TSTP Solution File: NUM925_2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM925_2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.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 10:49:04 EDT 2023
% Result : Theorem 0.66s 1.22s
% Output : Proof 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.22 % Problem : NUM925_2 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.23 % Command : do_cvc5 %s %d
% 0.23/0.44 % Computer : n009.cluster.edu
% 0.23/0.44 % Model : x86_64 x86_64
% 0.23/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.44 % Memory : 8042.1875MB
% 0.23/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.23/0.44 % CPULimit : 300
% 0.23/0.44 % WCLimit : 300
% 0.23/0.44 % DateTime : Fri Aug 25 15:04:36 EDT 2023
% 0.23/0.45 % CPUTime :
% 0.31/0.67 %----Proving TF0_NAR, FOF, or CNF
% 0.66/1.22 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.n6rq3LsiPT/cvc5---1.0.5_13311.p...
% 0.66/1.22 ------- get file name : TPTP file name is NUM925_2
% 0.66/1.22 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_13311.smt2...
% 0.66/1.22 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.66/1.22 % SZS status Theorem for NUM925_2
% 0.66/1.22 % SZS output start Proof for NUM925_2
% 0.66/1.22 (
% 0.66/1.22 (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.plus_plus_int tptp.one_one_int))) (let ((_let_5 (tptp.hAPP_int_int _let_4 (tptp.hAPP_nat_int tptp.semiri1621563631at_int tptp.n)))) (let ((_let_6 (tptp.hAPP_nat_int (tptp.power_power_int _let_5) _let_3))) (let ((_let_7 (not (not (= _let_6 tptp.zero_zero_int))))) (let ((_let_8 (tptp.number_number_of_int tptp.pls))) (let ((_let_9 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_10 (tptp.number_number_of_int _let_2))) (let ((_let_11 (tptp.bit1 _let_1))) (let ((_let_12 (tptp.number_number_of_int _let_11))) (let ((_let_13 (tptp.hBOOL (tptp.hAPP_int_bool _let_9 tptp.one_one_int)))) (let ((_let_14 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int))) (let ((_let_15 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_16 (tptp.hAPP_nat_int tptp.semiri1621563631at_int tptp.zero_zero_nat))) (let ((_let_17 (= _let_16 tptp.zero_zero_int))) (let ((_let_18 (forall ((N_17 tptp.nat) (A_60 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_60)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_60) N_17)))))))) (let ((_let_19 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_20 (tptp.hBOOL (tptp.hAPP_int_bool _let_19 tptp.one_one_int)))) (let ((_let_21 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_22 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int))) (let ((_let_23 (tptp.hAPP_nat_int tptp.semiri1621563631at_int tptp.one_one_nat))) (let ((_let_24 (= _let_23 tptp.one_one_int))) (let ((_let_25 (not (= tptp.zero_zero_int tptp.one_one_int)))) (let ((_let_26 (not (= tptp.zero_zero_real tptp.one_one_real)))) (let ((_let_27 (tptp.hAPP_real_real (tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_28 (tptp.hAPP_nat_nat (tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))) (let ((_let_29 (tptp.hAPP_int_int _let_4 tptp.one_one_int))) (let ((_let_30 (tptp.number267125858f_real _let_1))) (let ((_let_31 (= _let_30 tptp.one_one_real))) (let ((_let_32 (tptp.number_number_of_nat _let_1))) (let ((_let_33 (= _let_32 tptp.one_one_nat))) (let ((_let_34 (tptp.number_number_of_int _let_1))) (let ((_let_35 (= _let_34 tptp.one_one_int))) (let ((_let_36 (tptp.number267125858f_real tptp.pls))) (let ((_let_37 (= tptp.zero_zero_int _let_8))) (let ((_let_38 (= _let_36 tptp.zero_zero_real))) (let ((_let_39 (= _let_8 tptp.zero_zero_int))) (let ((_let_40 (tptp.number_number_of_nat tptp.pls))) (let ((_let_41 (= _let_40 tptp.zero_zero_nat))) (let ((_let_42 (= tptp.pls tptp.zero_zero_int))) (let ((_let_43 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls))) (let ((_let_44 (= tptp.one_one_int _let_34))) (let ((_let_45 (tptp.hBOOL (tptp.hAPP_int_bool _let_43 tptp.pls)))) (let ((_let_46 (not _let_45))) (let ((_let_47 (= _let_28 _let_3))) (let ((_let_48 (= _let_27 (tptp.number267125858f_real _let_2)))) (let ((_let_49 (= _let_29 _let_10))) (let ((_let_50 (tptp.hBOOL (tptp.hAPP_int_bool _let_19 _let_5)))) (let ((_let_51 (forall ((N_17 tptp.nat) (A_60 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (or (not (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_60))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_60) N_17)))))))) (let ((_let_52 (tptp.hBOOL (tptp.hAPP_int_bool _let_19 _let_6)))) (let ((_let_53 (not _let_50))) (let ((_let_54 (or _let_53 _let_52))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (not _let_54))) (let ((_let_57 (= tptp.zero_zero_int _let_6))) (let ((_let_58 (= tptp.zero_zero_int tptp.pls))) (let ((_let_59 (not _let_52))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (SYMM (ASSUME :args (_let_42))))) (let ((_let_62 (ASSUME :args (_let_46)))) (let ((_let_63 (and _let_46 _let_58 _let_57))) (let ((_let_64 (_let_46 _let_58 _let_57))) (let ((_let_65 (APPLY_UF tptp.hAPP_int_bool))) (let ((_let_66 (SYMM (SYMM _let_61)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (_let_3 _let_5 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_nat_int (tptp.power_power_int A_60) N_17)))) :args (_let_51))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_53 _let_52 _let_56))) (ASSUME :args (_let_50)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_63)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_62 _let_61 _let_60) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS (CONG (CONG (REFL :args (tptp.ord_less_int)) _let_66 :args (APPLY_UF tptp.hAPP_i1948725293t_bool)) (SYMM _let_60) :args _let_65) (CONG (REFL :args (_let_43)) _let_66 :args _let_65)) :args (APPLY_UF tptp.hBOOL)) (FALSE_INTRO _let_62))) :args _let_64)) :args _let_64)) :args (true _let_63)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) (REFL :args ((not _let_58))) (REFL :args ((not _let_57))) (REFL :args (_let_59)) :args (or))) _let_62 _let_61 _let_60 :args (_let_59 true _let_45 false _let_58 false _let_57)) :args (_let_56 false _let_50 true _let_52)) _let_55 :args (false true _let_54 false _let_51)) :args (_let_50 (tptp.hBOOL (tptp.hAPP_int_bool _let_22 tptp.t)) (forall ((Xa tptp.int) (Ya 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 Xa) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Ya) _let_1)) tptp.zero_zero_int) (and (= Xa tptp.zero_zero_int) (= Ya tptp.zero_zero_int))))) (forall ((Xa tptp.real) (Ya 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 Xa) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Ya) _let_1)) tptp.zero_zero_real) (and (= Xa tptp.zero_zero_real) (= Ya tptp.zero_zero_real))))) (= (tptp.hAPP_nat_int (tptp.power_power_int tptp.one_one_int) _let_3) tptp.one_one_int) (= (tptp.hAPP_nat_nat (tptp.power_power_nat tptp.one_one_nat) _let_3) tptp.one_one_nat) (= (tptp.hAPP_nat_real (tptp.power_power_real tptp.one_one_real) _let_3) tptp.one_one_real) (= (tptp.hAPP_nat_int (tptp.power_power_int tptp.zero_zero_int) _let_3) tptp.zero_zero_int) (= (tptp.hAPP_nat_nat (tptp.power_power_nat tptp.zero_zero_nat) _let_3) tptp.zero_zero_nat) (= (tptp.hAPP_nat_real (tptp.power_power_real tptp.zero_zero_real) _let_3) tptp.zero_zero_real) (forall ((A_24 tptp.int)) (= (= (tptp.hAPP_nat_int (tptp.power_power_int A_24) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.zero_zero_int) (= A_24 tptp.zero_zero_int))) (forall ((A_24 tptp.real)) (= (= (tptp.hAPP_nat_real (tptp.power_power_real A_24) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.zero_zero_real) (= A_24 tptp.zero_zero_real))) (forall ((W_8 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) (tptp.number_number_of_int W_8)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit1 tptp.pls)) W_8)))) (forall ((W_8 tptp.int)) (= (tptp.hAPP_real_real (tptp.plus_plus_real tptp.one_one_real) (tptp.number267125858f_real W_8)) (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit1 tptp.pls)) W_8)))) (forall ((V_11 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_11)) tptp.one_one_int) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V_11) (tptp.bit1 tptp.pls))))) (forall ((V_11 tptp.int)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real V_11)) tptp.one_one_real) (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int V_11) (tptp.bit1 tptp.pls))))) _let_49 _let_48 _let_49 _let_47 _let_48 (forall ((X tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.power_power_int X))) (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)))))))) (forall ((W_7 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_7))) (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))))))) (forall ((W_7 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_7))) (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_7 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_7))) (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))))))) _let_44 (= tptp.one_one_real _let_30) _let_35 _let_31 (tptp.hBOOL (tptp.hAPP_nat_bool _let_15 tptp.n)) (forall ((X tptp.int) (Y tptp.int)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) Y)) (= X Y) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y) X)))) (forall ((K_2 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_2)) (tptp.number_number_of_int L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_2) L_1)))) (forall ((V_6 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_6)) (tptp.number_number_of_int W)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V_6) W)))) (forall ((Xa tptp.int) (Ya tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int Xa)) (tptp.number_number_of_int Ya))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Xa) Ya)))) (forall ((Xa tptp.int) (Ya tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.number267125858f_real Xa)) (tptp.number267125858f_real Ya))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Xa) Ya)))) _let_37 (forall ((M_1 tptp.nat) (N_1 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_1)) N_1) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.power_power_nat M_1) N_1)))) (forall ((M_1 tptp.nat) (N_1 tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.power_power_nat M_1) N_1)) (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_1)) N_1))) (forall ((M_1 tptp.nat) (N_1 tptp.nat) (Z_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_1)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1)) Z_2)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_1) N_1))) Z_2))) (forall ((M_1 tptp.nat) (N_1 tptp.nat)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_1) N_1)))) _let_24 _let_41 (= tptp.zero_zero_nat _let_40) (forall ((Na tptp.nat)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Na) tptp.zero_zero_int) (= Na tptp.zero_zero_nat))) _let_17 _let_47 (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_2 tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K_2)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_2) L_1)))) _let_46 (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_2 tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 K_2)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_2) L_1)))) (forall ((K tptp.int) (I_2 tptp.int) (J_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_2) J_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int I_2) K)) (tptp.hAPP_int_int (tptp.plus_plus_int J_2) K))))) (forall ((V_10 tptp.int) (V_6 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat V_10))) (let ((_let_2 (tptp.number_number_of_nat V_6))) (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_10) tptp.pls)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_6) 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_6) V_10))))))))))))) _let_44 _let_33 (= tptp.one_one_nat _let_32) (forall ((Xa tptp.int) (Ya tptp.int)) (= (= (tptp.number_number_of_int Xa) (tptp.number_number_of_int Ya)) (= Xa Ya))) (forall ((Xa tptp.int) (Ya tptp.int)) (= (= (tptp.number267125858f_real Xa) (tptp.number267125858f_real Ya)) (= Xa Ya))) (forall ((Wa tptp.int) (Xa tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat Wa))) (= (= _let_1 Xa) (= Xa _let_1)))) (forall ((Wa tptp.int) (Xa tptp.int)) (let ((_let_1 (tptp.number_number_of_int Wa))) (= (= _let_1 Xa) (= Xa _let_1)))) (forall ((Wa tptp.int) (Xa tptp.real)) (let ((_let_1 (tptp.number267125858f_real Wa))) (= (= _let_1 Xa) (= Xa _let_1)))) (forall ((K_2 tptp.int) (L_1 tptp.int)) (= (= (tptp.bit1 K_2) (tptp.bit1 L_1)) (= K_2 L_1))) (forall ((K_2 tptp.int) (L_1 tptp.int)) (= (= (tptp.bit0 K_2) (tptp.bit0 L_1)) (= K_2 L_1))) (forall ((A_24 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_24) A_24)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_24) tptp.zero_zero_int)))) (forall ((A_24 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_24) A_24)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_24) tptp.zero_zero_real)))) (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 tptp.int) (Y tptp.int) (Z_2 tptp.int)) (let ((_let_1 (tptp.plus_plus_int X))) (let ((_let_2 (tptp.plus_plus_int Y))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 Z_2)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 Z_2)))))) (forall ((Z_2 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int Z_2) W) (tptp.hAPP_int_int (tptp.plus_plus_int W) Z_2))) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Na)) (= Ma Na))) (forall ((Xa tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int Xa)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Xa) tptp.pls)))) (forall ((Xa tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.number267125858f_real Xa)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Xa) tptp.pls)))) (forall ((Ya 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 Ya))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) Ya)))) (forall ((Ya tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.number267125858f_real Ya))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) Ya)))) (forall ((K_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K_2)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_2) 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_2 tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K_2)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_2) L_1)))) (forall ((K_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 K_2)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_2) tptp.pls)))) (forall ((K_2 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_2))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K_2))))) (forall ((Wa tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 Wa)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Wa) tptp.zero_zero_int)))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_43 tptp.zero_zero_int))) (forall ((Wa tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 Wa)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Wa) tptp.zero_zero_int)))) _let_20 (forall ((Wa tptp.int) (Z_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Wa))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int Z_3) tptp.one_one_int))) (or (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_3)) (= Wa Z_3))))) (forall ((K tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int K)) tptp.zero_zero_int)))) (forall ((Xa tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int Xa)) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Xa) (tptp.bit1 tptp.pls))))) (forall ((Xa tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.number267125858f_real Xa)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Xa) (tptp.bit1 tptp.pls))))) (forall ((Ya 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 Ya))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 tptp.pls)) Ya)))) (forall ((Ya tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) (tptp.number267125858f_real Ya))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 tptp.pls)) Ya)))) (forall ((Z_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.plus_plus_int tptp.one_one_int) Z_3)) Z_3)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_3) tptp.zero_zero_int)))) (forall ((A_24 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.plus_plus_int A_24) A_24) tptp.zero_zero_int) (= A_24 tptp.zero_zero_int))) (forall ((A_24 tptp.real)) (= (= (tptp.hAPP_real_real (tptp.plus_plus_real A_24) A_24) tptp.zero_zero_real) (= A_24 tptp.zero_zero_real))) (forall ((K tptp.int)) (not (= (tptp.bit1 K) tptp.pls))) (forall ((L tptp.int)) (not (= tptp.pls (tptp.bit1 L)))) (forall ((K tptp.int) (L tptp.int)) (not (= (tptp.bit1 K) (tptp.bit0 L)))) (forall ((K tptp.int) (L tptp.int)) (not (= (tptp.bit0 K) (tptp.bit1 L)))) (forall ((K_2 tptp.int)) (= (= (tptp.bit0 K_2) tptp.pls) (= K_2 tptp.pls))) (forall ((L_1 tptp.int)) (= (= tptp.pls (tptp.bit0 L_1)) (= tptp.pls L_1))) (= (tptp.bit0 tptp.pls) tptp.pls) _let_42 _let_25 (forall ((K tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int K) tptp.pls) K)) (forall ((K tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int tptp.pls) K) K)) (forall ((K tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit0 K)) (tptp.bit0 L)) (tptp.bit0 (tptp.hAPP_int_int (tptp.plus_plus_int K) L)))) (forall ((K tptp.int)) (= (tptp.bit0 K) (tptp.hAPP_int_int (tptp.plus_plus_int K) K))) (forall ((Z_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int Z_2) tptp.zero_zero_int) Z_2)) (forall ((Z_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int tptp.zero_zero_int) Z_2) Z_2)) _let_39 _let_41 _let_38 _let_39 _let_38 _let_37 (= tptp.zero_zero_real _let_36) (forall ((A_68 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int tptp.pls)) A_68) A_68)) (forall ((A_68 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real tptp.pls)) A_68) A_68)) (forall ((A_67 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int A_67) (tptp.number_number_of_int tptp.pls)) A_67)) (forall ((A_67 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real A_67) (tptp.number267125858f_real tptp.pls)) A_67)) (forall ((A_24 tptp.int) (Wa tptp.int)) (let ((_let_1 (tptp.number_number_of_nat Wa))) (= (= (tptp.hAPP_nat_int (tptp.power_power_int A_24) _let_1) tptp.zero_zero_int) (and (= A_24 tptp.zero_zero_int) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A_24 tptp.nat) (Wa tptp.int)) (let ((_let_1 (tptp.number_number_of_nat Wa))) (= (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_24) _let_1) tptp.zero_zero_nat) (and (= A_24 tptp.zero_zero_nat) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A_24 tptp.real) (Wa tptp.int)) (let ((_let_1 (tptp.number_number_of_nat Wa))) (= (= (tptp.hAPP_nat_real (tptp.power_power_real A_24) _let_1) tptp.zero_zero_real) (and (= A_24 tptp.zero_zero_real) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((V_9 tptp.int) (W_6 tptp.int) (Z_5 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_9)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int W_6)) Z_5)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V_9) W_6))) Z_5))) (forall ((V_9 tptp.int) (W_6 tptp.int) (Z_5 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real V_9)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real W_6)) Z_5)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int V_9) W_6))) Z_5))) (forall ((V_8 tptp.int) (W_5 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_8)) (tptp.number_number_of_int W_5)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V_8) W_5)))) (forall ((V_8 tptp.int) (W_5 tptp.int)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real V_8)) (tptp.number267125858f_real W_5)) (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int V_8) W_5)))) (forall ((V_7 tptp.int) (W_4 tptp.int)) (= (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V_7) W_4)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_7)) (tptp.number_number_of_int W_4)))) (forall ((V_7 tptp.int) (W_4 tptp.int)) (= (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int V_7) W_4)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real V_7)) (tptp.number267125858f_real W_4)))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit1 K)) (tptp.bit0 L)) (tptp.bit1 (tptp.hAPP_int_int (tptp.plus_plus_int K) L)))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit0 K)) (tptp.bit1 L)) (tptp.bit1 (tptp.hAPP_int_int (tptp.plus_plus_int K) L)))) (forall ((K tptp.int)) (= (tptp.bit1 K) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) K)) K))) (forall ((Z_2 tptp.int)) (not (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) Z_2)) Z_2) tptp.zero_zero_int))) (forall ((N_29 tptp.nat)) (= (tptp.number_number_of_nat (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_29)) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_29))) (forall ((N_29 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_29))) (= (tptp.number_number_of_int _let_1) _let_1))) (forall ((N_29 tptp.nat)) (= (tptp.number267125858f_real (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_29)) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_29))) (forall ((A_24 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_24) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (not (= A_24 tptp.zero_zero_int)))) (forall ((A_24 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_24) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (not (= A_24 tptp.zero_zero_real)))) (forall ((A_66 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_66) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) tptp.zero_zero_int)))) (forall ((A_66 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_66) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) tptp.zero_zero_real)))) (forall ((Xa tptp.int) (Ya 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 Xa) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Ya) _let_1)))) (or (not (= Xa tptp.zero_zero_int)) (not (= Ya tptp.zero_zero_int)))))) (forall ((Xa tptp.real) (Ya 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 Xa) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Ya) _let_1)))) (or (not (= Xa tptp.zero_zero_real)) (not (= Ya tptp.zero_zero_real)))))) (forall ((X_16 tptp.int) (Y_13 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_16) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y_13) _let_1))) tptp.zero_zero_int))))) (forall ((X_16 tptp.real) (Y_13 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_16) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_13) _let_1))) tptp.zero_zero_real))))) (forall ((W_3 tptp.int)) (let ((_let_1 (tptp.number_number_of_int W_3))) (= (tptp.number_number_of_int (tptp.bit0 W_3)) (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.bit0 W_3)) (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_2 tptp.int)) (let ((_let_1 (tptp.number_number_of_int W_2))) (= (tptp.number_number_of_int (tptp.bit1 W_2)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) _let_1)) _let_1)))) (forall ((W_2 tptp.int)) (let ((_let_1 (tptp.number267125858f_real W_2))) (= (tptp.number267125858f_real (tptp.bit1 W_2)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.plus_plus_real tptp.one_one_real) _let_1)) _let_1)))) _let_35 _let_33 _let_31 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.m1) _let_5)) (forall ((N_28 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_28)) (tptp.hAPP_nat_int (tptp.power_power_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) N_28)))) (forall ((N_28 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real tptp.semiri132038758t_real N_28)) (tptp.hAPP_nat_real (tptp.power_power_real (tptp.number267125858f_real (tptp.bit0 (tptp.bit1 tptp.pls)))) N_28)))) (= _let_10 (tptp.hAPP_nat_int tptp.semiri1621563631at_int _let_3)) (= _let_12 (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.number_number_of_nat _let_11))) (forall ((Xa tptp.real) (Ya 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 Xa) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Ya) _let_1)) tptp.zero_zero_real) (and (= Xa tptp.zero_zero_real) (= Ya tptp.zero_zero_real))))) (forall ((Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Na)))) (forall ((Na 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.semiri984289939at_nat Na))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na))))) (forall ((Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_nat_real tptp.semiri132038758t_real Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Na)))) (forall ((N_27 tptp.nat) (A_65 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 A_65)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_27)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_65) N_27))))))) (forall ((N_27 tptp.nat) (A_65 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 A_65)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_27)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_65) N_27))))))) (forall ((N_27 tptp.nat) (A_65 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 A_65)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_27)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_65) N_27))))))) (forall ((N_26 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_int (tptp.power_power_int tptp.zero_zero_int) N_26))) (let ((_let_2 (= N_26 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((N_26 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat tptp.zero_zero_nat) N_26))) (let ((_let_2 (= N_26 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N_26 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_real (tptp.power_power_real tptp.zero_zero_real) N_26))) (let ((_let_2 (= N_26 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((A_64 tptp.int) (N_25 tptp.nat) (N_24 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_64))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_25) N_24)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_64)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_64) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int _let_1 N_24)) (tptp.hAPP_nat_int _let_1 N_25)))))))) (forall ((A_64 tptp.nat) (N_25 tptp.nat) (N_24 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_64))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_25) N_24)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_64)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_64) tptp.one_one_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 N_24)) (tptp.hAPP_nat_nat _let_1 N_25)))))))) (forall ((A_64 tptp.real) (N_25 tptp.nat) (N_24 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_64))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_25) N_24)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_64)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_64) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real _let_1 N_24)) (tptp.hAPP_nat_real _let_1 N_25)))))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_19 _let_29)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_15 _let_28)) (tptp.hBOOL (tptp.hAPP_real_bool _let_21 _let_27)) (forall ((P_1 tptp.fun_int_bool) (K_2 tptp.int) (I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_2) I)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.plus_plus_int K_2) tptp.one_one_int))) (=> (forall ((I_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_2) I_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_1)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.plus_plus_int I_1) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 I)))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_15 tptp.tn)) (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)))) _let_26 (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 ((I_2 tptp.nat) (J_2 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_2) J_2)) I_2)))) (forall ((J_2 tptp.nat) (I_2 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_2) I_2)) I_2)))) (forall ((K tptp.int)) (= (tptp.number_number_of_int K) K)) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (not (= Ma Na)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) Na)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) Ma))))) (forall ((M_1 tptp.nat) (N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_1) N_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) M_1))) (forall ((X tptp.nat) (Y tptp.nat) (Z_2 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat X))) (let ((_let_2 (tptp.plus_plus_nat Y))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Z_2)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Z_2)))))) (forall ((M_1 tptp.nat) (N_1 tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat M_1))) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 N_1)) K) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) K))))) (forall ((K_2 tptp.nat) (Ma tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat K_2))) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 Na)) (= Ma Na)))) (forall ((Ma tptp.nat) (K_2 tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat Ma) K_2) (tptp.hAPP_nat_nat (tptp.plus_plus_nat Na) K_2)) (= Ma Na))) (forall ((K_2 tptp.nat) (Ma tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat K_2))) (= (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 Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) Na))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X) Y))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y) X))))) (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_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) M_1)) (not (= M_1 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 ((M_1 tptp.nat) (I_2 tptp.nat) (J_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_2) M_1)))))) (forall ((M_1 tptp.nat) (I_2 tptp.nat) (J_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_1) J_2)))))) (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_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 I_2) K)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_2) K))))) (forall ((K tptp.nat) (L tptp.nat) (I_2 tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K) L)) (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)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_2) L)))))) (forall ((M_1 tptp.nat) (N_1 tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K) L)) (=> (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_1) L) (tptp.hAPP_nat_nat (tptp.plus_plus_nat K) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_1))))) (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 (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_2) J_2)) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) K)))) (forall ((P_1 tptp.fun_nat_fun_nat_bool) (Ma tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool P_1 Na) Ma)))) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) Na)) _let_1) (=> (=> (= Ma Na) _let_1) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) Ma)) _let_1) _let_1))))) (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_1 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_1)) (not (= N_1 tptp.zero_zero_nat)))) (forall ((M_1 tptp.nat) (N_1 tptp.nat) (I_2 tptp.nat)) (let ((_let_1 (tptp.power_power_nat I_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) I_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M_1)) (tptp.hAPP_nat_nat _let_1 N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_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 ((Xa tptp.nat) (Na 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 Xa) Na))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Xa)) (= Na tptp.zero_zero_nat))))) (forall ((Ma tptp.nat) (Na 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) Na))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)))))) (forall ((Na tptp.nat)) (= (not (= Na tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Na)))) (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 ((Xa tptp.nat) (Na 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 Xa) Na))) (or (= Na tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Xa)))))) (forall ((Xa tptp.nat) (Ya tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Xa)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ya))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Xa) Ya)))) (forall ((Xa tptp.nat) (Wa 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 Wa))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat Xa) _let_2))) (or (= _let_2 tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Xa))))))) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) Na)))) (forall ((Va tptp.int) (V tptp.int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Va) V)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.number_number_of_nat Va)) (tptp.number_number_of_nat V))) (and (=> _let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) V))) _let_1)))) (forall ((X_15 tptp.real) (Y_12 tptp.real)) (=> (not (= X_15 Y_12)) (=> (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_15) Y_12))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_12) X_15))))) (forall ((X_15 tptp.int) (Y_12 tptp.int)) (=> (not (= X_15 Y_12)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_15) Y_12))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y_12) X_15))))) (forall ((M_1 tptp.nat) (N_1 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_1) N_1) M_1) (= N_1 tptp.zero_zero_nat))) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat Ma) Na) tptp.zero_zero_nat) (and (= Ma tptp.zero_zero_nat) (= Na tptp.zero_zero_nat)))) (forall ((M_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_1) tptp.zero_zero_nat) M_1)) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat tptp.zero_zero_nat) N_1) N_1)) (forall ((A_63 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real A_63) tptp.one_one_nat) A_63)) (forall ((A_63 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_63) tptp.one_one_nat) A_63)) (forall ((A_63 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int A_63) tptp.one_one_nat) A_63)) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_real tptp.semiri132038758t_real Ma) (tptp.hAPP_nat_real tptp.semiri132038758t_real Na)) (= Ma Na))) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat Ma) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat Na)) (= Ma Na))) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Na)) (= Ma Na))) (forall ((Xa tptp.nat) (Ya tptp.nat)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Xa) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ya)) (= Xa Ya))) (forall ((Xa tptp.nat) (Ya tptp.nat) (P_1 tptp.bool)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.if_nat P_1 Xa) Ya)))) (let ((_let_2 (tptp.hBOOL P_1))) (and (=> _let_2 (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Xa) _let_1)) (=> (not _let_2) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ya) _let_1)))))) (forall ((Va 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 Va))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) Va)))) (forall ((Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Na)))) (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)) _let_26 (not (= tptp.zero_zero_nat tptp.one_one_nat)) _let_25 (forall ((N_23 tptp.nat) (A_62 tptp.real)) (=> (not (= A_62 tptp.zero_zero_real)) (not (= (tptp.hAPP_nat_real (tptp.power_power_real A_62) N_23) tptp.zero_zero_real)))) (forall ((N_23 tptp.nat) (A_62 tptp.int)) (=> (not (= A_62 tptp.zero_zero_int)) (not (= (tptp.hAPP_nat_int (tptp.power_power_int A_62) N_23) tptp.zero_zero_int)))) (forall ((N_22 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.power_power_real tptp.one_one_real) N_22) tptp.one_one_real)) (forall ((N_22 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat tptp.one_one_nat) N_22) tptp.one_one_nat)) (forall ((N_22 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.power_power_int tptp.one_one_int) N_22) tptp.one_one_int)) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real tptp.semiri132038758t_real Ma)) (tptp.hAPP_nat_real tptp.semiri132038758t_real Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) Na)))) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat Ma)) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) Na)))) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) Na)))) (forall ((M_9 tptp.nat) (N_21 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_9) N_21)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real tptp.semiri132038758t_real M_9)) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_21))))) (forall ((M_9 tptp.nat) (N_21 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_9) N_21)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_9)) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_21))))) (forall ((M_9 tptp.nat) (N_21 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_9) N_21)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_9)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_21))))) (forall ((M_8 tptp.nat) (N_20 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real tptp.semiri132038758t_real M_8)) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_20))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_8) N_20)))) (forall ((M_8 tptp.nat) (N_20 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_8)) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_20))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_8) N_20)))) (forall ((M_8 tptp.nat) (N_20 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_8)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_20))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_8) N_20)))) (forall ((M_7 tptp.nat) (N_19 tptp.nat)) (= (tptp.hAPP_nat_real tptp.semiri132038758t_real (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_7) N_19)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real tptp.semiri132038758t_real M_7)) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_19)))) (forall ((M_7 tptp.nat) (N_19 tptp.nat)) (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_7) N_19)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_7)) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_19)))) (forall ((M_7 tptp.nat) (N_19 tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_7) N_19)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_7)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_19)))) (= (tptp.hAPP_nat_real tptp.semiri132038758t_real tptp.one_one_nat) tptp.one_one_real) (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat tptp.one_one_nat) tptp.one_one_nat) _let_24 (forall ((M_6 tptp.nat) (N_18 tptp.nat)) (= (tptp.hAPP_nat_real tptp.semiri132038758t_real (tptp.hAPP_nat_nat (tptp.power_power_nat M_6) N_18)) (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_nat_real tptp.semiri132038758t_real M_6)) N_18))) (forall ((M_6 tptp.nat) (N_18 tptp.nat)) (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat (tptp.hAPP_nat_nat (tptp.power_power_nat M_6) N_18)) (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_6)) N_18))) (forall ((M_6 tptp.nat) (N_18 tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.power_power_nat M_6) N_18)) (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_6)) N_18))) (= tptp.one_one_int _let_23) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.plus_plus_nat X) Y)))) (forall ((X tptp.nat) (N_1 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X)) N_1) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.power_power_nat X) N_1)))) (forall ((B_41 tptp.real) (C_31 tptp.real) (A_61 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_41))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_61)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_31)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real A_61) C_31))))))) (forall ((B_41 tptp.nat) (C_31 tptp.nat) (A_61 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_41))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_61)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_31)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_61) C_31))))))) (forall ((B_41 tptp.int) (C_31 tptp.int) (A_61 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_41))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_61)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_31)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int A_61) C_31))))))) (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 _let_22 tptp.zero_zero_int))) (tptp.hBOOL (tptp.hAPP_real_bool _let_21 tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_15 tptp.one_one_nat)) _let_20 (forall ((N_17 tptp.nat) (A_60 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_60)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_60) N_17)))))) (forall ((N_17 tptp.nat) (A_60 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_60)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_60) N_17)))))) _let_18 (forall ((A_59 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_59) (tptp.hAPP_real_real (tptp.plus_plus_real A_59) tptp.one_one_real)))) (forall ((A_59 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_59) (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_59) tptp.one_one_nat)))) (forall ((A_59 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_59) (tptp.hAPP_int_int (tptp.plus_plus_int A_59) tptp.one_one_int)))) (forall ((Ma tptp.nat) (Na tptp.nat) (A_24 tptp.real)) (let ((_let_1 (tptp.power_power_real A_24))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A_24)) (= (= (tptp.hAPP_nat_real _let_1 Ma) (tptp.hAPP_nat_real _let_1 Na)) (= Ma Na))))) (forall ((Ma tptp.nat) (Na tptp.nat) (A_24 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_24))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A_24)) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 Na)) (= Ma Na))))) (forall ((Ma tptp.nat) (Na tptp.nat) (A_24 tptp.int)) (let ((_let_1 (tptp.power_power_int A_24))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_24)) (= (= (tptp.hAPP_nat_int _let_1 Ma) (tptp.hAPP_nat_int _let_1 Na)) (= Ma Na))))) (forall ((Xa tptp.nat) (Ya tptp.nat) (B_21 tptp.real)) (let ((_let_1 (tptp.power_power_real B_21))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) B_21)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real _let_1 Xa)) (tptp.hAPP_nat_real _let_1 Ya))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Xa) Ya)))))) (forall ((Xa tptp.nat) (Ya tptp.nat) (B_21 tptp.nat)) (let ((_let_1 (tptp.power_power_nat B_21))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) B_21)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 Xa)) (tptp.hAPP_nat_nat _let_1 Ya))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Xa) Ya)))))) (forall ((Xa tptp.nat) (Ya tptp.nat) (B_21 tptp.int)) (let ((_let_1 (tptp.power_power_int B_21))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B_21)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int _let_1 Xa)) (tptp.hAPP_nat_int _let_1 Ya))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Xa) Ya)))))) (forall ((M_5 tptp.nat) (N_16 tptp.nat) (A_58 tptp.real)) (let ((_let_1 (tptp.power_power_real A_58))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A_58)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real _let_1 M_5)) (tptp.hAPP_nat_real _let_1 N_16))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_5) N_16)))))) (forall ((M_5 tptp.nat) (N_16 tptp.nat) (A_58 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_58))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A_58)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M_5)) (tptp.hAPP_nat_nat _let_1 N_16))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_5) N_16)))))) (forall ((M_5 tptp.nat) (N_16 tptp.nat) (A_58 tptp.int)) (let ((_let_1 (tptp.power_power_int A_58))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_58)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int _let_1 M_5)) (tptp.hAPP_nat_int _let_1 N_16))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_5) N_16)))))) (forall ((A_57 tptp.real) (N_15 tptp.nat) (N_14 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_57))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_15) N_14)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A_57)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real _let_1 N_15)) (tptp.hAPP_nat_real _let_1 N_14))))))) (forall ((A_57 tptp.nat) (N_15 tptp.nat) (N_14 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_57))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_15) N_14)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A_57)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 N_15)) (tptp.hAPP_nat_nat _let_1 N_14))))))) (forall ((A_57 tptp.int) (N_15 tptp.nat) (N_14 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_57))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_15) N_14)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_57)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int _let_1 N_15)) (tptp.hAPP_nat_int _let_1 N_14))))))) (forall ((A_24 tptp.real) (Na tptp.nat)) (= (= (tptp.hAPP_nat_real (tptp.power_power_real A_24) Na) tptp.zero_zero_real) (and (= A_24 tptp.zero_zero_real) (not (= Na tptp.zero_zero_nat))))) (forall ((A_24 tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_24) Na) tptp.zero_zero_nat) (and (= A_24 tptp.zero_zero_nat) (not (= Na tptp.zero_zero_nat))))) (forall ((A_24 tptp.int) (Na tptp.nat)) (= (= (tptp.hAPP_nat_int (tptp.power_power_int A_24) Na) tptp.zero_zero_int) (and (= A_24 tptp.zero_zero_int) (not (= Na tptp.zero_zero_nat))))) (forall ((M_4 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real tptp.semiri132038758t_real M_4)) tptp.zero_zero_real)))) (forall ((M_4 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_4)) tptp.zero_zero_nat)))) (forall ((M_4 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_4)) tptp.zero_zero_int)))) (forall ((A_56 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real A_56) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A_56 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_56) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A_56 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int A_56) tptp.zero_zero_nat) tptp.one_one_int)) (= (tptp.hAPP_nat_real tptp.semiri132038758t_real tptp.zero_zero_nat) tptp.zero_zero_real) (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat tptp.zero_zero_nat) tptp.zero_zero_nat) _let_17 (= tptp.zero_zero_int _let_16) (tptp.hBOOL (tptp.hAPP_nat_bool _let_15 _let_3)) (forall ((K tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) K)) (exists ((N tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= K (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)))))) (forall ((I_2 tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_2)) (exists ((K_1 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_2) K_1) J_2))))) (forall ((Xa tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.power_power_nat