0.00/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.13/0.14 % Command : do_cvc5 %s %d 0.14/0.35 % Computer : n002.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 : 1200 0.14/0.35 % WCLimit : 120 0.14/0.35 % DateTime : Tue Jul 13 15:49:18 EDT 2021 0.14/0.35 % CPUTime : 0.20/0.54 %----THF division 0.20/0.54 ------- cvc5-thf casc 28 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 120... 0.20/0.54 --- Run --ho-elim --full-saturate-quant at 10... 0.70/0.87 % SZS status Theorem for theBenchmark 0.70/0.90 % SZS output start Proof for theBenchmark 0.70/0.90 (proof 0.70/0.90 (let ((_let_1 (bit1 pls))) (let ((_let_2 (bit0 _let_1))) (let ((_let_3 ((plus_plus_int ((times_times_int (number_number_of_int (bit0 _let_2))) m)) one_one_int))) (let ((_let_4 (number_number_of_nat _let_2))) (let ((_let_5 ((power_power_int s1) _let_4))) (let ((_let_6 ((power_power_int s) _let_4))) (let ((_let_7 (zcong _let_6))) (let ((_let_8 (number_number_of_int min))) (let ((_let_9 ((minus_minus_int _let_6) _let_8))) (let ((_let_10 (dvd_dvd_int _let_3))) (let ((_let_11 (number_number_of_int pls))) (let ((_let_12 (number_number_of_nat _let_1))) (let ((_let_13 (ord_less_int min))) (let ((_let_14 (ord_less_eq_int min))) (let ((_let_15 (= ((legendre _let_8) _let_3) one_one_int))) (let ((_let_16 ((quadRes _let_3) _let_8))) (let ((_let_17 ((times_times_int _let_3) t))) (let ((_let_18 (ord_less_int pls))) (let ((_let_19 (ord_less_eq_int pls))) (let ((_let_20 (= zero_zero_int _let_11))) (let ((_let_21 (number_number_of_int _let_1))) (let ((_let_22 (number267125858f_real pls))) (let ((_let_23 (= zero_zero_real _let_22))) (let ((_let_24 (forall ((X_2 int) (Y_2 int)) (=> ((ord_less_eq_int X_2) Y_2) (=> (not (= X_2 Y_2)) ((ord_less_int X_2) Y_2)))))) (let ((_let_25 ((ord_less_int one_one_int) t))) (let ((_let_26 (=> _let_25 (exists ((X int) (Y int)) (let ((_let_1 (bit0 (bit1 pls)))) (let ((_let_2 (number_number_of_nat _let_1))) (= ((plus_plus_int ((power_power_int X) _let_2)) ((power_power_int Y) _let_2)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 _let_1))) m)) one_one_int)))))))) (let ((_let_27 (ord_less_int zero_zero_int))) (let ((_let_28 (ord_less_eq_int zero_zero_int))) (let ((_let_29 (number_number_of_int _let_2))) (let ((_let_30 (number_number_of_nat pls))) (let ((_let_31 (= zero_zero_nat _let_30))) (let ((_let_32 (power_power_nat zero_zero_nat))) (let ((_let_33 (forall ((N_27 nat)) (let ((_let_1 ((power_power_nat zero_zero_nat) N_27))) (let ((_let_2 (= N_27 zero_zero_nat))) (and (=> _let_2 (= _let_1 one_one_nat)) (=> (not _let_2) (= _let_1 zero_zero_nat)))))))) (let ((_let_34 ((plus_plus_int _let_6) one_one_int))) (let ((_let_35 (number267125858f_real _let_1))) (let ((_let_36 (= one_one_real _let_35))) (let ((_let_37 (=> (= t one_one_int) (exists ((X int) (Y int)) (let ((_let_1 (bit0 (bit1 pls)))) (let ((_let_2 (number_number_of_nat _let_1))) (= ((plus_plus_int ((power_power_int X) _let_2)) ((power_power_int Y) _let_2)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 _let_1))) m)) one_one_int)))))))) (let ((_let_38 (= one_one_int _let_21))) (let ((_let_39 (not (exists ((X int) (Y int)) (let ((_let_1 (bit0 (bit1 pls)))) (let ((_let_2 (number_number_of_nat _let_1))) (= ((plus_plus_int ((power_power_int X) _let_2)) ((power_power_int Y) _let_2)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 _let_1))) m)) one_one_int)))))))) (let ((_let_40 ((ord_less_eq_int one_one_int) t))) (let ((_let_41 (forall ((X_2 int) (Y_2 int)) (or (not (ho_16 (ho_15 k_14 X_2) Y_2)) (= X_2 Y_2) (ho_16 (ho_15 k_36 X_2) Y_2))))) (let ((_let_42 (ho_3 k_19 (ho_3 k_8 pls)))) (let ((_let_43 (ho_16 (ho_15 k_36 _let_42) t))) (let ((_let_44 (= t _let_42))) (let ((_let_45 (ho_16 (ho_15 k_14 _let_42) t))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_44 _let_43))) (let ((_let_48 (EQ_RESOLVE (ASSUME |:args| (_let_24)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_24 7 12)) (PREPROCESS |:args| ((= (forall ((X_2 int) (Y_2 int)) (or (not ((ord_less_eq_int X_2) Y_2)) (= X_2 Y_2) ((ord_less_int X_2) Y_2))) _let_41))))))) (let ((_let_49 (not _let_47))) (let ((_let_50 (ASSUME |:args| (_let_20)))) (let ((_let_51 (ASSUME |:args| (_let_38)))) (let ((_let_52 (ASSUME |:args| (_let_31)))) (let ((_let_53 (EQ_RESOLVE (AND_ELIM (EQ_RESOLVE (ASSUME |:args| (_let_33)) (MACRO_SR_EQ_INTRO |:args| (_let_33 7 12))) |:args| (0)) (MACRO_SR_EQ_INTRO _let_52 _let_51 _let_50 |:args| ((= one_one_nat (_let_32 zero_zero_nat)) 7 12))))) (let ((_let_54 (ASSUME |:args| (_let_23)))) (let ((_let_55 (ASSUME |:args| (_let_36)))) (let ((_let_56 (forall ((X int) (Y int)) (let ((_let_1 (ho_3 k_8 pls))) (let ((_let_2 (ho_3 k_20 _let_1))) (let ((_let_3 (ho_23 k_22 _let_2))) (not (= (ho_3 (ho_2 k_1 (ho_3 (ho_2 k_21 (ho_3 k_19 (ho_3 k_20 _let_2))) m)) (ho_3 k_19 _let_1)) (ho_3 (ho_2 k_1 (ho_26 (ho_25 k_24 X) _let_3)) (ho_26 (ho_25 k_24 Y) _let_3)))))))))) (let ((_let_57 (not _let_44))) (let ((_let_58 (forall ((X int) (Y int)) (let ((_let_1 (ho_3 k_8 pls))) (let ((_let_2 (ho_3 k_20 _let_1))) (let ((_let_3 (ho_23 k_22 _let_2))) (not (= (ho_3 (ho_2 k_1 (ho_3 (ho_2 k_21 (ho_3 k_19 (ho_3 k_20 _let_2))) m)) (ho_3 k_19 _let_1)) (ho_3 (ho_2 k_1 (ho_26 (ho_25 k_24 X) _let_3)) (ho_26 (ho_25 k_24 Y) _let_3)))))))))) (let ((_let_59 (forall ((X int) (Y int)) (let ((_let_1 (ho_3 k_8 pls))) (let ((_let_2 (ho_3 k_20 _let_1))) (let ((_let_3 (ho_23 k_22 _let_2))) (not (= (ho_3 (ho_2 k_1 (ho_3 (ho_2 k_21 (ho_3 k_19 (ho_3 k_20 _let_2))) m)) (ho_3 k_19 _let_1)) (ho_3 (ho_2 k_1 (ho_26 (ho_25 k_24 X) _let_3)) (ho_26 (ho_25 k_24 Y) _let_3)))))))))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (THEORY_LEMMA |:args| ((= _let_59 _let_58) 12))) |:args| ((or _let_58 (not _let_59)))) (EQ_RESOLVE (ASSUME |:args| (_let_39)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_39 7 12)) (MACRO_SR_EQ_INTRO _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 |:args| ((forall ((X int) (Y int)) (let ((_let_1 (bit0 (bit1 pls)))) (let ((_let_2 (number_number_of_nat _let_1))) (not (= ((plus_plus_int ((times_times_int (number_number_of_int (bit0 _let_1))) m)) one_one_int) ((plus_plus_int ((power_power_int X) _let_2)) ((power_power_int Y) _let_2))))))) 7 12)) (PREPROCESS |:args| ((= (forall ((X int) (Y int)) (let ((_let_1 (bit1 pls))) (let ((_let_2 (bit0 _let_1))) (let ((_let_3 (number_number_of_nat _let_2))) (not (= ((plus_plus_int ((power_power_int X) _let_3)) ((power_power_int Y) _let_3)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 _let_2))) m)) (number_number_of_int _let_1)))))))) _let_59))))) |:args| (_let_58 false _let_59)))) (let ((_let_61 (not _let_58))) (let ((_let_62 (not _let_56))) (let ((_let_63 (not _let_43))) (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_48 |:args| (_let_42 t)) |:args| (_let_41)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_47)) |:args| ((or _let_43 _let_44 _let_46 _let_49))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME |:args| (_let_26)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_26 7 12)) (MACRO_SR_EQ_INTRO _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 |:args| ((=> _let_25 (not (forall ((X int) (Y int)) (let ((_let_1 (bit0 (bit1 pls)))) (let ((_let_2 (number_number_of_nat _let_1))) (not (= ((plus_plus_int ((times_times_int (number_number_of_int (bit0 _let_1))) m)) one_one_int) ((plus_plus_int ((power_power_int X) _let_2)) ((power_power_int Y) _let_2))))))))) 7 12)) (PREPROCESS |:args| ((= (=> ((ord_less_int _let_21) t) (not (forall ((X int) (Y int)) (let ((_let_1 (bit1 pls))) (let ((_let_2 (bit0 _let_1))) (let ((_let_3 (number_number_of_nat _let_2))) (not (= ((plus_plus_int ((power_power_int X) _let_3)) ((power_power_int Y) _let_3)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 _let_2))) m)) (number_number_of_int _let_1)))))))))) (=> _let_43 _let_61))))))) |:args| ((or _let_61 _let_63))) _let_60 |:args| (_let_63 false _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME |:args| (_let_37)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_37 7 12)) (MACRO_SR_EQ_INTRO _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 |:args| ((=> (= one_one_int t) (not (forall ((X int) (Y int)) (let ((_let_1 (bit0 (bit1 pls)))) (let ((_let_2 (number_number_of_nat _let_1))) (not (= ((plus_plus_int ((times_times_int (number_number_of_int (bit0 _let_1))) m)) one_one_int) ((plus_plus_int ((power_power_int X) _let_2)) ((power_power_int Y) _let_2))))))))) 7 12)) (PREPROCESS |:args| ((= (=> (= t _let_21) (not (forall ((X int) (Y int)) (let ((_let_1 (bit1 pls))) (let ((_let_2 (bit0 _let_1))) (let ((_let_3 (number_number_of_nat _let_2))) (not (= ((plus_plus_int ((power_power_int X) _let_3)) ((power_power_int Y) _let_3)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 _let_2))) m)) (number_number_of_int _let_1)))))))))) (=> _let_44 _let_62))))))) |:args| ((or _let_62 _let_57))) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM2 (THEORY_LEMMA |:args| ((= _let_56 _let_58) 12))) |:args| ((or _let_61 _let_56))) _let_60 |:args| (_let_56 false _let_58)) |:args| (_let_57 false _let_56)) (EQ_RESOLVE (ASSUME |:args| (_let_40)) (TRANS (MACRO_SR_EQ_INTRO _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 |:args| (_let_40 7 12)) (PREPROCESS |:args| ((= ((ord_less_eq_int _let_21) t) _let_45))))) |:args| (_let_49 true _let_43 true _let_44 false _let_45)) _let_48 |:args| (false true _let_47 false _let_41)) |:args| ((not false) (forall ((W_13 nat) (Y_24 nat) (X_26 nat) (Z_8 nat)) (let ((_let_1 (times_times_nat X_26))) (let ((_let_2 (times_times_nat W_13))) (= (= ((plus_plus_nat (_let_2 Y_24)) (_let_1 Z_8)) ((plus_plus_nat (_let_2 Z_8)) (_let_1 Y_24))) (or (= W_13 X_26) (= Y_24 Z_8)))))) (forall ((Lx_6 int) (Ly_4 int) (Rx_6 int) (Ry_4 int)) (let ((_let_1 (times_times_int Lx_6))) (= ((times_times_int (_let_1 Ly_4)) ((times_times_int Rx_6) Ry_4)) ((times_times_int (_let_1 Rx_6)) ((times_times_int Ly_4) Ry_4))))) (forall ((W_2 int)) (let ((_let_1 (number_number_of_nat W_2))) (let ((_let_2 ((power_power_real zero_zero_real) _let_1))) (let ((_let_3 (= _let_1 zero_zero_nat))) (and (=> _let_3 (= _let_2 one_one_real)) (=> (not _let_3) (= _let_2 zero_zero_real))))))) (forall ((A_16 int)) (not ((ord_less_int ((power_power_int A_16) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int))) (forall ((A_5 nat) (N_5 nat) (N_4 nat)) (let ((_let_1 (power_power_nat A_5))) (=> ((ord_less_nat N_5) N_4) (=> ((ord_less_nat one_one_nat) A_5) ((ord_less_nat (_let_1 N_5)) (_let_1 N_4)))))) (forall ((A_59 nat) (C_6 nat) (D_3 nat)) (let ((_let_1 (plus_plus_nat A_59))) (let ((_let_2 (plus_plus_nat C_6))) (= (_let_1 (_let_2 D_3)) (_let_2 (_let_1 D_3)))))) (forall ((X_4 int)) (= ((power_power_int X_4) zero_zero_nat) one_one_int)) (forall ((N_26 nat) (A_35 real) (B_8 real)) (=> ((ord_less_real A_35) B_8) (=> ((ord_less_eq_real zero_zero_real) A_35) (=> ((ord_less_nat zero_zero_nat) N_26) ((ord_less_real ((power_power_real A_35) N_26)) ((power_power_real B_8) N_26)))))) (forall ((A_8 real) (N_9 nat) (N_8 nat)) (let ((_let_1 (power_power_real A_8))) (=> ((ord_less_eq_nat N_9) N_8) (=> ((ord_less_eq_real one_one_real) A_8) ((ord_less_eq_real (_let_1 N_9)) (_let_1 N_8)))))) (forall ((W int) (Z int)) (let ((_let_1 (ord_less_int W))) (= (_let_1 ((plus_plus_int Z) one_one_int)) (or (_let_1 Z) (= W Z))))) (not (= min pls)) (forall ((A_53 int)) (= ((times_times_int A_53) one_one_int) A_53)) _let_40 (_let_13 zero_zero_int) (forall ((N_10 nat) (A_9 nat)) (let ((_let_1 (ord_less_eq_nat one_one_nat))) (=> (_let_1 A_9) (_let_1 ((power_power_nat A_9) N_10))))) (forall ((M int) (Y_1 int) (X_1 int)) (let ((_let_1 (ord_less_int zero_zero_int))) (=> (_let_1 X_1) (=> (_let_1 Y_1) (=> (_let_1 M) (=> (((zcong X_1) Y_1) M) (=> ((ord_less_int X_1) M) (=> ((ord_less_int Y_1) M) (= X_1 Y_1))))))))) (forall ((Lx_1 nat) (Rx_1 nat) (Ry_1 nat)) (let ((_let_1 (times_times_nat Lx_1))) (= (_let_1 ((times_times_nat Rx_1) Ry_1)) ((times_times_nat (_let_1 Rx_1)) Ry_1)))) (forall ((A_64 int) (B_20 int)) (= ((times_times_int A_64) B_20) ((times_times_int B_20) A_64))) (forall ((W int)) ((ord_less_eq_int W) W)) (forall ((C_1 real) (D_1 real) (A_21 real) (B_4 real) (R_3 real)) (let ((_let_1 (times_times_real R_3))) (=> (not (= R_3 zero_zero_real)) (=> (and (= A_21 B_4) (not (= C_1 D_1))) (not (= ((plus_plus_real A_21) (_let_1 C_1)) ((plus_plus_real B_4) (_let_1 D_1)))))))) (not (forall ((S int)) (let ((_let_1 ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) (not (and ((ord_less_int S) _let_1) (((zcong s1) S) _let_1) ((ord_less_eq_int zero_zero_int) S)))))) (forall ((K int) (L int)) (= ((minus_minus_int (bit0 K)) (bit0 L)) (bit0 ((minus_minus_int K) L)))) (forall ((K int)) (= (bit0 K) ((plus_plus_int K) K))) (forall ((V_1 int)) (= ((ord_less_nat zero_zero_nat) (number_number_of_nat V_1)) ((ord_less_int pls) V_1))) ((ord_less_int t) _let_3) (forall ((W_14 int) (X_29 int)) (let ((_let_1 (number_number_of_int W_14))) (= (= X_29 _let_1) (= _let_1 X_29)))) (forall ((A_39 int) (M_8 nat) (N_33 nat)) (let ((_let_1 (power_power_int A_39))) (=> ((ord_less_eq_nat M_8) N_33) ((dvd_dvd_int (_let_1 M_8)) (_let_1 N_33))))) _let_15 (forall ((K int)) (= ((ord_less_eq_int pls) K) ((ord_less_int pls) (bit1 K)))) (forall ((X_1 int) (P int)) (= (((zcong X_1) zero_zero_int) P) ((dvd_dvd_int P) X_1))) (forall ((A int) (P int)) (let ((_let_1 ((minus_minus_int P) one_one_int))) (= (((zcong ((times_times_int A) _let_1)) one_one_int) P) (((zcong A) _let_1) P)))) (forall ((X_6 real) (Y_4 real)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (= (or (not (= X_6 zero_zero_real)) (not (= Y_4 zero_zero_real))) ((ord_less_real zero_zero_real) ((plus_plus_real ((power_power_real X_6) _let_1)) ((power_power_real