%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM926_3 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n002.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 10:49:09 EDT 2023

% Result   : Theorem 1.65s 1.85s
% Output   : Proof 1.65s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.28/0.28  % Problem    : NUM926_3 : TPTP v8.1.2. Released v5.3.0.
% 0.28/0.29  % Command    : do_cvc5 %s %d
% 0.28/0.50  % Computer : n002.cluster.edu
% 0.28/0.50  % Model    : x86_64 x86_64
% 0.28/0.50  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.28/0.50  % Memory   : 8042.1875MB
% 0.28/0.50  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.28/0.50  % CPULimit   : 300
% 0.28/0.50  % WCLimit    : 300
% 0.28/0.50  % DateTime   : Fri Aug 25 15:17:02 EDT 2023
% 0.28/0.50  % CPUTime    : 
% 0.61/0.80  %----Proving TF0_NAR, FOF, or CNF
% 1.65/1.85  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.8b2BdZwSOh/cvc5---1.0.5_14939.p...
% 1.65/1.85  ------- get file name : TPTP file name is NUM926_3
% 1.65/1.85  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_14939.smt2...
% 1.65/1.85  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.65/1.85  % SZS status Theorem for NUM926_3
% 1.65/1.85  % SZS output start Proof for NUM926_3
% 1.65/1.85  (
% 1.65/1.85  (let ((_let_1 (not (exists ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X) _let_2)) (tptp.hAPP_nat_int (tptp.power_power_int Y) _let_2)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)))))))) (let ((_let_2 (tptp.number_number_of_int tptp.pls))) (let ((_let_3 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_4 (not (= tptp.zero_zero_int tptp.one_one_int)))) (let ((_let_5 (not (= tptp.zero_zero_real tptp.one_one_real)))) (let ((_let_6 (tptp.bit1 tptp.pls))) (let ((_let_7 (tptp.bit0 _let_6))) (let ((_let_8 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_7))) tptp.m)) tptp.one_one_int))) (let ((_let_9 (tptp.number_number_of_int tptp.min))) (let ((_let_10 (= (tptp.legendre _let_9 _let_8) tptp.one_one_int))) (let ((_let_11 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.quadRes _let_8) _let_9)))) (let ((_let_12 (tptp.number_number_of_nat _let_7))) (let ((_let_13 (tptp.hAPP_nat_int (tptp.power_power_int tptp.s) _let_12))) (let ((_let_14 (tptp.hAPP_int_int (tptp.plus_plus_int _let_13) tptp.one_one_int))) (let ((_let_15 (tptp.hAPP_int_int (tptp.minus_minus_int _let_13) _let_9))) (let ((_let_16 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int _let_8))) (let ((_let_17 (forall ((X_8 tptp.int) (Y_7 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_8) Y_7)) (=> (not (= X_8 Y_7)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_8) Y_7))))))) (let ((_let_18 (tptp.number_number_of_nat tptp.pls))) (let ((_let_19 (= _let_18 tptp.zero_zero_nat))) (let ((_let_20 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.min))) (let ((_let_21 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (let ((_let_22 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.min))) (let ((_let_23 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls))) (let ((_let_24 (tptp.number_number_of_int _let_7))) (let ((_let_25 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_26 (= tptp.zero_zero_int _let_2))) (let ((_let_27 (tptp.number267125858f_real tptp.pls))) (let ((_let_28 (= _let_27 tptp.zero_zero_real))) (let ((_let_29 (= _let_2 tptp.zero_zero_int))) (let ((_let_30 (tptp.hAPP_nat_int (tptp.power_power_int tptp.s1) _let_12))) (let ((_let_31 (tptp.hAPP_int_int (tptp.times_times_int _let_8) tptp.t))) (let ((_let_32 (= (tptp.hAPP_real_real (tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (tptp.number267125858f_real _let_7)))) (let ((_let_33 (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) _let_12))) (let ((_let_34 (= (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) _let_24))) (let ((_let_35 (tptp.number_number_of_int _let_6))) (let ((_let_36 (= tptp.one_one_int _let_35))) (let ((_let_37 (tptp.number267125858f_real _let_6))) (let ((_let_38 (= _let_37 tptp.one_one_real))) (let ((_let_39 (= _let_35 tptp.one_one_int))) (let ((_let_40 (tptp.number_number_of_nat _let_6))) (let ((_let_41 (= _let_40 tptp.one_one_nat))) (let ((_let_42 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) tptp.t)))) (let ((_let_43 (=> _let_42 (exists ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X) _let_2)) (tptp.hAPP_nat_int (tptp.power_power_int Y) _let_2)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)))))))) (let ((_let_44 (=> (= tptp.t tptp.one_one_int) (exists ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X) _let_2)) (tptp.hAPP_nat_int (tptp.power_power_int Y) _let_2)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)))))))) (let ((_let_45 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) tptp.t)))) (let ((_let_46 (forall ((X_8 tptp.int) (Y_7 tptp.int)) (or (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_8) Y_7))) (= X_8 Y_7) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_8) Y_7)))))) (let ((_let_47 (= tptp.one_one_int tptp.t))) (let ((_let_48 (not _let_45))) (let ((_let_49 (or _let_48 _let_47 _let_42))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (not _let_49))) (let ((_let_52 (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (not (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X) _let_2)) (tptp.hAPP_nat_int (tptp.power_power_int Y) _let_2)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)))))))) (let ((_let_53 (not _let_47))) (let ((_let_54 (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (not (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X) _let_2)) (tptp.hAPP_nat_int (tptp.power_power_int Y) _let_2))))))))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (TRANS (ALPHA_EQUIV :args (_let_52 (= X X) (= Y Y))) (MACRO_SR_PRED_INTRO :args ((= (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (not (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X) _let_2)) (tptp.hAPP_nat_int (tptp.power_power_int Y) _let_2)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)))))) _let_54) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (_let_52 false _let_54)))) (let ((_let_56 (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (not (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X) _let_2)) (tptp.hAPP_nat_int (tptp.power_power_int Y) _let_2))))))))) (let ((_let_57 (not _let_42))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (tptp.one_one_int tptp.t QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_8) Y_7)))) :args (_let_46))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_42 _let_47 _let_48 _let_51))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_43)) (MACRO_SR_EQ_INTRO :args (_let_43 SB_DEFAULT SBA_FIXPOINT)))) :args ((or (not _let_56) _let_57))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (TRANS (ALPHA_EQUIV :args (_let_52 (= X X) (= Y Y))) (MACRO_SR_PRED_INTRO :args ((= (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (not (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X) _let_2)) (tptp.hAPP_nat_int (tptp.power_power_int Y) _let_2)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)))))) _let_56) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) _let_55 :args (_let_56 false _let_52)) :args (_let_57 false _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_44)) (MACRO_SR_EQ_INTRO :args (_let_44 SB_DEFAULT SBA_FIXPOINT)))) :args ((or (not _let_52) _let_53))) _let_55 :args (_let_53 false _let_52)) (ASSUME :args (_let_45)) :args (_let_51 true _let_42 true _let_47 false _let_45)) _let_50 :args (false true _let_49 false _let_46)) :args (_let_45 _let_44 _let_43 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.t) _let_8)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime _let_8)) (= _let_14 _let_31) (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu820444569sum2sq _let_31)) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_int_int (tptp.plus_plus_int A) B)) _let_2) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int A) _let_2)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int _let_1)) A)) B))) (tptp.hAPP_nat_int (tptp.power_power_int B) _let_2)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit1 _let_1))) (let ((_let_3 (tptp.number_number_of_nat _let_2))) (let ((_let_4 (tptp.power_power_int B))) (let ((_let_5 (tptp.number_number_of_nat (tptp.bit0 _let_1)))) (let ((_let_6 (tptp.times_times_int (tptp.number_number_of_int _let_2)))) (let ((_let_7 (tptp.power_power_int A))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_int_int (tptp.plus_plus_int A) B)) _let_3) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int _let_7 _let_3)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_6 (tptp.hAPP_nat_int _let_7 _let_5))) B))) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_6 A)) (tptp.hAPP_nat_int _let_4 _let_5)))) (tptp.hAPP_nat_int _let_4 _let_3))))))))))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_int_int (tptp.plus_plus_int X_2) Y_2)) _let_2) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X_2) _let_2)) (tptp.hAPP_nat_int (tptp.power_power_int Y_2) _let_2))) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int _let_1)) X_2)) Y_2)))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat X_2) Y_2)) _let_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_2) _let_1)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_2) _let_1))) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.times_times_nat _let_1) X_2)) Y_2))))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_real_real (tptp.plus_plus_real X_2) Y_2)) _let_2) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X_2) _let_2)) (tptp.hAPP_nat_real (tptp.power_power_real Y_2) _let_2))) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real _let_1)) X_2)) Y_2)))))) (forall ((W_16 tptp.int)) (let ((_let_1 (tptp.number_number_of_int W_16))) (= (tptp.hAPP_nat_int (tptp.power_power_int _let_1) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.times_times_int _let_1) _let_1)))) (forall ((W_16 tptp.int)) (let ((_let_1 (tptp.number267125858f_real W_16))) (= (tptp.hAPP_nat_real (tptp.power_power_real _let_1) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real (tptp.times_times_real _let_1) _let_1)))) (forall ((W_16 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_16))) (= (tptp.hAPP_nat_nat (tptp.power_power_nat _let_1) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_nat (tptp.times_times_nat _let_1) _let_1)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.power_power_int A))) (= (tptp.hAPP_int_int (tptp.times_times_int A) (tptp.hAPP_nat_int _let_2 (tptp.number_number_of_nat (tptp.bit0 _let_1)))) (tptp.hAPP_nat_int _let_2 (tptp.number_number_of_nat (tptp.bit1 _let_1))))))) (= (tptp.hAPP_nat_int (tptp.power_power_int tptp.one_one_int) _let_12) tptp.one_one_int) (= (tptp.hAPP_nat_nat (tptp.power_power_nat tptp.one_one_nat) _let_12) tptp.one_one_nat) (= (tptp.hAPP_nat_real (tptp.power_power_real tptp.one_one_real) _let_12) tptp.one_one_real) (forall ((X_26 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int X_26) X_26) (tptp.hAPP_nat_int (tptp.power_power_int X_26) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (forall ((X_26 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real X_26) X_26) (tptp.hAPP_nat_real (tptp.power_power_real X_26) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (forall ((X_26 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat X_26) X_26) (tptp.hAPP_nat_nat (tptp.power_power_nat X_26) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (forall ((A_112 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int A_112) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.times_times_int A_112) A_112))) (forall ((A_112 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real A_112) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real (tptp.times_times_real A_112) A_112))) (forall ((A_112 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_112) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_nat (tptp.times_times_nat A_112) A_112))) (forall ((X_25 tptp.int) (N_40 tptp.nat)) (let ((_let_1 (tptp.power_power_int X_25))) (let ((_let_2 (tptp.hAPP_nat_int _let_1 N_40))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_40)) (tptp.hAPP_int_int (tptp.times_times_int _let_2) _let_2))))) (forall ((X_25 tptp.real) (N_40 tptp.nat)) (let ((_let_1 (tptp.power_power_real X_25))) (let ((_let_2 (tptp.hAPP_nat_real _let_1 N_40))) (= (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_40)) (tptp.hAPP_real_real (tptp.times_times_real _let_2) _let_2))))) (forall ((X_25 tptp.nat) (N_40 tptp.nat)) (let ((_let_1 (tptp.power_power_nat X_25))) (let ((_let_2 (tptp.hAPP_nat_nat _let_1 N_40))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_40)) (tptp.hAPP_nat_nat (tptp.times_times_nat _let_2) _let_2))))) (forall ((W_15 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) (tptp.number_number_of_int W_15)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit1 tptp.pls)) W_15)))) (forall ((W_15 tptp.int)) (= (tptp.hAPP_real_real (tptp.plus_plus_real tptp.one_one_real) (tptp.number267125858f_real W_15)) (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit1 tptp.pls)) W_15)))) (forall ((V_21 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_21)) tptp.one_one_int) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V_21) (tptp.bit1 tptp.pls))))) (forall ((V_21 tptp.int)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real V_21)) tptp.one_one_real) (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int V_21) (tptp.bit1 tptp.pls))))) _let_34 _let_32 (not (forall ((T_1 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (not (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int tptp.s) (tptp.number_number_of_nat _let_1))) tptp.one_one_int) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)) T_1)))))) (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)) (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 ((Z_1 tptp.int) (W_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_1) W_1)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_1) W_1)) (not (= Z_1 W_1))))) (forall ((X_1 tptp.int) (Y_1 tptp.int)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) Y_1)) (= X_1 Y_1) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y_1) X_1)))) (forall ((K_1 tptp.int) (I_1 tptp.int) (J_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 J_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int J_1) K_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K_1)))))) (forall ((Z tptp.int) (W tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z) W)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) Z)) (= Z W)))) (forall ((X_24 tptp.int) (P_7 tptp.nat) (Q_7 tptp.nat)) (let ((_let_1 (tptp.power_power_int X_24))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int _let_1 P_7)) Q_7) (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat P_7) Q_7))))) (forall ((X_24 tptp.real) (P_7 tptp.nat) (Q_7 tptp.nat)) (let ((_let_1 (tptp.power_power_real X_24))) (= (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_nat_real _let_1 P_7)) Q_7) (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat P_7) Q_7))))) (forall ((X_24 tptp.nat) (P_7 tptp.nat) (Q_7 tptp.nat)) (let ((_let_1 (tptp.power_power_nat X_24))) (= (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.hAPP_nat_nat _let_1 P_7)) Q_7) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat P_7) Q_7))))) (forall ((X_23 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int X_23) tptp.one_one_nat) X_23)) (forall ((X_23 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real X_23) tptp.one_one_nat) X_23)) (forall ((X_23 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat X_23) tptp.one_one_nat) X_23)) (forall ((X_1 tptp.int) (Y_1 tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.power_power_int X_1))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int _let_1 Y_1)) Z) (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat Y_1) Z))))) (forall ((V_7 tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_int V_7))) (let ((_let_2 (tptp.number_number_of_int W_1))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_2) _let_1))))))) (forall ((V_7 tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat V_7))) (let ((_let_2 (tptp.number_number_of_nat W_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat _let_2) _let_1))))))) (forall ((V_7 tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.number267125858f_real V_7))) (let ((_let_2 (tptp.number267125858f_real W_1))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_2) _let_1))))))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int X_2)) (tptp.number_number_of_int Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) Y_2)))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.number267125858f_real X_2)) (tptp.number267125858f_real Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) Y_2)))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int X_2)) (tptp.number_number_of_int Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_2) Y_2)))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.number267125858f_real X_2)) (tptp.number267125858f_real Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_2) Y_2)))) (forall ((Z_10 tptp.int) (Z tptp.int) (W_14 tptp.int) (W tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_14) W)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_10) Z)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int W_14) Z_10)) (tptp.hAPP_int_int (tptp.plus_plus_int W) Z)))))) (forall ((X_22 tptp.int) (P_6 tptp.nat) (Q_6 tptp.nat)) (let ((_let_1 (tptp.power_power_int X_22))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_nat_int _let_1 P_6)) (tptp.hAPP_nat_int _let_1 Q_6)) (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat P_6) Q_6))))) (forall ((X_22 tptp.real) (P_6 tptp.nat) (Q_6 tptp.nat)) (let ((_let_1 (tptp.power_power_real X_22))) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_nat_real _let_1 P_6)) (tptp.hAPP_nat_real _let_1 Q_6)) (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat P_6) Q_6))))) (forall ((X_22 tptp.nat) (P_6 tptp.nat) (Q_6 tptp.nat)) (let ((_let_1 (tptp.power_power_nat X_22))) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 P_6)) (tptp.hAPP_nat_nat _let_1 Q_6)) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat P_6) Q_6))))) (forall ((X_1 tptp.int) (Y_1 tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.power_power_int X_1))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat Y_1) Z)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_nat_int _let_1 Y_1)) (tptp.hAPP_nat_int _let_1 Z))))) (forall ((Z tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) Z) (tptp.hAPP_nat_nat (tptp.plus_plus_nat Z) Z))) (forall ((Z tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat Z) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_nat (tptp.plus_plus_nat Z) Z))) _let_33 (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)))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K1)) (tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K1) K2)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) L_1)))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_23 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)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_21 tptp.pls)) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K1)) (tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K1) K2)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) L_1)))) (forall ((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 ((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 ((K_1 tptp.int) (I_1 tptp.int) (J_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_1) J_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int I_1) K_1)) (tptp.hAPP_int_int (tptp.plus_plus_int J_1) K_1))))) (forall ((K_1 tptp.int) (I_1 tptp.int) (J_1 tptp.int)) (let ((_let_1 (tptp.plus_plus_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_1) J_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 I_1)) (tptp.hAPP_int_int _let_1 J_1)))))) (forall ((V_6 tptp.int) (V tptp.int)) (let ((_let_1 (tptp.number_number_of_nat V_6))) (let ((_let_2 (tptp.number_number_of_nat V))) (let ((_let_3 (tptp.hAPP_nat_nat (tptp.plus_plus_nat _let_2) _let_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_6) tptp.pls)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V) tptp.pls)))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.plus_plus_int V) V_6))))))))))))) _let_41 (= tptp.one_one_nat _let_40) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) tptp.pls)))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) K)))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K1)) (tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K1) K2)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K)) (tptp.bit0 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) L_1)))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 K1)) (tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K1) K2)))) (forall ((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 ((W tptp.int) (Z tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W) Z)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.plus_plus_int W) tptp.one_one_int)) Z)))) (forall ((W_1 tptp.int) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.plus_plus_int W_1) tptp.one_one_int)) Z_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) Z_1)))) (forall ((W_1 tptp.int) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) (tptp.hAPP_int_int (tptp.plus_plus_int Z_1) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W_1) Z_1)))) (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime _let_24)) (forall ((Y_1 tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu820444569sum2sq X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu820444569sum2sq Y_1)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu820444569sum2sq (tptp.hAPP_int_int (tptp.times_times_int X_1) Y_1)))))) (forall ((Lx_6 tptp.int) (Ly_4 tptp.int) (Rx_6 tptp.int) (Ry_4 tptp.int)) (let ((_let_1 (tptp.times_times_int Lx_6))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_1 Ly_4)) (tptp.hAPP_int_int (tptp.times_times_int Rx_6) Ry_4)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_1 Rx_6)) (tptp.hAPP_int_int (tptp.times_times_int Ly_4) Ry_4))))) (forall ((Lx_6 tptp.nat) (Ly_4 tptp.nat) (Rx_6 tptp.nat) (Ry_4 tptp.nat)) (let ((_let_1 (tptp.times_times_nat Lx_6))) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Ly_4)) (tptp.hAPP_nat_nat (tptp.times_times_nat Rx_6) Ry_4)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Rx_6)) (tptp.hAPP_nat_nat (tptp.times_times_nat Ly_4) Ry_4))))) (forall ((Lx_6 tptp.real) (Ly_4 tptp.real) (Rx_6 tptp.real) (Ry_4 tptp.real)) (let ((_let_1 (tptp.times_times_real Lx_6))) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real _let_1 Ly_4)) (tptp.hAPP_real_real (tptp.times_times_real Rx_6) Ry_4)) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real _let_1 Rx_6)) (tptp.hAPP_real_real (tptp.times_times_real Ly_4) Ry_4))))) (forall ((Lx_5 tptp.int) (Ly_3 tptp.int) (Rx_5 tptp.int) (Ry_3 tptp.int)) (let ((_let_1 (tptp.times_times_int (tptp.hAPP_int_int (tptp.times_times_int Lx_5) Ly_3)))) (let ((_let_2 (tptp.times_times_int Rx_5))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 Ry_3)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 Ry_3)))))) (forall ((Lx_5 tptp.nat) (Ly_3 tptp.nat) (Rx_5 tptp.nat) (Ry_3 tptp.nat)) (let ((_let_1 (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.times_times_nat Lx_5) Ly_3)))) (let ((_let_2 (tptp.times_times_nat Rx_5))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Ry_3)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Ry_3)))))) (forall ((Lx_5 tptp.real) (Ly_3 tptp.real) (Rx_5 tptp.real) (Ry_3 tptp.real)) (let ((_let_1 (tptp.times_times_real (tptp.hAPP_real_real (tptp.times_times_real Lx_5) Ly_3)))) (let ((_let_2 (tptp.times_times_real Rx_5))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real _let_2 Ry_3)) (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real _let_1 Ry_3)))))) (forall ((Lx_4 tptp.int) (Ly_2 tptp.int) (Rx_4 tptp.int) (Ry_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.times_times_int Rx_4) Ry_2))) (let ((_let_2 (tptp.times_times_int Lx_4))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_2 Ly_2)) _let_1) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int (tptp.times_times_int Ly_2) _let_1)))))) (forall ((Lx_4 tptp.nat) (Ly_2 tptp.nat) (Rx_4 tptp.nat) (Ry_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat Rx_4) Ry_2))) (let ((_let_2 (tptp.times_times_nat Lx_4))) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_2 Ly_2)) _let_1) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat (tptp.times_times_nat Ly_2) _let_1)))))) (forall ((Lx_4 tptp.real) (Ly_2 tptp.real) (Rx_4 tptp.real) (Ry_2 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.times_times_real Rx_4) Ry_2))) (let ((_let_2 (tptp.times_times_real Lx_4))) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real _let_2 Ly_2)) _let_1) (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real (tptp.times_times_real Ly_2) _let_1)))))) (forall ((Lx_3 tptp.int) (Ly_1 tptp.int) (Rx_3 tptp.int)) (let ((_let_1 (tptp.times_times_int Lx_3))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_1 Ly_1)) Rx_3) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_1 Rx_3)) Ly_1)))) (forall ((Lx_3 tptp.nat) (Ly_1 tptp.nat) (Rx_3 tptp.nat)) (let ((_let_1 (tptp.times_times_nat Lx_3))) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Ly_1)) Rx_3) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Rx_3)) Ly_1)))) (forall ((Lx_3 tptp.real) (Ly_1 tptp.real) (Rx_3 tptp.real)) (let ((_let_1 (tptp.times_times_real Lx_3))) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real _let_1 Ly_1)) Rx_3) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real _let_1 Rx_3)) Ly_1)))) (forall ((Lx_2 tptp.int) (Ly tptp.int) (Rx_2 tptp.int)) (let ((_let_1 (tptp.times_times_int Lx_2))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_1 Ly)) Rx_2) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.times_times_int Ly) Rx_2))))) (forall ((Lx_2 tptp.nat) (Ly tptp.nat) (Rx_2 tptp.nat)) (let ((_let_1 (tptp.times_times_nat Lx_2))) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Ly)) Rx_2) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat Ly) Rx_2))))) (forall ((Lx_2 tptp.real) (Ly tptp.real) (Rx_2 tptp.real)) (let ((_let_1 (tptp.times_times_real Lx_2))) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real _let_1 Ly)) Rx_2) (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.times_times_real Ly) Rx_2))))) (forall ((Lx_1 tptp.int) (Rx_1 tptp.int) (Ry_1 tptp.int)) (let ((_let_1 (tptp.times_times_int Lx_1))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.times_times_int Rx_1) Ry_1)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_1 Rx_1)) Ry_1)))) (forall ((Lx_1 tptp.nat) (Rx_1 tptp.nat) (Ry_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat Lx_1))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat Rx_1) Ry_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Rx_1)) Ry_1)))) (forall ((Lx_1 tptp.real) (Rx_1 tptp.real) (Ry_1 tptp.real)) (let ((_let_1 (tptp.times_times_real Lx_1))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.times_times_real Rx_1) Ry_1)) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real _let_1 Rx_1)) Ry_1)))) (forall ((Lx tptp.int) (Rx tptp.int) (Ry tptp.int)) (let ((_let_1 (tptp.times_times_int Lx))) (let ((_let_2 (tptp.times_times_int Rx))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 Ry)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 Ry)))))) (forall ((Lx tptp.nat) (Rx tptp.nat) (Ry tptp.nat)) (let ((_let_1 (tptp.times_times_nat Lx))) (let ((_let_2 (tptp.times_times_nat Rx))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Ry)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Ry)))))) (forall ((Lx tptp.real) (Rx tptp.real) (Ry tptp.real)) (let ((_let_1 (tptp.times_times_real Lx))) (let ((_let_2 (tptp.times_times_real Rx))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real _let_2 Ry)) (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real _let_1 Ry)))))) (forall ((A_111 tptp.int) (B_63 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int A_111) B_63) (tptp.hAPP_int_int (tptp.times_times_int B_63) A_111))) (forall ((A_111 tptp.nat) (B_63 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat A_111) B_63) (tptp.hAPP_nat_nat (tptp.times_times_nat B_63) A_111))) (forall ((A_111 tptp.real) (B_63 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real A_111) B_63) (tptp.hAPP_real_real (tptp.times_times_real B_63) A_111))) (forall ((A_110 tptp.int) (B_62 tptp.int) (C_35 tptp.int) (D_11 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_110))) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_62)) (tptp.hAPP_int_int (tptp.plus_plus_int C_35) D_11)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 C_35)) (tptp.hAPP_int_int (tptp.plus_plus_int B_62) D_11))))) (forall ((A_110 tptp.nat) (B_62 tptp.nat) (C_35 tptp.nat) (D_11 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_110))) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_62)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat C_35) D_11)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 C_35)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_62) D_11))))) (forall ((A_110 tptp.real) (B_62 tptp.real) (C_35 tptp.real) (D_11 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_110))) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_62)) (tptp.hAPP_real_real (tptp.plus_plus_real C_35) D_11)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 C_35)) (tptp.hAPP_real_real (tptp.plus_plus_real B_62) D_11))))) (forall ((X_2 tptp.int) (A_109 tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.member_int X_2 A_109)) (tptp.hBOOL (tptp.hAPP_int_bool A_109 X_2)))) (forall ((P_2 tptp.fun_int_bool)) (= (tptp.collect_int P_2) P_2)) (forall ((A_108 tptp.int) (B_61 tptp.int) (C_34 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_108))) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_61)) C_34) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 C_34)) B_61)))) (forall ((A_108 tptp.nat) (B_61 tptp.nat) (C_34 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_108))) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_61)) C_34) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 C_34)) B_61)))) (forall ((A_108 tptp.real) (B_61 tptp.real) (C_34 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_108))) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_61)) C_34) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 C_34)) B_61)))) (forall ((A_107 tptp.int) (B_60 tptp.int) (C_33 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_107))) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_60)) C_33) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int B_60) C_33))))) (forall ((A_107 tptp.nat) (B_60 tptp.nat) (C_33 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_107))) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_60)) C_33) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_60) C_33))))) (forall ((A_107 tptp.real) (B_60 tptp.real) (C_33 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_107))) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_60)) C_33) (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real B_60) C_33))))) (forall ((A_106 tptp.int) (C_32 tptp.int) (D_10 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_106))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int C_32) D_10)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 C_32)) D_10)))) (forall ((A_106 tptp.nat) (C_32 tptp.nat) (D_10 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_106))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat C_32) D_10)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 C_32)) D_10)))) (forall ((A_106 tptp.real) (C_32 tptp.real) (D_10 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_106))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real C_32) D_10)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 C_32)) D_10)))) (forall ((A_105 tptp.int) (C_31 tptp.int) (D_9 tptp.int)) (let ((_let_1 (tptp.plus_plus_int A_105))) (let ((_let_2 (tptp.plus_plus_int C_31))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 D_9)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 D_9)))))) (forall ((A_105 tptp.nat) (C_31 tptp.nat) (D_9 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat A_105))) (let ((_let_2 (tptp.plus_plus_nat C_31))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 D_9)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 D_9)))))) (forall ((A_105 tptp.real) (C_31 tptp.real) (D_9 tptp.real)) (let ((_let_1 (tptp.plus_plus_real A_105))) (let ((_let_2 (tptp.plus_plus_real C_31))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real _let_2 D_9)) (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real _let_1 D_9)))))) (forall ((A_104 tptp.int) (C_30 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int A_104) C_30) (tptp.hAPP_int_int (tptp.plus_plus_int C_30) A_104))) (forall ((A_104 tptp.nat) (C_30 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_104) C_30) (tptp.hAPP_nat_nat (tptp.plus_plus_nat C_30) A_104))) (forall ((A_104 tptp.real) (C_30 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real A_104) C_30) (tptp.hAPP_real_real (tptp.plus_plus_real C_30) A_104))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (= (tptp.number_number_of_int X_2) (tptp.number_number_of_int Y_2)) (= X_2 Y_2))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (= (tptp.number267125858f_real X_2) (tptp.number267125858f_real Y_2)) (= X_2 Y_2))) (forall ((W_1 tptp.int) (X_2 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat W_1))) (= (= _let_1 X_2) (= X_2 _let_1)))) (forall ((W_1 tptp.int) (X_2 tptp.int)) (let ((_let_1 (tptp.number_number_of_int W_1))) (= (= _let_1 X_2) (= X_2 _let_1)))) (forall ((W_1 tptp.int) (X_2 tptp.real)) (let ((_let_1 (tptp.number267125858f_real W_1))) (= (= _let_1 X_2) (= X_2 _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 ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (tptp.times_times_int Z1))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_1 Z2)) Z3) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.times_times_int Z2) Z3))))) (forall ((Z tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int Z) W) (tptp.hAPP_int_int (tptp.times_times_int W) Z))) (forall ((K_1 tptp.int)) (= (tptp.number_number_of_int K_1) K_1)) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (tptp.plus_plus_int Z1))) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Z2)) Z3) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int Z2) Z3))))) (forall ((X_1 tptp.int) (Y_1 tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.plus_plus_int X_1))) (let ((_let_2 (tptp.plus_plus_int Y_1))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 Z)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 Z)))))) (forall ((Z tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int Z) W) (tptp.hAPP_int_int (tptp.plus_plus_int W) Z))) (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 ((K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K))))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K1)) (tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K1) K2)))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K)) (tptp.bit1 L_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) L_1)))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit0 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) tptp.pls)))) (forall ((K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K))))) (forall ((W_1 tptp.int) (Z_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int Z_1) tptp.one_one_int))) (or (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_1)) (= W_1 Z_1))))) (forall ((A_103 tptp.int) (N_39 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power_int A_103))) (= (tptp.hAPP_nat_int _let_2 (tptp.hAPP_nat_nat (tptp.times_times_nat _let_1) N_39)) (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int _let_2 N_39)) _let_1))))) (forall ((A_103 tptp.real) (N_39 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power_real A_103))) (= (tptp.hAPP_nat_real _let_2 (tptp.hAPP_nat_nat (tptp.times_times_nat _let_1) N_39)) (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_nat_real _let_2 N_39)) _let_1))))) (forall ((A_103 tptp.nat) (N_39 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power_nat A_103))) (= (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat (tptp.times_times_nat _let_1) N_39)) (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.hAPP_nat_nat _let_2 N_39)) _let_1))))) (forall ((X_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int X_2)) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) (tptp.bit1 tptp.pls))))) (forall ((X_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.number267125858f_real X_2)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) (tptp.bit1 tptp.pls))))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) (tptp.number_number_of_int Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 tptp.pls)) Y_2)))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) (tptp.number267125858f_real Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 tptp.pls)) Y_2)))) (forall ((X_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int X_2)) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_2) (tptp.bit1 tptp.pls))))) (forall ((X_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.number267125858f_real X_2)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_2) (tptp.bit1 tptp.pls))))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.number_number_of_int Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 tptp.pls)) Y_2)))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.number267125858f_real Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 tptp.pls)) Y_2)))) (forall ((W_1 tptp.int) (Y_2 tptp.int) (X_2 tptp.int) (Z_1 tptp.int)) (let ((_let_1 (tptp.times_times_int X_2))) (let ((_let_2 (tptp.times_times_int W_1))) (= (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_2 Y_2)) (tptp.hAPP_int_int _let_1 Z_1)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_2 Z_1)) (tptp.hAPP_int_int _let_1 Y_2))) (or (= W_1 X_2) (= Y_2 Z_1)))))) (forall ((W_1 tptp.nat) (Y_2 tptp.nat) (X_2 tptp.nat) (Z_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat X_2))) (let ((_let_2 (tptp.times_times_nat W_1))) (= (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_2 Y_2)) (tptp.hAPP_nat_nat _let_1 Z_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_2 Z_1)) (tptp.hAPP_nat_nat _let_1 Y_2))) (or (= W_1 X_2) (= Y_2 Z_1)))))) (forall ((W_1 tptp.real) (Y_2 tptp.real) (X_2 tptp.real) (Z_1 tptp.real)) (let ((_let_1 (tptp.times_times_real X_2))) (let ((_let_2 (tptp.times_times_real W_1))) (= (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_2 Y_2)) (tptp.hAPP_real_real _let_1 Z_1)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_2 Z_1)) (tptp.hAPP_real_real _let_1 Y_2))) (or (= W_1 X_2) (= Y_2 Z_1)))))) (forall ((A_102 tptp.int) (M_13 tptp.int) (B_59 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int A_102) M_13)) (tptp.hAPP_int_int (tptp.times_times_int B_59) M_13)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int A_102) B_59)) M_13))) (forall ((A_102 tptp.nat) (M_13 tptp.nat) (B_59 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_102) M_13)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_59) M_13)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_102) B_59)) M_13))) (forall ((A_102 tptp.real) (M_13 tptp.real) (B_59 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real A_102) M_13)) (tptp.hAPP_real_real (tptp.times_times_real B_59) M_13)) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real A_102) B_59)) M_13))) (forall ((A_101 tptp.int) (B_58 tptp.int) (C_29 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int A_101) B_58)) C_29) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int A_101) C_29)) (tptp.hAPP_int_int (tptp.times_times_int B_58) C_29)))) (forall ((A_101 tptp.nat) (B_58 tptp.nat) (C_29 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_101) B_58)) C_29) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_101) C_29)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_58) C_29)))) (forall ((A_101 tptp.real) (B_58 tptp.real) (C_29 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real A_101) B_58)) C_29) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real A_101) C_29)) (tptp.hAPP_real_real (tptp.times_times_real B_58) C_29)))) (forall ((C_2 tptp.int) (D tptp.int) (A_2 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.times_times_int B_2))) (let ((_let_2 (tptp.times_times_int A_2))) (= (and (not (= A_2 B_2)) (not (= C_2 D))) (not (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_2 C_2)) (tptp.hAPP_int_int _let_1 D)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_2 D)) (tptp.hAPP_int_int _let_1 C_2)))))))) (forall ((C_2 tptp.nat) (D tptp.nat) (A_2 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.times_times_nat B_2))) (let ((_let_2 (tptp.times_times_nat A_2))) (= (and (not (= A_2 B_2)) (not (= C_2 D))) (not (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_2 C_2)) (tptp.hAPP_nat_nat _let_1 D)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_2 D)) (tptp.hAPP_nat_nat _let_1 C_2)))))))) (forall ((C_2 tptp.real) (D tptp.real) (A_2 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.times_times_real B_2))) (let ((_let_2 (tptp.times_times_real A_2))) (= (and (not (= A_2 B_2)) (not (= C_2 D))) (not (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_2 C_2)) (tptp.hAPP_real_real _let_1 D)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_2 D)) (tptp.hAPP_real_real _let_1 C_2)))))))) (forall ((X_21 tptp.int) (Y_18 tptp.int) (Z_9 tptp.int)) (let ((_let_1 (tptp.times_times_int X_21))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int Y_18) Z_9)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Y_18)) (tptp.hAPP_int_int _let_1 Z_9))))) (forall ((X_21 tptp.nat) (Y_18 tptp.nat) (Z_9 tptp.nat)) (let ((_let_1 (tptp.times_times_nat X_21))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat Y_18) Z_9)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 Y_18)) (tptp.hAPP_nat_nat _let_1 Z_9))))) (forall ((X_21 tptp.real) (Y_18 tptp.real) (Z_9 tptp.real)) (let ((_let_1 (tptp.times_times_real X_21))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real Y_18) Z_9)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 Y_18)) (tptp.hAPP_real_real _let_1 Z_9))))) (forall ((A_100 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int A_100) tptp.one_one_int) A_100)) (forall ((A_100 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat A_100) tptp.one_one_nat) A_100)) (forall ((A_100 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real A_100) tptp.one_one_real) A_100)) (forall ((A_99 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int tptp.one_one_int) A_99) A_99)) (forall ((A_99 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat tptp.one_one_nat) A_99) A_99)) (forall ((A_99 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real