Xa) Na) tptp.one_one_nat) (or (= Xa tptp.one_one_nat) (= Na tptp.zero_zero_nat)))) (forall ((X_14 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real X_14) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((X_14 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat X_14) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((X_14 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int X_14) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((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 (tptp.hAPP_real_real (tptp.plus_plus_real A_24) A_24))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_24))))) (forall ((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 (tptp.hAPP_int_int (tptp.plus_plus_int A_24) A_24))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_24))))) (forall ((A_24 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_24) A_24)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_24) tptp.zero_zero_real)))) (forall ((A_24 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_24) A_24)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_24) tptp.zero_zero_int)))) (forall ((Xa tptp.real)) (= (= tptp.zero_zero_real Xa) (= Xa tptp.zero_zero_real))) (forall ((Xa tptp.nat)) (= (= tptp.zero_zero_nat Xa) (= Xa tptp.zero_zero_nat))) (forall ((Xa tptp.int)) (= (= tptp.zero_zero_int Xa) (= Xa tptp.zero_zero_int))) (forall ((B_40 tptp.real) (A_55 tptp.real) (C_30 tptp.real)) (=> (= (tptp.hAPP_real_real (tptp.plus_plus_real B_40) A_55) (tptp.hAPP_real_real (tptp.plus_plus_real C_30) A_55)) (= B_40 C_30))) (forall ((B_40 tptp.nat) (A_55 tptp.nat) (C_30 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_40) A_55) (tptp.hAPP_nat_nat (tptp.plus_plus_nat C_30) A_55)) (= B_40 C_30))) (forall ((B_40 tptp.int) (A_55 tptp.int) (C_30 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.plus_plus_int B_40) A_55) (tptp.hAPP_int_int (tptp.plus_plus_int C_30) A_55)) (= B_40 C_30))) (forall ((A_54 tptp.real) (B_39 tptp.real) (C_29 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_54))) (=> (= (tptp.hAPP_real_real _let_1 B_39) (tptp.hAPP_real_real _let_1 C_29)) (= B_39 C_29)))) (forall ((A_54 tptp.nat) (B_39 tptp.nat) (C_29 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_54))) (=> (= (tptp.hAPP_nat_nat _let_1 B_39) (tptp.hAPP_nat_nat _let_1 C_29)) (= B_39 C_29)))) (forall ((A_54 tptp.int) (B_39 tptp.int) (C_29 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_54))) (=> (= (tptp.hAPP_int_int _let_1 B_39) (tptp.hAPP_int_int _let_1 C_29)) (= B_39 C_29)))) (forall ((A_53 tptp.real) (B_38 tptp.real) (C_28 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_53))) (=> (= (tptp.hAPP_real_real _let_1 B_38) (tptp.hAPP_real_real _let_1 C_28)) (= B_38 C_28)))) (forall ((A_53 tptp.nat) (B_38 tptp.nat) (C_28 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_53))) (=> (= (tptp.hAPP_nat_nat _let_1 B_38) (tptp.hAPP_nat_nat _let_1 C_28)) (= B_38 C_28)))) (forall ((A_53 tptp.int) (B_38 tptp.int) (C_28 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_53))) (=> (= (tptp.hAPP_int_int _let_1 B_38) (tptp.hAPP_int_int _let_1 C_28)) (= B_38 C_28)))) (forall ((A_52 tptp.real) (B_37 tptp.real) (C_27 tptp.real) (D_6 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_52))) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_37)) (tptp.hAPP_real_real (tptp.plus_plus_real C_27) D_6)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 C_27)) (tptp.hAPP_real_real (tptp.plus_plus_real B_37) D_6))))) (forall ((A_52 tptp.nat) (B_37 tptp.nat) (C_27 tptp.nat) (D_6 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_52))) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_37)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat C_27) D_6)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 C_27)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_37) D_6))))) (forall ((A_52 tptp.int) (B_37 tptp.int) (C_27 tptp.int) (D_6 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_52))) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_37)) (tptp.hAPP_int_int (tptp.plus_plus_int C_27) D_6)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 C_27)) (tptp.hAPP_int_int (tptp.plus_plus_int B_37) D_6))))) (forall ((B_21 tptp.real) (A_24 tptp.real) (C_15 tptp.real)) (= (= (tptp.hAPP_real_real (tptp.plus_plus_real B_21) A_24) (tptp.hAPP_real_real (tptp.plus_plus_real C_15) A_24)) (= B_21 C_15))) (forall ((B_21 tptp.nat) (A_24 tptp.nat) (C_15 tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_21) A_24) (tptp.hAPP_nat_nat (tptp.plus_plus_nat C_15) A_24)) (= B_21 C_15))) (forall ((B_21 tptp.int) (A_24 tptp.int) (C_15 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.plus_plus_int B_21) A_24) (tptp.hAPP_int_int (tptp.plus_plus_int C_15) A_24)) (= B_21 C_15))) (forall ((A_24 tptp.real) (B_21 tptp.real) (C_15 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_24))) (= (= (tptp.hAPP_real_real _let_1 B_21) (tptp.hAPP_real_real _let_1 C_15)) (= B_21 C_15)))) (forall ((A_24 tptp.nat) (B_21 tptp.nat) (C_15 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_24))) (= (= (tptp.hAPP_nat_nat _let_1 B_21) (tptp.hAPP_nat_nat _let_1 C_15)) (= B_21 C_15)))) (forall ((A_24 tptp.int) (B_21 tptp.int) (C_15 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_24))) (= (= (tptp.hAPP_int_int _let_1 B_21) (tptp.hAPP_int_int _let_1 C_15)) (= B_21 C_15)))) (forall ((A_51 tptp.real) (B_36 tptp.real) (C_26 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_51))) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_36)) C_26) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 C_26)) B_36)))) (forall ((A_51 tptp.nat) (B_36 tptp.nat) (C_26 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_51))) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_36)) C_26) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 C_26)) B_36)))) (forall ((A_51 tptp.int) (B_36 tptp.int) (C_26 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_51))) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_36)) C_26) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 C_26)) B_36)))) (forall ((A_50 tptp.real) (B_35 tptp.real) (C_25 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_50))) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_35)) C_25) (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real B_35) C_25))))) (forall ((A_50 tptp.nat) (B_35 tptp.nat) (C_25 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_50))) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_35)) C_25) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_35) C_25))))) (forall ((A_50 tptp.int) (B_35 tptp.int) (C_25 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_50))) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_35)) C_25) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int B_35) C_25))))) (forall ((A_49 tptp.real) (B_34 tptp.real) (C_24 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_49))) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_34)) C_24) (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real B_34) C_24))))) (forall ((A_49 tptp.nat) (B_34 tptp.nat) (C_24 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_49))) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_34)) C_24) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_34) C_24))))) (forall ((A_49 tptp.int) (B_34 tptp.int) (C_24 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_49))) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_34)) C_24) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int B_34) C_24))))) (forall ((A_48 tptp.real) (C_23 tptp.real) (D_5 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_48))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real C_23) D_5)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 C_23)) D_5)))) (forall ((A_48 tptp.nat) (C_23 tptp.nat) (D_5 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_48))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat C_23) D_5)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 C_23)) D_5)))) (forall ((A_48 tptp.int) (C_23 tptp.int) (D_5 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_48))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int C_23) D_5)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 C_23)) D_5)))) (forall ((A_47 tptp.real) (C_22 tptp.real) (D_4 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_47))) (let ((_let_2 (tptp.plus_plus_real C_22))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real _let_2 D_4)) (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real _let_1 D_4)))))) (forall ((A_47 tptp.nat) (C_22 tptp.nat) (D_4 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_47))) (let ((_let_2 (tptp.plus_plus_nat C_22))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 D_4)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 D_4)))))) (forall ((A_47 tptp.int) (C_22 tptp.int) (D_4 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_47))) (let ((_let_2 (tptp.plus_plus_int C_22))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 D_4)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 D_4)))))) (forall ((A_46 tptp.real) (C_21 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real A_46) C_21) (tptp.hAPP_real_real (tptp.plus_plus_real C_21) A_46))) (forall ((A_46 tptp.nat) (C_21 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_46) C_21) (tptp.hAPP_nat_nat (tptp.plus_plus_nat C_21) A_46))) (forall ((A_46 tptp.int) (C_21 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int A_46) C_21) (tptp.hAPP_int_int (tptp.plus_plus_int C_21) A_46))) (forall ((Xa tptp.real)) (= (= tptp.one_one_real Xa) (= Xa tptp.one_one_real))) (forall ((Xa tptp.nat)) (= (= tptp.one_one_nat Xa) (= Xa tptp.one_one_nat))) (forall ((Xa tptp.int)) (= (= tptp.one_one_int Xa) (= Xa tptp.one_one_int))) (forall ((B_21 tptp.real) (A_24 tptp.real)) (= (= B_21 (tptp.hAPP_real_real (tptp.plus_plus_real B_21) A_24)) (= A_24 tptp.zero_zero_real))) (forall ((B_21 tptp.nat) (A_24 tptp.nat)) (= (= B_21 (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_21) A_24)) (= A_24 tptp.zero_zero_nat))) (forall ((B_21 tptp.int) (A_24 tptp.int)) (= (= B_21 (tptp.hAPP_int_int (tptp.plus_plus_int B_21) A_24)) (= A_24 tptp.zero_zero_int))) (forall ((A_45 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real A_45) tptp.zero_zero_real) A_45)) (forall ((A_45 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_45) tptp.zero_zero_nat) A_45)) (forall ((A_45 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int A_45) tptp.zero_zero_int) A_45)) (forall ((A_44 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real A_44) tptp.zero_zero_real) A_44)) (forall ((A_44 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_44) tptp.zero_zero_nat) A_44)) (forall ((A_44 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int A_44) tptp.zero_zero_int) A_44)) (forall ((A_43 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real A_43) tptp.zero_zero_real) A_43)) (forall ((A_43 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_43) tptp.zero_zero_nat) A_43)) (forall ((A_43 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int A_43) tptp.zero_zero_int) A_43)) (forall ((A_24 tptp.real)) (= (= tptp.zero_zero_real (tptp.hAPP_real_real (tptp.plus_plus_real A_24) A_24)) (= A_24 tptp.zero_zero_real))) (forall ((A_24 tptp.int)) (= (= tptp.zero_zero_int (tptp.hAPP_int_int (tptp.plus_plus_int A_24) A_24)) (= A_24 tptp.zero_zero_int))) (forall ((A_42 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real tptp.zero_zero_real) A_42) A_42)) (forall ((A_42 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat tptp.zero_zero_nat) A_42) A_42)) (forall ((A_42 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int tptp.zero_zero_int) A_42) A_42)) (forall ((A_41 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real tptp.zero_zero_real) A_41) A_41)) (forall ((A_41 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat tptp.zero_zero_nat) A_41) A_41)) (forall ((A_41 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int tptp.zero_zero_int) A_41) A_41)) (forall ((A_40 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real tptp.zero_zero_real) A_40) A_40)) (forall ((A_40 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat tptp.zero_zero_nat) A_40) A_40)) (forall ((A_40 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int tptp.zero_zero_int) A_40) A_40)) (forall ((C_20 tptp.real) (A_39 tptp.real) (B_33 tptp.real)) (let ((_let_1 (tptp.plus_plus_real C_20))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_39)) (tptp.hAPP_real_real _let_1 B_33))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_39) B_33))))) (forall ((C_20 tptp.nat) (A_39 tptp.nat) (B_33 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat C_20))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A_39)) (tptp.hAPP_nat_nat _let_1 B_33))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_39) B_33))))) (forall ((C_20 tptp.int) (A_39 tptp.int) (B_33 tptp.int)) (let ((_let_1 (tptp.plus_plus_int C_20))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_39)) (tptp.hAPP_int_int _let_1 B_33))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_39) B_33))))) (forall ((A_38 tptp.real) (C_19 tptp.real) (B_32 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_38) C_19)) (tptp.hAPP_real_real (tptp.plus_plus_real B_32) C_19))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_38) B_32)))) (forall ((A_38 tptp.nat) (C_19 tptp.nat) (B_32 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_38) C_19)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_32) C_19))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_38) B_32)))) (forall ((A_38 tptp.int) (C_19 tptp.int) (B_32 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_38) C_19)) (tptp.hAPP_int_int (tptp.plus_plus_int B_32) C_19))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_38) B_32)))) (forall ((C_18 tptp.real) (D_3 tptp.real) (A_37 tptp.real) (B_31 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_37) B_31)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_18) D_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.plus_plus_real A_37) C_18)) (tptp.hAPP_real_real (tptp.plus_plus_real B_31) D_3)))))) (forall ((C_18 tptp.nat) (D_3 tptp.nat) (A_37 tptp.nat) (B_31 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_37) B_31)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_18) D_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_37) C_18)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_31) D_3)))))) (forall ((C_18 tptp.int) (D_3 tptp.int) (A_37 tptp.int) (B_31 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_37) B_31)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_18) D_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int A_37) C_18)) (tptp.hAPP_int_int (tptp.plus_plus_int B_31) D_3)))))) (forall ((C_17 tptp.real) (A_36 tptp.real) (B_30 tptp.real)) (let ((_let_1 (tptp.plus_plus_real C_17))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_36) B_30)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_36)) (tptp.hAPP_real_real _let_1 B_30)))))) (forall ((C_17 tptp.nat) (A_36 tptp.nat) (B_30 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat C_17))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_36) B_30)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A_36)) (tptp.hAPP_nat_nat _let_1 B_30)))))) (forall ((C_17 tptp.int) (A_36 tptp.int) (B_30 tptp.int)) (let ((_let_1 (tptp.plus_plus_int C_17))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_36) B_30)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_36)) (tptp.hAPP_int_int _let_1 B_30)))))) (forall ((C_16 tptp.real) (A_35 tptp.real) (B_29 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_35) B_29)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.plus_plus_real A_35) C_16)) (tptp.hAPP_real_real (tptp.plus_plus_real B_29) C_16))))) (forall ((C_16 tptp.nat) (A_35 tptp.nat) (B_29 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_35) B_29)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_35) C_16)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_29) C_16))))) (forall ((C_16 tptp.int) (A_35 tptp.int) (B_29 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_35) B_29)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int A_35) C_16)) (tptp.hAPP_int_int (tptp.plus_plus_int B_29) C_16))))) (forall ((C_15 tptp.real) (A_24 tptp.real) (B_21 tptp.real)) (let ((_let_1 (tptp.plus_plus_real C_15))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_24)) (tptp.hAPP_real_real _let_1 B_21))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_24) B_21))))) (forall ((C_15 tptp.nat) (A_24 tptp.nat) (B_21 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat C_15))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A_24)) (tptp.hAPP_nat_nat _let_1 B_21))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_24) B_21))))) (forall ((C_15 tptp.int) (A_24 tptp.int) (B_21 tptp.int)) (let ((_let_1 (tptp.plus_plus_int C_15))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_24)) (tptp.hAPP_int_int _let_1 B_21))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_24) B_21))))) (forall ((A_24 tptp.real) (C_15 tptp.real) (B_21 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_24) C_15)) (tptp.hAPP_real_real (tptp.plus_plus_real B_21) C_15))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_24) B_21)))) (forall ((A_24 tptp.nat) (C_15 tptp.nat) (B_21 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_24) C_15)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_21) C_15))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_24) B_21)))) (forall ((A_24 tptp.int) (C_15 tptp.int) (B_21 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_24) C_15)) (tptp.hAPP_int_int (tptp.plus_plus_int B_21) C_15))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_24) B_21)))) (forall ((X_13 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real X_13) tptp.one_one_nat) X_13)) (forall ((X_13 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat X_13) tptp.one_one_nat) X_13)) (forall ((X_13 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int X_13) tptp.one_one_nat) X_13)) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.power_power_nat Ma) Na) tptp.zero_zero_nat) (and (not (= Na tptp.zero_zero_nat)) (= Ma tptp.zero_zero_nat)))) (forall ((B_28 tptp.real) (A_34 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_34) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_28) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.plus_plus_real A_34) B_28)) tptp.zero_zero_real))))) (forall ((B_28 tptp.nat) (A_34 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_34) tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_28) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_34) B_28)) tptp.zero_zero_nat))))) (forall ((B_28 tptp.int) (A_34 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_34) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_28) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int A_34) B_28)) tptp.zero_zero_int))))) (forall ((B_27 tptp.real) (A_33 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_33)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_27)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real A_33) B_27))))))) (forall ((B_27 tptp.nat) (A_33 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_33)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_27)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_33) B_27))))))) (forall ((B_27 tptp.int) (A_33 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_33)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_27)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int A_33) B_27))))))) (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_12 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_12)) (= (tptp.hAPP_nat_real (tptp.power_power_real X_12) N_1) A) (forall ((Y_11 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Y_11)) (= (tptp.hAPP_nat_real (tptp.power_power_real Y_11) N_1) A)) (= Y_11 X_12)))))))) (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 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) R)) (= (tptp.hAPP_nat_real (tptp.power_power_real R) N_1) A)))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_14 tptp.t)) (forall ((V_6 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.number_number_of_nat V_6)) tptp.one_one_nat))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_6) tptp.pls)))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (tptp.number_number_of_nat (tptp.succ V_6)))))))) (forall ((V_6 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat tptp.one_one_nat) (tptp.number_number_of_nat V_6)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_6) tptp.pls)))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (tptp.number_number_of_nat (tptp.succ V_6)))))))) (forall ((A_24 tptp.real) (C_15 tptp.real) (B_21 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 A_24) C_15)) (tptp.hAPP_real_real (tptp.plus_plus_real B_21) C_15))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_24) B_21)))) (forall ((A_24 tptp.nat) (C_15 tptp.nat) (B_21 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 A_24) C_15)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_21) C_15))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_24) B_21)))) (forall ((A_24 tptp.int) (C_15 tptp.int) (B_21 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 A_24) C_15)) (tptp.hAPP_int_int (tptp.plus_plus_int B_21) C_15))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_24) B_21)))) (forall ((C_15 tptp.real) (A_24 tptp.real) (B_21 tptp.real)) (let ((_let_1 (tptp.plus_plus_real C_15))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_24)) (tptp.hAPP_real_real _let_1 B_21))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_24) B_21))))) (forall ((C_15 tptp.nat) (A_24 tptp.nat) (B_21 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat C_15))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_24)) (tptp.hAPP_nat_nat _let_1 B_21))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_24) B_21))))) (forall ((C_15 tptp.int) (A_24 tptp.int) (B_21 tptp.int)) (let ((_let_1 (tptp.plus_plus_int C_15))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_24)) (tptp.hAPP_int_int _let_1 B_21))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_24) B_21))))) (forall ((C_14 tptp.real) (A_32 tptp.real) (B_26 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_32) B_26)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.plus_plus_real A_32) C_14)) (tptp.hAPP_real_real (tptp.plus_plus_real B_26) C_14))))) (forall ((C_14 tptp.nat) (A_32 tptp.nat) (B_26 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_32) B_26)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_32) C_14)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_26) C_14))))) (forall ((C_14 tptp.int) (A_32 tptp.int) (B_26 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_32) B_26)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.plus_plus_int A_32) C_14)) (tptp.hAPP_int_int (tptp.plus_plus_int B_26) C_14))))) (forall ((C_13 tptp.real) (A_31 tptp.real) (B_25 tptp.real)) (let ((_let_1 (tptp.plus_plus_real C_13))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_31) B_25)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_31)) (tptp.hAPP_real_real _let_1 B_25)))))) (forall ((C_13 tptp.nat) (A_31 tptp.nat) (B_25 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat C_13))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_31) B_25)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_31)) (tptp.hAPP_nat_nat _let_1 B_25)))))) (forall ((C_13 tptp.int) (A_31 tptp.int) (B_25 tptp.int)) (let ((_let_1 (tptp.plus_plus_int C_13))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_31) B_25)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_31)) (tptp.hAPP_int_int _let_1 B_25)))))) (forall ((C_12 tptp.real) (D_2 tptp.real) (A_30 tptp.real) (B_24 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_30) B_24)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_12) D_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.plus_plus_real A_30) C_12)) (tptp.hAPP_real_real (tptp.plus_plus_real B_24) D_2)))))) (forall ((C_12 tptp.nat) (D_2 tptp.nat) (A_30 tptp.nat) (B_24 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_30) B_24)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_12) D_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_30) C_12)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_24) D_2)))))) (forall ((C_12 tptp.int) (D_2 tptp.int) (A_30 tptp.int) (B_24 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_30) B_24)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_12) D_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.plus_plus_int A_30) C_12)) (tptp.hAPP_int_int (tptp.plus_plus_int B_24) D_2)))))) (forall ((A_29 tptp.real) (C_11 tptp.real) (B_23 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 A_29) C_11)) (tptp.hAPP_real_real (tptp.plus_plus_real B_23) C_11))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_29) B_23)))) (forall ((A_29 tptp.nat) (C_11 tptp.nat) (B_23 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 A_29) C_11)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_23) C_11))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_29) B_23)))) (forall ((A_29 tptp.int) (C_11 tptp.int) (B_23 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 A_29) C_11)) (tptp.hAPP_int_int (tptp.plus_plus_int B_23) C_11))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_29) B_23)))) (forall ((C_10 tptp.real) (A_28 tptp.real) (B_22 tptp.real)) (let ((_let_1 (tptp.plus_plus_real C_10))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_28)) (tptp.hAPP_real_real _let_1 B_22))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_28) B_22))))) (forall ((C_10 tptp.nat) (A_28 tptp.nat) (B_22 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat C_10))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_28)) (tptp.hAPP_nat_nat _let_1 B_22))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_28) B_22))))) (forall ((C_10 tptp.int) (A_28 tptp.int) (B_22 tptp.int)) (let ((_let_1 (tptp.plus_plus_int C_10))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_28)) (tptp.hAPP_int_int _let_1 B_22))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_28) B_22))))) (forall ((A_27 tptp.real) (N_13 tptp.nat) (N_12 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_27))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_13) N_12)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) A_27)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real _let_1 N_13)) (tptp.hAPP_nat_real _let_1 N_12))))))) (forall ((A_27 tptp.nat) (N_13 tptp.nat) (N_12 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_27))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_13) N_12)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.one_one_nat) A_27)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 N_13)) (tptp.hAPP_nat_nat _let_1 N_12))))))) (forall ((A_27 tptp.int) (N_13 tptp.nat) (N_12 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_27))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_13) N_12)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) A_27)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int _let_1 N_13)) (tptp.hAPP_nat_int _let_1 N_12))))))) (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_2 tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K_2)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_2) L_1)))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) 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_2 tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K_2)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_2) L_1)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_9 tptp.zero_zero_int)) (forall ((W tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) W))) (forall ((Z_2 tptp.int) (W tptp.int)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_2) W)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) Z_2)))) (forall ((K tptp.int) (I_2 tptp.int) (J_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 J_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int J_2) K)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K)))))) (forall ((Z_2 tptp.int) (W tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_2) W)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) Z_2)) (= Z_2 W)))) (forall ((Xa tptp.int) (Ya tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.number267125858f_real Xa)) (tptp.number267125858f_real Ya))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Xa) Ya)))) (forall ((Xa tptp.int) (Ya tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int Xa)) (tptp.number_number_of_int Ya))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Xa) Ya)))) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real tptp.semiri132038758t_real Ma)) (tptp.hAPP_nat_real tptp.semiri132038758t_real Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) Na)))) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat Ma)) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) Na)))) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) Na)))) (forall ((Z_3 tptp.int) (Wa tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_3) Wa)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_3) Wa)) (not (= Z_3 Wa))))) (forall ((K tptp.int) (I_2 tptp.int) (J_2 tptp.int)) (let ((_let_1 (tptp.plus_plus_int K))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_2) J_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 I_2)) (tptp.hAPP_int_int _let_1 J_2)))))) (forall ((K_2 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_2)) (tptp.number_number_of_int L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_2) L_1)))) (forall ((Ya tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.number267125858f_real Ya))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) Ya)))) (forall ((Ya 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 Ya))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) Ya)))) (forall ((Xa tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.number267125858f_real Xa)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Xa) tptp.pls)))) (forall ((Xa tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int Xa)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Xa) tptp.pls)))) (forall ((A_26 tptp.real) (N_11 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_26))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_11) N_10)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_26)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_26) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real _let_1 N_10)) (tptp.hAPP_nat_real _let_1 N_11)))))))) (forall ((A_26 tptp.nat) (N_11 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_26))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_11) N_10)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_26)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_26) tptp.one_one_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 