TSTP Solution File: NUM925_3 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM925_3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n011.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 10:49:05 EDT 2023
% Result : Theorem 1.71s 1.94s
% Output : Proof 1.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.28 % Problem : NUM925_3 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.29 % Command : do_cvc5 %s %d
% 0.29/0.50 % Computer : n011.cluster.edu
% 0.29/0.50 % Model : x86_64 x86_64
% 0.29/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.29/0.50 % Memory : 8042.1875MB
% 0.29/0.50 % OS : Linux 3.10.0-693.el7.x86_64
% 0.29/0.50 % CPULimit : 300
% 0.29/0.50 % WCLimit : 300
% 0.29/0.50 % DateTime : Fri Aug 25 17:13:08 EDT 2023
% 0.29/0.50 % CPUTime :
% 0.35/0.79 %----Proving TF0_NAR, FOF, or CNF
% 1.71/1.94 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.2UHfyc691K/cvc5---1.0.5_14482.p...
% 1.71/1.94 ------- get file name : TPTP file name is NUM925_3
% 1.71/1.94 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_14482.smt2...
% 1.71/1.94 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.71/1.94 % SZS status Theorem for NUM925_3
% 1.71/1.94 % SZS output start Proof for NUM925_3
% 1.71/1.94 (
% 1.71/1.94 (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 (tptp.hAPP_nat_int tptp.semiri1621563631at_int tptp.n)))) (let ((_let_5 (tptp.hAPP_nat_int (tptp.power_power_int _let_4) _let_3))) (let ((_let_6 (not (not (= _let_5 tptp.zero_zero_int))))) (let ((_let_7 (tptp.number_number_of_int tptp.pls))) (let ((_let_8 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_9 (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_2)) tptp.m) tptp.one_one_int))) (let ((_let_10 (tptp.hAPP_nat_int (tptp.power_power_int tptp.s1) _let_3))) (let ((_let_11 (tptp.hAPP_nat_int (tptp.power_power_int tptp.s) _let_3))) (let ((_let_12 (tptp.number_number_of_int tptp.min))) (let ((_let_13 (= (tptp.legendre _let_12 _let_9) tptp.one_one_int))) (let ((_let_14 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.quadRes _let_9) _let_12)))) (let ((_let_15 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.min))) (let ((_let_16 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (let ((_let_17 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.min))) (let ((_let_18 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls))) (let ((_let_19 (tptp.minus_minus_int _let_11 _let_12))) (let ((_let_20 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int _let_9))) (let ((_let_21 (tptp.plus_plus_int _let_11 tptp.one_one_int))) (let ((_let_22 (tptp.number_number_of_int _let_2))) (let ((_let_23 (tptp.times_times_int _let_9 _let_4))) (let ((_let_24 (tptp.times_times_int _let_9 tptp.t))) (let ((_let_25 (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu820444569sum2sq _let_23)))) (let ((_let_26 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_4) _let_9)))) (let ((_let_27 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_28 (tptp.hAPP_nat_int tptp.semiri1621563631at_int tptp.zero_zero_nat))) (let ((_let_29 (tptp.bit1 _let_1))) (let ((_let_30 (tptp.number_number_of_int _let_29))) (let ((_let_31 (tptp.number_number_of_nat _let_29))) (let ((_let_32 (tptp.nat_1 tptp.zero_zero_int))) (let ((_let_33 (tptp.minus_minus_nat (tptp.nat_1 tptp.t) tptp.one_one_nat))) (let ((_let_34 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_35 (= _let_28 tptp.zero_zero_int))) (let ((_let_36 (forall ((N_14 tptp.nat) (A_92 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_92)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_92) N_14)))))))) (let ((_let_37 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_38 (tptp.hBOOL (tptp.hAPP_int_bool _let_27 tptp.one_one_int)))) (let ((_let_39 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int))) (let ((_let_40 (tptp.hAPP_nat_int tptp.semiri1621563631at_int tptp.one_one_nat))) (let ((_let_41 (= _let_40 tptp.one_one_int))) (let ((_let_42 (not (= tptp.zero_zero_real tptp.one_one_real)))) (let ((_let_43 (not (= tptp.zero_zero_int tptp.one_one_int)))) (let ((_let_44 (tptp.plus_plus_real tptp.one_one_real tptp.one_one_real))) (let ((_let_45 (tptp.plus_plus_nat tptp.one_one_nat tptp.one_one_nat))) (let ((_let_46 (tptp.plus_plus_int tptp.one_one_int tptp.one_one_int))) (let ((_let_47 (tptp.number267125858f_real _let_1))) (let ((_let_48 (= _let_47 tptp.one_one_real))) (let ((_let_49 (tptp.number_number_of_nat _let_1))) (let ((_let_50 (= _let_49 tptp.one_one_nat))) (let ((_let_51 (tptp.number_number_of_int _let_1))) (let ((_let_52 (= _let_51 tptp.one_one_int))) (let ((_let_53 (forall ((A_1 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_1) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (not (= A_1 tptp.zero_zero_int)))))) (let ((_let_54 (tptp.number267125858f_real tptp.pls))) (let ((_let_55 (= tptp.zero_zero_int _let_7))) (let ((_let_56 (= _let_54 tptp.zero_zero_real))) (let ((_let_57 (= _let_7 tptp.zero_zero_int))) (let ((_let_58 (tptp.number_number_of_nat tptp.pls))) (let ((_let_59 (= _let_58 tptp.zero_zero_nat))) (let ((_let_60 (= tptp.one_one_int _let_51))) (let ((_let_61 (= _let_45 _let_3))) (let ((_let_62 (= _let_44 (tptp.number267125858f_real _let_2)))) (let ((_let_63 (= _let_46 _let_22))) (let ((_let_64 (forall ((A_1 tptp.int)) (= (= (tptp.hAPP_nat_int (tptp.power_power_int A_1) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.zero_zero_int) (= A_1 tptp.zero_zero_int))))) (let ((_let_65 (tptp.hBOOL (tptp.hAPP_int_bool _let_27 _let_4)))) (let ((_let_66 (= tptp.zero_zero_int _let_4))) (let ((_let_67 (not _let_66))) (let ((_let_68 (tptp.hBOOL (tptp.hAPP_int_bool _let_27 _let_5)))) (let ((_let_69 (= _let_68 _let_67))) (let ((_let_70 (forall ((A_1 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_1) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (not (= tptp.zero_zero_int A_1)))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_53)) (MACRO_SR_EQ_INTRO :args (_let_53 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (= tptp.zero_zero_int _let_5))) (let ((_let_73 (= _let_72 _let_66))) (let ((_let_74 (forall ((A_1 tptp.int)) (= (= tptp.zero_zero_int (tptp.hAPP_nat_int (tptp.power_power_int A_1) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= tptp.zero_zero_int A_1))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_64)) (MACRO_SR_EQ_INTRO :args (_let_64 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (not _let_65))) (let ((_let_77 (or _let_76 _let_68))) (let ((_let_78 (forall ((N_14 tptp.nat) (A_92 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_92))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_92) N_14)))))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_69)) :args ((or _let_67 (not _let_68) (not _let_69)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_76 _let_68 (not _let_77)))) (ASSUME :args (_let_65)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (_let_3 _let_4 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_nat_int (tptp.power_power_int A_92) N_14)))) :args (_let_78))) _let_79 :args (_let_77 false _let_78)) :args (_let_68 false _let_65 false _let_77)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_73)) :args ((or (not _let_72) _let_66 (not _let_73)))) (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (_let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.power_power_int A_1)))) :args (_let_74))) _let_75 :args (_let_73 false _let_74)) :args (_let_66 false _let_72 false _let_73)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (_let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.power_power_int A_1)))) :args (_let_70))) _let_71 :args (_let_69 false _let_70)) :args (false false _let_68 false _let_66 false _let_69)) :args (_let_65 (tptp.hBOOL (tptp.hAPP_int_bool _let_39 tptp.t)) (forall ((Xa tptp.int) (Ya tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (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.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) _let_64 (forall ((A_1 tptp.real)) (= (= (tptp.hAPP_nat_real (tptp.power_power_real A_1) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.zero_zero_real) (= A_1 tptp.zero_zero_real))) (forall ((W_13 tptp.int)) (= (tptp.plus_plus_int tptp.one_one_int (tptp.number_number_of_int W_13)) (tptp.number_number_of_int (tptp.plus_plus_int (tptp.bit1 tptp.pls) W_13)))) (forall ((W_13 tptp.int)) (= (tptp.plus_plus_real tptp.one_one_real (tptp.number267125858f_real W_13)) (tptp.number267125858f_real (tptp.plus_plus_int (tptp.bit1 tptp.pls) W_13)))) (forall ((V_17 tptp.int)) (= (tptp.plus_plus_int (tptp.number_number_of_int V_17) tptp.one_one_int) (tptp.number_number_of_int (tptp.plus_plus_int V_17 (tptp.bit1 tptp.pls))))) (forall ((V_17 tptp.int)) (= (tptp.plus_plus_real (tptp.number267125858f_real V_17) tptp.one_one_real) (tptp.number267125858f_real (tptp.plus_plus_int V_17 (tptp.bit1 tptp.pls))))) _let_63 _let_62 _let_63 _let_61 _let_62 (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_12 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_12))) (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_12 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_12))) (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_12 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_12))) (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_60 (= tptp.one_one_real _let_47) _let_52 _let_48 (tptp.hBOOL (tptp.hAPP_nat_bool _let_34 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 tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int K)) (tptp.number_number_of_int L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) L_1)))) (forall ((V_1 tptp.int) (W tptp.int)) (= (tptp.plus_plus_int (tptp.number_number_of_int V_1) (tptp.number_number_of_int W)) (tptp.number_number_of_int (tptp.plus_plus_int V_1 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_55 (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) N) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.power_power_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.power_power_nat M) N)) (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) N))) (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (= (tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M) (tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N) Z)) (tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.plus_plus_nat M N)) Z))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.plus_plus_nat M N)))) _let_41 _let_59 (= tptp.zero_zero_nat _let_58) (forall ((Na tptp.nat)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Na) tptp.zero_zero_int) (= Na tptp.zero_zero_nat))) _let_35 _let_61 (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K1)) (tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K1) K2)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) L_1)))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_18 tptp.pls))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 K1)) (tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K1) K2)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 K)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) L_1)))) (forall ((K_1 tptp.int) (I_2 tptp.int) (J_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_2) J_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int I_2 K_1)) (tptp.plus_plus_int J_1 K_1))))) (forall ((V_2 tptp.int) (V_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat V_2))) (let ((_let_2 (tptp.number_number_of_nat V_1))) (let ((_let_3 (tptp.plus_plus_nat _let_2 _let_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_2) tptp.pls)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_1) 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.plus_plus_int V_1 V_2))))))))))))) _let_60 _let_50 (= tptp.one_one_nat _let_49) (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 tptp.int) (L_1 tptp.int)) (= (= (tptp.bit1 K) (tptp.bit1 L_1)) (= K L_1))) (forall ((K tptp.int) (L_1 tptp.int)) (= (= (tptp.bit0 K) (tptp.bit0 L_1)) (= K L_1))) (forall ((A_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int A_1 A_1)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_1) tptp.zero_zero_int)))) (forall ((A_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.plus_plus_real A_1 A_1)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_1) tptp.zero_zero_real)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (= (tptp.plus_plus_int (tptp.plus_plus_int Z1 Z2) Z3) (tptp.plus_plus_int Z1 (tptp.plus_plus_int Z2 Z3)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (tptp.plus_plus_int X (tptp.plus_plus_int Y Z)) (tptp.plus_plus_int Y (tptp.plus_plus_int X Z)))) (forall ((Z tptp.int) (W tptp.int)) (= (tptp.plus_plus_int Z W) (tptp.plus_plus_int W Z))) (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 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) tptp.pls)))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K1)) (tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K1) K2)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) L_1)))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) tptp.pls)))) (forall ((K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K))))) (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_18 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_38 (forall ((Wa tptp.int) (Z_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Wa))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.plus_plus_int Z_1 tptp.one_one_int))) (or (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_1)) (= Wa Z_1))))) (forall ((K_1 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_1)) 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_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int (tptp.plus_plus_int tptp.one_one_int Z_1) Z_1)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_1) tptp.zero_zero_int)))) (forall ((A_1 tptp.int)) (= (= (tptp.plus_plus_int A_1 A_1) tptp.zero_zero_int) (= A_1 tptp.zero_zero_int))) (forall ((A_1 tptp.real)) (= (= (tptp.plus_plus_real A_1 A_1) tptp.zero_zero_real) (= A_1 tptp.zero_zero_real))) (forall ((K_1 tptp.int)) (not (= (tptp.bit1 K_1) tptp.pls))) (forall ((L tptp.int)) (not (= tptp.pls (tptp.bit1 L)))) (forall ((K_1 tptp.int) (L tptp.int)) (not (= (tptp.bit1 K_1) (tptp.bit0 L)))) (forall ((K_1 tptp.int) (L tptp.int)) (not (= (tptp.bit0 K_1) (tptp.bit1 L)))) (forall ((K tptp.int)) (= (= (tptp.bit0 K) tptp.pls) (= K tptp.pls))) (forall ((L_1 tptp.int)) (= (= tptp.pls (tptp.bit0 L_1)) (= tptp.pls L_1))) (= (tptp.bit0 tptp.pls) tptp.pls) (= tptp.pls tptp.zero_zero_int) _let_43 (forall ((K_1 tptp.int)) (= (tptp.plus_plus_int K_1 tptp.pls) K_1)) (forall ((K_1 tptp.int)) (= (tptp.plus_plus_int tptp.pls K_1) K_1)) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.plus_plus_int (tptp.bit0 K_1) (tptp.bit0 L)) (tptp.bit0 (tptp.plus_plus_int K_1 L)))) (forall ((K_1 tptp.int)) (= (tptp.bit0 K_1) (tptp.plus_plus_int K_1 K_1))) (forall ((Z tptp.int)) (= (tptp.plus_plus_int Z tptp.zero_zero_int) Z)) (forall ((Z tptp.int)) (= (tptp.plus_plus_int tptp.zero_zero_int Z) Z)) _let_57 _let_59 _let_56 _let_57 _let_56 _let_55 (= tptp.zero_zero_real _let_54) (forall ((A_100 tptp.int)) (= (tptp.plus_plus_int (tptp.number_number_of_int tptp.pls) A_100) A_100)) (forall ((A_100 tptp.real)) (= (tptp.plus_plus_real (tptp.number267125858f_real tptp.pls) A_100) A_100)) (forall ((A_99 tptp.int)) (= (tptp.plus_plus_int A_99 (tptp.number_number_of_int tptp.pls)) A_99)) (forall ((A_99 tptp.real)) (= (tptp.plus_plus_real A_99 (tptp.number267125858f_real tptp.pls)) A_99)) (forall ((A_1 tptp.int) (Wa tptp.int)) (let ((_let_1 (tptp.number_number_of_nat Wa))) (= (= (tptp.hAPP_nat_int (tptp.power_power_int A_1) _let_1) tptp.zero_zero_int) (and (= A_1 tptp.zero_zero_int) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A_1 tptp.nat) (Wa tptp.int)) (let ((_let_1 (tptp.number_number_of_nat Wa))) (= (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_1) _let_1) tptp.zero_zero_nat) (and (= A_1 tptp.zero_zero_nat) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A_1 tptp.real) (Wa tptp.int)) (let ((_let_1 (tptp.number_number_of_nat Wa))) (= (= (tptp.hAPP_nat_real (tptp.power_power_real A_1) _let_1) tptp.zero_zero_real) (and (= A_1 tptp.zero_zero_real) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((V_16 tptp.int) (W_11 tptp.int) (Z_6 tptp.int)) (= (tptp.plus_plus_int (tptp.number_number_of_int V_16) (tptp.plus_plus_int (tptp.number_number_of_int W_11) Z_6)) (tptp.plus_plus_int (tptp.number_number_of_int (tptp.plus_plus_int V_16 W_11)) Z_6))) (forall ((V_16 tptp.int) (W_11 tptp.int) (Z_6 tptp.real)) (= (tptp.plus_plus_real (tptp.number267125858f_real V_16) (tptp.plus_plus_real (tptp.number267125858f_real W_11) Z_6)) (tptp.plus_plus_real (tptp.number267125858f_real (tptp.plus_plus_int V_16 W_11)) Z_6))) (forall ((V_15 tptp.int) (W_10 tptp.int)) (= (tptp.plus_plus_int (tptp.number_number_of_int V_15) (tptp.number_number_of_int W_10)) (tptp.number_number_of_int (tptp.plus_plus_int V_15 W_10)))) (forall ((V_15 tptp.int) (W_10 tptp.int)) (= (tptp.plus_plus_real (tptp.number267125858f_real V_15) (tptp.number267125858f_real W_10)) (tptp.number267125858f_real (tptp.plus_plus_int V_15 W_10)))) (forall ((V_14 tptp.int) (W_9 tptp.int)) (= (tptp.number_number_of_int (tptp.plus_plus_int V_14 W_9)) (tptp.plus_plus_int (tptp.number_number_of_int V_14) (tptp.number_number_of_int W_9)))) (forall ((V_14 tptp.int) (W_9 tptp.int)) (= (tptp.number267125858f_real (tptp.plus_plus_int V_14 W_9)) (tptp.plus_plus_real (tptp.number267125858f_real V_14) (tptp.number267125858f_real W_9)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.plus_plus_int (tptp.bit1 K_1) (tptp.bit0 L)) (tptp.bit1 (tptp.plus_plus_int K_1 L)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.plus_plus_int (tptp.bit0 K_1) (tptp.bit1 L)) (tptp.bit1 (tptp.plus_plus_int K_1 L)))) (forall ((K_1 tptp.int)) (= (tptp.bit1 K_1) (tptp.plus_plus_int (tptp.plus_plus_int tptp.one_one_int K_1) K_1))) (forall ((Z tptp.int)) (not (= (tptp.plus_plus_int (tptp.plus_plus_int tptp.one_one_int Z) Z) tptp.zero_zero_int))) (forall ((N_26 tptp.nat)) (= (tptp.number_number_of_nat (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_26)) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_26))) (forall ((N_26 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_26))) (= (tptp.number_number_of_int _let_1) _let_1))) (forall ((N_26 tptp.nat)) (= (tptp.number267125858f_real (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_26)) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_26))) _let_53 (forall ((A_1 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_1) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (not (= A_1 tptp.zero_zero_real)))) (forall ((A_98 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_98) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) tptp.zero_zero_int)))) (forall ((A_98 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_98) (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.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.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_15 tptp.int) (Y_11 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.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X_15) _let_1) (tptp.hAPP_nat_int (tptp.power_power_int Y_11) _let_1))) tptp.zero_zero_int))))) (forall ((X_15 tptp.real) (Y_11 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.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X_15) _let_1) (tptp.hAPP_nat_real (tptp.power_power_real Y_11) _let_1))) tptp.zero_zero_real))))) (forall ((W_8 tptp.int)) (let ((_let_1 (tptp.number_number_of_int W_8))) (= (tptp.number_number_of_int (tptp.bit0 W_8)) (tptp.plus_plus_int (tptp.plus_plus_int tptp.zero_zero_int _let_1) _let_1)))) (forall ((W_8 tptp.int)) (let ((_let_1 (tptp.number267125858f_real W_8))) (= (tptp.number267125858f_real (tptp.bit0 W_8)) (tptp.plus_plus_real (tptp.plus_plus_real tptp.zero_zero_real _let_1) _let_1)))) (forall ((W_7 tptp.int)) (let ((_let_1 (tptp.number_number_of_int W_7))) (= (tptp.number_number_of_int (tptp.bit1 W_7)) (tptp.plus_plus_int (tptp.plus_plus_int tptp.one_one_int _let_1) _let_1)))) (forall ((W_7 tptp.int)) (let ((_let_1 (tptp.number267125858f_real W_7))) (= (tptp.number267125858f_real (tptp.bit1 W_7)) (tptp.plus_plus_real (tptp.plus_plus_real tptp.one_one_real _let_1) _let_1)))) _let_52 _let_50 _let_48 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.m1) _let_4)) (forall ((N_25 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_25)) (tptp.hAPP_nat_int (tptp.power_power_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) N_25)))) (forall ((N_25 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real tptp.semiri132038758t_real N_25)) (tptp.hAPP_nat_real (tptp.power_power_real (tptp.number267125858f_real (tptp.bit0 (tptp.bit1 tptp.pls)))) N_25)))) (= _let_22 (tptp.hAPP_nat_int tptp.semiri1621563631at_int _let_3)) (= _let_30 (tptp.hAPP_nat_int tptp.semiri1621563631at_int _let_31)) (forall ((Xa tptp.real) (Ya tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (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_24 tptp.nat) (A_97 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_97)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_24)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_97) N_24))))))) (forall ((N_24 tptp.nat) (A_97 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_97)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_24)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_97) N_24))))))) (forall ((N_24 tptp.nat) (A_97 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_97)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_24)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_97) N_24))))))) (forall ((N_23 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_int (tptp.power_power_int tptp.zero_zero_int) N_23))) (let ((_let_2 (= N_23 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((N_23 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat tptp.zero_zero_nat) N_23))) (let ((_let_2 (= N_23 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N_23 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_real (tptp.power_power_real tptp.zero_zero_real) N_23))) (let ((_let_2 (= N_23 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((A_96 tptp.int) (N_22 tptp.nat) (N_21 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_96))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_22) N_21)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_96)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_96) 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_21)) (tptp.hAPP_nat_int _let_1 N_22)))))))) (forall ((A_96 tptp.nat) (N_22 tptp.nat) (N_21 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_96))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_22) N_21)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_96)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_96) 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_21)) (tptp.hAPP_nat_nat _let_1 N_22)))))))) (forall ((A_96 tptp.real) (N_22 tptp.nat) (N_21 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_96))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_22) N_21)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_96)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_96) 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_21)) (tptp.hAPP_nat_real _let_1 N_22)))))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_27 _let_46)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_34 _let_45)) (tptp.hBOOL (tptp.hAPP_real_bool _let_37 _let_44)) (forall ((P_1 tptp.fun_int_bool) (K tptp.int) (I_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) I_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.plus_plus_int K tptp.one_one_int))) (=> (forall ((I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) I)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 I)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.plus_plus_int I tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_1)))))) (= tptp.zero_zero_int _let_28) (tptp.hBOOL (tptp.hAPP_nat_bool _let_34 tptp.tn)) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) _let_42 (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N)))) (forall ((I_2 tptp.nat) (J_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat I_2 J_1)) I_2)))) (forall ((J_1 tptp.nat) (I_2 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat J_1 I_2)) I_2)))) (forall ((K_1 tptp.int)) (= (tptp.number_number_of_int K_1) K_1)) (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 tptp.nat) (N tptp.nat)) (= (tptp.plus_plus_nat M N) (tptp.plus_plus_nat N M))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (tptp.plus_plus_nat X (tptp.plus_plus_nat Y Z)) (tptp.plus_plus_nat Y (tptp.plus_plus_nat X Z)))) (forall ((M tptp.nat) (N tptp.nat) (K_1 tptp.nat)) (= (tptp.plus_plus_nat (tptp.plus_plus_nat M N) K_1) (tptp.plus_plus_nat M (tptp.plus_plus_nat N K_1)))) (forall ((K tptp.nat) (Ma tptp.nat) (Na tptp.nat)) (= (= (tptp.plus_plus_nat K Ma) (tptp.plus_plus_nat K Na)) (= Ma Na))) (forall ((Ma tptp.nat) (K tptp.nat) (Na tptp.nat)) (= (= (tptp.plus_plus_nat Ma K) (tptp.plus_plus_nat Na K)) (= Ma Na))) (forall ((K tptp.nat) (Ma tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat K Ma)) (tptp.plus_plus_nat K 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 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) M)) (not (= M N)))) (forall ((S_1 tptp.nat) (T_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat S_1) T_1)) (not (= S_1 T_1)))) (forall ((M tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.plus_plus_nat J_1 M)))))) (forall ((M tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.plus_plus_nat M J_1)))))) (forall ((K_1 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat I_2 K_1)) (tptp.plus_plus_nat J_1 K_1))))) (forall ((K_1 tptp.nat) (L tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_1) L)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat I_2 K_1)) (tptp.plus_plus_nat J_1 L)))))) (forall ((M tptp.nat) (N tptp.nat) (K_1 tptp.nat) (L tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_1) L)) (=> (= (tptp.plus_plus_nat M L) (tptp.plus_plus_nat K_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N))))) (forall ((I_2 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat I_2 J_1)) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) K_1)))) (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 tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (not (= N tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N 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)) (tptp.hAPP_nat_nat _let_1 N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)))))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) 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.