%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM924_3 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 10:48:55 EDT 2023

% Result   : Theorem 1.61s 1.88s
% Output   : Proof 1.61s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.27/0.28  % Problem    : NUM924_3 : TPTP v8.1.2. Released v5.3.0.
% 0.27/0.29  % Command    : do_cvc5 %s %d
% 0.29/0.50  % Computer : n013.cluster.edu
% 0.29/0.50  % Model    : x86_64 x86_64
% 0.29/0.50  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.29/0.50  % Memory   : 8042.1875MB
% 0.29/0.50  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.29/0.50  % CPULimit   : 300
% 0.29/0.50  % WCLimit    : 300
% 0.29/0.50  % DateTime   : Fri Aug 25 14:50:47 EDT 2023
% 0.29/0.50  % CPUTime    : 
% 0.35/0.77  %----Proving TF0_NAR, FOF, or CNF
% 1.61/1.88  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.8Y4RroYb5x/cvc5---1.0.5_22410.p...
% 1.61/1.88  ------- get file name : TPTP file name is NUM924_3
% 1.61/1.88  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_22410.smt2...
% 1.61/1.88  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.61/1.88  % SZS status Theorem for NUM924_3
% 1.61/1.88  % SZS output start Proof for NUM924_3
% 1.61/1.88  (
% 1.61/1.88  (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit0 _let_1))) (let ((_let_3 (tptp.number_number_of_nat _let_2))) (let ((_let_4 (tptp.hAPP_nat_int (tptp.power_power_int tptp.s) _let_3))) (let ((_let_5 (tptp.hAPP_int_int (tptp.plus_plus_int _let_4) tptp.one_one_int))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_5) tptp.zero_zero_int)))) (let ((_let_7 (not _let_6))) (let ((_let_8 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_2))) tptp.m)) tptp.one_one_int))) (let ((_let_9 (tptp.times_times_int _let_8))) (let ((_let_10 (tptp.hAPP_int_int _let_9 tptp.t))) (let ((_let_11 (tptp.number_number_of_int tptp.pls))) (let ((_let_12 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_13 (not (= tptp.zero_zero_real tptp.one_one_real)))) (let ((_let_14 (tptp.number_number_of_int tptp.min))) (let ((_let_15 (= (tptp.legendre _let_14 _let_8) tptp.one_one_int))) (let ((_let_16 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.quadRes _let_8) _let_14)))) (let ((_let_17 (tptp.hAPP_int_int (tptp.minus_minus_int _let_4) _let_14))) (let ((_let_18 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int _let_8))) (let ((_let_19 (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_20 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_21 (tptp.hAPP_nat_nat (tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))) (let ((_let_22 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_23 (tptp.hAPP_real_real (tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_24 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_25 (tptp.hBOOL (tptp.hAPP_int_bool _let_20 tptp.one_one_int)))) (let ((_let_26 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int))) (let ((_let_27 (tptp.hBOOL (tptp.hAPP_int_bool _let_12 tptp.one_one_int)))) (let ((_let_28 (not (= tptp.zero_zero_int tptp.one_one_int)))) (let ((_let_29 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (let ((_let_30 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.min))) (let ((_let_31 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.min))) (let ((_let_32 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls))) (let ((_let_33 (forall ((A_90 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int A_90) tptp.zero_zero_int) tptp.zero_zero_int)))) (let ((_let_34 (tptp.number_number_of_int _let_2))) (let ((_let_35 (tptp.hAPP_nat_int (tptp.power_power_int tptp.s1) _let_3))) (let ((_let_36 (= _let_19 _let_34))) (let ((_let_37 (= _let_23 (tptp.number267125858f_real _let_2)))) (let ((_let_38 (= _let_21 _let_3))) (let ((_let_39 (tptp.number_number_of_int _let_1))) (let ((_let_40 (= tptp.one_one_int _let_39))) (let ((_let_41 (tptp.number267125858f_real _let_1))) (let ((_let_42 (= _let_39 tptp.one_one_int))) (let ((_let_43 (= _let_41 tptp.one_one_real))) (let ((_let_44 (tptp.number_number_of_nat _let_1))) (let ((_let_45 (= _let_44 tptp.one_one_nat))) (let ((_let_46 (= tptp.zero_zero_int _let_11))) (let ((_let_47 (tptp.number267125858f_real tptp.pls))) (let ((_let_48 (= _let_11 tptp.zero_zero_int))) (let ((_let_49 (= _let_47 tptp.zero_zero_real))) (let ((_let_50 (tptp.number_number_of_nat tptp.pls))) (let ((_let_51 (= _let_50 tptp.zero_zero_nat))) (let ((_let_52 (forall ((T_1 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (not (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int tptp.s) (tptp.number_number_of_nat _let_1))) tptp.one_one_int) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)) T_1))))))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.t))) (let ((_let_55 (= _let_5 _let_10))) (let ((_let_56 (tptp.hAPP_int_int _let_9 tptp.zero_zero_int))) (let ((_let_57 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_10) _let_56)))) (let ((_let_58 (= _let_10 _let_5))) (let ((_let_59 (= _let_5 (tptp.hAPP_int_int _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_60 (= tptp.zero_zero_int _let_56))) (let ((_let_61 (ASSUME :args (_let_57)))) (let ((_let_62 (SYMM (ASSUME :args (_let_55))))) (let ((_let_63 (ASSUME :args (_let_7)))) (let ((_let_64 (_let_53))) (let ((_let_65 (ASSUME :args _let_64))) (let ((_let_66 (or))) (let ((_let_67 (_let_59))) (let ((_let_68 (not _let_59))) (let ((_let_69 (forall ((A_90 tptp.int)) (= tptp.zero_zero_int (tptp.hAPP_int_int (tptp.times_times_int A_90) tptp.zero_zero_int))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (not _let_60))) (let ((_let_72 (not _let_58))) (let ((_let_73 (not _let_57))) (let ((_let_74 (APPLY_UF tptp.hBOOL))) (let ((_let_75 (APPLY_UF tptp.hAPP_int_bool))) (let ((_let_76 (ASSUME :args (_let_60)))) (let ((_let_77 (APPLY_UF tptp.hAPP_i1948725293t_bool))) (let ((_let_78 (SYMM _let_62))) (let ((_let_79 (REFL :args (tptp.ord_less_int)))) (let ((_let_80 (ASSUME :args _let_67))) (let ((_let_81 (CONG _let_79 (TRANS (SYMM _let_80) _let_78) :args _let_77))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_63 _let_62 _let_80 _let_76 _let_61) :args (_let_57 _let_7 _let_58 _let_59 _let_60)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_61)) (CONG (CONG (SYMM _let_81) (REFL :args (_let_56)) :args _let_75) :args _let_74) (CONG (CONG (TRANS _let_81 (CONG _let_79 (SYMM _let_78) :args _let_77)) (SYMM _let_76) :args _let_75) :args _let_74) (FALSE_INTRO _let_63))) :args (_let_7 _let_58 _let_59 _let_60 _let_57)) :args ((not (and _let_57 _let_7 _let_58 _let_59 _let_60)) SB_LITERAL))) (CONG (REFL :args (_let_73)) (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_6))) (REFL :args (_let_72)) (REFL :args (_let_68)) (REFL :args (_let_71)) :args _let_66)) :args ((or _let_6 _let_73 _let_72 _let_68 _let_71))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (_let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.times_times_int A_90)))) :args (_let_69))) _let_70 :args (_let_60 false _let_69)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_65) :args _let_64) (REWRITE :args ((=> _let_53 (not _let_68)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) (REFL :args _let_67) :args _let_66)) _let_65 :args (_let_59 true _let_52)) _let_63 _let_62 _let_61 :args (false false _let_60 false _let_59 true _let_6 false _let_58 false _let_57)) :args ((tptp.hBOOL (tptp.hAPP_int_bool _let_54 tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_54 tptp.one_one_int)) _let_57 _let_55 (=> (= tptp.t tptp.zero_zero_int) (= _let_5 tptp.zero_zero_int)) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_26 tptp.t))) (tptp.hBOOL (tptp.hAPP_int_bool _let_20 _let_8)) (forall ((X_1 tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X_1) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y) _let_1))) tptp.zero_zero_real))))) (forall ((X_1 tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X_1) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y) _let_1))) tptp.zero_zero_int))))) (forall ((X tptp.real) (Y_1 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_1) _let_1)))) (or (not (= X tptp.zero_zero_real)) (not (= Y_1 tptp.zero_zero_real)))))) (forall ((X tptp.int) (Y_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y_1) _let_1)))) (or (not (= X tptp.zero_zero_int)) (not (= Y_1 tptp.zero_zero_int)))))) (forall ((X tptp.real) (Y_1 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_1) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y_1 tptp.zero_zero_real))))) (forall ((X tptp.int) (Y_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y_1) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y_1 tptp.zero_zero_int))))) (forall ((A_110 tptp.real)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real (tptp.power_power_real A_110) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) tptp.zero_zero_real)))) (forall ((A_110 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int (tptp.power_power_int A_110) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) tptp.zero_zero_int)))) (forall ((A_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_nat_real (tptp.power_power_real A_2) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (not (= A_2 tptp.zero_zero_real)))) (forall ((A_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_nat_int (tptp.power_power_int A_2) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (not (= A_2 tptp.zero_zero_int)))) (= (tptp.hAPP_nat_real (tptp.power_power_real tptp.one_one_real) _let_3) tptp.one_one_real) (= (tptp.hAPP_nat_nat (tptp.power_power_nat tptp.one_one_nat) _let_3) tptp.one_one_nat) (= (tptp.hAPP_nat_int (tptp.power_power_int tptp.one_one_int) _let_3) tptp.one_one_int) (= (tptp.hAPP_nat_real (tptp.power_power_real tptp.zero_zero_real) _let_3) tptp.zero_zero_real) (= (tptp.hAPP_nat_nat (tptp.power_power_nat tptp.zero_zero_nat) _let_3) tptp.zero_zero_nat) (= (tptp.hAPP_nat_int (tptp.power_power_int tptp.zero_zero_int) _let_3) tptp.zero_zero_int) (forall ((A_2 tptp.real)) (= (= (tptp.hAPP_nat_real (tptp.power_power_real A_2) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.zero_zero_real) (= A_2 tptp.zero_zero_real))) (forall ((A_2 tptp.int)) (= (= (tptp.hAPP_nat_int (tptp.power_power_int A_2) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.zero_zero_int) (= A_2 tptp.zero_zero_int))) (forall ((W_14 tptp.int)) (= (tptp.hAPP_real_real (tptp.plus_plus_real tptp.one_one_real) (tptp.number267125858f_real W_14)) (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit1 tptp.pls)) W_14)))) (forall ((W_14 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) (tptp.number_number_of_int W_14)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit1 tptp.pls)) W_14)))) (forall ((V_17 tptp.int)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real V_17)) tptp.one_one_real) (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int V_17) (tptp.bit1 tptp.pls))))) (forall ((V_17 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_17)) tptp.one_one_int) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V_17) (tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_54 _let_8)) _let_53 (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime _let_8)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu820444569sum2sq _let_10)) (forall ((W tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) W))) (forall ((K_1 tptp.int)) (= (tptp.number_number_of_int K_1) K_1)) (forall ((Z tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int Z) W) (tptp.hAPP_int_int (tptp.times_times_int W) Z))) (forall ((Z tptp.int) (W tptp.int)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z) W)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) Z)))) (forall ((V tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int V)) (tptp.number_number_of_int W)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.times_times_int V) W)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int K)) (tptp.number_number_of_int L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) L_1)))) (forall ((X tptp.int) (Y_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.number267125858f_real X)) (tptp.number267125858f_real Y_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X) Y_1)))) (forall ((X tptp.int) (Y_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int X)) (tptp.number_number_of_int Y_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X) Y_1)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (tptp.times_times_int Z1))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_1 Z2)) Z3) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.times_times_int Z2) Z3))))) (forall ((K_1 tptp.int) (I_1 tptp.int) (J_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 J_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int J_1) K_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K_1)))))) (forall ((Z tptp.int) (W tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z) W)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) Z)) (= Z W)))) (forall ((X_1 tptp.int) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.power_power_int X_1))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat Y) Z)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_nat_int _let_1 Y)) (tptp.hAPP_nat_int _let_1 Z))))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K1)) (tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K1) K2)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) L_1)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_29 tptp.pls)) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K1)) (tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K1) K2)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) L_1)))) (forall ((Z_1 tptp.int) (W_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_1) W_1)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_1) W_1)) (not (= Z_1 W_1))))) (forall ((K_1 tptp.int) (I_1 tptp.int) (J_1 tptp.int)) (let ((_let_1 (tptp.plus_plus_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_1) J_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 I_1)) (tptp.hAPP_int_int _let_1 J_1)))))) (forall ((V_4 tptp.int)) (= (= (tptp.number_number_of_nat V_4) tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int V_4) tptp.pls)))) (forall ((V_4 tptp.int)) (= (= tptp.zero_zero_nat (tptp.number_number_of_nat V_4)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int V_4) tptp.pls)))) (forall ((V_16 tptp.int) (V_15 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_15)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_16)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real V_15)) (tptp.number267125858f_real V_16)) (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.times_times_int V_15) V_16))))))) (forall ((V_16 tptp.int) (V_15 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_15)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_16)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat V_15)) (tptp.number_number_of_nat V_16)) (tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.times_times_int V_15) V_16))))))) (forall ((V_16 tptp.int) (V_15 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_15)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_16)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int V_15)) (tptp.number_number_of_int V_16)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.times_times_int V_15) V_16))))))) (forall ((V_14 tptp.int) (W_13 tptp.int) (Z_9 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real V_14)) (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real W_13)) Z_9)) (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.times_times_int V_14) W_13))) Z_9))) (forall ((V_14 tptp.int) (W_13 tptp.int) (Z_9 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int V_14)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int W_13)) Z_9)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.times_times_int V_14) W_13))) Z_9))) (forall ((V_13 tptp.int) (W_12 tptp.int)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real V_13)) (tptp.number267125858f_real W_12)) (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.times_times_int V_13) W_12)))) (forall ((V_13 tptp.int) (W_12 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int V_13)) (tptp.number_number_of_int W_12)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.times_times_int V_13) W_12)))) (forall ((V_12 tptp.int) (W_11 tptp.int)) (= (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.times_times_int V_12) W_11)) (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real V_12)) (tptp.number267125858f_real W_11)))) (forall ((V_12 tptp.int) (W_11 tptp.int)) (= (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.times_times_int V_12) W_11)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int V_12)) (tptp.number_number_of_int W_11)))) (forall ((X tptp.real) (Y_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real X) X)) (tptp.hAPP_real_real (tptp.times_times_real Y_1) Y_1))) tptp.zero_zero_real)) (and (= X tptp.zero_zero_real) (= Y_1 tptp.zero_zero_real)))) (forall ((X tptp.int) (Y_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int X) X)) (tptp.hAPP_int_int (tptp.times_times_int Y_1) Y_1))) tptp.zero_zero_int)) (and (= X tptp.zero_zero_int) (= Y_1 tptp.zero_zero_int)))) (forall ((X_24 tptp.real) (Y_18 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real X_24) X_24)) (tptp.hAPP_real_real (tptp.times_times_real Y_18) Y_18))))) (forall ((X_24 tptp.int) (Y_18 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int X_24) X_24)) (tptp.hAPP_int_int (tptp.times_times_int Y_18) Y_18))))) (forall ((X tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.number267125858f_real X)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X) tptp.pls)))) (forall ((X tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int X)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X) tptp.pls)))) (forall ((Y_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.number267125858f_real Y_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) Y_1)))) (forall ((Y_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.number_number_of_int Y_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) Y_1)))) (forall ((V_4 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.number_number_of_nat V_4))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) V_4)))) (forall ((V_4 tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.number267125858f_real V_4))) (let ((_let_2 (tptp.number267125858f_real W_1))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_2) _let_1))))))) (forall ((V_4 tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat V_4))) (let ((_let_2 (tptp.number_number_of_nat W_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat _let_2) _let_1))))))) (forall ((V_4 tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_int V_4))) (let ((_let_2 (tptp.number_number_of_int W_1))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_2) _let_1))))))) (forall ((K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K))))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K1)) (tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K1) K2)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) L_1)))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) tptp.pls)))) (forall ((K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K))))) (forall ((Z_8 tptp.int) (Z tptp.int) (W_10 tptp.int) (W tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_10) W)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_8) Z)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int W_10) Z_8)) (tptp.hAPP_int_int (tptp.plus_plus_int W) Z)))))) _let_51 (= tptp.zero_zero_nat _let_50) (forall ((X tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.number267125858f_real X)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X) (tptp.bit1 tptp.pls))))) (forall ((X tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int X)) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X) (tptp.bit1 tptp.pls))))) (forall ((Y_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.number267125858f_real Y_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 tptp.pls)) Y_1)))) (forall ((Y_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.number_number_of_int Y_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 tptp.pls)) Y_1)))) _let_38 (forall ((W tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int tptp.pls) W) tptp.pls)) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.bit0 K_1)) L) (tptp.bit0 (tptp.hAPP_int_int (tptp.times_times_int K_1) L)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int K)) (tptp.number_number_of_int L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) L_1)))) (forall ((Z tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int Z) tptp.one_one_int) Z)) (forall ((Z tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int tptp.one_one_int) Z) Z)) (forall ((V tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V)) (tptp.number_number_of_int W)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V) W)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int Z1) Z2)) W) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int Z1) W)) (tptp.hAPP_int_int (tptp.times_times_int Z2) W)))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (tptp.times_times_int W))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int Z1) Z2)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Z1)) (tptp.hAPP_int_int _let_1 Z2))))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) tptp.pls)))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) K)))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K1)) (tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K1) K2)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) L_1)))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 K1)) (tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K1) K2)))) (forall ((X tptp.int) (A_109 tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.member_int X A_109)) (tptp.hBOOL (tptp.hAPP_int_bool A_109 X)))) (forall ((P_1 tptp.fun_int_bool)) (= (tptp.collect_int P_1) P_1)) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 K)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) L_1)))) (forall ((V_4 tptp.int) (V_3 tptp.int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_4) V_3)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.number_number_of_nat V_4)) (tptp.number_number_of_nat V_3))) (and (=> _let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) V_3))) _let_1)))) (forall ((Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) Z_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Z_1)))) _let_45 (= tptp.one_one_nat _let_44) (forall ((W tptp.int) (Z tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W) Z)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.plus_plus_int W) tptp.one_one_int)) Z)))) (forall ((W_1 tptp.int) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.plus_plus_int W_1) tptp.one_one_int)) Z_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) Z_1)))) (forall ((W_1 tptp.int) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) (tptp.hAPP_int_int (tptp.plus_plus_int Z_1) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W_1) Z_1)))) (forall ((V_11 tptp.int) (V_10 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_10)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_11)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real V_10)) (tptp.number267125858f_real V_11)) (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int V_10) V_11))))))) (forall ((V_11 tptp.int) (V_10 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_10)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_11)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.number_number_of_nat V_10)) (tptp.number_number_of_nat V_11)) (tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.plus_plus_int V_10) V_11))))))) (forall ((V_11 tptp.int) (V_10 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_10)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_11)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_10)) (tptp.number_number_of_int V_11)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V_10) V_11))))))) (forall ((V_2 tptp.int) (V tptp.int)) (let ((_let_1 (tptp.number_number_of_nat V_2))) (let ((_let_2 (tptp.number_number_of_nat V))) (let ((_let_3 (tptp.hAPP_nat_nat (tptp.plus_plus_nat _let_2) _let_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_2) tptp.pls)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V) tptp.pls)))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.plus_plus_int V) V_2))))))))))))) (forall ((Z tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) Z))))) (forall ((X tptp.int) (Y_1 tptp.int)) (= (= (tptp.number267125858f_real X) (tptp.number267125858f_real Y_1)) (= X Y_1))) (forall ((X tptp.int) (Y_1 tptp.int)) (= (= (tptp.number_number_of_int X) (tptp.number_number_of_int Y_1)) (= X Y_1))) (forall ((W_1 tptp.int) (X tptp.real)) (let ((_let_1 (tptp.number267125858f_real W_1))) (= (= _let_1 X) (= X _let_1)))) (forall ((W_1 tptp.int) (X tptp.int)) (let ((_let_1 (tptp.number_number_of_int W_1))) (= (= _let_1 X) (= X _let_1)))) (forall ((W_1 tptp.int) (X tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat W_1))) (= (= _let_1 X) (= X _let_1)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (= (tptp.bit1 K) (tptp.bit1 L_1)) (= K L_1))) (forall ((K tptp.int) (L_1 tptp.int)) (= (= (tptp.bit0 K) (tptp.bit0 L_1)) (= K L_1))) (forall ((X_1 tptp.int) (Y tptp.int)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) Y)) (= X_1 Y) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y) X_1)))) (forall ((X tptp.real) (Y_1 tptp.real)) (= (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real X) X)) (tptp.hAPP_real_real (tptp.times_times_real Y_1) Y_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y_1 tptp.zero_zero_real)))) (forall ((X tptp.int) (Y_1 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int X) X)) (tptp.hAPP_int_int (tptp.times_times_int Y_1) Y_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y_1 tptp.zero_zero_int)))) (forall ((A_108 tptp.real) (B_68 tptp.real) (V_9 tptp.int)) (let ((_let_1 (tptp.number267125858f_real V_9))) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real A_108) B_68)) _let_1) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real A_108) _let_1)) (tptp.hAPP_real_real (tptp.times_times_real B_68) _let_1))))) (forall ((A_108 tptp.nat) (B_68 tptp.nat) (V_9 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat V_9))) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_108) B_68)) _let_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_108) _let_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_68) _let_1))))) (forall ((A_108 tptp.int) (B_68 tptp.int) (V_9 tptp.int)) (let ((_let_1 (tptp.number_number_of_int V_9))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int A_108) B_68)) _let_1) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int A_108) _let_1)) (tptp.hAPP_int_int (tptp.times_times_int B_68) _let_1))))) (forall ((V_8 tptp.int) (B_67 tptp.real) (C_42 tptp.real)) (let ((_let_1 (tptp.times_times_real (tptp.number267125858f_real V_8)))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real B_67) C_42)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_67)) (tptp.hAPP_real_real _let_1 C_42))))) (forall ((V_8 tptp.int) (B_67 tptp.nat) (C_42 tptp.nat)) (let ((_let_1 (tptp.times_times_nat (tptp.number_number_of_nat V_8)))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_67) C_42)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_67)) (tptp.hAPP_nat_nat _let_1 C_42))))) (forall ((V_8 tptp.int) (B_67 tptp.int) (C_42 tptp.int)) (let ((_let_1 (tptp.times_times_int (tptp.number_number_of_int V_8)))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int B_67) C_42)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_67)) (tptp.hAPP_int_int _let_1 C_42))))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (tptp.plus_plus_int Z1))) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Z2)) Z3) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int Z2) Z3))))) (forall ((X_1 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.plus_plus_int X_1))) (let ((_let_2 (tptp.plus_plus_int Y))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 Z)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 Z)))))) (forall ((Z tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int Z) W) (tptp.hAPP_int_int (tptp.plus_plus_int W) Z))) _let_46 (forall ((K_1 tptp.int) (I_1 tptp.int) (J_1 tptp.int)) (let ((_let_1 (tptp.times_times_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) K_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 I_1)) (tptp.hAPP_int_int _let_1 J_1))))))) (forall ((X_23 tptp.real) (Y_17 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (= (tptp.hAPP_nat_real (tptp.power_power_real X_23) _let_2) (tptp.hAPP_nat_real (tptp.power_power_real Y_17) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_23)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_17)) (= X_23 Y_17))))))) (forall ((X_23 tptp.nat) (Y_17 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (= (tptp.hAPP_nat_nat (tptp.power_power_nat X_23) _let_2) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_17) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_23)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_17)) (= X_23 Y_17))))))) (forall ((X_23 tptp.int) (Y_17 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (= (tptp.hAPP_nat_int (tptp.power_power_int X_23) _let_2) (tptp.hAPP_nat_int (tptp.power_power_int Y_17) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_23)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_17)) (= X_23 Y_17))))))) (forall ((X_22 tptp.real) (Y_16 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real (tptp.power_power_real