_6, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( skv_7, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( skv_8, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (or (not (is_int N)) (not (is_int Ma)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Ma))) (= (= one_one_int (hAPP_int_int (times_times_int Ma) N)) (and (= one_one_int N) (= one_one_int Ma)))) ) 1.14/1.35 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( m, (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.35 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((B_35 $$unsorted) (A_38 $$unsorted) (C_17 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool dvd_dvd_int A_38))) (or (not (hBOOL (hAPP_int_bool _let_0 C_17))) (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (times_times_int B_35) C_17))))) ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_3 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A_85 $$unsorted) (N_32 $$unsorted) (B_54 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (or (not (is_int B_54)) (not (is_int A_85)) (not (= (hAPP_nat_int (power_power_int B_54) N_32) (hAPP_nat_int (power_power_int A_85) N_32))) (not (hBOOL (hAPP_int_bool _let_0 A_85))) (not (hBOOL (hAPP_int_bool _let_0 B_54))) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_32))) (= A_85 B_54))) ) 1.14/1.35 ( min, zero_zero_nat, zero_zero_int ) 1.14/1.35 ( zero_zero_int, (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, (number_number_of_nat (bit0 (bit1 pls))), one_one_int ) 1.14/1.35 ( pls, (number_number_of_nat (bit0 (bit1 pls))), skv_4 ) 1.14/1.35 ( one_one_int, (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int ) 1.14/1.35 ( t, (number_number_of_nat (bit0 (bit1 pls))), skv_6 ) 1.14/1.35 ( m, (number_number_of_nat (bit0 (bit1 pls))), s ) 1.14/1.35 ( s1, (number_number_of_nat (bit0 (bit1 pls))), skv_8 ) 1.14/1.35 ( s, (number_number_of_nat (bit0 (bit1 pls))), skv_5 ) 1.14/1.35 ( (undefined_int int), (number_number_of_nat (bit0 (bit1 pls))), s1 ) 1.14/1.35 ( skv_1, (number_number_of_nat (bit0 (bit1 pls))), skv_7 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((W_16 $$unsorted)) (let ((_let_0 (number_number_of_nat W_16))) (= (hAPP_nat_nat (times_times_nat _let_0) _let_0) (hAPP_nat_nat (power_power_nat _let_0) (number_number_of_nat (bit0 (bit1 pls)))))) ) 1.14/1.35 ( pls ) 1.14/1.35 ( (bit1 pls) ) 1.14/1.35 ( (bit0 (bit1 pls)) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((W_5 $$unsorted)) (let ((_let_0 (number_number_of_int W_5))) (= (hAPP_int_int (plus_plus_int (hAPP_int_int (plus_plus_int zero_zero_int) _let_0)) _let_0) (number_number_of_int (bit0 W_5)))) ) 1.14/1.35 ( pls ) 1.14/1.35 ( (bit1 pls) ) 1.14/1.35 ( (bit0 (bit1 pls)) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A_2 $$unsorted) (B_2 $$unsorted)) (or (not (is_int B_2)) (not (is_int A_2)) (= (hBOOL (hAPP_int_bool (zcong A_2 B_2) zero_zero_int)) (= A_2 B_2))) ) 1.14/1.35 ( s1, s ) 1.14/1.35 ( s1, skv_1 ) 1.14/1.35 ( s1, skv_2 ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int skv_4) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((X_2 $$unsorted)) (or (not (is_int X_2)) (= (hBOOL (hAPP_int_bool twoSqu1154269391sum2sq X_2)) (not (forall ((A_3 $$unsorted) (B_3 $$unsorted)) (or (not (is_int A_3)) (not (= X_2 (twoSqu1241645765sum2sq (product_Pair_int_int A_3 B_3)))) (not (is_int B_3))) )))) ) 1.14/1.35 ( min ) 1.14/1.35 ( zero_zero_int ) 1.14/1.35 ( one_one_int ) 1.14/1.35 ( t ) 1.14/1.35 ( m ) 1.14/1.35 ( s1 ) 1.14/1.35 ( s ) 1.14/1.35 ( (hAPP_int_int (times_times_int (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t) ) 1.14/1.35 ( (undefined_int int) ) 1.14/1.35 ( skv_1 ) 1.14/1.35 ( skv_2 ) 1.14/1.35 ( skv_3 ) 1.14/1.35 ( skv_4 ) 1.14/1.35 ( skv_5 ) 1.14/1.35 ( skv_6 ) 1.14/1.35 ( skv_7 ) 1.14/1.35 ( skv_8 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((X_1 $$unsorted)) (or (not (is_int X_1)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_1))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_1) (number_number_of_int (bit0 (bit1 pls)))))) (= zero_zero_int X_1) (= one_one_int X_1)) ) 1.14/1.35 ( min ) 1.14/1.35 ( zero_zero_int ) 1.14/1.35 ( pls ) 1.14/1.35 ( one_one_int ) 1.14/1.35 ( t ) 1.14/1.35 ( m ) 1.14/1.35 ( s1 ) 1.14/1.35 ( (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.35 ( (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.35 ( (number_number_of_int pls) ) 1.14/1.35 ( s ) 1.14/1.35 ( (undefined_int int) ) 1.14/1.35 ( skv_1 ) 1.14/1.35 ( skv_2 ) 1.14/1.35 ( skv_3 ) 1.14/1.35 ( skv_4 ) 1.14/1.35 ( skv_5 ) 1.14/1.35 ( skv_6 ) 1.14/1.35 ( skv_7 ) 1.14/1.35 ( skv_8 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A $$unsorted) (P_1 $$unsorted)) (or (not (is_int A)) (not (hBOOL (hAPP_int_bool zprime P_1))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) P_1))) (not (hBOOL (hAPP_int_bool (zcong (hAPP_int_int (times_times_int A) A) one_one_int) P_1))) (= one_one_int A) (= A (hAPP_int_int (minus_minus_int P_1) one_one_int))) ) 1.14/1.35 ( min, min ) 1.14/1.35 ( min, zero_zero_int ) 1.14/1.35 ( pls, min ) 1.14/1.35 ( pls, zero_zero_int ) 1.14/1.35 ( pls, one_one_int ) 1.14/1.35 ( pls, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( one_one_int, t ) 1.14/1.35 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (or (not (is_int B_1_1)) (not (is_int B_2_1)) (is_int (legendre B_1_1 B_2_1))) ) 1.14/1.35 ( (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((V_20 $$unsorted) (V_19 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (or (not (hBOOL (hAPP_int_bool _let_0 V_19))) (not (hBOOL (hAPP_int_bool _let_0 V_20))) (= (number267125858f_real (hAPP_int_int (times_times_int V_19) V_20)) (hAPP_real_real (times_times_real (number267125858f_real V_19)) (number267125858f_real V_20))))) ) 1.14/1.35 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( m, (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.35 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A_2 $$unsorted) (W_1 $$unsorted)) (let ((_let_0 (number_number_of_nat W_1))) (= (= zero_zero_nat (hAPP_nat_nat (power_power_nat A_2) _let_0)) (and (not (= zero_zero_nat _let_0)) (= zero_zero_nat A_2)))) ) 1.14/1.35 ( zero_zero_nat, pls ) 1.14/1.35 ( zero_zero_nat, (bit0 (bit1 pls)) ) 1.14/1.35 ( one_one_nat, (bit0 (bit1 pls)) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((Z $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Z))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) (hAPP_int_int (plus_plus_int one_one_int) Z)))) ) 1.14/1.35 ( min ) 1.14/1.35 ( one_one_int ) 1.14/1.35 ( (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.35 ( (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.35 ( (number_number_of_int pls) ) 1.14/1.35 ( s ) 1.14/1.35 ( skv_1 ) 1.14/1.35 ( skv_2 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((V_20 $$unsorted) (V_19 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (or (not (hBOOL (hAPP_int_bool _let_0 V_19))) (not (hBOOL (hAPP_int_bool _let_0 V_20))) (= (hAPP_nat_nat (times_times_nat (number_number_of_nat V_19)) (number_number_of_nat V_20)) (number_number_of_nat (hAPP_int_int (times_times_int V_19) V_20))))) ) 1.14/1.35 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( m, (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.35 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((N_19 $$unsorted) (A_71 $$unsorted)) (let ((_let_0 (power_power_int A_71))) (let ((_let_1 (hAPP_nat_int _let_0 N_19))) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_71))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_71) one_one_int))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (times_times_int