tptp.one_one_real) A_99) A_99)) (forall ((X_20 tptp.int) (Y_17 tptp.int) (Q_5 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_int_int (tptp.times_times_int X_20) Y_17)) Q_5) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_nat_int (tptp.power_power_int X_20) Q_5)) (tptp.hAPP_nat_int (tptp.power_power_int Y_17) Q_5)))) (forall ((X_20 tptp.real) (Y_17 tptp.real) (Q_5 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_real_real (tptp.times_times_real X_20) Y_17)) Q_5) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_nat_real (tptp.power_power_real X_20) Q_5)) (tptp.hAPP_nat_real (tptp.power_power_real Y_17) Q_5)))) (forall ((X_20 tptp.nat) (Y_17 tptp.nat) (Q_5 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.hAPP_nat_nat (tptp.times_times_nat X_20) Y_17)) Q_5) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_20) Q_5)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_17) Q_5)))) (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) (forall ((W tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int tptp.pls) W) tptp.pls)) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.bit0 K_1)) L) (tptp.bit0 (tptp.hAPP_int_int (tptp.times_times_int K_1) L)))) (forall ((K_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int K_1) tptp.pls) K_1)) (forall ((K_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int tptp.pls) K_1) K_1)) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit0 K_1)) (tptp.bit0 L)) (tptp.bit0 (tptp.hAPP_int_int (tptp.plus_plus_int K_1) L)))) (forall ((K_1 tptp.int)) (= (tptp.bit0 K_1) (tptp.hAPP_int_int (tptp.plus_plus_int K_1) K_1))) (forall ((Z tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int Z) tptp.one_one_int) Z)) (forall ((Z tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int tptp.one_one_int) Z) Z)) (forall ((V tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int V)) (tptp.number_number_of_int W)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.times_times_int V) W)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int Z1) Z2)) W) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int Z1) W)) (tptp.hAPP_int_int (tptp.times_times_int Z2) W)))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (tptp.times_times_int W))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int Z1) Z2)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Z1)) (tptp.hAPP_int_int _let_1 Z2))))) (forall ((V tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V)) (tptp.number_number_of_int W)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V) W)))) (forall ((V_20 tptp.int) (V_19 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_19)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_20)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int V_19)) (tptp.number_number_of_int V_20)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.times_times_int V_19) V_20))))))) (forall ((V_20 tptp.int) (V_19 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_19)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_20)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat V_19)) (tptp.number_number_of_nat V_20)) (tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.times_times_int V_19) V_20))))))) (forall ((V_20 tptp.int) (V_19 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_19)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_20)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real V_19)) (tptp.number267125858f_real V_20)) (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.times_times_int V_19) V_20))))))) (forall ((V_18 tptp.int) (V_17 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_17)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_18)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_17)) (tptp.number_number_of_int V_18)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V_17) V_18))))))) (forall ((V_18 tptp.int) (V_17 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_17)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_18)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.number_number_of_nat V_17)) (tptp.number_number_of_nat V_18)) (tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.plus_plus_int V_17) V_18))))))) (forall ((V_18 tptp.int) (V_17 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_17)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_18)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real V_17)) (tptp.number267125858f_real V_18)) (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int V_17) V_18))))))) (forall ((X_1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) (tptp.hAPP_nat_int (tptp.power_power_int X_1) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))))) (forall ((A_98 tptp.int) (B_57 tptp.int) (V_16 tptp.int)) (let ((_let_1 (tptp.number_number_of_int V_16))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int A_98) B_57)) _let_1) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int A_98) _let_1)) (tptp.hAPP_int_int (tptp.times_times_int B_57) _let_1))))) (forall ((A_98 tptp.nat) (B_57 tptp.nat) (V_16 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat V_16))) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_98) B_57)) _let_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_98) _let_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_57) _let_1))))) (forall ((A_98 tptp.real) (B_57 tptp.real) (V_16 tptp.int)) (let ((_let_1 (tptp.number267125858f_real V_16))) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real A_98) B_57)) _let_1) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real A_98) _let_1)) (tptp.hAPP_real_real (tptp.times_times_real B_57) _let_1))))) (forall ((V_15 tptp.int) (B_56 tptp.int) (C_28 tptp.int)) (let ((_let_1 (tptp.times_times_int (tptp.number_number_of_int V_15)))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int B_56) C_28)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_56)) (tptp.hAPP_int_int _let_1 C_28))))) (forall ((V_15 tptp.int) (B_56 tptp.nat) (C_28 tptp.nat)) (let ((_let_1 (tptp.times_times_nat (tptp.number_number_of_nat V_15)))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_56) C_28)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_56)) (tptp.hAPP_nat_nat _let_1 C_28))))) (forall ((V_15 tptp.int) (B_56 tptp.real) (C_28 tptp.real)) (let ((_let_1 (tptp.times_times_real (tptp.number267125858f_real V_15)))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real B_56) C_28)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_56)) (tptp.hAPP_real_real _let_1 C_28))))) (forall ((A_97 tptp.int) (M_12 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int A_97) M_12)) M_12) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int A_97) tptp.one_one_int)) M_12))) (forall ((A_97 tptp.nat) (M_12 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_97) M_12)) M_12) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_97) tptp.one_one_nat)) M_12))) (forall ((A_97 tptp.real) (M_12 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real A_97) M_12)) M_12) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real A_97) tptp.one_one_real)) M_12))) (forall ((M_11 tptp.int) (A_96 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int M_11) (tptp.hAPP_int_int (tptp.times_times_int A_96) M_11)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int A_96) tptp.one_one_int)) M_11))) (forall ((M_11 tptp.nat) (A_96 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_11) (tptp.hAPP_nat_nat (tptp.times_times_nat A_96) M_11)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_96) tptp.one_one_nat)) M_11))) (forall ((M_11 tptp.real) (A_96 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real M_11) (tptp.hAPP_real_real (tptp.times_times_real A_96) M_11)) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real A_96) tptp.one_one_real)) M_11))) (forall ((M_10 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int M_10) M_10) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)) M_10))) (forall ((M_10 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_10) M_10) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)) M_10))) (forall ((M_10 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real M_10) M_10) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)) M_10))) (forall ((A_95 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int tptp.pls)) A_95) A_95)) (forall ((A_95 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real tptp.pls)) A_95) A_95)) (forall ((A_94 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int A_94) (tptp.number_number_of_int tptp.pls)) A_94)) (forall ((A_94 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real A_94) (tptp.number267125858f_real tptp.pls)) A_94)) (forall ((V_14 tptp.int) (W_13 tptp.int) (Z_8 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int V_14)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int W_13)) Z_8)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.times_times_int V_14) W_13))) Z_8))) (forall ((V_14 tptp.int) (W_13 tptp.int) (Z_8 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real V_14)) (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real W_13)) Z_8)) (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.times_times_int V_14) W_13))) Z_8))) (forall ((V_13 tptp.int) (W_12 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int V_13)) (tptp.number_number_of_int W_12)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.times_times_int V_13) W_12)))) (forall ((V_13 tptp.int) (W_12 tptp.int)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real V_13)) (tptp.number267125858f_real W_12)) (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.times_times_int V_13) W_12)))) (forall ((V_12 tptp.int) (W_11 tptp.int)) (= (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.times_times_int V_12) W_11)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int V_12)) (tptp.number_number_of_int W_11)))) (forall ((V_12 tptp.int) (W_11 tptp.int)) (= (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.times_times_int V_12) W_11)) (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real V_12)) (tptp.number267125858f_real W_11)))) (forall ((V_11 tptp.int) (W_10 tptp.int) (Z_7 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_11)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int W_10)) Z_7)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V_11) W_10))) Z_7))) (forall ((V_11 tptp.int) (W_10 tptp.int) (Z_7 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real V_11)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real W_10)) Z_7)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int V_11) W_10))) Z_7))) (forall ((V_10 tptp.int) (W_9 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_10)) (tptp.number_number_of_int W_9)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V_10) W_9)))) (forall ((V_10 tptp.int) (W_9 tptp.int)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real V_10)) (tptp.number267125858f_real W_9)) (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int V_10) W_9)))) (forall ((V_9 tptp.int) (W_8 tptp.int)) (= (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V_9) W_8)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_9)) (tptp.number_number_of_int W_8)))) (forall ((V_9 tptp.int) (W_8 tptp.int)) (= (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int V_9) W_8)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real V_9)) (tptp.number267125858f_real W_8)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit1 K_1)) (tptp.bit0 L)) (tptp.bit1 (tptp.hAPP_int_int (tptp.plus_plus_int K_1) L)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit0 K_1)) (tptp.bit1 L)) (tptp.bit1 (tptp.hAPP_int_int (tptp.plus_plus_int K_1) L)))) (forall ((K_1 tptp.int)) (= (tptp.bit1 K_1) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) K_1)) K_1))) (forall ((W_7 tptp.int)) (let ((_let_1 (tptp.number_number_of_int W_7))) (= (tptp.number_number_of_int (tptp.bit1 W_7)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) _let_1)) _let_1)))) (forall ((W_7 tptp.int)) (let ((_let_1 (tptp.number267125858f_real W_7))) (= (tptp.number267125858f_real (tptp.bit1 W_7)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.plus_plus_real tptp.one_one_real) _let_1)) _let_1)))) (forall ((A_93 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit1 tptp.pls))) A_93) A_93)) (forall ((A_93 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real (tptp.bit1 tptp.pls))) A_93) A_93)) (forall ((A_92 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int A_92) (tptp.number_number_of_int (tptp.bit1 tptp.pls))) A_92)) (forall ((A_92 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real A_92) (tptp.number267125858f_real (tptp.bit1 tptp.pls))) A_92)) _let_39 _let_41 _let_38 _let_39 _let_38 _let_36 (= tptp.one_one_real _let_37) _let_36 (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.bit1 K_1)) L) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.bit0 (tptp.hAPP_int_int (tptp.times_times_int K_1) L))) L))) (forall ((W_6 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)) (tptp.number_number_of_int W_6)) (tptp.number_number_of_int (tptp.bit0 W_6)))) (forall ((W_6 tptp.int)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)) (tptp.number267125858f_real W_6)) (tptp.number267125858f_real (tptp.bit0 W_6)))) (forall ((A_91 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int A_91) (tptp.number_number_of_nat (tptp.bit1 (tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.times_times_int A_91) A_91)) A_91))) (forall ((A_91 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real A_91) (tptp.number_number_of_nat (tptp.bit1 (tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.times_times_real A_91) A_91)) A_91))) (forall ((A_91 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_91) (tptp.number_number_of_nat (tptp.bit1 (tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_91) A_91)) A_91))) (forall ((X_1 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.power_power_int X_1))) (let ((_let_3 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int _let_2 _let_3)) _let_3) (tptp.hAPP_nat_int _let_2 (tptp.number_number_of_nat (tptp.bit0 _let_1)))))))) (forall ((Z_6 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) Z_6) (tptp.hAPP_int_int (tptp.plus_plus_int Z_6) Z_6))) (forall ((Z_6 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) Z_6) (tptp.hAPP_nat_nat (tptp.plus_plus_nat Z_6) Z_6))) (forall ((Z_6 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real (tptp.bit0 (tptp.bit1 tptp.pls)))) Z_6) (tptp.hAPP_real_real (tptp.plus_plus_real Z_6) Z_6))) (forall ((Z_5 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) Z_5) (tptp.hAPP_int_int (tptp.plus_plus_int Z_5) Z_5))) (forall ((Z_5 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real (tptp.bit0 (tptp.bit1 tptp.pls)))) Z_5) (tptp.hAPP_real_real (tptp.plus_plus_real Z_5) Z_5))) (forall ((Z_4 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int Z_4) (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.plus_plus_int Z_4) Z_4))) (forall ((Z_4 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat Z_4) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_nat (tptp.plus_plus_nat Z_4) Z_4))) (forall ((Z_4 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real Z_4) (tptp.number267125858f_real (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real (tptp.plus_plus_real Z_4) Z_4))) (forall ((Z_3 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int Z_3) (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.plus_plus_int Z_3) Z_3))) (forall ((Z_3 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real Z_3) (tptp.number267125858f_real (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real (tptp.plus_plus_real Z_3) Z_3))) _let_34 _let_33 _let_32 (tptp.hBOOL (tptp.hAPP_int_bool _let_25 _let_8)) (tptp.hBOOL (tptp.hAPP_int_bool _let_16 _let_14)) (forall ((P_1 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_1)) (=> (not (= P_1 (tptp.number_number_of_int _let_2))) (=> (not (= P_1 (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_1)))))))) (= (tptp.twoSqu949963151sum2sq (tptp.product_Pair_int_int tptp.s tptp.one_one_int)) _let_31) (forall ((X_1 tptp.real) (Y_1 tptp.real)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_real_real (tptp.plus_plus_real X_1) Y_1)) _let_2) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X_1) _let_2)) (tptp.hAPP_nat_real (tptp.power_power_real Y_1) _let_2))) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real _let_1)) X_1)) Y_1)))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real (tptp.bit0 _let_1))) (tptp.hAPP_nat_real (tptp.power_power_real X_1) _let_2)) (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real _let_1)) X_1)) _let_2))))) (forall ((N_38 tptp.nat) (A_90 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_90) N_38))) (=> (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 _let_1) (tptp.hAPP_int_int (tptp.times_times_int A_90) _let_1)))))) (forall ((N_38 tptp.nat) (A_90 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_90) N_38))) (=> (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 _let_1) (tptp.hAPP_nat_nat (tptp.times_times_nat A_90) _let_1)))))) (forall ((N_38 tptp.nat) (A_90 tptp.real)) (let ((_let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_90) N_38))) (=> (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 _let_1) (tptp.hAPP_real_real (tptp.times_times_real A_90) _let_1)))))) (forall ((N_37 tptp.nat) (A_89 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_89)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int A_89) (tptp.hAPP_nat_int (tptp.power_power_int A_89) N_37))))))) (forall ((N_37 tptp.nat) (A_89 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_89)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat A_89) (tptp.hAPP_nat_nat (tptp.power_power_nat A_89) N_37))))))) (forall ((N_37 tptp.nat) (A_89 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_89)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real A_89) (tptp.hAPP_nat_real (tptp.power_power_real A_89) N_37))))))) (forall ((M_9 tptp.nat) (N_36 tptp.nat) (A_88 tptp.int)) (let ((_let_1 (tptp.power_power_int A_88))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_88)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int _let_1 M_9)) (tptp.hAPP_nat_int _let_1 N_36))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_9) N_36)))))) (forall ((M_9 tptp.nat) (N_36 tptp.nat) (A_88 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_88))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A_88)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 M_9)) (tptp.hAPP_nat_nat _let_1 N_36))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_9) N_36)))))) (forall ((M_9 tptp.nat) (N_36 tptp.nat) (A_88 tptp.real)) (let ((_let_1 (tptp.power_power_real A_88))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A_88)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real _let_1 M_9)) (tptp.hAPP_nat_real _let_1 N_36))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_9) N_36)))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat) (B_2 tptp.int)) (let ((_let_1 (tptp.power_power_int B_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B_2)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int _let_1 X_2)) (tptp.hAPP_nat_int _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) Y_2)))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.power_power_nat B_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) B_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 X_2)) (tptp.hAPP_nat_nat _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) Y_2)))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat) (B_2 tptp.real)) (let ((_let_1 (tptp.power_power_real B_2))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) B_2)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real _let_1 X_2)) (tptp.hAPP_nat_real _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) Y_2)))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong _let_13 _let_30) _let_8)) (and (tptp.hBOOL (tptp.hAPP_int_bool _let_3 tptp.s)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.s) _let_8)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong tptp.s1 tptp.s) _let_8))) (exists ((X tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong tptp.s1 X) _let_1)) (forall ((Y tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong tptp.s1 Y) _let_1))) (= Y X))))))) (not (forall ((S_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (not (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) S_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int S_1) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong tptp.s1 S_1) _let_1))))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong _let_30 _let_9) _let_8)) (forall ((A_2 tptp.int) (N tptp.nat)) (= (= (tptp.hAPP_nat_int (tptp.power_power_int A_2) N) tptp.zero_zero_int) (and (= A_2 tptp.zero_zero_int) (not (= N tptp.zero_zero_nat))))) (forall ((A_2 tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_2) N) tptp.zero_zero_nat) (and (= A_2 tptp.zero_zero_nat) (not (= N tptp.zero_zero_nat))))) (forall ((A_2 tptp.real) (N tptp.nat)) (= (= (tptp.hAPP_nat_real (tptp.power_power_real A_2) N) tptp.zero_zero_real) (and (= A_2 tptp.zero_zero_real) (not (= N tptp.zero_zero_nat))))) (forall ((A_87 tptp.real) (M_8 tptp.nat) (N_35 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_87))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_8) N_35)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_nat_real _let_1 M_8)) (tptp.hAPP_nat_real _let_1 N_35)))))) (forall ((A_87 tptp.int) (M_8 tptp.nat) (N_35 