X_22) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_16) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y_16)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_22) Y_16)))))) (forall ((X_22 tptp.nat) (Y_16 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_22) _let_1)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_16) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) Y_16)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_22) Y_16)))))) (forall ((X_22 tptp.int) (Y_16 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int (tptp.power_power_int X_22) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y_16) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y_16)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_22) Y_16)))))) (forall ((A_107 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real (tptp.power_power_real A_107) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))))) (forall ((A_107 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_nat_int (tptp.power_power_int A_107) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))))) (forall ((X_21 tptp.real) (Y_15 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real (tptp.power_power_real X_21) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_15) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y_15)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_21) Y_15)))))) (forall ((X_21 tptp.nat) (Y_15 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_21) _let_1)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_15) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) Y_15)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_21) Y_15)))))) (forall ((X_21 tptp.int) (Y_15 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int (tptp.power_power_int X_21) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y_15) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y_15)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_21) Y_15)))))) (forall ((X tptp.real) (Y_1 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_1) _let_1))) tptp.zero_zero_real)) (and (= X tptp.zero_zero_real) (= Y_1 tptp.zero_zero_real))))) (forall ((X tptp.int) (Y_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y_1) _let_1))) tptp.zero_zero_int)) (and (= X tptp.zero_zero_int) (= Y_1 tptp.zero_zero_int))))) (forall ((X_20 tptp.real) (Y_14 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X_20) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_14) _let_1)))))) (forall ((X_20 tptp.int) (Y_14 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X_20) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y_14) _let_1)))))) (forall ((X tptp.real) (Y_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real X) X)) (tptp.hAPP_real_real (tptp.times_times_real Y_1) Y_1)))) (or (not (= X tptp.zero_zero_real)) (not (= Y_1 tptp.zero_zero_real))))) (forall ((X tptp.int) (Y_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int X) X)) (tptp.hAPP_int_int (tptp.times_times_int Y_1) Y_1)))) (or (not (= X tptp.zero_zero_int)) (not (= Y_1 tptp.zero_zero_int))))) (forall ((X_19 tptp.real) (Y_13 tptp.real)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real X_19) X_19)) (tptp.hAPP_real_real (tptp.times_times_real Y_13) Y_13))) tptp.zero_zero_real)))) (forall ((X_19 tptp.int) (Y_13 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int X_19) X_19)) (tptp.hAPP_int_int (tptp.times_times_int Y_13) Y_13))) tptp.zero_zero_int)))) (forall ((A_106 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real (tptp.bit1 tptp.pls))) A_106) A_106)) (forall ((A_106 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit1 tptp.pls))) A_106) A_106)) (forall ((A_105 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real A_105) (tptp.number267125858f_real (tptp.bit1 tptp.pls))) A_105)) (forall ((A_105 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int A_105) (tptp.number_number_of_int (tptp.bit1 tptp.pls))) A_105)) _let_40 (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.bit1 K_1)) L) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit0 (tptp.hAPP_int_int (tptp.times_times_int K_1) L))) L))) (forall ((N tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Ma)) (= (= (tptp.hAPP_int_int (tptp.times_times_int Ma) N) tptp.one_one_int) (and (= Ma tptp.one_one_int) (= N tptp.one_one_int))))) (forall ((A_2 tptp.real)) (= (= (tptp.hAPP_real_real (tptp.plus_plus_real A_2) A_2) tptp.zero_zero_real) (= A_2 tptp.zero_zero_real))) (forall ((A_2 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.plus_plus_int A_2) A_2) tptp.zero_zero_int) (= A_2 tptp.zero_zero_int))) (forall ((K_1 tptp.int)) (not (= (tptp.bit1 K_1) tptp.pls))) (forall ((L tptp.int)) (not (= tptp.pls (tptp.bit1 L)))) (forall ((K_1 tptp.int) (L tptp.int)) (not (= (tptp.bit1 K_1) (tptp.bit0 L)))) (forall ((K_1 tptp.int) (L tptp.int)) (not (= (tptp.bit0 K_1) (tptp.bit1 L)))) (forall ((K tptp.int)) (= (= (tptp.bit0 K) tptp.pls) (= K tptp.pls))) (forall ((L_1 tptp.int)) (= (= tptp.pls (tptp.bit0 L_1)) (= tptp.pls L_1))) (= (tptp.bit0 tptp.pls) tptp.pls) (= tptp.pls tptp.zero_zero_int) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K1)) (tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K1) K2)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) L_1)))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_32 tptp.pls))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 K1)) (tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K1) K2)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 K)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) L_1)))) _let_28 (forall ((K_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int K_1) tptp.pls) K_1)) (forall ((K_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int tptp.pls) K_1) K_1)) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit0 K_1)) (tptp.bit0 L)) (tptp.bit0 (tptp.hAPP_int_int (tptp.plus_plus_int K_1) L)))) (forall ((K_1 tptp.int)) (= (tptp.bit0 K_1) (tptp.hAPP_int_int (tptp.plus_plus_int K_1) K_1))) (forall ((Z tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int Z) tptp.zero_zero_int) Z)) (forall ((Z tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int tptp.zero_zero_int) Z) Z)) (forall ((K_1 tptp.int) (I_1 tptp.int) (J_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_1) J_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int I_1) K_1)) (tptp.hAPP_int_int (tptp.plus_plus_int J_1) K_1))))) (forall ((W_9 tptp.int)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)) (tptp.number267125858f_real W_9)) (tptp.number267125858f_real (tptp.bit0 W_9)))) (forall ((W_9 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)) (tptp.number_number_of_int W_9)) (tptp.number_number_of_int (tptp.bit0 W_9)))) (forall ((A_104 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real A_104) (tptp.number_number_of_nat (tptp.bit1 (tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.times_times_real A_104) A_104)) A_104))) (forall ((A_104 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_104) (tptp.number_number_of_nat (tptp.bit1 (tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_104) A_104)) A_104))) (forall ((A_104 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int A_104) (tptp.number_number_of_nat (tptp.bit1 (tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.times_times_int A_104) A_104)) A_104))) (forall ((Z_7 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real (tptp.bit0 (tptp.bit1 tptp.pls)))) Z_7) (tptp.hAPP_real_real (tptp.plus_plus_real Z_7) Z_7))) (forall ((Z_7 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) Z_7) (tptp.hAPP_nat_nat (tptp.plus_plus_nat Z_7) Z_7))) (forall ((Z_7 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) Z_7) (tptp.hAPP_int_int (tptp.plus_plus_int Z_7) Z_7))) (forall ((Z_6 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real (tptp.bit0 (tptp.bit1 tptp.pls)))) Z_6) (tptp.hAPP_real_real (tptp.plus_plus_real Z_6) Z_6))) (forall ((Z_6 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) Z_6) (tptp.hAPP_int_int (tptp.plus_plus_int Z_6) Z_6))) (forall ((Z_5 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real Z_5) (tptp.number267125858f_real (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real (tptp.plus_plus_real Z_5) Z_5))) (forall ((Z_5 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat Z_5) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_nat (tptp.plus_plus_nat Z_5) Z_5))) (forall ((Z_5 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int Z_5) (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.plus_plus_int Z_5) Z_5))) (forall ((Z_4 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real Z_4) (tptp.number267125858f_real (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real (tptp.plus_plus_real Z_4) Z_4))) (forall ((Z_4 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int Z_4) (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.plus_plus_int Z_4) Z_4))) (forall ((A_103 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real A_103) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real (tptp.times_times_real A_103) A_103))) (forall ((A_103 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_103) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_nat (tptp.times_times_nat A_103) A_103))) (forall ((A_103 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int A_103) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.times_times_int A_103) A_103))) (forall ((A_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.plus_plus_real A_2) A_2)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_2) tptp.zero_zero_real)))) (forall ((A_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int A_2) A_2)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) tptp.zero_zero_int)))) _let_49 _let_51 _let_48 _let_49 _let_48 (= tptp.zero_zero_real _let_47) _let_46 (forall ((A_102 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real tptp.pls)) A_102) A_102)) (forall ((A_102 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int tptp.pls)) A_102) A_102)) (forall ((A_101 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real A_101) (tptp.number267125858f_real tptp.pls)) A_101)) (forall ((A_101 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int A_101) (tptp.number_number_of_int tptp.pls)) A_101)) (forall ((X tptp.int) (Y_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.number267125858f_real X)) (tptp.number267125858f_real Y_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) Y_1)))) (forall ((X tptp.int) (Y_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int X)) (tptp.number_number_of_int Y_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) Y_1)))) (forall ((V_7 tptp.int) (W_8 tptp.int) (Z_3 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real V_7)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real W_8)) Z_3)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int V_7) W_8))) Z_3))) (forall ((V_7 tptp.int) (W_8 tptp.int) (Z_3 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_7)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int W_8)) Z_3)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V_7) W_8))) Z_3))) (forall ((V_6 tptp.int) (W_7 tptp.int)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real V_6)) (tptp.number267125858f_real W_7)) (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int V_6) W_7)))) (forall ((V_6 tptp.int) (W_7 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_6)) (tptp.number_number_of_int W_7)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V_6) W_7)))) (forall ((V_5 tptp.int) (W_6 tptp.int)) (= (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int V_5) W_6)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real V_5)) (tptp.number267125858f_real W_6)))) (forall ((V_5 tptp.int) (W_6 tptp.int)) (= (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V_5) W_6)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_5)) (tptp.number_number_of_int W_6)))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) tptp.pls)))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K1)) (tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K1) K2)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) L_1)))) (forall ((W_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 W_1)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) tptp.zero_zero_int)))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) tptp.pls)))) (forall ((K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K))))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_32 tptp.zero_zero_int))) (forall ((W_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 W_1)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) tptp.zero_zero_int)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit1 K_1)) (tptp.bit0 L)) (tptp.bit1 (tptp.hAPP_int_int (tptp.plus_plus_int K_1) L)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit0 K_1)) (tptp.bit1 L)) (tptp.bit1 (tptp.hAPP_int_int (tptp.plus_plus_int K_1) L)))) _let_25 (forall ((K_1 tptp.int)) (= (tptp.bit1 K_1) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) K_1)) K_1))) (forall ((Z tptp.int)) (not (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))) (forall ((W_1 tptp.int) (Z_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int Z_1) tptp.one_one_int))) (or (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_1)) (= W_1 Z_1))))) (forall ((W_5 tptp.int)) (let ((_let_1 (tptp.number267125858f_real W_5))) (= (tptp.hAPP_nat_real (tptp.power_power_real _let_1) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real (tptp.times_times_real _let_1) _let_1)))) (forall ((W_5 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_5))) (= (tptp.hAPP_nat_nat (tptp.power_power_nat _let_1) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_nat (tptp.times_times_nat _let_1) _let_1)))) (forall ((W_5 tptp.int)) (let ((_let_1 (tptp.number_number_of_int W_5))) (= (tptp.hAPP_nat_int (tptp.power_power_int _let_1) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.times_times_int _let_1) _let_1)))) (forall ((X_18 tptp.real) (Y_12 tptp.real)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_real_real (tptp.plus_plus_real X_18) Y_12)) _let_2) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X_18) _let_2)) (tptp.hAPP_nat_real (tptp.power_power_real Y_12) _let_2))) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real _let_1)) X_18)) Y_12)))))) (forall ((X_18 tptp.nat) (Y_12 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat X_18) Y_12)) _let_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_18) _let_1)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_12) _let_1))) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.times_times_nat _let_1) X_18)) Y_12))))) (forall ((X_18 tptp.int) (Y_12 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_int_int (tptp.plus_plus_int X_18) Y_12)) _let_2) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X_18) _let_2)) (tptp.hAPP_nat_int (tptp.power_power_int Y_12) _let_2))) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int _let_1)) X_18)) Y_12)))))) (forall ((W_4 tptp.int)) (let ((_let_1 (tptp.number267125858f_real W_4))) (= (tptp.number267125858f_real (tptp.bit0 W_4)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.plus_plus_real tptp.zero_zero_real) _let_1)) _let_1)))) (forall ((W_4 tptp.int)) (let ((_let_1 (tptp.number_number_of_int W_4))) (= (tptp.number_number_of_int (tptp.bit0 W_4)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.zero_zero_int) _let_1)) _let_1)))) (forall ((W_3 tptp.int)) (let ((_let_1 (tptp.number267125858f_real W_3))) (= (tptp.number267125858f_real (tptp.bit1 W_3)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.plus_plus_real tptp.one_one_real) _let_1)) _let_1)))) (forall ((W_3 tptp.int)) (let ((_let_1 (tptp.number_number_of_int W_3))) (= (tptp.number_number_of_int (tptp.bit1 W_3)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) _let_1)) _let_1)))) _let_43 _let_45 _let_42 _let_43 _let_42 (= tptp.one_one_real _let_41) _let_40 (forall ((Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) Z_1)) Z_1)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_1) tptp.zero_zero_int)))) (forall ((X tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.number267125858f_real X)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) tptp.pls)))) (forall ((X tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int X)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) tptp.pls)))) (forall ((Y_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.number267125858f_real Y_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) Y_1)))) (forall ((Y_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.number_number_of_int Y_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) Y_1)))) _let_37 _let_38 _let_36 _let_37 _let_36 (forall ((X tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.number267125858f_real X)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) (tptp.bit1 tptp.pls))))) (forall ((X tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int X)) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) (tptp.bit1 tptp.pls))))) (forall ((Y_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) (tptp.number267125858f_real Y_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 tptp.pls)) Y_1)))) (forall ((Y_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) (tptp.number_number_of_int Y_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 tptp.pls)) Y_1)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_18 _let_5)) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit1 _let_1))) (let ((_let_3 (tptp.number_number_of_nat _let_2))) (let ((_let_4 (tptp.power_power_int B))) (let ((_let_5 (tptp.number_number_of_nat (tptp.bit0 _let_1)))) (let ((_let_6 (tptp.times_times_int (tptp.number_number_of_int _let_2)))) (let ((_let_7 (tptp.power_power_int A))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_int_int (tptp.plus_plus_int A) B)) _let_3) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int _let_7 _let_3)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_6 (tptp.hAPP_nat_int _let_7 _let_5))) B))) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_6 A)) (tptp.hAPP_nat_int _let_4 _let_5)))) (tptp.hAPP_nat_int _let_4 _let_3))))))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_int_int (tptp.plus_plus_int A) B)) _let_2) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int A) _let_2)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int _let_1)) A)) B))) (tptp.hAPP_nat_int (tptp.power_power_int B) _let_2)))))) (forall ((X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls))))) (or (= X_1 tptp.zero_zero_int) (= X_1 tptp.one_one_int))))) (and (tptp.hBOOL (tptp.hAPP_int_bool _let_12 tptp.s)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.s) _let_8)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong tptp.s1 tptp.s) _let_8))) (forall ((A tptp.int)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.power_power_int A))) (= (tptp.hAPP_int_int (tptp.times_times_int A) (tptp.hAPP_nat_int _let_2 (tptp.number_number_of_nat (tptp.bit0 _let_1)))) (tptp.hAPP_nat_int _let_2 (tptp.number_number_of_nat (tptp.bit1 _let_1))))))) (forall ((X_1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) (tptp.hAPP_nat_int (tptp.power_power_int X_1) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))))) (forall ((R_1 tptp.int) (Q_1 tptp.int) (A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (= A (tptp.hAPP_int_int (tptp.plus_plus_int R_1) (tptp.hAPP_int_int (tptp.times_times_int A) Q_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_1) A)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) Q_1)))))) (forall ((R_1 tptp.int) (Q_1 tptp.int) (A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (= A (tptp.hAPP_int_int (tptp.plus_plus_int R_1) (tptp.hAPP_int_int (tptp.times_times_int A) Q_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_1) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_12 _let_34)) (forall ((X_17 tptp.real) (N_24 tptp.nat)) (let ((_let_1 (tptp.power_power_real X_17))) (let ((_let_2 (tptp.hAPP_nat_real _let_1 N_24))) (= (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_24)) (tptp.hAPP_real_real (tptp.times_times_real _let_2) _let_2))))) (forall ((X_17 tptp.nat) (N_24 tptp.nat)) (let ((_let_1 (tptp.power_power_nat X_17))) (let ((_let_2 (tptp.hAPP_nat_nat _let_1 N_24))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_24)) (tptp.hAPP_nat_nat (tptp.times_times_nat _let_2) _let_2))))) (forall ((X_17 tptp.int) (N_24 tptp.nat)) (let ((_let_1 (tptp.power_power_int X_17))) (let ((_let_2 (tptp.hAPP_nat_int _let_1 N_24))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_24)) (tptp.hAPP_int_int (tptp.times_times_int _let_2) _let_2))))) (forall ((X_16 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real X_16) X_16) (tptp.hAPP_nat_real (tptp.power_power_real X_16) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (forall ((X_16 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat X_16) X_16) (tptp.hAPP_nat_nat (tptp.power_power_nat X_16) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (forall ((X_16 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int X_16) X_16) (tptp.hAPP_nat_int (tptp.power_power_int X_16) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong _let_4 _let_35) _let_8)) (exists ((X_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong tptp.s1 X_2) _let_1)) (forall ((Y_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y_2) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong tptp.s1 Y_2) _let_1))) (= Y_2 X_2))))))) (not (forall ((S_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (not (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) S_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int S_1) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong tptp.s1 S_1) _let_1))))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong _let_35 _let_14) _let_8)) (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat X) N))) (or (= N tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X)))))) (forall ((A tptp.int) (N_1 tptp.nat) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A) N_1))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)))))) (forall ((X_15 tptp.real) (P_7 tptp.nat) (Q_7 tptp.nat)) (let ((_let_1 (tptp.power_power_real X_15))) (= (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_nat_real _let_1 P_7)) Q_7) (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat P_7) Q_7))))) (forall ((X_15 tptp.nat) (P_7 tptp.nat) (Q_7 tptp.nat)) (let ((_let_1 (tptp.power_power_nat X_15))) (= (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.hAPP_nat_nat _let_1 P_7)) Q_7) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat P_7) Q_7))))) (forall ((X_15 tptp.int) (P_7 tptp.nat) (Q_7 tptp.nat)) (let ((_let_1 (tptp.power_power_int X_15))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int _let_1 P_7)) Q_7) (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat P_7) Q_7))))) (forall ((N_1 tptp.nat) (A tptp.int) (B tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.power_power_int P_3) N_1)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3) B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int A) B))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A))))))) (forall ((N_1 tptp.nat) (B tptp.int) (A tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.power_power_int P_3) N_1)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3) A))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int A) B))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B))))))) (forall ((X_1 tptp.int) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.power_power_int X_1))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int _let_1 Y)) Z) (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat Y) Z))))) (forall ((N_1 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int M) N_1)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int N_1) M)))))) (forall ((N_1 tptp.int) (M tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int M) N_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int N_1) M)) (= M N_1))))))) (forall ((K_1 tptp.int) (M tptp.int) (N_1 tptp.int)) (let ((_let_1 (tptp.times_times_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int _let_1 M)) (tptp.hAPP_int_int _let_1 N_1))) (=> (not (= K_1 tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int M) N_1)))))) (forall ((K tptp.int) (N tptp.int) (Ma tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int N) (tptp.hAPP_int_int (tptp.times_times_int K) Ma)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N))))) (forall ((C_1 tptp.int) (X tptp.int) (Ta tptp.int) (A_2 tptp.int) (D tptp.int)) (let ((_let_1 (tptp.plus_plus_int X))) (let ((_let_2 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_2 D)) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_2 (tptp.hAPP_int_int _let_1 Ta))) (tptp.hBOOL (tptp.hAPP_int_bool _let_2 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.times_times_int C_1) D))) Ta)))))))) (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime _let_34)) (forall ((Z tptp.int) (N_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Z) N_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) N_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z) N_1))))) (forall ((Y tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu820444569sum2sq X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu820444569sum2sq Y)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu820444569sum2sq (tptp.hAPP_int_int (tptp.times_times_int X_1) Y)))))) (forall ((V_4 tptp.int) (V_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int V_4))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.number_number_of_nat V_4)) (tptp.number_number_of_nat V_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_3))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 tptp.pls)))))) (forall ((Lx_6 tptp.real) (Ly_4 tptp.real) (Rx_6 tptp.real) (Ry_4 tptp.real)) (let ((_let_1 (tptp.times_times_real Lx_6))) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real _let_1 Ly_4)) (tptp.hAPP_real_real (tptp.times_times_real Rx_6) Ry_4)) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real _let_1 Rx_6)) (tptp.hAPP_real_real (tptp.times_times_real Ly_4) Ry_4))))) (forall ((Lx_6 tptp.nat) (Ly_4 tptp.nat) (Rx_6 tptp.nat) (Ry_4 tptp.nat)) (let ((_let_1 (tptp.times_times_nat Lx_6))) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Ly_4)) (tptp.hAPP_nat_nat (tptp.times_times_nat Rx_6) Ry_4)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Rx_6)) (tptp.hAPP_nat_nat (tptp.times_times_nat Ly_4) Ry_4))))) (forall ((Lx_6 tptp.int) (Ly_4 tptp.int) (Rx_6 tptp.int) (Ry_4 tptp.int)) (let ((_let_1 (tptp.times_times_int Lx_6))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_1 Ly_4)) (tptp.hAPP_int_int (tptp.times_times_int Rx_6) Ry_4)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_1 Rx_6)) (tptp.hAPP_int_int (tptp.times_times_int Ly_4) Ry_4))))) (forall ((Lx_5 tptp.real) (Ly_3 tptp.real) (Rx_5 tptp.real) (Ry_3 tptp.real)) (let ((_let_1 (tptp.times_times_real (tptp.hAPP_real_real (tptp.times_times_real Lx_5) Ly_3)))) (let ((_let_2 (tptp.times_times_real Rx_5))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real _let_2 Ry_3)) (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real _let_1 Ry_3)))))) (forall ((Lx_5 tptp.nat) (Ly_3 tptp.nat) (Rx_5 tptp.nat) (Ry_3 tptp.nat)) (let ((_let_1 (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.times_times_nat Lx_5) Ly_3)))) (let ((_let_2 (tptp.times_times_nat Rx_5))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Ry_3)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Ry_3)))))) (forall ((Lx_5 tptp.int) (Ly_3 tptp.int) (Rx_5 tptp.int) (Ry_3 tptp.int)) (let ((_let_1 (tptp.times_times_int (tptp.hAPP_int_int (tptp.times_times_int Lx_5) Ly_3)))) (let ((_let_2 (tptp.times_times_int Rx_5))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 Ry_3)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 Ry_3)))))) (forall ((Lx_4 tptp.real) (Ly_2 tptp.real) (Rx_4 tptp.real) (Ry_2 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.times_times_real Rx_4) Ry_2))) (let ((_let_2 (tptp.times_times_real Lx_4))) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real _let_2 Ly_2)) _let_1) (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real (tptp.times_times_real Ly_2) _let_1)))))) (forall ((Lx_4 tptp.nat) (Ly_2 tptp.nat) (Rx_4 tptp.nat) (Ry_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat Rx_4) Ry_2))) (let ((_let_2 (tptp.times_times_nat Lx_4))) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_2 Ly_2)) _let_1) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat (tptp.times_times_nat Ly_2) _let_1)))))) (forall ((Lx_4 tptp.int) (Ly_2 tptp.int) (Rx_4 tptp.int) (Ry_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.times_times_int Rx_4) Ry_2))) (let ((_let_2 (tptp.times_times_int Lx_4))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_2 Ly_2)) _let_1) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int (tptp.times_times_int Ly_2) _let_1)))))) (forall ((Lx_3 tptp.real) (Ly_1 tptp.real) (Rx_3 tptp.real)) (let ((_let_1 (tptp.times_times_real Lx_3))) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real _let_1 Ly_1)) Rx_3) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real _let_1 Rx_3)) Ly_1)))) (forall ((Lx_3 tptp.nat) (Ly_1 tptp.nat) (Rx_3 tptp.nat)) (let ((_let_1 (tptp.times_times_nat Lx_3))) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Ly_1)) Rx_3) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Rx_3)) Ly_1)))) (forall ((Lx_3 tptp.int) (Ly_1 tptp.int) (Rx_3 tptp.int)) (let ((_let_1 (tptp.times_times_int Lx_3))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_1 Ly_1)) Rx_3) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_1 Rx_3)) Ly_1)))) (forall ((Lx_2 tptp.real) (Ly tptp.real) (Rx_2 tptp.real)) (let ((_let_1 (tptp.times_times_real Lx_2))) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real _let_1 Ly)) Rx_2) (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.times_times_real Ly) Rx_2))))) (forall ((Lx_2 tptp.nat) (Ly tptp.nat) (Rx_2 tptp.nat)) (let ((_let_1 (tptp.times_times_nat Lx_2))) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Ly)) Rx_2) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat Ly) Rx_2))))) (forall ((Lx_2 tptp.int) (Ly tptp.int) (Rx_2 tptp.int)) (let ((_let_1 (tptp.times_times_int Lx_2))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_1 Ly)) Rx_2) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.times_times_int Ly) Rx_2))))) (forall ((Lx_1 tptp.real) (Rx_1 tptp.real) (Ry_1 tptp.real)) (let ((_let_1 (tptp.times_times_real Lx_1))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.times_times_real Rx_1) Ry_1)) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real _let_1 Rx_1)) Ry_1)))) (forall ((Lx_1 tptp.nat) (Rx_1 tptp.nat) (Ry_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat Lx_1))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat Rx_1) Ry_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Rx_1)) Ry_1)))) (forall ((Lx_1 tptp.int) (Rx_1 tptp.int) (Ry_1 tptp.int)) (let ((_let_1 (tptp.times_times_int Lx_1))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.times_times_int Rx_1) Ry_1)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_1 Rx_1)) Ry_1)))) (forall ((Lx tptp.real) (Rx tptp.real) (Ry tptp.real)) (let ((_let_1 (tptp.times_times_real Lx))) (let ((_let_2 (tptp.times_times_real Rx))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real _let_2 Ry)) (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real _let_1 Ry)))))) (forall ((Lx tptp.nat) (Rx tptp.nat) (Ry tptp.nat)) (let ((_let_1 (tptp.times_times_nat Lx))) (let ((_let_2 (tptp.times_times_nat Rx))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Ry)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Ry)))))) (forall ((Lx tptp.int) (Rx tptp.int) (Ry tptp.int)) (let ((_let_1 (tptp.times_times_int Lx))) (let ((_let_2 (tptp.times_times_int Rx))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 Ry)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 Ry)))))) (forall ((A_100 tptp.real) (B_66 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real A_100) B_66) (tptp.hAPP_real_real (tptp.times_times_real B_66) A_100))) (forall ((A_100 tptp.nat) (B_66 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat A_100) B_66) (tptp.hAPP_nat_nat (tptp.times_times_nat B_66) A_100))) (forall ((A_100 tptp.int) (B_66 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int A_100) B_66) (tptp.hAPP_int_int (tptp.times_times_int B_66) A_100))) (forall ((A_99 tptp.real) (C_41 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real A_99) C_41) (tptp.hAPP_real_real (tptp.plus_plus_real C_41) A_99))) (forall ((A_99 tptp.nat) (C_41 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_99) C_41) (tptp.hAPP_nat_nat (tptp.plus_plus_nat C_41) A_99))) (forall ((A_99 tptp.int) (C_41 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int A_99) C_41) (tptp.hAPP_int_int (tptp.plus_plus_int C_41) A_99))) (forall ((A_98 tptp.real) (C_40 tptp.real) (D_14 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_98))) (let ((_let_2 (tptp.plus_plus_real C_40))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real _let_2 D_14)) (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real _let_1 D_14)))))) (forall ((A_98 tptp.nat) (C_40 tptp.nat) (D_14 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_98))) (let ((_let_2 (tptp.plus_plus_nat C_40))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 D_14)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 D_14)))))) (forall ((A_98 tptp.int) (C_40 tptp.int) (D_14 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_98))) (let ((_let_2 (tptp.plus_plus_int C_40))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 D_14)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 D_14)))))) (forall ((A_97 tptp.real) (C_39 tptp.real) (D_13 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_97))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real C_39) D_13)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 C_39)) D_13)))) (forall ((A_97 tptp.nat) (C_39 tptp.nat) (D_13 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_97))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat C_39) D_13)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 C_39)) D_13)))) (forall ((A_97 tptp.int) (C_39 tptp.int) (D_13 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_97))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int C_39) D_13)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 C_39)) D_13)))) (forall ((A_96 tptp.real) (B_65 tptp.real) (C_38 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_96))) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_65)) C_38) (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real B_65) C_38))))) (forall ((A_96 tptp.nat) (B_65 tptp.nat) (C_38 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_96))) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_65)) C_38) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_65) C_38))))) (forall ((A_96 tptp.int) (B_65 tptp.int) (C_38 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_96))) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_65)) C_38) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int B_65) C_38))))) (forall ((A_95 tptp.real) (B_64 tptp.real) (C_37 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_95))) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_64)) C_37) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 C_37)) B_64)))) (forall ((A_95 tptp.nat) (B_64 tptp.nat) (C_37 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_95))) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_64)) C_37) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 C_37)) B_64)))) (forall ((A_95 tptp.int) (B_64 tptp.int) (C_37 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_95))) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_64)) C_37) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 C_37)) B_64)))) (forall ((A_94 tptp.real) (B_63 tptp.real) (C_36 tptp.real) (D_12 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_94))) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_63)) (tptp.hAPP_real_real (tptp.plus_plus_real C_36) D_12)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 C_36)) (tptp.hAPP_real_real (tptp.plus_plus_real B_63) D_12))))) (forall ((A_94 tptp.nat) (B_63 tptp.nat) (C_36 tptp.nat) (D_12 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_94))) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_63)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat C_36) D_12)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 C_36)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_63) D_12))))) (forall ((A_94 tptp.int) (B_63 tptp.int) (C_36 tptp.int) (D_12 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_94))) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_63)) (tptp.hAPP_int_int (tptp.plus_plus_int C_36) D_12)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 C_36)) (tptp.hAPP_int_int (tptp.plus_plus_int B_63) D_12))))) (forall ((X_14 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real X_14) tptp.one_one_nat) X_14)) (forall ((X_14 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat X_14) tptp.one_one_nat) X_14)) (forall ((X_14 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int X_14) tptp.one_one_nat) X_14)) (forall ((X tptp.nat) (W_1 tptp.int)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.number_number_of_nat W_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat X) _let_2))) (or (= _let_2 tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X))))))) (forall ((Z tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat Z) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_nat (tptp.plus_plus_nat Z) Z))) (forall ((Z tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) Z) (tptp.hAPP_nat_nat (tptp.plus_plus_nat Z) Z))) (forall ((V_2 tptp.int) (V tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat V)) (tptp.number_number_of_nat V_2)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V) tptp.pls)))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.times_times_int V) V_2)))))))) (forall ((V_2 tptp.int) (K_1 tptp.nat) (V tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat V)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat V_2)) K_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V) tptp.pls)))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.times_times_int V) V_2))) K_1))))))) (forall ((A_93 tptp.real) (N_23 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power_real A_93))) (= (tptp.hAPP_nat_real _let_2 (tptp.hAPP_nat_nat (tptp.times_times_nat _let_1) N_23)) (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_nat_real _let_2 N_23)) _let_1))))) (forall ((A_93 tptp.nat) (N_23 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power_nat A_93))) (= (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat (tptp.times_times_nat _let_1) N_23)) (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.hAPP_nat_nat _let_2 N_23)) _let_1))))) (forall ((A_93 tptp.int) (N_23 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power_int A_93))) (= (tptp.hAPP_nat_int _let_2 (tptp.hAPP_nat_nat (tptp.times_times_nat _let_1) N_23)) (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int _let_2 N_23)) _let_1))))) (forall ((A_92 tptp.real) (K_4 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real (tptp.power_power_real A_92) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) K_4))) tptp.zero_zero_real)) (= A_92 tptp.zero_zero_real))) (forall ((A_92 tptp.int) (K_4 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int (tptp.power_power_int A_92) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) K_4))) tptp.zero_zero_int)) (= A_92 tptp.zero_zero_int))) (forall ((A_91 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real tptp.zero_zero_real) A_91) tptp.zero_zero_real)) (forall ((A_91 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat tptp.zero_zero_nat) A_91) tptp.zero_zero_nat)) (forall ((A_91 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int tptp.zero_zero_int) A_91) tptp.zero_zero_int)) (forall ((A_90 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real A_90) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A_90 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat A_90) tptp.zero_zero_nat) tptp.zero_zero_nat)) _let_33 (forall ((A_89 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real tptp.zero_zero_real) A_89) A_89)) (forall ((A_89 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat tptp.zero_zero_nat) A_89) A_89)) (forall ((A_89 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int tptp.zero_zero_int) A_89) A_89)) (forall ((A_88 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real A_88) tptp.zero_zero_real) A_88)) (forall ((A_88 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_88) tptp.zero_zero_nat) A_88)) (forall ((A_88 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int A_88) tptp.zero_zero_int) A_88)) (forall ((B_2 tptp.real) (A_2 tptp.real)) (= (= B_2 (tptp.hAPP_real_real (tptp.plus_plus_real B_2) A_2)) (= A_2 tptp.zero_zero_real))) (forall ((B_2 tptp.nat) (A_2 tptp.nat)) (= (= B_2 (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_2) A_2)) (= A_2 tptp.zero_zero_nat))) (forall ((B_2 tptp.int) (A_2 tptp.int)) (= (= B_2 (tptp.hAPP_int_int (tptp.plus_plus_int B_2) A_2)) (= A_2 tptp.zero_zero_int))) (forall ((X_13 tptp.real) (Y_11 tptp.real) (Z_2 tptp.real)) (let ((_let_1 (tptp.times_times_real X_13))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real Y_11) Z_2)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 Y_11)) (tptp.hAPP_real_real _let_1 Z_2))))) (forall ((X_13 tptp.nat) (Y_11 tptp.nat) (Z_2 tptp.nat)) (let ((_let_1 (tptp.times_times_nat X_13))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat Y_11) Z_2)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 Y_11)) (tptp.hAPP_nat_nat _let_1 Z_2))))) (forall ((X_13 tptp.int) (Y_11 tptp.int) (Z_2 tptp.int)) (let ((_let_1 (tptp.times_times_int X_13))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int Y_11) Z_2)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Y_11)) (tptp.hAPP_int_int _let_1 Z_2))))) (forall ((C_1 tptp.real) (D tptp.real) (A_2 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.times_times_real B_2))) (let ((_let_2 (tptp.times_times_real A_2))) (= (and (not (= A_2 B_2)) (not (= C_1 D))) (not (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_2 C_1)) (tptp.hAPP_real_real _let_1 D)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_2 D)) (tptp.hAPP_real_real _let_1 C_1)))))))) (forall ((C_1 tptp.nat) (D tptp.nat) (A_2 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.times_times_nat B_2))) (let ((_let_2 (tptp.times_times_nat A_2))) (= (and (not (= A_2 B_2)) (not (= C_1 D))) (not (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_2 C_1)) (tptp.hAPP_nat_nat _let_1 D)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_2 D)) (tptp.hAPP_nat_nat _let_1 C_1)))))))) (forall ((C_1 tptp.int) (D tptp.int) (A_2 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.times_times_int B_2))) (let ((_let_2 (tptp.times_times_int A_2))) (= (and (not (= A_2 B_2)) (not (= C_1 D))) (not (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_2 C_1)) (tptp.hAPP_int_int _let_1 D)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_2 D)) (tptp.hAPP_int_int _let_1 C_1)))))))) (forall ((A_87 tptp.real) (B_62 tptp.real) (C_35 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real A_87) B_62)) C_35) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real A_87) C_35)) (tptp.hAPP_real_real (tptp.times_times_real B_62) C_35)))) (forall ((A_87 tptp.nat) (B_62 tptp.nat) (C_35 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_87) B_62)) C_35) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_87) C_35)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_62) C_35)))) (forall ((A_87 tptp.int) (B_62 tptp.int) (C_35 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int A_87) B_62)) C_35) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int A_87) C_35)) (tptp.hAPP_int_int (tptp.times_times_int B_62) C_35)))) (forall ((A_86 tptp.real) (M_12 tptp.real) (B_61 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real A_86) M_12)) (tptp.hAPP_real_real (tptp.times_times_real B_61) M_12)) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real A_86) B_61)) M_12))) (forall ((A_86 tptp.nat) (M_12 tptp.nat) (B_61 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_86) M_12)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_61) M_12)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_86) B_61)) M_12))) (forall ((A_86 tptp.int) (M_12 tptp.int) (B_61 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int A_86) M_12)) (tptp.hAPP_int_int (tptp.times_times_int B_61) M_12)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int A_86) B_61)) M_12))) (forall ((W_1 tptp.real) (Y_1 tptp.real) (X tptp.real) (Z_1 tptp.real)) (let ((_let_1 (tptp.times_times_real X))) (let ((_let_2 (tptp.times_times_real W_1))) (= (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_2 Y_1)) (tptp.hAPP_real_real _let_1 Z_1)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_2 Z_1)) (tptp.hAPP_real_real _let_1 Y_1))) (or (= W_1 X) (= Y_1 Z_1)))))) (forall ((W_1 tptp.nat) (Y_1 tptp.nat) (X tptp.nat) (Z_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat X))) (let ((_let_2 (tptp.times_times_nat W_1))) (= (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_2 Y_1)) (tptp.hAPP_nat_nat _let_1 Z_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_2 Z_1)) (tptp.hAPP_nat_nat _let_1 Y_1))) (or (= W_1 X) (= Y_1 Z_1)))))) (forall ((W_1 tptp.int) (Y_1 tptp.int) (X tptp.int) (Z_1 tptp.int)) (let ((_let_1 (tptp.times_times_int X))) (let ((_let_2 (tptp.times_times_int W_1))) (= (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_2 Y_1)) (tptp.hAPP_int_int _let_1 Z_1)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_2 Z_1)) (tptp.hAPP_int_int _let_1 Y_1))) (or (= W_1 X) (= Y_1 Z_1)))))) (forall ((A_85 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real tptp.one_one_real) A_85) A_85)) (forall ((A_85 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat tptp.one_one_nat) A_85) A_85)) (forall ((A_85 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int tptp.one_one_int) A_85) A_85)) (forall ((A_84 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real A_84) tptp.one_one_real) A_84)) (forall ((A_84 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat A_84) tptp.one_one_nat) A_84)) (forall ((A_84 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int A_84) tptp.one_one_int) A_84)) (forall ((X_12 tptp.real) (Y_10 tptp.real) (Q_6 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_real_real (tptp.times_times_real X_12) Y_10)) Q_6) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_nat_real (tptp.power_power_real X_12) Q_6)) (tptp.hAPP_nat_real (tptp.power_power_real Y_10) Q_6)))) (forall ((X_12 tptp.nat) (Y_10 tptp.nat) (Q_6 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.hAPP_nat_nat (tptp.times_times_nat X_12) Y_10)) Q_6) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_12) Q_6)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_10) Q_6)))) (forall ((X_12 tptp.int) (Y_10 tptp.int) (Q_6 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_int_int (tptp.times_times_int X_12) Y_10)) Q_6) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_nat_int (tptp.power_power_int X_12) Q_6)) (tptp.hAPP_nat_int (tptp.power_power_int Y_10) Q_6)))) (forall ((X_11 tptp.real) (P_6 tptp.nat) (Q_5 tptp.nat)) (let ((_let_1 (tptp.power_power_real X_11))) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_nat_real _let_1 P_6)) (tptp.hAPP_nat_real _let_1 Q_5)) (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat P_6) Q_5))))) (forall ((X_11 tptp.nat) (P_6 tptp.nat) (Q_5 tptp.nat)) (let ((_let_1 (tptp.power_power_nat X_11))) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 P_6)) (tptp.hAPP_nat_nat _let_1 Q_5)) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat P_6) Q_5))))) (forall ((X_11 tptp.int) (P_6 tptp.nat) (Q_5 tptp.nat)) (let ((_let_1 (tptp.power_power_int X_11))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_nat_int _let_1 P_6)) (tptp.hAPP_nat_int _let_1 Q_5)) (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat P_6) Q_5))))) (forall ((X_10 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real X_10) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((X_10 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat X_10) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((X_10 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int X_10) tptp.zero_zero_nat) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_12 tptp.zero_zero_int)) (forall ((A_83 tptp.real) (N_22 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real (tptp.power_power_real A_83) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_22))))) (forall ((A_83 tptp.int) (N_22 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_nat_int (tptp.power_power_int A_83) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_22))))) (forall ((C_34 tptp.real) (D_11 tptp.real) (A_82 tptp.real) (B_60 tptp.real) (R_4 tptp.real)) (let ((_let_1 (tptp.times_times_real R_4))) (=> (not (= R_4 tptp.zero_zero_real)) (=> (and (= A_82 B_60) (not (= C_34 D_11))) (not (= (tptp.hAPP_real_real (tptp.plus_plus_real A_82) (tptp.hAPP_real_real _let_1 C_34)) (tptp.hAPP_real_real (tptp.plus_plus_real B_60) (tptp.hAPP_real_real _let_1 D_11)))))))) (forall ((C_34 tptp.nat) (D_11 tptp.nat) (A_82 tptp.nat) (B_60 tptp.nat) (R_4 tptp.nat)) (let ((_let_1 (tptp.times_times_nat R_4))) (=> (not (= R_4 tptp.zero_zero_nat)) (=> (and (= A_82 B_60) (not (= C_34 D_11))) (not (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_82) (tptp.hAPP_nat_nat _let_1 C_34)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_60) (tptp.hAPP_nat_nat _let_1 D_11)))))))) (forall ((C_34 tptp.int) (D_11 tptp.int) (A_82 tptp.int) (B_60 tptp.int) (R_4 tptp.int)) (let ((_let_1 (tptp.times_times_int R_4))) (=> (not (= R_4 tptp.zero_zero_int)) (=> (and (= A_82 B_60) (not (= C_34 D_11))) (not (= (tptp.hAPP_int_int (tptp.plus_plus_int A_82) (tptp.hAPP_int_int _let_1 C_34)) (tptp.hAPP_int_int (tptp.plus_plus_int B_60) (tptp.hAPP_int_int _let_1 D_11)))))))) (forall ((M_11 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real M_11) M_11) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)) M_11))) (forall ((M_11 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_11) M_11) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)) M_11))) (forall ((M_11 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int M_11) M_11) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)) M_11))) (forall ((M_10 tptp.real) (A_81 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real M_10) (tptp.hAPP_real_real (tptp.times_times_real A_81) M_10)) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real A_81) tptp.one_one_real)) M_10))) (forall ((M_10 tptp.nat) (A_81 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_10) (tptp.hAPP_nat_nat (tptp.times_times_nat A_81) M_10)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_81) tptp.one_one_nat)) M_10))) (forall ((M_10 tptp.int) (A_81 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int M_10) (tptp.hAPP_int_int (tptp.times_times_int A_81) M_10)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int A_81) tptp.one_one_int)) M_10))) (forall ((A_80 tptp.real) (M_9 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real A_80) M_9)) M_9) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real A_80) tptp.one_one_real)) M_9))) (forall ((A_80 tptp.nat) (M_9 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_80) M_9)) M_9) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_80) tptp.one_one_nat)) M_9))) (forall ((A_80 tptp.int) (M_9 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int A_80) M_9)) M_9) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int A_80) tptp.one_one_int)) M_9))) (forall ((A_2 tptp.real) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_1))) (= (= (tptp.hAPP_nat_real (tptp.power_power_real A_2) _let_1) tptp.zero_zero_real) (and (= A_2 tptp.zero_zero_real) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A_2 tptp.nat) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_1))) (= (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_2) _let_1) tptp.zero_zero_nat) (and (= A_2 tptp.zero_zero_nat) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A_2 tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_1))) (= (= (tptp.hAPP_nat_int (tptp.power_power_int A_2) _let_1) tptp.zero_zero_int) (and (= A_2 tptp.zero_zero_int) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int A) B))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B)))))) _let_27 (forall ((Y tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int X_1) Y))))))) (forall ((Y tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int X_1) Y))))))) (forall ((N_1 tptp.nat) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int X_1) N_1)))))) (forall ((W_2 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_2))) (let ((_let_2 (tptp.hAPP_nat_real (tptp.power_power_real tptp.zero_zero_real) _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 tptp.zero_zero_real))))))) (forall ((W_2 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_2))) (let ((_let_2 (tptp.hAPP_nat_nat (tptp.power_power_nat tptp.zero_zero_nat) _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 tptp.zero_zero_nat))))))) (forall ((W_2 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_2))) (let ((_let_2 (tptp.hAPP_nat_int (tptp.power_power_int tptp.zero_zero_int) _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 tptp.zero_zero_int))))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_12 (tptp.number_number_of_int (tptp.bit1 _let_1)))) (forall ((B_59 tptp.int) (Q_4 tptp.int) (R_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B_59) Q_4)) R_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_3) B_59)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_59)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Q_4))))))) (forall ((B_59 tptp.int) (Q_4 tptp.int) (R_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B_59) Q_4)) R_3)) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_59)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_4) tptp.zero_zero_int)))))) (forall ((B tptp.int) (Q_4 tptp.int) (R_3 tptp.int) (Q_1 tptp.int) (R_1 tptp.int)) (let ((_let_1 (tptp.times_times_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Q_4)) R_3)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Q_1)) R_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_3) B)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_1) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_4) Q_1)))))))) (forall ((B tptp.int) (Q_1 tptp.int) (R_1 tptp.int) (B_59 tptp.int) (Q_4 tptp.int) (R_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B_59) Q_4)) R_3))) (=> (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B) Q_1)) R_1) _let_2) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 _let_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_3) B_59)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 R_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_59)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_59) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_1) Q_4))))))))))) (forall ((B tptp.int) (Q_4 tptp.int) (R_3 tptp.int) (Q_1 tptp.int) (R_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B))) (let ((_let_2 (tptp.times_times_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_2 Q_4)) R_3)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_2 Q_1)) R_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int R_1) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 R_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 R_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_1) Q_4))))))))) (forall ((B tptp.int) (Q_1 tptp.int) (R_1 tptp.int) (B_59 tptp.int) (Q_4 tptp.int) (R_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B_59) Q_4)) R_3))) (=> (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B) Q_1)) R_1) _let_1) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_1) B)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_59)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_59) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_4) Q_1)))))))))) (forall ((X_1 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.power_power_int X_1))) (let ((_let_3 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int _let_2 _let_3)) _let_3) (tptp.hAPP_nat_int _let_2 (tptp.number_number_of_nat (tptp.bit0 _let_1)))))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong _let_4 _let_14) _let_8)) (forall ((Y tptp.int) (X_1 tptp.int) (P_3 tptp.int)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.power_power_int Y) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) X_1) P_3)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3) Y)))))) (forall ((P_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) P_2)) (forall ((M_2 tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) M_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int M_2) P_2))) (or (= M_2 tptp.one_one_int) (= M_2 P_2))))))) (forall ((P_3 tptp.int)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit0 _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (= P_3 (tptp.number_number_of_int _let_2))) (=> (not (= P_3 (tptp.number_number_of_int (tptp.bit1 _let_1)))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int (tptp.bit1 _let_2))) P_3)))))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_22 _let_3)) (forall ((N_21 tptp.nat) (A_79 tptp.real) (B_58 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_79) B_58)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_79)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_21)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real (tptp.power_power_real A_79) N_21)) (tptp.hAPP_nat_real (tptp.power_power_real B_58) N_21))))))) (forall ((N_21 tptp.nat) (A_79 tptp.nat) (B_58 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_79) B_58)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_79)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_21)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.power_power_nat A_79) N_21)) (tptp.hAPP_nat_nat (tptp.power_power_nat B_58) N_21))))))) (forall ((N_21 tptp.nat) (A_79 tptp.int) (B_58 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_79) B_58)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_79)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_21)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int (tptp.power_power_int A_79) N_21)) (tptp.hAPP_nat_int (tptp.power_power_int B_58) N_21))))))) (forall ((V_1 tptp.real) (U_2 tptp.real) (Y_9 tptp.real) (X_9 tptp.real) (A_78 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_9) A_78)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_9) A_78)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 U_2)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 V_1)) (=> (= (tptp.hAPP_real_real (tptp.plus_plus_real U_2) V_1) tptp.one_one_real) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real U_2) X_9)) (tptp.hAPP_real_real (tptp.times_times_real V_1) Y_9))) A_78))))))))) (forall ((V_1 tptp.int) (U_2 tptp.int) (Y_9 tptp.int) (X_9 tptp.int) (A_78 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_9) A_78)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y_9) A_78)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 