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 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) 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_3 tptp.int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Va) V_3)))) (= (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_3))) (and (=> _let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) V_3))) _let_1)))) (forall ((X_14 tptp.int) (Y_10 tptp.int)) (=> (not (= X_14 Y_10)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_14) Y_10))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y_10) X_14))))) (forall ((X_14 tptp.real) (Y_10 tptp.real)) (=> (not (= X_14 Y_10)) (=> (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_14) Y_10))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_10) X_14))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= (tptp.plus_plus_nat M N) M) (= N tptp.zero_zero_nat))) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (= (tptp.plus_plus_nat Ma Na) tptp.zero_zero_nat) (and (= Ma tptp.zero_zero_nat) (= Na tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (= (tptp.plus_plus_nat M tptp.zero_zero_nat) M)) (forall ((N tptp.nat)) (= (tptp.plus_plus_nat tptp.zero_zero_nat N) N)) (forall ((A_95 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int A_95) tptp.one_one_nat) A_95)) (forall ((A_95 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_95) tptp.one_one_nat) A_95)) (forall ((A_95 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real A_95) tptp.one_one_nat) A_95)) (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.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_int tptp.zero_zero_int)) (not (= tptp.one_one_nat tptp.zero_zero_nat)) (not (= tptp.one_one_real tptp.zero_zero_real)) _let_43 (not (= tptp.zero_zero_nat tptp.one_one_nat)) _let_42 (forall ((N_20 tptp.nat) (A_94 tptp.int)) (=> (not (= A_94 tptp.zero_zero_int)) (not (= (tptp.hAPP_nat_int (tptp.power_power_int A_94) N_20) tptp.zero_zero_int)))) (forall ((N_20 tptp.nat) (A_94 tptp.real)) (=> (not (= A_94 tptp.zero_zero_real)) (not (= (tptp.hAPP_nat_real (tptp.power_power_real A_94) N_20) tptp.zero_zero_real)))) (forall ((N_19 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.power_power_int tptp.one_one_int) N_19) tptp.one_one_int)) (forall ((N_19 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat tptp.one_one_nat) N_19) tptp.one_one_nat)) (forall ((N_19 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.power_power_real tptp.one_one_real) N_19) tptp.one_one_real)) (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 ((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_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 ((M_10 tptp.nat) (N_18 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_10) N_18)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_10)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_18))))) (forall ((M_10 tptp.nat) (N_18 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_10) N_18)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_10)) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_18))))) (forall ((M_10 tptp.nat) (N_18 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_10) N_18)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real tptp.semiri132038758t_real M_10)) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_18))))) (forall ((M_9 tptp.nat) (N_17 tptp.nat)) (=> (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_17))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_9) N_17)))) (forall ((M_9 tptp.nat) (N_17 tptp.nat)) (=> (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_17))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_9) N_17)))) (forall ((M_9 tptp.nat) (N_17 tptp.nat)) (=> (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_17))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_9) N_17)))) (forall ((M_8 tptp.nat) (N_16 tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.plus_plus_nat M_8 N_16)) (tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_8) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_16)))) (forall ((M_8 tptp.nat) (N_16 tptp.nat)) (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat (tptp.plus_plus_nat M_8 N_16)) (tptp.plus_plus_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_8) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_16)))) (forall ((M_8 tptp.nat) (N_16 tptp.nat)) (= (tptp.hAPP_nat_real tptp.semiri132038758t_real (tptp.plus_plus_nat M_8 N_16)) (tptp.plus_plus_real (tptp.hAPP_nat_real tptp.semiri132038758t_real M_8) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_16)))) _let_41 (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat tptp.one_one_nat) tptp.one_one_nat) (= (tptp.hAPP_nat_real tptp.semiri132038758t_real tptp.one_one_nat) tptp.one_one_real) (forall ((M_7 tptp.nat) (N_15 tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.power_power_nat M_7) N_15)) (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_7)) N_15))) (forall ((M_7 tptp.nat) (N_15 tptp.nat)) (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat (tptp.hAPP_nat_nat (tptp.power_power_nat M_7) N_15)) (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_7)) N_15))) (forall ((M_7 tptp.nat) (N_15 tptp.nat)) (= (tptp.hAPP_nat_real tptp.semiri132038758t_real (tptp.hAPP_nat_nat (tptp.power_power_nat M_7) N_15)) (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_nat_real tptp.semiri132038758t_real M_7)) N_15))) (= tptp.one_one_int _let_40) (forall ((X tptp.nat) (Y tptp.nat)) (= (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.plus_plus_nat X Y)))) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X)) N) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.power_power_nat X) N)))) (forall ((B_61 tptp.int) (C_45 tptp.int) (A_93 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_61))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_93)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_45)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.plus_plus_int A_93 C_45))))))) (forall ((B_61 tptp.nat) (C_45 tptp.nat) (A_93 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_61))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_93)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_45)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.plus_plus_nat A_93 C_45))))))) (forall ((B_61 tptp.real) (C_45 tptp.real) (A_93 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_61))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_93)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_45)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.plus_plus_real A_93 C_45))))))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_39 tptp.zero_zero_int))) (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_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real))) _let_38 (tptp.hBOOL (tptp.hAPP_nat_bool _let_34 tptp.one_one_nat)) (tptp.hBOOL (tptp.hAPP_real_bool _let_37 tptp.one_one_real)) _let_36 (forall ((N_14 tptp.nat) (A_92 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_92)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_92) N_14)))))) (forall ((N_14 tptp.nat) (A_92 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_92)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_92) N_14)))))) (forall ((A_91 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_91) (tptp.plus_plus_int A_91 tptp.one_one_int)))) (forall ((A_91 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_91) (tptp.plus_plus_nat A_91 tptp.one_one_nat)))) (forall ((A_91 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_91) (tptp.plus_plus_real A_91 tptp.one_one_real)))) (forall ((Ma tptp.nat) (Na tptp.nat) (A_1 tptp.int)) (let ((_let_1 (tptp.power_power_int A_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_1)) (= (= (tptp.hAPP_nat_int _let_1 Ma) (tptp.hAPP_nat_int _let_1 Na)) (= Ma Na))))) (forall ((Ma tptp.nat) (Na tptp.nat) (A_1 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A_1)) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 Na)) (= Ma Na))))) (forall ((Ma tptp.nat) (Na tptp.nat) (A_1 tptp.real)) (let ((_let_1 (tptp.power_power_real A_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A_1)) (= (= (tptp.hAPP_nat_real _let_1 Ma) (tptp.hAPP_nat_real _let_1 Na)) (= Ma Na))))) (forall ((Xa tptp.nat) (Ya tptp.nat) (B tptp.int)) (let ((_let_1 (tptp.power_power_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B)) (= (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 ((Xa tptp.nat) (Ya tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.power_power_nat B))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) B)) (= (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 tptp.real)) (let ((_let_1 (tptp.power_power_real B))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) B)) (= (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 ((M_6 tptp.nat) (N_13 tptp.nat) (A_90 tptp.int)) (let ((_let_1 (tptp.power_power_int A_90))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_90)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int _let_1 M_6)) (tptp.hAPP_nat_int _let_1 N_13))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_6) N_13)))))) (forall ((M_6 tptp.nat) (N_13 tptp.nat) (A_90 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_90))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A_90)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M_6)) (tptp.hAPP_nat_nat _let_1 N_13))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_6) N_13)))))) (forall ((M_6 tptp.nat) (N_13 tptp.nat) (A_90 tptp.real)) (let ((_let_1 (tptp.power_power_real A_90))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A_90)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real _let_1 M_6)) (tptp.hAPP_nat_real _let_1 N_13))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_6) N_13)))))) (forall ((A_89 tptp.int) (N_12 tptp.nat) (N_11 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_89))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_12) N_11)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_89)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int _let_1 N_12)) (tptp.hAPP_nat_int _let_1 N_11))))))) (forall ((A_89 tptp.nat) (N_12 tptp.nat) (N_11 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_89))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_12) N_11)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A_89)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 N_12)) (tptp.hAPP_nat_nat _let_1 N_11))))))) (forall ((A_89 tptp.real) (N_12 tptp.nat) (N_11 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_89))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_12) N_11)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A_89)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real _let_1 N_12)) (tptp.hAPP_nat_real _let_1 N_11))))))) (forall ((A_1 tptp.int) (Na tptp.nat)) (= (= (tptp.hAPP_nat_int (tptp.power_power_int A_1) Na) tptp.zero_zero_int) (and (= A_1 tptp.zero_zero_int) (not (= Na tptp.zero_zero_nat))))) (forall ((A_1 tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_1) Na) tptp.zero_zero_nat) (and (= A_1 tptp.zero_zero_nat) (not (= Na tptp.zero_zero_nat))))) (forall ((A_1 tptp.real) (Na tptp.nat)) (= (= (tptp.hAPP_nat_real (tptp.power_power_real A_1) Na) tptp.zero_zero_real) (and (= A_1 tptp.zero_zero_real) (not (= Na tptp.zero_zero_nat))))) (forall ((M_5 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_5)) tptp.zero_zero_int)))) (forall ((M_5 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_5)) tptp.zero_zero_nat)))) (forall ((M_5 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_5)) tptp.zero_zero_real)))) (forall ((A_88 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int A_88) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((A_88 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_88) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A_88 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real A_88) tptp.zero_zero_nat) tptp.one_one_real)) _let_35 (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (= (tptp.hAPP_nat_real tptp.semiri132038758t_real tptp.zero_zero_nat) tptp.zero_zero_real) (tptp.hBOOL (tptp.hAPP_nat_bool _let_34 _let_3)) (forall ((K_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) K_1)) (exists ((N_1 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= K_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1)))))) (forall ((I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_1)) (exists ((K_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_2)) (= (tptp.plus_plus_nat I_2 K_2) J_1))))) (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_13 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int X_13) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((X_13 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat X_13) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((X_13 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real X_13) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.plus_plus_int A_1 A_1))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_1))))) (forall ((A_1 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.plus_plus_real A_1 A_1))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_1))))) (forall ((A_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int A_1 A_1)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_1) tptp.zero_zero_int)))) (forall ((A_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.plus_plus_real A_1 A_1)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_1) tptp.zero_zero_real)))) (forall ((B_60 tptp.int) (A_87 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_87)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_60)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.plus_plus_int A_87 B_60))))))) (forall ((B_60 tptp.nat) (A_87 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_87)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_60)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.plus_plus_nat A_87 B_60))))))) (forall ((B_60 tptp.real) (A_87 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_87)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_60)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.plus_plus_real A_87 B_60))))))) (forall ((B_59 tptp.int) (A_86 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_86) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_59) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int A_86 B_59)) tptp.zero_zero_int))))) (forall ((B_59 tptp.nat) (A_86 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_86) tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_59) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat A_86 B_59)) tptp.zero_zero_nat))))) (forall ((B_59 tptp.real) (A_86 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_86) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_59) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.plus_plus_real A_86 B_59)) tptp.zero_zero_real))))) (forall ((Xa tptp.int)) (= (= tptp.zero_zero_int Xa) (= Xa tptp.zero_zero_int))) (forall ((Xa tptp.nat)) (= (= tptp.zero_zero_nat Xa) (= Xa tptp.zero_zero_nat))) (forall ((Xa tptp.real)) (= (= tptp.zero_zero_real Xa) (= Xa tptp.zero_zero_real))) (forall ((B_58 tptp.int) (A_85 tptp.int) (C_44 tptp.int)) (=> (= (tptp.plus_plus_int B_58 A_85) (tptp.plus_plus_int C_44 A_85)) (= B_58 C_44))) (forall ((B_58 tptp.nat) (A_85 tptp.nat) (C_44 tptp.nat)) (=> (= (tptp.plus_plus_nat B_58 A_85) (tptp.plus_plus_nat C_44 A_85)) (= B_58 C_44))) (forall ((B_58 tptp.real) (A_85 tptp.real) (C_44 tptp.real)) (=> (= (tptp.plus_plus_real B_58 A_85) (tptp.plus_plus_real C_44 A_85)) (= B_58 C_44))) (forall ((A_84 tptp.int) (B_57 tptp.int) (C_43 tptp.int)) (=> (= (tptp.plus_plus_int A_84 B_57) (tptp.plus_plus_int A_84 C_43)) (= B_57 C_43))) (forall ((A_84 tptp.nat) (B_57 tptp.nat) (C_43 tptp.nat)) (=> (= (tptp.plus_plus_nat A_84 B_57) (tptp.plus_plus_nat A_84 C_43)) (= B_57 C_43))) (forall ((A_84 tptp.real) (B_57 tptp.real) (C_43 tptp.real)) (=> (= (tptp.plus_plus_real A_84 B_57) (tptp.plus_plus_real A_84 C_43)) (= B_57 C_43))) (forall ((A_83 tptp.int) (B_56 tptp.int) (C_42 tptp.int)) (=> (= (tptp.plus_plus_int A_83 B_56) (tptp.plus_plus_int A_83 C_42)) (= B_56 C_42))) (forall ((A_83 tptp.nat) (B_56 tptp.nat) (C_42 tptp.nat)) (=> (= (tptp.plus_plus_nat A_83 B_56) (tptp.plus_plus_nat A_83 C_42)) (= B_56 C_42))) (forall ((A_83 tptp.real) (B_56 tptp.real) (C_42 tptp.real)) (=> (= (tptp.plus_plus_real A_83 B_56) (tptp.plus_plus_real A_83 C_42)) (= B_56 C_42))) (forall ((A_82 tptp.int) (B_55 tptp.int) (C_41 tptp.int) (D_14 tptp.int)) (= (tptp.plus_plus_int (tptp.plus_plus_int A_82 B_55) (tptp.plus_plus_int C_41 D_14)) (tptp.plus_plus_int (tptp.plus_plus_int A_82 C_41) (tptp.plus_plus_int B_55 D_14)))) (forall ((A_82 tptp.nat) (B_55 tptp.nat) (C_41 tptp.nat) (D_14 tptp.nat)) (= (tptp.plus_plus_nat (tptp.plus_plus_nat A_82 B_55) (tptp.plus_plus_nat C_41 D_14)) (tptp.plus_plus_nat (tptp.plus_plus_nat A_82 C_41) (tptp.plus_plus_nat B_55 D_14)))) (forall ((A_82 tptp.real) (B_55 tptp.real) (C_41 tptp.real) (D_14 tptp.real)) (= (tptp.plus_plus_real (tptp.plus_plus_real A_82 B_55) (tptp.plus_plus_real C_41 D_14)) (tptp.plus_plus_real (tptp.plus_plus_real A_82 C_41) (tptp.plus_plus_real B_55 D_14)))) (forall ((B tptp.int) (A_1 tptp.int) (C_1 tptp.int)) (= (= (tptp.plus_plus_int B A_1) (tptp.plus_plus_int C_1 A_1)) (= B C_1))) (forall ((B tptp.nat) (A_1 tptp.nat) (C_1 tptp.nat)) (= (= (tptp.plus_plus_nat B A_1) (tptp.plus_plus_nat C_1 A_1)) (= B C_1))) (forall ((B tptp.real) (A_1 tptp.real) (C_1 tptp.real)) (= (= (tptp.plus_plus_real B A_1) (tptp.plus_plus_real C_1 A_1)) (= B C_1))) (forall ((A_1 tptp.int) (B tptp.int) (C_1 tptp.int)) (= (= (tptp.plus_plus_int A_1 B) (tptp.plus_plus_int A_1 C_1)) (= B C_1))) (forall ((A_1 tptp.nat) (B tptp.nat) (C_1 tptp.nat)) (= (= (tptp.plus_plus_nat A_1 B) (tptp.plus_plus_nat A_1 C_1)) (= B C_1))) (forall ((A_1 tptp.real) (B tptp.real) (C_1 tptp.real)) (= (= (tptp.plus_plus_real A_1 B) (tptp.plus_plus_real A_1 C_1)) (= B C_1))) (forall ((A_81 tptp.int) (B_54 tptp.int) (C_40 tptp.int)) (= (tptp.plus_plus_int (tptp.plus_plus_int A_81 B_54) C_40) (tptp.plus_plus_int (tptp.plus_plus_int A_81 C_40) B_54))) (forall ((A_81 tptp.nat) (B_54 tptp.nat) (C_40 tptp.nat)) (= (tptp.plus_plus_nat (tptp.plus_plus_nat A_81 B_54) C_40) (tptp.plus_plus_nat (tptp.plus_plus_nat A_81 C_40) B_54))) (forall ((A_81 tptp.real) (B_54 tptp.real) (C_40 tptp.real)) (= (tptp.plus_plus_real (tptp.plus_plus_real A_81 B_54) C_40) (tptp.plus_plus_real (tptp.plus_plus_real A_81 C_40) B_54))) (forall ((A_80 tptp.int) (B_53 tptp.int) (C_39 tptp.int)) (= (tptp.plus_plus_int (tptp.plus_plus_int A_80 B_53) C_39) (tptp.plus_plus_int A_80 (tptp.plus_plus_int B_53 C_39)))) (forall ((A_80 tptp.nat) (B_53 tptp.nat) (C_39 tptp.nat)) (= (tptp.plus_plus_nat (tptp.plus_plus_nat A_80 B_53) C_39) (tptp.plus_plus_nat A_80 (tptp.plus_plus_nat B_53 C_39)))) (forall ((A_80 tptp.real) (B_53 tptp.real) (C_39 tptp.real)) (= (tptp.plus_plus_real (tptp.plus_plus_real A_80 B_53) C_39) (tptp.plus_plus_real A_80 (tptp.plus_plus_real B_53 C_39)))) (forall ((A_79 tptp.int) (B_52 tptp.int) (C_38 tptp.int)) (= (tptp.plus_plus_int (tptp.plus_plus_int A_79 B_52) C_38) (tptp.plus_plus_int A_79 (tptp.plus_plus_int B_52 C_38)))) (forall ((A_79 tptp.nat) (B_52 tptp.nat) (C_38 tptp.nat)) (= (tptp.plus_plus_nat (tptp.plus_plus_nat A_79 B_52) C_38) (tptp.plus_plus_nat A_79 (tptp.plus_plus_nat B_52 C_38)))) (forall ((A_79 tptp.real) (B_52 tptp.real) (C_38 tptp.real)) (= (tptp.plus_plus_real (tptp.plus_plus_real A_79 B_52) C_38) (tptp.plus_plus_real A_79 (tptp.plus_plus_real B_52 C_38)))) (forall ((A_78 tptp.int) (C_37 tptp.int) (D_13 tptp.int)) (= (tptp.plus_plus_int A_78 (tptp.plus_plus_int C_37 D_13)) (tptp.plus_plus_int (tptp.plus_plus_int A_78 C_37) D_13))) (forall ((A_78 tptp.nat) (C_37 tptp.nat) (D_13 tptp.nat)) (= (tptp.plus_plus_nat A_78 (tptp.plus_plus_nat C_37 D_13)) (tptp.plus_plus_nat (tptp.plus_plus_nat A_78 C_37) D_13))) (forall ((A_78 tptp.real) (C_37 tptp.real) (D_13 tptp.real)) (= (tptp.plus_plus_real A_78 (tptp.plus_plus_real C_37 D_13)) (tptp.plus_plus_real (tptp.plus_plus_real A_78 C_37) D_13))) (forall ((A_77 tptp.int) (C_36 tptp.int) (D_12 tptp.int)) (= (tptp.plus_plus_int A_77 (tptp.plus_plus_int C_36 D_12)) (tptp.plus_plus_int C_36 (tptp.plus_plus_int A_77 D_12)))) (forall ((A_77 tptp.nat) (C_36 tptp.nat) (D_12 tptp.nat)) (= (tptp.plus_plus_nat A_77 (tptp.plus_plus_nat C_36 D_12)) (tptp.plus_plus_nat C_36 (tptp.plus_plus_nat A_77 D_12)))) (forall ((A_77 tptp.real) (C_36 tptp.real) (D_12 tptp.real)) (= (tptp.plus_plus_real A_77 (tptp.plus_plus_real C_36 D_12)) (tptp.plus_plus_real C_36 (tptp.plus_plus_real A_77 D_12)))) (forall ((A_76 tptp.int) (C_35 tptp.int)) (= (tptp.plus_plus_int A_76 C_35) (tptp.plus_plus_int C_35 A_76))) (forall ((A_76 tptp.nat) (C_35 tptp.nat)) (= (tptp.plus_plus_nat A_76 C_35) (tptp.plus_plus_nat C_35 A_76))) (forall ((A_76 tptp.real) (C_35 tptp.real)) (= (tptp.plus_plus_real A_76 C_35) (tptp.plus_plus_real C_35 A_76))) (forall ((Xa tptp.int)) (= (= tptp.one_one_int Xa) (= Xa tptp.one_one_int))) (forall ((Xa tptp.nat)) (= (= tptp.one_one_nat Xa) (= Xa tptp.one_one_nat))) (forall ((Xa tptp.real)) (= (= tptp.one_one_real Xa) (= Xa tptp.one_one_real))) (forall ((B tptp.int) (A_1 tptp.int)) (= (= B (tptp.plus_plus_int B A_1)) (= A_1 tptp.zero_zero_int))) (forall ((B tptp.nat) (A_1 tptp.nat)) (= (= B (tptp.plus_plus_nat B A_1)) (= A_1 tptp.zero_zero_nat))) (forall ((B tptp.real) (A_1 tptp.real)) (= (= B (tptp.plus_plus_real B A_1)) (= A_1 tptp.zero_zero_real))) (forall ((A_75 tptp.int)) (= (tptp.plus_plus_int A_75 tptp.zero_zero_int) A_75)) (forall ((A_75 tptp.nat)) (= (tptp.plus_plus_nat A_75 tptp.zero_zero_nat) A_75)) (forall ((A_75 tptp.real)) (= (tptp.plus_plus_real A_75 tptp.zero_zero_real) A_75)) (forall ((A_74 tptp.int)) (= (tptp.plus_plus_int A_74 tptp.zero_zero_int) A_74)) (forall ((A_74 tptp.nat)) (= (tptp.plus_plus_nat A_74 tptp.zero_zero_nat) A_74)) (forall ((A_74 tptp.real)) (= (tptp.plus_plus_real A_74 tptp.zero_zero_real) A_74)) (forall ((A_73 tptp.int)) (= (tptp.plus_plus_int A_73 tptp.zero_zero_int) A_73)) (forall ((A_73 tptp.nat)) (= (tptp.plus_plus_nat A_73 tptp.zero_zero_nat) A_73)) (forall ((A_73 tptp.real)) (= (tptp.plus_plus_real A_73 tptp.zero_zero_real) A_73)) (forall ((A_1 tptp.int)) (= (= tptp.zero_zero_int (tptp.plus_plus_int A_1 A_1)) (= A_1 tptp.zero_zero_int))) (forall ((A_1 tptp.real)) (= (= tptp.zero_zero_real (tptp.plus_plus_real A_1 A_1)) (= A_1 tptp.zero_zero_real))) (forall ((A_72 tptp.int)) (= (tptp.plus_plus_int tptp.zero_zero_int A_72) A_72)) (forall ((A_72 tptp.nat)) (= (tptp.plus_plus_nat tptp.zero_zero_nat A_72) A_72)) (forall ((A_72 tptp.real)) (= (tptp.plus_plus_real tptp.zero_zero_real A_72) A_72)) (forall ((A_71 tptp.int)) (= (tptp.plus_plus_int tptp.zero_zero_int A_71) A_71)) (forall ((A_71 tptp.nat)) (= (tptp.plus_plus_nat tptp.zero_zero_nat A_71) A_71)) (forall ((A_71 tptp.real)) (= (tptp.plus_plus_real tptp.zero_zero_real A_71) A_71)) (forall ((A_70 tptp.int)) (= (tptp.plus_plus_int tptp.zero_zero_int A_70) A_70)) (forall ((A_70 tptp.nat)) (= (tptp.plus_plus_nat tptp.zero_zero_nat A_70) A_70)) (forall ((A_70 tptp.real)) (= (tptp.plus_plus_real tptp.zero_zero_real A_70) A_70)) (forall ((C_34 tptp.int) (A_69 tptp.int) (B_51 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int C_34 A_69)) (tptp.plus_plus_int C_34 B_51))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_69) B_51)))) (forall ((C_34 tptp.nat) (A_69 tptp.nat) (B_51 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat C_34 A_69)) (tptp.plus_plus_nat C_34 B_51))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_69) B_51)))) (forall ((C_34 tptp.real) (A_69 tptp.real) (B_51 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.plus_plus_real C_34 A_69)) (tptp.plus_plus_real C_34 B_51))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_69) B_51)))) (forall ((A_68 tptp.int) (C_33 tptp.int) (B_50 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int A_68 C_33)) (tptp.plus_plus_int B_50 C_33))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_68) B_50)))) (forall ((A_68 tptp.nat) (C_33 tptp.nat) (B_50 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat A_68 C_33)) (tptp.plus_plus_nat B_50 C_33))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_68) B_50)))) (forall ((A_68 tptp.real) (C_33 tptp.real) (B_50 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.plus_plus_real A_68 C_33)) (tptp.plus_plus_real B_50 C_33))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_68) B_50)))) (forall ((C_32 tptp.int) (D_11 tptp.int) (A_67 tptp.int) (B_49 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_67) B_49)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_32) D_11)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int A_67 C_32)) (tptp.plus_plus_int B_49 D_11)))))) (forall ((C_32 tptp.nat) (D_11 tptp.nat) (A_67 tptp.nat) (B_49 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_67) B_49)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_32) D_11)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat A_67 