A_71) _let_1)) _let_1))))) ) 1.14/1.35 ( zero_zero_nat, zero_zero_int ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_int ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), s1 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), s ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_4 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_5 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_6 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_7 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_8 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((C_16 $$unsorted) (A_37 $$unsorted) (B_34 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool dvd_dvd_int A_37))) (or (not (hBOOL (hAPP_int_bool _let_0 B_34))) (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (times_times_int B_34) C_16))))) ) 1.14/1.35 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((B_4 $$unsorted) (C_1 $$unsorted) (A_4 $$unsorted)) (let ((_let_0 (hAPP_n1699378549t_bool ord_less_nat B_4))) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) A_4))) (not (hBOOL (hAPP_nat_bool _let_0 C_1))) (hBOOL (hAPP_nat_bool _let_0 (hAPP_nat_nat (plus_plus_nat A_4) C_1))))) ) 1.14/1.35 ( zero_zero_nat, one_one_nat, one_one_nat ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((M_10 $$unsorted)) (= (hAPP_real_real (times_times_real (hAPP_real_real (plus_plus_real one_one_real) one_one_real)) M_10) (hAPP_real_real (plus_plus_real M_10) M_10)) ) 1.14/1.35 ( one_one_real ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (bit0 (bit1 pls)))) (let ((_let_1 (number_number_of_nat _let_0))) (= (hAPP_real_real (plus_plus_real (hAPP_real_real (plus_plus_real (hAPP_nat_real (power_power_real X_2) _let_1)) (hAPP_nat_real (power_power_real Y_2) _let_1))) (hAPP_real_real (times_times_real (hAPP_real_real (times_times_real (number267125858f_real _let_0)) X_2)) Y_2)) (hAPP_nat_real (power_power_real (hAPP_real_real (plus_plus_real X_2) Y_2)) _let_1)))) ) 1.14/1.35 ( one_one_real, one_one_real ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((C_27 $$unsorted) (D_8 $$unsorted) (B_50 $$unsorted) (R_4 $$unsorted)) (let ((_let_0 (plus_plus_int B_50))) (let ((_let_1 (times_times_int R_4))) (or (not (is_int C_27)) (not (is_int R_4)) (not (is_int D_8)) (= zero_zero_int R_4) (= C_27 D_8) (not (= (hAPP_int_int _let_0 (hAPP_int_int _let_1 D_8)) (hAPP_int_int _let_0 (hAPP_int_int _let_1 C_27))))))) ) 1.14/1.35 ( min, min, one_one_int, min ) 1.14/1.35 ( min, min, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m), min ) 1.14/1.35 ( min, min, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), min ) 1.14/1.35 ( min, min, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), min ) 1.14/1.35 ( min, min, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), min ) 1.14/1.35 ( min, zero_zero_int, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m), min ) 1.14/1.35 ( zero_zero_int, min, one_one_int, zero_zero_int ) 1.14/1.35 ( zero_zero_int, min, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, min, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), one_one_int ) 1.14/1.35 ( zero_zero_int, min, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, min, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, pls, one_one_int, zero_zero_int ) 1.14/1.35 ( zero_zero_int, pls, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, pls, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, pls, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, one_one_int, one_one_int, zero_zero_int ) 1.14/1.35 ( zero_zero_int, one_one_int, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, one_one_int, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, one_one_int, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, t, one_one_int, zero_zero_int ) 1.14/1.35 ( zero_zero_int, t, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, t, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, t, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, m, one_one_int, zero_zero_int ) 1.14/1.35 ( zero_zero_int, m, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, m, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, m, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, s1, one_one_int, zero_zero_int ) 1.14/1.35 ( zero_zero_int, s1, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, s1, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, s1, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, s, one_one_int, zero_zero_int ) 1.14/1.35 ( zero_zero_int, s, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, s, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, s, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, (undefined_int int), one_one_int, zero_zero_int ) 1.14/1.35 ( zero_zero_int, (undefined_int int), (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, (undefined_int int), (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, (undefined_int int), (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_1, one_one_int, zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_1, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_1, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_1, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_2, one_one_int, zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_2, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_2, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_2, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_3, one_one_int, zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_3, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_3, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_3, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_4, one_one_int, zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_4, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_4, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_4, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_5, one_one_int, zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_5, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_5, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_5, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_6, one_one_int, zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_6, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_6, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_6, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_7, one_one_int, zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_7, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_7, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_7, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_8, one_one_int, zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_8, (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_8, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( zero_zero_int, skv_8, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, pls, one_one_int, zero_zero_int ) 1.14/1.35 ( one_one_int, pls, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, pls, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, one_one_int, one_one_int, zero_zero_int ) 1.14/1.35 ( one_one_int, one_one_int, one_one_int, m ) 1.14/1.35 ( one_one_int, one_one_int, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, one_one_int, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), m ) 1.14/1.35 ( one_one_int, one_one_int, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, one_one_int, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), m ) 1.14/1.35 ( one_one_int, t, one_one_int, zero_zero_int ) 1.14/1.35 ( one_one_int, t, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, t, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, m, one_one_int, zero_zero_int ) 1.14/1.35 ( one_one_int, m, one_one_int, m ) 1.14/1.35 ( one_one_int, m, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, m, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, s1, one_one_int, zero_zero_int ) 1.14/1.35 ( one_one_int, s1, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, s1, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, s, one_one_int, zero_zero_int ) 1.14/1.35 ( one_one_int, s, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, s, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, (undefined_int int), one_one_int, zero_zero_int ) 1.14/1.35 ( one_one_int, (undefined_int int), (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, (undefined_int int), (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, skv_1, one_one_int, zero_zero_int ) 1.14/1.35 ( one_one_int, skv_1, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, skv_1, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, skv_2, one_one_int, zero_zero_int ) 1.14/1.35 ( one_one_int, skv_2, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, skv_2, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, skv_3, one_one_int, zero_zero_int ) 1.14/1.35 ( one_one_int, skv_3, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, skv_3, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, skv_4, one_one_int, zero_zero_int ) 1.14/1.35 ( one_one_int, skv_4, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, skv_4, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, skv_5, one_one_int, zero_zero_int ) 1.14/1.35 ( one_one_int, skv_5, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, skv_5, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, skv_6, one_one_int, zero_zero_int ) 1.14/1.35 ( one_one_int, skv_6, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, skv_6, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, skv_7, one_one_int, zero_zero_int ) 1.14/1.35 ( one_one_int, skv_7, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, skv_7, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, skv_8, one_one_int, zero_zero_int ) 1.14/1.35 ( one_one_int, skv_8, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( one_one_int, skv_8, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, pls, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, pls, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, one_one_int, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, one_one_int, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), (undefined_int int) ) 1.14/1.35 ( m, one_one_int, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, t, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, t, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, s1, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, s1, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, s, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, s, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, (undefined_int int), (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, (undefined_int int), (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, skv_1, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, skv_1, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, skv_2, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, skv_2, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, skv_3, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, skv_3, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, skv_4, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, skv_4, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, skv_5, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, skv_5, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, skv_6, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, skv_6, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, skv_7, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, skv_7, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, skv_8, (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( m, skv_8, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( (undefined_int int), pls, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( (undefined_int int), pls, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), pls ) 1.14/1.35 ( (undefined_int int), t, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( (undefined_int int), s1, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( (undefined_int int), s, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( (undefined_int int), (undefined_int int), (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( (undefined_int int), (undefined_int int), (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), pls ) 1.14/1.35 ( (undefined_int int), skv_1, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( (undefined_int int), skv_2, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( (undefined_int int), skv_3, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( (undefined_int int), skv_4, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( (undefined_int int), skv_5, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( (undefined_int int), skv_6, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( (undefined_int int), skv_7, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ( (undefined_int int), skv_8, (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), zero_zero_int ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A_79 $$unsorted)) (= A_79 (hAPP_real_real (plus_plus_real A_79) zero_zero_real)) ) 1.14/1.35 ( one_one_real ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((V_21 $$unsorted)) (= (hAPP_int_int (plus_plus_int (number_number_of_int V_21)) one_one_int) (number_number_of_int (hAPP_int_int (plus_plus_int V_21) (bit1 pls)))) ) 1.14/1.35 ( (bit1 pls) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((L $$unsorted)) (let ((_let_0 (minus_minus_int min))) (= (hAPP_int_int _let_0 (bit0 L)) (bit1 (hAPP_int_int _let_0 L)))) ) 1.14/1.35 ( pls ) 1.14/1.35 ( (bit1 pls) ) 1.14/1.35 ( (bit0 (bit1 pls)) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int N_1) M))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int M) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int N_1) M))) ) 1.14/1.35 ( min, min ) 1.14/1.35 ( min, pls ) 1.14/1.35 ( pls, min ) 1.14/1.35 ( pls, one_one_int ) 1.14/1.35 ( pls, (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.35 ( pls, (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.35 ( pls, (number_number_of_int pls) ) 1.14/1.35 ( pls, s ) 1.14/1.35 ( pls, skv_1 ) 1.14/1.35 ( pls, skv_2 ) 1.14/1.35 ( one_one_int, t ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A_2 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Ma))) (= (hBOOL (hAPP_int_bool (zcong A_2 B_2) Ma)) (= (hAPP_int_int (div_mod_int B_2) Ma) (hAPP_int_int (div_mod_int A_2) Ma)))) ) 1.14/1.35 ( s1, s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( s1, skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( s1, skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int skv_4) (number_number_of_nat (bit0 (bit1 pls)))), (number_number_of_int min), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A_85 $$unsorted) (N_32 $$unsorted) (B_54 $$unsorted)) (let ((_let_0 (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat))) (or (not (= (hAPP_nat_nat (power_power_nat A_85) N_32) (hAPP_nat_nat (power_power_nat B_54) N_32))) (not (hBOOL (hAPP_nat_bool _let_0 A_85))) (not (hBOOL (hAPP_nat_bool _let_0 B_54))) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_32))) (= A_85 B_54))) ) 1.14/1.35 ( zero_zero_nat, zero_zero_nat, zero_zero_nat ) 1.14/1.35 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.35 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))), one_one_nat ) 1.14/1.35 ( one_one_nat, (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((Z $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP_int_bool (zcong X_1 Y_1) M))) (hBOOL (hAPP_int_bool (zcong (hAPP_nat_int (power_power_int X_1) Z) (hAPP_nat_int (power_power_int Y_1) Z)) M))) ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), s, s1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (or (not (hBOOL (hAPP_int_bool _let_0 (number_number_of_int N_1)))) (and (hBOOL (hAPP_int_bool _let_0 (number_number_of_int (bit0 N_1)))) (hBOOL (hAPP_int_bool _let_0 (number_number_of_int (bit1 N_1))))))) ) 1.14/1.35 ( min ) 1.14/1.35 ( pls ) 1.14/1.35 ( (bit1 pls) ) 1.14/1.35 ( (bit0 (bit1 pls)) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((N_30 $$unsorted) (A_84 $$unsorted)) (or (not (is_int A_84)) (= zero_zero_int A_84) (not (= zero_zero_int (hAPP_nat_int (power_power_int A_84) N_30)))) ) 1.14/1.35 ( zero_zero_nat, zero_zero_int ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_int ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), s1 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), s ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_4 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_5 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_6 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_7 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), skv_8 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((X_14 $$unsorted) (Y_11 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (or (not (= (hAPP_nat_real (power_power_real Y_11) _let_0) (hAPP_nat_real (power_power_real X_14) _let_0))) (not (hBOOL (hAPP_real_bool _let_1 X_14))) (not (hBOOL (hAPP_real_bool _let_1 Y_11))) (= X_14 Y_11)))) ) 1.14/1.35 ( one_one_real, one_one_real ) 1.14/1.35 ( one_one_real, zero_zero_real ) 1.14/1.35 ( zero_zero_real, one_one_real ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((X_15 $$unsorted) (Y_12 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int (power_power_int X_15) _let_0)) (hAPP_nat_int (power_power_int Y_12) _let_0)))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Y_12))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_15) Y_12)))) ) 1.14/1.35 ( zero_zero_int, zero_zero_int ) 1.14/1.35 ( zero_zero_int, one_one_int ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (= (hAPP_int_int (times_times_int (hAPP_int_int (plus_plus_int A) B)) (hAPP_int_int (minus_minus_int A) B)) (hAPP_int_int (minus_minus_int (hAPP_nat_int (power_power_int A) _let_0)) (hAPP_nat_int (power_power_int B) _let_0)))) ) 1.14/1.35 ( one_one_int, one_one_int ) 1.14/1.35 ( (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m), one_one_int ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), one_one_int ) 1.14/1.35 ( (hAPP_nat_int (power_power_int skv_5) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_6) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int skv_7) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_nat_int (power_power_int skv_8) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((Ma $$unsorted) (N $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (power_power_int A_2))) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A_2))) (= (= (hAPP_nat_int _let_0 Ma) (hAPP_nat_int _let_0 N)) (= Ma N)))) ) 1.14/1.35 ( zero_zero_nat, zero_zero_nat, zero_zero_int ) 1.14/1.35 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat, zero_zero_int ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))), one_one_int ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))), s1 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))), s ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))), skv_4 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))), skv_5 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))), skv_6 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))), skv_7 ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))), skv_8 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((B_2 $$unsorted) (A_2 $$unsorted)) (= (= zero_zero_real A_2) (= B_2 (hAPP_real_real (plus_plus_real B_2) A_2))) ) 1.14/1.35 ( one_one_real, one_one_real ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N)) (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N)) (= Ma N))) ) 1.14/1.35 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((B_1_1 $$unsorted)) (or (not (is_int B_1_1)) (is_int (bit1 B_1_1))) ) 1.14/1.35 ( min ) 1.14/1.35 ( pls ) 1.14/1.35 ( (bit1 pls) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((W $$unsorted) (Z $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W) Z))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (plus_plus_int W) one_one_int)) Z))) ) 1.14/1.35 ( min, min ) 1.14/1.35 ( min, zero_zero_int ) 1.14/1.35 ( pls, min ) 1.14/1.35 ( pls, zero_zero_int ) 1.14/1.35 ( pls, one_one_int ) 1.14/1.35 ( pls, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( one_one_int, t ) 1.14/1.35 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((X_2 $$unsorted) (W_1 $$unsorted)) (let ((_let_0 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (let ((_let_1 (number_number_of_nat W_1))) (= (hBOOL (hAPP_nat_bool _let_0 (hAPP_nat_nat (power_power_nat X_2) _let_1))) (or (hBOOL (hAPP_nat_bool _let_0 X_2)) (= zero_zero_nat _let_1))))) ) 1.14/1.35 ( zero_zero_nat, pls ) 1.14/1.35 ( zero_zero_nat, (bit0 (bit1 pls)) ) 1.14/1.35 ( one_one_nat, (bit0 (bit1 pls)) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((P_5 $$unsorted) (P_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (let ((_let_1 (hBOOL P_5))) (let ((_let_2 (hBOOL P_2))) (let ((_let_3 (not (hBOOL (hAPP_int_bool _let_0 X_2))))) (or (and (hBOOL (hAPP_int_bool _let_0 X_2)) (= (not _let_1) _let_2)) (= (or _let_3 _let_2) (or _let_3 _let_1))))))) ) 1.14/1.35 ( (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int t) (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)), (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int t) (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)), min ) 1.14/1.35 ( (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int t) (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)), (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int min) min), min ) 1.14/1.35 ( (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int min) min), (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int t) (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)), (number_number_of_int pls) ) 1.14/1.35 ( (hAPP_int_bool zprime (number_number_of_int (bit0 (bit1 pls)))), (hAPP_int_bool zprime (number_number_of_int (bit0 (bit1 pls)))), s ) 1.14/1.35 ( (hAPP_int_bool zprime (number_number_of_int (bit0 (bit1 pls)))), (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int pls) min), s ) 1.14/1.35 ( (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int pls) min), (hAPP_int_bool zprime (number_number_of_int (bit0 (bit1 pls)))), (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.35 ( (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (number_number_of_int pls)), (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (number_number_of_int pls)), (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.35 ( (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (number_number_of_int pls)), (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) zero_zero_int), (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.35 ( (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) zero_zero_int), (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (number_number_of_int pls)), one_one_int ) 1.14/1.35 ( (hAPP_int_bool (quadRes (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) (number_number_of_int min)), (hAPP_int_bool (quadRes (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) (number_number_of_int min)), skv_1 ) 1.14/1.35 ( (hAPP_int_bool (quadRes (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) (number_number_of_int min)), (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls)))), skv_1 ) 1.14/1.35 ( (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_bool (quadRes (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) (number_number_of_int min)), skv_2 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((X_1 $$unsorted) (P_1 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1))) (not (hBOOL (hAPP_int_bool (zcong X_1 (number_number_of_int min)) P_1))) (not (hBOOL (hAPP_int_bool (zcong X_1 one_one_int) P_1)))) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( (hAPP_nat_int (power_power_int skv_4) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((B_9 $$unsorted) (A_10 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (or (not (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (times_times_int B_9) A_10)))) (not (hBOOL (hAPP_int_bool _let_0 A_10))) (hBOOL (hAPP_int_bool _let_0 B_9)))) ) 1.14/1.35 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_3 ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A $$unsorted) (P_1 $$unsorted)) (or (not (is_int A)) (not (hBOOL (hAPP_int_bool zprime P_1))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P_1))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) P_1))) (= A (inv P_1 (inv P_1 A)))) ) 1.14/1.35 ( min, min ) 1.14/1.35 ( min, zero_zero_int ) 1.14/1.35 ( pls, min ) 1.14/1.35 ( pls, zero_zero_int ) 1.14/1.35 ( pls, one_one_int ) 1.14/1.35 ( pls, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( one_one_int, t ) 1.14/1.35 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((BOUND_VARIABLE_22038 $$unsorted) (BOUND_VARIABLE_22039 $$unsorted)) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) BOUND_VARIABLE_22039))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real BOUND_VARIABLE_22038) (hAPP_nat_real (power_power_real BOUND_VARIABLE_22038) BOUND_VARIABLE_22039)))) ) 1.14/1.35 ( one_one_real, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( zero_zero_real, zero_zero_nat ) 1.14/1.35 ( zero_zero_real, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((BOUND_VARIABLE_22052 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real one_one_real) (hAPP_nat_real (power_power_real one_one_real) BOUND_VARIABLE_22052))) ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool dvd_dvd_int P_1))) (or (not (hBOOL (hAPP_int_bool zprime P_1))) (not (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (times_times_int M) N_1)))) (hBOOL (hAPP_int_bool _let_0 M)) (hBOOL (hAPP_int_bool _let_0 N_1)))) ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A_64 $$unsorted) (M_4 $$unsorted) (N_14 $$unsorted)) (let ((_let_0 (power_power_nat A_64))) (= (hAPP_nat_nat _let_0 (hAPP_nat_nat (times_times_nat M_4) N_14)) (hAPP_nat_nat (power_power_nat (hAPP_nat_nat _let_0 M_4)) N_14))) ) 1.14/1.35 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.35 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( one_one_nat, (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((Ma $$unsorted) (K $$unsorted) (N $$unsorted)) (= (= Ma N) (= (hAPP_nat_nat (plus_plus_nat N) K) (hAPP_nat_nat (plus_plus_nat Ma) K))) ) 1.14/1.35 ( one_one_nat, one_one_nat, one_one_nat ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((M_3 $$unsorted) (N_9 $$unsorted) (A_60 $$unsorted)) (let ((_let_0 (power_power_int A_60))) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A_60))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int _let_0 M_3)) (hAPP_nat_int _let_0 N_9)))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_3) N_9)))) ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat, zero_zero_int ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((BOUND_VARIABLE_22158 $$unsorted) (BOUND_VARIABLE_22159 $$unsorted)) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) BOUND_VARIABLE_22159))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int BOUND_VARIABLE_22158) (hAPP_nat_int (power_power_int BOUND_VARIABLE_22158) BOUND_VARIABLE_22159)))) ) 1.14/1.35 ( zero_zero_int, zero_zero_nat ) 1.14/1.35 ( zero_zero_int, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( one_one_int, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( s1, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( s, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( skv_4, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( skv_5, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( skv_6, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( skv_7, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( skv_8, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((BOUND_VARIABLE_22172 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int one_one_int) (hAPP_nat_int (power_power_int one_one_int) BOUND_VARIABLE_22172))) ) 1.14/1.35 ( (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((P_2 $$unsorted) (Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP_n1699378549t_bool P_2 N))) (let ((_let_1 (hBOOL (hAPP_nat_bool _let_0 Ma)))) (let ((_let_2 (not _let_1))) (or (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N)) _let_2) (and (= Ma N) _let_2) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) Ma)) _let_2) _let_1)))) ) 1.14/1.35 ( ord_less_nat, (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (not (is_int Y_1)) (not (is_int X_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Y_1) X_1)) (= X_1 Y_1) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_1) Y_1))) ) 1.14/1.35 ( min, min ) 1.14/1.35 ( min, zero_zero_int ) 1.14/1.35 ( min, pls ) 1.14/1.35 ( zero_zero_int, min ) 1.14/1.35 ( zero_zero_int, pls ) 1.14/1.35 ( pls, min ) 1.14/1.35 ( pls, zero_zero_int ) 1.14/1.35 ( pls, one_one_int ) 1.14/1.35 ( pls, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( one_one_int, pls ) 1.14/1.35 ( one_one_int, t ) 1.14/1.35 ( t, one_one_int ) 1.14/1.35 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), pls ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), s ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_1 ) 1.14/1.35 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_2 ) 1.14/1.35 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((A_67 $$unsorted) (N_18 $$unsorted)) (let ((_let_0 (power_power_nat A_67))) (let ((_let_1 (hAPP_nat_nat _let_0 N_18))) (= (hAPP_nat_nat (times_times_nat A_67) _let_1) (hAPP_nat_nat (times_times_nat _let_1) A_67)))) ) 1.14/1.35 ( zero_zero_nat, zero_zero_nat ) 1.14/1.35 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ( one_one_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.35 ) 1.14/1.36 (instantiation (forall ((Ma $$unsorted) (N $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (power_power_real A_2))) (or (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) A_2))) (= (= Ma N) (= (hAPP_nat_real _let_0 N) (hAPP_nat_real _let_0 Ma))))) ) 1.14/1.36 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))), zero_zero_real ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat, zero_zero_real ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))), one_one_real ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), (number_number_of_nat (bit0 (bit1 pls))), zero_zero_real ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (not (= (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int X) _let_0)) (hAPP_nat_int (power_power_int Y) _let_0))))) ) 1.14/1.36 ( one_one_int, one_one_int ) 1.14/1.36 ( s, one_one_int ) 1.14/1.36 ( skv_5, skv_6 ) 1.14/1.36 ( skv_7, skv_8 ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((B $$unsorted) (Q_1 $$unsorted) (R_1 $$unsorted) (B_48 $$unsorted) (Q_4 $$unsorted) (R_3 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (let ((_let_1 (times_times_int B_48))) (let ((_let_2 (plus_plus_int (hAPP_int_int _let_1 Q_4)))) (let ((_let_3 (hAPP_int_int _let_2 R_3))) (or (not (= _let_3 (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int B) Q_1)) R_1))) (not (hBOOL (hAPP_int_bool _let_0 _let_3))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int R_3) B_48))) (not (hBOOL (hAPP_int_bool _let_0 R_1))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_48))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_48) B))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Q_1) Q_4))))))) ) 1.14/1.36 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m, one_one_int, (number_number_of_int (bit0 (bit0 (bit1 pls)))), m, one_one_int ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N_1)) (= M (hAPP_nat_nat (plus_plus_nat N_1) (hAPP_nat_nat (minus_minus_nat M) N_1)))) ) 1.14/1.36 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((B_4 $$unsorted) (C_1 $$unsorted) (A_4 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_int B_4))) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_4))) (not (hBOOL (hAPP_int_bool _let_0 C_1))) (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (plus_plus_int A_4) C_1))))) ) 1.14/1.36 ( pls, one_one_int, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.36 ( t, one_one_int, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.36 ( s, one_one_int, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.36 ( skv_1, one_one_int, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.36 ( skv_2, one_one_int, (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((A_103 $$unsorted) (N_39 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (let ((_let_1 (power_power_int A_103))) (= (hAPP_nat_int (power_power_int (hAPP_nat_int _let_1 N_39)) _let_0) (hAPP_nat_int _let_1 (hAPP_nat_nat (times_times_nat _let_0) N_39))))) ) 1.14/1.36 ( zero_zero_int, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.36 ( one_one_int, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((N_12 $$unsorted) (A_62 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int one_one_int))) (or (not (hBOOL (hAPP_int_bool _let_0 A_62))) (hBOOL (hAPP_int_bool _let_0 (hAPP_nat_int (power_power_int A_62) N_12))))) ) 1.14/1.36 ( zero_zero_nat, zero_zero_int ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_int ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), s1 ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), s ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), skv_4 ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), skv_5 ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), skv_6 ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), skv_7 ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), skv_8 ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((L $$unsorted)) (let ((_let_0 (minus_minus_int min))) (= (bit0 (hAPP_int_int _let_0 L)) (hAPP_int_int _let_0 (bit1 L)))) ) 1.14/1.36 ( min ) 1.14/1.36 ( pls ) 1.14/1.36 ( (bit1 pls) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (or (not (is_int B_2_1)) (is_bool (hAPP_int_bool B_1_1 B_2_1))) ) 1.14/1.36 ( zprime, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( zprime, (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_int one_one_int), t ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_int t), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_int zero_zero_int), one_one_int ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_int zero_zero_int), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int), one_one_int ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int), (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int), (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int), (number_number_of_int pls) ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int), s ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int), skv_1 ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int), skv_2 ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_int min), min ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_int min), zero_zero_int ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int pls), min ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int min), min ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int min), pls ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int one_one_int), t ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_int pls), min ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_int pls), zero_zero_int ) 1.14/1.36 ( (quadRes (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)), (number_number_of_int min) ) 1.14/1.36 ( twoSqu1154269391sum2sq, (hAPP_int_int (times_times_int (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t) ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_int s), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( (zcong s1 s), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)), (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int) ) 1.14/1.36 ( (zcong (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) (number_number_of_int min)), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( (zcong (hAPP_nat_int (power_power_int s1) (number_number_of_nat (bit0 (bit1 pls)))) (number_number_of_int min)), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (zcong (hAPP_nat_int (power_power_int s) _let_0) (hAPP_nat_int (power_power_int s1) _let_0))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( (zcong s1 skv_1), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_int skv_1), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_int skv_2), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( (zcong s1 skv_2), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( (zcong (hAPP_nat_int (power_power_int skv_4) (number_number_of_nat (bit0 (bit1 pls)))) (number_number_of_int min)), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((N_30 $$unsorted) (A_84 $$unsorted)) (or (= zero_zero_real A_84) (not (= zero_zero_real (hAPP_nat_real (power_power_real A_84) N_30)))) ) 1.14/1.36 ( zero_zero_nat, zero_zero_real ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_real ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_real ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((P_2 $$unsorted) (I_2 $$unsorted) (K $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int I_2) K))) (not (hBOOL (hAPP_int_bool P_2 K))) (not (forall ((I $$unsorted)) (or (not (is_int I)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int I) K))) (not (hBOOL (hAPP_int_bool P_2 I))) (hBOOL (hAPP_int_bool P_2 (hAPP_int_int (minus_minus_int I) one_one_int)))) )) (hBOOL (hAPP_int_bool P_2 I_2))) ) 1.14/1.36 ( zprime, pls, (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_int zero_zero_int), pls, one_one_int ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int), pls, (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int), pls, (number_number_of_int pls) ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int), pls, s ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int), pls, skv_1 ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int), pls, skv_2 ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_int min), pls, min ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int pls), min, min ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_eq_int one_one_int), one_one_int, t ) 1.14/1.36 ( (hAPP_i1948725293t_bool ord_less_int pls), min, pls ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((N_28 $$unsorted) (A_83 $$unsorted) (B_53 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_83) B_53))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_83))) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_28))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int (power_power_int A_83) N_28)) (hAPP_nat_int (power_power_int B_53) N_28)))) ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int, zero_zero_int ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int, one_one_int ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((N_37 $$unsorted) (A_89 $$unsorted)) (let ((_let_0 (hAPP_n1699378549t_bool ord_less_nat one_one_nat))) (or (not (hBOOL (hAPP_nat_bool _let_0 A_89))) (hBOOL (hAPP_nat_bool _let_0 (hAPP_nat_nat (times_times_nat A_89) (hAPP_nat_nat (power_power_nat A_89) N_37)))))) ) 1.14/1.36 ( zero_zero_nat, zero_zero_nat ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_nat ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_nat ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((A_2 $$unsorted) (B_2 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) B_2))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_2) A_2))) (hBOOL (member_int B_2 (d22set A_2)))) ) 1.14/1.36 ( min, min ) 1.14/1.36 ( min, pls ) 1.14/1.36 ( pls, min ) 1.14/1.36 ( one_one_int, pls ) 1.14/1.36 ( t, one_one_int ) 1.14/1.36 ( (number_number_of_int (bit0 (bit1 pls))), pls ) 1.14/1.36 ( (number_number_of_int (bit1 (bit1 pls))), pls ) 1.14/1.36 ( (number_number_of_int pls), pls ) 1.14/1.36 ( s, pls ) 1.14/1.36 ( skv_1, pls ) 1.14/1.36 ( skv_2, pls ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((Z $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int Z) N_1))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) N_1))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Z) N_1))) ) 1.14/1.36 ( min, min ) 1.14/1.36 ( min, pls ) 1.14/1.36 ( pls, min ) 1.14/1.36 ( pls, one_one_int ) 1.14/1.36 ( pls, (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.36 ( pls, (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.36 ( pls, (number_number_of_int pls) ) 1.14/1.36 ( pls, s ) 1.14/1.36 ( pls, skv_1 ) 1.14/1.36 ( pls, skv_2 ) 1.14/1.36 ( one_one_int, t ) 1.14/1.36 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (hAPP_int_int (plus_plus_int (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int N) (hAPP_int_int (minus_minus_int X_2) Y_2))) (= (hAPP_int_int (div_mod_int X_2) N) (hAPP_int_int (div_mod_int Y_2) N))) ) 1.14/1.36 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))), (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (number_number_of_int min) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((A $$unsorted) (B $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A) (hAPP_int_int (minus_minus_int B) one_one_int)))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) B))) ) 1.14/1.36 ( min, min ) 1.14/1.36 ( min, zero_zero_int ) 1.14/1.36 ( pls, min ) 1.14/1.36 ( pls, zero_zero_int ) 1.14/1.36 ( pls, one_one_int ) 1.14/1.36 ( pls, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( one_one_int, t ) 1.14/1.36 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( s, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( skv_1, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( skv_2, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((B_48 $$unsorted) (Q_4 $$unsorted) (R_3 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (or (not (hBOOL (hAPP_int_bool _let_0 (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int B_48) Q_4)) R_3)))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int R_3) B_48))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_48))) (hBOOL (hAPP_int_bool _let_0 Q_4)))) ) 1.14/1.36 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m, one_one_int ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((BOUND_VARIABLE_22657 $$unsorted)) (or (= zero_zero_nat BOUND_VARIABLE_22657) (= zero_zero_real (hAPP_nat_real (power_power_real zero_zero_real) BOUND_VARIABLE_22657))) ) 1.14/1.36 ( zero_zero_nat ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((A_103 $$unsorted) (N_39 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (let ((_let_1 (power_power_nat A_103))) (= (hAPP_nat_nat (power_power_nat (hAPP_nat_nat _let_1 N_39)) _let_0) (hAPP_nat_nat _let_1 (hAPP_nat_nat (times_times_nat _let_0) N_39))))) ) 1.14/1.36 ( zero_zero_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.36 ( one_one_nat, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((A_91 $$unsorted)) (= (hAPP_nat_int (power_power_int A_91) (number_number_of_nat (bit1 (bit1 pls)))) (hAPP_int_int (times_times_int (hAPP_int_int (times_times_int A_91) A_91)) A_91)) ) 1.14/1.36 ( zero_zero_int ) 1.14/1.36 ( one_one_int ) 1.14/1.36 ( s1 ) 1.14/1.36 ( s ) 1.14/1.36 ( skv_4 ) 1.14/1.36 ( skv_5 ) 1.14/1.36 ( skv_6 ) 1.14/1.36 ( skv_7 ) 1.14/1.36 ( skv_8 ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((B_11 $$unsorted) (A_12 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_12) zero_zero_int))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_11) zero_zero_int))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) (hAPP_int_int (times_times_int A_12) B_11)))) ) 1.14/1.36 ( t, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( m, (number_number_of_int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.36 ( skv_3, (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((P_2 $$unsorted) (K $$unsorted) (I_2 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K) I_2))) (not (hBOOL (hAPP_int_bool P_2 (hAPP_int_int (plus_plus_int K) one_one_int)))) (not (forall ((I $$unsorted)) (or (not (is_int I)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K) I))) (not (hBOOL (hAPP_int_bool P_2 I))) (hBOOL (hAPP_int_bool P_2 (hAPP_int_int (plus_plus_int I) one_one_int)))) )) (hBOOL (hAPP_int_bool P_2 I_2))) ) 1.14/1.36 ( zprime, one_one_int, t ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((N_25 $$unsorted) (A_76 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (or (not (hBOOL (hAPP_int_bool _let_0 A_76))) (hBOOL (hAPP_int_bool _let_0 (hAPP_nat_int (power_power_int A_76) N_25))))) ) 1.14/1.36 ( zero_zero_nat, zero_zero_int ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_int ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), s1 ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), s ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), skv_4 ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), skv_5 ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), skv_6 ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), skv_7 ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), skv_8 ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((N_6 $$unsorted) (A_56 $$unsorted)) (let ((_let_0 (hAPP_r1134773055l_bool ord_less_real one_one_real))) (or (not (hBOOL (hAPP_real_bool _let_0 A_56))) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_6))) (hBOOL (hAPP_real_bool _let_0 (hAPP_nat_real (power_power_real A_56) N_6))))) ) 1.14/1.36 ( zero_zero_nat, zero_zero_real ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), one_one_real ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_real ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((N_26 $$unsorted) (A_77 $$unsorted) (B_52 $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_77) B_52))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_77))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int (power_power_int A_77) N_26)) (hAPP_nat_int (power_power_int B_52) N_26)))) ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int, zero_zero_int ) 1.14/1.36 ( (number_number_of_nat (bit0 (bit1 pls))), zero_zero_int, one_one_int ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((P_3 $$unsorted)) (or (not (is_int P_3)) (= (hBOOL (hAPP_int_bool zprime P_3)) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) P_3)) (forall ((M_2 $$unsorted)) (or (not (is_int M_2)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) M_2))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int M_2) P_3))) (= one_one_int M_2) (= P_3 M_2)) )))) ) 1.14/1.36 ( min ) 1.14/1.36 ( zero_zero_int ) 1.14/1.36 ( one_one_int ) 1.14/1.36 ( t ) 1.14/1.36 ( m ) 1.14/1.36 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( s1 ) 1.14/1.36 ( (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.36 ( s ) 1.14/1.36 ( (undefined_int int) ) 1.14/1.36 ( skv_1 ) 1.14/1.36 ( skv_2 ) 1.14/1.36 ( skv_3 ) 1.14/1.36 ( skv_4 ) 1.14/1.36 ( skv_5 ) 1.14/1.36 ( skv_6 ) 1.14/1.36 ( skv_7 ) 1.14/1.36 ( skv_8 ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (or (not (is_int Y_2)) (not (is_int X_2)) (= (= (number_number_of_int X_2) (number_number_of_int Y_2)) (= X_2 Y_2))) ) 1.14/1.36 ( min, min ) 1.14/1.36 ( min, zero_zero_int ) 1.14/1.36 ( zero_zero_int, min ) 1.14/1.36 ( pls, (undefined_int int) ) 1.14/1.36 ( one_one_int, one_one_int ) 1.14/1.36 ( one_one_int, m ) 1.14/1.36 ( t, t ) 1.14/1.36 ( t, s ) 1.14/1.36 ( m, one_one_int ) 1.14/1.36 ( s1, s1 ) 1.14/1.36 ( s1, skv_1 ) 1.14/1.36 ( s, t ) 1.14/1.36 ( (undefined_int int), pls ) 1.14/1.36 ( (undefined_int int), (undefined_int int) ) 1.14/1.36 ( skv_1, s1 ) 1.14/1.36 ( skv_2, skv_2 ) 1.14/1.36 ( skv_2, skv_3 ) 1.14/1.36 ( skv_3, skv_2 ) 1.14/1.36 ( skv_4, skv_4 ) 1.14/1.36 ( skv_4, skv_5 ) 1.14/1.36 ( skv_5, skv_4 ) 1.14/1.36 ( skv_6, skv_6 ) 1.14/1.36 ( skv_6, skv_8 ) 1.14/1.36 ( skv_7, skv_7 ) 1.14/1.36 ( skv_8, skv_6 ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (= zero_zero_nat (hAPP_nat_nat (minus_minus_nat N_1) (hAPP_nat_nat (plus_plus_nat N_1) M))) ) 1.14/1.36 ( one_one_nat, one_one_nat ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((W_7 $$unsorted)) (let ((_let_0 (number267125858f_real W_7))) (= (number267125858f_real (bit1 W_7)) (hAPP_real_real (plus_plus_real (hAPP_real_real (plus_plus_real one_one_real) _let_0)) _let_0))) ) 1.14/1.36 ( min ) 1.14/1.36 ( pls ) 1.14/1.36 ( (bit1 pls) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((B_1 $$unsorted) (Q_3 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (let ((_let_1 (hBOOL (hAPP_int_bool _let_0 B_1)))) (or (not (is_int Y_1)) (not (is_int B_1)) (and _let_1 (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Y_1) B_1))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Y_1))))) (and (not _let_1) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_1) Y_1))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Y_1) zero_zero_int))))) (= zero_zero_int B_1) (= Y_1 (hAPP_int_int (div_mod_int (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int B_1) Q_3)) Y_1)) B_1))))) ) 1.14/1.36 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m, one_one_int ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (number_number_of_int min))) (or (not (is_int N)) (not (is_int Ma)) (= (= one_one_int (hAPP_int_int (times_times_int Ma) N)) (or (and (= _let_0 N) (= _let_0 Ma)) (and (= one_one_int Ma) (= one_one_int N)))))) ) 1.14/1.36 ( (number_number_of_int (bit0 (bit0 (bit1 pls)))), m ) 1.14/1.36 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), t ) 1.14/1.36 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), skv_3 ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((Ma $$unsorted) (X_2 $$unsorted)) (= (not (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP_int_bool (zcong (hAPP_nat_int (power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))) X_2) Ma))) (not (is_int Y))) )) (hBOOL (hAPP_int_bool (quadRes Ma) X_2))) ) 1.14/1.36 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int), (number_number_of_int min) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (number_number_of_nat (bit0 (bit1 pls))))) (= (hAPP_nat_nat (times_times_nat (hAPP_nat_nat (plus_plus_nat X_1) Y_1)) (hAPP_nat_nat (minus_minus_nat X_1) Y_1)) (hAPP_nat_nat (minus_minus_nat (hAPP_nat_nat (power_power_nat X_1) _let_0)) (hAPP_nat_nat (power_power_nat Y_1) _let_0)))) ) 1.14/1.36 ( one_one_nat, one_one_nat ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((A_67 $$unsorted) (N_18 $$unsorted)) (let ((_let_0 (power_power_real A_67))) (let ((_let_1 (hAPP_nat_real _let_0 N_18))) (= (hAPP_real_real (times_times_real A_67) _let_1) (hAPP_real_real (times_times_real _let_1) A_67)))) ) 1.14/1.36 ( one_one_real, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.36 ( zero_zero_real, zero_zero_nat ) 1.14/1.36 ( zero_zero_real, (number_number_of_nat (bit0 (bit1 pls))) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((B $$unsorted)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B))) (= (hAPP_int_int (minus_minus_int B) one_one_int) (hAPP_int_int (div_mod_int (number_number_of_int min)) B))) ) 1.14/1.36 ( min ) 1.14/1.36 ( zero_zero_int ) 1.14/1.36 ( one_one_int ) 1.14/1.36 ( (hAPP_int_int (plus_plus_int (hAPP_int_int (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int) ) 1.14/1.36 ( (hAPP_nat_int (power_power_int s) (number_number_of_nat (bit0 (bit1 pls)))) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((Y $$unsorted)) (let ((_let_0 (times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))))) (let ((_let_1 (plus_plus_int (hAPP_int_int _let_0 m)))) (let ((_let_2 (hAPP_int_int _let_1 one_one_int))) (or (not (is_int Y)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Y))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Y) _let_2))) (not (hBOOL (hAPP_int_bool (zcong s1 Y) _let_2))) (= Y skv_1))))) ) 1.14/1.36 ( min ) 1.14/1.36 ( zero_zero_int ) 1.14/1.36 ( pls ) 1.14/1.36 ( one_one_int ) 1.14/1.36 ( t ) 1.14/1.36 ( m ) 1.14/1.36 ( s1 ) 1.14/1.36 ( (number_number_of_int (bit0 (bit1 pls))) ) 1.14/1.36 ( (number_number_of_int (bit1 (bit1 pls))) ) 1.14/1.36 ( (number_number_of_int pls) ) 1.14/1.36 ( s ) 1.14/1.36 ( (undefined_int int) ) 1.14/1.36 ( skv_1 ) 1.14/1.36 ( skv_2 ) 1.14/1.36 ( skv_3 ) 1.14/1.36 ( skv_4 ) 1.14/1.36 ( skv_5 ) 1.14/1.36 ( skv_6 ) 1.14/1.36 ( skv_7 ) 1.14/1.36 ( skv_8 ) 1.14/1.36 ) 1.14/1.36 % SZS output end Proof for theBenchmark 1.14/1.36 EOF