U_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_1)) (=> (= (tptp.hAPP_int_int (tptp.plus_plus_int U_2) V_1) tptp.one_one_int) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int U_2) X_9)) (tptp.hAPP_int_int (tptp.times_times_int V_1) Y_9))) A_78))))))))) (forall ((Y tptp.int) (N_1 tptp.nat) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int Y) N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y))))))) (forall ((A_77 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_77) tptp.zero_zero_nat))) (forall ((A_77 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_77) tptp.zero_zero_int))) (forall ((A_77 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_77) tptp.zero_zero_real))) (not (forall ((S1 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.power_power_int S1) (tptp.number_number_of_nat _let_1)) (tptp.number_number_of_int tptp.min)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int))))))) _let_15 (forall ((K tptp.int)) (= (= (tptp.bit1 K) tptp.min) (= K tptp.min))) (forall ((L_1 tptp.int)) (= (= tptp.min (tptp.bit1 L_1)) (= tptp.min L_1))) (= (tptp.bit1 tptp.min) tptp.min) (not (= tptp.pls tptp.min)) (not (= tptp.min tptp.pls)) (forall ((K_1 tptp.int)) (not (= (tptp.bit0 K_1) tptp.min))) (forall ((L tptp.int)) (not (= tptp.min (tptp.bit0 L)))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_31 tptp.min))) (tptp.hBOOL (tptp.hAPP_int_bool _let_30 tptp.min)) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K)) tptp.min)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) tptp.min)))) (forall ((K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.min))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K))))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_32 tptp.min))) (tptp.hBOOL (tptp.hAPP_int_bool _let_31 tptp.pls)) (forall ((K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.min))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_31 tptp.zero_zero_int)) (forall ((K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.min))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K))))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K)) tptp.min)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) tptp.min)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_30 tptp.pls)) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_29 tptp.min))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K)) tptp.min)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) tptp.min)))) (not (= _let_11 _let_14)) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 K)) tptp.min)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) tptp.min)))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.min) (tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.min) K)))) (forall ((Ma tptp.int) (N tptp.int)) (let ((_let_1 (tptp.number_number_of_int tptp.min))) (= (= (tptp.hAPP_int_int (tptp.times_times_int Ma) N) tptp.one_one_int) (or (and (= Ma tptp.one_one_int) (= N tptp.one_one_int)) (and (= Ma _let_1) (= N _let_1)))))) (forall ((M tptp.int) (N_1 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.times_times_int M) N_1) tptp.one_one_int) (or (= M tptp.one_one_int) (= M (tptp.number_number_of_int tptp.min))))) (forall ((X_8 tptp.real) (Y_8 tptp.real)) (=> (not (= X_8 Y_8)) (=> (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_8) Y_8))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_8) X_8))))) (forall ((X_8 tptp.int) (Y_8 tptp.int)) (=> (not (= X_8 Y_8)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_8) Y_8))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y_8) X_8))))) (forall ((A_76 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_76) A_76))) (forall ((A_76 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_76) A_76))) (forall ((C_33 tptp.nat) (A_75 tptp.nat) (B_57 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_75))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_57)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_57) C_33)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_33)))))) (forall ((C_33 tptp.int) (A_75 tptp.int) (B_57 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_75))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_57)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int B_57) C_33)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_33)))))) (forall ((A_2 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 B_2) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong B_2 A_2) Ma)))) (forall ((K_1 tptp.int) (M tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong K_1 K_1) M))) (forall ((D_3 tptp.int) (C tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (=> (= B C) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C D_3) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A D_3) M)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong B C) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A C) M))))) (forall ((X_1 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 (tptp.number_number_of_int tptp.min)) P_3)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.one_one_int) P_3)))))) (forall ((X_7 tptp.real) (Y_7 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_7) Y_7)) (=> (not (= X_7 Y_7)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_7) Y_7))))) (forall ((X_7 tptp.nat) (Y_7 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_7) Y_7)) (=> (not (= X_7 Y_7)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_7) Y_7))))) (forall ((X_7 tptp.int) (Y_7 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_7) Y_7)) (=> (not (= X_7 Y_7)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_7) Y_7))))) (forall ((A_74 tptp.real) (B_56 tptp.real)) (=> (= (tptp.hAPP_real_real (tptp.times_times_real A_74) B_56) tptp.zero_zero_real) (or (= A_74 tptp.zero_zero_real) (= B_56 tptp.zero_zero_real)))) (forall ((A_74 tptp.nat) (B_56 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.times_times_nat A_74) B_56) tptp.zero_zero_nat) (or (= A_74 tptp.zero_zero_nat) (= B_56 tptp.zero_zero_nat)))) (forall ((A_74 tptp.int) (B_56 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.times_times_int A_74) B_56) tptp.zero_zero_int) (or (= A_74 tptp.zero_zero_int) (= B_56 tptp.zero_zero_int)))) (forall ((B_55 tptp.real) (A_73 tptp.real)) (=> (not (= A_73 tptp.zero_zero_real)) (=> (not (= B_55 tptp.zero_zero_real)) (not (= (tptp.hAPP_real_real (tptp.times_times_real A_73) B_55) tptp.zero_zero_real))))) (forall ((B_55 tptp.nat) (A_73 tptp.nat)) (=> (not (= A_73 tptp.zero_zero_nat)) (=> (not (= B_55 tptp.zero_zero_nat)) (not (= (tptp.hAPP_nat_nat (tptp.times_times_nat A_73) B_55) tptp.zero_zero_nat))))) (forall ((B_55 tptp.int) (A_73 tptp.int)) (=> (not (= A_73 tptp.zero_zero_int)) (=> (not (= B_55 tptp.zero_zero_int)) (not (= (tptp.hAPP_int_int (tptp.times_times_int A_73) B_55) tptp.zero_zero_int))))) (forall ((A_2 tptp.real) (B_2 tptp.real)) (= (= (tptp.hAPP_real_real (tptp.times_times_real A_2) B_2) tptp.zero_zero_real) (or (= A_2 tptp.zero_zero_real) (= B_2 tptp.zero_zero_real)))) (forall ((A_2 tptp.int) (B_2 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.times_times_int A_2) B_2) tptp.zero_zero_int) (or (= A_2 tptp.zero_zero_int) (= B_2 tptp.zero_zero_int)))) (forall ((A_72 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real A_72) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A_72 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat A_72) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A_72 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int A_72) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A_71 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real tptp.zero_zero_real) A_71) tptp.zero_zero_real)) (forall ((A_71 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat tptp.zero_zero_nat) A_71) tptp.zero_zero_nat)) (forall ((A_71 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int tptp.zero_zero_int) A_71) tptp.zero_zero_int)) _let_13 (not (= tptp.zero_zero_nat tptp.one_one_nat)) _let_28 (not (= tptp.one_one_real tptp.zero_zero_real)) (not (= tptp.one_one_nat tptp.zero_zero_nat)) (not (= tptp.one_one_int tptp.zero_zero_int)) (forall ((A_70 tptp.real) (E tptp.real) (B_54 tptp.real) (C_32 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real A_70) E)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real B_54) E)) C_32)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real A_70) B_54)) E)) C_32))) (forall ((A_70 tptp.nat) (E tptp.nat) (B_54 tptp.nat) (C_32 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_70) E)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat B_54) E)) C_32)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_70) B_54)) E)) C_32))) (forall ((A_70 tptp.int) (E tptp.int) (B_54 tptp.int) (C_32 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int A_70) E)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B_54) E)) C_32)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int A_70) B_54)) E)) C_32))) (forall ((A_69 tptp.real) (B_53 tptp.real) (C_31 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real A_69) B_53)) C_31) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real A_69) C_31)) (tptp.hAPP_real_real (tptp.times_times_real B_53) C_31)))) (forall ((A_69 tptp.nat) (B_53 tptp.nat) (C_31 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_69) B_53)) C_31) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_69) C_31)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_53) C_31)))) (forall ((A_69 tptp.int) (B_53 tptp.int) (C_31 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int A_69) B_53)) C_31) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int A_69) C_31)) (tptp.hAPP_int_int (tptp.times_times_int B_53) C_31)))) (forall ((N_20 tptp.nat) (A_68 tptp.real)) (=> (not (= A_68 tptp.zero_zero_real)) (not (= (tptp.hAPP_nat_real (tptp.power_power_real A_68) N_20) tptp.zero_zero_real)))) (forall ((N_20 tptp.nat) (A_68 tptp.int)) (=> (not (= A_68 tptp.zero_zero_int)) (not (= (tptp.hAPP_nat_int (tptp.power_power_int A_68) N_20) tptp.zero_zero_int)))) (forall ((A_67 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A_67)) (= A_67 tptp.zero_zero_nat))) (forall ((A_67 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int tptp.zero_zero_int) A_67)) (= A_67 tptp.zero_zero_int))) (forall ((A_67 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real tptp.zero_zero_real) A_67)) (= A_67 tptp.zero_zero_real))) (forall ((A_66 tptp.real) (B_52 tptp.real) (N_19 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_real_real (tptp.times_times_real A_66) B_52)) N_19) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_nat_real (tptp.power_power_real A_66) N_19)) (tptp.hAPP_nat_real (tptp.power_power_real B_52) N_19)))) (forall ((A_66 tptp.nat) (B_52 tptp.nat) (N_19 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_66) B_52)) N_19) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.power_power_nat A_66) N_19)) (tptp.hAPP_nat_nat (tptp.power_power_nat B_52) N_19)))) (forall ((A_66 tptp.int) (B_52 tptp.int) (N_19 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_int_int (tptp.times_times_int A_66) B_52)) N_19) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_nat_int (tptp.power_power_int A_66) N_19)) (tptp.hAPP_nat_int (tptp.power_power_int B_52) N_19)))) (forall ((A_65 tptp.real) (N_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_65) N_18))) (= (tptp.hAPP_real_real (tptp.times_times_real _let_1) A_65) (tptp.hAPP_real_real (tptp.times_times_real A_65) _let_1)))) (forall ((A_65 tptp.nat) (N_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_65) N_18))) (= (tptp.hAPP_nat_nat (tptp.times_times_nat _let_1) A_65) (tptp.hAPP_nat_nat (tptp.times_times_nat A_65) _let_1)))) (forall ((A_65 tptp.int) (N_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_65) N_18))) (= (tptp.hAPP_int_int (tptp.times_times_int _let_1) A_65) (tptp.hAPP_int_int (tptp.times_times_int A_65) _let_1)))) (forall ((A_64 tptp.nat) (B_51 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_64) (tptp.hAPP_nat_nat (tptp.times_times_nat A_64) B_51)))) (forall ((A_64 tptp.int) (B_51 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_64) (tptp.hAPP_int_int (tptp.times_times_int A_64) B_51)))) (forall ((A_64 tptp.real) (B_51 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_64) (tptp.hAPP_real_real (tptp.times_times_real A_64) B_51)))) (forall ((A_63 tptp.nat) (B_50 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_63) (tptp.hAPP_nat_nat (tptp.times_times_nat B_50) A_63)))) (forall ((A_63 tptp.int) (B_50 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_63) (tptp.hAPP_int_int (tptp.times_times_int B_50) A_63)))) (forall ((A_63 tptp.real) (B_50 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_63) (tptp.hAPP_real_real (tptp.times_times_real B_50) A_63)))) (forall ((C_30 tptp.nat) (A_62 tptp.nat) (B_49 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_62))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_49)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat B_49) C_30)))))) (forall ((C_30 tptp.int) (A_62 tptp.int) (B_49 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_62))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_49)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int B_49) C_30)))))) (forall ((C_30 tptp.real) (A_62 tptp.real) (B_49 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_62))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_49)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real B_49) C_30)))))) (forall ((B_48 tptp.nat) (A_61 tptp.nat) (C_29 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_61))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_29)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat B_48) C_29)))))) (forall ((B_48 tptp.int) (A_61 tptp.int) (C_29 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_61))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_29)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int B_48) C_29)))))) (forall ((B_48 tptp.real) (A_61 tptp.real) (C_29 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_61))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_29)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real B_48) C_29)))))) (forall ((C_28 tptp.nat) (D_10 tptp.nat) (A_60 tptp.nat) (B_47 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_60) B_47)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat C_28) D_10)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_60) C_28)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_47) D_10)))))) (forall ((C_28 tptp.int) (D_10 tptp.int) (A_60 tptp.int) (B_47 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_60) B_47)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int C_28) D_10)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.times_times_int A_60) C_28)) (tptp.hAPP_int_int (tptp.times_times_int B_47) D_10)))))) (forall ((C_28 tptp.real) (D_10 tptp.real) (A_60 tptp.real) (B_47 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_60) B_47)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real C_28) D_10)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_real_real (tptp.times_times_real A_60) C_28)) (tptp.hAPP_real_real (tptp.times_times_real B_47) D_10)))))) (forall ((A_59 tptp.nat) (B_46 tptp.nat) (K_3 tptp.nat)) (=> (= A_59 (tptp.hAPP_nat_nat (tptp.times_times_nat B_46) K_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_46) A_59)))) (forall ((A_59 tptp.int) (B_46 tptp.int) (K_3 tptp.int)) (=> (= A_59 (tptp.hAPP_int_int (tptp.times_times_int B_46) K_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int B_46) A_59)))) (forall ((A_59 tptp.real) (B_46 tptp.real) (K_3 tptp.real)) (=> (= A_59 (tptp.hAPP_real_real (tptp.times_times_real B_46) K_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real B_46) A_59)))) (forall ((A_58 tptp.nat) (B_45 tptp.nat) (C_27 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_58) B_45)) C_27)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_58) C_27)))) (forall ((A_58 tptp.int) (B_45 tptp.int) (C_27 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.times_times_int A_58) B_45)) C_27)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_58) C_27)))) (forall ((A_58 tptp.real) (B_45 tptp.real) (C_27 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_real_real (tptp.times_times_real A_58) B_45)) C_27)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_58) C_27)))) (forall ((A_57 tptp.nat) (B_44 tptp.nat) (C_26 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_57) B_44)) C_26)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_44) C_26)))) (forall ((A_57 tptp.int) (B_44 tptp.int) (C_26 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.times_times_int A_57) B_44)) C_26)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int B_44) C_26)))) (forall ((A_57 tptp.real) (B_44 tptp.real) (C_26 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_real_real (tptp.times_times_real A_57) B_44)) C_26)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real B_44) C_26)))) (forall ((C_25 tptp.nat) (A_56 tptp.nat) (B_43 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_56))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_43)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_25)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_43) C_25))))))) (forall ((C_25 tptp.int) (A_56 tptp.int) (B_43 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_56))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_43)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_25)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int B_43) C_25))))))) (forall ((C_25 tptp.real) (A_56 tptp.real) (B_43 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_56))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_43)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_25)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real B_43) C_25))))))) (forall ((N_17 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.power_power_real tptp.one_one_real) N_17) tptp.one_one_real)) (forall ((N_17 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat tptp.one_one_nat) N_17) tptp.one_one_nat)) (forall ((N_17 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.power_power_int tptp.one_one_int) N_17) tptp.one_one_int)) (forall ((A_55 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.one_one_nat) A_55))) (forall ((A_55 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int tptp.one_one_int) A_55))) (forall ((A_55 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real tptp.one_one_real) A_55))) (forall ((N_16 tptp.nat) (X_6 tptp.nat) (Y_6 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_6) Y_6)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_6) N_16)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_6) N_16))))) (forall ((N_16 tptp.nat) (X_6 tptp.int) (Y_6 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int X_6) Y_6)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.power_power_int X_6) N_16)) (tptp.hAPP_nat_int (tptp.power_power_int Y_6) N_16))))) (forall ((N_16 tptp.nat) (X_6 tptp.real) (Y_6 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real X_6) Y_6)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_nat_real (tptp.power_power_real X_6) N_16)) (tptp.hAPP_nat_real (tptp.power_power_real Y_6) N_16))))) (forall ((M_8 tptp.nat) (A_54 tptp.nat) (N_15 tptp.nat) (B_42 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_54))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 N_15)) B_42)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_8) N_15)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 M_8)) B_42)))))) (forall ((M_8 tptp.nat) (A_54 tptp.int) (N_15 tptp.nat) (B_42 tptp.int)) (let ((_let_1 (tptp.power_power_int A_54))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int _let_1 N_15)) B_42)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_8) N_15)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int _let_1 M_8)) B_42)))))) (forall ((M_8 tptp.nat) (A_54 tptp.real) (N_15 tptp.nat) (B_42 tptp.real)) (let ((_let_1 (tptp.power_power_real A_54))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_nat_real _let_1 N_15)) B_42)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_8) N_15)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_nat_real _let_1 M_8)) B_42)))))) (forall ((N_14 tptp.nat) (M_7 tptp.nat) (X_5 tptp.nat) (Y_5 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_5) Y_5)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_14) M_7)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_5) N_14)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_5) M_7)))))) (forall ((N_14 tptp.nat) (M_7 tptp.nat) (X_5 tptp.int) (Y_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int X_5) Y_5)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_14) M_7)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.power_power_int X_5) N_14)) (tptp.hAPP_nat_int (tptp.power_power_int Y_5) M_7)))))) (forall ((N_14 tptp.nat) (M_7 tptp.nat) (X_5 tptp.real) (Y_5 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real X_5) Y_5)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_14) M_7)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_nat_real (tptp.power_power_real X_5) N_14)) (tptp.hAPP_nat_real (tptp.power_power_real Y_5) M_7)))))) (forall ((A_53 tptp.nat) (M_6 tptp.nat) (N_13 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_53))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_6) N_13)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 M_6)) (tptp.hAPP_nat_nat _let_1 N_13)))))) (forall ((A_53 tptp.int) (M_6 tptp.nat) (N_13 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_53))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_6) N_13)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int _let_1 M_6)) (tptp.hAPP_nat_int _let_1 N_13)))))) (forall ((A_53 tptp.real) (M_6 tptp.nat) (N_13 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_53))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_6) N_13)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_nat_real _let_1 M_6)) (tptp.hAPP_nat_real _let_1 N_13)))))) (forall ((M tptp.nat) (N_1 tptp.nat) (I_1 tptp.nat)) (let ((_let_1 (tptp.power_power_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) I_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1)))))) (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat X) N))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X)) (= N tptp.zero_zero_nat))))) (forall ((A_52 tptp.real) (M_5 tptp.nat) (N_12 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_52))) (= (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat M_5) N_12)) (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_nat_real _let_1 M_5)) N_12)))) (forall ((A_52 tptp.nat) (M_5 tptp.nat) (N_12 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_52))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat M_5) N_12)) (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.hAPP_nat_nat _let_1 M_5)) N_12)))) (forall ((A_52 tptp.int) (M_5 tptp.nat) (N_12 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_52))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat M_5) N_12)) (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int _let_1 M_5)) N_12)))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) C)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) C)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B) A)))))) (forall ((A_51 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real A_51) tptp.one_one_nat) A_51)) (forall ((A_51 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_51) tptp.one_one_nat) A_51)) (forall ((A_51 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int A_51) tptp.one_one_nat) A_51)) (forall ((M tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong M tptp.zero_zero_int) M))) (forall ((A_2 tptp.int) (B_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 B_2) tptp.zero_zero_int)) (= A_2 B_2))) (forall ((A tptp.int) (B tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) tptp.one_one_int))) (forall ((A tptp.int) (M tptp.int) (B tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A) M) (tptp.hAPP_int_int (tptp.times_times_int B) M)) M))) (forall ((C_1 tptp.int) (D tptp.int) (A_2 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 B_2) Ma)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C_1 (tptp.hAPP_int_int (tptp.times_times_int A_2) D)) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C_1 (tptp.hAPP_int_int (tptp.times_times_int B_2) D)) Ma))))) (forall ((C_1 tptp.int) (D tptp.int) (A_2 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (let ((_let_1 (tptp.times_times_int D))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 B_2) Ma)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C_1 (tptp.hAPP_int_int _let_1 A_2)) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C_1 (tptp.hAPP_int_int _let_1 B_2)) Ma)))))) (forall ((K_1 tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A) K_1) (tptp.hAPP_int_int (tptp.times_times_int B) K_1)) M)))) (forall ((K_1 tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (let ((_let_1 (tptp.times_times_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int _let_1 A) (tptp.hAPP_int_int _let_1 B)) M))))) (forall ((C tptp.int) (D_3 tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C D_3) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A) C) (tptp.hAPP_int_int (tptp.times_times_int B) D_3)) M))))) (forall ((C tptp.int) (D_3 tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C D_3) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.plus_plus_int A) C) (tptp.hAPP_int_int (tptp.plus_plus_int B) D_3)) M))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.plus_plus_int A) C) (tptp.hAPP_int_int (tptp.plus_plus_int B) C)) M)))) (forall ((Z tptp.nat) (X_1 tptp.int) (Y tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 Y) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.power_power_int X_1) Z) (tptp.hAPP_nat_int (tptp.power_power_int Y) Z)) M)))) (forall ((N_11 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.power_power_real (tptp.number267125858f_real tptp.min)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_11)) tptp.one_one_real)) (forall ((N_11 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.number_number_of_int tptp.min)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_11)) tptp.one_one_int)) (forall ((B_41 tptp.real) (A_50 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_50)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_41) tptp.zero_zero_real))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_50) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_41)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real A_50) B_41)) tptp.zero_zero_real))))) (forall ((B_41 tptp.nat) (A_50 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_50)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_41) tptp.zero_zero_nat))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_50) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_41)))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_50) B_41)) tptp.zero_zero_nat))))) (forall ((B_41 tptp.int) (A_50 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_50)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_41) tptp.zero_zero_int))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_50) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_41)))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int A_50) B_41)) tptp.zero_zero_int))))) (forall ((B_40 tptp.real) (A_49 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_49)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_40))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_49) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_40) tptp.zero_zero_real)))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real A_49) B_40)))))) (forall ((B_40 tptp.int) (A_49 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_49)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_40))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_49) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_40) tptp.zero_zero_int)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int A_49) B_40)))))) (forall ((C_24 tptp.real) (D_9 tptp.real) (A_48 tptp.real) (B_39 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_48) B_39)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_24) D_9)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_39)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_24)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real A_48) C_24)) (tptp.hAPP_real_real (tptp.times_times_real B_39) D_9))))))))) (forall ((C_24 tptp.nat) (D_9 tptp.nat) (A_48 tptp.nat) (B_39 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_48) B_39)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_24) D_9)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_39)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_24)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_48) C_24)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_39) D_9))))))))) (forall ((C_24 tptp.int) (D_9 tptp.int) (A_48 tptp.int) (B_39 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_48) B_39)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_24) D_9)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_39)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_24)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int A_48) C_24)) (tptp.hAPP_int_int (tptp.times_times_int B_39) D_9))))))))) (forall ((C_23 tptp.real) (D_8 tptp.real) (A_47 tptp.real) (B_38 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_47) B_38)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_23) D_8)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_47)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_23)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real