C_32)) (tptp.plus_plus_nat B_49 D_11)))))) (forall ((C_32 tptp.real) (D_11 tptp.real) (A_67 tptp.real) (B_49 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_67) B_49)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_32) D_11)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.plus_plus_real A_67 C_32)) (tptp.plus_plus_real B_49 D_11)))))) (forall ((C_31 tptp.int) (A_66 tptp.int) (B_48 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_66) B_48)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int C_31 A_66)) (tptp.plus_plus_int C_31 B_48))))) (forall ((C_31 tptp.nat) (A_66 tptp.nat) (B_48 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_66) B_48)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat C_31 A_66)) (tptp.plus_plus_nat C_31 B_48))))) (forall ((C_31 tptp.real) (A_66 tptp.real) (B_48 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_66) B_48)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.plus_plus_real C_31 A_66)) (tptp.plus_plus_real C_31 B_48))))) (forall ((C_30 tptp.int) (A_65 tptp.int) (B_47 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_65) B_47)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int A_65 C_30)) (tptp.plus_plus_int B_47 C_30))))) (forall ((C_30 tptp.nat) (A_65 tptp.nat) (B_47 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_65) B_47)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat A_65 C_30)) (tptp.plus_plus_nat B_47 C_30))))) (forall ((C_30 tptp.real) (A_65 tptp.real) (B_47 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_65) B_47)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.plus_plus_real A_65 C_30)) (tptp.plus_plus_real B_47 C_30))))) (forall ((C_1 tptp.int) (A_1 tptp.int) (B tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int C_1 A_1)) (tptp.plus_plus_int C_1 B))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_1) B)))) (forall ((C_1 tptp.nat) (A_1 tptp.nat) (B tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat C_1 A_1)) (tptp.plus_plus_nat C_1 B))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_1) B)))) (forall ((C_1 tptp.real) (A_1 tptp.real) (B tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.plus_plus_real C_1 A_1)) (tptp.plus_plus_real C_1 B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_1) B)))) (forall ((A_1 tptp.int) (C_1 tptp.int) (B tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int A_1 C_1)) (tptp.plus_plus_int B C_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_1) B)))) (forall ((A_1 tptp.nat) (C_1 tptp.nat) (B tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat A_1 C_1)) (tptp.plus_plus_nat B C_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_1) B)))) (forall ((A_1 tptp.real) (C_1 tptp.real) (B tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.plus_plus_real A_1 C_1)) (tptp.plus_plus_real B C_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_1) B)))) (forall ((X_12 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int X_12) tptp.one_one_nat) X_12)) (forall ((X_12 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat X_12) tptp.one_one_nat) X_12)) (forall ((X_12 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real X_12) tptp.one_one_nat) X_12)) (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 ((A tptp.real) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (exists ((X_1 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_1)) (= (tptp.hAPP_nat_real (tptp.power_power_real X_1) N) A) (forall ((Y_1 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Y_1)) (= (tptp.hAPP_nat_real (tptp.power_power_real Y_1) N) A)) (= Y_1 X_1)))))))) (forall ((A tptp.real) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (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) A)))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) tptp.t)) (forall ((V_1 tptp.int)) (let ((_let_1 (tptp.plus_plus_nat (tptp.number_number_of_nat V_1) tptp.one_one_nat))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_1) tptp.pls)))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (tptp.number_number_of_nat (tptp.succ V_1)))))))) (forall ((V_1 tptp.int)) (let ((_let_1 (tptp.plus_plus_nat tptp.one_one_nat (tptp.number_number_of_nat V_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_1) tptp.pls)))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (tptp.number_number_of_nat (tptp.succ V_1)))))))) (forall ((A tptp.int) (B_1 tptp.int)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit1 _let_1))) (let ((_let_3 (tptp.number_number_of_nat _let_2))) (let ((_let_4 (tptp.power_power_int B_1))) (let ((_let_5 (tptp.number_number_of_nat (tptp.bit0 _let_1)))) (let ((_let_6 (tptp.number_number_of_int _let_2))) (let ((_let_7 (tptp.power_power_int A))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.plus_plus_int A B_1)) _let_3) (tptp.plus_plus_int (tptp.plus_plus_int (tptp.plus_plus_int (tptp.hAPP_nat_int _let_7 _let_3) (tptp.times_times_int (tptp.times_times_int _let_6 (tptp.hAPP_nat_int _let_7 _let_5)) B_1)) (tptp.times_times_int (tptp.times_times_int _let_6 A) (tptp.hAPP_nat_int _let_4 _let_5))) (tptp.hAPP_nat_int _let_4 _let_3))))))))))) (forall ((A tptp.int) (B_1 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.plus_plus_int A B_1)) _let_2) (tptp.plus_plus_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_1)) (tptp.hAPP_nat_int (tptp.power_power_int B_1) _let_2)))))) (= tptp.tn _let_33) (tptp.hBOOL (tptp.hAPP_nat_bool _let_34 _let_33)) (forall ((A_1 tptp.int) (B tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_1) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.minus_minus_int A_1 B)) tptp.zero_zero_int)))) (forall ((A_1 tptp.real) (B tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_1) B)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.minus_minus_real A_1 B)) tptp.zero_zero_real)))) (forall ((A_64 tptp.int) (B_46 tptp.int)) (= (tptp.times_times_int A_64 B_46) (tptp.times_times_int B_46 A_64))) (forall ((A_64 tptp.nat) (B_46 tptp.nat)) (= (tptp.times_times_nat A_64 B_46) (tptp.times_times_nat B_46 A_64))) (forall ((A_64 tptp.real) (B_46 tptp.real)) (= (tptp.times_times_real A_64 B_46) (tptp.times_times_real B_46 A_64))) (forall ((Lx_6 tptp.int) (Rx_6 tptp.int) (Ry_4 tptp.int)) (= (tptp.times_times_int Lx_6 (tptp.times_times_int Rx_6 Ry_4)) (tptp.times_times_int Rx_6 (tptp.times_times_int Lx_6 Ry_4)))) (forall ((Lx_6 tptp.nat) (Rx_6 tptp.nat) (Ry_4 tptp.nat)) (= (tptp.times_times_nat Lx_6 (tptp.times_times_nat Rx_6 Ry_4)) (tptp.times_times_nat Rx_6 (tptp.times_times_nat Lx_6 Ry_4)))) (forall ((Lx_6 tptp.real) (Rx_6 tptp.real) (Ry_4 tptp.real)) (= (tptp.times_times_real Lx_6 (tptp.times_times_real Rx_6 Ry_4)) (tptp.times_times_real Rx_6 (tptp.times_times_real Lx_6 Ry_4)))) (forall ((Lx_5 tptp.int) (Rx_5 tptp.int) (Ry_3 tptp.int)) (= (tptp.times_times_int Lx_5 (tptp.times_times_int Rx_5 Ry_3)) (tptp.times_times_int (tptp.times_times_int Lx_5 Rx_5) Ry_3))) (forall ((Lx_5 tptp.nat) (Rx_5 tptp.nat) (Ry_3 tptp.nat)) (= (tptp.times_times_nat Lx_5 (tptp.times_times_nat Rx_5 Ry_3)) (tptp.times_times_nat (tptp.times_times_nat Lx_5 Rx_5) Ry_3))) (forall ((Lx_5 tptp.real) (Rx_5 tptp.real) (Ry_3 tptp.real)) (= (tptp.times_times_real Lx_5 (tptp.times_times_real Rx_5 Ry_3)) (tptp.times_times_real (tptp.times_times_real Lx_5 Rx_5) Ry_3))) (forall ((A_63 tptp.int) (B_45 tptp.int) (C_29 tptp.int)) (= (tptp.times_times_int (tptp.times_times_int A_63 B_45) C_29) (tptp.times_times_int A_63 (tptp.times_times_int B_45 C_29)))) (forall ((A_63 tptp.nat) (B_45 tptp.nat) (C_29 tptp.nat)) (= (tptp.times_times_nat (tptp.times_times_nat A_63 B_45) C_29) (tptp.times_times_nat A_63 (tptp.times_times_nat B_45 C_29)))) (forall ((A_63 tptp.real) (B_45 tptp.real) (C_29 tptp.real)) (= (tptp.times_times_real (tptp.times_times_real A_63 B_45) C_29) (tptp.times_times_real A_63 (tptp.times_times_real B_45 C_29)))) (forall ((Lx_4 tptp.int) (Ly_4 tptp.int) (Rx_4 tptp.int)) (= (tptp.times_times_int (tptp.times_times_int Lx_4 Ly_4) Rx_4) (tptp.times_times_int Lx_4 (tptp.times_times_int Ly_4 Rx_4)))) (forall ((Lx_4 tptp.nat) (Ly_4 tptp.nat) (Rx_4 tptp.nat)) (= (tptp.times_times_nat (tptp.times_times_nat Lx_4 Ly_4) Rx_4) (tptp.times_times_nat Lx_4 (tptp.times_times_nat Ly_4 Rx_4)))) (forall ((Lx_4 tptp.real) (Ly_4 tptp.real) (Rx_4 tptp.real)) (= (tptp.times_times_real (tptp.times_times_real Lx_4 Ly_4) Rx_4) (tptp.times_times_real Lx_4 (tptp.times_times_real Ly_4 Rx_4)))) (forall ((Lx_3 tptp.int) (Ly_3 tptp.int) (Rx_3 tptp.int)) (= (tptp.times_times_int (tptp.times_times_int Lx_3 Ly_3) Rx_3) (tptp.times_times_int (tptp.times_times_int Lx_3 Rx_3) Ly_3))) (forall ((Lx_3 tptp.nat) (Ly_3 tptp.nat) (Rx_3 tptp.nat)) (= (tptp.times_times_nat (tptp.times_times_nat Lx_3 Ly_3) Rx_3) (tptp.times_times_nat (tptp.times_times_nat Lx_3 Rx_3) Ly_3))) (forall ((Lx_3 tptp.real) (Ly_3 tptp.real) (Rx_3 tptp.real)) (= (tptp.times_times_real (tptp.times_times_real Lx_3 Ly_3) Rx_3) (tptp.times_times_real (tptp.times_times_real Lx_3 Rx_3) Ly_3))) (forall ((Lx_2 tptp.int) (Ly_2 tptp.int) (Rx_2 tptp.int) (Ry_2 tptp.int)) (let ((_let_1 (tptp.times_times_int Rx_2 Ry_2))) (= (tptp.times_times_int (tptp.times_times_int Lx_2 Ly_2) _let_1) (tptp.times_times_int Lx_2 (tptp.times_times_int Ly_2 _let_1))))) (forall ((Lx_2 tptp.nat) (Ly_2 tptp.nat) (Rx_2 tptp.nat) (Ry_2 tptp.nat)) (let ((_let_1 (tptp.times_times_nat Rx_2 Ry_2))) (= (tptp.times_times_nat (tptp.times_times_nat Lx_2 Ly_2) _let_1) (tptp.times_times_nat Lx_2 (tptp.times_times_nat Ly_2 _let_1))))) (forall ((Lx_2 tptp.real) (Ly_2 tptp.real) (Rx_2 tptp.real) (Ry_2 tptp.real)) (let ((_let_1 (tptp.times_times_real Rx_2 Ry_2))) (= (tptp.times_times_real (tptp.times_times_real Lx_2 Ly_2) _let_1) (tptp.times_times_real Lx_2 (tptp.times_times_real Ly_2 _let_1))))) (forall ((Lx_1 tptp.real) (Ly_1 tptp.real) (Rx_1 tptp.real) (Ry_1 tptp.real)) (let ((_let_1 (tptp.times_times_real Lx_1 Ly_1))) (= (tptp.times_times_real _let_1 (tptp.times_times_real Rx_1 Ry_1)) (tptp.times_times_real Rx_1 (tptp.times_times_real _let_1 Ry_1))))) (forall ((Lx_1 tptp.nat) (Ly_1 tptp.nat) (Rx_1 tptp.nat) (Ry_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat Lx_1 Ly_1))) (= (tptp.times_times_nat _let_1 (tptp.times_times_nat Rx_1 Ry_1)) (tptp.times_times_nat Rx_1 (tptp.times_times_nat _let_1 Ry_1))))) (forall ((Lx_1 tptp.int) (Ly_1 tptp.int) (Rx_1 tptp.int) (Ry_1 tptp.int)) (let ((_let_1 (tptp.times_times_int Lx_1 Ly_1))) (= (tptp.times_times_int _let_1 (tptp.times_times_int Rx_1 Ry_1)) (tptp.times_times_int Rx_1 (tptp.times_times_int _let_1 Ry_1))))) (forall ((Lx tptp.real) (Ly tptp.real) (Rx tptp.real) (Ry tptp.real)) (= (tptp.times_times_real (tptp.times_times_real Lx Ly) (tptp.times_times_real Rx Ry)) (tptp.times_times_real (tptp.times_times_real Lx Rx) (tptp.times_times_real Ly Ry)))) (forall ((Lx tptp.nat) (Ly tptp.nat) (Rx tptp.nat) (Ry tptp.nat)) (= (tptp.times_times_nat (tptp.times_times_nat Lx Ly) (tptp.times_times_nat Rx Ry)) (tptp.times_times_nat (tptp.times_times_nat Lx Rx) (tptp.times_times_nat Ly Ry)))) (forall ((Lx tptp.int) (Ly tptp.int) (Rx tptp.int) (Ry tptp.int)) (= (tptp.times_times_int (tptp.times_times_int Lx Ly) (tptp.times_times_int Rx Ry)) (tptp.times_times_int (tptp.times_times_int Lx Rx) (tptp.times_times_int Ly Ry)))) (forall ((A_1 tptp.int) (B tptp.int) (C_1 tptp.int) (D tptp.int)) (=> (= (tptp.minus_minus_int A_1 B) (tptp.minus_minus_int C_1 D)) (= (= A_1 B) (= C_1 D)))) (forall ((A_1 tptp.real) (B tptp.real) (C_1 tptp.real) (D tptp.real)) (=> (= (tptp.minus_minus_real A_1 B) (tptp.minus_minus_real C_1 D)) (= (= A_1 B) (= C_1 D)))) (forall ((A_1 tptp.int) (B tptp.int) (C_1 tptp.int) (D tptp.int)) (=> (= (tptp.minus_minus_int A_1 B) (tptp.minus_minus_int C_1 D)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_1) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_1) D))))) (forall ((A_1 tptp.real) (B tptp.real) (C_1 tptp.real) (D tptp.real)) (=> (= (tptp.minus_minus_real A_1 B) (tptp.minus_minus_real C_1 D)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_1) B)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_1) D))))) (forall ((V_13 tptp.int) (V_12 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_12)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_13)) (= (tptp.times_times_real (tptp.number267125858f_real V_12) (tptp.number267125858f_real V_13)) (tptp.number267125858f_real (tptp.times_times_int V_12 V_13))))))) (forall ((V_13 tptp.int) (V_12 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_12)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_13)) (= (tptp.times_times_nat (tptp.number_number_of_nat V_12) (tptp.number_number_of_nat V_13)) (tptp.number_number_of_nat (tptp.times_times_int V_12 V_13))))))) (forall ((V_13 tptp.int) (V_12 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_12)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_13)) (= (tptp.times_times_int (tptp.number_number_of_int V_12) (tptp.number_number_of_int V_13)) (tptp.number_number_of_int (tptp.times_times_int V_12 V_13))))))) (forall ((W tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) W))) (forall ((Z tptp.int) (W tptp.int)) (= (tptp.times_times_int Z W) (tptp.times_times_int W Z))) (forall ((Z tptp.int) (W tptp.int)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z) W)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) Z)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (= (tptp.times_times_int (tptp.times_times_int Z1 Z2) Z3) (tptp.times_times_int Z1 (tptp.times_times_int Z2 Z3)))) (forall ((K_1 tptp.int) (I_2 tptp.int) (J_1 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_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int J_1) K_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K_1)))))) (forall ((Z tptp.int) (W tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z) W)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) Z)) (= Z W)))) (forall ((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 ((V_11 tptp.int) (W_6 tptp.int)) (= (tptp.number267125858f_real (tptp.times_times_int V_11 W_6)) (tptp.times_times_real (tptp.number267125858f_real V_11) (tptp.number267125858f_real W_6)))) (forall ((V_11 tptp.int) (W_6 tptp.int)) (= (tptp.number_number_of_int (tptp.times_times_int V_11 W_6)) (tptp.times_times_int (tptp.number_number_of_int V_11) (tptp.number_number_of_int W_6)))) (forall ((V_10 tptp.int) (W_5 tptp.int)) (= (tptp.times_times_real (tptp.number267125858f_real V_10) (tptp.number267125858f_real W_5)) (tptp.number267125858f_real (tptp.times_times_int V_10 W_5)))) (forall ((V_10 tptp.int) (W_5 tptp.int)) (= (tptp.times_times_int (tptp.number_number_of_int V_10) (tptp.number_number_of_int W_5)) (tptp.number_number_of_int (tptp.times_times_int V_10 W_5)))) (forall ((V_9 tptp.int) (W_4 tptp.int) (Z_5 tptp.real)) (= (tptp.times_times_real (tptp.number267125858f_real V_9) (tptp.times_times_real (tptp.number267125858f_real W_4) Z_5)) (tptp.times_times_real (tptp.number267125858f_real (tptp.times_times_int V_9 W_4)) Z_5))) (forall ((V_9 tptp.int) (W_4 tptp.int) (Z_5 tptp.int)) (= (tptp.times_times_int (tptp.number_number_of_int V_9) (tptp.times_times_int (tptp.number_number_of_int W_4) Z_5)) (tptp.times_times_int (tptp.number_number_of_int (tptp.times_times_int V_9 W_4)) Z_5))) (forall ((Z_4 tptp.int) (Z_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 Z_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_4)) (= (= (tptp.nat_1 Z_1) (tptp.nat_1 Z_4)) (= Z_1 Z_4)))))) (forall ((V_8 tptp.int) (B_44 tptp.int) (C_28 tptp.int)) (let ((_let_1 (tptp.number_number_of_int V_8))) (= (tptp.times_times_int _let_1 (tptp.minus_minus_int B_44 C_28)) (tptp.minus_minus_int (tptp.times_times_int _let_1 B_44) (tptp.times_times_int _let_1 C_28))))) (forall ((V_8 tptp.int) (B_44 tptp.real) (C_28 tptp.real)) (let ((_let_1 (tptp.number267125858f_real V_8))) (= (tptp.times_times_real _let_1 (tptp.minus_minus_real B_44 C_28)) (tptp.minus_minus_real (tptp.times_times_real _let_1 B_44) (tptp.times_times_real _let_1 C_28))))) (forall ((A_62 tptp.int) (B_43 tptp.int) (V_7 tptp.int)) (let ((_let_1 (tptp.number_number_of_int V_7))) (= (tptp.times_times_int (tptp.minus_minus_int A_62 B_43) _let_1) (tptp.minus_minus_int (tptp.times_times_int A_62 _let_1) (tptp.times_times_int B_43 _let_1))))) (forall ((A_62 tptp.real) (B_43 tptp.real) (V_7 tptp.int)) (let ((_let_1 (tptp.number267125858f_real V_7))) (= (tptp.times_times_real (tptp.minus_minus_real A_62 B_43) _let_1) (tptp.minus_minus_real (tptp.times_times_real A_62 _let_1) (tptp.times_times_real B_43 _let_1))))) (forall ((V_6 tptp.int) (W_3 tptp.int)) (= (tptp.number_number_of_int (tptp.minus_minus_int V_6 W_3)) (tptp.minus_minus_int (tptp.number_number_of_int V_6) (tptp.number_number_of_int W_3)))) (forall ((V_6 tptp.int) (W_3 tptp.int)) (= (tptp.number267125858f_real (tptp.minus_minus_int V_6 W_3)) (tptp.minus_minus_real (tptp.number267125858f_real V_6) (tptp.number267125858f_real W_3)))) (forall ((M_4 tptp.nat) (N_10 tptp.nat)) (= (tptp.hAPP_nat_real tptp.semiri132038758t_real (tptp.times_times_nat M_4 N_10)) (tptp.times_times_real (tptp.hAPP_nat_real tptp.semiri132038758t_real M_4) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_10)))) (forall ((M_4 tptp.nat) (N_10 tptp.nat)) (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat (tptp.times_times_nat M_4 N_10)) (tptp.times_times_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_4) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_10)))) (forall ((M_4 tptp.nat) (N_10 tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.times_times_nat M_4 N_10)) (tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_4) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_10)))) (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 ((I_2 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (= (tptp.minus_minus_nat (tptp.minus_minus_nat I_2 J_1) K_1) (tptp.minus_minus_nat (tptp.minus_minus_nat I_2 K_1) J_1))) (forall ((Xa tptp.int) (Ya tptp.int) (P_1 tptp.bool)) (let ((_let_1 (tptp.nat_1 (tptp.if_int P_1 Xa Ya)))) (let ((_let_2 (tptp.hBOOL P_1))) (and (=> _let_2 (= (tptp.nat_1 Xa) _let_1)) (=> (not _let_2) (= (tptp.nat_1 Ya) _let_1)))))) (forall ((B_42 tptp.real) (A_61 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_61)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_42) tptp.zero_zero_real))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_61) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_42)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real A_61 B_42)) tptp.zero_zero_real))))) (forall ((B_42 tptp.nat) (A_61 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_61)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_42) tptp.zero_zero_nat))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_61) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_42)))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat A_61 B_42)) tptp.zero_zero_nat))))) (forall ((B_42 tptp.int) (A_61 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_61)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_42) tptp.zero_zero_int))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_61) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_42)))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int A_61 B_42)) tptp.zero_zero_int))))) (forall ((B_41 tptp.real) (A_60 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_60)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_41))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_60) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_41) tptp.zero_zero_real)))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.times_times_real A_60 B_41)))))) (forall ((B_41 tptp.int) (A_60 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_60)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_41))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_60) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_41) tptp.zero_zero_int)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.times_times_int A_60 B_41)))))) (forall ((C_27 tptp.real) (D_10 tptp.real) (A_59 tptp.real) (B_40 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_59) B_40)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_27) D_10)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_40)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_27)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real A_59 C_27)) (tptp.times_times_real B_40 D_10))))))))) (forall ((C_27 tptp.nat) (D_10 tptp.nat) (A_59 tptp.nat) (B_40 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_59) B_40)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_27) D_10)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_40)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_27)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat A_59 C_27)) (tptp.times_times_nat B_40 D_10))))))))) (forall ((C_27 tptp.int) (D_10 tptp.int) (A_59 tptp.int) (B_40 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_59) B_40)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_27) D_10)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_40)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_27)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int A_59 C_27)) (tptp.times_times_int B_40 D_10))))))))) (forall ((C_26 tptp.real) (D_9 tptp.real) (A_58 tptp.real) (B_39 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_58) B_39)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_26) D_9)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_58)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_26)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real A_58 C_26)) (tptp.times_times_real B_39 D_9))))))))) (forall ((C_26 tptp.nat) (D_9 tptp.nat) (A_58 tptp.nat) (B_39 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_58) B_39)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_26) D_9)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_58)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_26)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat A_58 C_26)) (tptp.times_times_nat B_39 D_9))))))))) (forall ((C_26 tptp.int) (D_9 tptp.int) (A_58 tptp.int) (B_39 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_58) B_39)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_26) D_9)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_58)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_26)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int A_58 C_26)) (tptp.times_times_int B_39 D_9))))))))) (forall ((C_25 tptp.real) (B_38 tptp.real) (A_57 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_38) A_57)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_25) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real C_25 A_57)) (tptp.times_times_real C_25 B_38)))))) (forall ((C_25 tptp.int) (B_38 tptp.int) (A_57 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_38) A_57)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_25) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int C_25 A_57)) (tptp.times_times_int C_25 B_38)))))) (forall ((C_24 tptp.real) (B_37 tptp.real) (A_56 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_37) A_56)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_24) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real A_56 C_24)) (tptp.times_times_real B_37 C_24)))))) (forall ((C_24 tptp.int) (B_37 tptp.int) (A_56 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_37) A_56)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_24) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int A_56 C_24)) (tptp.times_times_int B_37 C_24)))))) (forall ((C_23 tptp.real) (A_55 tptp.real) (B_36 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_55) B_36)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_23)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real C_23 A_55)) (tptp.times_times_real C_23 B_36)))))) (forall ((C_23 tptp.nat) (A_55 tptp.nat) (B_36 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_55) B_36)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_23)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat C_23 A_55)) (tptp.times_times_nat C_23 B_36)))))) (forall ((C_23 tptp.int) (A_55 tptp.int) (B_36 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_55) B_36)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_23)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int C_23 A_55)) (tptp.times_times_int C_23 B_36)))))) (forall ((C_22 tptp.real) (A_54 tptp.real) (B_35 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_54) B_35)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_22)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real C_22 A_54)) (tptp.times_times_real C_22 B_35)))))) (forall ((C_22 tptp.nat) (A_54 tptp.nat) (B_35 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_54) B_35)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_22)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat C_22 A_54)) (tptp.times_times_nat C_22 B_35)))))) (forall ((C_22 tptp.int) (A_54 tptp.int) (B_35 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_54) B_35)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_22)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int C_22 A_54)) (tptp.times_times_int C_22 B_35)))))) (forall ((C_21 tptp.real) (A_53 tptp.real) (B_34 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_53) B_34)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_21)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real A_53 C_21)) (tptp.times_times_real B_34 C_21)))))) (forall ((C_21 tptp.nat) (A_53 tptp.nat) (B_34 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_53) B_34)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_21)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat A_53 C_21)) (tptp.times_times_nat B_34 C_21)))))) (forall ((C_21 tptp.int) (A_53 tptp.int) (B_34 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_53) B_34)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_21)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int A_53 C_21)) (tptp.times_times_int B_34 C_21)))))) (forall ((B_33 tptp.real) (A_52 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_52) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_33) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.times_times_real A_52 B_33)))))) (forall ((B_33 tptp.int) (A_52 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_52) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_33) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.times_times_int A_52 B_33)))))) (forall ((B_32 tptp.real) (A_51 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_51) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B_32)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real A_51 B_32)) tptp.zero_zero_real))))) (forall ((B_32 tptp.nat) (A_51 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_51) tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B_32)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat A_51 B_32)) tptp.zero_zero_nat))))) (forall ((B_32 tptp.int) (A_51 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_51) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) B_32)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int A_51 B_32)) tptp.zero_zero_int))))) (forall ((B_31 tptp.real) (A_50 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_50)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_31) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real B_31 A_50)) tptp.zero_zero_real))))) (forall ((B_31 tptp.nat) (A_50 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_50)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_31) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat B_31 A_50)) tptp.zero_zero_nat))))) (forall ((B_31 tptp.int) (A_50 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_50)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_31) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int B_31 A_50)) tptp.zero_zero_int))))) (forall ((B_30 tptp.real) (A_49 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_49)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_30) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real A_49 B_30)) tptp.zero_zero_real))))) (forall ((B_30 tptp.nat) (A_49 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_49)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_30) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat A_49 B_30)) tptp.zero_zero_nat))))) (forall ((B_30 tptp.int) (A_49 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_49)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_30) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int A_49 B_30)) tptp.zero_zero_int))))) (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.nat_1 Xa) (tptp.nat_1 Ya)) (= Xa Ya)))))) (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.times_times_int X Y))))))) (forall ((B_29 tptp.real) (A_48 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_48)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_29)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.times_times_real A_48 B_29))))))) (forall ((B_29 tptp.nat) (A_48 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_48)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_29)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.times_times_nat A_48 B_29))))))) (forall ((B_29 tptp.int) (A_48 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_48)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_29)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.times_times_int A_48 B_29))))))) (forall ((A_1 tptp.real) (E_1 tptp.real) (C_1 tptp.real) (B tptp.real) (D tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.plus_plus_real (tptp.times_times_real A_1 E_1) C_1)) (tptp.plus_plus_real (tptp.times_times_real B E_1) D))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.plus_plus_real (tptp.times_times_real (tptp.minus_minus_real A_1 B) E_1) C_1)) D)))) (forall ((A_1 tptp.int) (E_1 tptp.int) (C_1 tptp.int) (B tptp.int) (D tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.plus_plus_int (tptp.times_times_int A_1 E_1) C_1)) (tptp.plus_plus_int (tptp.times_times_int B E_1) D))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.plus_plus_int (tptp.times_times_int (tptp.minus_minus_int A_1 B) E_1) C_1)) D)))) (forall ((A_1 tptp.real) (E_1 tptp.real) (C_1 tptp.real) (B tptp.real) (D tptp.real)) (= (= (tptp.plus_plus_real (tptp.times_times_real A_1 E_1) C_1) (tptp.plus_plus_real (tptp.times_times_real B E_1) D)) (= (tptp.plus_plus_real (tptp.times_times_real (tptp.minus_minus_real A_1 B) E_1) C_1) D))) (forall ((A_1 tptp.int) (E_1 tptp.int) (C_1 tptp.int) (B tptp.int) (D tptp.int)) (= (= (tptp.plus_plus_int (tptp.times_times_int A_1 E_1) C_1) (tptp.plus_plus_int (tptp.times_times_int B E_1) D)) (= (tptp.plus_plus_int (tptp.times_times_int (tptp.minus_minus_int A_1 B) E_1) C_1) D))) (forall ((A_1 tptp.real) (E_1 tptp.real) (C_1 tptp.real) (B tptp.real) (D tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.plus_plus_real (tptp.times_times_real A_1 E_1) C_1)) (tptp.plus_plus_real (tptp.times_times_real B E_1) D))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_1) (tptp.plus_plus_real (tptp.times_times_real (tptp.minus_minus_real B A_1) E_1) D))))) (forall ((A_1 tptp.int) (E_1 tptp.int) (C_1 tptp.int) (B tptp.int) (D tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.plus_plus_int (tptp.times_times_int A_1 E_1) C_1)) (tptp.plus_plus_int (tptp.times_times_int B E_1) D))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_1) (tptp.plus_plus_int (tptp.times_times_int (tptp.minus_minus_int B A_1) E_1) D))))) (forall ((A_1 tptp.real) (E_1 tptp.real) (C_1 tptp.real) (B tptp.real) (D tptp.real)) (= (= (tptp.plus_plus_real (tptp.times_times_real A_1 E_1) C_1) (tptp.plus_plus_real (tptp.times_times_real B E_1) D)) (= C_1 (tptp.plus_plus_real (tptp.times_times_real (tptp.minus_minus_real B A_1) E_1) D)))) (forall ((A_1 tptp.int) (E_1 tptp.int) (C_1 tptp.int) (B tptp.int) (D tptp.int)) (= (= (tptp.plus_plus_int (tptp.times_times_int A_1 E_1) C_1) (tptp.plus_plus_int (tptp.times_times_int B E_1) D)) (= C_1 (tptp.plus_plus_int (tptp.times_times_int (tptp.minus_minus_int B A_1) E_1) D)))) (forall ((X_11 tptp.real) (Y_9 tptp.real) (A_47 tptp.real) (B_28 tptp.real)) (= (tptp.minus_minus_real (tptp.times_times_real X_11 Y_9) (tptp.times_times_real A_47 B_28)) (tptp.plus_plus_real (tptp.times_times_real X_11 (tptp.minus_minus_real Y_9 B_28)) (tptp.times_times_real (tptp.minus_minus_real X_11 A_47) B_28)))) (forall ((X_11 tptp.int) (Y_9 tptp.int) (A_47 tptp.int) (B_28 tptp.int)) (= (tptp.minus_minus_int (tptp.times_times_int X_11 Y_9) (tptp.times_times_int A_47 B_28)) (tptp.plus_plus_int (tptp.times_times_int X_11 (tptp.minus_minus_int Y_9 B_28)) (tptp.times_times_int (tptp.minus_minus_int X_11 A_47) B_28)))) (forall ((A_1 tptp.real) (B tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real A_1 B)) tptp.zero_zero_real)) (or (and (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B) tptp.zero_zero_real))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_1) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B))))))) (forall ((A_1 tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int A_1 B)) tptp.zero_zero_int)) (or (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B) tptp.zero_zero_int))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_1) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B))))))) (forall ((A_1 tptp.real) (B 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.times_times_real A_1 B))) (or (and (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_1) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B) tptp.zero_zero_real))))))) (forall ((A_1 tptp.int) (B 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.times_times_int A_1 B))) (or (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_1) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B) tptp.zero_zero_int))))))) (forall ((P_1 tptp.fun_nat_bool)) (= (forall ((X1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 X1))) (forall ((X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.nat_1 X_1))))))) (forall ((P_1 tptp.fun_nat_bool)) (= (exists ((X1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 X1))) (exists ((X_1 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.nat_1 X_1))))))) (forall ((A_46 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.times_times_real A_46 A_46)))) (forall ((A_46 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.times_times_int A_46 A_46)))) (forall ((A_1 tptp.real) (E_1 tptp.real) (C_1 tptp.real) (B tptp.real) (D tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.plus_plus_real (tptp.times_times_real A_1 E_1) C_1)) (tptp.plus_plus_real (tptp.times_times_real B E_1) D))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.plus_plus_real (tptp.times_times_real (tptp.minus_minus_real A_1 B) E_1) C_1)) D)))) (forall ((A_1 tptp.int) (E_1 tptp.int) (C_1 tptp.int) (B tptp.int) (D tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int (tptp.times_times_int A_1 E_1) C_1)) (tptp.plus_plus_int (tptp.times_times_int B E_1) D))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int (tptp.times_times_int (tptp.minus_minus_int A_1 B) E_1) C_1)) D)))) (forall ((A_1 tptp.real) (E_1 tptp.real) (C_1 tptp.real) (B tptp.real) (D tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.plus_plus_real (tptp.times_times_real A_1 E_1) C_1)) (tptp.plus_plus_real (tptp.times_times_real B E_1) D))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_1) (tptp.plus_plus_real (tptp.times_times_real (tptp.minus_minus_real B A_1) E_1) D))))) (forall ((A_1 tptp.int) (E_1 tptp.int) (C_1 tptp.int) (B tptp.int) (D tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int (tptp.times_times_int A_1 E_1) C_1)) (tptp.plus_plus_int (tptp.times_times_int B E_1) D))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_1) (tptp.plus_plus_int (tptp.times_times_int (tptp.minus_minus_int B A_1) E_1) D))))) (forall ((X_10 tptp.real)) (= (tptp.minus_minus_real (tptp.times_times_real X_10 X_10) tptp.one_one_real) (tptp.times_times_real (tptp.plus_plus_real X_10 tptp.one_one_real) (tptp.minus_minus_real X_10 tptp.one_one_real)))) (forall ((X_10 tptp.int)) (= (tptp.minus_minus_int (tptp.times_times_int X_10 X_10) tptp.one_one_int) (tptp.times_times_int (tptp.plus_plus_int X_10 tptp.one_one_int) (tptp.minus_minus_int X_10 tptp.one_one_int)))) (forall ((C_20 tptp.real) (A_45 tptp.real) (B_27 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real C_20 A_45)) (tptp.times_times_real C_20 B_27))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_20)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_45) B_27))))) (forall ((C_20 tptp.nat) (A_45 tptp.nat) (B_27 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat C_20 A_45)) (tptp.times_times_nat C_20 B_27))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_20)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_45) B_27))))) (forall ((C_20 tptp.int) (A_45 tptp.int) (B_27 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int C_20 A_45)) (tptp.times_times_int C_20 B_27))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_20)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_45) B_27))))) (forall ((A_44 tptp.real) (C_19 tptp.real) (B_26 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real A_44 C_19)) (tptp.times_times_real B_26 C_19))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_19)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_44) B_26))))) (forall ((A_44 tptp.nat) (C_19 tptp.nat) (B_26 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat A_44 C_19)) (tptp.times_times_nat B_26 C_19))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_19)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_44) B_26))))) (forall ((A_44 tptp.int) (C_19 tptp.int) (B_26 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int A_44 C_19)) (tptp.times_times_int B_26 C_19))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_19)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_44) B_26))))) (forall ((C_18 tptp.real) (A_43 tptp.real) (B_25 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.times_times_real C_18 A_43)) (tptp.times_times_real C_18 B_25))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_18)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_43) B_25))))) (forall ((C_18 tptp.nat) (A_43 tptp.nat) (B_25 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.times_times_nat C_18 A_43)) (tptp.times_times_nat C_18 B_25))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_18)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_43) B_25))))) (forall ((C_18 tptp.int) (A_43 tptp.int) (B_25 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.times_times_int C_18 A_43)) (tptp.times_times_int C_18 B_25))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_18)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_43) B_25))))) (forall ((C_17 tptp.real) (A_42 tptp.real) (B_24 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.times_times_real C_17 A_42)) (tptp.times_times_real C_17 B_24))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_17)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_42) B_24))))) (forall ((C_17 tptp.nat) (A_42 tptp.nat) (B_24 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.times_times_nat C_17 A_42)) (tptp.times_times_nat C_17 B_24))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_17)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_42) B_24))))) (forall ((C_17 tptp.int) (A_42 tptp.int) (B_24 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.times_times_int C_17 A_42)) (tptp.times_times_int C_17 B_24))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_17)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_42) B_24))))) (forall ((A_41 tptp.real) (C_16 tptp.real) (B_23 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.times_times_real A_41 C_16)) (tptp.times_times_real B_23 C_16))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_16)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_41) B_23))))) (forall ((A_41 tptp.nat) (C_16 tptp.nat) (B_23 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.times_times_nat A_41 C_16)) (tptp.times_times_nat B_23 C_16))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_16)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_41) B_23))))) (forall ((A_41 tptp.int) (C_16 tptp.int) (B_23 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.times_times_int A_41 C_16)) (tptp.times_times_int B_23 C_16))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_16)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_41) B_23))))) (forall ((A_40 tptp.real) (C_15 tptp.real) (B_22 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.times_times_real A_40 C_15)) (tptp.times_times_real B_22 C_15))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_15)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_40) B_22))))) (forall ((A_40 tptp.nat) (C_15 tptp.nat) (B_22 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.times_times_nat A_40 C_15)) (tptp.times_times_nat B_22 C_15))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_15)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_40) B_22))))) (forall ((A_40 tptp.int) (C_15 tptp.int) (B_22 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.times_times_int A_40 C_15)) (tptp.times_times_int B_22 C_15))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_15)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_40) B_22))))) (forall ((C_14 tptp.real) (D_8 tptp.real) (A_39 tptp.real) (B_21 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_39) B_21)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_14) D_8)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_39)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_14)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.times_times_real A_39 C_14)) (tptp.times_times_real B_21 D_8)))))))) (forall ((C_14 tptp.nat) (D_8 tptp.nat) (A_39 tptp.nat) (B_21 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_39) B_21)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_14) D_8)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_39)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_14)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.times_times_nat A_39 C_14)) (tptp.times_times_nat B_21 D_8)))))))) (forall ((C_14 tptp.int) (D_8 tptp.int) (A_39 tptp.int) (B_21 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_39) B_21)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_14) D_8)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_39)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_14)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.times_times_int A_39 C_14)) (tptp.times_times_int B_21 D_8)))))))) (forall ((C_13 tptp.real) (D_7 tptp.real) (A_38 tptp.real) (B_20 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_38) B_20)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_13) D_7)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_38)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_13)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.times_times_real A_38 C_13)) (tptp.times_times_real B_20 D_7)))))))) (forall ((C_13 tptp.nat) (D_7 tptp.nat) (A_38 tptp.nat) (B_20 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_38) B_20)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_13) D_7)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_38)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_13)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.times_times_nat A_38 C_13)) (tptp.times_times_nat B_20 D_7)))))))) (forall ((C_13 tptp.int) (D_7 tptp.int) (A_38 tptp.int) (B_20 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_38) B_20)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_13) D_7)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_38)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_13)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.times_times_int A_38 C_13)) (tptp.times_times_int B_20 D_7)))))))) (forall ((C_12 tptp.real) (D_6 tptp.real) (A_37 tptp.real) (B_19 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_37) B_19)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_12) D_6)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_37)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_12)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.times_times_real A_37 C_12)) (tptp.times_times_real B_19 D_6))))))))) (forall ((C_12 tptp.nat) (D_6 tptp.nat) (A_37 tptp.nat) (B_19 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_37) B_19)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_12) D_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_37)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_12)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.times_times_nat A_37 C_12)) (tptp.times_times_nat B_19 D_6))))))))) (forall ((C_12 tptp.int) (D_6 tptp.int) (A_37 tptp.int) (B_19 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_37) B_19)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_12) D_6)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_37)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_12)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.times_times_int A_37 C_12)) (tptp.times_times_int B_19 D_6))))))))) (forall ((C_11 tptp.real) (D_5 tptp.real) (A_36 tptp.real) (B_18 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_36) B_18)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_11) D_5)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) B_18)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_11)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.times_times_real A_36 C_11)) (tptp.times_times_real B_18 D_5)))))))) (forall ((C_11 tptp.nat) (D_5 tptp.nat) (A_36 tptp.nat) (B_18 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_36) B_18)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_11) D_5)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) B_18)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_11)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.times_times_nat A_36 C_11)) (tptp.times_times_nat B_18 D_5)))))))) (forall ((C_11 tptp.int) (D_5 tptp.int) (A_36 tptp.int) (B_18 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_36) B_18)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_11) D_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_18)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_11)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.times_times_int A_36 C_11)) (tptp.times_times_int B_18 D_5)))))))) (forall ((A_1 tptp.real) (B tptp.real) (C_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_1) tptp.zero_zero_real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real C_1 A_1)) (tptp.times_times_real C_1 B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B) A_1))))) (forall ((A_1 tptp.int) (B tptp.int) (C_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_1) tptp.zero_zero_int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int C_1 A_1)) (tptp.times_times_int C_1 B))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B) A_1))))) (forall ((A_1 tptp.real) (B tptp.real) (C_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real C_1 A_1)) (tptp.times_times_real C_1 B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_1) B))))) (forall ((A_1 tptp.int) (B tptp.int) (C_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_1)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int C_1 A_1)) (tptp.times_times_int C_1 B))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_1) B))))) (forall ((X_9 tptp.real) (Y_8 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.plus_plus_real (tptp.times_times_real X_9 X_9) (tptp.times_times_real Y_8 Y_8))))) (forall ((X_9 tptp.int) (Y_8 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.plus_plus_int (tptp.times_times_int X_9 X_9) (tptp.times_times_int Y_8 Y_8))))) (forall ((Xa tptp.real) (Ya tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.plus_plus_real (tptp.times_times_real Xa Xa) (tptp.times_times_real Ya Ya))) tptp.zero_zero_real)) (and (= Xa tptp.zero_zero_real) (= Ya tptp.zero_zero_real)))) (forall ((Xa tptp.int) (Ya tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.plus_plus_int (tptp.times_times_int Xa Xa) (tptp.times_times_int Ya Ya))) tptp.zero_zero_int)) (and (= Xa tptp.zero_zero_int) (= Ya tptp.zero_zero_int)))) (forall ((Y_7 tptp.real) (X_8 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_8)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_7)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_7) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real X_8 Y_7)) X_8))))))) (forall ((Y_7 tptp.int) (X_8 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_8)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_7)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_7) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int X_8 Y_7)) X_8))))))) (forall ((Y_6 tptp.real) (X_7 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_7)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_6)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_6) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real Y_6 X_7)) X_7))))))) (forall ((Y_6 tptp.int) (X_7 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_7)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_6)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_6) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int Y_6 X_7)) X_7))))))) (forall ((Z tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z) tptp.zero_zero_int)) (= (tptp.nat_1 Z) tptp.zero_zero_nat))) (forall ((I_1 tptp.int)) (= (= (tptp.nat_1 I_1) tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_1) tptp.zero_zero_int)))) (forall ((A_35 tptp.real) (N_9 tptp.nat) (N_8 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_35))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_9) N_8)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) A_35)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real _let_1 N_9)) (tptp.hAPP_nat_real _let_1 N_8))))))) (forall ((A_35 tptp.nat) (N_9 tptp.nat) (N_8 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_35))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_9) N_8)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.one_one_nat) A_35)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 N_9)) (tptp.hAPP_nat_nat _let_1 N_8))))))) (forall ((A_35 tptp.int) (N_9 tptp.nat) (N_8 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_35))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_9) N_8)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) A_35)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int _let_1 N_9)) (tptp.hAPP_nat_int _let_1 N_8))))))) (forall ((Z tptp.int)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.nat_1 Z)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)))) (and (=> _let_2 (= _let_1 Z)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((Ma tptp.nat) (Z_1 tptp.int)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma) Z_1) (and (= Ma (tptp.nat_1 Z_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z_1))))) (forall ((Z tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.nat_1 Z)) Z))) (forall ((A_1 tptp.real) (B tptp.real)) (= (= (tptp.minus_minus_real A_1 B) tptp.zero_zero_real) (= A_1 B))) (forall ((A_1 tptp.int) (B tptp.int)) (= (= (tptp.minus_minus_int A_1 B) tptp.zero_zero_int) (= A_1 B))) (forall ((A_1 tptp.real) (B tptp.real)) (= (= A_1 B) (= (tptp.minus_minus_real A_1 B) tptp.zero_zero_real))) (forall ((A_1 tptp.int) (B tptp.int)) (= (= A_1 B) (= (tptp.minus_minus_int A_1 B) tptp.zero_zero_int))) (forall ((A_34 tptp.real)) (= (tptp.minus_minus_real A_34 A_34) tptp.zero_zero_real)) (forall ((A_34 tptp.int)) (= (tptp.minus_minus_int A_34 A_34) tptp.zero_zero_int)) (forall ((A_33 tptp.real)) (= (tptp.minus_minus_real A_33 tptp.zero_zero_real) A_33)) (forall ((A_33 tptp.int)) (= (tptp.minus_minus_int A_33 tptp.zero_zero_int) A_33)) (forall ((A_1 tptp.int) (B tptp.int) (C_1 tptp.int) (D tptp.int)) (=> (= (tptp.minus_minus_int A_1 B) (tptp.minus_minus_int C_1 D)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_1) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_1) D))))) (forall ((A_1 tptp.real) (B tptp.real) (C_1 tptp.real) (D tptp.real)) (=> (= (tptp.minus_minus_real A_1 B) (tptp.minus_minus_real C_1 D)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_1) B)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_1) D))))) (forall ((A_32 tptp.real) (C_10 tptp.real) (B_17 tptp.real) (D_4 tptp.real)) (= (tptp.minus_minus_real (tptp.plus_plus_real A_32 C_10) (tptp.plus_plus_real B_17 D_4)) (tptp.plus_plus_real (tptp.minus_minus_real A_32 B_17) (tptp.minus_minus_real C_10 D_4)))) (forall ((A_32 tptp.int) (C_10 tptp.int) (B_17 tptp.int) (D_4 tptp.int)) (= (tptp.minus_minus_int (tptp.plus_plus_int A_32 C_10) (tptp.plus_plus_int B_17 D_4)) (tptp.plus_plus_int (tptp.minus_minus_int A_32 B_17) (tptp.minus_minus_int C_10 D_4)))) (forall ((A_31 tptp.real) (B_16 tptp.real)) (= (tptp.minus_minus_real (tptp.plus_plus_real A_31 B_16) B_16) A_31)) (forall ((A_31 tptp.int) (B_16 tptp.int)) (= (tptp.minus_minus_int (tptp.plus_plus_int A_31 B_16) B_16) A_31)) (forall ((A_30 tptp.real) (B_15 tptp.real)) (= (tptp.plus_plus_real (tptp.minus_minus_real A_30 B_15) B_15) A_30)) (forall ((A_30 tptp.int) (B_15 tptp.int)) (= (tptp.plus_plus_int (tptp.minus_minus_int A_30 B_15) B_15) A_30)) (forall ((A_29 tptp.real)) (= (tptp.times_times_real tptp.zero_zero_real A_29) tptp.zero_zero_real)) (forall ((A_29 tptp.nat)) (= (tptp.times_times_nat tptp.zero_zero_nat A_29) tptp.zero_zero_nat)) (forall ((A_29 tptp.int)) (= (tptp.times_times_int tptp.zero_zero_int A_29) tptp.zero_zero_int)) (forall ((A_28 tptp.real)) (= (tptp.times_times_real A_28 tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A_28 tptp.nat)) (= (tptp.times_times_nat A_28 tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A_28 tptp.int)) (= (tptp.times_times_int A_28 tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A_1 tptp.real) (B tptp.real)) (= (= (tptp.times_times_real A_1 B) tptp.zero_zero_real) (or (= A_1 tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (forall ((A_1 tptp.int) (B tptp.int)) (= (= (tptp.times_times_int A_1 B) tptp.zero_zero_int) (or (= A_1 tptp.zero_zero_int) (= B tptp.zero_zero_int)))) (forall ((B_14 tptp.real) (A_27 tptp.real)) (=> (not (= A_27 tptp.zero_zero_real)) (=> (not (= B_14 tptp.zero_zero_real)) (not (= (tptp.times_times_real A_27 B_14) tptp.zero_zero_real))))) (forall ((B_14 tptp.nat) (A_27 tptp.nat)) (=> (not (= A_27 tptp.zero_zero_nat)) (=> (not (= B_14 tptp.zero_zero_nat)) (not (= (tptp.times_times_nat A_27 B_14) tptp.zero_zero_nat))))) (forall ((B_14 tptp.int) (A_27 tptp.int)) (=> (not (= A_27 tptp.zero_zero_int)) (=> (not (= B_14 tptp.zero_zero_int)) (not (= (tptp.times_times_int A_27 B_14) tptp.zero_zero_int))))) (forall ((A_26 tptp.real) (B_13 tptp.real)) (=> (= (tptp.times_times_real A_26 B_13) tptp.zero_zero_real) (or (= A_26 tptp.zero_zero_real) (= B_13 tptp.zero_zero_real)))) (forall ((A_26 tptp.nat) (B_13 tptp.nat)) (=> (= (tptp.times_times_nat A_26 B_13) tptp.zero_zero_nat) (or (= A_26 tptp.zero_zero_nat) (= B_13 tptp.zero_zero_nat)))) (forall ((A_26 tptp.int) (B_13 tptp.int)) (=> (= (tptp.times_times_int A_26 B_13) tptp.zero_zero_int) (or (= A_26 tptp.zero_zero_int) (= B_13 tptp.zero_zero_int)))) (forall ((A_25 tptp.real)) (= (tptp.times_times_real A_25 tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A_25 tptp.nat)) (= (tptp.times_times_nat A_25 tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A_25 tptp.int)) (= (tptp.times_times_int A_25 tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A_24 tptp.real)) (= (tptp.times_times_real tptp.zero_zero_real A_24) tptp.zero_zero_real)) (forall ((A_24 tptp.nat)) (= (tptp.times_times_nat tptp.zero_zero_nat A_24) tptp.zero_zero_nat)) (forall ((A_24 tptp.int)) (= (tptp.times_times_int tptp.zero_zero_int A_24) tptp.zero_zero_int)) (forall ((M tptp.nat) (N tptp.nat)) (=> (= (tptp.minus_minus_nat M N) tptp.zero_zero_nat) (=> (= (tptp.minus_minus_nat N M) tptp.zero_zero_nat) (= M N)))) (forall ((M tptp.nat)) (= (tptp.minus_minus_nat M M) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (= (tptp.minus_minus_nat M tptp.zero_zero_nat) M)) (forall ((N tptp.nat)) (= (tptp.minus_minus_nat tptp.zero_zero_nat N) tptp.zero_zero_nat)) (forall ((A_23 tptp.real) (B_12 tptp.real) (C_9 tptp.real)) (= (tptp.times_times_real (tptp.plus_plus_real A_23 B_12) C_9) (tptp.plus_plus_real (tptp.times_times_real A_23 C_9) (tptp.times_times_real B_12 C_9)))) (forall ((A_23 tptp.nat) (B_12 tptp.nat) (C_9 tptp.nat)) (= (tptp.times_times_nat (tptp.plus_plus_nat A_23 B_12) C_9) (tptp.plus_plus_nat (tptp.times_times_nat A_23 C_9) (tptp.times_times_nat B_12 C_9)))) (forall ((A_23 tptp.int) (B_12 tptp.int) (C_9 tptp.int)) (= (tptp.times_times_int (tptp.plus_plus_int A_23 B_12) C_9) (tptp.plus_plus_int (tptp.times_times_int A_23 C_9) (tptp.times_times_int B_12 C_9)))) (forall ((A_22 tptp.real) (E tptp.real) (B_11 tptp.real) (C_8 tptp.real)) (= (tptp.plus_plus_real (tptp.times_times_real A_22 E) (tptp.plus_plus_real (tptp.times_times_real B_11 E) C_8)) (tptp.plus_plus_real (tptp.times_times_real (tptp.plus_plus_real A_22 B_11) E) C_8))) (forall ((A_22 tptp.nat) (E tptp.nat) (B_11 tptp.nat) (C_8 tptp.nat)) (= (tptp.plus_plus_nat (tptp.times_times_nat A_22 E) (tptp.plus_plus_nat (tptp.times_times_nat B_11 E) C_8)) (tptp.plus_plus_nat (tptp.times_times_nat (tptp.plus_plus_nat A_22 B_11) E) C_8))) (forall ((A_22 tptp.int) (E tptp.int) (B_11 tptp.int) (C_8 tptp.int)) (= (tptp.plus_plus_int (tptp.times_times_int A_22 E) (tptp.plus_plus_int (tptp.times_times_int B_11 E) C_8)) (tptp.plus_plus_int (tptp.times_times_int (tptp.plus_plus_int A_22 B_11) E) C_8))) (forall ((Wa tptp.real) (Ya tptp.real) (Xa tptp.real) (Z_1 tptp.real)) (= (= (tptp.plus_plus_real (tptp.times_times_real Wa Ya) (tptp.times_times_real Xa Z_1)) (tptp.plus_plus_real (tptp.times_times_real Wa Z_1) (tptp.times_times_real Xa Ya))) (or (= Wa Xa) (= Ya Z_1)))) (forall ((Wa tptp.nat) (Ya tptp.nat) (Xa tptp.nat) (Z_1 tptp.nat)) (= (= (tptp.plus_plus_nat (tptp.times_times_nat Wa Ya) (tptp.times_times_nat Xa Z_1)) (tptp.plus_plus_nat (tptp.times_times_nat Wa Z_1) (tptp.times_times_nat Xa Ya))) (or (= Wa Xa) (= Ya Z_1)))) (forall ((Wa tptp.int) (Ya tptp.int) (Xa tptp.int) (Z_1 tptp.int)) (= (= (tptp.plus_plus_int (tptp.times_times_int Wa Ya) (tptp.times_times_int Xa Z_1)) (tptp.plus_plus_int (tptp.times_times_int Wa Z_1) (tptp.times_times_int Xa Ya))) (or (= Wa Xa) (= Ya Z_1)))) (forall ((A_21 tptp.real) (M_3 tptp.real) (B_10 tptp.real)) (= (tptp.plus_plus_real (tptp.times_times_real A_21 M_3) (tptp.times_times_real B_10 M_3)) (tptp.times_times_real (tptp.plus_plus_real A_21 B_10) M_3))) (forall ((A_21 tptp.nat) (M_3 tptp.nat) (B_10 tptp.nat)) (= (tptp.plus_plus_nat (tptp.times_times_nat A_21 M_3) (tptp.times_times_nat B_10 M_3)) (tptp.times_times_nat (tptp.plus_plus_nat A_21 B_10) M_3))) (forall ((A_21 tptp.int) (M_3 tptp.int) (B_10 tptp.int)) (= (tptp.plus_plus_int (tptp.times_times_int A_21 M_3) (tptp.times_times_int B_10 M_3)) (tptp.times_times_int (tptp.plus_plus_int A_21 B_10) M_3))) (forall ((A_20 tptp.real) (B_9 tptp.real) (C_7 tptp.real)) (= (tptp.times_times_real (tptp.plus_plus_real A_20 B_9) C_7) (tptp.plus_plus_real (tptp.times_times_real A_20 C_7) (tptp.times_times_real B_9 C_7)))) (forall ((A_20 tptp.nat) (B_9 tptp.nat) (C_7 tptp.nat)) (= (tptp.times_times_nat (tptp.plus_plus_nat A_20 B_9) C_7) (tptp.plus_plus_nat (tptp.times_times_nat A_20 C_7) (tptp.times_times_nat B_9 C_7)))) (forall ((A_20 tptp.int) (B_9 tptp.int) (C_7 tptp.int)) (= (tptp.times_times_int (tptp.plus_plus_int A_20 B_9) C_7) (tptp.plus_plus_int (tptp.times_times_int A_20 C_7) (tptp.times_times_int B_9 C_7)))) (forall ((C_1 tptp.real) (D tptp.real) (A_1 tptp.real) (B tptp.real)) (= (and (not (= A_1 B)) (not (= C_1 D))) (not (= (tptp.plus_plus_real (tptp.times_times_real A_1 C_1) (tptp.times_times_real B D)) (tptp.plus_plus_real (tptp.times_times_real A_1 D) (tptp.times_times_real B C_1)))))) (forall ((C_1 tptp.nat) (D tptp.nat) (A_1 tptp.nat) (B tptp.nat)) (= (and (not (= A_1 B)) (not (= C_1 D))) (not (= (tptp.plus_plus_nat (tptp.times_times_nat A_1 C_1) (tptp.times_times_nat B D)) (tptp.plus_plus_nat (tptp.times_times_nat A_1 D) (tptp.times_times_nat B C_1)))))) (forall ((C_1 tptp.int) (D tptp.int) (A_1 tptp.int) (B tptp.int)) (= (and (not (= A_1 B)) (not (= C_1 D))) (not (= (tptp.plus_plus_int (tptp.times_times_int A_1 C_1) (tptp.times_times_int B D)) (tptp.plus_plus_int (tptp.times_times_int A_1 D) (tptp.times_times_int B C_1)))))) (forall ((X_6 tptp.real) (Y_5 tptp.real) (Z_3 tptp.real)) (= (tptp.times_times_real X_6 (tptp.plus_plus_real Y_5 Z_3)) (tptp.plus_plus_real (tptp.times_times_real X_6 Y_5) (tptp.times_times_real X_6 Z_3)))) (forall ((X_6 tptp.nat) (Y_5 tptp.nat) (Z_3 tptp.nat)) (= (tptp.times_times_nat X_6 (tptp.plus_plus_nat Y_5 Z_3)) (tptp.plus_plus_nat (tptp.times_times_nat X_6 Y_5) (tptp.times_times_nat X_6 Z_3)))) (forall ((X_6 tptp.int) (Y_5 tptp.int) (Z_3 tptp.int)) (= (tptp.times_times_int X_6 (tptp.plus_plus_int Y_5 Z_3)) (tptp.plus_plus_int (tptp.times_times_int X_6 Y_5) (tptp.times_times_int X_6 Z_3)))) (forall ((N tptp.nat)) (= (tptp.nat_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) N)) (forall ((A_19 tptp.real)) (= (tptp.times_times_real A_19 tptp.one_one_real) A_19)) (forall ((A_19 tptp.nat)) (= (tptp.times_times_nat A_19 tptp.one_one_nat) A_19)) (forall ((A_19 tptp.int)) (= (tptp.times_times_int A_19 tptp.one_one_int) A_19)) (forall ((A_18 tptp.real)) (= (tptp.times_times_real A_18 tptp.one_one_real) A_18)) (forall ((A_18 tptp.nat)) (= (tptp.times_times_nat A_18 tptp.one_one_nat) A_18)) (forall ((A_18 tptp.int)) (= (tptp.times_times_int A_18 tptp.one_one_int) A_18)) (forall ((A_17 tptp.real)) (= (tptp.times_times_real A_17 tptp.one_one_real) A_17)) (forall ((A_17 tptp.nat)) (= (tptp.times_times_nat A_17 tptp.one_one_nat) A_17)) (forall ((A_17 tptp.int)) (= (tptp.times_times_int A_17 tptp.one_one_int) A_17)) (forall ((A_16 tptp.real)) (= (tptp.times_times_real tptp.one_one_real A_16) A_16)) (forall ((A_16 tptp.nat)) (= (tptp.times_times_nat tptp.one_one_nat A_16) A_16)) (forall ((A_16 tptp.int)) (= (tptp.times_times_int tptp.one_one_int A_16) A_16)) (forall ((A_15 tptp.real)) (= (tptp.times_times_real tptp.one_one_real A_15) A_15)) (forall ((A_15 tptp.nat)) (= (tptp.times_times_nat tptp.one_one_nat A_15) A_15)) (forall ((A_15 tptp.int)) (= (tptp.times_times_int tptp.one_one_int A_15) A_15)) (forall ((A_14 tptp.real)) (= (tptp.times_times_real tptp.one_one_real A_14) A_14)) (forall ((A_14 tptp.nat)) (= (tptp.times_times_nat tptp.one_one_nat A_14) A_14)) (forall ((A_14 tptp.int)) (= (tptp.times_times_int tptp.one_one_int A_14) A_14)) (forall ((C_6 tptp.real) (A_13 tptp.real) (B_8 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.plus_plus_real C_6 A_13)) (tptp.plus_plus_real C_6 B_8))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_13) B_8)))) (forall ((C_6 tptp.nat) (A_13 tptp.nat) (B_8 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.plus_plus_nat C_6 A_13)) (tptp.plus_plus_nat C_6 B_8))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_13) B_8)))) (forall ((C_6 tptp.int) (A_13 tptp.int) (B_8 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.plus_plus_int C_6 A_13)) (tptp.plus_plus_int C_6 B_8))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_13) B_8)))) (forall ((A_12 tptp.real) (C_5 tptp.real) (B_7 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.plus_plus_real A_12 C_5)) (tptp.plus_plus_real B_7 C_5))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_12) B_7)))) (forall ((A_12 tptp.nat) (C_5 tptp.nat) (B_7 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.plus_plus_nat A_12 C_5)) (tptp.plus_plus_nat B_7 C_5))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_12) B_7)))) (forall ((A_12 tptp.int) (C_5 tptp.int) (B_7 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.plus_plus_int A_12 C_5)) (tptp.plus_plus_int B_7 C_5))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_12) B_7)))) (forall ((C_4 tptp.real) (D_3 tptp.real) (A_11 tptp.real) (B_6 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_11) B_6)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_4) D_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.plus_plus_real A_11 C_4)) (tptp.plus_plus_real B_6 D_3)))))) (forall ((C_4 tptp.nat) (D_3 tptp.nat) (A_11 tptp.nat) (B_6 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_11) B_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_4) D_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.plus_plus_nat A_11 C_4)) (tptp.plus_plus_nat B_6 D_3)))))) (forall ((C_4 tptp.int) (D_3 tptp.int) (A_11 tptp.int) (B_6 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_11) B_6)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_4) D_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.plus_plus_int A_11 C_4)) (tptp.plus_plus_int B_6 D_3)))))) (forall ((C_3 tptp.real) (A_10 tptp.real) (B_5 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_10) B_5)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.plus_plus_real C_3 A_10)) (tptp.plus_plus_real C_3 B_5))))) (forall ((C_3 tptp.nat) (A_10 tptp.nat) (B_5 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_10) B_5)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.plus_plus_nat C_3 A_10)) (tptp.plus_plus_nat C_3 B_5))))) (forall ((C_3 tptp.int) (A_10 tptp.int) (B_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_10) B_5)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.plus_plus_int C_3 A_10)) (tptp.plus_plus_int C_3 B_5))))) (forall ((C_2 tptp.real) (A_9 tptp.real) (B_4 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_9) B_4)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.plus_plus_real A_9 C_2)) (tptp.plus_plus_real B_4 C_2))))) (forall ((C_2 tptp.nat) (A_9 tptp.nat) (B_4 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_9) B_4)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.plus_plus_nat A_9 C_2)) (tptp.plus_plus_nat B_4 C_2))))) (forall ((C_2 tptp.int) (A_9 tptp.int) (B_4 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_9) B_4)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.plus_plus_int A_9 C_2)) (tptp.plus_plus_int B_4 C_2))))) (forall ((C_1 tptp.real) (A_1 tptp.real) (B tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.plus_plus_real C_1 A_1)) (tptp.plus_plus_real C_1 B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_1) B)))) (forall ((C_1 tptp.nat) (A_1 tptp.nat) (B tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.plus_plus_nat C_1 A_1)) (tptp.plus_plus_nat C_1 B))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_1) B)))) (forall ((C_1 tptp.int) (A_1 tptp.int) (B tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.plus_plus_int C_1 A_1)) (tptp.plus_plus_int C_1 B))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_1) B)))) (forall ((A_1 tptp.real) (C_1 tptp.real) (B tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.plus_plus_real A_1 C_1)) (tptp.plus_plus_real B C_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_1) B)))) (forall ((A_1 tptp.nat) (C_1 tptp.nat) (B tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.plus_plus_nat A_1 C_1)) (tptp.plus_plus_nat B C_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_1) B)))) (forall ((A_1 tptp.int) (C_1 tptp.int) (B tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.plus_plus_int A_1 C_1)) (tptp.plus_plus_int B C_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_1) B)))) (forall ((N tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J_1) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.minus_minus_nat J_1 N)) K_1)))) (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 L)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.minus_minus_nat L N)) (tptp.minus_minus_nat L M))))))) (forall ((A_8 tptp.real) (N_7 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_8) N_7))) (= (tptp.times_times_real _let_1 A_8) (tptp.times_times_real A_8 _let_1)))) (forall ((A_8 tptp.nat) (N_7 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_8) N_7))) (= (tptp.times_times_nat _let_1 A_8) (tptp.times_times_nat A_8 _let_1)))) (forall ((A_8 tptp.int) (N_7 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_8) N_7))) (= (tptp.times_times_int _let_1 A_8) (tptp.times_times_int A_8 _let_1)))) (forall ((A_7 tptp.real) (B_3 tptp.real) (N_6 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.power_power_real (tptp.times_times_real A_7 B_3)) N_6) (tptp.times_times_real (tptp.hAPP_nat_real (tptp.power_power_real A_7) N_6) (tptp.hAPP_nat_real (tptp.power_power_real B_3) N_6)))) (forall ((A_7 tptp.nat) (B_3 tptp.nat) (N_6 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.times_times_nat A_7 B_3)) N_6) (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.power_power_nat A_7) N_6) (tptp.hAPP_nat_nat (tptp.power_power_nat B_3) N_6)))) (forall ((A_7 tptp.int) (B_3 tptp.int) (N_6 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.times_times_int A_7 B_3)) N_6) (tptp.times_times_int (tptp.hAPP_nat_int (tptp.power_power_int A_7) N_6) (tptp.hAPP_nat_int (tptp.power_power_int B_3) N_6)))) (forall ((X_5 tptp.real) (Y_4 tptp.real) (Q_2 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.power_power_real (tptp.times_times_real X_5 Y_4)) Q_2) (tptp.times_times_real (tptp.hAPP_nat_real (tptp.power_power_real X_5) Q_2) (tptp.hAPP_nat_real (tptp.power_power_real Y_4) Q_2)))) (forall ((X_5 tptp.nat) (Y_4 tptp.nat) (Q_2 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.times_times_nat X_5 Y_4)) Q_2) (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_5) Q_2) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_4) Q_2)))) (forall ((X_5 tptp.int) (Y_4 tptp.int) (Q_2 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.times_times_int X_5 Y_4)) Q_2) (tptp.times_times_int (tptp.hAPP_nat_int (tptp.power_power_int X_5) Q_2) (tptp.hAPP_nat_int (tptp.power_power_int Y_4) Q_2)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.minus_minus_nat (tptp.plus_plus_nat M N) N) M)) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.minus_minus_nat (tptp.plus_plus_nat N M) N) M)) (forall ((I_2 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (= (tptp.minus_minus_nat (tptp.minus_minus_nat I_2 J_1) K_1) (tptp.minus_minus_nat I_2 (tptp.plus_plus_nat J_1 K_1)))) (forall ((K_1 tptp.nat) (M tptp.nat) (N tptp.nat)) (= (tptp.minus_minus_nat (tptp.plus_plus_nat K_1 M) (tptp.plus_plus_nat K_1 N)) (tptp.minus_minus_nat M N))) (forall ((M tptp.nat) (K_1 tptp.nat) (N tptp.nat)) (= (tptp.minus_minus_nat (tptp.plus_plus_nat M K_1) (tptp.plus_plus_nat N K_1)) (tptp.minus_minus_nat M N))) (forall ((W tptp.int)) (= (tptp.times_times_int tptp.pls W) tptp.pls)) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.times_times_int (tptp.bit0 K_1) L) (tptp.bit0 (tptp.times_times_int K_1 L)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) L_1)))) (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)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_16 tptp.pls)) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) L_1)))) (forall ((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)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_8 tptp.zero_zero_int)) (forall ((Z tptp.int)) (= (tptp.times_times_int tptp.one_one_int Z) Z)) (forall ((Z tptp.int)) (= (tptp.times_times_int Z tptp.one_one_int) Z)) (forall ((Z_1 tptp.int) (Wa tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_1) Wa)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_1) Wa)) (not (= Z_1 Wa))))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (= (tptp.times_times_int W (tptp.plus_plus_int Z1 Z2)) (tptp.plus_plus_int (tptp.times_times_int W Z1) (tptp.times_times_int W Z2)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (tptp.times_times_int (tptp.plus_plus_int Z1 Z2) W) (tptp.plus_plus_int (tptp.times_times_int Z1 W) (tptp.times_times_int Z2 W)))) (forall ((K_1 tptp.int) (I_2 tptp.int) (J_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_2) J_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.plus_plus_int K_1 I_2)) (tptp.plus_plus_int K_1 J_1))))) (forall ((V_1 tptp.int) (W tptp.int)) (= (tptp.times_times_int (tptp.number_number_of_int V_1) (tptp.number_number_of_int W)) (tptp.number_number_of_int (tptp.times_times_int V_1 W)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int K)) (tptp.number_number_of_int L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) L_1)))) (forall ((V_5 tptp.real) (U_3 tptp.real) (Y_3 tptp.real) (X_4 tptp.real) (A_6 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_4) A_6)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_3) A_6)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 U_3)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 V_5)) (=> (= (tptp.plus_plus_real U_3 V_5) tptp.one_one_real) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.plus_plus_real (tptp.times_times_real U_3 X_4) (tptp.times_times_real V_5 Y_3))) A_6))))))))) (forall ((V_5 tptp.int) (U_3 tptp.int) (Y_3 tptp.int) (X_4 tptp.int) (A_6 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_4) A_6)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_3) A_6)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 U_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_5)) (=> (= (tptp.plus_plus_int U_3 V_5) tptp.one_one_int) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.plus_plus_int (tptp.times_times_int U_3 X_4) (tptp.times_times_int V_5 Y_3))) A_6))))))))) (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.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.nat_1 Xa)) (tptp.nat_1 Ya))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Xa) Ya))))))) (forall ((Z_1 tptp.int) (Wa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Wa)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.nat_1 Wa)) (tptp.nat_1 Z_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Wa) Z_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_5 tptp.real) (N_5 tptp.nat) (N_4 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_5))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_5) N_4)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_5)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_5) 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_4)) (tptp.hAPP_nat_real _let_1 N_5)))))))) (forall ((A_5 tptp.nat) (N_5 tptp.nat) (N_4 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_5))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_5) N_4)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_5)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_5) 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_4)) (tptp.hAPP_nat_nat _let_1 N_5)))))))) (forall ((A_5 tptp.int) (N_5 tptp.nat) (N_4 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_5))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_5) N_4)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_5) 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_4)) (tptp.hAPP_nat_int _let_1 N_5)))))))) (forall ((Xa tptp.nat) (Ya tptp.nat) (B tptp.real)) (let ((_let_1 (tptp.power_power_real B))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) B)) (= (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 tptp.nat)) (let ((_let_1 (tptp.power_power_nat B))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) B)) (= (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 tptp.int)) (let ((_let_1 (tptp.power_power_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B)) (= (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_2 tptp.nat) (N_3 tptp.nat) (A_4 tptp.real)) (let ((_let_1 (tptp.power_power_real A_4))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A_4)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real _let_1 M_2)) (tptp.hAPP_nat_real _let_1 N_3))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_3)))))) (forall ((M_2 tptp.nat) (N_3 tptp.nat) (A_4 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_4))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A_4)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 M_2)) (tptp.hAPP_nat_nat _let_1 N_3))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_3)))))) (forall ((M_2 tptp.nat) (N_3 tptp.nat) (A_4 tptp.int)) (let ((_let_1 (tptp.power_power_int A_4))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_4)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int _let_1 M_2)) (tptp.hAPP_nat_int _let_1 N_3))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_3)))))) (forall ((Ma tptp.nat) (Wa tptp.int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Wa)))) (= (= Ma (tptp.nat_1 Wa)) (and (=> _let_1 (= Wa (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma))) (=> (not _let_1) (= Ma tptp.zero_zero_nat)))))) (forall ((Wa tptp.int) (Ma tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Wa)))) (= (= (tptp.nat_1 Wa) Ma) (and (=> _let_1 (= Wa (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma))) (=> (not _let_1) (= Ma tptp.zero_zero_nat)))))) (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.plus_plus_nat (tptp.nat_1 X) (tptp.nat_1 Y)) (tptp.nat_1 (tptp.plus_plus_int X Y))))))) (forall ((Z_2 tptp.int) (Z 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 Z)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_2)) (= (tptp.nat_1 (tptp.plus_plus_int Z Z_2)) (tptp.plus_plus_nat (tptp.nat_1 Z) (tptp.nat_1 Z_2))))))) (forall ((Ma tptp.nat) (Va tptp.int)) (let ((_let_1 (tptp.number_number_of_int Va))) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma) _let_1) (and (= Ma (tptp.nat_1 _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_1)))))) (forall ((N tptp.nat) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.nat_1 X)) N) (tptp.nat_1 (tptp.hAPP_nat_int (tptp.power_power_int X) N))))) (forall ((N tptp.nat) (Z tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (tptp.nat_1 (tptp.hAPP_nat_int (tptp.power_power_int Z) N)) (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.nat_1 Z)) N)))) (forall ((V_4 tptp.real) (U_2 tptp.real) (Y_2 tptp.real) (X_3 tptp.real) (A_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_3) A_3)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_2) A_3)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 U_2)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 V_4)) (=> (= (tptp.plus_plus_real U_2 V_4) tptp.one_one_real) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.plus_plus_real (tptp.times_times_real U_2 X_3) (tptp.times_times_real V_4 Y_2))) A_3))))))))) (forall ((V_4 tptp.int) (U_2 tptp.int) (Y_2 tptp.int) (X_3 tptp.int) (A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_3) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y_2) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 U_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_4)) (=> (= (tptp.plus_plus_int U_2 V_4) tptp.one_one_int) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int (tptp.times_times_int U_2 X_3) (tptp.times_times_int V_4 Y_2))) A_3))))))))) (forall ((Ma tptp.nat) (Wa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Wa)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.nat_1 Wa)) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Wa) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)))))) (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 ((X_2 tptp.real) (N_2 tptp.nat)) (let ((_let_1 (tptp.power_power_real X_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_2)) (= (tptp.times_times_real (tptp.hAPP_nat_real _let_1 (tptp.minus_minus_nat N_2 tptp.one_one_nat)) X_2) (tptp.hAPP_nat_real _let_1 N_2))))) (forall ((X_2 tptp.nat) (N_2 tptp.nat)) (let ((_let_1 (tptp.power_power_nat X_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_2)) (= (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 (tptp.minus_minus_nat N_2 tptp.one_one_nat)) X_2) (tptp.hAPP_nat_nat _let_1 N_2))))) (forall ((X_2 tptp.int) (N_2 tptp.nat)) (let ((_let_1 (tptp.power_power_int X_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_2)) (= (tptp.times_times_int (tptp.hAPP_nat_int _let_1 (tptp.minus_minus_nat N_2 tptp.one_one_nat)) X_2) (tptp.hAPP_nat_int _let_1 N_2))))) (forall ((A_1 tptp.real) (B tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_1) B)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.minus_minus_real A_1 B)) tptp.zero_zero_real)))) (forall ((A_1 tptp.int) (B tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_1) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.minus_minus_int A_1 B)) tptp.zero_zero_int)))) (= tptp.zero_zero_nat _let_32) (= _let_32 tptp.zero_zero_nat) (forall ((A_2 tptp.real)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.times_times_real A_2 A_2)) tptp.zero_zero_real)))) (forall ((A_2 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.times_times_int A_2 A_2)) tptp.zero_zero_int)))) (forall ((A_1 tptp.real) (C_1 tptp.real) (B tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.times_times_real A_1 C_1)) (tptp.times_times_real B C_1))) (or (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_1) B))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_1) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B) A_1)))))) (forall ((A_1 tptp.int) (C_1 tptp.int) (B tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.times_times_int A_1 C_1)) (tptp.times_times_int B C_1))) (or (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_1) B))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_1) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) A_1)))))) (forall ((W tptp.int)) (= (tptp.nat_1 (tptp.number_number_of_int W)) (tptp.number_number_of_nat W))) (forall ((V_1 tptp.int)) (= (tptp.number_number_of_nat V_1) (tptp.nat_1 (tptp.number_number_of_int V_1)))) (= tptp.one_one_nat (tptp.nat_1 tptp.one_one_int)) (forall ((Na tptp.nat) (Ma tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.minus_minus_nat Na Ma))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) Na)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.minus_minus_nat M N)) M)))))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.minus_minus_nat N (tptp.plus_plus_nat N M)) tptp.zero_zero_nat)) (forall ((I_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) (tptp.minus_minus_nat J K))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat I_1 K)) J)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N))) (= (tptp.plus_plus_nat N (tptp.minus_minus_nat M N)) M))) (forall ((K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K))))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) L_1)))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K1)) (tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K1) K2)))) (forall ((K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K))))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) tptp.pls)))) (forall ((B_1 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.times_times_int A B_1))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_1)))))) (forall ((K_1 tptp.int) (I_2 tptp.int) (J_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) K_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.times_times_int K_1 I_2)) (tptp.times_times_int K_1 J_1)))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_8 tptp.one_one_int)) (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.plus_plus_int X Y))))))) (forall ((Z_2 tptp.int) (Z tptp.int) (W_2 tptp.int) (W tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_2) W)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_2) Z)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int W_2 Z_2)) (tptp.plus_plus_int W Z)))))) (forall ((Z 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)))) (forall ((P_1 tptp.fun_int_bool)) (= (exists ((X_1 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_1)))) (exists ((X_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1)))))) (forall ((P_1 tptp.fun_int_bool)) (= (forall ((X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_1)))) (forall ((X_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1)))))) (forall ((N 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)))) (forall ((N 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)))))) (forall ((Wa tptp.int) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Wa) Z_1)) (exists ((N_1 tptp.nat)) (= Z_1 (tptp.plus_plus_int Wa (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1)))))) (forall ((X tptp.int) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.power_power_int X))) (= (tptp.hAPP_nat_int _let_1 (tptp.plus_plus_nat Y Z)) (tptp.times_times_int (tptp.hAPP_nat_int _let_1 Y) (tptp.hAPP_nat_int _let_1 Z))))) (forall ((Wa tptp.int) (Z_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Z_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.nat_1 Wa)) (tptp.nat_1 Z_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Wa) Z_1))))) (forall ((Wa tptp.int) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.nat_1 Wa)) (tptp.nat_1 Z_1))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Z_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Wa) Z_1))))) (forall ((Ma tptp.nat) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) (tptp.nat_1 Z_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)) Z_1)))) (forall ((P_1 tptp.fun_nat_bool) (A_1 tptp.nat) (B tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.minus_minus_nat A_1 B))) (not (or (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_1) B)) (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat)))) (exists ((D_2 tptp.nat)) (and (= A_1 (tptp.plus_plus_nat B D_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 D_2))))))))) (forall ((P_1 tptp.fun_nat_bool) (A_1 tptp.nat) (B tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.minus_minus_nat A_1 B))) (and (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_1) B)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat))) (forall ((D_2 tptp.nat)) (=> (= A_1 (tptp.plus_plus_nat B D_2)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 D_2))))))) (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 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) K)))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) tptp.pls)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 K)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) L_1)))) (forall ((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 tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) L_1)))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K1)) (tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K1) K2)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.times_times_int (tptp.bit1 K_1) L) (tptp.plus_plus_int (tptp.bit0 (tptp.times_times_int K_1 L)) L))) (forall ((Na tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Ma)) (= (= (tptp.times_times_int Ma Na) tptp.one_one_int) (and (= Ma tptp.one_one_int) (= Na tptp.one_one_int))))) (forall ((Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) Z_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Z_1)))) (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_1 tptp.int)) (= (tptp.succ (tptp.bit0 K_1)) (tptp.bit1 K_1))) (forall ((K_1 tptp.int)) (= (tptp.succ (tptp.bit1 K_1)) (tptp.bit0 (tptp.succ K_1)))) (forall ((Wa tptp.int) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Wa) (tptp.plus_plus_int Z_1 tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Wa) Z_1)))) (forall ((Wa tptp.int) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.plus_plus_int Wa tptp.one_one_int)) Z_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Wa) Z_1)))) (forall ((W tptp.int) (Z tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W) Z)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.plus_plus_int W tptp.one_one_int)) Z)))) (forall ((K_1 tptp.int)) (= (tptp.succ K_1) (tptp.plus_plus_int K_1 tptp.one_one_int))) (forall ((Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.nat_1 Z_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Z_1)))) (= _let_31 (tptp.nat_1 _let_30)) (forall ((P_1 tptp.fun_nat_bool) (I_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.nat_1 I_1))) (and (forall ((N_1 tptp.nat)) (=> (= I_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 N_1)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_1) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat)))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_8 _let_30)) (forall ((Z tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.plus_plus_int tptp.one_one_int Z))))) (forall ((K_1 tptp.nat) (I_2 tptp.int) (J_1 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.times_times_int _let_1 I_2)) (tptp.times_times_int _let_1 J_1))))))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.plus_plus_int (tptp.bit1 K_1) (tptp.bit1 L)) (tptp.bit0 (tptp.plus_plus_int K_1 (tptp.succ L))))) (= _let_3 (tptp.nat_1 _let_22)) (tptp.hBOOL (tptp.hAPP_int_bool _let_8 _let_22)) (forall ((A tptp.int)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.power_power_int A))) (= (tptp.times_times_int A (tptp.hAPP_nat_int _let_2 (tptp.number_number_of_nat (tptp.bit0 _let_1)))) (tptp.hAPP_nat_int _let_2 (tptp.number_number_of_nat (tptp.bit1 _let_1))))))) (forall ((X 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 ((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 ((A tptp.int) (P_2 tptp.int)) (let ((_let_1 (tptp.nat_1 P_2))) (let ((_let_2 (tptp.power_power_int A))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) P_2)) (= (tptp.hAPP_nat_int _let_2 _let_1) (tptp.times_times_int A (tptp.hAPP_nat_int _let_2 (tptp.minus_minus_nat _let_1 tptp.one_one_nat)))))))) (forall ((R_1 tptp.int) (Q tptp.int) (A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (= A (tptp.plus_plus_int R_1 (tptp.times_times_int A Q))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q) tptp.one_one_int)))))) (forall ((R_1 tptp.int) (Q tptp.int) (A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (= A (tptp.plus_plus_int R_1 (tptp.times_times_int A Q))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_1) A)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) Q)))))) (not (=> _let_26 (not _let_25))) (forall ((B_2 tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.plus_plus_int (tptp.times_times_int B_2 Q_1) R_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_2) B_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Q_1))))))) (forall ((B_2 tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.plus_plus_int (tptp.times_times_int B_2 Q_1) R_2)) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_1) tptp.zero_zero_int)))))) (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu820444569sum2sq (tptp.times_times_int _let_9 (tptp.plus_plus_int tptp.one_one_int _let_28))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N))) (tptp.hBOOL (tptp.hAPP_int_bool _let_27 _let_9)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.t) _let_9)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu820444569sum2sq _let_24)) (and _let_26 _let_25) (not (forall ((X_1 tptp.int) (Y_1 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (not (= (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X_1) _let_2) (tptp.hAPP_nat_int (tptp.power_power_int Y_1) _let_2)) (tptp.times_times_int (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int) (tptp.plus_plus_int tptp.one_one_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int tptp.n))))))))) (= _let_21 _let_24) (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime _let_9)) (=> (= tptp.t tptp.one_one_int) (exists ((X_1 tptp.int) (Y_1 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X_1) _let_2) (tptp.hAPP_nat_int (tptp.power_power_int Y_1) _let_2)) (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int)))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) N))) (forall ((M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.times_times_nat M M)))) (forall ((M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.times_times_nat M (tptp.times_times_nat M M))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.times_times_nat M N) (tptp.times_times_nat N M))) (forall ((M tptp.nat) (N tptp.nat)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)))) (forall ((M tptp.nat) (N tptp.nat) (K_1 tptp.nat)) (= (tptp.times_times_nat (tptp.times_times_nat M N) K_1) (tptp.times_times_nat M (tptp.times_times_nat N K_1)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((K_1 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat I_2 K_1)) (tptp.times_times_nat J_1 K_1))))) (forall ((K_1 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat K_1 I_2)) (tptp.times_times_nat K_1 J_1))))) (forall ((K_1 tptp.nat) (I_2 tptp.nat) (J_1 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_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 K_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= M N)))) (forall ((K_1 tptp.nat) (L tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) L)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat I_2 K_1)) (tptp.times_times_nat J_1 L)))))) (forall ((Xa tptp.real) (Ya tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Xa) Ya)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.minus_minus_real Xa Ya)) tptp.zero_zero_real)))) (forall ((Ma tptp.nat) (K tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat Ma K)) (tptp.times_times_nat Na K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) Na))))) (forall ((K tptp.nat) (Ma tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat K Ma)) (tptp.times_times_nat K Na))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) Na))))) (forall ((Xa tptp.real) (Ya tptp.real) (Z_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Z_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real Xa Z_1)) (tptp.times_times_real Ya Z_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Xa) Ya))))) (forall ((Xa tptp.real) (Ya tptp.real) (Z_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Z_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.times_times_real Z_1 Xa)) (tptp.times_times_real Z_1 Ya))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Xa) Ya))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.minus_minus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.minus_minus_nat M N))))) (forall ((K_1 tptp.int)) (= (tptp.minus_minus_int K_1 tptp.pls) K_1)) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.minus_minus_int (tptp.bit0 K_1) (tptp.bit0 L)) (tptp.bit0 (tptp.minus_minus_int K_1 L)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (tptp.times_times_int (tptp.minus_minus_int Z1 Z2) W) (tptp.minus_minus_int (tptp.times_times_int Z1 W) (tptp.times_times_int Z2 W)))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (= (tptp.times_times_int W (tptp.minus_minus_int Z1 Z2)) (tptp.minus_minus_int (tptp.times_times_int W Z1) (tptp.times_times_int W Z2)))) (forall ((N tptp.nat)) (= (tptp.times_times_nat tptp.zero_zero_nat N) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (= (tptp.times_times_nat M tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (= (tptp.times_times_nat Ma Na) tptp.zero_zero_nat) (or (= Ma tptp.zero_zero_nat) (= Na tptp.zero_zero_nat)))) (forall ((K tptp.nat) (Ma tptp.nat) (Na tptp.nat)) (= (= (tptp.times_times_nat K Ma) (tptp.times_times_nat K Na)) (or (= Ma Na) (= K tptp.zero_zero_nat)))) (forall ((Ma tptp.nat) (K tptp.nat) (Na tptp.nat)) (= (= (tptp.times_times_nat Ma K) (tptp.times_times_nat Na K)) (or (= Ma Na) (= K tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N))) (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 ((A_1 tptp.real) (B tptp.real) (C_1 tptp.real)) (=> (not (= C_1 tptp.zero_zero_real)) (= (= (tptp.times_times_real C_1 A_1) (tptp.times_times_real C_1 B)) (= A_1 B)))) (forall ((A_1 tptp.real) (B tptp.real) (C_1 tptp.real)) (=> (not (= C_1 tptp.zero_zero_real)) (= (= (tptp.times_times_real A_1 C_1) (tptp.times_times_real B C_1)) (= A_1 B)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (= M N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (=> (not (= M N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N))))) (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_eq_nat M) N)))) (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 ((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 ((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 ((M tptp.nat) (N tptp.nat) (K_1 tptp.nat)) (= (tptp.times_times_nat (tptp.plus_plus_nat M N) K_1) (tptp.plus_plus_nat (tptp.times_times_nat M K_1) (tptp.times_times_nat N K_1)))) (forall ((K_1 tptp.nat) (M tptp.nat) (N tptp.nat)) (= (tptp.times_times_nat K_1 (tptp.plus_plus_nat M N)) (tptp.plus_plus_nat (tptp.times_times_nat K_1 M) (tptp.times_times_nat K_1 N)))) (forall ((M tptp.nat) (K_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.plus_plus_nat M K_1)) N)) (not (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) N))))))) (forall ((M tptp.nat) (K_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.plus_plus_nat M K_1)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (K_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.plus_plus_nat M K_1)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) N)))) (forall ((K_1 tptp.nat) (L tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) L)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.plus_plus_nat I_2 K_1)) (tptp.plus_plus_nat J_1 L)))))) (forall ((K_1 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.plus_plus_nat I_2 K_1)) (tptp.plus_plus_nat J_1 K_1))))) (forall ((M tptp.nat) (I_2 tptp.nat) (J_1 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_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.plus_plus_nat M J_1)))))) (forall ((M tptp.nat) (I_2 tptp.nat) (J_1 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_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.plus_plus_nat J_1 M)))))) (forall ((K tptp.nat) (Ma tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.plus_plus_nat K Ma)) (tptp.plus_plus_nat K 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 Ma) Na)) (exists ((K_2 tptp.nat)) (= Na (tptp.plus_plus_nat Ma K_2))))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) (tptp.plus_plus_nat N M)))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) (tptp.plus_plus_nat M N)))) (forall ((Na tptp.nat) (Ma tptp.nat)) (= (= (tptp.times_times_nat Na Ma) tptp.one_one_nat) (and (= Na tptp.one_one_nat) (= Ma tptp.one_one_nat)))) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (= (tptp.times_times_nat Ma Na) tptp.one_one_nat) (and (= Ma tptp.one_one_nat) (= Na tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.times_times_nat N tptp.one_one_nat) N)) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (= tptp.one_one_nat (tptp.times_times_nat Ma Na)) (and (= Ma tptp.one_one_nat) (= Na tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.times_times_nat tptp.one_one_nat N) N)) (forall ((M tptp.nat) (N tptp.nat) (K_1 tptp.nat)) (= (tptp.times_times_nat (tptp.minus_minus_nat M N) K_1) (tptp.minus_minus_nat (tptp.times_times_nat M K_1) (tptp.times_times_nat N K_1)))) (forall ((K_1 tptp.nat) (M tptp.nat) (N tptp.nat)) (= (tptp.times_times_nat K_1 (tptp.minus_minus_nat M N)) (tptp.minus_minus_nat (tptp.times_times_nat K_1 M) (tptp.times_times_nat K_1 N)))) (forall ((Z tptp.real)) (= (tptp.times_times_real tptp.one_one_real Z) Z)) (forall ((Na tptp.nat) (K tptp.nat) (Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.minus_minus_nat Ma K)) (tptp.minus_minus_nat Na K))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) Na))))))) (forall ((N tptp.nat) (K_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (= (tptp.minus_minus_nat (tptp.minus_minus_nat M K_1) (tptp.minus_minus_nat N K_1)) (tptp.minus_minus_nat M N)))))) (forall ((Na tptp.nat) (K tptp.nat) (Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)) (= (= (tptp.minus_minus_nat Ma K) (tptp.minus_minus_nat Na K)) (= Ma Na)))))) (forall ((I_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) N)) (= (tptp.minus_minus_nat N (tptp.minus_minus_nat N I_2)) I_2))) (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.minus_minus_nat M L)) (tptp.minus_minus_nat N L))))) (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.minus_minus_nat L N)) (tptp.minus_minus_nat L M))))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.minus_minus_nat M N)) M))) (forall ((Z1 tptp.real) (Z2 tptp.real) (W tptp.real)) (= (tptp.times_times_real (tptp.plus_plus_real Z1 Z2) W) (tptp.plus_plus_real (tptp.times_times_real Z1 W) (tptp.times_times_real Z2 W)))) (forall ((X tptp.int) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.power_power_int X))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int _let_1 Y)) Z) (tptp.hAPP_nat_int _let_1 (tptp.times_times_nat Y Z))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (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.plus_plus_real Z X)) (tptp.plus_plus_real Z Y))))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.minus_minus_int (tptp.bit1 K_1) (tptp.bit1 L)) (tptp.bit0 (tptp.minus_minus_int K_1 L)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.minus_minus_int (tptp.bit1 K_1) (tptp.bit0 L)) (tptp.bit1 (tptp.minus_minus_int K_1 L)))) (forall ((L tptp.int)) (= (tptp.minus_minus_int tptp.pls (tptp.bit0 L)) (tptp.bit0 (tptp.minus_minus_int tptp.pls L)))) (forall ((A tptp.int) (X tptp.int)) (let ((_let_1 (tptp.minus_minus_int A tptp.one_one_int))) (let ((_let_2 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_2 A)) (=> (not (= X _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_2 _let_1)))))))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) L_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.minus_minus_int K L_1)) tptp.zero_zero_int)))) (forall ((K_1 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.times_times_nat K_1 I_2)) (tptp.times_times_nat K_1 J_1)))))) (forall ((K_1 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.times_times_nat I_2 K_1)) (tptp.times_times_nat J_1 K_1)))))) (forall ((Ma tptp.nat) (K tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.times_times_nat Ma K)) (tptp.times_times_nat Na K))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) Na))))) (forall ((K tptp.nat) (Ma tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.times_times_nat K Ma)) (tptp.times_times_nat K Na))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) Na))))) (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.times_times_nat Ma Na))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)))))) (forall ((Xa tptp.real)) (= (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.times_times_real Xa Xa)))) (= Xa tptp.zero_zero_real))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Z)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.times_times_real Z X)) (tptp.times_times_real Z Y)))))) (forall ((Y tptp.real) (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 Y)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.times_times_real X Y))))))) (forall ((Xa tptp.real) (Ya tptp.real) (Z_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Z_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.times_times_real Xa Z_1)) (tptp.times_times_real Ya Z_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Xa) Ya))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M (tptp.times_times_nat M N)) (or (= N tptp.one_one_nat) (= M tptp.zero_zero_nat)))) (forall ((Ma tptp.nat) (Na tptp.nat)) (= (= (tptp.minus_minus_nat Ma Na) tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) Na)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (= (tptp.minus_minus_nat M N) tptp.zero_zero_nat))) (forall ((Xa tptp.real) (Ya tptp.real)) (= (= (tptp.plus_plus_real (tptp.times_times_real Xa Xa) (tptp.times_times_real Ya Ya)) tptp.zero_zero_real) (and (= Xa tptp.zero_zero_real) (= Ya tptp.zero_zero_real)))) (forall ((C tptp.nat) (A tptp.nat) (B_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A) B_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C) A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.minus_minus_nat A C)) (tptp.minus_minus_nat B_1 C)))))) (forall ((Na tptp.nat) (K tptp.nat) (Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.minus_minus_nat Ma K)) (tptp.minus_minus_nat Na K))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) Na))))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.times_times_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.times_times_nat X Y)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.times_times_nat M N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.times_times_nat M N)) (tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)))) (forall ((I_2 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J_1)) (= (tptp.minus_minus_nat I_2 (tptp.minus_minus_nat J_1 K_1)) (tptp.minus_minus_nat (tptp.plus_plus_nat I_2 K_1) J_1)))) (forall ((J tptp.nat) (K tptp.nat) (I_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.minus_minus_nat J K)) I_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J) (tptp.plus_plus_nat I_1 K))))) (forall ((M tptp.nat) (K_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.minus_minus_nat (tptp.plus_plus_nat N M) K_1))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.plus_plus_nat N (tptp.minus_minus_nat M N)) M))) (forall ((I_2 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J_1)) (= (tptp.plus_plus_nat I_2 (tptp.minus_minus_nat J_1 K_1)) (tptp.minus_minus_nat (tptp.plus_plus_nat I_2 J_1) K_1)))) (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) (tptp.minus_minus_nat J K))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.plus_plus_nat I_1 K)) J))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.plus_plus_nat (tptp.minus_minus_nat M N) N) M))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J)) (= (= (tptp.minus_minus_nat J I_1) K) (= J (tptp.plus_plus_nat K I_1))))) (forall ((I_2 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J_1)) (= (tptp.minus_minus_nat (tptp.plus_plus_nat I_2 J_1) K_1) (tptp.plus_plus_nat I_2 (tptp.minus_minus_nat J_1 K_1))))) (forall ((I_2 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J_1)) (= (tptp.plus_plus_nat (tptp.minus_minus_nat J_1 K_1) I_2) (tptp.minus_minus_nat (tptp.plus_plus_nat J_1 I_2) K_1)))) (forall ((I_2 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J_1)) (= (tptp.minus_minus_nat (tptp.plus_plus_nat J_1 I_2) K_1) (tptp.plus_plus_nat (tptp.minus_minus_nat J_1 K_1) I_2)))) (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 ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu820444569sum2sq X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu820444569sum2sq Y)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu820444569sum2sq (tptp.times_times_int X Y)))))) (forall ((Wa tptp.int) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Wa) (tptp.minus_minus_int Z_1 tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Wa) Z_1)))) (forall ((Va tptp.int) (V_3 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_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_3))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 tptp.pls)))))) (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.