Y_4) _let_1)))))) (forall ((A int) (P int)) (let ((_let_1 (zcong A))) (=> (zprime P) (=> ((ord_less_int zero_zero_int) A) (=> (((zcong ((times_times_int A) A)) one_one_int) P) (or ((_let_1 ((minus_minus_int P) one_one_int)) P) ((_let_1 one_one_int) P))))))) (forall ((K int) (L int)) (= ((times_times_int (bit0 K)) L) (bit0 ((times_times_int K) L)))) (forall ((A int)) (let ((_let_1 (bit1 pls))) (let ((_let_2 (power_power_int A))) (= ((times_times_int A) (_let_2 (number_number_of_nat (bit0 _let_1)))) (_let_2 (number_number_of_nat (bit1 _let_1))))))) (not (= zero_zero_int one_one_int)) (forall ((N_32 nat) (M_7 nat) (X_22 real) (Y_20 real)) (=> ((dvd_dvd_real X_22) Y_20) (=> ((ord_less_eq_nat N_32) M_7) ((dvd_dvd_real ((power_power_real X_22) N_32)) ((power_power_real Y_20) M_7))))) (forall ((K int) (L int)) (= ((ord_less_int K) L) ((ord_less_int (bit0 K)) (bit0 L)))) (forall ((X_12 int) (Y_10 int)) (let ((_let_1 (ord_less_eq_int zero_zero_int))) (let ((_let_2 (number_number_of_nat (bit0 (bit1 pls))))) (=> (= ((power_power_int X_12) _let_2) ((power_power_int Y_10) _let_2)) (=> (_let_1 X_12) (=> (_let_1 Y_10) (= X_12 Y_10))))))) (forall ((C int) (D int) (A int) (B_1 int) (M int)) (=> (((zcong A) B_1) M) (=> (((zcong C) D) M) (((zcong ((plus_plus_int A) C)) ((plus_plus_int B_1) D)) M)))) (forall ((K int)) (= ((ord_less_int K) pls) ((ord_less_eq_int (bit1 K)) pls))) ((ord_less_nat zero_zero_nat) _let_4) (forall ((X_12 nat) (Y_10 nat)) (let ((_let_1 (ord_less_eq_nat zero_zero_nat))) (let ((_let_2 (number_number_of_nat (bit0 (bit1 pls))))) (=> (= ((power_power_nat X_12) _let_2) ((power_power_nat Y_10) _let_2)) (=> (_let_1 X_12) (=> (_let_1 Y_10) (= X_12 Y_10))))))) (forall ((A_65 int)) (= ((power_power_int A_65) (number_number_of_nat (bit0 (bit1 pls)))) ((times_times_int A_65) A_65))) (forall ((A int) (X_1 int)) (let ((_let_1 ((minus_minus_int A) one_one_int))) (let ((_let_2 (ord_less_int X_1))) (=> ((ord_less_int zero_zero_int) X_1) (=> (_let_2 A) (=> (not (= X_1 _let_1)) (_let_2 _let_1))))))) (forall ((K int) (L int)) (= ((minus_minus_int (bit1 K)) (bit1 L)) (bit0 ((minus_minus_int K) L)))) (forall ((N nat) (X_1 nat) (Y_1 nat)) (=> ((dvd_dvd_nat X_1) Y_1) ((dvd_dvd_nat ((power_power_nat X_1) N)) ((power_power_nat Y_1) N)))) _let_39 (forall ((K int)) (let ((_let_1 (ord_less_eq_int pls))) (= (_let_1 (bit0 K)) (_let_1 K)))) (forall ((Lx_5 real) (Ly_3 real) (Rx_5 real) (Ry_3 real)) (let ((_let_1 (times_times_real ((times_times_real Lx_5) Ly_3)))) (let ((_let_2 (times_times_real Rx_5))) (= (_let_1 (_let_2 Ry_3)) (_let_2 (_let_1 Ry_3)))))) (forall ((Z int)) (= ((times_times_int Z) one_one_int) Z)) (forall ((C_1 int) (D_1 int) (A_21 int) (B_4 int) (R_3 int)) (let ((_let_1 (times_times_int R_3))) (=> (not (= R_3 zero_zero_int)) (=> (and (not (= C_1 D_1)) (= A_21 B_4)) (not (= ((plus_plus_int A_21) (_let_1 C_1)) ((plus_plus_int B_4) (_let_1 D_1)))))))) (forall ((Lx_6 nat) (Ly_4 nat) (Rx_6 nat) (Ry_4 nat)) (let ((_let_1 (times_times_nat Lx_6))) (= ((times_times_nat (_let_1 Ly_4)) ((times_times_nat Rx_6) Ry_4)) ((times_times_nat (_let_1 Rx_6)) ((times_times_nat Ly_4) Ry_4))))) (forall ((Z_1 real)) (= ((times_times_real Z_1) (number267125858f_real (bit0 (bit1 pls)))) ((plus_plus_real Z_1) Z_1))) (forall ((A_60 real) (C_7 real) (D_4 real)) (let ((_let_1 (plus_plus_real A_60))) (= (_let_1 ((plus_plus_real C_7) D_4)) ((plus_plus_real (_let_1 C_7)) D_4)))) (= _let_34 _let_17) (forall ((N nat) (B_1 int) (A int) (P int)) (let ((_let_1 (dvd_dvd_int ((power_power_int P) N)))) (=> (zprime P) (=> (not ((dvd_dvd_int P) A)) (=> (_let_1 ((times_times_int A) B_1)) (_let_1 B_1)))))) (forall ((K int) (I int) (J int)) (let ((_let_1 (ord_less_eq_int I))) (=> (_let_1 J) (=> ((ord_less_eq_int J) K) (_let_1 K))))) (forall ((M nat) (N nat)) (= (= ((power_power_nat M) N) zero_zero_nat) (and (not (= N zero_zero_nat)) (= M zero_zero_nat)))) (forall ((Z nat)) (= ((times_times_nat Z) (number_number_of_nat (bit0 (bit1 pls)))) ((plus_plus_nat Z) Z))) (forall ((M int) (X_1 int)) (=> ((ord_less_int zero_zero_int) X_1) (=> ((ord_less_int X_1) M) (not (((zcong X_1) zero_zero_int) M))))) (forall ((N nat) (M nat)) (= (and (= M one_one_nat) (= N one_one_nat)) (= ((times_times_nat N) M) one_one_nat))) (forall ((A_33 real)) (= ((times_times_real A_33) zero_zero_real) zero_zero_real)) (forall ((N_3 nat) (A_2 nat)) (let ((_let_1 (ord_less_nat one_one_nat))) (=> (_let_1 A_2) (=> ((ord_less_nat zero_zero_nat) N_3) (_let_1 ((power_power_nat A_2) N_3)))))) (forall ((A int) (B_1 int) (M int)) (= (((zcong A) B_1) M) (exists ((K_1 int)) (= B_1 ((plus_plus_int A) ((times_times_int M) K_1)))))) (forall ((A_56 real) (M_13 real) (B_16 real)) (= ((plus_plus_real ((times_times_real A_56) M_13)) ((times_times_real B_16) M_13)) ((times_times_real ((plus_plus_real A_56) B_16)) M_13))) (forall ((Lx_5 int) (Ly_3 int) (Rx_5 int) (Ry_3 int)) (let ((_let_1 (times_times_int ((times_times_int Lx_5) Ly_3)))) (let ((_let_2 (times_times_int Rx_5))) (= (_let_1 (_let_2 Ry_3)) (_let_2 (_let_1 Ry_3)))))) (forall ((A_24 int) (N_21 nat) (N_20 nat)) (let ((_let_1 (power_power_int A_24))) (=> ((ord_less_eq_nat N_21) N_20) (=> ((ord_less_eq_int zero_zero_int) A_24) (=> ((ord_less_eq_int A_24) one_one_int) ((ord_less_eq_int (_let_1 N_20)) (_let_1 N_21))))))) (forall ((M_10 nat)) (= ((plus_plus_nat M_10) M_10) ((times_times_nat ((plus_plus_nat one_one_nat) one_one_nat)) M_10))) (forall ((A_8 nat) (N_9 nat) (N_8 nat)) (let ((_let_1 (power_power_nat A_8))) (=> ((ord_less_eq_nat N_9) N_8) (=> ((ord_less_eq_nat one_one_nat) A_8) ((ord_less_eq_nat (_let_1 N_9)) (_let_1 N_8)))))) (forall ((X_7 int) (Y_5 int)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (not ((ord_less_int ((plus_plus_int ((power_power_int X_7) _let_1)) ((power_power_int Y_5) _let_1))) zero_zero_int)))) (forall ((X_38 nat) (Y_30 nat)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (= ((power_power_nat ((plus_plus_nat X_38) Y_30)) _let_1) ((plus_plus_nat ((plus_plus_nat ((power_power_nat X_38) _let_1)) ((power_power_nat Y_30) _let_1))) ((times_times_nat ((times_times_nat _let_1) X_38)) Y_30))))) (forall ((M_6 nat) (A_38 real) (N_31 nat) (B_10 real)) (let ((_let_1 (power_power_real A_38))) (=> ((dvd_dvd_real (_let_1 N_31)) B_10) (=> ((ord_less_eq_nat M_6) N_31) ((dvd_dvd_real (_let_1 M_6)) B_10))))) (forall ((K1 int) (K2 int)) (= ((ord_less_eq_int K1) K2) ((ord_less_eq_int (bit0 K1)) (bit0 K2)))) (forall ((X_1 int) (Y_1 int)) (or ((ord_less_int Y_1) X_1) (= X_1 Y_1) ((ord_less_int X_1) Y_1))) (forall ((X_24 real) (Y_22 real) (Q_2 nat)) (= ((power_power_real ((times_times_real X_24) Y_22)) Q_2) ((times_times_real ((power_power_real X_24) Q_2)) ((power_power_real Y_22) Q_2)))) (forall ((N nat)) ((ord_less_eq_real one_one_real) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N))) (forall ((N_37 nat) (A_43 int)) (let ((_let_1 ((power_power_int A_43) N_37))) (=> ((ord_less_int one_one_int) A_43) ((ord_less_int _let_1) ((times_times_int A_43) _let_1))))) (forall ((K int)) (= ((ord_less_int (bit0 K)) pls) ((ord_less_int K) pls))) (forall ((Z_9 int) (Z int) (W_15 int) (W int)) (=> ((ord_less_int W_15) W) (=> ((ord_less_eq_int Z_9) Z) ((ord_less_int ((plus_plus_int W_15) Z_9)) ((plus_plus_int W) Z))))) (forall ((C int) (X_1 int) (T int) (A int) (D int)) (let ((_let_1 (plus_plus_int X_1))) (let ((_let_2 (dvd_dvd_int A))) (=> (_let_2 D) (= (_let_2 (_let_1 T)) (_let_2 ((plus_plus_int (_let_1 ((times_times_int C) D))) T))))))) (forall ((A_18 int)) (= (= A_18 zero_zero_int) (= ((power_power_int A_18) (number_number_of_nat (bit0 (bit1 pls)))) zero_zero_int))) (forall ((A_39 nat) (M_8 nat) (N_33 nat)) (let ((_let_1 (power_power_nat A_39))) (=> ((ord_less_eq_nat M_8) N_33) ((dvd_dvd_nat (_let_1 M_8)) (_let_1 N_33))))) (forall ((A_48 real)) (= ((plus_plus_real (number267125858f_real pls)) A_48) A_48)) (forall ((Z int) (N int)) (=> ((dvd_dvd_int Z) N) (=> ((ord_less_int zero_zero_int) N) ((ord_less_eq_int Z) N)))) (forall ((Z_3 int)) (= ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_3) ((plus_plus_int Z_3) Z_3))) (forall ((X_37 int)) (= ((times_times_int X_37) X_37) ((power_power_int X_37) (number_number_of_nat (bit0 (bit1 pls)))))) (forall ((X_1 int)) ((ord_less_eq_int X_1) ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls)))))) (forall ((M int)) (let ((_let_1 ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) M)) one_one_int))) (=> (zprime _let_1) (= ((legendre (number_number_of_int min)) _let_1) one_one_int)))) (forall ((Z_4 nat)) (= ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z_4) ((plus_plus_nat Z_4) Z_4))) (forall ((A_14 real) (N_16 nat)) (let ((_let_1 ((power_power_real A_14) N_16))) (= ((times_times_real _let_1) A_14) ((times_times_real A_14) _let_1)))) (forall ((A_62 nat) (B_18 nat) (C_9 nat)) (let ((_let_1 (plus_plus_nat A_62))) (= ((plus_plus_nat (_let_1 B_18)) C_9) ((plus_plus_nat (_let_1 C_9)) B_18)))) (forall ((K int)) (= ((ord_less_int min) K) ((ord_less_eq_int min) (bit0 K)))) (forall ((K int)) (= ((plus_plus_int K) pls) K)) (forall ((V_14 int) (V_13 int)) (let ((_let_1 (ord_less_eq_int pls))) (=> (_let_1 V_13) (=> (_let_1 V_14) (= ((times_times_nat (number_number_of_nat V_13)) (number_number_of_nat V_14)) (number_number_of_nat ((times_times_int V_13) V_14))))))) (forall ((A_37 real) (N_30 nat) (B_9 real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> (= ((power_power_real A_37) N_30) ((power_power_real B_9) N_30)) (=> (_let_1 A_37) (=> (_let_1 B_9) (=> ((ord_less_nat zero_zero_nat) N_30) (= A_37 B_9))))))) (_let_28 zero_zero_int) (forall ((Y_13 int)) (= ((ord_less_int pls) Y_13) ((ord_less_real zero_zero_real) (number267125858f_real Y_13)))) (forall ((W_6 int)) (let ((_let_1 (number267125858f_real W_6))) (= (number267125858f_real (bit1 W_6)) ((plus_plus_real ((plus_plus_real one_one_real) _let_1)) _let_1)))) (not (_let_18 zero_zero_int)) (forall ((B_1 int) (M int) (A int)) (let ((_let_1 (ord_less_int zero_zero_int))) (=> (_let_1 A) (=> ((ord_less_int A) M) (=> (_let_1 B_1) (=> ((ord_less_int B_1) A) (not (((zcong A) B_1) M)))))))) (forall ((X_1 real) (Y_1 real)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (= (and (= X_1 zero_zero_real) (= Y_1 zero_zero_real)) (= ((plus_plus_real ((power_power_real X_1) _let_1)) ((power_power_real Y_1) _let_1)) zero_zero_real)))) (forall ((K1 int) (K2 int)) (= ((ord_less_eq_int (bit1 K1)) (bit0 K2)) ((ord_less_int K1) K2))) (forall ((N_25 nat) (A_28 int)) (let ((_let_1 (ord_less_eq_int zero_zero_int))) (=> (_let_1 A_28) (_let_1 ((power_power_int A_28) N_25))))) (forall ((W_14 int) (X_29 nat)) (let ((_let_1 (number_number_of_nat W_14))) (= (= _let_1 X_29) (= X_29 _let_1)))) (= ((power_power_nat one_one_nat) _let_4) one_one_nat) (forall ((A_48 int)) (= ((plus_plus_int (number_number_of_int pls)) A_48) A_48)) (forall ((A_57 nat) (N_38 nat)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (let ((_let_2 (power_power_nat A_57))) (= (_let_2 ((times_times_nat _let_1) N_38)) ((power_power_nat (_let_2 N_38)) _let_1))))) (forall ((A_17 real)) ((ord_less_eq_real zero_zero_real) ((power_power_real A_17) (number_number_of_nat (bit0 (bit1 pls)))))) (_let_28 (number_number_of_int (bit1 _let_1))) (forall ((A int) (B_1 int) (M int)) (= (((zcong A) B_1) M) ((dvd_dvd_int M) ((minus_minus_int A) B_1)))) (forall ((X_3 real) (N_2 nat)) (=> (or ((ord_less_nat zero_zero_nat) N_2) (= X_3 one_one_real)) ((dvd_dvd_real X_3) ((power_power_real X_3) N_2)))) (forall ((X_1 real) (Y_1 real)) (= (and (= Y_1 zero_zero_real) (= X_1 zero_zero_real)) (= ((plus_plus_real ((times_times_real X_1) X_1)) ((times_times_real Y_1) Y_1)) zero_zero_real))) (forall ((A_47 int)) (= ((plus_plus_int A_47) (number_number_of_int pls)) A_47)) (forall ((K int)) (let ((_let_1 (ord_less_int min))) (= (_let_1 (bit0 K)) (_let_1 K)))) (forall ((A_52 real)) (= ((times_times_real one_one_real) A_52) A_52)) (forall ((K int)) (= ((ord_less_int K) pls) ((ord_less_int (bit1 K)) pls))) (forall ((K int) (L int)) (not (= (bit1 K) (bit0 L)))) (forall ((A_55 nat) (B_15 nat) (C_4 nat)) (= ((times_times_nat ((plus_plus_nat A_55) B_15)) C_4) ((plus_plus_nat ((times_times_nat A_55) C_4)) ((times_times_nat B_15) C_4)))) (forall ((A int) (P int)) (=> (zprime P) (=> ((ord_less_int zero_zero_int) A) (=> ((ord_less_int A) P) (=> (((zcong ((times_times_int A) A)) one_one_int) P) (or (= A ((minus_minus_int P) one_one_int)) (= A one_one_int))))))) (forall ((A_56 int) (M_13 int) (B_16 int)) (= ((plus_plus_int ((times_times_int A_56) M_13)) ((times_times_int B_16) M_13)) ((times_times_int ((plus_plus_int A_56) B_16)) M_13))) (forall ((X_14 int)) (= ((ord_less_eq_int (number_number_of_int X_14)) zero_zero_int) ((ord_less_eq_int X_14) pls))) (forall ((Lx_2 nat) (Ly nat) (Rx_2 nat)) (let ((_let_1 (times_times_nat Lx_2))) (= ((times_times_nat (_let_1 Ly)) Rx_2) (_let_1 ((times_times_nat Ly) Rx_2))))) (forall ((W int)) (= ((ord_less_int W) zero_zero_int) ((ord_less_int (bit0 W)) zero_zero_int))) (= one_one_nat _let_12) (forall ((B_1 nat) (D nat) (A nat)) (let ((_let_1 (dvd_dvd_nat D))) (=> (_let_1 A) (=> (_let_1 ((plus_plus_nat A) B_1)) (_let_1 B_1))))) (forall ((N_28 nat) (A_36 real)) (=> (not (= A_36 zero_zero_real)) (not (= ((power_power_real A_36) N_28) zero_zero_real)))) (forall ((X_15 int)) (= ((ord_less_int X_15) pls) ((ord_less_int (number_number_of_int X_15)) zero_zero_int))) (forall ((A_63 int) (B_19 int) (C_10 int) (D_5 int)) (let ((_let_1 (plus_plus_int A_63))) (= ((plus_plus_int (_let_1 B_19)) ((plus_plus_int C_10) D_5)) ((plus_plus_int (_let_1 C_10)) ((plus_plus_int B_19) D_5))))) (not (forall ((T_1 int)) (let ((_let_1 (bit0 (bit1 pls)))) (not (= ((plus_plus_int ((power_power_int