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_87))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_8) N_35)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int _let_1 M_8)) (tptp.hAPP_nat_int _let_1 N_35)))))) (forall ((A_87 tptp.nat) (M_8 tptp.nat) (N_35 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_87))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_8) N_35)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 M_8)) (tptp.hAPP_nat_nat _let_1 N_35)))))) (forall ((N_34 tptp.nat) (M_7 tptp.nat) (X_19 tptp.real) (Y_16 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real X_19) Y_16)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_34) M_7)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_nat_real (tptp.power_power_real X_19) N_34)) (tptp.hAPP_nat_real (tptp.power_power_real Y_16) M_7)))))) (forall ((N_34 tptp.nat) (M_7 tptp.nat) (X_19 tptp.int) (Y_16 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int X_19) Y_16)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_34) M_7)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.power_power_int X_19) N_34)) (tptp.hAPP_nat_int (tptp.power_power_int Y_16) M_7)))))) (forall ((N_34 tptp.nat) (M_7 tptp.nat) (X_19 tptp.nat) (Y_16 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_19) Y_16)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_34) M_7)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_19) N_34)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_16) M_7)))))) (forall ((M_6 tptp.nat) (A_86 tptp.real) (N_33 tptp.nat) (B_55 tptp.real)) (let ((_let_1 (tptp.power_power_real A_86))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_nat_real _let_1 N_33)) B_55)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_6) N_33)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_nat_real _let_1 M_6)) B_55)))))) (forall ((M_6 tptp.nat) (A_86 tptp.int) (N_33 tptp.nat) (B_55 tptp.int)) (let ((_let_1 (tptp.power_power_int A_86))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int _let_1 N_33)) B_55)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_6) N_33)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int _let_1 M_6)) B_55)))))) (forall ((M_6 tptp.nat) (A_86 tptp.nat) (N_33 tptp.nat) (B_55 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_86))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 N_33)) B_55)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_6) N_33)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 M_6)) B_55)))))) (forall ((A_85 tptp.int) (N_32 tptp.nat) (B_54 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (tptp.hAPP_nat_int (tptp.power_power_int A_85) N_32) (tptp.hAPP_nat_int (tptp.power_power_int B_54) N_32)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_85)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_54)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_32)) (= A_85 B_54))))))) (forall ((A_85 tptp.nat) (N_32 tptp.nat) (B_54 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_85) N_32) (tptp.hAPP_nat_nat (tptp.power_power_nat B_54) N_32)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_85)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_54)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_32)) (= A_85 B_54))))))) (forall ((A_85 tptp.real) (N_32 tptp.nat) (B_54 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (tptp.hAPP_nat_real (tptp.power_power_real A_85) N_32) (tptp.hAPP_nat_real (tptp.power_power_real B_54) N_32)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_85)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_54)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_32)) (= A_85 B_54))))))) (forall ((N_1 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int M) N_1)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int N_1) M)))))) (forall ((N_1 tptp.int) (M tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int M) N_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int N_1) M)) (= M N_1))))))) (forall ((K_1 tptp.int) (M tptp.int) (N_1 tptp.int)) (let ((_let_1 (tptp.times_times_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int _let_1 M)) (tptp.hAPP_int_int _let_1 N_1))) (=> (not (= K_1 tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int M) N_1)))))) (forall ((N_31 tptp.nat) (X_18 tptp.real) (Y_15 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real X_18) Y_15)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_nat_real (tptp.power_power_real X_18) N_31)) (tptp.hAPP_nat_real (tptp.power_power_real Y_15) N_31))))) (forall ((N_31 tptp.nat) (X_18 tptp.int) (Y_15 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int X_18) Y_15)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.power_power_int X_18) N_31)) (tptp.hAPP_nat_int (tptp.power_power_int Y_15) N_31))))) (forall ((N_31 tptp.nat) (X_18 tptp.nat) (Y_15 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_18) Y_15)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_18) N_31)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_15) N_31))))) (forall ((N_30 tptp.nat) (A_84 tptp.int)) (=> (not (= A_84 tptp.zero_zero_int)) (not (= (tptp.hAPP_nat_int (tptp.power_power_int A_84) N_30) tptp.zero_zero_int)))) (forall ((N_30 tptp.nat) (A_84 tptp.real)) (=> (not (= A_84 tptp.zero_zero_real)) (not (= (tptp.hAPP_nat_real (tptp.power_power_real A_84) N_30) tptp.zero_zero_real)))) (forall ((N_29 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_int (tptp.power_power_int tptp.zero_zero_int) N_29))) (let ((_let_2 (= N_29 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((N_29 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat tptp.zero_zero_nat) N_29))) (let ((_let_2 (= N_29 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N_29 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_real (tptp.power_power_real tptp.zero_zero_real) N_29))) (let ((_let_2 (= N_29 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((Z tptp.int) (N_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Z) N_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) N_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z) N_1))))) (forall ((N_28 tptp.nat) (A_83 tptp.int) (B_53 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_83) B_53)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_83)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_28)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int (tptp.power_power_int A_83) N_28)) (tptp.hAPP_nat_int (tptp.power_power_int B_53) N_28))))))) (forall ((N_28 tptp.nat) (A_83 tptp.nat) (B_53 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_83) B_53)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_83)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_28)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.power_power_nat A_83) N_28)) (tptp.hAPP_nat_nat (tptp.power_power_nat B_53) N_28))))))) (forall ((N_28 tptp.nat) (A_83 tptp.real) (B_53 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_83) B_53)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_83)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_28)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real (tptp.power_power_real A_83) N_28)) (tptp.hAPP_nat_real (tptp.power_power_real B_53) N_28))))))) (forall ((A_82 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int tptp.zero_zero_int) A_82) tptp.zero_zero_int)) (forall ((A_82 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat tptp.zero_zero_nat) A_82) tptp.zero_zero_nat)) (forall ((A_82 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real tptp.zero_zero_real) A_82) tptp.zero_zero_real)) (forall ((A_81 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int A_81) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A_81 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat A_81) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A_81 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real A_81) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A_80 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int tptp.zero_zero_int) A_80) A_80)) (forall ((A_80 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat tptp.zero_zero_nat) A_80) A_80)) (forall ((A_80 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real tptp.zero_zero_real) A_80) A_80)) (forall ((A_79 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int A_79) tptp.zero_zero_int) A_79)) (forall ((A_79 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_79) tptp.zero_zero_nat) A_79)) (forall ((A_79 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real A_79) tptp.zero_zero_real) A_79)) (forall ((B_2 tptp.int) (A_2 tptp.int)) (= (= B_2 (tptp.hAPP_int_int (tptp.plus_plus_int B_2) A_2)) (= A_2 tptp.zero_zero_int))) (forall ((B_2 tptp.nat) (A_2 tptp.nat)) (= (= B_2 (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_2) A_2)) (= A_2 tptp.zero_zero_nat))) (forall ((B_2 tptp.real) (A_2 tptp.real)) (= (= B_2 (tptp.hAPP_real_real (tptp.plus_plus_real B_2) A_2)) (= A_2 tptp.zero_zero_real))) (forall ((A_2 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.plus_plus_int A_2) A_2) tptp.zero_zero_int) (= A_2 tptp.zero_zero_int))) (forall ((A_2 tptp.real)) (= (= (tptp.hAPP_real_real (tptp.plus_plus_real A_2) A_2) tptp.zero_zero_real) (= A_2 tptp.zero_zero_real))) (= tptp.pls tptp.zero_zero_int) _let_4 (forall ((Z tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int tptp.zero_zero_int) Z) Z)) (forall ((Z tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int Z) tptp.zero_zero_int) Z)) (forall ((N_27 tptp.nat) (A_78 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_78)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_78) N_27)))))) (forall ((N_27 tptp.nat) (A_78 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_78)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_78) N_27)))))) (forall ((N_27 tptp.nat) (A_78 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_78)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_78) N_27)))))) (forall ((N_26 tptp.nat) (A_77 tptp.int) (B_52 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_77) B_52)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_77)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int (tptp.power_power_int A_77) N_26)) (tptp.hAPP_nat_int (tptp.power_power_int B_52) N_26)))))) (forall ((N_26 tptp.nat) (A_77 tptp.nat) (B_52 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_77) B_52)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_77)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.power_power_nat A_77) N_26)) (tptp.hAPP_nat_nat (tptp.power_power_nat B_52) N_26)))))) (forall ((N_26 tptp.nat) (A_77 tptp.real) (B_52 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_77) B_52)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_77)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real (tptp.power_power_real A_77) N_26)) (tptp.hAPP_nat_real (tptp.power_power_real B_52) N_26)))))) (forall ((N_25 tptp.nat) (A_76 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_76)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_76) N_25)))))) (forall ((N_25 tptp.nat) (A_76 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_76)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_76) N_25)))))) (forall ((N_25 tptp.nat) (A_76 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_76)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_76) N_25)))))) (forall ((Z tptp.nat) (X_1 tptp.int) (Y_1 tptp.nat) (P_1 tptp.int)) (let ((_let_1 (tptp.power_power_int X_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_nat_int _let_1 Y_1) tptp.one_one_int) P_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat Y_1) Z)) tptp.one_one_int) P_1))))) (forall ((K tptp.int) (N tptp.int) (Ma tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int N) (tptp.hAPP_int_int (tptp.times_times_int K) Ma)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N))))) (forall ((C_2 tptp.int) (X_2 tptp.int) (Ta tptp.int) (A_2 tptp.int) (D tptp.int)) (let ((_let_1 (tptp.plus_plus_int X_2))) (let ((_let_2 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_2 D)) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_2 (tptp.hAPP_int_int _let_1 Ta))) (tptp.hBOOL (tptp.hAPP_int_bool _let_2 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.times_times_int C_2) D))) Ta)))))))) (forall ((A_75 tptp.int) (N_24 tptp.nat) (B_51 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int (tptp.power_power_int A_75) N_24)) (tptp.hAPP_nat_int (tptp.power_power_int B_51) N_24))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) B_51)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_75) B_51))))) (forall ((A_75 tptp.nat) (N_24 tptp.nat) (B_51 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.power_power_nat A_75) N_24)) (tptp.hAPP_nat_nat (tptp.power_power_nat B_51) N_24))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B_51)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_75) B_51))))) (forall ((A_75 tptp.real) (N_24 tptp.nat) (B_51 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real (tptp.power_power_real A_75) N_24)) (tptp.hAPP_nat_real (tptp.power_power_real B_51) N_24))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B_51)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_75) B_51))))) (forall ((A_74 tptp.int) (N_23 tptp.nat) (N_22 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_74))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_23) N_22)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_74)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_74) 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_22)) (tptp.hAPP_nat_int _let_1 N_23)))))))) (forall ((A_74 tptp.nat) (N_23 tptp.nat) (N_22 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_74))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_23) N_22)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_74)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_74) 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_22)) (tptp.hAPP_nat_nat _let_1 N_23)))))))) (forall ((A_74 tptp.real) (N_23 tptp.nat) (N_22 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_74))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_23) N_22)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_74)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_74) 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_22)) (tptp.hAPP_nat_real _let_1 N_23)))))))) (forall ((A_73 tptp.int) (N_21 tptp.nat) (N_20 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_73))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_21) N_20)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_73)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_73) 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_20)) (tptp.hAPP_nat_int _let_1 N_21)))))))) (forall ((A_73 tptp.nat) (N_21 tptp.nat) (N_20 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_73))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_21) N_20)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_73)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_73) 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_20)) (tptp.hAPP_nat_nat _let_1 N_21)))))))) (forall ((A_73 tptp.real) (N_21 tptp.nat) (N_20 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_73))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_21) N_20)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_73)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_73) 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_20)) (tptp.hAPP_nat_real _let_1 N_21)))))))) (forall ((A_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int A_2) A_2)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) tptp.zero_zero_int)))) (forall ((A_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.plus_plus_real A_2) A_2)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_2) tptp.zero_zero_real)))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int X_2) X_2)) (tptp.hAPP_int_int (tptp.times_times_int Y_2) Y_2)) tptp.zero_zero_int) (and (= X_2 tptp.zero_zero_int) (= Y_2 tptp.zero_zero_int)))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (= (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real X_2) X_2)) (tptp.hAPP_real_real (tptp.times_times_real Y_2) Y_2)) tptp.zero_zero_real) (and (= X_2 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real)))) (forall ((C_27 tptp.int) (D_8 tptp.int) (A_72 tptp.int) (B_50 tptp.int) (R_4 tptp.int)) (let ((_let_1 (tptp.times_times_int R_4))) (=> (not (= R_4 tptp.zero_zero_int)) (=> (and (= A_72 B_50) (not (= C_27 D_8))) (not (= (tptp.hAPP_int_int (tptp.plus_plus_int A_72) (tptp.hAPP_int_int _let_1 C_27)) (tptp.hAPP_int_int (tptp.plus_plus_int B_50) (tptp.hAPP_int_int _let_1 D_8)))))))) (forall ((C_27 tptp.nat) (D_8 tptp.nat) (A_72 tptp.nat) (B_50 tptp.nat) (R_4 tptp.nat)) (let ((_let_1 (tptp.times_times_nat R_4))) (=> (not (= R_4 tptp.zero_zero_nat)) (=> (and (= A_72 B_50) (not (= C_27 D_8))) (not (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_72) (tptp.hAPP_nat_nat _let_1 C_27)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_50) (tptp.hAPP_nat_nat _let_1 D_8)))))))) (forall ((C_27 tptp.real) (D_8 tptp.real) (A_72 tptp.real) (B_50 tptp.real) (R_4 tptp.real)) (let ((_let_1 (tptp.times_times_real R_4))) (=> (not (= R_4 tptp.zero_zero_real)) (=> (and (= A_72 B_50) (not (= C_27 D_8))) (not (= (tptp.hAPP_real_real (tptp.plus_plus_real A_72) (tptp.hAPP_real_real _let_1 C_27)) (tptp.hAPP_real_real (tptp.plus_plus_real B_50) (tptp.hAPP_real_real _let_1 D_8)))))))) (forall ((A tptp.int) (N_1 tptp.nat) (P_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A) N_1))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)))))) _let_26 (= tptp.zero_zero_real _let_27) _let_29 _let_28 _let_29 _let_19 _let_28 (forall ((W_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 W_1)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) tptp.zero_zero_int)))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_23 tptp.zero_zero_int))) (forall ((W_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit0 W_1)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) tptp.zero_zero_int)))) _let_26 (tptp.hBOOL (tptp.hAPP_int_bool _let_25 tptp.one_one_int)) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int A) B))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B)))))) (forall ((K_1 tptp.int) (I_1 tptp.int) (J_1 tptp.int)) (let ((_let_1 (tptp.times_times_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) K_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 I_1)) (tptp.hAPP_int_int _let_1 J_1))))))) (forall ((Z tptp.int)) (not (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))) (forall ((N_19 tptp.nat) (A_71 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_71) N_19))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_71)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_71) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_71) _let_1)) _let_1)))))) (forall ((N_19 tptp.nat) (A_71 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_71) N_19))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_71)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_71) tptp.one_one_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_71) _let_1)) _let_1)))))) (forall ((N_19 tptp.nat) (A_71 tptp.real)) (let ((_let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_71) N_19))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_71)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_71) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_71) _let_1)) _let_1)))))) (forall ((N_1 tptp.nat) (B tptp.int) (A tptp.int) (P_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.power_power_int P_1) N_1)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_1) A))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int A) B))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B))))))) (forall ((N_1 tptp.nat) (A tptp.int) (B tptp.int) (P_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.power_power_int P_1) N_1)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_1) B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int A) B))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A))))))) (forall ((X_17 tptp.int) (Y_14 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int X_17) X_17)) (tptp.hAPP_int_int (tptp.times_times_int Y_14) Y_14))))) (forall ((X_17 tptp.real) (Y_14 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real X_17) X_17)) (tptp.hAPP_real_real (tptp.times_times_real Y_14) Y_14))))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int X_2) X_2)) (tptp.hAPP_int_int (tptp.times_times_int Y_2) Y_2))) tptp.zero_zero_int)) (and (= X_2 tptp.zero_zero_int) (= Y_2 tptp.zero_zero_int)))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real X_2) X_2)) (tptp.hAPP_real_real (tptp.times_times_real Y_2) Y_2))) tptp.zero_zero_real)) (and (= X_2 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real)))) (forall ((V_7 tptp.int) (V_8 tptp.int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_7) V_8)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.number_number_of_nat V_7)) (tptp.number_number_of_nat V_8))) (and (=> _let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) V_8))) _let_1)))) (forall ((X_16 tptp.int) (Y_13 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int X_16) X_16)) (tptp.hAPP_int_int (tptp.times_times_int Y_13) Y_13))) tptp.zero_zero_int)))) (forall ((X_16 tptp.real) (Y_13 tptp.real)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real X_16) X_16)) (tptp.hAPP_real_real (tptp.times_times_real Y_13) Y_13))) tptp.zero_zero_real)))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int