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.nat_1 Xa)) (tptp.nat_1 Ya))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Xa) Ya))))))) (forall ((Z tptp.int) (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_eq_int Z_2) Z)) (= (tptp.nat_1 (tptp.minus_minus_int Z Z_2)) (tptp.minus_minus_nat (tptp.nat_1 Z) (tptp.nat_1 Z_2)))))) (forall ((Z_2 tptp.int) (Z tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (tptp.nat_1 (tptp.times_times_int Z Z_2)) (tptp.times_times_nat (tptp.nat_1 Z) (tptp.nat_1 Z_2))))) (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.times_times_nat (tptp.nat_1 X) (tptp.nat_1 Y)) (tptp.nat_1 (tptp.times_times_int X Y))))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.times_times_nat M N))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.plus_plus_nat N (tptp.times_times_nat (tptp.minus_minus_nat M tptp.one_one_nat) N)))))))) (forall ((Z_1 tptp.int) (Wa tptp.int)) (=> (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Wa)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.nat_1 Wa)) (tptp.nat_1 Z_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Wa) Z_1))))) (forall ((P_2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_power_nat P_2))) (let ((_let_2 (tptp.hAPP_nat_nat _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 (tptp.times_times_nat P_2 (tptp.hAPP_nat_nat _let_1 (tptp.minus_minus_nat M tptp.one_one_nat)))))))))) (forall ((Z tptp.nat)) (= (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))) Z) (tptp.plus_plus_nat Z Z))) (forall ((Z tptp.nat)) (= (tptp.times_times_nat Z (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.plus_plus_nat Z Z))) (forall ((V_2 tptp.int) (K_1 tptp.nat) (V_1 tptp.int)) (let ((_let_1 (tptp.times_times_nat (tptp.number_number_of_nat V_1) (tptp.times_times_nat (tptp.number_number_of_nat V_2) K_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_1) tptp.pls)))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.times_times_nat (tptp.number_number_of_nat (tptp.times_times_int V_1 V_2)) K_1))))))) (forall ((V_2 tptp.int) (V_1 tptp.int)) (let ((_let_1 (tptp.times_times_nat (tptp.number_number_of_nat V_1) (tptp.number_number_of_nat V_2)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_1) tptp.pls)))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.number_number_of_nat (tptp.times_times_int V_1 V_2)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.times_times_real (tptp.number267125858f_real (tptp.bit0 _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real X) _let_2)) (tptp.hAPP_nat_real (tptp.power_power_real (tptp.times_times_real (tptp.number267125858f_real _let_1) X)) _let_2))))) (forall ((N 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)))) (forall ((B_1 tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) C)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_1) C)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) B_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_1) A)))))) (forall ((A tptp.int) (B_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.times_times_int (tptp.plus_plus_int A B_1) (tptp.minus_minus_int A B_1)) (tptp.minus_minus_int (tptp.hAPP_nat_int (tptp.power_power_int A) _let_1) (tptp.hAPP_nat_int (tptp.power_power_int B_1) _let_1))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X) _let_1) (tptp.hAPP_nat_nat (tptp.power_power_nat Y) _let_1)) (tptp.times_times_nat (tptp.plus_plus_nat X Y) (tptp.minus_minus_nat X Y))))) (forall ((A tptp.int) (B_1 tptp.int)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit1 _let_1))) (let ((_let_3 (tptp.number_number_of_nat _let_2))) (let ((_let_4 (tptp.power_power_int B_1))) (let ((_let_5 (tptp.number_number_of_nat (tptp.bit0 _let_1)))) (let ((_let_6 (tptp.number_number_of_int _let_2))) (let ((_let_7 (tptp.power_power_int A))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.minus_minus_int A B_1)) _let_3) (tptp.minus_minus_int (tptp.plus_plus_int (tptp.minus_minus_int (tptp.hAPP_nat_int _let_7 _let_3) (tptp.times_times_int (tptp.times_times_int _let_6 (tptp.hAPP_nat_int _let_7 _let_5)) B_1)) (tptp.times_times_int (tptp.times_times_int _let_6 A) (tptp.hAPP_nat_int _let_4 _let_5))) (tptp.hAPP_nat_int _let_4 _let_3))))))))))) (forall ((A tptp.int) (B_1 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.minus_minus_int A B_1)) _let_2) (tptp.plus_plus_int (tptp.minus_minus_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_1)) (tptp.hAPP_nat_int (tptp.power_power_int B_1) _let_2)))))) (forall ((B_1 tptp.int) (Q tptp.int) (R_1 tptp.int) (B_2 tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (let ((_let_1 (tptp.plus_plus_int (tptp.times_times_int B_2 Q_1) R_2))) (=> (= (tptp.plus_plus_int (tptp.times_times_int B_1 Q) R_1) _let_1) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) B_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_1) Q)))))))))) (forall ((B_1 tptp.int) (Q_1 tptp.int) (R_2 tptp.int) (Q tptp.int) (R_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.plus_plus_int (tptp.times_times_int B_1 Q_1) R_2)) (tptp.plus_plus_int (tptp.times_times_int B_1 Q) R_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int R_1) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 R_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 R_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q) Q_1)))))))) (forall ((B_1 tptp.int) (Q tptp.int) (R_1 tptp.int) (B_2 tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.plus_plus_int (tptp.times_times_int B_2 Q_1) R_2))) (=> (= (tptp.plus_plus_int (tptp.times_times_int B_1 Q) R_1) _let_2) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 _let_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_2) B_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 R_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) B_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q) Q_1))))))))))) (forall ((B_1 tptp.int) (Q_1 tptp.int) (R_2 tptp.int) (Q tptp.int) (R_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.plus_plus_int (tptp.times_times_int B_1 Q_1) R_2)) (tptp.plus_plus_int (tptp.times_times_int B_1 Q) R_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_1) B_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_1) Q))))))) (= (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int tptp.x) _let_3) (tptp.hAPP_nat_int (tptp.power_power_int tptp.y) _let_3)) _let_23) (forall ((P_2 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_int _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_2) P_2)) (= (tptp.minus_minus_nat (tptp.nat_1 P_2) (tptp.number_number_of_nat _let_1)) (tptp.nat_1 (tptp.minus_minus_int P_2 _let_2))))))) (forall ((P_2 tptp.int)) (let ((_let_1 (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) P_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.nat_1 (tptp.minus_minus_int P_2 _let_1))))))) (not (forall ((T tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (not (= (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int tptp.s) (tptp.number_number_of_nat _let_1)) tptp.one_one_int) (tptp.times_times_int (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int) T)))))) (forall ((W tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real W) W))) (forall ((Z tptp.real) (W tptp.real)) (= (tptp.times_times_real Z W) (tptp.times_times_real W Z))) (forall ((Z tptp.real) (W tptp.real)) (or (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Z) W)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real W) Z)))) (forall ((Z1 tptp.real) (Z2 tptp.real) (Z3 tptp.real)) (= (tptp.times_times_real (tptp.times_times_real Z1 Z2) Z3) (tptp.times_times_real Z1 (tptp.times_times_real Z2 Z3)))) (forall ((K_1 tptp.real) (I_2 tptp.real) (J_1 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_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real J_1) K_1)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 K_1)))))) (forall ((Z tptp.real) (W tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Z) W)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real W) Z)) (= Z W)))) (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime _let_22)) (forall ((A tptp.int) (B_1 tptp.int) (C tptp.int)) (=> (= (tptp.minus_minus_int A B_1) C) (= A (tptp.plus_plus_int C B_1)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_20 _let_21)) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_real (tptp.power_power_real (tptp.plus_plus_real X Y)) _let_2) (tptp.plus_plus_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X) _let_2) (tptp.hAPP_nat_real (tptp.power_power_real Y) _let_2)) (tptp.times_times_real (tptp.times_times_real (tptp.number267125858f_real _let_1) X) Y)))))) (= _let_19 _let_21) (tptp.hBOOL (tptp.hAPP_int_bool _let_20 _let_19)) _let_13 (forall ((K_1 tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.minus_minus_int M N))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)))))) (forall ((M tptp.int) (N tptp.int) (P_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.times_times_int M N))) (or (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N))))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_17 tptp.min)) (forall ((N tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int N) M)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int M) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int N) M))))) (forall ((A tptp.int) (N tptp.nat) (P_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A) N))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)))))) (forall ((N tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int M) N)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int N) M)))))) (forall ((K_1 tptp.int) (M tptp.int) (N tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.times_times_int K_1 M)) (tptp.times_times_int K_1 N))) (=> (not (= K_1 tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int M) N))))) (forall ((N tptp.int) (M tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int M) N)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int N) M)) (= M N))))))) (forall ((K tptp.int) (Na tptp.int) (Ma tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.plus_plus_int Na (tptp.times_times_int K Ma)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Na))))) (forall ((C_1 tptp.int) (Xa tptp.int) (Ta tptp.int) (A_1 tptp.int) (D tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 D)) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.plus_plus_int Xa Ta))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.plus_plus_int (tptp.plus_plus_int Xa (tptp.times_times_int C_1 D)) Ta))))))) (forall ((K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.min))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K))))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K)) tptp.min)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) tptp.min)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_15 tptp.pls)) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_18 tptp.min))) (forall ((K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.min))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K))))) (forall ((K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.min))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K))))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K)) tptp.min)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) tptp.min)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_15 tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_17 tptp.pls)) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_16 tptp.min))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K)) tptp.min)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) tptp.min)))) (not (= _let_7 _let_12)) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_15 tptp.min))) (forall ((L tptp.int)) (not (= tptp.min (tptp.bit0 L)))) (forall ((K_1 tptp.int)) (not (= (tptp.bit0 K_1) tptp.min))) (not (= tptp.min tptp.pls)) (not (= tptp.pls tptp.min)) (= (tptp.bit1 tptp.min) tptp.min) (forall ((L_1 tptp.int)) (= (= tptp.min (tptp.bit1 L_1)) (= tptp.min L_1))) (forall ((K tptp.int)) (= (= (tptp.bit1 K) tptp.min) (= K tptp.min))) (= (tptp.succ tptp.min) tptp.pls) (forall ((K_1 tptp.int)) (= (tptp.minus_minus_int K_1 tptp.min) (tptp.succ K_1))) (forall ((Z tptp.int) (N tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Z) N)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) N)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z) N))))) (forall ((P_2 tptp.int) (Y tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int Y) N))))))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.min) (tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.min) K)))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 K)) tptp.min)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) tptp.min)))) (forall ((L tptp.int)) (= (tptp.minus_minus_int tptp.pls (tptp.bit1 L)) (tptp.bit1 (tptp.minus_minus_int tptp.min L)))) (forall ((L tptp.int)) (= (tptp.minus_minus_int tptp.min (tptp.bit1 L)) (tptp.bit0 (tptp.minus_minus_int tptp.min L)))) (forall ((L tptp.int)) (= (tptp.minus_minus_int tptp.min (tptp.bit0 L)) (tptp.bit1 (tptp.minus_minus_int tptp.min L)))) (forall ((Ma tptp.int) (Na tptp.int)) (let ((_let_1 (tptp.number_number_of_int tptp.min))) (= (= (tptp.times_times_int Ma Na) tptp.one_one_int) (or (and (= Ma tptp.one_one_int) (= Na tptp.one_one_int)) (and (= Ma _let_1) (= Na _let_1)))))) (forall ((M tptp.int) (N tptp.int)) (=> (= (tptp.times_times_int M N) tptp.one_one_int) (or (= M tptp.one_one_int) (= M (tptp.number_number_of_int tptp.min))))) (forall ((N tptp.nat) (A tptp.int) (B_1 tptp.int) (P_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.power_power_int P_2) N)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_2) B_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.times_times_int A B_1))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A))))))) (forall ((N tptp.nat) (B_1 tptp.int) (A tptp.int) (P_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.power_power_int P_2) N)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_2) A))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.times_times_int A B_1))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_1))))))) (forall ((Y tptp.int) (N tptp.nat) (P_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int Y) N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y))))))) _let_14 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong _let_11 _let_12) _let_9)) (=> (not _let_14) (not _let_13)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong _let_10 _let_12) _let_9)) (and (tptp.hBOOL (tptp.hAPP_int_bool _let_8 tptp.s)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.s) _let_9)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong tptp.s1 tptp.s) _let_9))) (not (forall ((S1 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.power_power_int S1) (tptp.number_number_of_nat _let_1)) (tptp.number_number_of_int tptp.min)) (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int))))))) (forall ((C tptp.nat) (A tptp.nat) (B_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.times_times_nat A C)) (tptp.times_times_nat B_1 C))))) (forall ((C tptp.nat) (A tptp.nat) (B_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.times_times_nat C A)) (tptp.times_times_nat C B_1))))) (forall ((N tptp.nat) (K_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.minus_minus_nat M N))))))) (forall ((Xa tptp.int) (P_3 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong Xa tptp.zero_zero_int) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3) Xa)))) (forall ((A_1 tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_1 tptp.zero_zero_int) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Ma) A_1)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N) M)))))) (forall ((A tptp.nat) (B_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B_1)) (or (= B_1 tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A) B_1))))) (forall ((Ma tptp.nat) (K tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.times_times_nat Ma K)) (tptp.times_times_nat Na K))) (or (= K tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) Na))))) (forall ((K_1 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.minus_minus_nat M N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M))))))) (forall ((K_1 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.minus_minus_nat M N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N))))))) (forall ((A tptp.nat) (N tptp.nat) (B_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.power_power_nat A) N)) (tptp.hAPP_nat_nat (tptp.power_power_nat B_1) N))) (=> (not (= N tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B_1))))) (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X) N)) Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y))))) (forall ((Xa tptp.nat) (Ya tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_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.dvd_dvd_nat Xa) Ya)))) (forall ((Xa tptp.nat) (Ya tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Xa) Ya)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Xa)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ya))))) (forall ((N tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X) N)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y) N))))) (forall ((Ma tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) tptp.one_one_nat)) (= Ma tptp.one_one_nat))) (forall ((K tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.plus_plus_nat Na K))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na))))) (forall ((B_1 tptp.nat) (D_1 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat D_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.plus_plus_nat A B_1))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_1)))))) (forall ((M tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong M tptp.zero_zero_int) M))) (forall ((C tptp.int) (A tptp.int) (B_1 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B_1) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.plus_plus_int A C) (tptp.plus_plus_int B_1 C)) M)))) (forall ((D_1 tptp.int) (C tptp.int) (A tptp.int) (B_1 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B_1) M)) (=> (= B_1 C) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C D_1) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A D_1) M)))))) (forall ((Z tptp.nat) (X tptp.int) (Y tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X Y) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.power_power_int X) Z) (tptp.hAPP_nat_int (tptp.power_power_int Y) Z)) M)))) (forall ((M tptp.int) (Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X Y) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y) M)) (= X Y))))))))) (forall ((M tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) M)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X tptp.zero_zero_int) M)))))) (forall ((C_1 tptp.int) (D tptp.int) (A_1 tptp.int) (B tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_1 B) Ma)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C_1 (tptp.times_times_int A_1 D)) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C_1 (tptp.times_times_int B D)) Ma))))) (forall ((C_1 tptp.int) (D tptp.int) (A_1 tptp.int) (B tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_1 B) Ma)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C_1 (tptp.times_times_int D A_1)) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C_1 (tptp.times_times_int D B)) Ma))))) (forall ((M tptp.int) (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) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X tptp.zero_zero_int) M)) (= X tptp.zero_zero_int))))) (forall ((Y tptp.int) (X tptp.int) (P_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X tptp.zero_zero_int) P_2))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong Y tptp.zero_zero_int) P_2))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.times_times_int X Y) tptp.zero_zero_int) P_2))))))) (forall ((K_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_1) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) N))))) (forall ((K_1 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.times_times_nat K_1 M)) (tptp.times_times_nat K_1 N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M) N))))) (forall ((B_1 tptp.int) (A tptp.int) (P_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.times_times_int A B_1) tptp.zero_zero_int) P_2)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A tptp.zero_zero_int) P_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong B_1 tptp.zero_zero_int) P_2))))))) (forall ((B_1 tptp.int) (A tptp.int) (P_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (and (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A tptp.zero_zero_int) P_2))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong B_1 tptp.zero_zero_int) P_2)))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.times_times_int A B_1) tptp.zero_zero_int) P_2))))))) (forall ((X tptp.nat) (Q tptp.nat) (N tptp.nat) (R_1 tptp.nat)) (=> (= X (tptp.plus_plus_nat (tptp.times_times_nat Q N) R_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) R_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat R_1) N)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N) X))))))) (forall ((Na tptp.nat) (Ma tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Ma)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.times_times_nat Ma Na)) Ma)) (= Na tptp.one_one_nat)))) (forall ((Na tptp.nat) (Ma tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Ma)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.times_times_nat Na Ma)) Ma)) (= Na tptp.one_one_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.