s) (number_number_of_nat _let_1))) one_one_int) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 _let_1))) m)) one_one_int)) T_1)))))) (forall ((X_18 real) (Y_16 real)) (= (and (= X_18 zero_zero_real) (= Y_16 zero_zero_real)) ((ord_less_eq_real ((plus_plus_real ((times_times_real X_18) X_18)) ((times_times_real Y_16) Y_16))) zero_zero_real))) (forall ((A nat) (N nat) (B_1 nat)) (=> ((dvd_dvd_nat ((power_power_nat A) N)) ((power_power_nat B_1) N)) (=> (not (= N zero_zero_nat)) ((dvd_dvd_nat A) B_1)))) (forall ((A_50 real) (M_12 real)) (= ((plus_plus_real ((times_times_real A_50) M_12)) M_12) ((times_times_real ((plus_plus_real A_50) one_one_real)) M_12))) (= ((plus_plus_int one_one_int) one_one_int) _let_29) (forall ((Lx int) (Rx int) (Ry int)) (let ((_let_1 (times_times_int Lx))) (let ((_let_2 (times_times_int Rx))) (= (_let_1 (_let_2 Ry)) (_let_2 (_let_1 Ry)))))) (forall ((A_11 nat) (M_4 nat) (N_12 nat)) (let ((_let_1 (power_power_nat A_11))) (= (_let_1 ((times_times_nat M_4) N_12)) ((power_power_nat (_let_1 M_4)) N_12)))) (forall ((V_1 int)) (= ((ord_less_eq_int V_1) pls) (= zero_zero_nat (number_number_of_nat V_1)))) (forall ((B_7 int) (A_30 int)) (= (= B_7 ((plus_plus_int B_7) A_30)) (= A_30 zero_zero_int))) (forall ((A_45 real)) (= ((times_times_real A_45) (number267125858f_real (bit1 pls))) A_45)) (forall ((V_2 int) (V_1 int)) (let ((_let_1 (number_number_of_nat V_2))) (let ((_let_2 (number_number_of_nat V_1))) (let ((_let_3 ((plus_plus_nat _let_2) _let_1))) (let ((_let_4 ((ord_less_int V_1) pls))) (let ((_let_5 ((ord_less_int V_2) pls))) (and (=> (not _let_4) (and (=> _let_5 (= _let_3 _let_2)) (=> (not _let_5) (= _let_3 (number_number_of_nat ((plus_plus_int V_1) V_2)))))) (=> _let_4 (= _let_3 _let_1))))))))) (forall ((X_32 int) (Y_28 int)) (= ((ord_less_eq_int X_32) Y_28) ((ord_less_eq_int (number_number_of_int X_32)) (number_number_of_int Y_28)))) (forall ((A int) (B_1 int) (M int)) (= (((zcong B_1) A) M) (((zcong A) B_1) M))) (forall ((A_10 int) (N_11 nat)) ((ord_less_eq_int zero_zero_int) ((power_power_int A_10) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_11)))) (forall ((A_23 real) (N_19 nat) (N_18 nat)) (let ((_let_1 (power_power_real A_23))) (=> ((ord_less_nat N_19) N_18) (=> ((ord_less_real zero_zero_real) A_23) (=> ((ord_less_real A_23) one_one_real) ((ord_less_real (_let_1 N_18)) (_let_1 N_19))))))) (forall ((X_1 int) (Y_1 int) (Z int)) (let ((_let_1 (plus_plus_int X_1))) (let ((_let_2 (plus_plus_int Y_1))) (= (_let_1 (_let_2 Z)) (_let_2 (_let_1 Z)))))) (forall ((W int) (Z int)) (= ((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z) ((ord_less_int W) Z))) (forall ((D int) (C int) (A int) (B_1 int) (M int)) (let ((_let_1 (zcong A))) (=> ((_let_1 B_1) M) (=> (= B_1 C) (=> (((zcong C) D) M) ((_let_1 D) M)))))) (forall ((Y_1 int) (N nat) (P int)) (let ((_let_1 (dvd_dvd_int P))) (=> (zprime P) (=> (_let_1 ((power_power_int Y_1) N)) (=> ((ord_less_nat zero_zero_nat) N) (_let_1 Y_1)))))) (_let_28 one_one_int) (forall ((X_19 real) (Y_17 real)) ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((times_times_real X_19) X_19)) ((times_times_real Y_17) Y_17)))) (forall ((N_10 nat) (A_9 int)) (let ((_let_1 (ord_less_eq_int one_one_int))) (=> (_let_1 A_9) (_let_1 ((power_power_int A_9) N_10))))) (forall ((A int) (B_1 int)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (= ((times_times_int ((plus_plus_int A) B_1)) ((minus_minus_int A) B_1)) ((minus_minus_int ((power_power_int A) _let_1)) ((power_power_int B_1) _let_1))))) (forall ((A_61 nat) (B_17 nat) (C_8 nat)) (let ((_let_1 (plus_plus_nat A_61))) (= ((plus_plus_nat (_let_1 B_17)) C_8) (_let_1 ((plus_plus_nat B_17) C_8))))) (forall ((X_28 int)) (= ((ord_less_int X_28) (bit1 pls)) ((ord_less_int (number_number_of_int X_28)) one_one_int))) _let_38 (= _let_35 one_one_real) (forall ((Z_3 real)) (= ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_3) ((plus_plus_real Z_3) Z_3))) (forall ((X_1 real) (Y_1 real)) (= ((ord_less_eq_real X_1) Y_1) ((ord_less_eq_real ((minus_minus_real X_1) Y_1)) zero_zero_real))) (forall ((M_10 real)) (= ((plus_plus_real M_10) M_10) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) M_10))) (forall ((V_9 int) (B_12 nat) (C_2 nat)) (let ((_let_1 (times_times_nat (number_number_of_nat V_9)))) (= (_let_1 ((plus_plus_nat B_12) C_2)) ((plus_plus_nat (_let_1 B_12)) (_let_1 C_2))))) (forall ((K int) (L int)) (= ((ord_less_int (number_number_of_int K)) (number_number_of_int L)) ((ord_less_int K) L))) (forall ((X_1 real) (Y_1 real)) (= ((ord_less_eq_real X_1) Y_1) (or ((ord_less_real X_1) Y_1) (= X_1 Y_1)))) (forall ((K1 int) (K2 int)) (= ((ord_less_int K1) K2) ((ord_less_int (bit1 K1)) (bit1 K2)))) (forall ((V_15 int) (W_16 int)) (let ((_let_1 (number_number_of_int W_16))) (let ((_let_2 (number_number_of_int V_15))) (= (not ((ord_less_int _let_1) _let_2)) ((ord_less_eq_int _let_2) _let_1))))) (forall ((K int) (L int)) (= ((ord_less_eq_int K) L) ((ord_less_int (bit0 K)) (bit1 L)))) (forall ((M_2 nat) (N_6 nat) (A_6 int)) (let ((_let_1 (power_power_int A_6))) (=> ((ord_less_int one_one_int) A_6) (=> ((ord_less_int (_let_1 M_2)) (_let_1 N_6)) ((ord_less_nat M_2) N_6))))) (forall ((X_35 int) (P_2 nat) (Q_4 nat)) (let ((_let_1 (power_power_int X_35))) (= ((power_power_int (_let_1 P_2)) Q_4) (_let_1 ((times_times_nat P_2) Q_4))))) (= (bit0 pls) pls) (forall ((M int) (X_1 int)) (=> ((ord_less_eq_int zero_zero_int) X_1) (=> ((ord_less_int X_1) M) (=> (((zcong X_1) zero_zero_int) M) (= X_1 zero_zero_int))))) (forall ((L int)) (= (= pls (bit0 L)) (= pls L))) (forall ((C nat) (A nat) (B_1 nat)) (=> ((dvd_dvd_nat A) B_1) ((dvd_dvd_nat ((times_times_nat A) C)) ((times_times_nat B_1) C)))) (forall ((Lx_2 real) (Ly real) (Rx_2 real)) (let ((_let_1 (times_times_real Lx_2))) (= ((times_times_real (_let_1 Ly)) Rx_2) (_let_1 ((times_times_real Ly) Rx_2))))) (forall ((N nat)) (let ((_let_1 (number_number_of_int min))) (let ((_let_2 ((power_power_int _let_1) N))) (or (= _let_2 one_one_int) (= _let_2 _let_1))))) (forall ((X_34 int)) (= ((power_power_int X_34) one_one_nat) X_34)) (forall ((X_24 nat) (Y_22 nat) (Q_2 nat)) (= ((power_power_nat ((times_times_nat X_24) Y_22)) Q_2) ((times_times_nat ((power_power_nat X_24) Q_2)) ((power_power_nat Y_22) Q_2)))) (forall ((X_14 int)) (= ((ord_less_eq_real (number267125858f_real X_14)) zero_zero_real) ((ord_less_eq_int X_14) pls))) (forall ((A_1 real) (W_3 int)) (let ((_let_1 (number_number_of_nat W_3))) (= (= ((power_power_real A_1) _let_1) zero_zero_real) (and (= A_1 zero_zero_real) (not (= _let_1 zero_zero_nat)))))) (forall ((Y_13 int)) (= ((ord_less_int zero_zero_int) (number_number_of_int Y_13)) ((ord_less_int pls) Y_13))) (forall ((A_13 real) (B_3 real) (N_15 nat)) (= ((power_power_real ((times_times_real A_13) B_3)) N_15) ((times_times_real ((power_power_real A_13) N_15)) ((power_power_real B_3) N_15)))) (forall ((N_10 nat) (A_9 real)) (let ((_let_1 (ord_less_eq_real one_one_real))) (=> (_let_1 A_9) (_let_1 ((power_power_real A_9) N_10))))) (forall ((X_23 nat) (Y_21 nat) (B_11 nat)) (let ((_let_1 (power_power_nat B_11))) (=> ((ord_less_nat one_one_nat) B_11) (= ((ord_less_eq_nat (_let_1 X_23)) (_let_1 Y_21)) ((ord_less_eq_nat X_23) Y_21))))) (forall ((N_36 nat) (A_42 int)) (let ((_let_1 (ord_less_int one_one_int))) (=> (_let_1 A_42) (_let_1 ((times_times_int A_42) ((power_power_int A_42) N_36)))))) (forall ((A_3 int)) (= ((power_power_int A_3) zero_zero_nat) one_one_int)) (forall ((X_1 nat) (Y_1 nat)) (= (and ((dvd_dvd_nat X_1) Y_1) ((dvd_dvd_nat Y_1) X_1)) (= X_1 Y_1))) (forall ((K1 int) (K2 int)) (= ((ord_less_int (bit1 K1)) (bit0 K2)) ((ord_less_int K1) K2))) _let_37 (forall ((A_15 real)) (= (not (= A_15 zero_zero_real)) ((ord_less_real zero_zero_real) ((power_power_real A_15) (number_number_of_nat (bit0 (bit1 pls))))))) (forall ((Z1 int) (Z2 int) (W int)) (= ((times_times_int ((minus_minus_int Z1) Z2)) W) ((minus_minus_int ((times_times_int Z1) W)) ((times_times_int Z2) W)))) (forall ((A int) (P int)) (let ((_let_1 ((legendre A) P))) (let ((_let_2 ((quadRes P) A))) (let ((_let_3 (((zcong A) zero_zero_int) P))) (and (=> _let_3 (= _let_1 zero_zero_int)) (=> (not _let_3) (and (=> (not _let_2) (= _let_1 (number_number_of_int min))) (=> _let_2 (= _let_1 one_one_int))))))))) (forall ((X_1 nat) (Y_1 nat) (N nat)) (=> (not (= N zero_zero_nat)) (=> ((dvd_dvd_nat ((power_power_nat X_1) N)) Y_1) ((dvd_dvd_nat X_1) Y_1)))) (forall ((A_50 int) (M_12 int)) (= ((plus_plus_int ((times_times_int A_50) M_12)) M_12) ((times_times_int ((plus_plus_int A_50) one_one_int)) M_12))) (forall ((Lx_6 real) (Ly_4 real) (Rx_6 real) (Ry_4 real)) (let ((_let_1 (times_times_real Lx_6))) (= ((times_times_real (_let_1 Ly_4)) ((times_times_real Rx_6) Ry_4)) ((times_times_real (_let_1 Rx_6)) ((times_times_real Ly_4) Ry_4))))) (forall ((V_4 int) (W_8 int)) (= ((plus_plus_real (number267125858f_real V_4)) (number267125858f_real W_8)) (number267125858f_real ((plus_plus_int V_4) W_8)))) (forall ((M_3 nat) (N_7 nat) (A_7 int)) (let ((_let_1 (power_power_int A_7))) (=> ((ord_less_int one_one_int) A_7) (= (= M_3 N_7) (= (_let_1 M_3) (_let_1 N_7)))))) (forall ((X_17 real) (Y_15 real)) (not ((ord_less_real ((plus_plus_real ((times_times_real X_17) X_17)) ((times_times_real Y_15) Y_15))) zero_zero_real))) (forall ((A_37 int) (N_30 nat) (B_9 int)) (let ((_let_1 (ord_less_eq_int zero_zero_int))) (=> (= ((power_power_int A_37) N_30) ((power_power_int B_9) N_30)) (=> (_let_1 A_37) (=> (_let_1 B_9) (=> ((ord_less_nat zero_zero_nat) N_30) (= A_37 B_9))))))) (forall ((N_1 nat)) (= ((power_power_real (number267125858f_real min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_1)) one_one_real)) (forall ((N_23 nat) (A_26 nat)) (let ((_let_1 (ord_less_nat zero_zero_nat))) (=> (_let_1 A_26) (_let_1 ((power_power_nat A_26) N_23))))) (forall ((A_13 nat) (B_3 nat) (N_15 nat)) (= ((power_power_nat ((times_times_nat A_13) B_3)) N_15) ((times_times_nat ((power_power_nat A_13) N_15)) ((power_power_nat B_3) N_15)))) (forall ((C nat) (A nat) (B_1 nat)) (let ((_let_1 (times_times_nat C))) (=> ((dvd_dvd_nat A) B_1) ((dvd_dvd_nat (_let_1 A)) (_let_1 B_1))))) (forall ((A_1 int) (W_3 int)) (let ((_let_1 (number_number_of_nat W_3))) (= (= ((power_power_int A_1) _let_1) zero_zero_int) (and (= A_1 zero_zero_int) (not (= _let_1 zero_zero_nat)))))) (forall ((V_14 int) (V_13 int)) (let ((_let_1 (ord_less_eq_int pls))) (=> (_let_1 V_13) (=> (_let_1 V_14) (= ((times_times_real (number267125858f_real V_13)) (number267125858f_real V_14)) (number267125858f_real ((times_times_int V_13) V_14))))))) (forall ((A_14 int) (N_16 nat)) (let ((_let_1 ((power_power_int A_14) N_16))) (= ((times_times_int _let_1) A_14) ((times_times_int A_14) _let_1)))) (not (forall ((S1 int)) (let ((_let_1 (bit0 (bit1 pls)))) (not (((zcong ((power_power_int S1) (number_number_of_nat _let_1))) (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 _let_1))) m)) one_one_int)))))) (not (= zero_zero_real one_one_real)) (forall ((C int) (D int) (A int) (B_1 int) (M int)) (=> (((zcong A) B_1) M) (=> (((zcong C) D) M) (((zcong ((minus_minus_int A) C)) ((minus_minus_int B_1) D)) M)))) (forall ((A real) (B_1 real) (C real)) (let ((_let_1 (times_times_real C))) (=> (not (= C zero_zero_real)) (= (= (_let_1 A) (_let_1 B_1)) (= A B_1))))) (forall ((Lx_4 nat) (Ly_2 nat) (Rx_4 nat) (Ry_2 nat)) (let ((_let_1 ((times_times_nat Rx_4) Ry_2))) (let ((_let_2 (times_times_nat Lx_4))) (= ((times_times_nat (_let_2 Ly_2)) _let_1) (_let_2 ((times_times_nat Ly_2) _let_1)))))) (forall ((X_13 real) (Y_11 real)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (=> ((ord_less_eq_real ((power_power_real X_13) _let_1)) ((power_power_real Y_11) _let_1)) (=> ((ord_less_eq_real zero_zero_real) Y_11) ((ord_less_eq_real X_13) Y_11))))) (_let_10 _let_34) (forall ((N_13 nat)) (= ((power_power_int one_one_int) N_13) one_one_int)) (forall ((A_24 nat) (N_21 nat) (N_20 nat)) (let ((_let_1 (power_power_nat A_24))) (=> ((ord_less_eq_nat N_21) N_20) (=> ((ord_less_eq_nat zero_zero_nat) A_24) (=> ((ord_less_eq_nat A_24) one_one_nat) ((ord_less_eq_nat (_let_1 N_20)) (_let_1 N_21))))))) (forall ((X_11 int) (Y_9 int)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (= (= ((plus_plus_int ((power_power_int X_11) _let_1)) ((power_power_int Y_9) _let_1)) zero_zero_int) (and (= X_11 zero_zero_int) (= Y_9 zero_zero_int))))) (forall ((P int)) (= (zprime P) (and (forall ((M_1 int)) (=> (and ((dvd_dvd_int M_1) P) ((ord_less_eq_int zero_zero_int) M_1)) (or (= M_1 P) (= M_1 one_one_int)))) ((ord_less_int one_one_int) P)))) (forall ((A_65 real)) (= ((power_power_real A_65) (number_number_of_nat (bit0 (bit1 pls)))) ((times_times_real A_65) A_65))) (forall ((A real) (B_1 real) (C real)) (=> (not (= C zero_zero_real)) (= (= ((times_times_real A) C) ((times_times_real B_1) C)) (= A B_1)))) (forall ((X_1 int)) (=> ((ord_less_eq_int zero_zero_int) X_1) (=> ((ord_less_int X_1) (number_number_of_int (bit0 (bit1 pls)))) (or (= X_1 zero_zero_int) (= X_1 one_one_int))))) (forall ((B_1 int) (Q_1 int) (R_2 int) (Q int) (R_1 int)) (let ((_let_1 (times_times_int B_1))) (=> ((ord_less_eq_int ((plus_plus_int (_let_1 Q_1)) R_2)) ((plus_plus_int (_let_1 Q)) R_1)) (=> ((ord_less_eq_int zero_zero_int) R_2) (=> ((ord_less_int R_2) B_1) (=> ((ord_less_int R_1) B_1) ((ord_less_eq_int Q_1) Q))))))) (forall ((Z int)) (= ((times_times_int one_one_int) Z) Z)) (forall ((L int)) (not (= min (bit0 L)))) (forall ((W_4 int)) (let ((_let_1 (number267125858f_real W_4))) (= (number267125858f_real (bit0 W_4)) ((plus_plus_real ((plus_plus_real zero_zero_real) _let_1)) _let_1)))) _let_16 (forall ((A_31 int)) (= ((plus_plus_int