X_2) X_2)) (tptp.hAPP_int_int (tptp.times_times_int Y_2) Y_2)))) (or (not (= X_2 tptp.zero_zero_int)) (not (= Y_2 tptp.zero_zero_int))))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real X_2) X_2)) (tptp.hAPP_real_real (tptp.times_times_real Y_2) Y_2)))) (or (not (= X_2 tptp.zero_zero_real)) (not (= Y_2 tptp.zero_zero_real))))) (forall ((V_7 tptp.int) (V_8 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int V_7))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.number_number_of_nat V_7)) (tptp.number_number_of_nat V_8))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_8))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 tptp.pls)))))) (forall ((W_5 tptp.int)) (let ((_let_1 (tptp.number_number_of_int W_5))) (= (tptp.number_number_of_int (tptp.bit0 W_5)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.zero_zero_int) _let_1)) _let_1)))) (forall ((W_5 tptp.int)) (let ((_let_1 (tptp.number267125858f_real W_5))) (= (tptp.number267125858f_real (tptp.bit0 W_5)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.plus_plus_real tptp.zero_zero_real) _let_1)) _let_1)))) (forall ((A_70 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int A_70) tptp.one_one_nat) A_70)) (forall ((A_70 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real A_70) tptp.one_one_nat) A_70)) (forall ((A_70 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_70) tptp.one_one_nat) A_70)) (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 ((N tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Ma)) (= (= (tptp.hAPP_int_int (tptp.times_times_int Ma) N) tptp.one_one_int) (and (= Ma tptp.one_one_int) (= N tptp.one_one_int))))) (forall ((Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) Z_1)) Z_1)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_1) tptp.zero_zero_int)))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.number_number_of_int Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) Y_2)))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.number267125858f_real Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) Y_2)))) (forall ((X_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int X_2)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) tptp.pls)))) (forall ((X_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.number267125858f_real X_2)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) tptp.pls)))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.number267125858f_real Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) Y_2)))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.number_number_of_int Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) Y_2)))) (forall ((X_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.number267125858f_real X_2)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_2) tptp.pls)))) (forall ((X_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int X_2)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_2) tptp.pls)))) (forall ((Z tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) Z))))) (= (tptp.hAPP_nat_real (tptp.power_power_real tptp.zero_zero_real) _let_12) tptp.zero_zero_real) (= (tptp.hAPP_nat_nat (tptp.power_power_nat tptp.zero_zero_nat) _let_12) tptp.zero_zero_nat) (= (tptp.hAPP_nat_int (tptp.power_power_int tptp.zero_zero_int) _let_12) tptp.zero_zero_int) (forall ((A_2 tptp.real)) (= (= (tptp.hAPP_nat_real (tptp.power_power_real A_2) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.zero_zero_real) (= A_2 tptp.zero_zero_real))) (forall ((A_2 tptp.int)) (= (= (tptp.hAPP_nat_int (tptp.power_power_int A_2) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.zero_zero_int) (= A_2 tptp.zero_zero_int))) (forall ((A_69 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real (tptp.power_power_real A_69) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))))) (forall ((A_69 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_nat_int (tptp.power_power_int A_69) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))))) (forall ((X_15 tptp.real) (Y_12 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real (tptp.power_power_real X_15) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_12) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y_12)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_15) Y_12)))))) (forall ((X_15 tptp.nat) (Y_12 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_15) _let_1)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_12) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) Y_12)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_15) Y_12)))))) (forall ((X_15 tptp.int) (Y_12 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int (tptp.power_power_int X_15) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y_12) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y_12)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_15) Y_12)))))) (forall ((X_14 tptp.real) (Y_11 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (= (tptp.hAPP_nat_real (tptp.power_power_real X_14) _let_2) (tptp.hAPP_nat_real (tptp.power_power_real Y_11) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_14)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_11)) (= X_14 Y_11))))))) (forall ((X_14 tptp.nat) (Y_11 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (= (tptp.hAPP_nat_nat (tptp.power_power_nat X_14) _let_2) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_11) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_14)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_11)) (= X_14 Y_11))))))) (forall ((X_14 tptp.int) (Y_11 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (= (tptp.hAPP_nat_int (tptp.power_power_int X_14) _let_2) (tptp.hAPP_nat_int (tptp.power_power_int Y_11) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_14)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_11)) (= X_14 Y_11))))))) (forall ((A_68 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_68) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) tptp.zero_zero_real)))) (forall ((A_68 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_68) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) tptp.zero_zero_int)))) (forall ((A_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_nat_real (tptp.power_power_real A_2) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (not (= A_2 tptp.zero_zero_real)))) (forall ((A_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_nat_int (tptp.power_power_int A_2) (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (not (= A_2 tptp.zero_zero_int)))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X_2) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_2) _let_1)) tptp.zero_zero_real) (and (= X_2 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real))))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X_2) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y_2) _let_1)) tptp.zero_zero_int) (and (= X_2 tptp.zero_zero_int) (= Y_2 tptp.zero_zero_int))))) (forall ((A_67 tptp.nat) (N_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_67) N_18))) (= (tptp.hAPP_nat_nat (tptp.times_times_nat _let_1) A_67) (tptp.hAPP_nat_nat (tptp.times_times_nat A_67) _let_1)))) (forall ((A_67 tptp.real) (N_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_67) N_18))) (= (tptp.hAPP_real_real (tptp.times_times_real _let_1) A_67) (tptp.hAPP_real_real (tptp.times_times_real A_67) _let_1)))) (forall ((A_67 tptp.int) (N_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_67) N_18))) (= (tptp.hAPP_int_int (tptp.times_times_int _let_1) A_67) (tptp.hAPP_int_int (tptp.times_times_int A_67) _let_1)))) (forall ((A_66 tptp.nat) (B_49 tptp.nat) (N_17 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_66) B_49)) N_17) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.power_power_nat A_66) N_17)) (tptp.hAPP_nat_nat (tptp.power_power_nat B_49) N_17)))) (forall ((A_66 tptp.real) (B_49 tptp.real) (N_17 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_real_real (tptp.times_times_real A_66) B_49)) N_17) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_nat_real (tptp.power_power_real A_66) N_17)) (tptp.hAPP_nat_real (tptp.power_power_real B_49) N_17)))) (forall ((A_66 tptp.int) (B_49 tptp.int) (N_17 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_int_int (tptp.times_times_int A_66) B_49)) N_17) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_nat_int (tptp.power_power_int A_66) N_17)) (tptp.hAPP_nat_int (tptp.power_power_int B_49) N_17)))) (forall ((A_65 tptp.nat) (M_5 tptp.nat) (N_16 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_65))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_5) N_16)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 M_5)) (tptp.hAPP_nat_nat _let_1 N_16))))) (forall ((A_65 tptp.real) (M_5 tptp.nat) (N_16 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_65))) (= (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_5) N_16)) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_nat_real _let_1 M_5)) (tptp.hAPP_nat_real _let_1 N_16))))) (forall ((A_65 tptp.int) (M_5 tptp.nat) (N_16 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_65))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_5) N_16)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_nat_int _let_1 M_5)) (tptp.hAPP_nat_int _let_1 N_16))))) (forall ((N_15 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.power_power_real tptp.one_one_real) N_15) tptp.one_one_real)) (forall ((N_15 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat tptp.one_one_nat) N_15) tptp.one_one_nat)) (forall ((N_15 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.power_power_int tptp.one_one_int) N_15) tptp.one_one_int)) (forall ((A_64 tptp.nat) (M_4 tptp.nat) (N_14 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_64))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat M_4) N_14)) (tptp.hAPP_nat_nat (tptp.power_power_nat (tptp.hAPP_nat_nat _let_1 M_4)) N_14)))) (forall ((A_64 tptp.real) (M_4 tptp.nat) (N_14 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_64))) (= (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat M_4) N_14)) (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_nat_real _let_1 M_4)) N_14)))) (forall ((A_64 tptp.int) (M_4 tptp.nat) (N_14 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_64))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat M_4) N_14)) (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_nat_int _let_1 M_4)) N_14)))) (forall ((X_13 tptp.real) (Y_10 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real (tptp.power_power_real X_13) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_10) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y_10)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_13) Y_10)))))) (forall ((X_13 tptp.nat) (Y_10 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_13) _let_1)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_10) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) Y_10)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_13) Y_10)))))) (forall ((X_13 tptp.int) (Y_10 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int (tptp.power_power_int X_13) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y_10) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y_10)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_13) Y_10)))))) (forall ((X_12 tptp.real) (Y_9 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X_12) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_9) _let_1)))))) (forall ((X_12 tptp.int) (Y_9 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X_12) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y_9) _let_1)))))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X_2) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_2) _let_1))) tptp.zero_zero_real)) (and (= X_2 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real))))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X_2) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y_2) _let_1))) tptp.zero_zero_int)) (and (= X_2 tptp.zero_zero_int) (= Y_2 tptp.zero_zero_int))))) (forall ((X_11 tptp.real) (Y_8 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X_11) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_8) _let_1))) tptp.zero_zero_real))))) (forall ((X_11 tptp.int) (Y_8 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X_11) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y_8) _let_1))) tptp.zero_zero_int))))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X_2) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_2) _let_1)))) (or (not (= X_2 tptp.zero_zero_real)) (not (= Y_2 tptp.zero_zero_real)))))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X_2) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int Y_2) _let_1)))) (or (not (= X_2 tptp.zero_zero_int)) (not (= Y_2 tptp.zero_zero_int)))))) (forall ((A_63 tptp.real) (N_13 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real (tptp.power_power_real A_63) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_13))))) (forall ((A_63 tptp.int) (N_13 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_nat_int (tptp.power_power_int A_63) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_13))))) (forall ((N_12 tptp.nat) (A_62 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_62)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_62) N_12)))))) (forall ((N_12 tptp.nat) (A_62 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_62)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_62) N_12)))))) (forall ((N_12 tptp.nat) (A_62 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_62)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_62) N_12)))))) (forall ((A_61 tptp.real) (N_11 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_61))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_11) N_10)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) A_61)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real _let_1 N_11)) (tptp.hAPP_nat_real _let_1 N_10))))))) (forall ((A_61 tptp.nat) (N_11 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_61))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_11) N_10)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.one_one_nat) A_61)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 N_11)) (tptp.hAPP_nat_nat _let_1 N_10))))))) (forall ((A_61 tptp.int) (N_11 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_61))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_11) N_10)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) A_61)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int _let_1 N_11)) (tptp.hAPP_nat_int _let_1 N_10))))))) (forall ((Ma tptp.nat) (N tptp.nat) (A_2 tptp.real)) (let ((_let_1 (tptp.power_power_real A_2))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A_2)) (= (= (tptp.hAPP_nat_real _let_1 Ma) (tptp.hAPP_nat_real _let_1 N)) (= Ma N))))) (forall ((Ma tptp.nat) (N tptp.nat) (A_2 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A_2)) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 N)) (= Ma N))))) (forall ((Ma tptp.nat) (N tptp.nat) (A_2 tptp.int)) (let ((_let_1 (tptp.power_power_int A_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_2)) (= (= (tptp.hAPP_nat_int _let_1 Ma) (tptp.hAPP_nat_int _let_1 N)) (= Ma N))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat) (B_2 tptp.real)) (let ((_let_1 (tptp.power_power_real B_2))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) B_2)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real _let_1 X_2)) (tptp.hAPP_nat_real _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Y_2)))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.power_power_nat B_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) B_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 X_2)) (tptp.hAPP_nat_nat _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Y_2)))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat) (B_2 tptp.int)) (let ((_let_1 (tptp.power_power_int B_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B_2)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int _let_1 X_2)) (tptp.hAPP_nat_int _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Y_2)))))) (forall ((M_3 tptp.nat) (N_9 tptp.nat) (A_60 tptp.real)) (let ((_let_1 (tptp.power_power_real A_60))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A_60)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real _let_1 M_3)) (tptp.hAPP_nat_real _let_1 N_9))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_3) N_9)))))) (forall ((M_3 tptp.nat) (N_9 tptp.nat) (A_60 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_60))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A_60)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M_3)) (tptp.hAPP_nat_nat _let_1 N_9))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_3) N_9)))))) (forall ((M_3 tptp.nat) (N_9 tptp.nat) (A_60 tptp.int)) (let ((_let_1 (tptp.power_power_int A_60))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_60)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int _let_1 M_3)) (tptp.hAPP_nat_int _let_1 N_9))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_3) N_9)))))) (forall ((A_59 tptp.real) (N_8 tptp.nat) (N_7 tptp.nat)) (let ((_let_1 (tptp.power_power_real A_59))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_8) N_7)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A_59)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real _let_1 N_8)) (tptp.hAPP_nat_real _let_1 N_7))))))) (forall ((A_59 tptp.nat) (N_8 tptp.nat) (N_7 tptp.nat)) (let ((_let_1 (tptp.power_power_nat A_59))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_8) N_7)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A_59)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 N_8)) (tptp.hAPP_nat_nat _let_1 N_7))))))) (forall ((A_59 tptp.int) (N_8 tptp.nat) (N_7 tptp.nat)) (let ((_let_1 (tptp.power_power_int A_59))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_8) N_7)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_59)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int _let_1 N_8)) (tptp.hAPP_nat_int _let_1 N_7))))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong _let_13 _let_9) _let_8)) (forall ((Y_1 tptp.int) (X_1 tptp.int) (P_1 tptp.int)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_1))) (=> (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)))) X_1) P_1)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_1) Y_1)))))) (forall ((X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls))))) (or (= X_1 tptp.zero_zero_int) (= X_1 tptp.one_one_int))))) (forall ((A_58 tptp.real) (K_4 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real (tptp.power_power_real A_58) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) K_4))) tptp.zero_zero_real)) (= A_58 tptp.zero_zero_real))) (forall ((A_58 tptp.int) (K_4 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int (tptp.power_power_int A_58) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) K_4))) tptp.zero_zero_int)) (= A_58 tptp.zero_zero_int))) (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_2 tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) M_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int M_2) P_3))) (or (= M_2 tptp.one_one_int) (= M_2 P_3))))))) (forall ((R_1 tptp.int) (Q_1 tptp.int) (A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (= A (tptp.hAPP_int_int (tptp.plus_plus_int R_1) (tptp.hAPP_int_int (tptp.times_times_int A) Q_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_1) tptp.one_one_int)))))) (forall ((R_1 tptp.int) (Q_1 tptp.int) (A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (= A (tptp.hAPP_int_int (tptp.plus_plus_int R_1) (tptp.hAPP_int_int (tptp.times_times_int A) Q_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_1) A)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) Q_1)))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_3 _let_24)) (not (forall ((S1 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.power_power_int S1) (tptp.number_number_of_nat _let_1)) (tptp.number_number_of_int tptp.min)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int))))))) _let_10 (forall ((X_2 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat X_2) N))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_2)) (= N tptp.zero_zero_nat))))) (forall ((X_2 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat X_2) N))) (or (= N tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_2)))))) (forall ((X_2 tptp.nat) (W_1 tptp.int)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.number_number_of_nat W_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat X_2) _let_2))) (or (= _let_2 tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_2))))))) (forall ((M tptp.nat) (N_1 tptp.nat) (I_1 tptp.nat)) (let ((_let_1 (tptp.power_power_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) I_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1)))))) (forall ((K tptp.int)) (= (= (tptp.bit1 K) tptp.min) (= K tptp.min))) (forall ((L_1 tptp.int)) (= (= tptp.min (tptp.bit1 L_1)) (= tptp.min L_1))) (= (tptp.bit1 tptp.min) tptp.min) (not (= tptp.pls tptp.min)) (not (= tptp.min tptp.pls)) (forall ((K_1 tptp.int)) (not (= (tptp.bit0 K_1) tptp.min))) (forall ((L tptp.int)) (not (= tptp.min (tptp.bit0 L)))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_22 tptp.min))) (tptp.hBOOL (tptp.hAPP_int_bool _let_20 tptp.min)) (forall ((X_2 tptp.real)) (= (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.times_times_real X_2) X_2)))) (= X_2 tptp.zero_zero_real))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K)) tptp.min)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) tptp.min)))) (forall ((K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.min))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K))))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_23 tptp.min))) (tptp.hBOOL (tptp.hAPP_int_bool _let_22 tptp.pls)) (forall ((K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.min))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_22 tptp.zero_zero_int)) (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)))) (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))))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_21 tptp.min))) (tptp.hBOOL (tptp.hAPP_int_bool _let_20 tptp.pls)) (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_2 _let_9)) (forall ((I_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.power_power_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) I_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)))))) (forall ((X_10 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real X_10) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((X_10 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat X_10) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((X_10 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int X_10) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((A_57 tptp.real)) (= (tptp.hAPP_nat_real (tptp.power_power_real A_57) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A_57 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_57) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A_57 tptp.int)) (= (tptp.hAPP_nat_int (tptp.power_power_int A_57) tptp.zero_zero_nat) tptp.one_one_int)) _let_19 (= tptp.zero_zero_nat _let_18) (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 ((M tptp.int) (N_1 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.times_times_int M) N_1) tptp.one_one_int) (or (= M tptp.one_one_int) (= M (tptp.number_number_of_int tptp.min))))) (forall ((Ma tptp.int) (N tptp.int)) (let ((_let_1 (tptp.number_number_of_int tptp.min))) (= (= (tptp.hAPP_int_int (tptp.times_times_int Ma) N) tptp.one_one_int) (or (and (= Ma tptp.one_one_int) (= N tptp.one_one_int)) (and (= Ma _let_1) (= N _let_1)))))) (forall ((N_6 tptp.nat) (A_56 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_56)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_6)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.power_power_real A_56) N_6))))))) (forall ((N_6 tptp.nat) (A_56 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_56)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_6)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.power_power_nat A_56) N_6))))))) (forall ((N_6 tptp.nat) (A_56 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_56)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_6)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int A_56) N_6))))))) (forall ((X_9 tptp.real) (N_5 tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_5)) (= X_9 tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real X_9) (tptp.hAPP_nat_real (tptp.power_power_real X_9) N_5))))) (forall ((X_9 tptp.nat) (N_5 tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_5)) (= X_9 tptp.one_one_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_9) (tptp.hAPP_nat_nat (tptp.power_power_nat X_9) N_5))))) (forall ((X_9 tptp.int) (N_5 tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_5)) (= X_9 tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int X_9) (tptp.hAPP_nat_int (tptp.power_power_int X_9) N_5))))) (forall ((V_7 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.number_number_of_nat V_7))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) V_7)))) (forall ((V_7 tptp.int)) (= (= (tptp.number_number_of_nat V_7) tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int V_7) tptp.pls)))) (forall ((V_7 tptp.int)) (= (= tptp.zero_zero_nat (tptp.number_number_of_nat V_7)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int V_7) tptp.pls)))) (forall ((A_2 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 B_2) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong B_2 A_2) Ma)))) (forall ((K_1 tptp.int) (M tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong K_1 K_1) M))) (forall ((C tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong B C) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A C) M))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_12)) (forall ((V_6 tptp.int) (K_1 tptp.nat) (V tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat V)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat V_6)) K_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V) tptp.pls)))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.times_times_int V) V_6))) K_1))))))) (forall ((V_6 tptp.int) (V tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat V)) (tptp.number_number_of_nat V_6)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V) tptp.pls)))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.times_times_int V) V_6)))))))) (forall ((X_8 tptp.real) (Y_7 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_8) Y_7)) (=> (not (= X_8 Y_7)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_8) Y_7))))) (forall ((X_8 tptp.nat) (Y_7 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_8) Y_7)) (=> (not (= X_8 Y_7)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_8) Y_7))))) _let_17 (tptp.hBOOL (tptp.hAPP_int_bool _let_3 tptp.zero_zero_int)) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) C)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) C)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B) A)))))) (forall ((A_2 tptp.int) (B_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 B_2) tptp.zero_zero_int)) (= A_2 B_2))) (forall ((A tptp.int) (B tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) tptp.one_one_int))) (forall ((C tptp.int) (D_5 tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C D_5) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A) C) (tptp.hAPP_int_int (tptp.times_times_int B) D_5)) M))))) (forall ((K_1 tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (let ((_let_1 (tptp.times_times_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int _let_1 A) (tptp.hAPP_int_int _let_1 B)) M))))) (forall ((K_1 tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A) K_1) (tptp.hAPP_int_int (tptp.times_times_int B) K_1)) M)))) (forall ((A tptp.int) (M tptp.int) (B tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A) M) (tptp.hAPP_int_int (tptp.times_times_int B) M)) M))) (forall ((C tptp.int) (D_5 tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C D_5) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.plus_plus_int A) C) (tptp.hAPP_int_int (tptp.plus_plus_int B) D_5)) M))))) (forall ((N_4 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.power_power_real (tptp.number267125858f_real tptp.min)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_4)) tptp.one_one_real)) (forall ((N_4 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.number_number_of_int tptp.min)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_4)) tptp.one_one_int)) (forall ((A_2 tptp.real) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_1))) (= (= (tptp.hAPP_nat_real (tptp.power_power_real A_2) _let_1) tptp.zero_zero_real) (and (= A_2 tptp.zero_zero_real) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A_2 tptp.nat) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_1))) (= (= (tptp.hAPP_nat_nat (tptp.power_power_nat A_2) _let_1) tptp.zero_zero_nat) (and (= A_2 tptp.zero_zero_nat) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A_2 tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_1))) (= (= (tptp.hAPP_nat_int (tptp.power_power_int A_2) _let_1) tptp.zero_zero_int) (and (= A_2 tptp.zero_zero_int) (not (= _let_1 tptp.zero_zero_nat)))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_3 tptp.one_one_int)) (forall ((Y_1 tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int X_1) Y_1))))))) (forall ((Y_1 tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int X_1) Y_1))))))) (forall ((B tptp.int) (M tptp.int) (A tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) A)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M))))))))) (forall ((N_1 tptp.nat) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int X_1) N_1)))))) (forall ((A_2 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 B_2) Ma)) (exists ((K_2 tptp.int)) (= B_2 (tptp.hAPP_int_int (tptp.plus_plus_int A_2) (tptp.hAPP_int_int (tptp.times_times_int Ma) K_2)))))) (forall ((W_4 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_4))) (let ((_let_2 (tptp.hAPP_nat_real (tptp.power_power_real tptp.zero_zero_real) _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 tptp.zero_zero_real))))))) (forall ((W_4 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_4))) (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_4 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W_4))) (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 ((B tptp.int) (M tptp.int) (A tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (= A B)))))))) (forall ((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))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_3 (tptp.number_number_of_int (tptp.bit1 _let_6)))) (forall ((B tptp.int) (Q_1 tptp.int) (R_1 tptp.int) (B_48 tptp.int) (Q_4 tptp.int) (R_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B_48) Q_4)) R_3))) (=> (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B) Q_1)) R_1) _let_1) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_1) B)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_48)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_48) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_4) Q_1)))))))))) (forall ((B tptp.int) (Q_4 tptp.int) (R_3 tptp.int) (Q_1 tptp.int) (R_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B))) (let ((_let_2 (tptp.times_times_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_2 Q_4)) R_3)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_2 Q_1)) R_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int R_1) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 R_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 R_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_1) Q_4))))))))) (forall ((B tptp.int) (Q_1 tptp.int) (R_1 tptp.int) (B_48 tptp.int) (Q_4 tptp.int) (R_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B_48) Q_4)) R_3))) (=> (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B) Q_1)) R_1) _let_2) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 _let_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_3) B_48)) (=> (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_48)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_48) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_1) Q_4))))))))))) (forall ((B tptp.int) (Q_4 tptp.int) (R_3 tptp.int) (Q_1 tptp.int) (R_1 tptp.int)) (let ((_let_1 (tptp.times_times_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Q_4)) R_3)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Q_1)) R_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_3) B)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_1) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_4) Q_1)))))))) (forall ((B_48 tptp.int) (Q_4 tptp.int) (R_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B_48) Q_4)) R_3)) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_48)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_4) tptp.zero_zero_int)))))) (forall ((B_48 tptp.int) (Q_4 tptp.int) (R_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B_48) Q_4)) R_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_3) B_48)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_48)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Q_4))))))) (forall ((N_1 tptp.int) (P_1 tptp.int) (M tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_1))) (=> (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_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int M) N_1))) (or (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1)))))))) _let_11 (tptp.hBOOL (tptp.hAPP_int_bool _let_16 _let_15)) (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 ((X_1 tptp.int) (P_1 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_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 (tptp.number_number_of_int tptp.min)) P_1)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.one_one_int) P_1)))))) (forall ((M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) M)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong tptp.one_one_int (tptp.number_number_of_int tptp.min)) M))))) (= _let_15 _let_14) (=> (not _let_11) (not _let_10)) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.minus_minus_int A) B) C) (= A (tptp.hAPP_int_int (tptp.plus_plus_int C) B)))) (forall ((V_5 tptp.int) (W_3 tptp.int)) (= (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.minus_minus_int V_5) W_3)) (tptp.hAPP_real_real (tptp.minus_minus_real (tptp.number267125858f_real V_5)) (tptp.number267125858f_real W_3)))) (forall ((V_5 tptp.int) (W_3 tptp.int)) (= (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.minus_minus_int V_5) W_3)) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.number_number_of_int V_5)) (tptp.number_number_of_int W_3)))) (forall ((K_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.minus_minus_int K_1) tptp.pls) K_1)) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.bit0 K_1)) (tptp.bit0 L)) (tptp.bit0 (tptp.hAPP_int_int (tptp.minus_minus_int K_1) L)))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (tptp.times_times_int W))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.minus_minus_int Z1) Z2)) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int _let_1 Z1)) (tptp.hAPP_int_int _let_1 Z2))))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.minus_minus_int Z1) Z2)) W) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int (tptp.times_times_int Z1) W)) (tptp.hAPP_int_int (tptp.times_times_int Z2) W)))) (forall ((C tptp.int) (D_5 tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C D_5) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.minus_minus_int A) C) (tptp.hAPP_int_int (tptp.minus_minus_int B) D_5)) M))))) (forall ((K_1 tptp.int) (M tptp.int) (N_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.minus_minus_int M) N_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)))))) (forall ((V_4 tptp.int) (B_47 tptp.real) (C_26 tptp.real)) (let ((_let_1 (tptp.times_times_real (tptp.number267125858f_real V_4)))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.minus_minus_real B_47) C_26)) (tptp.hAPP_real_real (tptp.minus_minus_real (tptp.hAPP_real_real _let_1 B_47)) (tptp.hAPP_real_real _let_1 C_26))))) (forall ((V_4 tptp.int) (B_47 tptp.int) (C_26 tptp.int)) (let ((_let_1 (tptp.times_times_int (tptp.number_number_of_int V_4)))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.minus_minus_int B_47) C_26)) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int _let_1 B_47)) (tptp.hAPP_int_int _let_1 C_26))))) (forall ((A_55 tptp.real) (B_46 tptp.real) (V_3 tptp.int)) (let ((_let_1 (tptp.number267125858f_real V_3))) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.minus_minus_real A_55) B_46)) _let_1) (tptp.hAPP_real_real (tptp.minus_minus_real (tptp.hAPP_real_real (tptp.times_times_real A_55) _let_1)) (tptp.hAPP_real_real (tptp.times_times_real B_46) _let_1))))) (forall ((A_55 tptp.int) (B_46 tptp.int) (V_3 tptp.int)) (let ((_let_1 (tptp.number_number_of_int V_3))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.minus_minus_int A_55) B_46)) _let_1) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int (tptp.times_times_int A_55) _let_1)) (tptp.hAPP_int_int (tptp.times_times_int B_46) _let_1))))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.bit1 K_1)) (tptp.bit0 L)) (tptp.bit1 (tptp.hAPP_int_int (tptp.minus_minus_int K_1) L)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.bit1 K_1)) (tptp.bit1 L)) (tptp.bit0 (tptp.hAPP_int_int (tptp.minus_minus_int K_1) L)))) (forall ((L tptp.int)) (let ((_let_1 (tptp.minus_minus_int tptp.pls))) (= (tptp.hAPP_int_int _let_1 (tptp.bit0 L)) (tptp.bit0 (tptp.hAPP_int_int _let_1 L))))) (forall ((K tptp.int) (L_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) L_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.minus_minus_int K) L_1)) tptp.zero_zero_int)))) (forall ((A tptp.int) (R_1 tptp.int) (B tptp.int) (M tptp.int) (C tptp.int) (D_5 tptp.int) (N_1 tptp.int)) (let ((_let_1 (tptp.times_times_int R_1))) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.minus_minus_int A) (tptp.hAPP_int_int _let_1 B))) M)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.minus_minus_int C) (tptp.hAPP_int_int _let_1 D_5))) N_1)) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int A) M)) (tptp.hAPP_int_int (tptp.times_times_int C) N_1))) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B) M)) (tptp.hAPP_int_int (tptp.times_times_int D_5) N_1))))))) (forall ((A_2 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 B_2) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Ma) (tptp.hAPP_int_int (tptp.minus_minus_int A_2) B_2))))) (forall ((V_2 tptp.int) (W_2 tptp.int) (C_25 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.number267125858f_real V_2)) (tptp.hAPP_real_real (tptp.minus_minus_real (tptp.number267125858f_real W_2)) C_25)) (tptp.hAPP_real_real (tptp.minus_minus_real (tptp.number267125858f_real (tptp.hAPP_int_int (tptp.plus_plus_int V_2) W_2))) C_25))) (forall ((V_2 tptp.int) (W_2 tptp.int) (C_25 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.number_number_of_int V_2)) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.number_number_of_int W_2)) C_25)) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.plus_plus_int V_2) W_2))) C_25))) (forall ((A tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.minus_minus_int A) tptp.one_one_int))) (let ((_let_2 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_2 A)) (=> (not (= X_1 _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_2 _let_1)))))))) (forall ((W_1 tptp.int) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W_1) (tptp.hAPP_int_int (tptp.minus_minus_int Z_1) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) Z_1)))) (forall ((L tptp.int)) (= (tptp.hAPP_int_int (tptp.minus_minus_int tptp.pls) (tptp.bit1 L)) (tptp.bit1 (tptp.hAPP_int_int (tptp.minus_minus_int tptp.min) L)))) (forall ((L tptp.int)) (let ((_let_1 (tptp.minus_minus_int tptp.min))) (= (tptp.hAPP_int_int _let_1 (tptp.bit0 L)) (tptp.bit1 (tptp.hAPP_int_int _let_1 L))))) (forall ((L tptp.int)) (let ((_let_1 (tptp.minus_minus_int tptp.min))) (= (tptp.hAPP_int_int _let_1 (tptp.bit1 L)) (tptp.bit0 (tptp.hAPP_int_int _let_1 L))))) (forall ((A_2 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.minus_minus_int P_3) tptp.one_one_int))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A_2) _let_1) tptp.one_one_int) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 _let_1) P_3))))) (forall ((D_5 tptp.int) (C tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (=> (= B C) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C D_5) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A D_5) M)))))) (forall ((A tptp.int) (B tptp.int) (P_1 tptp.int) (Q_1 tptp.int)) (let ((_let_1 (tptp.times_times_int B))) (let ((_let_2 (tptp.times_times_int A))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.twoSqu949963151sum2sq (tptp.product_Pair_int_int A B))) (tptp.twoSqu949963151sum2sq (tptp.product_Pair_int_int P_1 Q_1))) (tptp.twoSqu949963151sum2sq (tptp.product_Pair_int_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_2 P_1)) (tptp.hAPP_int_int _let_1 Q_1)) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int _let_2 Q_1)) (tptp.hAPP_int_int _let_1 P_1)))))))) (forall ((A tptp.int) (P_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A) A) tptp.one_one_int) P_1)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A tptp.one_one_int) P_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A (tptp.hAPP_int_int (tptp.minus_minus_int P_1) tptp.one_one_int)) P_1))))))) (forall ((A tptp.int) (P_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (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_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A) A) tptp.one_one_int) P_1)) (or (= A tptp.one_one_int) (= A (tptp.hAPP_int_int (tptp.minus_minus_int P_1) tptp.one_one_int)))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int A) B)) (tptp.hAPP_int_int (tptp.minus_minus_int A) B)) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_nat_int (tptp.power_power_int A) _let_1)) (tptp.hAPP_nat_int (tptp.power_power_int B) _let_1))))) (forall ((M tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong M tptp.zero_zero_int) M))) (forall ((C_2 tptp.int) (D tptp.int) (A_2 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 B_2) Ma)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C_2 (tptp.hAPP_int_int (tptp.times_times_int A_2) D)) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C_2 (tptp.hAPP_int_int (tptp.times_times_int B_2) D)) Ma))))) (forall ((C_2 tptp.int) (D tptp.int) (A_2 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (let ((_let_1 (tptp.times_times_int D))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 B_2) Ma)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C_2 (tptp.hAPP_int_int _let_1 A_2)) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong C_2 (tptp.hAPP_int_int _let_1 B_2)) Ma)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A B) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.plus_plus_int A) C) (tptp.hAPP_int_int (tptp.plus_plus_int