A_47) C_23)) (tptp.hAPP_real_real (tptp.times_times_real B_38) D_8))))))))) (forall ((C_23 tptp.nat) (D_8 tptp.nat) (A_47 tptp.nat) (B_38 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_47) B_38)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_23) D_8)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_47)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_23)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_47) C_23)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_38) D_8))))))))) (forall ((C_23 tptp.int) (D_8 tptp.int) (A_47 tptp.int) (B_38 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_47) B_38)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_23) D_8)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_47)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_23)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int A_47) C_23)) (tptp.hAPP_int_int (tptp.times_times_int B_38) D_8))))))))) (forall ((C_22 tptp.real) (B_37 tptp.real) (A_46 tptp.real)) (let ((_let_1 (tptp.times_times_real C_22))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_37) A_46)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_22) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_46)) (tptp.hAPP_real_real _let_1 B_37))))))) (forall ((C_22 tptp.int) (B_37 tptp.int) (A_46 tptp.int)) (let ((_let_1 (tptp.times_times_int C_22))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_37) A_46)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_22) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_46)) (tptp.hAPP_int_int _let_1 B_37))))))) (forall ((C_21 tptp.real) (B_36 tptp.real) (A_45 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_36) A_45)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_21) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real A_45) C_21)) (tptp.hAPP_real_real (tptp.times_times_real B_36) C_21)))))) (forall ((C_21 tptp.int) (B_36 tptp.int) (A_45 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_36) A_45)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_21) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int A_45) C_21)) (tptp.hAPP_int_int (tptp.times_times_int B_36) C_21)))))) (forall ((C_20 tptp.real) (A_44 tptp.real) (B_35 tptp.real)) (let ((_let_1 (tptp.times_times_real C_20))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_44) B_35)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_20)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_44)) (tptp.hAPP_real_real _let_1 B_35))))))) (forall ((C_20 tptp.nat) (A_44 tptp.nat) (B_35 tptp.nat)) (let ((_let_1 (tptp.times_times_nat C_20))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_44) B_35)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_20)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_44)) (tptp.hAPP_nat_nat _let_1 B_35))))))) (forall ((C_20 tptp.int) (A_44 tptp.int) (B_35 tptp.int)) (let ((_let_1 (tptp.times_times_int C_20))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_44) B_35)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_20)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_44)) (tptp.hAPP_int_int _let_1 B_35))))))) (forall ((C_19 tptp.real) (A_43 tptp.real) (B_34 tptp.real)) (let ((_let_1 (tptp.times_times_real C_19))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_43) B_34)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_19)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_43)) (tptp.hAPP_real_real _let_1 B_34))))))) (forall ((C_19 tptp.nat) (A_43 tptp.nat) (B_34 tptp.nat)) (let ((_let_1 (tptp.times_times_nat C_19))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_43) B_34)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_19)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_43)) (tptp.hAPP_nat_nat _let_1 B_34))))))) (forall ((C_19 tptp.int) (A_43 tptp.int) (B_34 tptp.int)) (let ((_let_1 (tptp.times_times_int C_19))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_43) B_34)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_19)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_43)) (tptp.hAPP_int_int _let_1 B_34))))))) (forall ((C_18 tptp.real) (A_42 tptp.real) (B_33 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_42) B_33)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_18)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real A_42) C_18)) (tptp.hAPP_real_real (tptp.times_times_real B_33) C_18)))))) (forall ((C_18 tptp.nat) (A_42 tptp.nat) (B_33 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_42) B_33)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_18)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_42) C_18)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_33) C_18)))))) (forall ((C_18 tptp.int) (A_42 tptp.int) (B_33 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_42) B_33)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_18)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int A_42) C_18)) (tptp.hAPP_int_int (tptp.times_times_int B_33) C_18)))))) (forall ((B_32 tptp.real) (A_41 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_41) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_32) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.times_times_real A_41) B_32)))))) (forall ((B_32 tptp.int) (A_41 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_41) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_32) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.times_times_int A_41) B_32)))))) (forall ((B_31 tptp.real) (A_40 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_40) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B_31)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real A_40) B_31)) tptp.zero_zero_real))))) (forall ((B_31 tptp.nat) (A_40 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_40) tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B_31)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_40) B_31)) tptp.zero_zero_nat))))) (forall ((B_31 tptp.int) (A_40 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_40) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) B_31)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int A_40) B_31)) tptp.zero_zero_int))))) (forall ((B_30 tptp.real) (A_39 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_39)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_30) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real B_30) A_39)) tptp.zero_zero_real))))) (forall ((B_30 tptp.nat) (A_39 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_39)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_30) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat B_30) A_39)) tptp.zero_zero_nat))))) (forall ((B_30 tptp.int) (A_39 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_39)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_30) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int B_30) A_39)) tptp.zero_zero_int))))) (forall ((B_29 tptp.real) (A_38 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_38)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_29) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real A_38) B_29)) tptp.zero_zero_real))))) (forall ((B_29 tptp.nat) (A_38 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_38)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_29) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_38) B_29)) tptp.zero_zero_nat))))) (forall ((B_29 tptp.int) (A_38 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_38)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_29) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int A_38) B_29)) tptp.zero_zero_int))))) (forall ((B_28 tptp.real) (A_37 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_37)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_28)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real A_37) B_28))))))) (forall ((B_28 tptp.nat) (A_37 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_37)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_28)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat A_37) B_28))))))) (forall ((B_28 tptp.int) (A_37 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_37)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_28)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int A_37) B_28))))))) (forall ((A_2 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real A_2) B_2)) tptp.zero_zero_real)) (or (and (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_2) tptp.zero_zero_real))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_2) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_2))))))) (forall ((A_2 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int A_2) B_2)) tptp.zero_zero_int)) (or (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) tptp.zero_zero_int))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_2) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_2))))))) (forall ((A_2 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real A_2) B_2))) (or (and (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_2))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_2) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_2) tptp.zero_zero_real))))))) (forall ((A_2 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int A_2) B_2))) (or (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_2))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_2) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) tptp.zero_zero_int))))))) (forall ((A_36 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.times_times_real A_36) A_36)))) (forall ((A_36 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.times_times_int A_36) A_36)))) (forall ((C_17 tptp.real) (B_27 tptp.real) (A_35 tptp.real)) (let ((_let_1 (tptp.times_times_real C_17))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_27) A_35)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_17) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_35)) (tptp.hAPP_real_real _let_1 B_27))))))) (forall ((C_17 tptp.int) (B_27 tptp.int) (A_35 tptp.int)) (let ((_let_1 (tptp.times_times_int C_17))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_27) A_35)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_17) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_35)) (tptp.hAPP_int_int _let_1 B_27))))))) (forall ((C_16 tptp.real) (B_26 tptp.real) (A_34 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_26) A_34)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_16) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_34) C_16)) (tptp.hAPP_real_real (tptp.times_times_real B_26) C_16)))))) (forall ((C_16 tptp.int) (B_26 tptp.int) (A_34 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_26) A_34)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_16) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_34) C_16)) (tptp.hAPP_int_int (tptp.times_times_int B_26) C_16)))))) (forall ((C_15 tptp.real) (A_33 tptp.real) (B_25 tptp.real)) (let ((_let_1 (tptp.times_times_real C_15))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_33) B_25)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_15)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_33)) (tptp.hAPP_real_real _let_1 B_25))))))) (forall ((C_15 tptp.nat) (A_33 tptp.nat) (B_25 tptp.nat)) (let ((_let_1 (tptp.times_times_nat C_15))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_33) B_25)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_15)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A_33)) (tptp.hAPP_nat_nat _let_1 B_25))))))) (forall ((C_15 tptp.int) (A_33 tptp.int) (B_25 tptp.int)) (let ((_let_1 (tptp.times_times_int C_15))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_33) B_25)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_15)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_33)) (tptp.hAPP_int_int _let_1 B_25))))))) (forall ((C_14 tptp.real) (A_32 tptp.real) (B_24 tptp.real)) (let ((_let_1 (tptp.times_times_real C_14))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_32) B_24)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_14)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_32)) (tptp.hAPP_real_real _let_1 B_24))))))) (forall ((C_14 tptp.nat) (A_32 tptp.nat) (B_24 tptp.nat)) (let ((_let_1 (tptp.times_times_nat C_14))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_32) B_24)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_14)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A_32)) (tptp.hAPP_nat_nat _let_1 B_24))))))) (forall ((C_14 tptp.int) (A_32 tptp.int) (B_24 tptp.int)) (let ((_let_1 (tptp.times_times_int C_14))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_32) B_24)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_14)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_32)) (tptp.hAPP_int_int _let_1 B_24))))))) (forall ((C_13 tptp.real) (A_31 tptp.real) (B_23 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_31) B_23)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_13)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_31) C_13)) (tptp.hAPP_real_real (tptp.times_times_real B_23) C_13)))))) (forall ((C_13 tptp.nat) (A_31 tptp.nat) (B_23 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_31) B_23)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_13)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_31) C_13)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_23) C_13)))))) (forall ((C_13 tptp.int) (A_31 tptp.int) (B_23 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_31) B_23)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_13)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_31) C_13)) (tptp.hAPP_int_int (tptp.times_times_int B_23) C_13)))))) (forall ((B_22 tptp.real) (A_30 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_30) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_22) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.times_times_real A_30) B_22)))))) (forall ((B_22 tptp.int) (A_30 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_30) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_22) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.times_times_int A_30) B_22)))))) (forall ((B_21 tptp.real) (A_29 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_29) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) B_21)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_29) B_21)) tptp.zero_zero_real))))) (forall ((B_21 tptp.nat) (A_29 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_29) tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) B_21)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_29) B_21)) tptp.zero_zero_nat))))) (forall ((B_21 tptp.int) (A_29 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_29) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_21)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_29) B_21)) tptp.zero_zero_int))))) (forall ((A_2 tptp.real) (B_2 tptp.real) (C_1 tptp.real)) (let ((_let_1 (tptp.times_times_real C_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_1) tptp.zero_zero_real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_2)) (tptp.hAPP_real_real _let_1 B_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_2) A_2)))))) (forall ((A_2 tptp.int) (B_2 tptp.int) (C_1 tptp.int)) (let ((_let_1 (tptp.times_times_int C_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_1) tptp.zero_zero_int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_2)) (tptp.hAPP_int_int _let_1 B_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) A_2)))))) (forall ((B_20 tptp.real) (A_28 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real B_20) A_28))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_28)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_20)))))) (forall ((B_20 tptp.nat) (A_28 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat B_20) A_28))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_28)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_20)))))) (forall ((B_20 tptp.int) (A_28 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int B_20) A_28))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_28)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_20)))))) (forall ((A_27 tptp.real) (B_19 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real A_27) B_19))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_27)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_19)))))) (forall ((A_27 tptp.nat) (B_19 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat A_27) B_19))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_27)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_19)))))) (forall ((A_27 tptp.int) (B_19 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int A_27) B_19))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_27)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_19)))))) (forall ((B_18 tptp.real) (A_26 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_26)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_18) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real B_18) A_26)) tptp.zero_zero_real))))) (forall ((B_18 tptp.nat) (A_26 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_26)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_18) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat B_18) A_26)) tptp.zero_zero_nat))))) (forall ((B_18 tptp.int) (A_26 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_26)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_18) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int B_18) A_26)) tptp.zero_zero_int))))) (forall ((B_17 tptp.real) (A_25 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_25)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_17) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_25) B_17)) tptp.zero_zero_real))))) (forall ((B_17 tptp.nat) (A_25 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_25)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_17) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_25) B_17)) tptp.zero_zero_nat))))) (forall ((B_17 tptp.int) (A_25 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_25)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_17) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_25) B_17)) tptp.zero_zero_int))))) (forall ((B_16 tptp.real) (A_24 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_24)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_16)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real A_24) B_16))))))) (forall ((B_16 tptp.nat) (A_24 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_24)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_16)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat A_24) B_16))))))) (forall ((B_16 tptp.int) (A_24 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_24)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_16)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int A_24) B_16))))))) (forall ((A_2 tptp.real) (B_2 tptp.real) (C_1 tptp.real)) (let ((_let_1 (tptp.times_times_real C_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_2)) (tptp.hAPP_real_real _let_1 B_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_2) B_2)))))) (forall ((A_2 tptp.int) (B_2 tptp.int) (C_1 tptp.int)) (let ((_let_1 (tptp.times_times_int C_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_1)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_2)) (tptp.hAPP_int_int _let_1 B_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) B_2)))))) (forall ((C_1 tptp.real) (A_2 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.times_times_real C_1))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_2)) (tptp.hAPP_real_real _let_1 B_2))) (or (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_2) B_2))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_1) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_2) A_2))))))) (forall ((C_1 tptp.int) (A_2 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.times_times_int C_1))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_2)) (tptp.hAPP_int_int _let_1 B_2))) (or (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) B_2))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_1) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) A_2))))))) (forall ((A_2 tptp.real) (C_1 tptp.real) (B_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_2) C_1)) (tptp.hAPP_real_real (tptp.times_times_real B_2) C_1))) (or (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_2) B_2))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_1) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_2) A_2)))))) (forall ((A_2 tptp.int) (C_1 tptp.int) (B_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_2) C_1)) (tptp.hAPP_int_int (tptp.times_times_int B_2) C_1))) (or (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) B_2))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_1) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) A_2)))))) (forall ((A_23 tptp.real)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_23) A_23)) tptp.zero_zero_real)))) (forall ((A_23 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_23) A_23)) tptp.zero_zero_int)))) (forall ((B_15 tptp.real) (C_12 tptp.real) (A_22 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_15))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_22)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_12)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real A_22) C_12))))))) (forall ((B_15 tptp.nat) (C_12 tptp.nat) (A_22 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_15))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_22)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_12)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_22) C_12))))))) (forall ((B_15 tptp.int) (C_12 tptp.int) (A_22 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_15))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_22)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_12)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int A_22) C_12))))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat)) _let_27 (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real))) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_26 tptp.zero_zero_int))) (tptp.hBOOL (tptp.hAPP_real_bool _let_24 tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_22 tptp.one_one_nat)) _let_25 (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real))) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int))) (forall ((N_10 tptp.nat) (A_21 tptp.real) (B_14 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_21) B_14)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_21)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real (tptp.power_power_real A_21) N_10)) (tptp.hAPP_nat_real (tptp.power_power_real B_14) N_10)))))) (forall ((N_10 tptp.nat) (A_21 tptp.nat) (B_14 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_21) B_14)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_21)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.power_power_nat A_21) N_10)) (tptp.hAPP_nat_nat (tptp.power_power_nat B_14) N_10)))))) (forall ((N_10 tptp.nat) (A_21 tptp.int) (B_14 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_21) B_14)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_21)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int (tptp.power_power_int A_21) N_10)) (tptp.hAPP_nat_int (tptp.power_power_int B_14) N_10)))))) (forall ((N_9 tptp.nat) (A_20 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_20)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_20) N_9)))))) (forall ((N_9 tptp.nat) (A_20 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_20)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_20) N_9)))))) (forall ((N_9 tptp.nat) (A_20 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_20)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_20) N_9)))))) (forall ((N_8 tptp.real) (M_4 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 M_4)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 N_8)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real M_4) N_8))))))) (forall ((N_8 tptp.nat) (M_4 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_4)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_8)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat M_4) N_8))))))) (forall ((N_8 tptp.int) (M_4 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M_4)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_8)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int M_4) N_8))))))) (forall ((N_7 tptp.nat) (A_19 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_19)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_19) N_7)))))) (forall ((N_7 tptp.nat) (A_19 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_19)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_19) N_7)))))) (forall ((N_7 tptp.nat) (A_19 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_19)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_19) N_7)))))) (forall ((A_18 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_18) (tptp.hAPP_real_real (tptp.plus_plus_real A_18) tptp.one_one_real)))) (forall ((A_18 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_18) (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_18) tptp.one_one_nat)))) (forall ((A_18 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_18) (tptp.hAPP_int_int (tptp.plus_plus_int A_18) tptp.one_one_int)))) (forall ((C_1 tptp.int) (A_2 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.times_times_int C_1))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int _let_1 A_2)) (tptp.hAPP_int_int _let_1 B_2))) (or (= C_1 tptp.zero_zero_int) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_2) B_2)))))) (forall ((C_1 tptp.real) (A_2 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.times_times_real C_1))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_real_real _let_1 A_2)) (tptp.hAPP_real_real _let_1 B_2))) (or (= C_1 tptp.zero_zero_real) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_2) B_2)))))) (forall ((A_2 tptp.int) (C_1 tptp.int) (B_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.times_times_int A_2) C_1)) (tptp.hAPP_int_int (tptp.times_times_int B_2) C_1))) (or (= C_1 tptp.zero_zero_int) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_2) B_2))))) (forall ((A_2 tptp.real) (C_1 tptp.real) (B_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_real_real (tptp.times_times_real A_2) C_1)) (tptp.hAPP_real_real (tptp.times_times_real B_2) C_1))) (or (= C_1 tptp.zero_zero_real) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_2) B_2))))) (forall ((A_17 tptp.real) (N_6 tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_17))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_6) N_5)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) A_17)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real _let_1 N_6)) (tptp.hAPP_nat_real _let_1 N_5))))))) (forall ((A_17 tptp.nat) (N_6 tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_17))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_6) N_5)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.one_one_nat) A_17)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 N_6)) (tptp.hAPP_nat_nat _let_1 N_5))))))) (forall ((A_17 tptp.int) (N_6 tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_17))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_6) N_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) A_17)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int _let_1 N_6)) (tptp.hAPP_nat_int _let_1 N_5))))))) (forall ((N_4 tptp.nat) (A_16 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_16)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_16) N_4)))))) (forall ((N_4 tptp.nat) (A_16 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_16)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_16) N_4)))))) (forall ((N_4 tptp.nat) (A_16 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_16)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_16) N_4)))))) (forall ((Ma tptp.nat) (N tptp.nat) (A_2 tptp.real)) (let ((_let_1 (tptp.power_power_real A_2))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A_2)) (= (= (tptp.hAPP_nat_real _let_1 Ma) (tptp.hAPP_nat_real _let_1 N)) (= Ma N))))) (forall ((Ma tptp.nat) (N tptp.nat) (A_2 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A_2)) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 N)) (= Ma N))))) (forall ((Ma tptp.nat) (N tptp.nat) (A_2 tptp.int)) (let ((_let_1 (tptp.power_power_int A_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_2)) (= (= (tptp.hAPP_nat_int _let_1 Ma) (tptp.hAPP_nat_int _let_1 N)) (= Ma N))))) (forall ((A_2 tptp.real) (N tptp.nat)) (= (= (tptp.hAPP_nat_real (tptp.power_power_real A_2) N) tptp.zero_zero_real) (and (= A_2 tptp.zero_zero_real) (not (= N tptp.zero_zero_nat))))) (forall ((A_2 tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_2) N) tptp.zero_zero_nat) (and (= A_2 tptp.zero_zero_nat) (not (= N tptp.zero_zero_nat))))) (forall ((A_2 tptp.int) (N tptp.nat)) (= (= (tptp.hAPP_nat_int (tptp.power_power_int A_2) N) tptp.zero_zero_int) (and (= A_2 tptp.zero_zero_int) (not (= N tptp.zero_zero_nat))))) (forall ((A_15 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real A_15) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A_15 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_15) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A_15 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int A_15) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((A_14 tptp.real) (M_3 tptp.nat) (N_3 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_14))) (= (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_3) N_3)) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_nat_real _let_1 M_3)) (tptp.hAPP_nat_real _let_1 N_3))))) (forall ((A_14 tptp.nat) (M_3 tptp.nat) (N_3 