N_10)) (tptp.hAPP_nat_nat _let_1 N_11)))))))) (forall ((A_26 tptp.int) (N_11 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_26))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_11) N_10)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_26)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_26) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int _let_1 N_10)) (tptp.hAPP_nat_int _let_1 N_11)))))))) (forall ((Xa tptp.nat) (Ya tptp.nat) (B_21 tptp.real)) (let ((_let_1 (tptp.power_power_real B_21))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) B_21)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real _let_1 Xa)) (tptp.hAPP_nat_real _let_1 Ya))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Xa) Ya)))))) (forall ((Xa tptp.nat) (Ya tptp.nat) (B_21 tptp.nat)) (let ((_let_1 (tptp.power_power_nat B_21))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) B_21)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 Xa)) (tptp.hAPP_nat_nat _let_1 Ya))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Xa) Ya)))))) (forall ((Xa tptp.nat) (Ya tptp.nat) (B_21 tptp.int)) (let ((_let_1 (tptp.power_power_int B_21))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B_21)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int _let_1 Xa)) (tptp.hAPP_nat_int _let_1 Ya))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Xa) Ya)))))) (forall ((M_3 tptp.nat) (N_9 tptp.nat) (A_25 tptp.real)) (let ((_let_1 (tptp.power_power_real A_25))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A_25)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real _let_1 M_3)) (tptp.hAPP_nat_real _let_1 N_9))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_3) N_9)))))) (forall ((M_3 tptp.nat) (N_9 tptp.nat) (A_25 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_25))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A_25)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 M_3)) (tptp.hAPP_nat_nat _let_1 N_9))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_3) N_9)))))) (forall ((M_3 tptp.nat) (N_9 tptp.nat) (A_25 tptp.int)) (let ((_let_1 (tptp.power_power_int A_25))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_25)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int _let_1 M_3)) (tptp.hAPP_nat_int _let_1 N_9))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_3) N_9)))))) (forall ((Ya tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.number267125858f_real Ya))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 tptp.pls)) Ya)))) (forall ((Ya 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 Ya))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 tptp.pls)) Ya)))) (forall ((Xa tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.number267125858f_real Xa)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Xa) (tptp.bit1 tptp.pls))))) (forall ((Xa tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int Xa)) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Xa) (tptp.bit1 tptp.pls))))) (forall ((A_24 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.plus_plus_real A_24) A_24))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_24))))) (forall ((A_24 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 A_24) A_24))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_24))))) (forall ((A_24 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 A_24) A_24)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_24) tptp.zero_zero_real)))) (forall ((A_24 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 A_24) A_24)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_24) tptp.zero_zero_int)))) (forall ((B_20 tptp.real) (A_23 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_23)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_20)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real A_23) B_20))))))) (forall ((B_20 tptp.nat) (A_23 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_23)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_20)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_23) B_20))))))) (forall ((B_20 tptp.int) (A_23 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_23)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_20)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int A_23) B_20))))))) (forall ((Ya tptp.real) (Xa 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 Xa)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Ya)) (= (= (tptp.hAPP_real_real (tptp.plus_plus_real Xa) Ya) tptp.zero_zero_real) (and (= Xa tptp.zero_zero_real) (= Ya tptp.zero_zero_real))))))) (forall ((Ya tptp.nat) (Xa 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 Xa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ya)) (= (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat Xa) Ya) tptp.zero_zero_nat) (and (= Xa tptp.zero_zero_nat) (= Ya tptp.zero_zero_nat))))))) (forall ((Ya tptp.int) (Xa 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 Xa)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Ya)) (= (= (tptp.hAPP_int_int (tptp.plus_plus_int Xa) Ya) tptp.zero_zero_int) (and (= Xa tptp.zero_zero_int) (= Ya tptp.zero_zero_int))))))) (forall ((B_19 tptp.real) (C_9 tptp.real) (A_22 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_19))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_22)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_9)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real A_22) C_9))))))) (forall ((B_19 tptp.nat) (C_9 tptp.nat) (A_22 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_19))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_22)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_9)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_22) C_9))))))) (forall ((B_19 tptp.int) (C_9 tptp.int) (A_22 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_19))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_22)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_9)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int A_22) C_9))))))) (forall ((B_18 tptp.real) (A_21 tptp.real) (C_8 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_18))) (=> (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 _let_1 A_21)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real A_21) C_8))))))) (forall ((B_18 tptp.nat) (A_21 tptp.nat) (C_8 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_18))) (=> (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 _let_1 A_21)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_21) C_8))))))) (forall ((B_18 tptp.int) (A_21 tptp.int) (C_8 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_18))) (=> (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 _let_1 A_21)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int A_21) C_8))))))) (forall ((B_17 tptp.real) (A_20 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_20) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_17) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.plus_plus_real A_20) B_17)) tptp.zero_zero_real))))) (forall ((B_17 tptp.nat) (A_20 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_20) tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_17) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_20) B_17)) tptp.zero_zero_nat))))) (forall ((B_17 tptp.int) (A_20 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_20) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_17) 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 A_20) B_17)) tptp.zero_zero_int))))) (forall ((C_7 tptp.real) (D_1 tptp.real) (A_19 tptp.real) (B_16 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_19) B_16)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_7) D_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.plus_plus_real A_19) C_7)) (tptp.hAPP_real_real (tptp.plus_plus_real B_16) D_1)))))) (forall ((C_7 tptp.nat) (D_1 tptp.nat) (A_19 tptp.nat) (B_16 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_19) B_16)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_7) D_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_19) C_7)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_16) D_1)))))) (forall ((C_7 tptp.int) (D_1 tptp.int) (A_19 tptp.int) (B_16 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_19) B_16)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_7) D_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int A_19) C_7)) (tptp.hAPP_int_int (tptp.plus_plus_int B_16) D_1)))))) (forall ((C_6 tptp.real) (D tptp.real) (A_18 tptp.real) (B_15 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_18) B_15)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_6) D)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.plus_plus_real A_18) C_6)) (tptp.hAPP_real_real (tptp.plus_plus_real B_15) D)))))) (forall ((C_6 tptp.nat) (D tptp.nat) (A_18 tptp.nat) (B_15 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_18) B_15)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_6) D)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_18) C_6)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_15) D)))))) (forall ((C_6 tptp.int) (D tptp.int) (A_18 tptp.int) (B_15 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_18) B_15)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_6) D)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int A_18) C_6)) (tptp.hAPP_int_int (tptp.plus_plus_int B_15) D)))))) (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_14 tptp.zero_zero_int))) (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_13 (forall ((Va tptp.int) (Wa tptp.int)) (let ((_let_1 (tptp.number267125858f_real Va))) (let ((_let_2 (tptp.number267125858f_real Wa))) (= (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 ((Va tptp.int) (Wa tptp.int)) (let ((_let_1 (tptp.number_number_of_nat Va))) (let ((_let_2 (tptp.number_number_of_nat Wa))) (= (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 ((Va tptp.int) (Wa tptp.int)) (let ((_let_1 (tptp.number_number_of_int Va))) (let ((_let_2 (tptp.number_number_of_int Wa))) (= (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 ((N_8 tptp.nat) (A_17 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_17)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_17) N_8)))))) (forall ((N_8 tptp.nat) (A_17 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_17)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_17) N_8)))))) (forall ((N_8 tptp.nat) (A_17 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_17)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_17) N_8)))))) (forall ((N_7 tptp.nat) (A_16 tptp.real) (B_14 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_16) B_14)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_16)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real (tptp.power_power_real A_16) N_7)) (tptp.hAPP_nat_real (tptp.power_power_real B_14) N_7)))))) (forall ((N_7 tptp.nat) (A_16 tptp.nat) (B_14 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_16) B_14)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_16)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.power_power_nat A_16) N_7)) (tptp.hAPP_nat_nat (tptp.power_power_nat B_14) N_7)))))) (forall ((N_7 tptp.nat) (A_16 tptp.int) (B_14 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_16) B_14)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_16)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int (tptp.power_power_int A_16) N_7)) (tptp.hAPP_nat_int (tptp.power_power_int B_14) N_7)))))) (forall ((N_6 tptp.nat) (A_15 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_15)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_15) N_6)))))) (forall ((N_6 tptp.nat) (A_15 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_15)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_15) N_6)))))) (forall ((N_6 tptp.nat) (A_15 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_15)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_15) N_6)))))) (forall ((M_2 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.semiri132038758t_real M_2)))) (forall ((M_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_2)))) (forall ((M_2 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.semiri1621563631at_int M_2)))) (forall ((N_5 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.semiri132038758t_real N_5)))) (forall ((N_5 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_5)))) (forall ((N_5 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.semiri1621563631at_int N_5)))) (forall ((K_2 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_2))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K_2))))) (forall ((K_2 tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K_2)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_2) L_1)))) (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_2 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_2))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K_2))))) (forall ((K_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K_2)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_2) tptp.pls)))) _let_13 (forall ((Y tptp.int) (X 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)) (=> (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) Y))))))) (forall ((Z_4 tptp.int) (Z_2 tptp.int) (W_1 tptp.int) (W tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) W)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_4) Z_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int W_1) Z_4)) (tptp.hAPP_int_int (tptp.plus_plus_int W) Z_2)))))) (forall ((Z_2 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.semiri1621563631at_int Z_2)))) (forall ((P_1 tptp.fun_int_bool)) (= (exists ((X_12 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_12)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_12)))) (exists ((X_12 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_12)))))) (forall ((P_1 tptp.fun_int_bool)) (= (forall ((X_12 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_12)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_12)))) (forall ((X_12 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_12)))))) (forall ((N_1 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.semiri1621563631at_int N_1)))) (forall ((N_1 tptp.nat) (X 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)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int X) N_1)))))) (forall ((Wa tptp.int) (Z_3 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Wa) Z_3)) (exists ((N tptp.nat)) (= Z_3 (tptp.hAPP_int_int (tptp.plus_plus_int Wa) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)))))) (forall ((V_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) V_5)) (= (tptp.hAPP_real_real (tptp.plus_plus_real tptp.one_one_real) (tptp.number267125858f_real V_5)) (tptp.number267125858f_real (tptp.succ V_5))))) (forall ((V_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) V_5)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat tptp.one_one_nat) (tptp.number_number_of_nat V_5)) (tptp.number_number_of_nat (tptp.succ V_5))))) (forall ((V_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) V_5)) (= (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) (tptp.number_number_of_int V_5)) (tptp.number_number_of_int (tptp.succ V_5))))) (forall ((V_4 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) V_4)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real V_4)) tptp.one_one_real) (tptp.number267125858f_real (tptp.succ V_4))))) (forall ((V_4 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) V_4)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.number_number_of_nat