A_31) zero_zero_int) A_31)) (forall ((X_5 nat) (Y_3 nat) (B_2 real)) (let ((_let_1 (power_power_real B_2))) (=> ((ord_less_real one_one_real) B_2) (= ((ord_less_nat X_5) Y_3) ((ord_less_real (_let_1 X_5)) (_let_1 Y_3)))))) (forall ((Lx_5 nat) (Ly_3 nat) (Rx_5 nat) (Ry_3 nat)) (let ((_let_1 (times_times_nat ((times_times_nat Lx_5) Ly_3)))) (let ((_let_2 (times_times_nat Rx_5))) (= (_let_1 (_let_2 Ry_3)) (_let_2 (_let_1 Ry_3)))))) (forall ((Z nat) (X_1 int) (Y_1 nat) (P int)) (let ((_let_1 (power_power_int X_1))) (=> (((zcong (_let_1 Y_1)) one_one_int) P) (((zcong (_let_1 ((times_times_nat Y_1) Z))) one_one_int) P)))) (forall ((Z_2 real)) (= ((times_times_real Z_2) (number267125858f_real (bit0 (bit1 pls)))) ((plus_plus_real Z_2) Z_2))) (forall ((X_12 real) (Y_10 real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (let ((_let_2 (number_number_of_nat (bit0 (bit1 pls))))) (=> (= ((power_power_real X_12) _let_2) ((power_power_real Y_10) _let_2)) (=> (_let_1 X_12) (=> (_let_1 Y_10) (= X_12 Y_10))))))) (= _let_30 zero_zero_nat) _let_36 (= ((power_power_int one_one_int) _let_4) one_one_int) (forall ((N_23 nat) (A_26 real)) (let ((_let_1 (ord_less_real zero_zero_real))) (=> (_let_1 A_26) (_let_1 ((power_power_real A_26) N_23))))) (forall ((A_1 nat) (W_3 int)) (let ((_let_1 (number_number_of_nat W_3))) (= (= ((power_power_nat A_1) _let_1) zero_zero_nat) (and (= A_1 zero_zero_nat) (not (= _let_1 zero_zero_nat)))))) (forall ((K int) (L int)) (= (= K L) (= (bit0 K) (bit0 L)))) (forall ((A_12 nat) (M_5 nat) (N_14 nat)) (let ((_let_1 (power_power_nat A_12))) (= (_let_1 ((plus_plus_nat M_5) N_14)) ((times_times_nat (_let_1 M_5)) (_let_1 N_14))))) (forall ((B_7 nat) (A_30 nat)) (= (= A_30 zero_zero_nat) (= B_7 ((plus_plus_nat B_7) A_30)))) (forall ((W real)) ((ord_less_eq_real W) W)) (forall ((M_11 real) (A_49 real)) (= ((plus_plus_real M_11) ((times_times_real A_49) M_11)) ((times_times_real ((plus_plus_real A_49) one_one_real)) M_11))) (= _let_22 zero_zero_real) (= _let_9 _let_34) (forall ((A_40 real) (N_34 nat)) (= (= ((power_power_real A_40) N_34) zero_zero_real) (and (= A_40 zero_zero_real) (not (= N_34 zero_zero_nat))))) (forall ((K int) (L int)) (not (= (bit0 K) (bit1 L)))) (forall ((Z int)) (=> ((ord_less_eq_int zero_zero_int) Z) ((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) Z)))) (forall ((N_29 nat) (X_21 int) (Y_19 int)) (=> ((dvd_dvd_int X_21) Y_19) ((dvd_dvd_int ((power_power_int X_21) N_29)) ((power_power_int Y_19) N_29)))) (forall ((V_8 int) (W_12 int) (Z_6 real)) (= ((times_times_real (number267125858f_real V_8)) ((times_times_real (number267125858f_real W_12)) Z_6)) ((times_times_real (number267125858f_real ((times_times_int V_8) W_12))) Z_6))) (forall ((N_3 nat) (A_2 int)) (let ((_let_1 (ord_less_int one_one_int))) (=> (_let_1 A_2) (=> ((ord_less_nat zero_zero_nat) N_3) (_let_1 ((power_power_int A_2) N_3)))))) (forall ((X_36 real) (N_39 nat)) (let ((_let_1 (power_power_real X_36))) (let ((_let_2 (_let_1 N_39))) (= (_let_1 ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_39)) ((times_times_real _let_2) _let_2))))) (forall ((N_24 nat) (A_27 nat) (B_6 nat)) (=> ((ord_less_eq_nat A_27) B_6) (=> ((ord_less_eq_nat zero_zero_nat) A_27) ((ord_less_eq_nat ((power_power_nat A_27) N_24)) ((power_power_nat B_6) N_24))))) (forall ((N_29 nat) (X_21 nat) (Y_19 nat)) (=> ((dvd_dvd_nat X_21) Y_19) ((dvd_dvd_nat ((power_power_nat X_21) N_29)) ((power_power_nat Y_19) N_29)))) (forall ((X_25 nat) (Y_23 nat) (Z_7 nat)) (let ((_let_1 (times_times_nat X_25))) (= (_let_1 ((plus_plus_nat Y_23) Z_7)) ((plus_plus_nat (_let_1 Y_23)) (_let_1 Z_7))))) (forall ((K int)) (= (number_number_of_int K) K)) (forall ((A_50 nat) (M_12 nat)) (= ((plus_plus_nat ((times_times_nat A_50) M_12)) M_12) ((times_times_nat ((plus_plus_nat A_50) one_one_nat)) M_12))) (= ((plus_plus_real one_one_real) one_one_real) (number267125858f_real _let_2)) (forall ((V_15 int) (W_16 int)) (let ((_let_1 (number267125858f_real V_15))) (let ((_let_2 (number267125858f_real W_16))) (= ((ord_less_eq_real _let_1) _let_2) (not ((ord_less_real _let_2) _let_1)))))) (((zcong _let_5) _let_8) _let_3) (forall ((M_11 nat) (A_49 nat)) (= ((plus_plus_nat M_11) ((times_times_nat A_49) M_11)) ((times_times_nat ((plus_plus_nat A_49) one_one_nat)) M_11))) (forall ((K int) (L int)) (= ((ord_less_eq_int (number_number_of_int K)) (number_number_of_int L)) ((ord_less_eq_int K) L))) (forall ((A_58 nat) (C_5 nat)) (= ((plus_plus_nat A_58) C_5) ((plus_plus_nat C_5) A_58))) (forall ((Y_1 int) (X_1 int)) (let ((_let_1 (ord_less_eq_int zero_zero_int))) (=> (_let_1 X_1) (=> (_let_1 Y_1) (_let_1 ((plus_plus_int X_1) Y_1)))))) (forall ((N_37 nat) (A_43 nat)) (let ((_let_1 ((power_power_nat A_43) N_37))) (=> ((ord_less_nat one_one_nat) A_43) ((ord_less_nat _let_1) ((times_times_nat A_43) _let_1))))) (forall ((X_18 int) (Y_16 int)) (= ((ord_less_eq_int ((plus_plus_int ((times_times_int X_18) X_18)) ((times_times_int Y_16) Y_16))) zero_zero_int) (and (= Y_16 zero_zero_int) (= X_18 zero_zero_int)))) (forall ((K int) (L int)) (= ((ord_less_int K) L) ((ord_less_int (bit1 K)) (bit0 L)))) _let_33 (forall ((X_16 real) (Y_14 real)) (= ((ord_less_real zero_zero_real) ((plus_plus_real ((times_times_real X_16) X_16)) ((times_times_real Y_14) Y_14))) (or (not (= Y_14 zero_zero_real)) (not (= X_16 zero_zero_real))))) (forall ((V_9 int) (B_12 int) (C_2 int)) (let ((_let_1 (times_times_int (number_number_of_int V_9)))) (= (_let_1 ((plus_plus_int B_12) C_2)) ((plus_plus_int (_let_1 B_12)) (_let_1 C_2))))) (forall ((Lx_1 real) (Rx_1 real) (Ry_1 real)) (let ((_let_1 (times_times_real Lx_1))) (= (_let_1 ((times_times_real Rx_1) Ry_1)) ((times_times_real (_let_1 Rx_1)) Ry_1)))) (forall ((V_2 int) (V_1 int)) (let ((_let_1 ((times_times_nat (number_number_of_nat V_1)) (number_number_of_nat V_2)))) (let ((_let_2 ((ord_less_int V_1) pls))) (and (=> _let_2 (= _let_1 zero_zero_nat)) (=> (not _let_2) (= _let_1 (number_number_of_nat ((times_times_int V_1) V_2)))))))) (forall ((Lx_1 int) (Rx_1 int) (Ry_1 int)) (let ((_let_1 (times_times_int Lx_1))) (= (_let_1 ((times_times_int Rx_1) Ry_1)) ((times_times_int (_let_1 Rx_1)) Ry_1)))) (forall ((X_1 nat) (N nat)) (let ((_let_1 (ord_less_nat zero_zero_nat))) (= (_let_1 ((power_power_nat X_1) N)) (or (_let_1 X_1) (= N zero_zero_nat))))) (forall ((A_64 nat) (B_20 nat)) (= ((times_times_nat A_64) B_20) ((times_times_nat B_20) A_64))) (forall ((X_20 int) (Y_18 int)) (= (= ((plus_plus_int ((times_times_int X_20) X_20)) ((times_times_int Y_18) Y_18)) zero_zero_int) (and (= X_20 zero_zero_int) (= Y_18 zero_zero_int)))) (forall ((L int)) (let ((_let_1 (minus_minus_int min))) (= (_let_1 (bit0 L)) (bit1 (_let_1 L))))) (forall ((A_44 int)) (= ((power_power_int A_44) (number_number_of_nat (bit1 (bit1 pls)))) ((times_times_int ((times_times_int A_44) A_44)) A_44))) (forall ((N_24 nat) (A_27 int) (B_6 int)) (=> ((ord_less_eq_int A_27) B_6) (=> ((ord_less_eq_int zero_zero_int) A_27) ((ord_less_eq_int ((power_power_int A_27) N_24)) ((power_power_int B_6) N_24))))) (forall ((K int)) (= ((ord_less_eq_int K) min) ((ord_less_eq_int (bit0 K)) min))) (forall ((V_4 int) (W_8 int)) (= ((plus_plus_int (number_number_of_int V_4)) (number_number_of_int W_8)) (number_number_of_int ((plus_plus_int V_4) W_8)))) (forall ((X_24 int) (Y_22 int) (Q_2 nat)) (= ((power_power_int ((times_times_int X_24) Y_22)) Q_2) ((times_times_int ((power_power_int X_24) Q_2)) ((power_power_int Y_22) Q_2)))) (forall ((B_1 int) (Q_1 int) (R_2 int) (Q int) (R_1 int)) (let ((_let_1 (ord_less_int B_1))) (let ((_let_2 (times_times_int B_1))) (=> ((ord_less_eq_int ((plus_plus_int (_let_2 Q_1)) R_2)) ((plus_plus_int (_let_2 Q)) R_1)) (=> ((ord_less_eq_int R_1) zero_zero_int) (=> (_let_1 R_1) (=> (_let_1 R_2) ((ord_less_eq_int Q) Q_1)))))))) (forall ((Z real) (W real)) (= ((times_times_real Z) W) ((times_times_real W) Z))) (forall ((K int)) (= ((minus_minus_int K) pls) K)) (forall ((X_16 int) (Y_14 int)) (= (or (not (= Y_14 zero_zero_int)) (not (= X_16 zero_zero_int))) ((ord_less_int zero_zero_int) ((plus_plus_int ((times_times_int X_16) X_16)) ((times_times_int Y_14) Y_14))))) (forall ((W_14 int) (X_29 real)) (let ((_let_1 (number267125858f_real W_14))) (= (= _let_1 X_29) (= X_29 _let_1)))) (forall ((K int)) (= (bit1 K) ((plus_plus_int ((plus_plus_int one_one_int) K)) K))) (forall ((X_1 real) (Y_1 real) (Z real)) (let ((_let_1 (times_times_real Z))) (=> ((ord_less_real zero_zero_real) Z) (= ((ord_less_eq_real X_1) Y_1) ((ord_less_eq_real (_let_1 X_1)) (_let_1 Y_1)))))) (forall ((N_1 nat)) (= ((power_power_int (number_number_of_int min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_1)) one_one_int)) (forall ((A_31 real)) (= ((plus_plus_real A_31) zero_zero_real) A_31)) (forall ((N_27 nat)) (let ((_let_1 ((power_power_int zero_zero_int) N_27))) (let ((_let_2 (= N_27 zero_zero_nat))) (and (=> _let_2 (= _let_1 one_one_int)) (=> (not _let_2) (= _let_1 zero_zero_int)))))) (forall ((M int) (N int)) (=> (= ((times_times_int M) N) one_one_int) (or (= M (number_number_of_int min)) (= M one_one_int)))) (forall ((K int)) (= ((ord_less_eq_int (bit1 K)) min) ((ord_less_eq_int K) min))) (forall ((A int) (R_1 int) (B_1 int) (M int) (C int) (D int) (N int)) (let ((_let_1 (times_times_int R_1))) (= ((plus_plus_int ((times_times_int ((minus_minus_int A) (_let_1 B_1))) M)) ((times_times_int ((minus_minus_int C) (_let_1 D))) N)) ((minus_minus_int ((plus_plus_int ((times_times_int A) M)) ((times_times_int C) N))) (_let_1 ((plus_plus_int ((times_times_int B_1) M)) ((times_times_int D) N))))))) (forall ((A int) (M int)) (= (((zcong A) zero_zero_int) M) ((dvd_dvd_int M) A))) (forall ((X_1 real)) (let ((_let_1 (bit0 (bit1 pls)))) (let ((_let_2 (number_number_of_nat _let_1))) (= ((times_times_real (number267125858f_real (bit0 _let_1))) ((power_power_real X_1) _let_2)) ((power_power_real ((times_times_real (number267125858f_real _let_1)) X_1)) _let_2))))) (forall ((P int) (Y_1 int) (N nat)) (let ((_let_1 (dvd_dvd_int P))) (=> ((ord_less_nat zero_zero_nat) N) (=> (_let_1 Y_1) (_let_1 ((power_power_int Y_1) N)))))) (forall ((Z nat)) (= ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z) ((plus_plus_nat Z) Z))) (forall ((B_1 int) (A int) (C int)) (=> ((ord_less_int A) C) (=> ((ord_less_int B_1) C) (or ((ord_less_eq_int B_1) A) ((ord_less_eq_int A) B_1))))) (forall ((K int) (M int) (N int)) (let ((_let_1 (times_times_int K))) (=> ((dvd_dvd_int (_let_1 M)) (_let_1 N)) (=> (not (= K zero_zero_int)) ((dvd_dvd_int M) N))))) (not (_let_18 pls)) (= (_let_32 _let_4) zero_zero_nat) (forall ((A_32 real)) (= ((plus_plus_real zero_zero_real) A_32) A_32)) (forall ((A_11 real) (M_4 nat) (N_12 nat)) (let ((_let_1 (power_power_real A_11))) (= (_let_1 ((times_times_nat M_4) N_12)) ((power_power_real (_let_1 M_4)) N_12)))) (zprime _let_29) (forall ((N_29 nat) (X_21 real) (Y_19 real)) (=> ((dvd_dvd_real X_21) Y_19) ((dvd_dvd_real ((power_power_real X_21) N_29)) ((power_power_real Y_19) N_29)))) (forall ((B_1 int) (Q int) (R_1 int) (B int) (Q_1 int) (R_2 int)) (let ((_let_1 (ord_less_eq_int zero_zero_int))) (let ((_let_2 ((plus_plus_int ((times_times_int B) Q_1)) R_2))) (=> (= ((plus_plus_int ((times_times_int B_1) Q)) R_1) _let_2) (=> (_let_1 _let_2) (=> ((ord_less_int R_2) B) (=> (_let_1 R_1) (=> ((ord_less_int zero_zero_int) B) (=> ((ord_less_eq_int B) B_1) ((ord_less_eq_int Q) Q_1)))))))))) ((_let_7 _let_8) _let_3) (forall ((A_4 int) (K_2 nat)) (=> ((ord_less_eq_int ((power_power_int A_4) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_2))) zero_zero_int) (= A_4 zero_zero_int))) (forall ((Lx nat) (Rx nat) (Ry nat)) (let ((_let_1 (times_times_nat Lx))) (let ((_let_2 (times_times_nat Rx))) (= (_let_1 (_let_2 Ry)) (_let_2 (_let_1 Ry)))))) (forall ((Z_2 nat)) (= ((times_times_nat Z_2) (number_number_of_nat (bit0 (bit1 pls)))) ((plus_plus_nat Z_2) Z_2))) (forall ((K int)) (= (= (bit0 K) pls) (= K pls))) (forall ((Y_26 int)) (= ((ord_less_int (bit1 pls)) Y_26) ((ord_less_int one_one_int) (number_number_of_int Y_26)))) (forall ((X_30 int) (Y_27 int)) (= (= X_30 Y_27) (= (number_number_of_int X_30) (number_number_of_int Y_27)))) (forall ((X_3 int) (N_2 nat)) (=> (or (= X_3 one_one_int) ((ord_less_nat zero_zero_nat) N_2)) ((dvd_dvd_int X_3) ((power_power_int X_3) N_2)))) (forall ((C_3 nat) (D_2 nat) (A_54 nat) (B_14 nat)) (let ((_let_1 (times_times_nat B_14))) (let ((_let_2 (times_times_nat A_54))) (= (not (= ((plus_plus_nat (_let_2 C_3)) (_let_1 D_2)) ((plus_plus_nat (_let_2 D_2)) (_let_1 C_3)))) (and (not (= C_3 D_2)) (not (= A_54 B_14))))))) (forall ((A int) (B_1 int)) (let ((_let_1 (bit0 (bit1 pls)))) (let ((_let_2 (number_number_of_nat _let_1))) (= ((power_power_int ((plus_plus_int A) B_1)) _let_2) ((plus_plus_int ((plus_plus_int ((power_power_int A) _let_2)) ((times_times_int ((times_times_int (number_number_of_int _let_1)) A)) B_1))) ((power_power_int B_1) _let_2)))))) (forall ((Z int)) (= ((plus_plus_int zero_zero_int) Z) Z)) (forall ((W_2 int)) (let ((_let_1 (number_number_of_nat W_2))) (let ((_let_2 ((power_power_nat zero_zero_nat) _let_1))) (let ((_let_3 (= _let_1 zero_zero_nat))) (and (=> (not _let_3) (= _let_2 zero_zero_nat)) (=> _let_3 (= _let_2 one_one_nat))))))) (forall ((V_12 int) (V_11 int)) (let ((_let_1 (ord_less_eq_int pls))) (=> (_let_1 V_11) (=> (_let_1 V_12) (= ((plus_plus_int (number_number_of_int V_11)) (number_number_of_int V_12)) (number_number_of_int ((plus_plus_int V_11) V_12))))))) (forall ((C int) (D int) (A int) (B_1 int) (M int)) (let ((_let_1 (zcong C))) (=> (((zcong A) B_1) M) (= ((_let_1 ((times_times_int B_1) D)) M) ((_let_1 ((times_times_int A) D)) M))))) (forall ((A_55 real) (B_15 real) (C_4 