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_14))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_3) N_3)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 M_3)) (tptp.hAPP_nat_nat _let_1 N_3))))) (forall ((A_14 tptp.int) (M_3 tptp.nat) (N_3 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_14))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_3) N_3)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_nat_int _let_1 M_3)) (tptp.hAPP_nat_int _let_1 N_3))))) (forall ((B tptp.int) (M tptp.int) (A tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) A)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M))))))))) (forall ((M tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) M)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) M)))))) (forall ((M tptp.int) (Y tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 Y) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y) M)) (= X_1 Y))))))))) (forall ((N_1 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int N_1) M)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int M) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int N_1) M))))) (forall ((A_2 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 B_2) Ma)) (exists ((K_2 tptp.int)) (= B_2 (tptp.hAPP_int_int (tptp.plus_plus_int A_2) (tptp.hAPP_int_int (tptp.times_times_int Ma) K_2)))))) (forall ((X tptp.int) (P_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X tptp.zero_zero_int) P_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_2) X)))) (forall ((A_2 tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 tptp.zero_zero_int) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Ma) A_2)))) (forall ((M tptp.int) (N_1 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int M) N_1))) (or (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1))))))) (forall ((C_11 tptp.real) (A_13 tptp.real) (B_13 tptp.real)) (let ((_let_1 (tptp.times_times_real C_11))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_13)) (tptp.hAPP_real_real _let_1 B_13))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_11)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_13) B_13)))))) (forall ((C_11 tptp.nat) (A_13 tptp.nat) (B_13 tptp.nat)) (let ((_let_1 (tptp.times_times_nat C_11))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_13)) (tptp.hAPP_nat_nat _let_1 B_13))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_11)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_13) B_13)))))) (forall ((C_11 tptp.int) (A_13 tptp.int) (B_13 tptp.int)) (let ((_let_1 (tptp.times_times_int C_11))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_13)) (tptp.hAPP_int_int _let_1 B_13))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_11)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_13) B_13)))))) (forall ((A_12 tptp.real) (C_10 tptp.real) (B_12 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real A_12) C_10)) (tptp.hAPP_real_real (tptp.times_times_real B_12) C_10))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_10)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_12) B_12))))) (forall ((A_12 tptp.nat) (C_10 tptp.nat) (B_12 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_12) C_10)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_12) C_10))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_10)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_12) B_12))))) (forall ((A_12 tptp.int) (C_10 tptp.int) (B_12 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int A_12) C_10)) (tptp.hAPP_int_int (tptp.times_times_int B_12) C_10))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_10)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_12) B_12))))) (forall ((C_9 tptp.real) (A_11 tptp.real) (B_11 tptp.real)) (let ((_let_1 (tptp.times_times_real C_9))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_11)) (tptp.hAPP_real_real _let_1 B_11))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_9)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_11) B_11)))))) (forall ((C_9 tptp.nat) (A_11 tptp.nat) (B_11 tptp.nat)) (let ((_let_1 (tptp.times_times_nat C_9))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A_11)) (tptp.hAPP_nat_nat _let_1 B_11))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_9)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_11) B_11)))))) (forall ((C_9 tptp.int) (A_11 tptp.int) (B_11 tptp.int)) (let ((_let_1 (tptp.times_times_int C_9))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_11)) (tptp.hAPP_int_int _let_1 B_11))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_9)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_11) B_11)))))) (forall ((C_8 tptp.real) (A_10 tptp.real) (B_10 tptp.real)) (let ((_let_1 (tptp.times_times_real C_8))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_10)) (tptp.hAPP_real_real _let_1 B_10))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_8)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_10) B_10)))))) (forall ((C_8 tptp.nat) (A_10 tptp.nat) (B_10 tptp.nat)) (let ((_let_1 (tptp.times_times_nat C_8))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A_10)) (tptp.hAPP_nat_nat _let_1 B_10))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_8)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_10) B_10)))))) (forall ((C_8 tptp.int) (A_10 tptp.int) (B_10 tptp.int)) (let ((_let_1 (tptp.times_times_int C_8))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_10)) (tptp.hAPP_int_int _let_1 B_10))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_8)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_10) B_10)))))) (forall ((A_9 tptp.real) (C_7 tptp.real) (B_9 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_9) C_7)) (tptp.hAPP_real_real (tptp.times_times_real B_9) C_7))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_7)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_9) B_9))))) (forall ((A_9 tptp.nat) (C_7 tptp.nat) (B_9 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_9) C_7)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_9) C_7))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_7)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_9) B_9))))) (forall ((A_9 tptp.int) (C_7 tptp.int) (B_9 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_9) C_7)) (tptp.hAPP_int_int (tptp.times_times_int B_9) C_7))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_7)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_9) B_9))))) (forall ((A_8 tptp.real) (C_6 tptp.real) (B_8 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_8) C_6)) (tptp.hAPP_real_real (tptp.times_times_real B_8) C_6))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_6)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_8) B_8))))) (forall ((A_8 tptp.nat) (C_6 tptp.nat) (B_8 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_8) C_6)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_8) C_6))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_6)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_8) B_8))))) (forall ((A_8 tptp.int) (C_6 tptp.int) (B_8 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_8) C_6)) (tptp.hAPP_int_int (tptp.times_times_int B_8) C_6))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_6)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_8) B_8))))) (forall ((C_5 tptp.real) (D_7 tptp.real) (A_7 tptp.real) (B_7 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_7) B_7)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_5) D_7)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_7)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_5)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_7) C_5)) (tptp.hAPP_real_real (tptp.times_times_real B_7) D_7)))))))) (forall ((C_5 tptp.nat) (D_7 tptp.nat) (A_7 tptp.nat) (B_7 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_7) B_7)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_5) D_7)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_7)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_5)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_7) C_5)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_7) D_7)))))))) (forall ((C_5 tptp.int) (D_7 tptp.int) (A_7 tptp.int) (B_7 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_7) B_7)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_5) D_7)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_7)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_5)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_7) C_5)) (tptp.hAPP_int_int (tptp.times_times_int B_7) D_7)))))))) (forall ((C_4 tptp.real) (D_6 tptp.real) (A_6 tptp.real) (B_6 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_6) B_6)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_4) D_6)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_6)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_4)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_6) C_4)) (tptp.hAPP_real_real (tptp.times_times_real B_6) D_6)))))))) (forall ((C_4 tptp.nat) (D_6 tptp.nat) (A_6 tptp.nat) (B_6 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_6) B_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_4) D_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_4)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_6) C_4)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_6) D_6)))))))) (forall ((C_4 tptp.int) (D_6 tptp.int) (A_6 tptp.int) (B_6 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_6) B_6)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_4) D_6)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_6)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_4)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_6) C_4)) (tptp.hAPP_int_int (tptp.times_times_int B_6) D_6)))))))) (forall ((C_3 tptp.real) (D_5 tptp.real) (A_5 tptp.real) (B_5 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_5) B_5)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_3) D_5)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_5)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_5) C_3)) (tptp.hAPP_real_real (tptp.times_times_real B_5) D_5))))))))) (forall ((C_3 tptp.nat) (D_5 tptp.nat) (A_5 tptp.nat) (B_5 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_5) B_5)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_3) D_5)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_5)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_5) C_3)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_5) D_5))))))))) (forall ((C_3 tptp.int) (D_5 tptp.int) (A_5 tptp.int) (B_5 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_5) B_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_3) D_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_5) C_3)) (tptp.hAPP_int_int (tptp.times_times_int B_5) D_5))))))))) (forall ((C_2 tptp.real) (D_4 tptp.real) (A_4 tptp.real) (B_4 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_4) B_4)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_2) D_4)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) B_4)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_4) C_2)) (tptp.hAPP_real_real (tptp.times_times_real B_4) D_4)))))))) (forall ((C_2 tptp.nat) (D_4 tptp.nat) (A_4 tptp.nat) (B_4 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_4) B_4)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_2) D_4)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) B_4)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_4) C_2)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_4) D_4)))))))) (forall ((C_2 tptp.int) (D_4 tptp.int) (A_4 tptp.int) (B_4 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_4) B_4)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_2) D_4)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_4)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_4) C_2)) (tptp.hAPP_int_int (tptp.times_times_int B_4) D_4)))))))) (forall ((A_2 tptp.real) (B_2 tptp.real) (C_1 tptp.real)) (let ((_let_1 (tptp.times_times_real C_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_1) tptp.zero_zero_real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_2)) (tptp.hAPP_real_real _let_1 B_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_2) A_2)))))) (forall ((A_2 tptp.int) (B_2 tptp.int) (C_1 tptp.int)) (let ((_let_1 (tptp.times_times_int C_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_1) tptp.zero_zero_int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_2)) (tptp.hAPP_int_int _let_1 B_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) A_2)))))) (forall ((A_2 tptp.real) (B_2 tptp.real) (C_1 tptp.real)) (let ((_let_1 (tptp.times_times_real C_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_2)) (tptp.hAPP_real_real _let_1 B_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_2) B_2)))))) (forall ((A_2 tptp.int) (B_2 tptp.int) (C_1 tptp.int)) (let ((_let_1 (tptp.times_times_int C_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_1)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_2)) (tptp.hAPP_int_int _let_1 B_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_2) B_2)))))) (forall ((Y_4 tptp.real) (X_4 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_4)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_4)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_4) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real Y_4) X_4)) X_4))))))) (forall ((Y_4 tptp.int) (X_4 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_4)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_4)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_4) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int Y_4) X_4)) X_4))))))) (forall ((Y_3 tptp.real) (X_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_3)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_3)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_3) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real X_3) Y_3)) X_3))))))) (forall ((Y_3 tptp.int) (X_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_3) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int X_3) Y_3)) X_3))))))) (tptp.hBOOL (tptp.hAPP_real_bool _let_24 _let_23)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_22 _let_21)) (tptp.hBOOL (tptp.hAPP_int_bool _let_20 _let_19)) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real (tptp.bit0 _let_1))) (tptp.hAPP_nat_real (tptp.power_power_real X_1) _let_2)) (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real _let_1)) X_1)) _let_2))))) (forall ((M tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) M)) (= X_1 tptp.zero_zero_int))))) (forall ((M tptp.int) (A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A tptp.zero_zero_int) M)) (= A tptp.zero_zero_int))))) (forall ((B tptp.int) (M tptp.int) (A tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (= A B)))))))) (forall ((P_3 tptp.int) (Y tptp.int) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int Y) N_1))))))) (forall ((Z tptp.nat) (X_1 tptp.int) (Y tptp.nat) (P_3 tptp.int)) (let ((_let_1 (tptp.power_power_int X_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_nat_int _let_1 Y) tptp.one_one_int) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat Y) Z)) tptp.one_one_int) P_3))))) (forall ((Y tptp.int) (X_1 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong Y tptp.zero_zero_int) P_3))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int X_1) Y) tptp.zero_zero_int) P_3))))))) (forall ((B tptp.int) (A tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A) B) tptp.zero_zero_int) P_3)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A tptp.zero_zero_int) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong B tptp.zero_zero_int) P_3))))))) (forall ((B tptp.int) (A tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (and (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A tptp.zero_zero_int) P_3))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong B tptp.zero_zero_int) P_3)))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A) B) tptp.zero_zero_int) P_3))))))) (forall ((N_1 tptp.int) (P_3 tptp.int) (M tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int M) N_1))) (or (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1)))))))) _let_16 (tptp.hBOOL (tptp.hAPP_int_bool _let_18 _let_17)) (forall ((J_1 tptp.nat) (K_1 tptp.nat) (M tptp.int)) (let ((_let_1 (tptp.power_power_int (tptp.number_number_of_int tptp.min)))) (let ((_let_2 (tptp.hAPP_nat_int _let_1 K_1))) (let ((_let_3 (tptp.hAPP_nat_int _let_1 J_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong _let_3 _let_2) M)) (= _let_3 _let_2))))))) (forall ((M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) M)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong tptp.one_one_int (tptp.number_number_of_int tptp.min)) M))))) (= _let_17 _let_5) (=> (not _let_16) (not _let_15)) (forall ((X tptp.real)) (= (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.times_times_real X) X)))) (= X tptp.zero_zero_real))) (forall ((K_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.minus_minus_int K_1) tptp.pls) K_1)) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.bit0 K_1)) (tptp.bit0 L)) (tptp.bit0 (tptp.hAPP_int_int (tptp.minus_minus_int K_1) L)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.minus_minus_int Z1) Z2)) W) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int (tptp.times_times_int Z1) W)) (tptp.hAPP_int_int (tptp.times_times_int Z2) W)))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (tptp.times_times_int W))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.minus_minus_int Z1) Z2)) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int _let_1 Z1)) (tptp.hAPP_int_int _let_1 Z2))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.minus_minus_int A) B) C) (= A (tptp.hAPP_int_int (tptp.plus_plus_int C) B)))) (forall ((C tptp.int) (D_3 tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C D_3) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.minus_minus_int A) C) (tptp.hAPP_int_int (tptp.minus_minus_int B) D_3)) M))))) (forall ((K_1 tptp.int) (M tptp.int) (N_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.minus_minus_int M) N_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)))))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.bit1 K_1)) (tptp.bit0 L)) (tptp.bit1 (tptp.hAPP_int_int (tptp.minus_minus_int K_1) L)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.bit1 K_1)) (tptp.bit1 L)) (tptp.bit0 (tptp.hAPP_int_int (tptp.minus_minus_int K_1) L)))) (forall ((L tptp.int)) (let ((_let_1 (tptp.minus_minus_int tptp.pls))) (= (tptp.hAPP_int_int _let_1 (tptp.bit0 L)) (tptp.bit0 (tptp.hAPP_int_int _let_1 L))))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) L_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.minus_minus_int K) L_1)) tptp.zero_zero_int)))) (forall ((A tptp.int) (R_1 tptp.int) (B tptp.int) (M tptp.int) (C tptp.int) (D_3 tptp.int) (N_1 tptp.int)) (let ((_let_1 (tptp.times_times_int R_1))) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.minus_minus_int A) (tptp.hAPP_int_int _let_1 B))) M)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.minus_minus_int C) (tptp.hAPP_int_int _let_1 D_3))) N_1)) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int A) M)) (tptp.hAPP_int_int (tptp.times_times_int C) N_1))) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B) M)) (tptp.hAPP_int_int (tptp.times_times_int D_3) N_1))))))) (forall ((A_2 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 B_2) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Ma) (tptp.hAPP_int_int (tptp.minus_minus_int A_2) B_2))))) (forall ((A tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.minus_minus_int A) tptp.one_one_int))) (let ((_let_2 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_2 A)) (=> (not (= X_1 _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_2 _let_1)))))))) (forall ((W_1 tptp.int) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W_1) (tptp.hAPP_int_int (tptp.minus_minus_int Z_1) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) Z_1)))) (forall ((L tptp.int)) (= (tptp.hAPP_int_int (tptp.minus_minus_int tptp.pls) (tptp.bit1 L)) (tptp.bit1 (tptp.hAPP_int_int (tptp.minus_minus_int tptp.min) L)))) (forall ((L tptp.int)) (let ((_let_1 (tptp.minus_minus_int tptp.min))) (= (tptp.hAPP_int_int _let_1 (tptp.bit0 L)) (tptp.bit1 (tptp.hAPP_int_int _let_1 L))))) (forall ((L tptp.int)) (let ((_let_1 (tptp.minus_minus_int tptp.min))) (= (tptp.hAPP_int_int _let_1 (tptp.bit1 L)) (tptp.bit0 (tptp.hAPP_int_int _let_1 L))))) (forall ((A_2 tptp.int) (P_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.minus_minus_int P_2) tptp.one_one_int))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A_2) _let_1) tptp.one_one_int) P_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 _let_1) P_2))))) (forall ((I_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.power_power_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) I_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)))))) (forall ((A tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A) A) tptp.one_one_int) P_3)) (or (= A tptp.one_one_int) (= A (tptp.hAPP_int_int (tptp.minus_minus_int P_3) tptp.one_one_int)))))))) (forall ((A tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A) A) tptp.one_one_int) P_3)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A tptp.one_one_int) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A (tptp.hAPP_int_int (tptp.minus_minus_int P_3) tptp.one_one_int)) P_3))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int A) B)) (tptp.hAPP_int_int (tptp.minus_minus_int A) B)) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_nat_int (tptp.power_power_int A) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int B) _let_1))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_int_int (tptp.minus_minus_int A) B)) _let_2) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_nat_int (tptp.power_power_int A) _let_2)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int _let_1)) A)) B))) (tptp.hAPP_nat_int (tptp.power_power_int B) _let_2)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit1 _let_1))) (let ((_let_3 (tptp.number_number_of_nat _let_2))) (let ((_let_4 (tptp.power_power_int B))) (let ((_let_5 (tptp.number_number_of_nat (tptp.bit0 _let_1)))) (let ((_let_6 (tptp.times_times_int (tptp.number_number_of_int _let_2)))) (let ((_let_7 (tptp.power_power_int A))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_int_int (tptp.minus_minus_int A) B)) _let_3) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_nat_int _let_7 _let_3)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_6 (tptp.hAPP_nat_int _let_7 _let_5))) B))) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_6 A)) (tptp.hAPP_nat_int _let_4 _let_5)))) (tptp.hAPP_nat_int _let_4 _let_3))))))))))) (forall ((N_1 tptp.nat)) (let ((_let_1 (tptp.number_number_of_int tptp.min))) (let ((_let_2 (tptp.hAPP_nat_int (tptp.power_power_int _let_1) N_1))) (or (= _let_2 tptp.one_one_int) (= _let_2 _let_1))))) (forall ((M tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls))))) M)) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime _let_1)) (= (tptp.legendre (tptp.number_number_of_int tptp.min) _let_1) tptp.one_one_int)))) (forall ((A tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.legendre A P_3))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.quadRes P_3) A)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A tptp.zero_zero_int) P_3)))) (and (=> _let_3 (= _let_1 tptp.zero_zero_int)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.number_number_of_int tptp.min)))))))))) (forall ((Ma tptp.int) (X tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.quadRes Ma) X)) (exists ((Y_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.power_power_int Y_2) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) X) Ma))))) (forall ((X_1 tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_real_real (tptp.plus_plus_real X_1) Y)) _let_2) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X_1) _let_2)) (tptp.hAPP_nat_real (tptp.power_power_real Y) _let_2))) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real _let_1)) X_1)) Y)))))) (forall ((N_1 tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N_1) M)) (or (= M tptp.zero_zero_nat) (= M N_1) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_1)) M))))) (forall ((X tptp.nat) (Y_1 tptp.nat)) (= (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) X))) (= X Y_1))) (forall ((B tptp.nat) (D_3 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat D_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat A) B))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B)))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A) C)) (tptp.hAPP_nat_nat (tptp.times_times_nat B) C))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.times_times_nat C))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 A)) (tptp.hAPP_nat_nat _let_1 B)))))) (forall ((N_1 tptp.nat) (X_1 tptp.nat) (Y tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_1) N_1)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y) N_1))))) (forall ((N_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat M) N_1))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) tptp.one_one_nat)) N_1)))))))) (forall ((P_3 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_power_nat P_3))) (let ((_let_2 (tptp.hAPP_nat_nat _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat (tptp.times_times_nat P_3) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((X_1 tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_1) _let_1)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y) _let_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat X_1) Y)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat X_1) Y))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B)) (or (= B tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A) B))))) (forall ((Ma tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) K)) (tptp.hAPP_nat_nat (tptp.times_times_nat N) K))) (or (= K tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) N))))) (forall ((N tptp.nat) (Ma tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.times_times_nat N) Ma) tptp.one_one_nat) (and (= N tptp.one_one_nat) (= Ma tptp.one_one_nat)))) (forall ((Ma tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.power_power_nat Ma) N) tptp.zero_zero_nat) (and (not (= N tptp.zero_zero_nat)) (= Ma tptp.zero_zero_nat)))) (forall ((X_1 tptp.nat) (Y tptp.nat) (N_1 tptp.nat)) (=> (not (= N_1 tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_1) N_1)) Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y))))) (forall ((A tptp.nat) (N_1 tptp.nat) (B tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.power_power_nat A) N_1)) (tptp.hAPP_nat_nat (tptp.power_power_nat B) N_1))) (=> (not (= N_1 tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B))))) (forall ((X tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.power_power_nat X) N) tptp.one_one_nat) (or (= X tptp.one_one_nat) (= N tptp.zero_zero_nat)))) (forall ((X_1 tptp.nat) (Q_1 tptp.nat) (N_1 tptp.nat) (R_1 tptp.nat)) (=> (= X_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat Q_1) N_1)) R_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) R_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat R_1) N_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N_1) X_1))))))) (forall ((X tptp.real) (Y_1 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_1) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y_1 tptp.zero_zero_real))))) (forall ((A tptp.real) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (exists ((X_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_2)) (= (tptp.hAPP_nat_real (tptp.power_power_real X_2) N_1) A) (forall ((Y_2 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Y_2)) (= (tptp.hAPP_nat_real (tptp.power_power_real Y_2) N_1) A)) (= Y_2 X_2)))))))) (forall ((A tptp.real) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (exists ((R_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) R_2)) (= (tptp.hAPP_nat_real (tptp.power_power_real R_2) N_1) A)))))) (forall ((N tptp.nat) (Ma tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Ma)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.times_times_nat N) Ma)) Ma)) (= N tptp.one_one_nat)))) (forall ((X_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) X_1))) (forall ((N_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) tptp.zero_zero_nat)))) (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N_1))) (forall ((I_1 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.minus_minus_nat I_1))) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J_1)) K_1) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 K_1)) J_1)))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat tptp.zero_zero_nat) N_1) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) tptp.zero_zero_nat) M)) (forall ((M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) M) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1) tptp.zero_zero_nat) (=> (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat N_1) M) tptp.zero_zero_nat) (= M N_1)))) _let_13 (forall ((X tptp.real) (Y_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) Y_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.minus_minus_real X) Y_1)) tptp.zero_zero_real)))) (forall ((X tptp.real) (Y_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) Y_1)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) Y_1)) (not (= X Y_1))))) (forall ((X tptp.real) (Y_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) Y_1)) (or (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) Y_1)) (= X Y_1)))) (forall ((N_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) N_1)))) (forall ((Ma tptp.nat) (N tptp.nat)) (= (not (= Ma N)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) Ma))))) (forall ((X_1 tptp.nat) (Y tptp.nat)) (=> (not (= X_1 Y)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y) X_1))))) (forall ((N_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) N_1)))) (forall ((N_1 tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) M)) (not (= M N_1)))) (forall ((S tptp.nat) (T tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat S) T)) (not (= S T)))) (forall ((P_1 tptp.fun_nat_fun_nat_bool) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool P_1 N) Ma)))) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N)) _let_1) (=> (=> (= Ma N) _let_1) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) Ma)) _let_1) _let_1))))) (forall ((N_1 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J_1) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) N_1)) K_1)))) (forall ((L tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.minus_minus_nat L))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 L)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 N_1)) (tptp.hAPP_nat_nat _let_1 M)))))))) (forall ((X_1 tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X_1)))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((Z tptp.nat) (X_1 tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Z))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1))) (let ((_let_3 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Y)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_3 X_1)))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_3 Z)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Z)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_1)))))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B) A)))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((Z tptp.nat) (X_1 tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 X_1)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Z)) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Z) X_1))))))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B) A)))) (=> (= B C) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat C) A)))))))) (forall ((P_1 tptp.bool) (X tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) X)))) (=> (and _let_1 (not _let_2)) (=> (and _let_2 (not _let_1)) (tptp.hBOOL P_1)))))) (forall ((X_1 tptp.nat) (Y tptp.nat)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X_1)))) (not (= Y X_1)))) (forall ((X_1 tptp.nat) (Y tptp.nat)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X_1)))) (not (= X_1 Y)))) (forall ((X_1 tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X_1)))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((X_1 tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y)))) (=> (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X_1)))) _let_1))) (forall ((X_1 tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X_1)))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((X_1 tptp.nat) (Y tptp.nat)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X_1)))) (not (= X_1 Y)))) (forall ((Z tptp.nat) (X_1 tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Z))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Y)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) Z)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Z)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_1))))))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat C))) (=> (= A B) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B) C)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B)))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) C)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A)))))))) (forall ((N_1 tptp.nat) (K_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1))))))) (forall ((Z tptp.nat) (X_1 tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) Z)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z)))))) (forall ((X_1 tptp.nat) (Y tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X_1)) (= X_1 Y)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M) N_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N_1) M)) (= M N_1)))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B)) (=> (= B C) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C)))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (= A B) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B) C)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) C))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B)))) (=> _let_1 (=> (not (= A B)) (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B) A)))))))) (forall ((X_1 tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y)))) (=> _let_1 (or (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X_1)))) (= X_1 Y))))) (forall ((Y_1 tptp.nat) (X tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) X)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y_1)) (= X Y_1)))) (forall ((X_1 tptp.nat) (Y tptp.nat)) (=> (= X_1 Y) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B)))) (=> (not (= A B)) (=> _let_1 (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B) A)))))))) (forall ((X tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) X)))))) (= _let_1 _let_1))) (forall ((X tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y_1)))) (= (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) X)))) (and _let_1 (not (= X Y_1)))))) (forall ((X tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y_1)))) (= _let_1 (or (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) X)))) (= X Y_1))))) (forall ((X tptp.nat) (Y_1 tptp.nat)) (= (= X Y_1) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) X))))) (forall ((X_1 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) X_1)))) (not (and _let_1 (not _let_1))))) (forall ((M tptp.nat) (N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) N_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) M))) (forall ((X_1 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat X_1))) (let ((_let_2 (tptp.plus_plus_nat Y))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Z)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Z)))))) (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat M))) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 N_1)) K_1) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) K_1))))) (forall ((K tptp.nat) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat K))) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 N)) (= Ma N)))) (forall ((Ma tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat Ma) K) (tptp.hAPP_nat_nat (tptp.plus_plus_nat N) K)) (= Ma N))) (forall ((M tptp.nat) (N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) N_1)) N_1) M)) (forall ((N_1 tptp.nat) (M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) M)) N_1) M)) (forall ((I_1 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.minus_minus_nat I_1))) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J_1)) K_1) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) K_1))))) (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat K_1))) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)))) (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) K_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) K_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1))) (forall ((Z1 tptp.real) (Z2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (tptp.times_times_real Z1))) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real _let_1 Z2)) Z3) (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.times_times_real Z2) Z3))))) (forall ((Z tptp.real) (W tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real Z) W) (tptp.hAPP_real_real (tptp.times_times_real W) Z))) (forall ((Z tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real tptp.one_one_real) Z) Z)) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M)) (= M N_1)))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 K_1)))))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (= M N_1) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M)))) (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) N_1))) (forall ((N tptp.nat) (K tptp.nat) (Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat Ma) K)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat N) K))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N))))))) (forall ((N_1 tptp.nat) (K_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.minus_minus_nat M))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N_1)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 K_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat N_1) K_1)) (tptp.hAPP_nat_nat _let_1 N_1))))))) (forall ((N tptp.nat) (K tptp.nat) (Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (= (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat Ma) K) (tptp.hAPP_nat_nat (tptp.minus_minus_nat N) K)) (= Ma N)))))) (forall ((I_1 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.minus_minus_nat N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) N_1)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_1 I_1)) I_1)))) (forall ((L tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) L)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat N_1) L))))) (forall ((L tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.minus_minus_nat L))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 N_1)) (tptp.hAPP_nat_nat _let_1 M)))))) (forall ((M tptp.nat) (N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) M))) (forall ((M tptp.nat) (N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat M) N_1) (tptp.hAPP_nat_nat (tptp.times_times_nat N_1) M))) (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat M))) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 N_1)) K_1) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat N_1) K_1))))) (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat K_1))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N_1))))) (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) K_1) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat M) K_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat N_1) K_1)))) (forall ((Z tptp.real) (X_1 tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.plus_plus_real Z))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 X_1)) (tptp.hAPP_real_real _let_1 Y)))))) (forall ((N_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1)) (not (= N_1 tptp.zero_zero_nat)))) (forall ((N_1 tptp.nat)) (=> (not (= N_1 tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) M)))))) (forall ((N tptp.nat) (Ma tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat (tptp.minus_minus_nat N) Ma))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N)))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat tptp.zero_zero_nat) N_1) N_1)) (forall ((M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) tptp.zero_zero_nat) M)) (forall ((Ma tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat Ma) N) tptp.zero_zero_nat) (and (= Ma tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) N_1) M) (= N_1 tptp.zero_zero_nat))) (forall ((N_1 tptp.nat) (M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat N_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) M)) tptp.zero_zero_nat)) (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N_1))) (forall ((N tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))) (forall ((Ma tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat Ma) N) tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1) tptp.zero_zero_nat))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat tptp.zero_zero_nat) N_1) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((Ma tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) N) tptp.zero_zero_nat) (or (= Ma tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((K tptp.nat) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 N)) (or (= Ma N) (= K tptp.zero_zero_nat))))) (forall ((Ma tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) K) (tptp.hAPP_nat_nat (tptp.times_times_nat N) K)) (or (= Ma N) (= K tptp.zero_zero_nat)))) (forall ((A_2 tptp.real) (B_2 tptp.real) (C_1 tptp.real)) (let ((_let_1 (tptp.times_times_real C_1))) (=> (not (= C_1 tptp.zero_zero_real)) (= (= (tptp.hAPP_real_real _let_1 A_2) (tptp.hAPP_real_real _let_1 B_2)) (= A_2 B_2))))) (forall ((A_2 tptp.real) (B_2 tptp.real) (C_1 tptp.real)) (=> (not (= C_1 tptp.zero_zero_real)) (= (= (tptp.hAPP_real_real (tptp.times_times_real A_2) C_1) (tptp.hAPP_real_real (tptp.times_times_real B_2) C_1)) (= A_2 B_2)))) (forall ((I_1 tptp.nat) (J_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) J_1)) I_1)))) (forall ((J_1 tptp.nat) (I_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) I_1)) I_1)))) (forall ((K tptp.nat) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N))))) (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) M)))))) (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) J_1)))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) K_1))))) (forall ((K_1 tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_1) L)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) L)))))) (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat) (L tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_1) L)) (=> (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) L) (tptp.hAPP_nat_nat (tptp.plus_plus_nat K_1) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1))))) (forall ((I_1 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) J_1)) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) K_1)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1))) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) M))) (forall ((I_2 tptp.nat) (J_2 tptp.nat) (K tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) K))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_2) K)) J_2)))) (forall ((Ma tptp.nat) (N tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N)) (not (= Ma N))))) (forall ((Ma tptp.nat) (N tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N)) (= Ma N)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (=> (not (= M N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1))))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1)) (= M N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A) B)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C) A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat A) C)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat B) C)))))) (forall ((N tptp.nat) (K tptp.nat) (Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat Ma) K)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat N) K))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N))))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat N) K))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N))))) (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M))))))) (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1))))))) (forall ((N_1 tptp.nat) (M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) N_1)))) (forall ((N_1 tptp.nat) (M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) M)))) (forall ((Ma tptp.nat) (N tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N)) (exists ((K_2 tptp.nat)) (= N (tptp.hAPP_nat_nat (tptp.plus_plus_nat Ma) K_2))))) (forall ((K tptp.nat) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N))))) (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) M)))))) (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) J_1)))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) K_1))))) (forall ((K_1 tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) L)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) L)))))) (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) K_1)) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) N_1)))) (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) K_1)) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)))) (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) K_1)) N_1)) (not (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) N_1))))))) (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J_1)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat I_1) (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) K_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) K_1)) J_1)))) (forall ((J_2 tptp.nat) (K tptp.nat) (I_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) K)) I_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_2) (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_2) K))))) (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) M)) K_1))))) (forall ((N_1 tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) M))) (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J_1)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) K_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J_1)) K_1))))) (forall ((I_2 tptp.nat) (K tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) K))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_2) K)) J_2))))) (forall ((N_1 tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) N_1) M))) (forall ((K tptp.nat) (I_2 tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_2)) (= (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) I_2) K) (= J_2 (tptp.hAPP_nat_nat (tptp.plus_plus_nat K) I_2))))) (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J_1)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J_1)) K_1) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) K_1)))))) (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J_1)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) K_1)) I_1) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) I_1)) K_1)))) (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J_1)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) I_1)) K_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) K_1)) I_1)))) (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat K_1))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) N_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N_1))))) (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) N_1)) K_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat M) K_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat N_1) K_1)))) (forall ((Ma tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) tptp.one_one_nat)) (= Ma tptp.one_one_nat))) (forall ((M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.hAPP_nat_nat (tptp.times_times_nat M) M)))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.times_times_nat M))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_1 M)))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat J_1) K_1))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 I_1)) (tptp.hAPP_nat_nat _let_1 J_1)))))) (forall ((K_1 tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) L)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat J_1) L)))))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat tptp.one_one_nat) N_1) N_1)) (forall ((Ma tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) N)) (and (= Ma tptp.one_one_nat) (= N tptp.one_one_nat)))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat N_1) tptp.one_one_nat) N_1)) (forall ((Ma tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) N) tptp.one_one_nat) (and (= Ma tptp.one_one_nat) (= N tptp.one_one_nat)))) (forall ((Z1 tptp.real) (Z2 tptp.real) (W tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real Z1) Z2)) W) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real Z1) W)) (tptp.hAPP_real_real (tptp.times_times_real Z2) W)))) (forall ((N_1 tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N_1) M)))))) (forall ((Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat Ma) N))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)))))) (forall ((P_1 tptp.fun_nat_bool) (A_2 tptp.nat) (B_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat A_2) B_2))) (not (or (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_2) B_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat)))) (exists ((D_2 tptp.nat)) (and (= A_2 (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_2) D_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 D_2))))))))) (forall ((P_1 tptp.fun_nat_bool) (A_2 tptp.nat) (B_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat A_2) B_2))) (and (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_2) B_2)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat))) (forall ((D_2 tptp.nat)) (=> (= A_2 (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_2) D_2)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 D_2))))))) (forall ((Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) N))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)))))) (forall ((K tptp.nat) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N)))))) (forall ((Ma tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) K)) (tptp.hAPP_nat_nat (tptp.times_times_nat N) K))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat J_1) K_1)))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 I_1)) (tptp.hAPP_nat_nat _let_1 J_1))))))) (forall ((X tptp.real) (Y_1 tptp.real) (Z_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Z_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real X) Z_1)) (tptp.hAPP_real_real (tptp.times_times_real Y_1) Z_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) Y_1))))) (forall ((X tptp.real) (Y_1 tptp.real) (Z_1 tptp.real)) (let ((_let_1 (tptp.times_times_real Z_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Z_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 X)) (tptp.hAPP_real_real _let_1 Y_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) Y_1)))))) (forall ((X_1 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.times_times_real Z))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Z)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 X_1)) (tptp.hAPP_real_real _let_1 Y))))))) (forall ((Y tptp.real) (X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real X_1) Y))))))) (forall ((X tptp.real) (Y_1 tptp.real) (Z_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Z_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real X) Z_1)) (tptp.hAPP_real_real (tptp.times_times_real Y_1) Z_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) Y_1))))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (= M (tptp.hAPP_nat_nat (tptp.times_times_nat M) N_1)) (or (= N_1 tptp.one_one_nat) (= M tptp.zero_zero_nat)))) (forall ((X tptp.real) (Y_1 tptp.real)) (= (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real X) X)) (tptp.hAPP_real_real (tptp.times_times_real Y_1) Y_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y_1 tptp.zero_zero_real)))) (forall ((K_1 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_1) N_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) N_1))))) (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M) N_1)))))) (forall ((K tptp.nat) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N)))))) (forall ((Ma tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) K)) (tptp.hAPP_nat_nat (tptp.times_times_nat N) K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N))))) (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.hAPP_nat_real (tptp.power_power_real (tptp.number267125858f_real (tptp.bit0 (tptp.bit1 tptp.pls)))) N_1)))) (forall ((N tptp.nat) (Ma tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Ma)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) N)) Ma)) (= N tptp.one_one_nat)))) (forall ((N tptp.nat) (P_1 tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_1 N)) (exists ((K_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_2) N)) (forall ((I tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) K_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 I))))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat K_2) tptp.one_one_nat)))))))) (forall ((U tptp.nat) (Ma tptp.nat) (N tptp.nat) (I_2 tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_2) U)) Ma)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_2) U)) N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) I_2)) U)) N)))))) (forall ((U tptp.nat) (Ma tptp.nat) (N tptp.nat) (J_2 tptp.nat) (I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_2) I_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_2) U)) Ma)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_2) U)) N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat I_2) J_2)) U)) Ma)) N))))) (forall ((W tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real W) W))) (forall ((Z tptp.real) (W tptp.real)) (or (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Z) W)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real W) Z)))) (forall ((K_1 tptp.real) (I_1 tptp.real) (J_1 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real I_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 J_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real J_1) K_1)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 K_1)))))) (forall ((Z tptp.real) (W tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Z) W)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real W) Z)) (= Z W)))) (forall ((K tptp.nat) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 N)) (or (= K tptp.zero_zero_nat) (= Ma N))))) (forall ((I_1 tptp.nat) (U_1 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_1) U_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_1) U_1)) K_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) J_1)) U_1)) K_1))) (forall ((Ma tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N)))))) (forall ((Ma tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 N)) (= Ma N))))) (forall ((K tptp.nat) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N))) (or (= K tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) N)))))) (forall ((Ma tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) N)))))) (forall ((Ma tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N)))))) (forall ((U tptp.nat) (Ma tptp.nat) (N tptp.nat) (J_2 tptp.nat) (I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_2) I_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_2) U)) Ma)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_2) U)) N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat I_2) J_2)) U)) Ma)) N))))) (forall ((U_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat) (J_1 tptp.nat) (I_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) I_1)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_1) U_1)) M)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_1) U_1)) N_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat I_1) J_1)) U_1)) M)) N_1)))) (forall ((U tptp.nat) (Ma tptp.nat) (N tptp.nat) (J_2 tptp.nat) (I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_2) I_2)) (= (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_2) U)) Ma) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_2) U)) N)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat I_2) J_2)) U)) Ma) N)))) (forall ((U tptp.nat) (Ma tptp.nat) (N tptp.nat) (I_2 tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_2) U)) Ma)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_2) U)) N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) I_2)) U)) N)))))) (forall ((U_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_1) U_1)) M)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_1) U_1)) N_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) I_1)) U_1)) N_1))))) (forall ((U tptp.nat) (Ma tptp.nat) (N tptp.nat) (I_2 tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_2)) (= (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_2) U)) Ma) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_2) U)) N)) (= Ma (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) I_2)) U)) N))))) (forall ((N_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.number_number_of_int N_1))) (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.number_number_of_int (tptp.bit0 N_1)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.number_number_of_int (tptp.bit1 N_1)))))))) (forall ((A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A)) (exists ((P_5 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_5) A)))))) (forall ((P_4 tptp.bool) (P_1 tptp.bool) (X tptp.int)) (let ((_let_1 (tptp.hBOOL P_4))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)))) (let ((_let_3 (tptp.hBOOL P_1))) (=> (=> _let_2 (= _let_3 _let_1)) (= (and _let_2 _let_3) (and _let_2 _let_1))))))) (forall ((P_4 tptp.bool) (P_1 tptp.bool) (X tptp.int)) (let ((_let_1 (tptp.hBOOL P_4))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)))) (let ((_let_3 (tptp.hBOOL P_1))) (=> (=> _let_2 (= _let_3 _let_1)) (= (=> _let_2 _let_3) (=> _let_2 _let_1))))))) (forall ((Ma tptp.int) (Ta tptp.int) (K tptp.int)) (let ((_let_1 (tptp.times_times_int K))) (=> (not (= K tptp.zero_zero_int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Ma) Ta)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int _let_1 Ma)) (tptp.hAPP_int_int _let_1 Ta))))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_12 _let_11)) (forall ((K tptp.int) (P_1 tptp.fun_int_bool) (D tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.minus_minus_int X_2) D))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.minus_minus_int X_2) (tptp.hAPP_int_int (tptp.times_times_int K) D)))))))))) (forall ((K tptp.int) (P_1 tptp.fun_int_bool) (D tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.plus_plus_int X_2) D))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.plus_plus_int X_2) (tptp.hAPP_int_int (tptp.times_times_int K) D)))))))))) (forall ((A tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) M)) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A X_2) M)) (forall ((Y_2 tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y_2) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A Y_2) M))) (= Y_2 X_2))))))) (= (tptp.twoSqu949963151sum2sq (tptp.product_Pair_int_int tptp.s