V_4)) tptp.one_one_nat) (tptp.number_number_of_nat (tptp.succ V_4))))) (forall ((V_4 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) V_4)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_4)) tptp.one_one_int) (tptp.number_number_of_int (tptp.succ V_4))))) (forall ((B_13 tptp.real) (A_14 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_14)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B_13)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real A_14) B_13))))))) (forall ((B_13 tptp.nat) (A_14 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_14)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B_13)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_14) B_13))))))) (forall ((B_13 tptp.int) (A_14 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_14)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) B_13)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int A_14) B_13))))))) (forall ((B_12 tptp.real) (A_13 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_13)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_12)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real A_13) B_12))))))) (forall ((B_12 tptp.nat) (A_13 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_13)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_12)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_13) B_12))))))) (forall ((B_12 tptp.int) (A_13 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_13)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_12)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int A_13) B_12))))))) (forall ((B_11 tptp.real) (C_5 tptp.real) (A_12 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_12)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_11) C_5)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_11) (tptp.hAPP_real_real (tptp.plus_plus_real A_12) C_5)))))) (forall ((B_11 tptp.nat) (C_5 tptp.nat) (A_12 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_12)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_11) C_5)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_11) (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_12) C_5)))))) (forall ((B_11 tptp.int) (C_5 tptp.int) (A_12 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_12)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_11) C_5)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_11) (tptp.hAPP_int_int (tptp.plus_plus_int A_12) C_5)))))) (forall ((B_10 tptp.real) (C_4 tptp.real) (A_11 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_10))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_11)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_4)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real A_11) C_4))))))) (forall ((B_10 tptp.nat) (C_4 tptp.nat) (A_11 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_10))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_11)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_4)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_11) C_4))))))) (forall ((B_10 tptp.int) (C_4 tptp.int) (A_11 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_10))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_11)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_4)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int A_11) C_4))))))) (forall ((B_9 tptp.real) (A_10 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_10) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_9) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.plus_plus_real A_10) B_9)) tptp.zero_zero_real))))) (forall ((B_9 tptp.nat) (A_10 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_10) tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_9) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_10) B_9)) tptp.zero_zero_nat))))) (forall ((B_9 tptp.int) (A_10 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_10) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_9) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int A_10) B_9)) tptp.zero_zero_int))))) (forall ((B_8 tptp.real) (A_9 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_9) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_8) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.plus_plus_real A_9) B_8)) tptp.zero_zero_real))))) (forall ((B_8 tptp.nat) (A_9 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_9) tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_8) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_9) B_8)) tptp.zero_zero_nat))))) (forall ((B_8 tptp.int) (A_9 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_9) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_8) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int A_9) B_8)) tptp.zero_zero_int))))) (forall ((A_8 tptp.real) (N_4 tptp.nat) (B_7 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real (tptp.power_power_real A_8) N_4)) (tptp.hAPP_nat_real (tptp.power_power_real B_7) N_4))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B_7)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_8) B_7))))) (forall ((A_8 tptp.nat) (N_4 tptp.nat) (B_7 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.power_power_nat A_8) N_4)) (tptp.hAPP_nat_nat (tptp.power_power_nat B_7) N_4))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B_7)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_8) B_7))))) (forall ((A_8 tptp.int) (N_4 tptp.nat) (B_7 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int (tptp.power_power_int A_8) N_4)) (tptp.hAPP_nat_int (tptp.power_power_int B_7) N_4))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) B_7)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_8) B_7))))) (forall ((Va tptp.int)) (= (= tptp.zero_zero_nat (tptp.number_number_of_nat Va)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Va) tptp.pls)))) (forall ((Va tptp.int)) (= (= (tptp.number_number_of_nat Va) tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Va) tptp.pls)))) (forall ((K_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) (tptp.bit1 K_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) K_2)))) (forall ((K_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K_2)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_2) tptp.pls)))) (forall ((K_2 tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 K_2)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_2) 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 ((K_2 tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K_2)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_2) L_1)))) (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 ((Z_3 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) Z_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Z_3)))) (forall ((Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Na)) tptp.zero_zero_int)) (= Na tptp.zero_zero_nat))) (= (tptp.succ tptp.pls) _let_1) (forall ((K tptp.int)) (= (tptp.succ (tptp.bit0 K)) (tptp.bit1 K))) (forall ((K tptp.int)) (= (tptp.succ (tptp.bit1 K)) (tptp.bit0 (tptp.succ K)))) (forall ((Wa tptp.int) (Z_3 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Wa) (tptp.hAPP_int_int (tptp.plus_plus_int Z_3) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Wa) Z_3)))) (forall ((Wa tptp.int) (Z_3 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 Wa) tptp.one_one_int)) Z_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Wa) Z_3)))) (forall ((W tptp.int) (Z_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W) Z_2)) (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_2)))) (forall ((K tptp.int)) (= (tptp.succ K) (tptp.hAPP_int_int (tptp.plus_plus_int K) tptp.one_one_int))) (forall ((A_7 tptp.real) (N_3 tptp.nat) (B_6 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (tptp.hAPP_nat_real (tptp.power_power_real A_7) N_3) (tptp.hAPP_nat_real (tptp.power_power_real B_6) N_3)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_7)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_3)) (= A_7 B_6))))))) (forall ((A_7 tptp.nat) (N_3 tptp.nat) (B_6 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_7) N_3) (tptp.hAPP_nat_nat (tptp.power_power_nat B_6) N_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_7)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_3)) (= A_7 B_6))))))) (forall ((A_7 tptp.int) (N_3 tptp.nat) (B_6 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (tptp.hAPP_nat_int (tptp.power_power_int A_7) N_3) (tptp.hAPP_nat_int (tptp.power_power_int B_6) N_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_7)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_3)) (= A_7 B_6))))))) (forall ((V_3 tptp.int) (V_2 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_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_3)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real V_2)) (tptp.number267125858f_real V_3)) (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int V_2) V_3))))))) (forall ((V_3 tptp.int) (V_2 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_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_3)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.number_number_of_nat V_2)) (tptp.number_number_of_nat V_3)) (tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.plus_plus_int V_2) V_3))))))) (forall ((V_3 tptp.int) (V_2 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_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_3)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_2)) (tptp.number_number_of_int V_3)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V_2) V_3))))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_9 _let_12)) (forall ((Z_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z_2)) (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_2))))) (forall ((K_3 tptp.int)) (= (tptp.number267125858f_real (tptp.succ K_3)) (tptp.hAPP_real_real (tptp.plus_plus_real tptp.one_one_real) (tptp.number267125858f_real K_3)))) (forall ((K_3 tptp.int)) (= (tptp.number_number_of_int (tptp.succ K_3)) (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) (tptp.number_number_of_int K_3)))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit1 K)) (tptp.bit1 L)) (tptp.bit0 (tptp.hAPP_int_int (tptp.plus_plus_int K) (tptp.succ L))))) (forall ((N_2 tptp.nat) (A_6 tptp.real) (B_5 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_6) B_5)) (=> (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_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real (tptp.power_power_real A_6) N_2)) (tptp.hAPP_nat_real (tptp.power_power_real B_5) N_2))))))) (forall ((N_2 tptp.nat) (A_6 tptp.nat) (B_5 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_6) B_5)) (=> (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) N_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.power_power_nat A_6) N_2)) (tptp.hAPP_nat_nat (tptp.power_power_nat B_5) N_2))))))) (forall ((N_2 tptp.nat) (A_6 tptp.int) (B_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_6) B_5)) (=> (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_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int (tptp.power_power_int A_6) N_2)) (tptp.hAPP_nat_int (tptp.power_power_int B_5) N_2))))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_9 _let_10)) (forall ((X tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X) (tptp.hAPP_nat_int (tptp.power_power_int X) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))))) (forall ((A_5 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_5) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))))) (forall ((A_5 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_5) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))))) (forall ((X_11 tptp.real) (Y_10 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_11) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_10) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y_10)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_11) Y_10)))))) (forall ((X_11 tptp.nat) (Y_10 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_11) _let_1)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_10) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) Y_10)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_11) Y_10)))))) (forall ((X_11 tptp.int) (Y_10 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_11) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y_10) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y_10)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_11) Y_10)))))) (forall ((X_10 tptp.real) (Y_9 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_10) _let_2) (tptp.hAPP_nat_real (tptp.power_power_real Y_9) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_10)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_9)) (= X_10 Y_9))))))) (forall ((X_10 tptp.nat) (Y_9 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_10) _let_2) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_9) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_10)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_9)) (= X_10 Y_9))))))) (forall ((X_10 tptp.int) (Y_9 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_10) _let_2) (tptp.hAPP_nat_int (tptp.power_power_int Y_9) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_10)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_9)) (= X_10 Y_9))))))) (forall ((V_1 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_real tptp.semiri132038758t_real (tptp.number_number_of_nat V_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.number_number_of_int V_1))))) (and (=> _let_2 (= _let_1 (tptp.number267125858f_real V_1))) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((V_1 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.number_number_of_nat V_1)))) (let ((_let_2 (tptp.number_number_of_int V_1))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_2)))) (and (=> _let_3 (= _let_1 _let_2)) (=> (not _let_3) (= _let_1 tptp.zero_zero_int))))))) (forall ((X_9 tptp.real) (Y_8 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_9) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_8) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y_8)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_9) Y_8)))))) (forall ((X_9 tptp.nat) (Y_8 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_9) _let_1)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_8) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) Y_8)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_9) Y_8)))))) (forall ((X_9 tptp.int) (Y_8 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_9) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y_8) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y_8)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_9) Y_8)))))) (forall ((X_8 tptp.real) (Y_7 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_8) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_7) _let_1)))))) (forall ((X_8 tptp.int) (Y_7 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_8) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y_7) _let_1)))))) (forall ((Xa tptp.real) (Ya 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 Xa) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Ya) _let_1))) tptp.zero_zero_real)) (and (= Xa tptp.zero_zero_real) (= Ya tptp.zero_zero_real))))) (forall ((Xa tptp.int) (Ya 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 Xa) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Ya) _let_1))) tptp.zero_zero_int)) (and (= Xa tptp.zero_zero_int) (= Ya tptp.zero_zero_int))))) (forall ((X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls))))) (or (= X tptp.zero_zero_int) (= X tptp.one_one_int))))) (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)))))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_9 _let_8)) (forall ((K tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (exists ((N tptp.nat)) (= K (tptp.hAPP_nat_int tptp.semiri1621563631at_int N))))) (forall ((K tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (not (forall ((N tptp.nat)) (not (= K (tptp.hAPP_nat_int tptp.semiri1621563631at_int N))))))) (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_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 ((Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) tptp.zero_zero_nat)) (= Na tptp.zero_zero_nat))) (forall ((M_1 tptp.nat) (N_1 tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_1)) (= M_1 N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N_1)))) (forall ((M_1 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N_1)) (=> (not (= M_1 N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_1))))) (forall ((M_1 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N_1)))) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) Na)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) Na)) (= Ma Na)))) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) Na)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) Na)) (not (= Ma Na))))) (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 ((M_1 tptp.nat) (N_1 tptp.nat)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M_1)))) (forall ((M_1 tptp.nat) (N_1 tptp.nat)) (=> (= M_1 N_1) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N_1)))) (forall ((K tptp.nat) (I_2 tptp.nat) (J_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_2) K)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 K)))))) (forall ((M_1 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M_1)) (= M_1 N_1)))) (forall ((Xa tptp.real) (Ya tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Xa) Ya)) (or (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Xa) Ya)) (= Xa Ya)))) (forall ((Xa tptp.real) (Ya tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Xa) Ya)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Xa) Ya)) (not (= Xa Ya))))) (forall ((N_1 tptp.nat) (M_1 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_1) N_1)))) (forall ((N_1 tptp.nat) (M_1 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_1)))) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) Na)) (exists ((K_1 tptp.nat)) (= Na (tptp.hAPP_nat_nat (tptp.plus_plus_nat Ma) K_1))))) (forall ((K_2 tptp.nat) (Ma tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat K_2))) (= (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 Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) Na))))) (forall ((M_1 tptp.nat) (I_2 tptp.nat) (J_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_2) M_1)))))) (forall ((M_1 tptp.nat) (I_2 tptp.nat) (J_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_1) J_2)))))) (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.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)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_2) K))))) (forall ((K tptp.nat) (L 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 K) 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_2) K)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_2) L)))))) (forall ((M_1 tptp.nat) (K 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_1) K)) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) N_1)))) (forall ((M_1 tptp.nat) (K 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_1) K)) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N_1)))) (forall ((M_1 tptp.nat) (K 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_1) K)) N_1)) (not (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) N_1))))))) (forall ((Z_2 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.plus_plus_real Z_2))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) Y)) (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)))))) (forall ((Xa tptp.nat) (Ya tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Xa)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ya))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Xa) Ya)))) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) Na)))) (forall ((Va tptp.int) (V tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Va))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.number_number_of_nat Va)) (tptp.number_number_of_nat V))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 tptp.pls)))))) (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 ((P_2 tptp.bool) (P_1 tptp.bool) (Xa tptp.int)) (let ((_let_1 (tptp.hBOOL P_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Xa)))) (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_2 tptp.bool) (P_1 tptp.bool) (Xa tptp.int)) (let ((_let_1 (tptp.hBOOL P_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Xa)))) (let ((_let_3 (tptp.hBOOL P_1))) (=> (=> _let_2 (= _let_3 _let_1)) (= (=> _let_2 _let_3) (=> _let_2 _let_1))))))) (forall ((Na 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 Na)) (exists ((K_1 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_1) Na)) (forall ((I_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) K_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 I_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat K_1) tptp.one_one_nat)))))))) (forall ((Z_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z_2)) (not (forall ((M tptp.nat)) (not (= Z_2 (tptp.hAPP_nat_int tptp.semiri1621563631at_int M))))))) (forall ((Ma tptp.nat) (K_2 tptp.nat) (F tptp.fun_nat_nat)) (=> (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat F M)) (tptp.hAPP_nat_nat F 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 F Ma)) K_2)) (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat (tptp.plus_plus_nat Ma) K_2)))))) (forall ((W tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real W) W))) (forall ((Z_2 tptp.real) (W tptp.real)) (or (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Z_2) W)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real W) Z_2)))) (forall ((K tptp.real) (I_2 tptp.real) (J_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real I_2))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 J_2)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real J_2) K)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 K)))))) (forall ((Z_2 tptp.real) (W tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Z_2) W)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real W) Z_2)) (= Z_2 W)))) (forall ((P_1 tptp.fun_int_bool) (K_2 tptp.int) (I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_2) I)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 K_2)) (=> (forall ((I_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_2) I_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_1)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.plus_plus_int I_1) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 I)))))) (forall ((Na 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 Na)) (exists ((K_1 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) Na)) (forall ((I_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) K_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 I_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 K_1))))))) (forall ((I tptp.nat) (J tptp.nat) (F tptp.fun_nat_nat)) (=> (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)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat F I_1)) (tptp.hAPP_nat_nat F J_1))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat F I)) (tptp.hAPP_nat_nat F J)))))) (forall ((X_7 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_7) X_7))) (forall ((X_7 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_7) X_7))) (forall ((X_7 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_7) X_7))) (forall ((X_6 tptp.real) (Y_6 tptp.real)) (=> (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_6) Y_6))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_6) X_6)))) (forall ((X_6 tptp.nat) (Y_6 tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_6) Y_6))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_6) X_6)))) (forall ((X_6 tptp.int) (Y_6 tptp.int)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_6) Y_6))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_6) X_6)))) (forall ((Z_1 tptp.real) (Y_5 tptp.real) (X_5 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Z_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_5) X_5)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_5)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_5)))))) (forall ((Z_1 tptp.nat) (Y_5 tptp.nat) (X_5 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Z_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_5) X_5)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_5)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_5)))))) (forall ((Z_1 tptp.int) (Y_5 tptp.int) (X_5 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_5) X_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_5)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_5)))))) (forall ((Y_4 tptp.real) (X_4 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_4) X_4)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_4) Y_4)) (= X_4 Y_4)))) (forall ((Y_4 tptp.nat) (X_4 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_4) X_4)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_4) Y_4)) (= X_4 Y_4)))) (forall ((Y_4 tptp.int) (X_4 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_4) X_4)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_4) Y_4)) (= X_4 Y_4)))) (forall ((Z tptp.real) (X_3 tptp.real) (Y_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real 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) Z)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Z)))))) (forall ((Z tptp.nat) (X_3 tptp.nat) (Y_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_3) Z)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z)))))) (forall ((Z tptp.int) (X_3 tptp.int) (Y_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int 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) Z)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z)))))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_2) X_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_2) X_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_2) X_2)) (= X_2 Y_2)))) (forall ((C_3 tptp.real) (B_4 tptp.real) (A_4 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_4) A_4)) (=> (= B_4 C_3) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_3) A_4))))) (forall ((C_3 tptp.nat) (B_4 tptp.nat) (A_4 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_4) A_4)) (=> (= B_4 C_3) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_3) A_4))))) (forall ((C_3 tptp.int) (B_4 tptp.int) (A_4 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_4) A_4)) (=> (= B_4 C_3) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_3) A_4))))) (forall ((C_2 tptp.real) (A_3 tptp.real) (B_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_3))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_3)) (=> (= B_3 C_2) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_2)))))) (forall ((C_2 tptp.nat) (A_3 tptp.nat) (B_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_3)) (=> (= B_3 C_2) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_2)))))) (forall ((C_2 tptp.int) (A_3 tptp.int) (B_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_3)) (=> (= B_3 C_2) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_2)))))) (forall ((C_1 tptp.real) (A_2 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_1))) (=> (= A_2 B_2) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_2)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_2)))))) (forall ((C_1 tptp.nat) (A_2 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_1))) (=> (= A_2 B_2) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_2)))))) (forall ((C_1 tptp.int) (A_2 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_1))) (=> (= A_2 B_2) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_2)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_2)))))) (forall ((C tptp.real) (A_1 tptp.real) (B_1 tptp.real)) (=> (= A_1 B_1) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_1) C)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_1) C))))) (forall ((C tptp.nat) (A_1 tptp.nat) (B_1 tptp.nat)) (=> (= A_1 B_1) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_1) C)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_1) C))))) (forall ((C tptp.int) (A_1 tptp.int) (B_1 tptp.int)) (=> (= A_1 B_1) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_1) C)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_1) C))))) (forall ((Ya tptp.real) (Xa tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Ya) Xa)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Xa) Ya)) (= Xa Ya)))) (forall ((Ya tptp.nat) (Xa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ya) Xa)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Xa) Ya)) (= Xa Ya)))) (forall ((Ya tptp.int) (Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Ya) Xa)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Xa) Ya)) (= Xa Ya)))) (forall ((X_1 tptp.int) (Y_1 tptp.int)) (=> (= X_1 Y_1) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) Y_1)))) (forall ((D2 tptp.real) (D1 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 D1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 D2)) (exists ((E tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real E))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 D1)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 D2))))))))) (forall ((X tptp.real) (Y 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.sqrt (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) _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.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.times_times_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 ((K tptp.int) (L tptp.int)) (= (tptp.times_times_int (tptp.bit1 K) L) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit0 (tptp.times_times_int K L))) L))) (forall ((X 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)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.sqrt X)))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (not (= (tptp.sqrt X) tptp.zero_zero_real)))) (forall ((Xa tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.sqrt Xa)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Xa) tptp.zero_zero_real)))) (forall ((Ya 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.sqrt Ya))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Ya))))) (forall ((Xa tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.sqrt Xa)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Xa) tptp.one_one_real)))) (forall ((Ya 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 (tptp.sqrt Ya))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Ya))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.if_nat tptp.fTrue X) Y) X)) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.if_nat tptp.fFalse X) Y) Y)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) _let_7 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.66/1.22 )
% 0.66/1.22 % SZS output end Proof for NUM925_2
% 0.66/1.22 % cvc5---1.0.5 exiting
% 0.66/1.22 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------