real)) (= ((times_times_real ((plus_plus_real A_55) B_15)) C_4) ((plus_plus_real ((times_times_real A_55) C_4)) ((times_times_real B_15) C_4)))) (forall ((V_3 int) (W_7 int)) (= (number_number_of_int ((plus_plus_int V_3) W_7)) ((plus_plus_int (number_number_of_int V_3)) (number_number_of_int W_7)))) (forall ((A_12 real) (M_5 nat) (N_14 nat)) (let ((_let_1 (power_power_real A_12))) (= (_let_1 ((plus_plus_nat M_5) N_14)) ((times_times_real (_let_1 M_5)) (_let_1 N_14))))) (forall ((A_3 real)) (= ((power_power_real A_3) zero_zero_nat) one_one_real)) (= pls zero_zero_int) (forall ((X_28 int)) (= ((ord_less_real (number267125858f_real X_28)) one_one_real) ((ord_less_int X_28) (bit1 pls)))) (forall ((V_6 int) (W_10 int)) (= (number_number_of_int ((times_times_int V_6) W_10)) ((times_times_int (number_number_of_int V_6)) (number_number_of_int W_10)))) (forall ((L int)) (= ((minus_minus_int pls) (bit1 L)) (bit1 ((minus_minus_int min) L)))) (forall ((V_8 int) (W_12 int) (Z_6 int)) (= ((times_times_int (number_number_of_int V_8)) ((times_times_int (number_number_of_int W_12)) Z_6)) ((times_times_int (number_number_of_int ((times_times_int V_8) W_12))) Z_6))) (forall ((N_13 nat)) (= ((power_power_real one_one_real) N_13) one_one_real)) (forall ((K int)) (not (= (bit0 K) min))) (forall ((M int)) (((zcong M) zero_zero_int) M)) (forall ((A_33 nat)) (= ((times_times_nat A_33) zero_zero_nat) zero_zero_nat)) (forall ((A_40 int) (N_34 nat)) (= (= ((power_power_int A_40) N_34) zero_zero_int) (and (= A_40 zero_zero_int) (not (= N_34 zero_zero_nat))))) (forall ((K1 int) (K2 int)) (= ((ord_less_eq_int K1) K2) ((ord_less_int (bit0 K1)) (bit1 K2)))) (forall ((I nat) (M nat) (N nat)) (let ((_let_1 (power_power_nat I))) (=> ((dvd_dvd_nat (_let_1 M)) (_let_1 N)) (=> ((ord_less_nat one_one_nat) I) ((ord_less_eq_nat M) N))))) (forall ((W_18 int)) (let ((_let_1 (number_number_of_nat W_18))) (= ((power_power_nat _let_1) (number_number_of_nat (bit0 (bit1 pls)))) ((times_times_nat _let_1) _let_1)))) (forall ((A_37 nat) (N_30 nat) (B_9 nat)) (let ((_let_1 (ord_less_eq_nat zero_zero_nat))) (=> (= ((power_power_nat A_37) N_30) ((power_power_nat B_9) N_30)) (=> (_let_1 A_37) (=> (_let_1 B_9) (=> ((ord_less_nat zero_zero_nat) N_30) (= A_37 B_9))))))) (forall ((A int) (B_1 int) (C int)) (=> (= ((minus_minus_int A) B_1) C) (= A ((plus_plus_int C) B_1)))) (forall ((X_13 int) (Y_11 int)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (=> ((ord_less_eq_int ((power_power_int X_13) _let_1)) ((power_power_int Y_11) _let_1)) (=> ((ord_less_eq_int zero_zero_int) Y_11) ((ord_less_eq_int X_13) Y_11))))) (forall ((V_7 int) (W_11 int)) (= ((times_times_int (number_number_of_int V_7)) (number_number_of_int W_11)) (number_number_of_int ((times_times_int V_7) W_11)))) (forall ((X_1 int) (Y_1 nat) (Z nat)) (let ((_let_1 (power_power_int X_1))) (= ((power_power_int (_let_1 Y_1)) Z) (_let_1 ((times_times_nat Y_1) Z))))) (forall ((A int) (B_1 int)) (= (= A B_1) (((zcong A) B_1) zero_zero_int))) (forall ((N_23 nat) (A_26 int)) (let ((_let_1 (ord_less_int zero_zero_int))) (=> (_let_1 A_26) (_let_1 ((power_power_int A_26) N_23))))) (forall ((X_33 int) (Y_29 int)) (= ((ord_less_int X_33) Y_29) ((ord_less_int (number_number_of_int X_33)) (number_number_of_int Y_29)))) (forall ((W int) (Z1 int) (Z2 int)) (let ((_let_1 (times_times_int W))) (= (_let_1 ((minus_minus_int Z1) Z2)) ((minus_minus_int (_let_1 Z1)) (_let_1 Z2))))) (forall ((Z int) (W int)) (= ((times_times_int Z) W) ((times_times_int W) Z))) (forall ((A_57 int) (N_38 nat)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (let ((_let_2 (power_power_int A_57))) (= (_let_2 ((times_times_nat _let_1) N_38)) ((power_power_int (_let_2 N_38)) _let_1))))) _let_31 (forall ((X_1 int)) (let ((_let_1 (bit0 (bit1 pls)))) (let ((_let_2 (power_power_int X_1))) (let ((_let_3 (number_number_of_nat _let_1))) (= ((power_power_int (_let_2 _let_3)) _let_3) (_let_2 (number_number_of_nat (bit0 _let_1)))))))) (forall ((K int) (L int)) (= ((minus_minus_int (bit1 K)) (bit0 L)) (bit1 ((minus_minus_int K) L)))) (forall ((X_36 nat) (N_39 nat)) (let ((_let_1 (power_power_nat X_36))) (let ((_let_2 (_let_1 N_39))) (= (_let_1 ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_39)) ((times_times_nat _let_2) _let_2))))) (forall ((Z1 int) (Z2 int) (Z3 int)) (let ((_let_1 (times_times_int Z1))) (= ((times_times_int (_let_1 Z2)) Z3) (_let_1 ((times_times_int Z2) Z3))))) (forall ((X_31 nat) (P_1 nat) (Q_3 nat)) (let ((_let_1 (power_power_nat X_31))) (= ((times_times_nat (_let_1 P_1)) (_let_1 Q_3)) (_let_1 ((plus_plus_nat P_1) Q_3))))) (forall ((Z_4 real)) (= ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_4) ((plus_plus_real Z_4) Z_4))) (forall ((A_25 nat) (N_22 nat) (B_5 nat)) (=> ((ord_less_nat ((power_power_nat A_25) N_22)) ((power_power_nat B_5) N_22)) (=> ((ord_less_eq_nat zero_zero_nat) B_5) ((ord_less_nat A_25) B_5)))) (forall ((K int) (L int)) (= ((ord_less_eq_int (bit0 K)) (bit0 L)) ((ord_less_eq_int K) L))) (forall ((X_1 int) (Y_1 nat) (Z nat)) (let ((_let_1 (power_power_int X_1))) (= (_let_1 ((plus_plus_nat Y_1) Z)) ((times_times_int (_let_1 Y_1)) (_let_1 Z))))) (forall ((K int) (L int)) (= ((times_times_int (bit1 K)) L) ((plus_plus_int (bit0 ((times_times_int K) L))) L))) (forall ((W int)) (= ((times_times_int pls) W) pls)) (forall ((M nat) (N nat) (I nat)) (let ((_let_1 (power_power_nat I))) (=> ((ord_less_nat zero_zero_nat) I) (=> ((ord_less_nat (_let_1 M)) (_let_1 N)) ((ord_less_nat M) N))))) (forall ((K int) (L int)) (= ((ord_less_int K) L) ((ord_less_eq_int (bit1 K)) (bit0 L)))) (forall ((V_1 int)) (= (= (number_number_of_nat V_1) zero_zero_nat) ((ord_less_eq_int V_1) pls))) (forall ((N int) (M int)) (let ((_let_1 (ord_less_eq_int zero_zero_int))) (=> (_let_1 M) (=> (_let_1 N) (=> ((dvd_dvd_int M) N) (=> ((dvd_dvd_int N) M) (= M N))))))) (forall ((L int)) (= (= min L) (= min (bit1 L)))) (forall ((X_1 real) (Y_1 real) (Z real)) (=> ((ord_less_real zero_zero_real) Z) (= ((ord_less_real ((times_times_real X_1) Z)) ((times_times_real Y_1) Z)) ((ord_less_real X_1) Y_1)))) (forall ((N_25 nat) (A_28 real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> (_let_1 A_28) (_let_1 ((power_power_real A_28) N_25))))) (forall ((K int) (L int)) (= ((ord_less_eq_int (bit0 K)) (bit1 L)) ((ord_less_eq_int K) L))) (forall ((A_19 nat)) (= ((power_power_nat A_19) one_one_nat) A_19)) (forall ((V_1 int) (V_2 int)) (let ((_let_1 ((ord_less_int V_1) V_2))) (= (and _let_1 (=> _let_1 ((ord_less_int pls) V_2))) ((ord_less_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))))) (forall ((A_56 nat) (M_13 nat) (B_16 nat)) (= ((plus_plus_nat ((times_times_nat A_56) M_13)) ((times_times_nat B_16) M_13)) ((times_times_nat ((plus_plus_nat A_56) B_16)) M_13))) (forall ((X_36 int) (N_39 nat)) (let ((_let_1 (power_power_int X_36))) (let ((_let_2 (_let_1 N_39))) (= (_let_1 ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_39)) ((times_times_int _let_2) _let_2))))) (_let_28 _let_29) (forall ((A_61 int) (B_17 int) (C_8 int)) (let ((_let_1 (plus_plus_int A_61))) (= ((plus_plus_int (_let_1 B_17)) C_8) (_let_1 ((plus_plus_int B_17) C_8))))) (zprime _let_3) (forall ((N_36 nat) (A_42 nat)) (let ((_let_1 (ord_less_nat one_one_nat))) (=> (_let_1 A_42) (_let_1 ((times_times_nat A_42) ((power_power_nat A_42) N_36)))))) (forall ((A_58 int) (C_5 int)) (= ((plus_plus_int A_58) C_5) ((plus_plus_int C_5) A_58))) (forall ((K int)) (let ((_let_1 (ord_less_int pls))) (= (_let_1 (bit0 K)) (_let_1 K)))) (forall ((X_1 nat) (Y_1 nat)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (= ((minus_minus_nat ((power_power_nat X_1) _let_1)) ((power_power_nat Y_1) _let_1)) ((times_times_nat ((plus_plus_nat X_1) Y_1)) ((minus_minus_nat X_1) Y_1))))) (forall ((A_51 nat) (B_13 nat) (V_10 int)) (let ((_let_1 (number_number_of_nat V_10))) (= ((times_times_nat ((plus_plus_nat A_51) B_13)) _let_1) ((plus_plus_nat ((times_times_nat A_51) _let_1)) ((times_times_nat B_13) _let_1))))) (forall ((M_6 nat) (A_38 nat) (N_31 nat) (B_10 nat)) (let ((_let_1 (power_power_nat A_38))) (=> ((dvd_dvd_nat (_let_1 N_31)) B_10) (=> ((ord_less_eq_nat M_6) N_31) ((dvd_dvd_nat (_let_1 M_6)) B_10))))) (forall ((X_1 real) (Y_1 real)) (= ((ord_less_real X_1) Y_1) (and (not (= X_1 Y_1)) ((ord_less_eq_real X_1) Y_1)))) (forall ((N_17 nat) (A_20 int)) (let ((_let_1 ((power_power_int A_20) N_17))) (=> ((ord_less_int zero_zero_int) A_20) (=> ((ord_less_int A_20) one_one_int) ((ord_less_int ((times_times_int A_20) _let_1)) _let_1))))) (and (_let_28 s) ((ord_less_int s) _let_3) (((zcong s1) s) _let_3)) (forall ((X_34 real)) (= ((power_power_real X_34) one_one_nat) X_34)) (forall ((K int) (I int) (J int)) (=> ((ord_less_int I) J) ((ord_less_int ((plus_plus_int I) K)) ((plus_plus_int J) K)))) (forall ((Z int) (W int)) (= (and (not (= Z W)) ((ord_less_eq_int Z) W)) ((ord_less_int Z) W))) (forall ((M int) (X_1 int)) (= (exists ((Y int)) (((zcong ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls))))) X_1) M)) ((quadRes M) X_1))) (forall ((V_16 int)) (= ((plus_plus_real (number267125858f_real V_16)) one_one_real) (number267125858f_real ((plus_plus_int V_16) (bit1 pls))))) (forall ((A_12 int) (M_5 nat) (N_14 nat)) (let ((_let_1 (power_power_int A_12))) (= (_let_1 ((plus_plus_nat M_5) N_14)) ((times_times_int (_let_1 M_5)) (_let_1 N_14))))) (forall ((K int) (A int) (B_1 int) (M int)) (=> (((zcong A) B_1) M) (((zcong ((times_times_int A) K)) ((times_times_int B_1) K)) M))) (forall ((K int) (L int)) (= ((plus_plus_int (bit0 K)) (bit1 L)) (bit1 ((plus_plus_int K) L)))) (forall ((A_22 real)) (= ((ord_less_real A_22) zero_zero_real) ((ord_less_real ((plus_plus_real A_22) A_22)) zero_zero_real))) (forall ((A_39 real) (M_8 nat) (N_33 nat)) (let ((_let_1 (power_power_real A_39))) (=> ((ord_less_eq_nat M_8) N_33) ((dvd_dvd_real (_let_1 M_8)) (_let_1 N_33))))) (forall ((W int) (Z int)) (=> ((ord_less_int W) Z) ((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z))) (forall ((X_1 real) (Y_1 real) (Z real)) (=> ((ord_less_real zero_zero_real) Z) (= ((ord_less_eq_real X_1) Y_1) ((ord_less_eq_real ((times_times_real X_1) Z)) ((times_times_real Y_1) Z))))) (forall ((X_23 nat) (Y_21 nat) (B_11 int)) (let ((_let_1 (power_power_int B_11))) (=> ((ord_less_int one_one_int) B_11) (= ((ord_less_eq_int (_let_1 X_23)) (_let_1 Y_21)) ((ord_less_eq_nat X_23) Y_21))))) (forall ((K int)) (not (= (bit1 K) pls))) (_let_27 _let_3) (forall ((Y_1 real) (X_1 real)) (let ((_let_1 (ord_less_real zero_zero_real))) (=> (_let_1 X_1) (=> (_let_1 Y_1) (_let_1 ((times_times_real X_1) Y_1)))))) (forall ((Lx_3 nat) (Ly_1 nat) (Rx_3 nat)) (let ((_let_1 (times_times_nat Lx_3))) (= ((times_times_nat (_let_1 Ly_1)) Rx_3) ((times_times_nat (_let_1 Rx_3)) Ly_1)))) (forall ((X_10 nat) (Y_8 nat)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (=> ((ord_less_nat ((power_power_nat X_10) _let_1)) ((power_power_nat Y_8) _let_1)) (=> ((ord_less_eq_nat zero_zero_nat) Y_8) ((ord_less_nat X_10) Y_8))))) (forall ((X_8 int) (Y_6 int)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (= (and (= Y_6 zero_zero_int) (= X_8 zero_zero_int)) ((ord_less_eq_int ((plus_plus_int ((power_power_int X_8) _let_1)) ((power_power_int Y_6) _let_1))) zero_zero_int)))) (forall ((V_14 int) (V_13 int)) (let ((_let_1 (ord_less_eq_int pls))) (=> (_let_1 V_13) (=> (_let_1 V_14) (= ((times_times_int (number_number_of_int V_13)) (number_number_of_int V_14)) (number_number_of_int ((times_times_int V_13) V_14))))))) (forall ((A_33 int)) (= ((times_times_int A_33) zero_zero_int) zero_zero_int)) (_let_27 one_one_int) (forall ((K int) (I int) (J int)) (let ((_let_1 (times_times_int K))) (=> ((ord_less_int I) J) (=> ((ord_less_int zero_zero_int) K) ((ord_less_int (_let_1 I)) (_let_1 J)))))) (exists ((X int)) (let ((_let_1 ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) (and (forall ((Y int)) (let ((_let_1 ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) (=> (and ((ord_less_int Y) _let_1) (((zcong s1) Y) _let_1) ((ord_less_eq_int zero_zero_int) Y)) (= Y X)))) (((zcong s1) X) _let_1) ((ord_less_int X) _let_1) ((ord_less_eq_int zero_zero_int) X)))) (forall ((V_5 int) (W_9 int) (Z_5 real)) (= ((plus_plus_real (number267125858f_real V_5)) ((plus_plus_real (number267125858f_real W_9)) Z_5)) ((plus_plus_real (number267125858f_real ((plus_plus_int V_5) W_9))) Z_5))) (forall ((W_4 int)) (let ((_let_1 (number_number_of_int W_4))) (= (number_number_of_int (bit0 W_4)) ((plus_plus_int ((plus_plus_int zero_zero_int) _let_1)) _let_1)))) (forall ((N_36 nat) (A_42 real)) (let ((_let_1 (ord_less_real one_one_real))) (=> (_let_1 A_42) (_let_1 ((times_times_real A_42) ((power_power_real A_42) N_36)))))) (forall ((X_32 int) (Y_28 int)) (= ((ord_less_eq_int X_32) Y_28) ((ord_less_eq_real (number267125858f_real X_32)) (number267125858f_real Y_28)))) (forall ((A_58 real) (C_5 real)) (= ((plus_plus_real A_58) C_5) ((plus_plus_real C_5) A_58))) (forall ((M int) (N int)) (let ((_let_1 (number_number_of_int min))) (= (= ((times_times_int M) N) one_one_int) (or (and (= N one_one_int) (= M one_one_int)) (and (= N _let_1) (= M _let_1)))))) (forall ((Z_2 int)) (= ((times_times_int Z_2) (number_number_of_int (bit0 (bit1 pls)))) ((plus_plus_int Z_2) Z_2))) (forall ((M int) (A int)) (=> ((ord_less_eq_int zero_zero_int) A) (=> ((ord_less_int A) M) (=> (((zcong A) zero_zero_int) M) (= A zero_zero_int))))) (forall ((M_10 int)) (= ((plus_plus_int M_10) M_10) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) M_10))) (forall ((M_2 nat) (N_6 nat) (A_6 real)) (let ((_let_1 (power_power_real A_6))) (=> ((ord_less_real one_one_real) A_6) (=> ((ord_less_real (_let_1 M_2)) (_let_1 N_6)) ((ord_less_nat