tptp.one_one_int)) _let_10) (forall ((A tptp.int) (B tptp.int) (P_3 tptp.int) (Q_1 tptp.int)) (let ((_let_1 (tptp.times_times_int B))) (let ((_let_2 (tptp.times_times_int A))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.twoSqu949963151sum2sq (tptp.product_Pair_int_int A B))) (tptp.twoSqu949963151sum2sq (tptp.product_Pair_int_int P_3 Q_1))) (tptp.twoSqu949963151sum2sq (tptp.product_Pair_int_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_2 P_3)) (tptp.hAPP_int_int _let_1 Q_1)) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int _let_2 Q_1)) (tptp.hAPP_int_int _let_1 P_3)))))))) (forall ((X tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu820444569sum2sq X)) (exists ((A_3 tptp.int) (B_3 tptp.int)) (= (tptp.twoSqu949963151sum2sq (tptp.product_Pair_int_int A_3 B_3)) X)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) (tptp.hAPP_int_int (tptp.minus_minus_int B) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) B)))) (forall ((P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.zfact (tptp.hAPP_int_int (tptp.minus_minus_int P_3) tptp.one_one_int)) (tptp.number_number_of_int tptp.min)) P_3)))) (forall ((N_1 tptp.int)) (let ((_let_1 (tptp.zfact N_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int N_1) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.hAPP_int_int (tptp.times_times_int N_1) (tptp.zfact (tptp.hAPP_int_int (tptp.minus_minus_int N_1) tptp.one_one_int))))))))) (forall ((A tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int (tptp.bit1 (tptp.bit0 (tptp.bit1 tptp.pls))))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) P_3)) (= (tptp.inv P_3 (tptp.inv P_3 A)) A)))))) (forall ((A tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.minus_minus_int P_3) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.inv P_3 A)) _let_1))))))) (forall ((A tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) (tptp.hAPP_int_int (tptp.minus_minus_int P_3) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.inv P_3 A)))))))) (forall ((A tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.minus_minus_int P_3) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) _let_1)) (not (= (tptp.inv P_3 A) _let_1))))))) (forall ((A tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) (tptp.hAPP_int_int (tptp.minus_minus_int P_3) tptp.one_one_int))) (not (= (tptp.inv P_3 A) tptp.one_one_int)))))) (forall ((A tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) (tptp.hAPP_int_int (tptp.minus_minus_int P_3) tptp.one_one_int))) (not (= A (tptp.inv P_3 A))))))) (forall ((A tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) (tptp.hAPP_int_int (tptp.minus_minus_int P_3) tptp.one_one_int))) (not (= (tptp.inv P_3 A) tptp.zero_zero_int)))))) (forall ((A tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A) (tptp.inv P_3 A)) tptp.one_one_int) P_3)))))) (forall ((B_2 tptp.int) (A_2 tptp.int) (P_2 tptp.int)) (let ((_let_1 (tptp.wset A_2 P_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int (tptp.bit1 (tptp.bit0 (tptp.bit1 tptp.pls))))) P_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) (tptp.hAPP_int_int (tptp.minus_minus_int P_2) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.member_int B_2 _let_1)) (tptp.hBOOL (tptp.member_int (tptp.inv P_2 B_2) _let_1)))))))) (forall ((B_2 tptp.int) (A_2 tptp.int) (P_2 tptp.int)) (let ((_let_1 (tptp.wset A_2 P_2))) (let ((_let_2 (tptp.hAPP_int_int (tptp.minus_minus_int P_2) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int (tptp.bit1 (tptp.bit0 (tptp.bit1 tptp.pls))))) P_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) _let_2)) (=> (tptp.hBOOL (tptp.member_int (tptp.inv P_2 B_2) _let_1)) (tptp.hBOOL (tptp.member_int B_2 _let_1))))))))))) (forall ((P_2 tptp.int) (A_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_2)) (tptp.hBOOL (tptp.member_int A_2 (tptp.wset A_2 P_2))))) (forall ((B_2 tptp.int) (P_2 tptp.int) (A_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_2)) (=> (tptp.hBOOL (tptp.member_int B_2 (tptp.wset (tptp.hAPP_int_int (tptp.minus_minus_int A_2) tptp.one_one_int) P_2))) (tptp.hBOOL (tptp.member_int B_2 (tptp.wset A_2 P_2)))))) (forall ((B_2 tptp.int) (A_2 tptp.int) (P_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) (tptp.hAPP_int_int (tptp.minus_minus_int P_2) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.member_int B_2 (tptp.wset A_2 P_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B_2)))))) (forall ((B_2 tptp.int) (A_2 tptp.int) (P_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.minus_minus_int P_2) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) _let_1)) (=> (tptp.hBOOL (tptp.member_int B_2 (tptp.wset A_2 P_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) _let_1))))))) (forall ((B_2 tptp.int) (P_2 tptp.int) (A_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_2)) (=> (not (tptp.hBOOL (tptp.member_int B_2 (tptp.wset (tptp.hAPP_int_int (tptp.minus_minus_int A_2) tptp.one_one_int) P_2)))) (=> (tptp.hBOOL (tptp.member_int B_2 (tptp.wset A_2 P_2))) (or (= B_2 A_2) (= B_2 (tptp.inv P_2 A_2))))))) (forall ((B_2 tptp.int) (A_2 tptp.int) (P_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) (tptp.hAPP_int_int (tptp.minus_minus_int P_2) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) A_2)) (tptp.hBOOL (tptp.member_int B_2 (tptp.wset A_2 P_2)))))))) (forall ((J_1 tptp.int) (A tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A tptp.zero_zero_int) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 tptp.zero_zero_int) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.quadRes P_3) A))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 (tptp.hAPP_int_int (tptp.times_times_int A) (tptp.multInv P_3 J_1))) P_3))))))))) (forall ((P_1 tptp.fun_int_bool) (I_2 tptp.int) (K tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_2) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 K)) (=> (forall ((I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 I)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.minus_minus_int I) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_2)))))) (forall ((J_1 tptp.int) (A tptp.int) (P_3 tptp.int) (K_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.times_times_int A) (tptp.multInv P_3 K_1)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 _let_1) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int J_1) K_1) (tptp.hAPP_int_int (tptp.times_times_int _let_1) K_1)) P_3))))) (forall ((J_1 tptp.int) (K_1 tptp.int) (A tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.times_times_int (tptp.multInv P_3 J_1)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int J_1) K_1) A) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_1 J_1)) K_1) (tptp.hAPP_int_int _let_1 A)) P_3))))) (forall ((X_1 tptp.int) (Y tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 Y) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.multInv P_3 X_1) (tptp.multInv P_3 Y)) P_3))))) (forall ((A tptp.int) (J_1 tptp.int) (K_1 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.times_times_int A))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 K_1) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int _let_1 (tptp.multInv P_3 J_1)) (tptp.hAPP_int_int _let_1 (tptp.multInv P_3 K_1))) P_3)))))) (forall ((Y tptp.int) (X_1 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong Y tptp.zero_zero_int) P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.multInv P_3 X_1) (tptp.multInv P_3 Y)) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 Y) P_3)))))))) (forall ((X_1 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_3))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.multInv P_3 (tptp.multInv P_3 X_1)) X_1) P_3)))))) (forall ((X_1 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_3))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.multInv P_3 X_1) tptp.zero_zero_int) P_3))))))) (forall ((K_1 tptp.int) (A tptp.int) (J_1 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.multInv P_3 J_1))) (let ((_let_2 (tptp.times_times_int _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 tptp.zero_zero_int) P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_2 J_1)) K_1) (tptp.hAPP_int_int _let_2 A)) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong K_1 (tptp.hAPP_int_int (tptp.times_times_int A) _let_1)) P_3))))))))) (forall ((J_1 tptp.int) (A tptp.int) (K_1 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.times_times_int J_1) K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong K_1 tptp.zero_zero_int) P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong _let_1 (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.times_times_int A) (tptp.multInv P_3 K_1))) K_1)) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong _let_1 A) P_3)))))))) (forall ((A tptp.int) (J_1 tptp.int) (K_1 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.times_times_int A))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong K_1 tptp.zero_zero_int) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 tptp.zero_zero_int) P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 (tptp.hAPP_int_int _let_1 (tptp.multInv P_3 K_1))) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong K_1 (tptp.hAPP_int_int _let_1 (tptp.multInv P_3 J_1))) P_3))))))))) (forall ((J_1 tptp.int) (K_1 tptp.int) (A tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.times_times_int A))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A tptp.zero_zero_int) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong K_1 tptp.zero_zero_int) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 tptp.zero_zero_int) P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int _let_1 (tptp.multInv P_3 J_1)) (tptp.hAPP_int_int _let_1 (tptp.multInv P_3 K_1))) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 K_1) P_3)))))))))) (forall ((X_1 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.multInv P_3 X_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_3))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.times_times_int X_1) _let_1)) (tptp.multInv P_3 _let_1)) X_1) P_3))))))) (forall ((X_1 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.multInv P_3 X_1))) (let ((_let_2 (tptp.multInv P_3 _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_3))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong _let_2 (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.times_times_int X_1) _let_1)) _let_2)) P_3)))))))) (forall ((X_1 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_3))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int (tptp.multInv P_3 X_1)) X_1) tptp.one_one_int) P_3)))))) (forall ((X_1 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_3))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int X_1) (tptp.multInv P_3 X_1)) tptp.one_one_int) P_3)))))) (forall ((X tptp.int) (P_1 tptp.fun_int_bool)) (=> (forall ((A_3 tptp.int)) (=> (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_3)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.minus_minus_int A_3) tptp.one_one_int)))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 A_3)))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X)))) (forall ((P_1 tptp.fun_int_bool) (I_2 tptp.int) (K tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_2) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.minus_minus_int K) tptp.one_one_int))) (=> (forall ((I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 I)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.minus_minus_int I) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_2)))))) (forall ((P_1 tptp.fun_int_bool) (K tptp.int) (I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) I_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 K)) (=> (forall ((I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) I)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 I)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.plus_plus_int I) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_2)))))) (forall ((P_1 tptp.fun_int_bool) (K tptp.int) (I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) I_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.plus_plus_int K) tptp.one_one_int))) (=> (forall ((I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) I)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 I)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.plus_plus_int I) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_2)))))) (forall ((Ma tptp.nat) (K tptp.nat) (F_1 tptp.fun_nat_nat)) (=> (forall ((M_2 tptp.nat) (N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat F_1 M_2)) (tptp.hAPP_nat_nat F_1 N_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat F_1 Ma)) K)) (tptp.hAPP_nat_nat F_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat Ma) K)))))) (forall ((P_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.minus_minus_int P_2) (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (= (tptp.d22set _let_1) (tptp.wset _let_1 P_2))))) (forall ((A_2 tptp.int) (B_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) B_2)) (not (tptp.hBOOL (tptp.member_int B_2 (tptp.d22set A_2)))))) (forall ((B_2 tptp.int) (A_2 tptp.int)) (=> (tptp.hBOOL (tptp.member_int B_2 (tptp.d22set A_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) A_2)))) (forall ((B_2 tptp.int) (A_2 tptp.int)) (=> (tptp.hBOOL (tptp.member_int B_2 (tptp.d22set A_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B_2)))) (forall ((A_2 tptp.int) (B_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) A_2)) (tptp.hBOOL (tptp.member_int B_2 (tptp.d22set A_2)))))) (forall ((N tptp.nat) (P_1 tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_1 N)) (exists ((K_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) N)) (forall ((I tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) K_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 I))))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 K_2))))))) (forall ((I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J_1)) (exists ((K_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_2)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) K_2) J_1))))) (forall ((A_2 tptp.int) (B_2 tptp.int) (N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.power_power_int A_2) N)) (tptp.hAPP_nat_int (tptp.power_power_int B_2) N))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_2) B_2))))) (forall ((A tptp.int) (N_1 tptp.nat) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.power_power_int A) N_1)) (tptp.hAPP_nat_int (tptp.power_power_int B) N_1))) (=> (not (= N_1 tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A) B))))) (forall ((A tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A)) (= A tptp.zero_zero_nat))) (forall ((A_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A_2)) (= A_2 tptp.zero_zero_nat))) (forall ((A_2 tptp.nat)) (= (not (= A_2 tptp.zero_zero_nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_2) tptp.zero_zero_nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A_2)))))) (forall ((A tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) tptp.zero_zero_nat))) (forall ((A tptp.nat)) (not (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))))) (forall ((A tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= A tptp.one_one_nat))) (forall ((A_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_2) tptp.one_one_nat)) (= A_2 tptp.one_one_nat))) (forall ((A_2 tptp.nat)) (= (not (= A_2 tptp.one_one_nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.one_one_nat) A_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_2) tptp.one_one_nat)))))) (forall ((A tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.one_one_nat) A))) (forall ((A tptp.nat)) (not (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.one_one_nat) A)))))) (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)))))) (forall ((A_2 tptp.nat) (B_2 tptp.nat) (N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.power_power_nat A_2) N)) (tptp.hAPP_nat_nat (tptp.power_power_nat B_2) N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_2) B_2))))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M) N_1)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (= N_1 tptp.zero_zero_nat)))) (forall ((N_1 tptp.nat) (M tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (=> (= (tptp.hAPP_nat_nat _let_1 N_1) (tptp.hAPP_nat_nat _let_1 M)) (= N_1 M))))) (forall ((P_2 tptp.int)) (= (tptp.sr P_2) (tptp.collect_int (tptp.cOMBS_int_bool_bool (tptp.cOMBB_1652995168ol_int tptp.fconj (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int)) (tptp.cOMBC_int_int_bool tptp.ord_less_int P_2))))) (forall ((V tptp.int) (W tptp.int)) (let ((_let_1 (tptp.number_number_of_int W))) (let ((_let_2 (tptp.number_number_of_int V))) (let ((_let_3 (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))))) (let ((_let_4 (tptp.hAPP_int_int (tptp.div_mod_int (tptp.number_number_of_int (tptp.bit1 V))) (tptp.number_number_of_int (tptp.bit0 W))))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_1)))) (and (=> _let_5 (= _let_4 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_3 (tptp.hAPP_int_int (tptp.div_mod_int _let_2) _let_1))) tptp.one_one_int))) (=> (not _let_5) (= _let_4 (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int _let_3 (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1))) tptp.one_one_int)))))))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) (tptp.hAPP_int_int _let_1 B))) (tptp.hAPP_int_int _let_1 A)) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.plus_plus_int B) tptp.one_one_int)) A))) tptp.one_one_int))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.times_times_int A))) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int B) C))) C) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 B)) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.times_times_int A))) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 B)) C) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int B) C))) C)))) (forall ((A_2 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 B_2) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.div_mod_int A_2) Ma) (tptp.hAPP_int_int (tptp.div_mod_int B_2) Ma)) Ma)))) (forall ((X_1 tptp.int) (M tptp.int) (Y tptp.nat)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_int_int (tptp.div_mod_int X_1) M)) Y)) M) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_nat_int (tptp.power_power_int X_1) Y)) M))) (forall ((X_1 tptp.int) (M tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 (tptp.hAPP_int_int (tptp.div_mod_int X_1) M)) M))) (forall ((X_1 tptp.int) (M tptp.int) (Y tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.div_mod_int X_1) M) (tptp.hAPP_int_int (tptp.div_mod_int Y) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 Y) M)))) (forall ((N_1 tptp.int) (F tptp.int) (M tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int F))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.div_mod_int M) N_1))))))) (forall ((K_1 tptp.int) (M tptp.int) (N_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.div_mod_int M) N_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)))))) (forall ((A tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A) A) tptp.zero_zero_int)) (forall ((B tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int tptp.zero_zero_int) B) tptp.zero_zero_int)) (forall ((X tptp.int) (N tptp.int) (Y_1 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.div_mod_int X) N) (tptp.hAPP_int_int (tptp.div_mod_int Y_1) N)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int N) (tptp.hAPP_int_int (tptp.minus_minus_int X) Y_1))))) (forall ((Ma tptp.int) (D tptp.int)) (= (= (tptp.hAPP_int_int (tptp.div_mod_int Ma) D) tptp.zero_zero_int) (exists ((Q_2 tptp.int)) (= Ma (tptp.hAPP_int_int (tptp.times_times_int D) Q_2))))) (forall ((Y tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.div_mod_int X_1) Y))))))) (forall ((K_1 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.div_mod_int M) K_1)) M)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.div_mod_int A) B)) B)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.div_mod_int A) B)))))) (forall ((X_1 tptp.int) (M tptp.int) (Y tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int (tptp.div_mod_int X_1) M)) Y)) M) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.minus_minus_int X_1) Y)) M))) (forall ((X_1 tptp.int) (Y tptp.int) (M tptp.int)) (let ((_let_1 (tptp.minus_minus_int X_1))) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int Y) M))) M) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 Y)) M)))) (forall ((X tptp.int) (Y_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_int X))) (let ((_let_2 (tptp.number_number_of_int Y_1))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int _let_1) _let_2)) (= (tptp.hAPP_int_int (tptp.div_mod_int _let_2) _let_1) tptp.zero_zero_int))))) (forall ((A tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A) (tptp.number_number_of_int tptp.min)) tptp.zero_zero_int)) (forall ((A tptp.int) (B tptp.int) (M tptp.int)) (let ((_let_1 (tptp.div_mod_int A))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int M) B)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 B)) M) (tptp.hAPP_int_int _let_1 M)))))) (forall ((A_2 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Ma)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 B_2) Ma)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_2) Ma) (tptp.hAPP_int_int (tptp.div_mod_int B_2) Ma))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.div_mod_int A) B))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.div_mod_int A) B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) B)))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) B)) (= (tptp.hAPP_int_int (tptp.div_mod_int A) B) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.div_mod_int A) B)) tptp.zero_zero_int)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.div_mod_int A) B))) (let ((_let_2 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_2 tptp.zero_zero_int)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int _let_1) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_2 _let_1))))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) A)) (= (tptp.hAPP_int_int (tptp.div_mod_int A) B) A)))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.plus_plus_int A) B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int _let_1) tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A) B) _let_1))))) (forall ((V tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.number_number_of_int (tptp.bit0 V))) (tptp.number_number_of_int (tptp.bit0 W))) (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.number_number_of_int V)) (tptp.number_number_of_int W))))) (forall ((A_1 tptp.int) (B_1 tptp.int) (Q_3 tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_1)))) (=> (= A_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B_1) Q_3)) Y)) (=> (and (=> _let_1 (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y) B_1)))) (=> (not _let_1) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_1) Y)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y) tptp.zero_zero_int))))) (=> (not (= B_1 tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_1) B_1) Y)))))) (forall ((Q_1 tptp.int) (B tptp.int) (R_1 tptp.int) (C tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) R_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int R_1) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B) (tptp.hAPP_int_int (tptp.div_mod_int Q_1) C))) R_1)) tptp.zero_zero_int)))))) (forall ((Q_1 tptp.int) (B tptp.int) (R_1 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.times_times_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) R_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int R_1) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 C)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int Q_1) C))) R_1)))))))) (forall ((Q_1 tptp.int) (B tptp.int) (R_1 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.times_times_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_1) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int Q_1) C))) R_1)) (tptp.hAPP_int_int _let_1 C)))))))) (forall ((Q_1 tptp.int) (B tptp.int) (R_1 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 R_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_1) B)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B) (tptp.hAPP_int_int (tptp.div_mod_int Q_1) C))) R_1)))))))) (forall ((P_1 tptp.fun_int_bool) (N tptp.int) (K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.div_mod_int N) K))) (and (=> (= K tptp.zero_zero_int) (tptp.hBOOL (tptp.hAPP_int_bool P_1 N))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) K)) (forall ((I tptp.int) (J tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) J)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int J) K)) (= N (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int K) I)) J))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 J))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) tptp.zero_zero_int)) (forall ((I tptp.int) (J tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) J)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int J) tptp.zero_zero_int)) (= N (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int K) I)) J))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 J)))))))) (forall ((X tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.div_mod_int X) (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))) (forall ((B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.number_number_of_int tptp.min)) B) (tptp.hAPP_int_int (tptp.minus_minus_int B) tptp.one_one_int)))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.plus_plus_int tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 B))) (tptp.hAPP_int_int _let_1 A)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int B) A)))))))) (forall ((M_1 tptp.int) (D_1 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.div_mod_int M_1) D_1) tptp.zero_zero_int) (exists ((Q_2 tptp.int)) (= M_1 (tptp.hAPP_int_int (tptp.times_times_int D_1) Q_2))))) (forall ((X_1 tptp.int) (Y tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int (tptp.standardRes M X_1)) (tptp.standardRes M Y)) (tptp.hAPP_int_int (tptp.times_times_int X_1) Y)) M)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1)) N_1)))) (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat K_1))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1)) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N_1))))) (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1)) K_1) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.times_times_nat M) K_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat N_1) K_1)))) (forall ((M tptp.int) (X_1 tptp.int)) (= (tptp.standardRes M X_1) (tptp.hAPP_int_int (tptp.div_mod_int X_1) M))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1) M))) (forall ((N_1 tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) N_1)))) (forall ((K_1 tptp.nat) (N_1 tptp.nat) (M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat K_1) N_1)) M)) N_1) (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1))) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) N_1)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1)))) (and (=> _let_2 (= _let_1 M)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) N_1))))))) (forall ((Ma tptp.nat) (D tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.div_mod_nat Ma) D) tptp.zero_zero_nat) (exists ((Q_2 tptp.nat)) (= Ma (tptp.hAPP_nat_nat (tptp.times_times_nat D) Q_2))))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1)) N_1)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1)) M))) (forall ((Ma tptp.int) (X tptp.int)) (= (= (tptp.standardRes Ma X) tptp.zero_zero_int) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X tptp.zero_zero_int) Ma)))) (forall ((X tptp.int) (P_2 tptp.int)) (= (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X tptp.zero_zero_int) P_2))) (not (= (tptp.standardRes P_2 X) tptp.zero_zero_int)))) (forall ((X_1 tptp.int) (M tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 (tptp.standardRes M X_1)) M))) (forall ((X_1 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.standardRes P_3 X_1)) P_3)))) (forall ((X tptp.int) (P_2 tptp.int)) (=> (tptp.hBOOL (tptp.member_int X (tptp.sr P_2))) (= (tptp.standardRes P_2 X) X))) (forall ((P_1 tptp.fun_nat_bool) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (= K tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat N) K))) (and (=> _let_1 (tptp.hBOOL (tptp.hAPP_nat_bool P_1 N))) (=> (not _let_1) (forall ((I tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J) K)) (=> (= N (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat K) I)) J)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 J)))))))))) (forall ((Q_1 tptp.nat) (R_1 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.times_times_nat B))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat R_1) B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat Q_1) C))) R_1)) (tptp.hAPP_nat_nat _let_1 C))))))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((P tptp.fun_int_fun_int_bool) (Q tptp.int) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.cOMBC_int_int_bool P Q) R) (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P R) Q))) (forall ((P tptp.fun_in531499254l_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.cOMBS_int_bool_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_i68813070l_bool P R) (tptp.hAPP_int_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_i68813070l_bool (tptp.cOMBB_1652995168ol_int P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_int_bool Q R)))) _let_7 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.61/1.88  )
% 1.61/1.88  % SZS output end Proof for NUM924_3
% 1.61/1.88  % cvc5---1.0.5 exiting
% 1.73/1.88  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------