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.nat_1 Xa)) (tptp.nat_1 Ya))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Xa) Ya))))))) (forall ((I_2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_nat I_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) I_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))))) (forall ((Z_1 tptp.int) (Ma tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z_1)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.nat_1 Z_1)) Ma)) (and (=> _let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Z_1) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)))) (=> (not _let_1) (= Ma tptp.zero_zero_nat)))))) (forall ((X tptp.int) (P_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X (tptp.number_number_of_int tptp.min)) P_2)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X tptp.one_one_int) P_2)))))) (forall ((Y tptp.int) (X tptp.int) (P_2 tptp.int)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X tptp.zero_zero_int) P_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.power_power_int Y) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) X) P_2)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_2) Y)))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N) M)) (or (= M tptp.zero_zero_nat) (= M N) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))) N)) M))))) (forall ((M tptp.int)) (let ((_let_1 (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls)))) M) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime _let_1)) (= (tptp.legendre (tptp.number_number_of_int tptp.min) _let_1) tptp.one_one_int)))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong _let_11 _let_10) _let_9)) (exists ((X_1 tptp.int)) (let ((_let_1 (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.m) tptp.one_one_int))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong tptp.s1 X_1) _let_1)) (forall ((Y_1 tptp.int)) (let ((_let_1 (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.m) tptp.one_one_int))) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y_1) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong tptp.s1 Y_1) _let_1))) (= Y_1 X_1))))))) (forall ((X tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) X))) (not (forall ((S tptp.int)) (let ((_let_1 (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.m) tptp.one_one_int))) (not (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) S)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int S) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong tptp.s1 S) _let_1))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Z))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X))) (let ((_let_3 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Y)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_3 X)))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_3 Z)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Z)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X)))))))))) (forall ((A tptp.nat) (B_1 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_1) A)))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 X)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Z)) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Z) X))))))))) (forall ((C tptp.nat) (A tptp.nat) (B_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_1) A)))) (=> (= B_1 C) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat C) A)))))))) (forall ((P_1 tptp.bool) (Xa tptp.nat) (Ya tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Xa) Ya)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ya) Xa)))) (=> (and _let_1 (not _let_2)) (=> (and _let_2 (not _let_1)) (tptp.hBOOL P_1)))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)))) (not (= Y X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)))) (not (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)))) (=> (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)))) _let_1))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)))) (not (= X Y)))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Z))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Y)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) Z)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Z)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X))))))))) (forall ((C tptp.nat) (A tptp.nat) (B_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat C))) (=> (= A B_1) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_1) C)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_1)))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) C)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A)))))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) Z)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)) (= X Y)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N) M)) (= M N)))) (forall ((C tptp.nat) (A tptp.nat) (B_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_1)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C)))))) (forall ((C tptp.nat) (A tptp.nat) (B_1 tptp.nat)) (=> (= A B_1) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_1) C)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) C))))) (forall ((A tptp.nat) (B_1 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B_1)))) (=> _let_1 (=> (not (= A B_1)) (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_1) A)))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)))) (=> _let_1 (or (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)))) (= X Y))))) (forall ((Ya tptp.nat) (Xa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ya) Xa)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Xa) Ya)) (= Xa Ya)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)))) (forall ((A tptp.nat) (B_1 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B_1)))) (=> (not (= A B_1)) (=> _let_1 (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_1) A)))))))) (forall ((Xa tptp.nat) (Ya tptp.nat)) (let ((_let_1 (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Xa) Ya)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ya) Xa)))))) (= _let_1 _let_1))) (forall ((Xa tptp.nat) (Ya tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Xa) Ya)))) (= (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ya) Xa)))) (and _let_1 (not (= Xa Ya)))))) (forall ((Xa tptp.nat) (Ya tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Xa) Ya)))) (= _let_1 (or (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ya) Xa)))) (= Xa Ya))))) (forall ((Xa tptp.nat) (Ya tptp.nat)) (= (= Xa Ya) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Xa) Ya)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ya) Xa))))) (forall ((X tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) X)))) (not (and _let_1 (not _let_1))))) (forall ((Xa tptp.nat) (Ya tptp.nat)) (= (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Xa) Ya)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ya) Xa))) (= Xa Ya))) (forall ((J_1 tptp.nat) (K_1 tptp.nat) (M tptp.int)) (let ((_let_1 (tptp.power_power_int (tptp.number_number_of_int tptp.min)))) (let ((_let_2 (tptp.hAPP_nat_int _let_1 K_1))) (let ((_let_3 (tptp.hAPP_nat_int _let_1 J_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong _let_3 _let_2) M)) (= _let_3 _let_2))))))) (forall ((M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) M)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong tptp.one_one_int (tptp.number_number_of_int tptp.min)) M))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.number_number_of_int tptp.min))) (let ((_let_2 (tptp.hAPP_nat_int (tptp.power_power_int _let_1) N))) (or (= _let_2 tptp.one_one_int) (= _let_2 _let_1))))) (forall ((A tptp.int) (P_2 tptp.int)) (let ((_let_1 (tptp.legendre A P_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.quadRes P_2) A)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A tptp.zero_zero_int) P_2)))) (and (=> _let_3 (= _let_1 tptp.zero_zero_int)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.number_number_of_int tptp.min)))))))))) (forall ((Ma tptp.int) (Xa tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.quadRes Ma) Xa)) (exists ((Y_1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.power_power_int Y_1) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) Xa) Ma))))) (forall ((X tptp.int) (P_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_2) X))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.power_power_int X) (tptp.nat_1 (tptp.minus_minus_int P_2 tptp.one_one_int))) tptp.one_one_int) P_2))))) (forall ((A tptp.int) (P_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) P_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.times_times_int A A) tptp.one_one_int) P_2)) (or (= A tptp.one_one_int) (= A (tptp.minus_minus_int P_2 tptp.one_one_int)))))))) (forall ((C tptp.int) (A tptp.int) (B_1 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B_1) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong B_1 C) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A C) M))))) (forall ((K_1 tptp.int) (M tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong K_1 K_1) M))) (forall ((A_1 tptp.int) (B tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_1 B) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong B A_1) Ma)))) (forall ((A_1 tptp.int) (B tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_1 B) tptp.zero_zero_int)) (= A_1 B))) (forall ((A tptp.int) (B_1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B_1) tptp.one_one_int))) (forall ((A tptp.int) (M tptp.int) (B_1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.times_times_int A M) (tptp.times_times_int B_1 M)) M))) (forall ((K_1 tptp.int) (A tptp.int) (B_1 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B_1) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.times_times_int A K_1) (tptp.times_times_int B_1 K_1)) M)))) (forall ((K_1 tptp.int) (A tptp.int) (B_1 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B_1) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.times_times_int K_1 A) (tptp.times_times_int K_1 B_1)) M)))) (forall ((C tptp.int) (D_1 tptp.int) (A tptp.int) (B_1 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B_1) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C D_1) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.times_times_int A C) (tptp.times_times_int B_1 D_1)) M))))) (forall ((C tptp.int) (D_1 tptp.int) (A tptp.int) (B_1 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B_1) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C D_1) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.plus_plus_int A C) (tptp.plus_plus_int B_1 D_1)) M))))) (forall ((C tptp.int) (D_1 tptp.int) (A tptp.int) (B_1 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B_1) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C D_1) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.minus_minus_int A C) (tptp.minus_minus_int B_1 D_1)) M))))) (forall ((B_1 tptp.int) (M tptp.int) (A tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_1) A)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B_1) M))))))))) (forall ((A tptp.int) (R_1 tptp.int) (B_1 tptp.int) (M tptp.int) (C tptp.int) (D_1 tptp.int) (N tptp.int)) (= (tptp.plus_plus_int (tptp.times_times_int (tptp.minus_minus_int A (tptp.times_times_int R_1 B_1)) M) (tptp.times_times_int (tptp.minus_minus_int C (tptp.times_times_int R_1 D_1)) N)) (tptp.minus_minus_int (tptp.plus_plus_int (tptp.times_times_int A M) (tptp.times_times_int C N)) (tptp.times_times_int R_1 (tptp.plus_plus_int (tptp.times_times_int B_1 M) (tptp.times_times_int D_1 N)))))) (forall ((A_1 tptp.int) (B tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_1 B) Ma)) (exists ((K_2 tptp.int)) (= B (tptp.plus_plus_int A_1 (tptp.times_times_int Ma K_2)))))) (forall ((A_1 tptp.int) (B tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_1 B) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Ma) (tptp.minus_minus_int A_1 B))))) (forall ((A tptp.int) (B_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) (tptp.minus_minus_int B_1 tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) B_1)))) (forall ((M tptp.int) (A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A tptp.zero_zero_int) M)) (= A tptp.zero_zero_int))))) (forall ((B_1 tptp.int) (M tptp.int) (A tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_1) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B_1) M)) (= A B_1)))))))) (forall ((N tptp.int) (P_2 tptp.int) (M tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.times_times_int M N))) (or (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N)))))))) (forall ((P_3 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) P_3)) (forall ((M_1 tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) M_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int M_1) P_3))) (or (= M_1 tptp.one_one_int) (= M_1 P_3))))))) (forall ((A tptp.int) (P_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.times_times_int A A) tptp.one_one_int) P_2)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A tptp.one_one_int) P_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A (tptp.minus_minus_int P_2 tptp.one_one_int)) P_2))))))) (forall ((P_1 tptp.fun_int_bool) (Xa tptp.nat) (Ya tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.minus_minus_nat Xa Ya)))) (and (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ya) Xa)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.minus_minus_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)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 tptp.zero_zero_int)))))) (forall ((P_2 tptp.int)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit0 _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_2)) (=> (not (= P_2 (tptp.number_number_of_int _let_2))) (=> (not (= P_2 (tptp.number_number_of_int (tptp.bit1 _let_1)))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int (tptp.bit1 _let_2))) P_2)))))))) (forall ((P_4 tptp.bool) (P_1 tptp.bool) (Xa tptp.int)) (let ((_let_1 (tptp.hBOOL P_4))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) 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_4 tptp.bool) (P_1 tptp.bool) (Xa tptp.int)) (let ((_let_1 (tptp.hBOOL P_4))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Xa)))) (let ((_let_3 (tptp.hBOOL P_1))) (=> (=> _let_2 (= _let_3 _let_1)) (= (=> _let_2 _let_3) (=> _let_2 _let_1))))))) (forall ((Ma tptp.int) (Ta tptp.int) (K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Ma) Ta)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.times_times_int K Ma)) (tptp.times_times_int K Ta)))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_8 _let_7)) (forall ((A_1 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.minus_minus_int P_3 tptp.one_one_int))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.times_times_int A_1 _let_1) tptp.one_one_int) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_1 _let_1) P_3))))) (forall ((Z tptp.nat) (X tptp.int) (Y tptp.nat) (P_2 tptp.int)) (let ((_let_1 (tptp.power_power_int X))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_nat_int _let_1 Y) tptp.one_one_int) P_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_nat_int _let_1 (tptp.times_times_nat Y Z)) tptp.one_one_int) P_2))))) (forall ((N 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))) (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.number_number_of_int (tptp.bit0 N)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.number_number_of_int (tptp.bit1 N)))))))) (not (forall ((S tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.plus_plus_int tptp.one_one_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int tptp.n)))) (not (and (= W_1 (tptp.minus_minus_int tptp.y (tptp.times_times_int S _let_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls))) (tptp.abs_abs_int W_1))) _let_1))))))) (not (forall ((R tptp.int) (V tptp.int)) (let ((_let_1 (tptp.plus_plus_int tptp.one_one_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int tptp.n)))) (not (and (= V (tptp.minus_minus_int tptp.x (tptp.times_times_int R _let_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls))) (tptp.abs_abs_int V))) _let_1))))))) (forall ((D_1 tptp.int) (I_2 tptp.int)) (=> (not (= I_2 tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D_1) I_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.abs_abs_int D_1)) (tptp.abs_abs_int I_2)))))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.nat_1 (tptp.abs_abs_int (tptp.times_times_int W Z))) (tptp.times_times_nat (tptp.nat_1 (tptp.abs_abs_int W)) (tptp.nat_1 (tptp.abs_abs_int Z))))) (forall ((A tptp.int) (B_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A) B_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int B_1) A)) (= (tptp.abs_abs_int A) (tptp.abs_abs_int B_1))))) (forall ((Xa tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Xa) tptp.one_one_int)) (= (tptp.abs_abs_int Xa) tptp.one_one_int))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int M))) (= (tptp.abs_abs_int _let_1) _let_1))) (forall ((M tptp.int) (N tptp.int)) (=> (= (tptp.abs_abs_int (tptp.times_times_int M N)) tptp.one_one_int) (= (tptp.abs_abs_int M) tptp.one_one_int))) (forall ((X tptp.int) (N tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_nat_int (tptp.power_power_int (tptp.abs_abs_int X)) N)))) (forall ((Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.abs_abs_int Z_1)) tptp.one_one_int)) (= Z_1 tptp.zero_zero_int))) (forall ((Z_1 tptp.int)) (= (= (tptp.abs_abs_int Z_1) tptp.one_one_int) (or (= Z_1 tptp.one_one_int) (= Z_1 (tptp.number_number_of_int tptp.min))))) (forall ((X tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit1 (tptp.bit1 tptp.pls))))) (= (tptp.abs_abs_int (tptp.hAPP_nat_int (tptp.power_power_int X) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int (tptp.abs_abs_int X)) _let_1)))) (forall ((Xa tptp.int) (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.power_power_int (tptp.abs_abs_int Xa)) Na))) (or (not (= Xa tptp.zero_zero_int)) (= Na tptp.zero_zero_nat)))) (forall ((Na tptp.int) (Ma tptp.int)) (=> (not (= Ma tptp.zero_zero_int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.times_times_int Ma Na)) Ma)) (= (tptp.abs_abs_int Na) tptp.one_one_int)))) (forall ((Ma tptp.nat) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)) Z_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) (tptp.nat_1 (tptp.abs_abs_int Z_1)))))) (forall ((Z_1 tptp.int) (Ma tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Z_1) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.nat_1 (tptp.abs_abs_int Z_1))) Ma)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.abs_abs_int (tptp.hAPP_nat_int (tptp.power_power_int A) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int (tptp.abs_abs_int A)) _let_1)))) (forall ((A_1 tptp.int) (B tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (tptp.hAPP_nat_int (tptp.power_power_int A_1) _let_1) (tptp.hAPP_nat_int (tptp.power_power_int B) _let_1)) (= (tptp.abs_abs_int A_1) (tptp.abs_abs_int B))))) (forall ((A tptp.int)) (=> (= (tptp.hAPP_nat_int (tptp.power_power_int A) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.one_one_int) (= (tptp.abs_abs_int A) tptp.one_one_int))) (forall ((Z tptp.int) (X tptp.int) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z) (tptp.plus_plus_int X (tptp.times_times_int (tptp.plus_plus_int (tptp.abs_abs_int (tptp.minus_minus_int X Z)) tptp.one_one_int) D_1)))))) (forall ((X tptp.int) (Z tptp.int) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.minus_minus_int X (tptp.times_times_int (tptp.plus_plus_int (tptp.abs_abs_int (tptp.minus_minus_int X Z)) tptp.one_one_int) D_1))) Z)))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) X)) (exists ((N_1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls))) (tptp.abs_abs_int (tptp.minus_minus_int Y (tptp.times_times_int N_1 X))))) X))))) (forall ((K tptp.int) (P_1 tptp.fun_int_bool) (D tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.minus_minus_int X_1 D))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (forall ((X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.minus_minus_int X_1 (tptp.times_times_int K D)))))))))) (forall ((X tptp.real)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.plus_plus_real (tptp.abs_abs_real X) tptp.one_one_real)) X)))) (forall ((X tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.plus_plus_real tptp.one_one_real (tptp.abs_abs_real X))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.abs_abs_real X)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real (tptp.power_power_real X) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) tptp.one_one_real)))) (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_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_2) Na)) (forall ((I tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) K_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 I))))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.plus_plus_nat K_2 tptp.one_one_nat)))))))) (forall ((K tptp.int) (P_1 tptp.fun_int_bool) (D tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.plus_plus_int X_1 D))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (forall ((X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.plus_plus_int X_1 (tptp.times_times_int K D)))))))))) (forall ((U tptp.nat) (Ma tptp.nat) (Na tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J) I_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat (tptp.times_times_nat I_1 U) Ma)) (tptp.plus_plus_nat (tptp.times_times_nat J U) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat (tptp.times_times_nat (tptp.minus_minus_nat I_1 J) U) Ma)) Na))))) (forall ((U tptp.nat) (Ma tptp.nat) (Na tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.plus_plus_nat (tptp.times_times_nat I_1 U) Ma)) (tptp.plus_plus_nat (tptp.times_times_nat J U) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) (tptp.plus_plus_nat (tptp.times_times_nat (tptp.minus_minus_nat J I_1) U) Na)))))) (forall ((K tptp.nat) (Ma tptp.nat) (Na tptp.nat)) (= (= (tptp.times_times_nat K Ma) (tptp.times_times_nat K Na)) (or (= K tptp.zero_zero_nat) (= Ma Na)))) (forall ((I_2 tptp.nat) (U_1 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (= (tptp.plus_plus_nat (tptp.times_times_nat I_2 U_1) (tptp.plus_plus_nat (tptp.times_times_nat J_1 U_1) K_1)) (tptp.plus_plus_nat (tptp.times_times_nat (tptp.plus_plus_nat I_2 J_1) U_1) K_1))) (forall ((Ma tptp.nat) (Na tptp.nat) (K tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.times_times_nat K Ma)) (tptp.times_times_nat K Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) Na))))) (forall ((Ma tptp.nat) (Na tptp.nat) (K tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (= (tptp.times_times_nat K Ma) (tptp.times_times_nat K Na)) (= Ma Na)))) (forall ((K tptp.nat) (Ma tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.times_times_nat K Ma)) (tptp.times_times_nat K Na))) (or (= K tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) Na))))) (forall ((Ma tptp.nat) (Na tptp.nat) (K tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.times_times_nat K Ma)) (tptp.times_times_nat K Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) Na))))) (forall ((Ma tptp.nat) (Na tptp.nat) (K tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.times_times_nat K Ma)) (tptp.times_times_nat K Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) Na))))) (forall ((U tptp.nat) (Ma tptp.nat) (Na tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J) I_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.plus_plus_nat (tptp.times_times_nat I_1 U) Ma)) (tptp.plus_plus_nat (tptp.times_times_nat J U) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.plus_plus_nat (tptp.times_times_nat (tptp.minus_minus_nat I_1 J) U) Ma)) Na))))) (forall ((U_1 tptp.nat) (M tptp.nat) (N tptp.nat) (J_1 tptp.nat) (I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) I_2)) (= (tptp.minus_minus_nat (tptp.plus_plus_nat (tptp.times_times_nat I_2 U_1) M) (tptp.plus_plus_nat (tptp.times_times_nat J_1 U_1) N)) (tptp.minus_minus_nat (tptp.plus_plus_nat (tptp.times_times_nat (tptp.minus_minus_nat I_2 J_1) U_1) M) N)))) (forall ((U tptp.nat) (Ma tptp.nat) (Na tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J) I_1)) (= (= (tptp.plus_plus_nat (tptp.times_times_nat I_1 U) Ma) (tptp.plus_plus_nat (tptp.times_times_nat J U) Na)) (= (tptp.plus_plus_nat (tptp.times_times_nat (tptp.minus_minus_nat I_1 J) U) Ma) Na)))) (forall ((U tptp.nat) (Ma tptp.nat) (Na tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.plus_plus_nat (tptp.times_times_nat I_1 U) Ma)) (tptp.plus_plus_nat (tptp.times_times_nat J U) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) (tptp.plus_plus_nat (tptp.times_times_nat (tptp.minus_minus_nat J I_1) U) Na)))))) (forall ((U_1 tptp.nat) (M tptp.nat) (N tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_1)) (= (tptp.minus_minus_nat (tptp.plus_plus_nat (tptp.times_times_nat I_2 U_1) M) (tptp.plus_plus_nat (tptp.times_times_nat J_1 U_1) N)) (tptp.minus_minus_nat M (tptp.plus_plus_nat (tptp.times_times_nat (tptp.minus_minus_nat J_1 I_2) U_1) N))))) (forall ((U tptp.nat) (Ma tptp.nat) (Na tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J)) (= (= (tptp.plus_plus_nat (tptp.times_times_nat I_1 U) Ma) (tptp.plus_plus_nat (tptp.times_times_nat J U) Na)) (= Ma (tptp.plus_plus_nat (tptp.times_times_nat (tptp.minus_minus_nat J I_1) U) Na))))) (forall ((K tptp.int) (F tptp.fun_nat_int) (Na tptp.nat)) (=> (forall ((I tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) Na)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.abs_abs_int (tptp.minus_minus_int (tptp.hAPP_nat_int F (tptp.plus_plus_nat I tptp.one_one_nat)) (tptp.hAPP_nat_int F I)))) tptp.one_one_int)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int F tptp.zero_zero_nat)) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) (tptp.hAPP_nat_int F Na))) (exists ((I tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) Na)) (= (tptp.hAPP_nat_int F I) K))))))) (forall ((K tptp.int) (F tptp.fun_nat_int) (Na tptp.nat)) (=> (forall ((I tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) Na)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.abs_abs_int (tptp.minus_minus_int (tptp.hAPP_nat_int F (tptp.plus_plus_nat I tptp.one_one_nat)) (tptp.hAPP_nat_int F I)))) tptp.one_one_int)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int F tptp.zero_zero_nat)) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) (tptp.hAPP_nat_int F Na))) (exists ((I tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) Na)) (= (tptp.hAPP_nat_int F I) K))))))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.if_int tptp.fTrue X Y) X)) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.if_int tptp.fFalse X Y) Y)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.if_nat tptp.fTrue X Y) X)) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.if_nat tptp.fFalse X Y) Y)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) _let_6 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.71/1.94 )
% 1.71/1.94 % SZS output end Proof for NUM925_3
% 1.71/1.94 % cvc5---1.0.5 exiting
% 1.71/1.95 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------