M_2) N_6))))) (= (bit1 min) min) (forall ((X_34 nat)) (= ((power_power_nat X_34) one_one_nat) X_34)) (forall ((Lx_3 int) (Ly_1 int) (Rx_3 int)) (let ((_let_1 (times_times_int Lx_3))) (= ((times_times_int (_let_1 Ly_1)) Rx_3) ((times_times_int (_let_1 Rx_3)) Ly_1)))) (forall ((A_47 real)) (= ((plus_plus_real A_47) (number267125858f_real pls)) A_47)) (forall ((X_1 real)) (= (= X_1 zero_zero_real) (not ((ord_less_real zero_zero_real) ((times_times_real X_1) X_1))))) (forall ((B int) (Q_1 int) (R_2 int)) (let ((_let_1 (ord_less_eq_int zero_zero_int))) (=> (_let_1 ((plus_plus_int ((times_times_int B) Q_1)) R_2)) (=> ((ord_less_int R_2) B) (=> ((ord_less_int zero_zero_int) B) (_let_1 Q_1)))))) (= ((power_power_int zero_zero_int) _let_4) zero_zero_int) (forall ((A_52 nat)) (= ((times_times_nat one_one_nat) A_52) A_52)) (forall ((N_17 nat) (A_20 nat)) (let ((_let_1 ((power_power_nat A_20) N_17))) (=> ((ord_less_nat zero_zero_nat) A_20) (=> ((ord_less_nat A_20) one_one_nat) ((ord_less_nat ((times_times_nat A_20) _let_1)) _let_1))))) (forall ((A_18 real)) (= (= ((power_power_real A_18) (number_number_of_nat (bit0 (bit1 pls)))) zero_zero_real) (= A_18 zero_zero_real))) (forall ((A_16 real)) (not ((ord_less_real ((power_power_real A_16) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real))) (forall ((V_2 int) (K nat) (V_1 int)) (let ((_let_1 ((times_times_nat (number_number_of_nat V_1)) ((times_times_nat (number_number_of_nat V_2)) K)))) (let ((_let_2 ((ord_less_int V_1) pls))) (and (=> _let_2 (= _let_1 zero_zero_nat)) (=> (not _let_2) (= _let_1 ((times_times_nat (number_number_of_nat ((times_times_int V_1) V_2))) K))))))) (forall ((W_17 int)) (= ((plus_plus_real one_one_real) (number267125858f_real W_17)) (number267125858f_real ((plus_plus_int (bit1 pls)) W_17)))) (forall ((X_2 real) (Y_2 real)) (=> ((ord_less_eq_real X_2) Y_2) (=> (not (= X_2 Y_2)) ((ord_less_real X_2) Y_2)))) (forall ((W_18 int)) (let ((_let_1 (number267125858f_real W_18))) (= ((power_power_real _let_1) (number_number_of_nat (bit0 (bit1 pls)))) ((times_times_real _let_1) _let_1)))) (forall ((X_27 int)) (= ((ord_less_eq_int X_27) (bit1 pls)) ((ord_less_eq_int (number_number_of_int X_27)) one_one_int))) (forall ((W_13 int) (Y_24 int) (X_26 int) (Z_8 int)) (let ((_let_1 (times_times_int X_26))) (let ((_let_2 (times_times_int W_13))) (= (or (= W_13 X_26) (= Y_24 Z_8)) (= ((plus_plus_int (_let_2 Y_24)) (_let_1 Z_8)) ((plus_plus_int (_let_2 Z_8)) (_let_1 Y_24))))))) (forall ((X_4 nat)) (= ((power_power_nat X_4) zero_zero_nat) one_one_nat)) (forall ((N nat) (M nat)) (=> ((dvd_dvd_nat N) M) (or (= M zero_zero_nat) (= M N) ((ord_less_eq_nat ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N)) M)))) (forall ((C int) (D int) (A int) (B_1 int) (M int)) (let ((_let_1 (times_times_int D))) (let ((_let_2 (zcong C))) (=> (((zcong A) B_1) M) (= ((_let_2 (_let_1 B_1)) M) ((_let_2 (_let_1 A)) M)))))) (forall ((X_10 int) (Y_8 int)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (=> ((ord_less_int ((power_power_int X_10) _let_1)) ((power_power_int Y_8) _let_1)) (=> ((ord_less_eq_int zero_zero_int) Y_8) ((ord_less_int X_10) Y_8))))) (forall ((Z int) (W int)) (= ((plus_plus_int Z) W) ((plus_plus_int W) Z))) (forall ((B_7 real) (A_30 real)) (= (= A_30 zero_zero_real) (= B_7 ((plus_plus_real B_7) A_30)))) (forall ((A_29 real)) (= (= A_29 zero_zero_real) (= ((plus_plus_real A_29) A_29) zero_zero_real))) (forall ((N_32 nat) (M_7 nat) (X_22 nat) (Y_20 nat)) (=> ((dvd_dvd_nat X_22) Y_20) (=> ((ord_less_eq_nat N_32) M_7) ((dvd_dvd_nat ((power_power_nat X_22) N_32)) ((power_power_nat Y_20) M_7))))) (forall ((A int) (B_1 int)) (let ((_let_1 (bit1 pls))) (let ((_let_2 (bit1 _let_1))) (let ((_let_3 (number_number_of_nat _let_2))) (let ((_let_4 (power_power_int B_1))) (let ((_let_5 (number_number_of_nat (bit0 _let_1)))) (let ((_let_6 (times_times_int (number_number_of_int _let_2)))) (let ((_let_7 (power_power_int A))) (= ((power_power_int ((plus_plus_int A) B_1)) _let_3) ((plus_plus_int ((plus_plus_int ((plus_plus_int (_let_7 _let_3)) ((times_times_int (_let_6 (_let_7 _let_5))) B_1))) ((times_times_int (_let_6 A)) (_let_4 _let_5)))) (_let_4 _let_3))))))))))) (forall ((N_24 nat) (A_27 real) (B_6 real)) (=> ((ord_less_eq_real A_27) B_6) (=> ((ord_less_eq_real zero_zero_real) A_27) ((ord_less_eq_real ((power_power_real A_27) N_24)) ((power_power_real B_6) N_24))))) (forall ((P int)) (let ((_let_1 (bit1 pls))) (let ((_let_2 (bit0 _let_1))) (=> (zprime P) (=> (not (= P (number_number_of_int _let_2))) (=> (not (= P (number_number_of_int (bit1 _let_1)))) ((ord_less_eq_int (number_number_of_int (bit1 _let_2))) P))))))) (forall ((N int) (M int)) (=> ((ord_less_int zero_zero_int) M) (=> ((ord_less_int M) N) (not ((dvd_dvd_int N) M))))) (forall ((A_44 real)) (= ((power_power_real A_44) (number_number_of_nat (bit1 (bit1 pls)))) ((times_times_real ((times_times_real A_44) A_44)) A_44))) (forall ((A_29 int)) (= (= ((plus_plus_int A_29) A_29) zero_zero_int) (= A_29 zero_zero_int))) (forall ((K1 int) (K2 int)) (= ((ord_less_int K1) K2) ((ord_less_int (bit0 K1)) (bit0 K2)))) (forall ((Z int)) (not (= ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z) zero_zero_int))) (forall ((Y_26 int)) (= ((ord_less_int (bit1 pls)) Y_26) ((ord_less_real one_one_real) (number267125858f_real Y_26)))) (forall ((C int) (D int) (A int) (B_1 int) (M int)) (=> (((zcong A) B_1) M) (=> (((zcong C) D) M) (((zcong ((times_times_int A) C)) ((times_times_int B_1) D)) M)))) _let_26 (= (twoSqu1078207634sum2sq ((product_Pair_int_int s) one_one_int)) _let_17) (forall ((V_1 int) (W int)) (= ((plus_plus_int (number_number_of_int V_1)) (number_number_of_int W)) (number_number_of_int ((plus_plus_int V_1) W)))) (forall ((K real) (I real) (J real)) (let ((_let_1 (ord_less_eq_real I))) (=> (_let_1 J) (=> ((ord_less_eq_real J) K) (_let_1 K))))) (forall ((Lx_2 int) (Ly int) (Rx_2 int)) (let ((_let_1 (times_times_int Lx_2))) (= ((times_times_int (_let_1 Ly)) Rx_2) (_let_1 ((times_times_int Ly) Rx_2))))) (forall ((Y_25 int)) (= ((ord_less_eq_int (bit1 pls)) Y_25) ((ord_less_eq_real one_one_real) (number267125858f_real Y_25)))) (forall ((Y_1 int) (X_1 int)) (let ((_let_1 (ord_less_eq_int zero_zero_int))) (=> (_let_1 X_1) (=> (_let_1 Y_1) (_let_1 ((times_times_int X_1) Y_1)))))) (forall ((X_17 int) (Y_15 int)) (not ((ord_less_int ((plus_plus_int ((times_times_int X_17) X_17)) ((times_times_int Y_15) Y_15))) zero_zero_int))) (forall ((X_38 int) (Y_30 int)) (let ((_let_1 (bit0 (bit1 pls)))) (let ((_let_2 (number_number_of_nat _let_1))) (= ((power_power_int ((plus_plus_int X_38) Y_30)) _let_2) ((plus_plus_int ((plus_plus_int ((power_power_int X_38) _let_2)) ((power_power_int Y_30) _let_2))) ((times_times_int ((times_times_int (number_number_of_int _let_1)) X_38)) Y_30)))))) (forall ((J nat) (K nat) (M int)) (let ((_let_1 (power_power_int (number_number_of_int min)))) (let ((_let_2 (_let_1 K))) (let ((_let_3 (_let_1 J))) (=> ((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) M) (=> (((zcong _let_3) _let_2) M) (= _let_3 _let_2))))))) (forall ((Z_1 int)) (= ((times_times_int Z_1) (number_number_of_int (bit0 (bit1 pls)))) ((plus_plus_int Z_1) Z_1))) (forall ((W_5 int)) (= ((times_times_real ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real W_5)) (number267125858f_real (bit0 W_5)))) (forall ((A_60 nat) (C_7 nat) (D_4 nat)) (let ((_let_1 (plus_plus_nat A_60))) (= (_let_1 ((plus_plus_nat C_7) D_4)) ((plus_plus_nat (_let_1 C_7)) D_4)))) (forall ((A_51 real) (B_13 real) (V_10 int)) (let ((_let_1 (number267125858f_real V_10))) (= ((times_times_real ((plus_plus_real A_51) B_13)) _let_1) ((plus_plus_real ((times_times_real A_51) _let_1)) ((times_times_real B_13) _let_1))))) (forall ((A_24 real) (N_21 nat) (N_20 nat)) (let ((_let_1 (power_power_real A_24))) (=> ((ord_less_eq_nat N_21) N_20) (=> ((ord_less_eq_real zero_zero_real) A_24) (=> ((ord_less_eq_real A_24) one_one_real) ((ord_less_eq_real (_let_1 N_20)) (_let_1 N_21))))))) (forall ((L int)) (not (= pls (bit1 L)))) (forall ((M_3 nat) (N_7 nat) (A_7 nat)) (let ((_let_1 (power_power_nat A_7))) (=> ((ord_less_nat one_one_nat) A_7) (= (= (_let_1 M_3) (_let_1 N_7)) (= M_3 N_7))))) _let_24 (forall ((X_15 int)) (= ((ord_less_int X_15) pls) ((ord_less_real (number267125858f_real X_15)) zero_zero_real))) (forall ((A_59 real) (C_6 real) (D_3 real)) (let ((_let_1 (plus_plus_real A_59))) (let ((_let_2 (plus_plus_real C_6))) (= (_let_1 (_let_2 D_3)) (_let_2 (_let_1 D_3)))))) (forall ((N int) (P int) (M int)) (let ((_let_1 (dvd_dvd_int P))) (=> ((ord_less_eq_int zero_zero_int) M) (=> (zprime P) (=> (_let_1 ((times_times_int M) N)) (or (_let_1 N) (_let_1 M))))))) (forall ((X_38 real) (Y_30 real)) (let ((_let_1 (bit0 (bit1 pls)))) (let ((_let_2 (number_number_of_nat _let_1))) (= ((power_power_real ((plus_plus_real X_38) Y_30)) _let_2) ((plus_plus_real ((plus_plus_real ((power_power_real X_38) _let_2)) ((power_power_real Y_30) _let_2))) ((times_times_real ((times_times_real (number267125858f_real _let_1)) X_38)) Y_30)))))) (forall ((X_30 int) (Y_27 int)) (= (= (number267125858f_real X_30) (number267125858f_real Y_27)) (= X_30 Y_27))) (forall ((A_63 real) (B_19 real) (C_10 real) (D_5 real)) (let ((_let_1 (plus_plus_real A_63))) (= ((plus_plus_real (_let_1 B_19)) ((plus_plus_real C_10) D_5)) ((plus_plus_real (_let_1 C_10)) ((plus_plus_real B_19) D_5))))) (forall ((A real) (N nat)) (=> ((ord_less_nat zero_zero_nat) N) (=> ((ord_less_real zero_zero_real) A) (exists ((R real)) (and ((ord_less_real zero_zero_real) R) (= ((power_power_real R) N) A)))))) (forall ((X_5 nat) (Y_3 nat) (B_2 nat)) (let ((_let_1 (power_power_nat B_2))) (=> ((ord_less_nat one_one_nat) B_2) (= ((ord_less_nat (_let_1 X_5)) (_let_1 Y_3)) ((ord_less_nat X_5) Y_3))))) (forall ((A_61 real) (B_17 real) (C_8 real)) (let ((_let_1 (plus_plus_real A_61))) (= ((plus_plus_real (_let_1 B_17)) C_8) (_let_1 ((plus_plus_real B_17) C_8))))) (forall ((X_37 nat)) (= ((times_times_nat X_37) X_37) ((power_power_nat X_37) (number_number_of_nat (bit0 (bit1 pls)))))) (forall ((R_1 int) (Q int) (A int)) (=> ((ord_less_int zero_zero_int) A) (=> (= A ((plus_plus_int R_1) ((times_times_int A) Q))) (=> ((ord_less_eq_int zero_zero_int) R_1) ((ord_less_eq_int Q) one_one_int))))) (forall ((A_44 nat)) (= ((power_power_nat A_44) (number_number_of_nat (bit1 (bit1 pls)))) ((times_times_nat ((times_times_nat A_44) A_44)) A_44))) (forall ((X_9 real) (Y_7 real)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((power_power_real X_9) _let_1)) ((power_power_real Y_7) _let_1))))) (forall ((A_60 int) (C_7 int) (D_4 int)) (let ((_let_1 (plus_plus_int A_60))) (= (_let_1 ((plus_plus_int C_7) D_4)) ((plus_plus_int (_let_1 C_7)) D_4)))) (= ((power_power_real one_one_real) _let_4) one_one_real) (_let_14 pls) (forall ((M_9 nat) (N_35 nat) (A_41 real)) (let ((_let_1 (power_power_real A_41))) (=> ((ord_less_real one_one_real) A_41) (=> ((ord_less_eq_real (_let_1 M_9)) (_let_1 N_35)) ((ord_less_eq_nat M_9) N_35))))) (forall ((A int) (B_1 int)) (let ((_let_1 (bit1 pls))) (let ((_let_2 (bit1 _let_1))) (let ((_let_3 (number_number_of_nat _let_2))) (let ((_let_4 (power_power_int B_1))) (let ((_let_5 (number_number_of_nat (bit0 _let_1)))) (let ((_let_6 (times_times_int (number_number_of_int _let_2)))) (let ((_let_7 (power_power_int A))) (= ((power_power_int ((minus_minus_int A) B_1)) _let_3) ((minus_minus_int ((plus_plus_int ((minus_minus_int (_let_7 _let_3)) ((times_times_int (_let_6 (_let_7 _let_5))) B_1))) ((times_times_int (_let_6 A)) (_let_4 _let_5)))) (_let_4 _let_3))))))))))) (forall ((N_28 nat) (A_36 int)) (=> (not (= A_36 zero_zero_int)) (not (= ((power_power_int A_36) N_28) zero_zero_int)))) (forall ((C_3 real) (D_2 real) (A_54 real) (B_14 real)) (let ((_let_1 (times_times_real B_14))) (let ((_let_2 (times_times_real A_54))) (= (not (= ((plus_plus_real (_let_2 C_3)) (_let_1 D_2)) ((plus_plus_real (_let_2 D_2)) (_let_1 C_3)))) (and (not (= A_54 B_14)) (not (= C_3 D_2))))))) (forall ((A_40 nat) (N_34 nat)) (= (= ((power_power_nat A_40) N_34) zero_zero_nat) (and (= A_40 zero_zero_nat) (not (= N_34 zero_zero_nat))))) (forall ((X_1 nat) (N nat)) (= (= ((power_power_nat X_1) N) one_one_nat) (or (= N zero_zero_nat) (= X_1 one_one_nat)))) (forall ((A_25 int) (N_22 nat) (B_5 int)) (=> ((ord_less_int ((power_power_int A_25) N_22)) ((power_power_int B_5) N_22)) (=> ((ord_less_eq_int zero_zero_int) B_5) ((ord_less_int A_25) B_5)))) (forall ((K int)) (let ((_let_1 (ord_less_int min))) (= (_let_1 K) (_let_1 (bit1 K))))) (forall ((L int)) (let ((_let_1 (minus_minus_int min))) (= (_let_1 (bit1 L)) (bit0 (_let_1 L))))) (forall ((X_19 int) (Y_17 int)) ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int X_19) X_19)) ((times_times_int Y_17) Y_17)))) (forall ((X_6 int) (Y_4 int)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (= ((ord_less_int zero_zero_int) ((plus_plus_int ((power_power_int X_6) _let_1)) ((power_power_int Y_4) _let_1))) (or (not (= Y_4 zero_zero_int)) (not (= X_6 zero_zero_int)))))) (not (= _let_11 _let_8)) (forall ((A_3 nat)) (= ((power_power_nat A_3) zero_zero_nat) one_one_nat)) _let_23 (forall ((Z nat) (X_1 int) (Y_1 int) (M int)) (=> (((zcong X_1) Y_1) M) (((zcong ((power_power_int X_1) Z)) ((power_power_int Y_1) Z)) M))) (forall ((A_63 nat) (B_19 nat) (C_10 nat) (D_5 nat)) (let ((_let_1 (plus_plus_nat A_63))) (= ((plus_plus_nat (_let_1 B_19)) ((plus_plus_nat C_10) D_5)) ((plus_plus_nat (_let_1 C_10)) ((plus_plus_nat B_19) D_5))))) (forall ((K1 int) (K2 int)) (= ((ord_less_eq_int K1) K2) ((ord_less_eq_int (bit1 K1)) (bit1 K2)))) (forall ((X_23 nat) (Y_21 nat) (B_11 real)) (let ((_let_1 (power_power_real B_11))) (=> ((ord_less_real one_one_real) B_11) (= ((ord_less_eq_nat X_23) Y_21) ((ord_less_eq_real (_let_1 X_23)) (_let_1 Y_21)))))) (forall ((A_46 real)) (= ((times_times_real (number267125858f_real (bit1 pls))) A_46) A_46)) (forall ((B int) (Q_1 int) (R_2 int)) (=> ((ord_less_int ((plus_plus_int ((times_times_int B) Q_1)) R_2)) zero_zero_int) (=> ((ord_less_eq_int zero_zero_int) R_2) (=> ((ord_less_int zero_zero_int) B) ((ord_less_eq_int Q_1) zero_zero_int))))) (forall ((W_6 int)) (let ((_let_1 (number_number_of_int W_6))) (= (number_number_of_int (bit1 W_6)) ((plus_plus_int ((plus_plus_int one_one_int) _let_1)) _let_1)))) (forall ((N_32 nat) (M_7 nat) (X_22 int) (Y_20 int)) (=> ((dvd_dvd_int X_22) Y_20) (=> ((ord_less_eq_nat N_32) M_7) ((dvd_dvd_int ((power_power_int X_22) N_32)) ((power_power_int Y_20) M_7))))) (forall ((X_8 real) (Y_6 real)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (= ((ord_less_eq_real ((plus_plus_real ((power_power_real X_8) _let_1)) ((power_power_real Y_6) _let_1))) zero_zero_real) (and (= Y_6 zero_zero_real) (= X_8 zero_zero_real))))) (forall ((W int) (Z int)) (= ((ord_less_eq_int W) ((minus_minus_int Z) one_one_int)) ((ord_less_int W) Z))) (= _let_21 one_one_int) (forall ((Z int) (W int)) (or ((ord_less_eq_int Z) W) ((ord_less_eq_int W) Z))) (forall ((A_53 real)) (= ((times_times_real A_53) one_one_real) A_53)) (forall ((N int) (M int)) (=> ((dvd_dvd_int N) M) (or ((ord_less_eq_int M) zero_zero_int) ((ord_less_eq_int N) M)))) (forall ((C int) (A int) (B_1 int) (M int)) (let ((_let_1 (zcong A))) (=> ((_let_1 B_1) M) (=> (((zcong B_1) C) M) ((_let_1 C) M))))) (forall ((N_26 nat) (A_35 nat) (B_8 nat)) (=> ((ord_less_nat A_35) B_8) (=> ((ord_less_eq_nat zero_zero_nat) A_35) (=> ((ord_less_nat zero_zero_nat) N_26) ((ord_less_nat ((power_power_nat A_35) N_26)) ((power_power_nat B_8) N_26)))))) (forall ((Z real) (W real)) (=> ((ord_less_eq_real Z) W) (=> ((ord_less_eq_real W) Z) (= Z W)))) (forall ((A nat) (B_1 nat)) (=> ((dvd_dvd_nat A) B_1) (or (= B_1 zero_zero_nat) ((ord_less_eq_nat A) B_1)))) (forall ((M_6 nat) (A_38 int) (N_31 nat) (B_10 int)) (let ((_let_1 (power_power_int A_38))) (=> ((dvd_dvd_int (_let_1 N_31)) B_10) (=> ((ord_less_eq_nat M_6) N_31) ((dvd_dvd_int (_let_1 M_6)) B_10))))) (forall ((W int) (Z int)) (= ((ord_less_int W) ((plus_plus_int Z) one_one_int)) ((ord_less_eq_int W) Z))) (forall ((X_13 nat) (Y_11 nat)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (=> ((ord_less_eq_nat ((power_power_nat X_13) _let_1)) ((power_power_nat Y_11) _let_1)) (=> ((ord_less_eq_nat zero_zero_nat) Y_11) ((ord_less_eq_nat X_13) Y_11))))) (forall ((M nat) (K nat) (N nat)) (= (or ((dvd_dvd_nat M) N) (= K zero_zero_nat)) ((dvd_dvd_nat ((times_times_nat M) K)) ((times_times_nat N) K)))) (forall ((K1 int) (K2 int)) (= ((ord_less_eq_int (bit0 K1)) (bit1 K2)) ((ord_less_eq_int K1) K2))) (forall ((Z int) (W int)) (=> ((ord_less_eq_int Z) W) (=> ((ord_less_eq_int W) Z) (= Z W)))) (= ((plus_plus_nat one_one_nat) one_one_nat) _let_4) (forall ((X_1 nat) (W int)) (let ((_let_1 (ord_less_nat zero_zero_nat))) (let ((_let_2 (number_number_of_nat W))) (= (_let_1 ((power_power_nat X_1) _let_2)) (or (= _let_2 zero_zero_nat) (_let_1 X_1)))))) (forall ((W int)) (= ((ord_less_int W) zero_zero_int) ((ord_less_int (bit1 W)) zero_zero_int))) (forall ((V_16 int)) (= ((plus_plus_int (number_number_of_int V_16)) one_one_int) (number_number_of_int ((plus_plus_int V_16) (bit1 pls))))) (forall ((X_1 nat) (N nat)) (let ((_let_1 (ord_less_nat zero_zero_nat))) (= (or (= N zero_zero_nat) (_let_1 X_1)) (_let_1 ((power_power_nat X_1) N))))) (not (_let_13 min)) (forall ((A_8 int) (N_9 nat) (N_8 nat)) (let ((_let_1 (power_power_int A_8))) (=> ((ord_less_eq_nat N_9) N_8) (=> ((ord_less_eq_int one_one_int) A_8) ((ord_less_eq_int (_let_1 N_9)) (_let_1 N_8)))))) (forall ((X_31 real) (P_1 nat) (Q_3 nat)) (let ((_let_1 (power_power_real X_31))) (= ((times_times_real (_let_1 P_1)) (_let_1 Q_3)) (_let_1 ((plus_plus_nat P_1) Q_3))))) (not (_let_19 min)) (forall ((K int)) (= ((ord_less_int (bit0 K)) min) ((ord_less_eq_int K) min))) (forall ((V_12 int) (V_11 int)) (let ((_let_1 (ord_less_eq_int pls))) (=> (_let_1 V_11) (=> (_let_1 V_12) (= ((plus_plus_real (number267125858f_real V_11)) (number267125858f_real V_12)) (number267125858f_real ((plus_plus_int V_11) V_12))))))) (forall ((X_5 nat) (Y_3 nat) (B_2 int)) (let ((_let_1 (power_power_int B_2))) (=> ((ord_less_int one_one_int) B_2) (= ((ord_less_int (_let_1 X_5)) (_let_1 Y_3)) ((ord_less_nat X_5) Y_3))))) (forall ((Z int)) (= ((ord_less_int ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int) ((ord_less_int Z) zero_zero_int))) (forall ((X_7 real) (Y_5 real)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (not ((ord_less_real ((plus_plus_real ((power_power_real X_7) _let_1)) ((power_power_real Y_5) _let_1))) zero_zero_real)))) (forall ((N_25 nat) (A_28 nat)) (let ((_let_1 (ord_less_eq_nat zero_zero_nat))) (=> (_let_1 A_28) (_let_1 ((power_power_nat A_28) N_25))))) (forall ((X_35 real) (P_2 nat) (Q_4 nat)) (let ((_let_1 (power_power_real X_35))) (= ((power_power_real (_let_1 P_2)) Q_4) (_let_1 ((times_times_nat P_2) Q_4))))) (forall ((N_26 nat) (A_35 int) (B_8 int)) (=> ((ord_less_int A_35) B_8) (=> ((ord_less_eq_int zero_zero_int) A_35) (=> ((ord_less_nat zero_zero_nat) N_26) ((ord_less_int ((power_power_int A_35) N_26)) ((power_power_int B_8) N_26)))))) (forall ((A_23 int) (N_19 nat) (N_18 nat)) (let ((_let_1 (power_power_int A_23))) (=> ((ord_less_nat N_19) N_18) (=> ((ord_less_int zero_zero_int) A_23) (=> ((ord_less_int A_23) one_one_int) ((ord_less_int (_let_1 N_18)) (_let_1 N_19))))))) _let_20 (forall ((Z int)) (= ((plus_plus_int Z) zero_zero_int) Z)) (forall ((B_1 int) (Q int) (R_1 int) (B int) (Q_1 int) (R_2 int)) (let ((_let_1 ((plus_plus_int ((times_times_int B) Q_1)) R_2))) (=> (= ((plus_plus_int ((times_times_int B_1) Q)) R_1) _let_1) (=> ((ord_less_int _let_1) zero_zero_int) (=> ((ord_less_int R_1) B_1) (=> ((ord_less_eq_int zero_zero_int) R_2) (=> ((ord_less_int zero_zero_int) B) (=> ((ord_less_eq_int B) B_1) ((ord_less_eq_int Q_1) Q))))))))) (forall ((M_9 nat) (N_35 nat) (A_41 int)) (let ((_let_1 (power_power_int A_41))) (=> ((ord_less_int one_one_int) A_41) (=> ((ord_less_eq_int (_let_1 M_9)) (_let_1 N_35)) ((ord_less_eq_nat M_9) N_35))))) (forall ((A_59 int) (C_6 int) (D_3 int)) (let ((_let_1 (plus_plus_int A_59))) (let ((_let_2 (plus_plus_int C_6))) (= (_let_1 (_let_2 D_3)) (_let_2 (_let_1 D_3)))))) (forall ((A_17 int)) ((ord_less_eq_int zero_zero_int) ((power_power_int A_17) (number_number_of_nat (bit0 (bit1 pls)))))) (forall ((Z real) (W real)) (or ((ord_less_eq_real Z) W) ((ord_less_eq_real W) Z))) (forall ((A_13 int) (B_3 int) (N_15 nat)) (= ((power_power_int ((times_times_int A_13) B_3)) N_15) ((times_times_int ((power_power_int A_13) N_15)) ((power_power_int B_3) N_15)))) (forall ((C_1 nat) (D_1 nat) (A_21 nat) (B_4 nat) (R_3 nat)) (let ((_let_1 (times_times_nat R_3))) (=> (not (= R_3 zero_zero_nat)) (=> (and (not (= C_1 D_1)) (= A_21 B_4)) (not (= ((plus_plus_nat A_21) (_let_1 C_1)) ((plus_plus_nat B_4) (_let_1 D_1)))))))) (forall ((M_11 int) (A_49 int)) (= ((plus_plus_int M_11) ((times_times_int A_49) M_11)) ((times_times_int ((plus_plus_int A_49) one_one_int)) M_11))) (forall ((M_3 nat) (N_7 nat) (A_7 real)) (let ((_let_1 (power_power_real A_7))) (=> ((ord_less_real one_one_real) A_7) (= (= M_3 N_7) (= (_let_1 M_3) (_let_1 N_7)))))) (forall ((M int)) (=> ((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) M) (not (((zcong one_one_int) (number_number_of_int min)) M)))) (forall ((A_34 nat)) (= ((times_times_nat zero_zero_nat) A_34) zero_zero_nat)) (forall ((A int) (N nat) (P int)) (let ((_let_1 (dvd_dvd_int P))) (=> (zprime P) (=> (_let_1 ((power_power_int A) N)) (_let_1 A))))) (forall ((N_3 nat) (A_2 real)) (let ((_let_1 (ord_less_real one_one_real))) (=> (_let_1 A_2) (=> ((ord_less_nat zero_zero_nat) N_3) (_let_1 ((power_power_real A_2) N_3)))))) (not (= pls min)) (forall ((K int)) (let ((_let_1 (ord_less_eq_int pls))) (= (_let_1 (bit1 K)) (_let_1 K)))) (forall ((Z1 int) (Z2 int) (W int)) (= ((times_times_int ((plus_plus_int Z1) Z2)) W) ((plus_plus_int ((times_times_int Z1) W)) ((times_times_int Z2) W)))) (forall ((X_1 real) (Y_1 real) (Z real)) (let ((_let_1 (times_times_real Z))) (=> ((ord_less_real zero_zero_real) Z) (=> ((ord_less_real X_1) Y_1) ((ord_less_real (_let_1 X_1)) (_let_1 Y_1)))))) (forall ((B_1 int) (A int)) (let ((_let_1 (ord_less_int zero_zero_int))) (=> (_let_1 A) (=> (_let_1 ((times_times_int A) B_1)) (_let_1 B_1))))) (forall ((B_1 int) (A int) (P int)) (=> (zprime P) (=> ((ord_less_int zero_zero_int) A) (=> (((zcong ((times_times_int A) B_1)) zero_zero_int) P) (or (((zcong A) zero_zero_int) P) (((zcong B_1) zero_zero_int) P)))))) (forall ((X_1 real) (Y_1 real)) (let ((_let_1 (bit0 (bit1 pls)))) (let ((_let_2 (number_number_of_nat _let_1))) (= ((power_power_real ((plus_plus_real X_1) Y_1)) _let_2) ((plus_plus_real ((plus_plus_real ((power_power_real X_1) _let_2)) ((power_power_real Y_1) _let_2))) ((times_times_real ((times_times_real (number267125858f_real _let_1)) X_1)) Y_1)))))) (forall ((Y_1 int) (X_1 int)) (=> (twoSqu362149276sum2sq X_1) (=> (twoSqu362149276sum2sq Y_1) (twoSqu362149276sum2sq ((times_times_int X_1) Y_1))))) (_let_19 pls) (not (_let_18 min)) (forall ((A_31 nat)) (= ((plus_plus_nat A_31) zero_zero_nat) A_31)) (forall ((Lx real) (Rx real) (Ry real)) (let ((_let_1 (times_times_real Lx))) (let ((_let_2 (times_times_real Rx))) (= (_let_1 (_let_2 Ry)) (_let_2 (_let_1 Ry)))))) (forall ((W_17 int)) (= ((plus_plus_int one_one_int) (number_number_of_int W_17)) (number_number_of_int ((plus_plus_int (bit1 pls)) W_17)))) (forall ((K int) (L int)) (= ((ord_less_int K) L) ((ord_less_int ((minus_minus_int K) L)) zero_zero_int))) (forall ((X_20 real) (Y_18 real)) (= (= ((plus_plus_real ((times_times_real X_20) X_20)) ((times_times_real Y_18) Y_18)) zero_zero_real) (and (= Y_18 zero_zero_real) (= X_20 zero_zero_real)))) (forall ((K int) (L int)) (= ((plus_plus_int (bit1 K)) (bit0 L)) (bit1 ((plus_plus_int K) L)))) (twoSqu362149276sum2sq _let_17) (forall ((R_1 int) (Q int) (A int)) (=> ((ord_less_int zero_zero_int) A) (=> (= A ((plus_plus_int R_1) ((times_times_int A) Q))) (=> ((ord_less_int R_1) A) ((ord_less_eq_int one_one_int) Q))))) (forall ((V_7 int) (W_11 int)) (= ((times_times_real (number267125858f_real V_7)) (number267125858f_real W_11)) (number267125858f_real ((times_times_int V_7) W_11)))) (forall ((V_15 int) (W_16 int)) (let ((_let_1 (number_number_of_nat W_16))) (let ((_let_2 (number_number_of_nat V_15))) (= (not ((ord_less_nat _let_1) _let_2)) ((ord_less_eq_nat _let_2) _let_1))))) (forall ((N int) (M int)) (=> ((ord_less_int zero_zero_int) M) (= (and (= M one_one_int) (= N one_one_int)) (= ((times_times_int M) N) one_one_int)))) (forall ((C int) (A int) (B_1 int) (M int)) (=> (((zcong A) B_1) M) (((zcong ((plus_plus_int A) C)) ((plus_plus_int B_1) C)) M))) (forall ((A_11 int) (M_4 nat) (N_12 nat)) (let ((_let_1 (power_power_int A_11))) (= (_let_1 ((times_times_nat M_4) N_12)) ((power_power_int (_let_1 M_4)) N_12)))) (forall ((K int)) (= ((ord_less_int K) min) ((ord_less_int (bit1 K)) min))) (forall ((Z_4 int)) (= ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_4) ((plus_plus_int Z_4) Z_4))) (forall ((N nat) (A int) (B_1 int) (P int)) (let ((_let_1 (dvd_dvd_int ((power_power_int P) N)))) (=> (zprime P) (=> (not ((dvd_dvd_int P) B_1)) (=> (_let_1 ((times_times_int A) B_1)) (_let_1 A)))))) (forall ((K int) (A int) (B_1 int) (M int)) (let ((_let_1 (times_times_int K))) (=> (((zcong A) B_1) M) (((zcong (_let_1 A)) (_let_1 B_1)) M)))) (forall ((N nat) (X_1 int)) (let ((_let_1 (ord_less_eq_int zero_zero_int))) (=> (_let_1 X_1) (_let_1 ((power_power_int X_1) N))))) (forall ((X_11 real) (Y_9 real)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (= (= ((plus_plus_real ((power_power_real X_11) _let_1)) ((power_power_real Y_9) _let_1)) zero_zero_real) (and (= X_11 zero_zero_real) (= Y_9 zero_zero_real))))) (forall ((A_4 real) (K_2 nat)) (=> ((ord_less_eq_real ((power_power_real A_4) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_2))) zero_zero_real) (= A_4 zero_zero_real))) (forall ((Lx_4 real) (Ly_2 real) (Rx_4 real) (Ry_2 real)) (let ((_let_1 ((times_times_real Rx_4) Ry_2))) (let ((_let_2 (times_times_real Lx_4))) (= ((times_times_real (_let_2 Ly_2)) _let_1) (_let_2 ((times_times_real Ly_2) _let_1)))))) (forall ((Z1 real) (Z2 real) (W real)) (= ((times_times_real ((plus_plus_real Z1) Z2)) W) ((plus_plus_real ((times_times_real Z1) W)) ((times_times_real Z2) W)))) (forall ((K int) (L int)) (= ((ord_less_int (bit1 K)) (bit1 L)) ((ord_less_int K) L))) (forall ((Z int)) (= ((ord_less_int zero_zero_int) Z) ((ord_less_eq_int one_one_int) Z))) (forall ((V_1 int) (W int)) (= ((times_times_int (number_number_of_int V_1)) (number_number_of_int W)) (number_number_of_int ((times_times_int V_1) W)))) (forall ((N nat) (M nat)) (let ((_let_1 ((times_times_nat M) N))) (let ((_let_2 (= M zero_zero_nat))) (and (=> _let_2 (= _let_1 zero_zero_nat)) (=> (not _let_2) (= _let_1 ((plus_plus_nat N) ((times_times_nat ((minus_minus_nat M) one_one_nat)) N)))))))) (forall ((N_17 nat) (A_20 real)) (let ((_let_1 ((power_power_real A_20) N_17))) (=> ((ord_less_real zero_zero_real) A_20) (=> ((ord_less_real A_20) one_one_real) ((ord_less_real ((times_times_real A_20) _let_1)) _let_1))))) (forall ((Lx_4 int) (Ly_2 int) (Rx_4 int) (Ry_2 int)) (let ((_let_1 ((times_times_int Rx_4) Ry_2))) (let ((_let_2 (times_times_int Lx_4))) (= ((times_times_int (_let_2 Ly_2)) _let_1) (_let_2 ((times_times_int Ly_2) _let_1)))))) (forall ((K int)) (let ((_let_1 (ord_less_eq_int min))) (= (_let_1 (bit1 K)) (_let_1 K)))) (forall ((V_1 int) (V_2 int)) (let ((_let_1 (ord_less_eq_int V_1))) (= ((ord_less_eq_nat (number_number_of_nat V_1)) (number_number_of_nat V_2)) (=> (not (_let_1 V_2)) (_let_1 pls))))) (forall ((X_3 nat) (N_2 nat)) (=> (or ((ord_less_nat zero_zero_nat) N_2) (= X_3 one_one_nat)) ((dvd_dvd_nat X_3) ((power_power_nat X_3) N_2)))) (forall ((W int) (Z1 int) (Z2 int)) (let ((_let_1 (times_times_int W))) (= (_let_1 ((plus_plus_int Z1) Z2)) ((plus_plus_int (_let_1 Z1)) (_let_1 Z2))))) (forall ((A_14 nat) (N_16 nat)) (let ((_let_1 ((power_power_nat A_14) N_16))) (= ((times_times_nat _let_1) A_14) ((times_times_nat A_14) _let_1)))) (forall ((X_2 nat) (Y_2 nat)) (=> ((ord_less_eq_nat X_2) Y_2) (=> (not (= X_2 Y_2)) ((ord_less_nat X_2) Y_2)))) (forall ((Lx_3 real) (Ly_1 real) (Rx_3 real)) (let ((_let_1 (times_times_real Lx_3))) (= ((times_times_real (_let_1 Ly_1)) Rx_3) ((times_times_real (_let_1 Rx_3)) Ly_1)))) (forall ((X_33 int) (Y_29 int)) (= ((ord_less_int X_33) Y_29) ((ord_less_real (number267125858f_real X_33)) (number267125858f_real Y_29)))) (=> (not _let_16) (not _let_15)) (forall ((K int)) (= ((ord_less_eq_int (bit0 K)) pls) ((ord_less_eq_int K) pls))) (forall ((X_10 real) (Y_8 real)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (=> ((ord_less_real ((power_power_real X_10) _let_1)) ((power_power_real Y_8) _let_1)) (=> ((ord_less_eq_real zero_zero_real) Y_8) ((ord_less_real X_10) Y_8))))) (forall ((A_57 real) (N_38 nat)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) (let ((_let_2 (power_power_real A_57))) (= (_let_2 ((times_times_nat _let_1) N_38)) ((power_power_real (_let_2 N_38)) _let_1))))) (forall ((Z real) (X_1 real) (Y_1 real)) (let ((_let_1 (plus_plus_real Z))) (=> ((ord_less_eq_real X_1) Y_1) ((ord_less_eq_real (_let_1 X_1)) (_let_1 Y_1))))) (forall ((V_12 int) (V_11 int)) (let ((_let_1 (ord_less_eq_int pls))) (=> (_let_1 V_11) (=> (_let_1 V_12) (= ((plus_plus_nat (number_number_of_nat V_11)) (number_number_of_nat V_12)) (number_number_of_nat ((plus_plus_int V_11) V_12))))))) (forall ((X_31 int) (P_1 nat) (Q_3 nat)) (let ((_let_1 (power_power_int X_31))) (= ((times_times_int (_let_1 P_1)) (_let_1 Q_3)) (_let_1 ((plus_plus_nat P_1) Q_3))))) (forall ((A_19 real)) (= ((power_power_real A_19) one_one_nat) A_19)) (forall ((A_34 real)) (= ((times_times_real zero_zero_real) A_34) zero_zero_real)) (forall ((A_52 int)) (= ((times_times_int one_one_int) A_52) A_52)) (forall ((Y_12 int)) (= ((ord_less_eq_real zero_zero_real) (number267125858f_real Y_12)) ((ord_less_eq_int pls) Y_12))) (forall ((C_3 int) (D_2 int) (A_54 int) (B_14 int)) (let ((_let_1 (times_times_int B_14))) (let ((_let_2 (times_times_int A_54))) (= (and (not (= A_54 B_14)) (not (= C_3 D_2))) (not (= ((plus_plus_int (_let_2 C_3)) (_let_1 D_2)) ((plus_plus_int (_let_2 D_2)) (_let_1 C_3)))))))) (= ((power_power_real zero_zero_real) _let_4) zero_zero_real) (forall ((Y_25 int)) (= ((ord_less_eq_int (bit1 pls)) Y_25) ((ord_less_eq_int one_one_int) (number_number_of_int Y_25)))) (forall ((Y_1 int) (X_1 int) (P int)) (=> (not (((zcong X_1) zero_zero_int) P)) (=> (((zcong ((power_power_int Y_1) (number_number_of_nat (bit0 (bit1 pls))))) X_1) P) (not ((dvd_dvd_int P) Y_1))))) (forall ((A_53 nat)) (= ((times_times_nat A_53) one_one_nat) A_53)) (forall ((A_23 nat) (N_19 nat) (N_18 nat)) (let ((_let_1 (power_power_nat A_23))) (=> ((ord_less_nat N_19) N_18) (=> ((ord_less_nat zero_zero_nat) A_23) (=> ((ord_less_nat A_23) one_one_nat) ((ord_less_nat (_let_1 N_18)) (_let_1 N_19))))))) (forall ((A_46 int)) (= ((times_times_int (number_number_of_int (bit1 pls))) A_46) A_46)) (_let_14 min) (forall ((Z1 int) (Z2 int) (Z3 int)) (let ((_let_1 (plus_plus_int Z1))) (= ((plus_plus_int (_let_1 Z2)) Z3) (_let_1 ((plus_plus_int Z2) Z3))))) (forall ((V_5 int) (W_9 int) (Z_5 int)) (= ((plus_plus_int (number_number_of_int V_5)) ((plus_plus_int (number_number_of_int W_9)) Z_5)) ((plus_plus_int (number_number_of_int ((plus_plus_int V_5) W_9))) Z_5))) (forall ((X_37 real)) (= ((times_times_real X_37) X_37) ((power_power_real X_37) (number_number_of_nat (bit0 (bit1 pls)))))) (forall ((K int) (L int)) (= ((plus_plus_int (bit0 K)) (bit0 L)) (bit0 ((plus_plus_int K) L)))) (forall ((K int) (L int)) (= ((ord_less_eq_int (bit1 K)) (bit1 L)) ((ord_less_eq_int K) L))) (forall ((N_27 nat)) (let ((_let_1 ((power_power_real zero_zero_real) N_27))) (let ((_let_2 (= N_27 zero_zero_nat))) (and (=> (not _let_2) (= _let_1 zero_zero_real)) (=> _let_2 (= _let_1 one_one_real)))))) (forall ((A_64 real) (B_20 real)) (= ((times_times_real A_64) B_20) ((times_times_real B_20) A_64))) (forall ((P nat) (M nat)) (let ((_let_1 (power_power_nat P))) (let ((_let_2 (_let_1 M))) (let ((_let_3 (= M zero_zero_nat))) (and (=> (not _let_3) (= _let_2 ((times_times_nat P) (_let_1 ((minus_minus_nat M) one_one_nat))))) (=> _let_3 (= _let_2 one_one_nat))))))) (forall ((W_13 real) (Y_24 real) (X_26 real) (Z_8 real)) (let ((_let_1 (times_times_real X_26))) (let ((_let_2 (times_times_real W_13))) (= (or (= Y_24 Z_8) (= W_13 X_26)) (= ((plus_plus_real (_let_2 Y_24)) (_let_1 Z_8)) ((plus_plus_real (_let_2 Z_8)) (_let_1 Y_24))))))) (forall ((W_2 int)) (let ((_let_1 (number_number_of_nat W_2))) (let ((_let_2 ((power_power_int zero_zero_int) _let_1))) (let ((_let_3 (= _let_1 zero_zero_nat))) (and (=> (not _let_3) (= _let_2 zero_zero_int)) (=> _let_3 (= _let_2 one_one_int))))))) (forall ((K int)) (= (= K min) (= (bit1 K) min))) (forall ((A_5 real) (N_5 nat) (N_4 nat)) (let ((_let_1 (power_power_real A_5))) (=> ((ord_less_nat N_5) N_4) (=> ((ord_less_real one_one_real) A_5) ((ord_less_real (_let_1 N_5)) (_let_1 N_4)))))) (forall ((Y_1 int) (X_1 int) (P int)) (=> (zprime P) (=> (not (((zcong X_1) zero_zero_int) P)) (=> (not (((zcong Y_1) zero_zero_int) P)) (not (((zcong ((times_times_int X_1) Y_1)) zero_zero_int) P)))))) (forall ((A_55 int) (B_15 int) (C_4 int)) (= ((times_times_int ((plus_plus_int A_55) B_15)) C_4) ((plus_plus_int ((times_times_int A_55) C_4)) ((times_times_int B_15) C_4)))) (forall ((A_5 int) (N_5 nat) (N_4 nat)) (let ((_let_1 (power_power_int A_5))) (=> ((ord_less_nat N_5) N_4) (=> ((ord_less_int one_one_int) A_5) ((ord_less_int (_let_1 N_5)) (_let_1 N_4)))))) (forall ((W_5 int)) (= ((times_times_int ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int W_5)) (number_number_of_int (bit0 W_5)))) (forall ((X_1 nat) (Q nat) (N nat) (R_1 nat)) (=> (= X_1 ((plus_plus_nat ((times_times_nat Q) N)) R_1)) (=> ((ord_less_nat zero_zero_nat) R_1) (=> ((ord_less_nat R_1) N) (not ((dvd_dvd_nat N) X_1)))))) (_let_13 pls) (forall ((A_32 int)) (= ((plus_plus_int zero_zero_int) A_32) A_32)) (forall ((X_9 int) (Y_7 int)) (let ((_let_1 (number_number_of_nat (bit0 (bit1 pls))))) ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((power_power_int X_9) _let_1)) ((power_power_int Y_7) _let_1))))) (forall ((V_9 int) (B_12 real) (C_2 real)) (let ((_let_1 (times_times_real (number267125858f_real V_9)))) (= (_let_1 ((plus_plus_real B_12) C_2)) ((plus_plus_real (_let_1 B_12)) (_let_1 C_2))))) (forall ((M_9 nat) (N_35 nat) (A_41 nat)) (let ((_let_1 (power_power_nat A_41))) (=> ((ord_less_nat one_one_nat) A_41) (=> ((ord_less_eq_nat (_let_1 M_9)) (_let_1 N_35)) ((ord_less_eq_nat M_9) N_35))))) (forall ((X_25 real) (Y_23 real) (Z_7 real)) (let ((_let_1 (times_times_real X_25))) (= (_let_1 ((plus_plus_real Y_23) Z_7)) ((plus_plus_real (_let_1 Y_23)) (_let_1 Z_7))))) (forall ((Z real)) (= ((times_times_real one_one_real) Z) Z)) (forall ((A_34 int)) (= ((times_times_int zero_zero_int) A_34) zero_zero_int)) (= _let_12 one_one_nat) (forall ((K int) (I int) (J int)) (let ((_let_1 (plus_plus_int K))) (=> ((ord_less_eq_int I) J) ((ord_less_eq_int (_let_1 I)) (_let_1 J))))) (forall ((N_13 nat)) (= ((power_power_nat one_one_nat) N_13) one_one_nat)) (forall ((Z1 real) (Z2 real) (Z3 real)) (let ((_let_1 (times_times_real Z1))) (= ((times_times_real (_let_1 Z2)) Z3) (_let_1 ((times_times_real Z2) Z3))))) (forall ((A_65 nat)) (= ((power_power_nat A_65) (number_number_of_nat (bit0 (bit1 pls)))) ((times_times_nat A_65) A_65))) (forall ((A int) (B_1 int)) (((zcong A) B_1) one_one_int)) (forall ((A int) (B_1 int)) (let ((_let_1 (bit0 (bit1 pls)))) (let ((_let_2 (number_number_of_nat _let_1))) (= ((power_power_int ((minus_minus_int A) B_1)) _let_2) ((plus_plus_int ((minus_minus_int ((power_power_int A) _let_2)) ((times_times_int ((times_times_int (number_number_of_int _let_1)) A)) B_1))) ((power_power_int B_1) _let_2)))))) (forall ((K int)) (= ((plus_plus_int pls) K) K)) (forall ((A_15 int)) (= (not (= A_15 zero_zero_int)) ((ord_less_int zero_zero_int) ((power_power_int A_15) (number_number_of_nat (bit0 (bit1 pls))))))) (forall ((A_32 nat)) (= ((plus_plus_nat zero_zero_nat) A_32) A_32)) (forall ((A_45 int)) (= ((times_times_int A_45) (number_number_of_int (bit1 pls))) A_45)) (forall ((V_3 int) (W_7 int)) (= (number267125858f_real ((plus_plus_int V_3) W_7)) ((plus_plus_real (number267125858f_real V_3)) (number267125858f_real W_7)))) (= _let_11 zero_zero_int) (forall ((V int) (W_1 int)) (= (number_number_of_int ((minus_minus_int V) W_1)) ((minus_minus_int (number_number_of_int V)) (number_number_of_int W_1)))) (forall ((K int) (M int)) (((zcong K) K) M)) (forall ((L int)) (let ((_let_1 (minus_minus_int pls))) (= (_let_1 (bit0 L)) (bit0 (_let_1 L))))) (forall ((A_22 int)) (= ((ord_less_int A_22) zero_zero_int) ((ord_less_int ((plus_plus_int A_22) A_22)) zero_zero_int))) (_let_10 _let_9) (forall ((A_19 int)) (= ((power_power_int A_19) one_one_nat) A_19)) (forall ((K int) (L int)) (= (= K L) (= (bit1 K) (bit1 L)))) (forall ((X_4 real)) (= ((power_power_real X_4) zero_zero_nat) one_one_real)) (forall ((A int) (B_1 int) (P int) (Q int)) (let ((_let_1 (times_times_int B_1))) (let ((_let_2 (times_times_int A))) (= ((times_times_int (twoSqu1078207634sum2sq ((product_Pair_int_int A) B_1))) (twoSqu1078207634sum2sq ((product_Pair_int_int P) Q))) (twoSqu1078207634sum2sq ((product_Pair_int_int ((plus_plus_int (_let_2 P)) (_let_1 Q))) ((minus_minus_int (_let_2 Q)) (_let_1 P)))))))) (forall ((Y_12 int)) (= ((ord_less_eq_int zero_zero_int) (number_number_of_int Y_12)) ((ord_less_eq_int pls) Y_12))) (forall ((B_1 int) (M int) (A int)) (let ((_let_1 (ord_less_eq_int zero_zero_int))) (=> (_let_1 A) (=> ((ord_less_int A) M) (=> (_let_1 B_1) (=> ((ord_less_int B_1) M) (=> (((zcong A) B_1) M) (= A B_1)))))))) (forall ((X_1 int) (P int)) (let ((_let_1 (zcong X_1))) (=> ((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P) (=> ((_let_1 (number_number_of_int min)) P) (not ((_let_1 one_one_int) P)))))) (forall ((A_25 real) (N_22 nat) (B_5 real)) (=> ((ord_less_real ((power_power_real A_25) N_22)) ((power_power_real B_5) N_22)) (=> ((ord_less_eq_real zero_zero_real) B_5) ((ord_less_real A_25) B_5)))) (forall ((V_6 int) (W_10 int)) (= (number267125858f_real ((times_times_int V_6) W_10)) ((times_times_real (number267125858f_real V_6)) (number267125858f_real W_10)))) (forall ((A_62 real) (B_18 real) (C_9 real)) (let ((_let_1 (plus_plus_real A_62))) (= ((plus_plus_real (_let_1 B_18)) C_9) ((plus_plus_real (_let_1 C_9)) B_18)))) (forall ((M_2 nat) (N_6 nat) (A_6 nat)) (let ((_let_1 (power_power_nat A_6))) (=> ((ord_less_nat one_one_nat) A_6) (=> ((ord_less_nat (_let_1 M_2)) (_let_1 N_6)) ((ord_less_nat M_2) N_6))))) (forall ((A_51 int) (B_13 int) (V_10 int)) (let ((_let_1 (number_number_of_int V_10))) (= ((times_times_int ((plus_plus_int A_51) B_13)) _let_1) ((plus_plus_int ((times_times_int A_51) _let_1)) ((times_times_int B_13) _let_1))))) (forall ((W_18 int)) (let ((_let_1 (number_number_of_int W_18))) (= ((power_power_int _let_1) (number_number_of_nat (bit0 (bit1 pls)))) ((times_times_int _let_1) _let_1)))) (forall ((K int) (N int) (M int)) (let ((_let_1 (dvd_dvd_int K))) (= (_let_1 ((plus_plus_int N) ((times_times_int K) M))) (_let_1 N)))) (forall ((M int) (N int) (P int)) (let ((_let_1 (dvd_dvd_int P))) (=> (zprime P) (=> (_let_1 ((times_times_int M) N)) (or (_let_1 N) (_let_1 M)))))) ((_let_7 _let_5) _let_3) (forall ((N_37 nat) (A_43 real)) (let ((_let_1 ((power_power_real A_43) N_37))) (=> ((ord_less_real one_one_real) A_43) ((ord_less_real _let_1) ((times_times_real A_43) _let_1))))) (forall ((K int) (M int) (N int)) (let ((_let_1 (dvd_dvd_int K))) (=> (_let_1 ((minus_minus_int M) N)) (=> (_let_1 N) (_let_1 M))))) (forall ((B_1 int) (A int) (P int)) (=> (zprime P) (=> ((ord_less_int zero_zero_int) A) (=> (and (not (((zcong B_1) zero_zero_int) P)) (not (((zcong A) zero_zero_int) P))) (not (((zcong ((times_times_int A) B_1)) zero_zero_int) P)))))) (forall ((X_25 int) (Y_23 int) (Z_7 int)) (let ((_let_1 (times_times_int X_25))) (= (_let_1 ((plus_plus_int Y_23) Z_7)) ((plus_plus_int (_let_1 Y_23)) (_let_1 Z_7))))) (forall ((X_27 int)) (= ((ord_less_eq_int X_27) (bit1 pls)) ((ord_less_eq_real (number267125858f_real X_27)) one_one_real))) (forall ((A_10 real) (N_11 nat)) ((ord_less_eq_real zero_zero_real) ((power_power_real A_10) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_11)))) (forall ((A int) (M int) (B_1 int)) (((zcong ((times_times_int A) M)) ((times_times_int B_1) M)) M)) (forall ((X_35 nat) (P_2 nat) (Q_4 nat)) (let ((_let_1 (power_power_nat X_35))) (= ((power_power_nat (_let_1 P_2)) Q_4) (_let_1 ((times_times_nat P_2) Q_4))))) (forall ((A_62 int) (B_18 int) (C_9 int)) (let ((_let_1 (plus_plus_int A_62))) (= ((plus_plus_int (_let_1 B_18)) C_9) ((plus_plus_int (_let_1 C_9)) B_18))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0.70/0.90 ) 0.70/0.90 % SZS output end Proof for theBenchmark 0.70/0.90 EOF