B) C)) M)))) (forall ((Z tptp.nat) (X_1 tptp.int) (Y_1 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 Y_1) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.power_power_int X_1) Z) (tptp.hAPP_nat_int (tptp.power_power_int Y_1) Z)) M)))) (forall ((X_7 tptp.real) (Y_6 tptp.real)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_real (tptp.power_power_real (tptp.hAPP_real_real (tptp.minus_minus_real X_7) Y_6)) _let_2) (tptp.hAPP_real_real (tptp.minus_minus_real (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X_7) _let_2)) (tptp.hAPP_nat_real (tptp.power_power_real Y_6) _let_2))) (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.times_times_real (tptp.number267125858f_real _let_1)) X_7)) Y_6)))))) (forall ((X_7 tptp.int) (Y_6 tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_int_int (tptp.minus_minus_int X_7) Y_6)) _let_2) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.power_power_int X_7) _let_2)) (tptp.hAPP_nat_int (tptp.power_power_int Y_6) _let_2))) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int _let_1)) X_7)) Y_6)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_int_int (tptp.minus_minus_int A) B)) _let_2) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_nat_int (tptp.power_power_int A) _let_2)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int _let_1)) A)) B))) (tptp.hAPP_nat_int (tptp.power_power_int B) _let_2)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit1 _let_1))) (let ((_let_3 (tptp.number_number_of_nat _let_2))) (let ((_let_4 (tptp.power_power_int B))) (let ((_let_5 (tptp.number_number_of_nat (tptp.bit0 _let_1)))) (let ((_let_6 (tptp.times_times_int (tptp.number_number_of_int _let_2)))) (let ((_let_7 (tptp.power_power_int A))) (= (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_int_int (tptp.minus_minus_int A) B)) _let_3) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_nat_int _let_7 _let_3)) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_6 (tptp.hAPP_nat_int _let_7 _let_5))) B))) (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_6 A)) (tptp.hAPP_nat_int _let_4 _let_5)))) (tptp.hAPP_nat_int _let_4 _let_3))))))))))) (forall ((M tptp.int) (Y_1 tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 Y_1) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y_1) M)) (= X_1 Y_1))))))))) (forall ((M tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) M)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) M)))))) (forall ((N_1 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int N_1) M)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int M) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int N_1) M))))) (forall ((X_2 tptp.int) (P_3 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_2 tptp.zero_zero_int) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3) X_2)))) (forall ((A_2 tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 tptp.zero_zero_int) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Ma) A_2)))) (forall ((M tptp.int) (N_1 tptp.int) (P_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int M) N_1))) (or (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1))))))) (forall ((M tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) M)) (= X_1 tptp.zero_zero_int))))) (forall ((P_1 tptp.int) (Y_1 tptp.int) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int Y_1) N_1))))))) (forall ((N_1 tptp.nat)) (let ((_let_1 (tptp.number_number_of_int tptp.min))) (let ((_let_2 (tptp.hAPP_nat_int (tptp.power_power_int _let_1) N_1))) (or (= _let_2 tptp.one_one_int) (= _let_2 _let_1))))) (forall ((Y_1 tptp.int) (X_1 tptp.int) (P_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_1))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong Y_1 tptp.zero_zero_int) P_1))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int X_1) Y_1) tptp.zero_zero_int) P_1))))))) (forall ((B tptp.int) (A tptp.int) (P_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A) B) tptp.zero_zero_int) P_1)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A tptp.zero_zero_int) P_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong B tptp.zero_zero_int) P_1))))))) (forall ((B tptp.int) (A tptp.int) (P_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (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_1))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong B tptp.zero_zero_int) P_1)))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A) B) tptp.zero_zero_int) P_1))))))) (forall ((Y_1 tptp.int) (N_1 tptp.nat) (P_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.power_power_int Y_1) N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_1))))))) (forall ((M tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls))))) M)) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime _let_1)) (= (tptp.legendre (tptp.number_number_of_int tptp.min) _let_1) tptp.one_one_int)))) (forall ((A tptp.int) (P_1 tptp.int)) (let ((_let_1 (tptp.legendre A P_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.quadRes P_1) A)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A tptp.zero_zero_int) P_1)))) (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 ((N_1 tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N_1) M)) (or (= M tptp.zero_zero_nat) (= M N_1) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) N_1)) M))))) (forall ((Ma tptp.int) (X_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.quadRes Ma) X_2)) (exists ((Y tptp.int)) (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_2) Ma))))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.power_power_real X_2) _let_1)) (tptp.hAPP_nat_real (tptp.power_power_real Y_2) _let_1)) tptp.zero_zero_real) (and (= X_2 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real))))) (forall ((V_1 tptp.real) (U_2 tptp.real) (Y_5 tptp.real) (X_6 tptp.real) (A_54 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_6) A_54)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_5) A_54)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 U_2)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 V_1)) (=> (= (tptp.hAPP_real_real (tptp.plus_plus_real U_2) V_1) tptp.one_one_real) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real U_2) X_6)) (tptp.hAPP_real_real (tptp.times_times_real V_1) Y_5))) A_54))))))))) (forall ((V_1 tptp.int) (U_2 tptp.int) (Y_5 tptp.int) (X_6 tptp.int) (A_54 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_6) A_54)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y_5) A_54)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 U_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_1)) (=> (= (tptp.hAPP_int_int (tptp.plus_plus_int U_2) V_1) tptp.one_one_int) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int U_2) X_6)) (tptp.hAPP_int_int (tptp.times_times_int V_1) Y_5))) A_54))))))))) (forall ((A_53 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_53) tptp.zero_zero_real))) (forall ((A_53 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_53) tptp.zero_zero_nat))) (forall ((A_53 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_53) tptp.zero_zero_int))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.minus_minus_real X_2) Y_2)) tptp.zero_zero_real)))) (forall ((X_5 tptp.real) (Y_4 tptp.real)) (=> (not (= X_5 Y_4)) (=> (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_5) Y_4))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_4) X_5))))) (forall ((X_5 tptp.int) (Y_4 tptp.int)) (=> (not (= X_5 Y_4)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_5) Y_4))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y_4) X_5))))) (forall ((A_52 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_52) A_52))) (forall ((A_52 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_52) A_52))) (forall ((A_52 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_52) A_52))) (forall ((C_24 tptp.real) (A_51 tptp.real) (B_45 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_51))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_45)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real B_45) C_24)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_24)))))) (forall ((C_24 tptp.nat) (A_51 tptp.nat) (B_45 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_51))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_45)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_45) C_24)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_24)))))) (forall ((C_24 tptp.int) (A_51 tptp.int) (B_45 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_51))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_45)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int B_45) C_24)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_24)))))) _let_5 (forall ((X_2 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) Y_2)) (not (= X_2 Y_2))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (= (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_2) X_2))) (= X_2 Y_2))) (forall ((Z1 tptp.real) (Z2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (tptp.times_times_real Z1))) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real _let_1 Z2)) Z3) (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.times_times_real Z2) Z3))))) (forall ((Z tptp.real) (W tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real Z) W) (tptp.hAPP_real_real (tptp.times_times_real W) Z))) (forall ((Z tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real tptp.one_one_real) Z) Z)) (forall ((Z tptp.real) (X_1 tptp.real) (Y_1 tptp.real)) (let ((_let_1 (tptp.plus_plus_real Z))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 X_1)) (tptp.hAPP_real_real _let_1 Y_1)))))) (forall ((X_4 tptp.nat) (N_3 tptp.nat)) (let ((_let_1 (tptp.power_power_nat X_4))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_3)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat N_3) tptp.one_one_nat))) X_4) (tptp.hAPP_nat_nat _let_1 N_3))))) (forall ((X_4 tptp.real) (N_3 tptp.nat)) (let ((_let_1 (tptp.power_power_real X_4))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_3)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat N_3) tptp.one_one_nat))) X_4) (tptp.hAPP_nat_real _let_1 N_3))))) (forall ((X_4 tptp.int) (N_3 tptp.nat)) (let ((_let_1 (tptp.power_power_int X_4))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_3)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat N_3) tptp.one_one_nat))) X_4) (tptp.hAPP_nat_int _let_1 N_3))))) (forall ((N_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat M) N_1))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) tptp.one_one_nat)) N_1)))))))) (forall ((P_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_power_nat P_1))) (let ((_let_2 (tptp.hAPP_nat_nat _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat (tptp.times_times_nat P_1) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_1) _let_1)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_1) _let_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat X_1) Y_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat X_1) Y_1))))) (forall ((A_50 tptp.real) (B_44 tptp.real)) (=> (= (tptp.hAPP_real_real (tptp.times_times_real A_50) B_44) tptp.zero_zero_real) (or (= A_50 tptp.zero_zero_real) (= B_44 tptp.zero_zero_real)))) (forall ((A_50 tptp.nat) (B_44 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.times_times_nat A_50) B_44) tptp.zero_zero_nat) (or (= A_50 tptp.zero_zero_nat) (= B_44 tptp.zero_zero_nat)))) (forall ((A_50 tptp.int) (B_44 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.times_times_int A_50) B_44) tptp.zero_zero_int) (or (= A_50 tptp.zero_zero_int) (= B_44 tptp.zero_zero_int)))) (forall ((B_43 tptp.real) (A_49 tptp.real)) (=> (not (= A_49 tptp.zero_zero_real)) (=> (not (= B_43 tptp.zero_zero_real)) (not (= (tptp.hAPP_real_real (tptp.times_times_real A_49) B_43) tptp.zero_zero_real))))) (forall ((B_43 tptp.nat) (A_49 tptp.nat)) (=> (not (= A_49 tptp.zero_zero_nat)) (=> (not (= B_43 tptp.zero_zero_nat)) (not (= (tptp.hAPP_nat_nat (tptp.times_times_nat A_49) B_43) tptp.zero_zero_nat))))) (forall ((B_43 tptp.int) (A_49 tptp.int)) (=> (not (= A_49 tptp.zero_zero_int)) (=> (not (= B_43 tptp.zero_zero_int)) (not (= (tptp.hAPP_int_int (tptp.times_times_int A_49) B_43) tptp.zero_zero_int))))) (forall ((A_2 tptp.real) (B_2 tptp.real)) (= (= (tptp.hAPP_real_real (tptp.times_times_real A_2) B_2) tptp.zero_zero_real) (or (= A_2 tptp.zero_zero_real) (= B_2 tptp.zero_zero_real)))) (forall ((A_2 tptp.int) (B_2 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.times_times_int A_2) B_2) tptp.zero_zero_int) (or (= A_2 tptp.zero_zero_int) (= B_2 tptp.zero_zero_int)))) (forall ((A_48 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real A_48) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A_48 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat A_48) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A_48 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int A_48) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A_47 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real tptp.zero_zero_real) A_47) tptp.zero_zero_real)) (forall ((A_47 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat tptp.zero_zero_nat) A_47) tptp.zero_zero_nat)) (forall ((A_47 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int tptp.zero_zero_int) A_47) tptp.zero_zero_int)) _let_5 (not (= tptp.zero_zero_nat tptp.one_one_nat)) _let_4 (not (= tptp.one_one_real tptp.zero_zero_real)) (not (= tptp.one_one_nat tptp.zero_zero_nat)) (not (= tptp.one_one_int tptp.zero_zero_int)) (forall ((A_46 tptp.real) (E tptp.real) (B_42 tptp.real) (C_23 tptp.real)) (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real A_46) E)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real B_42) E)) C_23)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real A_46) B_42)) E)) C_23))) (forall ((A_46 tptp.nat) (E tptp.nat) (B_42 tptp.nat) (C_23 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_46) E)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat B_42) E)) C_23)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_46) B_42)) E)) C_23))) (forall ((A_46 tptp.int) (E tptp.int) (B_42 tptp.int) (C_23 tptp.int)) (= (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int A_46) E)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B_42) E)) C_23)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int A_46) B_42)) E)) C_23))) (forall ((A_45 tptp.real) (B_41 tptp.real) (C_22 tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real A_45) B_41)) C_22) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real A_45) C_22)) (tptp.hAPP_real_real (tptp.times_times_real B_41) C_22)))) (forall ((A_45 tptp.nat) (B_41 tptp.nat) (C_22 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_45) B_41)) C_22) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_45) C_22)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_41) C_22)))) (forall ((A_45 tptp.int) (B_41 tptp.int) (C_22 tptp.int)) (= (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.plus_plus_int A_45) B_41)) C_22) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int A_45) C_22)) (tptp.hAPP_int_int (tptp.times_times_int B_41) C_22)))) (forall ((A_44 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real tptp.zero_zero_real) A_44)) (= A_44 tptp.zero_zero_real))) (forall ((A_44 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A_44)) (= A_44 tptp.zero_zero_nat))) (forall ((A_44 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int tptp.zero_zero_int) A_44)) (= A_44 tptp.zero_zero_int))) (forall ((A_43 tptp.real) (C_21 tptp.real) (B_40 tptp.real) (D_7 tptp.real)) (= (tptp.hAPP_real_real (tptp.minus_minus_real (tptp.hAPP_real_real (tptp.plus_plus_real A_43) C_21)) (tptp.hAPP_real_real (tptp.plus_plus_real B_40) D_7)) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.minus_minus_real A_43) B_40)) (tptp.hAPP_real_real (tptp.minus_minus_real C_21) D_7)))) (forall ((A_43 tptp.int) (C_21 tptp.int) (B_40 tptp.int) (D_7 tptp.int)) (= (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int (tptp.plus_plus_int A_43) C_21)) (tptp.hAPP_int_int (tptp.plus_plus_int B_40) D_7)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.minus_minus_int A_43) B_40)) (tptp.hAPP_int_int (tptp.minus_minus_int C_21) D_7)))) (forall ((A_42 tptp.real) (B_39 tptp.real) (C_20 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_real_real (tptp.times_times_real A_42) B_39)) C_20)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real B_39) C_20)))) (forall ((A_42 tptp.nat) (B_39 tptp.nat) (C_20 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_42) B_39)) C_20)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_39) C_20)))) (forall ((A_42 tptp.int) (B_39 tptp.int) (C_20 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.times_times_int A_42) B_39)) C_20)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int B_39) C_20)))) (forall ((A_41 tptp.real) (B_38 tptp.real) (C_19 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_real_real (tptp.times_times_real A_41) B_38)) C_19)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_41) C_19)))) (forall ((A_41 tptp.nat) (B_38 tptp.nat) (C_19 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_41) B_38)) C_19)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_41) C_19)))) (forall ((A_41 tptp.int) (B_38 tptp.int) (C_19 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.times_times_int A_41) B_38)) C_19)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_41) C_19)))) (forall ((A_40 tptp.real) (B_37 tptp.real) (K_3 tptp.real)) (=> (= A_40 (tptp.hAPP_real_real (tptp.times_times_real B_37) K_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real B_37) A_40)))) (forall ((A_40 tptp.nat) (B_37 tptp.nat) (K_3 tptp.nat)) (=> (= A_40 (tptp.hAPP_nat_nat (tptp.times_times_nat B_37) K_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_37) A_40)))) (forall ((A_40 tptp.int) (B_37 tptp.int) (K_3 tptp.int)) (=> (= A_40 (tptp.hAPP_int_int (tptp.times_times_int B_37) K_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int B_37) A_40)))) (forall ((C_18 tptp.real) (D_6 tptp.real) (A_39 tptp.real) (B_36 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_39) B_36)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real C_18) D_6)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_real_real (tptp.times_times_real A_39) C_18)) (tptp.hAPP_real_real (tptp.times_times_real B_36) D_6)))))) (forall ((C_18 tptp.nat) (D_6 tptp.nat) (A_39 tptp.nat) (B_36 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_39) B_36)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat C_18) D_6)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_39) C_18)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_36) D_6)))))) (forall ((C_18 tptp.int) (D_6 tptp.int) (A_39 tptp.int) (B_36 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_39) B_36)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int C_18) D_6)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.times_times_int A_39) C_18)) (tptp.hAPP_int_int (tptp.times_times_int B_36) D_6)))))) (forall ((B_35 tptp.real) (A_38 tptp.real) (C_17 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_38))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_17)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real B_35) C_17)))))) (forall ((B_35 tptp.nat) (A_38 tptp.nat) (C_17 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_38))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_17)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat B_35) C_17)))))) (forall ((B_35 tptp.int) (A_38 tptp.int) (C_17 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_38))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_17)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int B_35) C_17)))))) (forall ((C_16 tptp.real) (A_37 tptp.real) (B_34 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_37))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_34)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real B_34) C_16)))))) (forall ((C_16 tptp.nat) (A_37 tptp.nat) (B_34 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_37))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_34)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat B_34) C_16)))))) (forall ((C_16 tptp.int) (A_37 tptp.int) (B_34 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_37))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_34)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int B_34) C_16)))))) (forall ((A_36 tptp.real) (B_33 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_36) (tptp.hAPP_real_real (tptp.times_times_real B_33) A_36)))) (forall ((A_36 tptp.nat) (B_33 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_36) (tptp.hAPP_nat_nat (tptp.times_times_nat B_33) A_36)))) (forall ((A_36 tptp.int) (B_33 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_36) (tptp.hAPP_int_int (tptp.times_times_int B_33) A_36)))) (forall ((A_35 tptp.real) (B_32 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_35) (tptp.hAPP_real_real (tptp.times_times_real A_35) B_32)))) (forall ((A_35 tptp.nat) (B_32 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_35) (tptp.hAPP_nat_nat (tptp.times_times_nat A_35) B_32)))) (forall ((A_35 tptp.int) (B_32 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_35) (tptp.hAPP_int_int (tptp.times_times_int A_35) B_32)))) (forall ((C_15 tptp.real) (A_34 tptp.real) (B_31 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_34))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_31)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_15)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.plus_plus_real B_31) C_15))))))) (forall ((C_15 tptp.nat) (A_34 tptp.nat) (B_31 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_34))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_31)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_15)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_31) C_15))))))) (forall ((C_15 tptp.int) (A_34 tptp.int) (B_31 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_34))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_31)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_15)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int B_31) C_15))))))) (forall ((A_33 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real tptp.one_one_real) A_33))) (forall ((A_33 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.one_one_nat) A_33))) (forall ((A_33 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int tptp.one_one_int) A_33))) (forall ((Z_2 tptp.real) (X_3 tptp.real) (Y_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real X_3))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_3)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Z_2)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.minus_minus_real Y_3) Z_2))))))) (forall ((Z_2 tptp.int) (X_3 tptp.int) (Y_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int X_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_2)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.minus_minus_int Y_3) Z_2))))))) (forall ((A_2 tptp.real) (B_2 tptp.real) (C_2 tptp.real)) (=> (not (= C_2 tptp.zero_zero_real)) (= (= (tptp.hAPP_real_real (tptp.times_times_real A_2) C_2) (tptp.hAPP_real_real (tptp.times_times_real B_2) C_2)) (= A_2 B_2)))) (forall ((A_2 tptp.real) (B_2 tptp.real) (C_2 tptp.real)) (let ((_let_1 (tptp.times_times_real C_2))) (=> (not (= C_2 tptp.zero_zero_real)) (= (= (tptp.hAPP_real_real _let_1 A_2) (tptp.hAPP_real_real _let_1 B_2)) (= A_2 B_2))))) (forall ((B tptp.nat) (D_5 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat D_5))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat A) B))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B)))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.times_times_nat C))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 A)) (tptp.hAPP_nat_nat _let_1 B)))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A) C)) (tptp.hAPP_nat_nat (tptp.times_times_nat B) C))))) (forall ((N tptp.nat) (Ma tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.times_times_nat N) Ma) tptp.one_one_nat) (and (= N tptp.one_one_nat) (= Ma tptp.one_one_nat)))) (forall ((Z1 tptp.real) (Z2 tptp.real) (W tptp.real)) (= (tptp.hAPP_real_real (tptp.times_times_real (tptp.hAPP_real_real (tptp.plus_plus_real Z1) Z2)) W) (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real Z1) W)) (tptp.hAPP_real_real (tptp.times_times_real Z2) W)))) (forall ((Ma tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.power_power_nat Ma) N) tptp.zero_zero_nat) (and (not (= N tptp.zero_zero_nat)) (= Ma tptp.zero_zero_nat)))) (forall ((N_1 tptp.nat) (X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_1) N_1)) (tptp.hAPP_nat_nat (tptp.power_power_nat Y_1) N_1))))) (forall ((B_30 tptp.real) (A_32 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_32)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_30) tptp.zero_zero_real))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_32) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_30)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real A_32) B_30)) tptp.zero_zero_real))))) (forall ((B_30 tptp.nat) (A_32 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_32)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_30) tptp.zero_zero_nat))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_32) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_30)))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_32) B_30)) tptp.zero_zero_nat))))) (forall ((B_30 tptp.int) (A_32 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_32)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_30) tptp.zero_zero_int))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_32) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_30)))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int A_32) B_30)) tptp.zero_zero_int))))) (forall ((B_29 tptp.real) (A_31 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_31)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_29))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_31) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_29) tptp.zero_zero_real)))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real A_31) B_29)))))) (forall ((B_29 tptp.int) (A_31 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_31)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_29))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_31) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_29) tptp.zero_zero_int)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int A_31) B_29)))))) (forall ((C_14 tptp.real) (D_4 tptp.real) (A_30 tptp.real) (B_28 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_30) B_28)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_14) D_4)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_28)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_14)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real A_30) C_14)) (tptp.hAPP_real_real (tptp.times_times_real B_28) D_4))))))))) (forall ((C_14 tptp.nat) (D_4 tptp.nat) (A_30 tptp.nat) (B_28 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_30) B_28)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_14) D_4)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_28)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_14)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_30) C_14)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_28) D_4))))))))) (forall ((C_14 tptp.int) (D_4 tptp.int) (A_30 tptp.int) (B_28 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_30) B_28)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_14) D_4)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_28)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_14)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int A_30) C_14)) (tptp.hAPP_int_int (tptp.times_times_int B_28) D_4))))))))) (forall ((C_13 tptp.real) (D_3 tptp.real) (A_29 tptp.real) (B_27 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_29) B_27)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_13) D_3)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_29)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_13)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real A_29) C_13)) (tptp.hAPP_real_real (tptp.times_times_real B_27) D_3))))))))) (forall ((C_13 tptp.nat) (D_3 tptp.nat) (A_29 tptp.nat) (B_27 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_29) B_27)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_13) D_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_29)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_13)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_29) C_13)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_27) D_3))))))))) (forall ((C_13 tptp.int) (D_3 tptp.int) (A_29 tptp.int) (B_27 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_29) B_27)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_13) D_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_29)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_13)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int A_29) C_13)) (tptp.hAPP_int_int (tptp.times_times_int B_27) D_3))))))))) (forall ((C_12 tptp.real) (B_26 tptp.real) (A_28 tptp.real)) (let ((_let_1 (tptp.times_times_real C_12))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_26) A_28)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_12) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_28)) (tptp.hAPP_real_real _let_1 B_26))))))) (forall ((C_12 tptp.int) (B_26 tptp.int) (A_28 tptp.int)) (let ((_let_1 (tptp.times_times_int C_12))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_26) A_28)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_12) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_28)) (tptp.hAPP_int_int _let_1 B_26))))))) (forall ((C_11 tptp.real) (B_25 tptp.real) (A_27 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_25) A_27)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_11) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real A_27) C_11)) (tptp.hAPP_real_real (tptp.times_times_real B_25) C_11)))))) (forall ((C_11 tptp.int) (B_25 tptp.int) (A_27 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_25) A_27)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_11) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int A_27) C_11)) (tptp.hAPP_int_int (tptp.times_times_int B_25) C_11)))))) (forall ((C_10 tptp.real) (A_26 tptp.real) (B_24 tptp.real)) (let ((_let_1 (tptp.times_times_real C_10))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_26) B_24)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_10)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_26)) (tptp.hAPP_real_real _let_1 B_24))))))) (forall ((C_10 tptp.nat) (A_26 tptp.nat) (B_24 tptp.nat)) (let ((_let_1 (tptp.times_times_nat C_10))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_26) B_24)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_10)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_26)) (tptp.hAPP_nat_nat _let_1 B_24))))))) (forall ((C_10 tptp.int) (A_26 tptp.int) (B_24 tptp.int)) (let ((_let_1 (tptp.times_times_int C_10))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_26) B_24)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_10)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_26)) (tptp.hAPP_int_int _let_1 B_24))))))) (forall ((C_9 tptp.real) (A_25 tptp.real) (B_23 tptp.real)) (let ((_let_1 (tptp.times_times_real C_9))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_25) B_23)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_9)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_25)) (tptp.hAPP_real_real _let_1 B_23))))))) (forall ((C_9 tptp.nat) (A_25 tptp.nat) (B_23 tptp.nat)) (let ((_let_1 (tptp.times_times_nat C_9))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_25) B_23)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_9)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_25)) (tptp.hAPP_nat_nat _let_1 B_23))))))) (forall ((C_9 tptp.int) (A_25 tptp.int) (B_23 tptp.int)) (let ((_let_1 (tptp.times_times_int C_9))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_25) B_23)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_9)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_25)) (tptp.hAPP_int_int _let_1 B_23))))))) (forall ((C_8 tptp.real) (A_24 tptp.real) (B_22 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_24) B_22)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_8)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real A_24) C_8)) (tptp.hAPP_real_real (tptp.times_times_real B_22) C_8)))))) (forall ((C_8 tptp.nat) (A_24 tptp.nat) (B_22 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_24) B_22)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_8)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_24) C_8)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_22) C_8)))))) (forall ((C_8 tptp.int) (A_24 tptp.int) (B_22 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_24) B_22)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_8)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int A_24) C_8)) (tptp.hAPP_int_int (tptp.times_times_int B_22) C_8)))))) (forall ((B_21 tptp.real) (A_23 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_23) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_21) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.times_times_real A_23) B_21)))))) (forall ((B_21 tptp.int) (A_23 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_23) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_21) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.times_times_int A_23) B_21)))))) (forall ((B_20 tptp.real) (A_22 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_22) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B_20)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real A_22) B_20)) tptp.zero_zero_real))))) (forall ((B_20 tptp.nat) (A_22 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_22) tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B_20)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_22) B_20)) tptp.zero_zero_nat))))) (forall ((B_20 tptp.int) (A_22 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_22) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) B_20)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int A_22) B_20)) tptp.zero_zero_int))))) (forall ((B_19 tptp.real) (A_21 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_21)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_19) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real B_19) A_21)) tptp.zero_zero_real))))) (forall ((B_19 tptp.nat) (A_21 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_21)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_19) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat B_19) A_21)) tptp.zero_zero_nat))))) (forall ((B_19 tptp.int) (A_21 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_21)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_19) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int B_19) A_21)) tptp.zero_zero_int))))) (forall ((B_18 tptp.real) (A_20 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_20)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_18) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real A_20) B_18)) tptp.zero_zero_real))))) (forall ((B_18 tptp.nat) (A_20 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_20)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_18) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_20) B_18)) tptp.zero_zero_nat))))) (forall ((B_18 tptp.int) (A_20 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_20)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_18) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int A_20) B_18)) tptp.zero_zero_int))))) (forall ((B_17 tptp.real) (A_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 _let_1 A_19)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_17)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real A_19) B_17))))))) (forall ((B_17 tptp.nat) (A_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 _let_1 A_19)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_17)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat A_19) B_17))))))) (forall ((B_17 tptp.int) (A_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 _let_1 A_19)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_17)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int A_19) B_17))))))) (forall ((A_2 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real A_2) B_2)) tptp.zero_zero_real)) (or (and (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_2) tptp.zero_zero_real))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_2) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_2))))))) (forall ((A_2 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.times_times_int A_2) B_2)) tptp.zero_zero_int)) (or (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) tptp.zero_zero_int))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_2) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_2))))))) (forall ((A_2 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real A_2) B_2))) (or (and (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_2))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_2) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_2) tptp.zero_zero_real))))))) (forall ((A_2 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int A_2) B_2))) (or (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_2))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_2) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) tptp.zero_zero_int))))))) (forall ((A_18 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.times_times_real A_18) A_18)))) (forall ((A_18 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.times_times_int A_18) A_18)))) (forall ((C_7 tptp.real) (B_16 tptp.real) (A_17 tptp.real)) (let ((_let_1 (tptp.times_times_real C_7))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_16) A_17)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_7) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_17)) (tptp.hAPP_real_real _let_1 B_16))))))) (forall ((C_7 tptp.int) (B_16 tptp.int) (A_17 tptp.int)) (let ((_let_1 (tptp.times_times_int C_7))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_16) A_17)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_7) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_17)) (tptp.hAPP_int_int _let_1 B_16))))))) (forall ((C_6 tptp.real) (B_15 tptp.real) (A_16 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_15) A_16)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_6) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_16) C_6)) (tptp.hAPP_real_real (tptp.times_times_real B_15) C_6)))))) (forall ((C_6 tptp.int) (B_15 tptp.int) (A_16 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_15) A_16)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_6) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_16) C_6)) (tptp.hAPP_int_int (tptp.times_times_int B_15) C_6)))))) (forall ((C_5 tptp.real) (A_15 tptp.real) (B_14 tptp.real)) (let ((_let_1 (tptp.times_times_real C_5))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_15) B_14)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_5)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_15)) (tptp.hAPP_real_real _let_1 B_14))))))) (forall ((C_5 tptp.nat) (A_15 tptp.nat) (B_14 tptp.nat)) (let ((_let_1 (tptp.times_times_nat C_5))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_15) B_14)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_5)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A_15)) (tptp.hAPP_nat_nat _let_1 B_14))))))) (forall ((C_5 tptp.int) (A_15 tptp.int) (B_14 tptp.int)) (let ((_let_1 (tptp.times_times_int C_5))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_15) B_14)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_5)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_15)) (tptp.hAPP_int_int _let_1 B_14))))))) (forall ((C_4 tptp.real) (A_14 tptp.real) (B_13 tptp.real)) (let ((_let_1 (tptp.times_times_real C_4))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_14) B_13)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_4)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_14)) (tptp.hAPP_real_real _let_1 B_13))))))) (forall ((C_4 tptp.nat) (A_14 tptp.nat) (B_13 tptp.nat)) (let ((_let_1 (tptp.times_times_nat C_4))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_14) B_13)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_4)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A_14)) (tptp.hAPP_nat_nat _let_1 B_13))))))) (forall ((C_4 tptp.int) (A_14 tptp.int) (B_13 tptp.int)) (let ((_let_1 (tptp.times_times_int C_4))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_14) B_13)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_4)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_14)) (tptp.hAPP_int_int _let_1 B_13))))))) (forall ((C_3 tptp.real) (A_13 tptp.real) (B_12 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_13) B_12)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_13) C_3)) (tptp.hAPP_real_real (tptp.times_times_real B_12) C_3)))))) (forall ((C_3 tptp.nat) (A_13 tptp.nat) (B_12 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_13) B_12)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_13) C_3)) (tptp.hAPP_nat_nat (tptp.times_times_nat B_12) C_3)))))) (forall ((C_3 tptp.int) (A_13 tptp.int) (B_12 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_13) B_12)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_13) C_3)) (tptp.hAPP_int_int (tptp.times_times_int B_12) C_3)))))) (forall ((B_11 tptp.real) (A_12 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_12) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_11) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.times_times_real A_12) B_11)))))) (forall ((B_11 tptp.int) (A_12 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_12) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_11) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.times_times_int A_12) B_11)))))) (forall ((B_10 tptp.real) (A_11 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_11) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) B_10)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_11) B_10)) tptp.zero_zero_real))))) (forall ((B_10 tptp.nat) (A_11 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_11) tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) B_10)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_11) B_10)) tptp.zero_zero_nat))))) (forall ((B_10 tptp.int) (A_11 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_11) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_10)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_11) B_10)) tptp.zero_zero_int))))) (forall ((A_2 tptp.real) (B_2 tptp.real) (C_2 tptp.real)) (let ((_let_1 (tptp.times_times_real C_2))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_2) tptp.zero_zero_real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_2)) (tptp.hAPP_real_real _let_1 B_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_2) A_2)))))) (forall ((A_2 tptp.int) (B_2 tptp.int) (C_2 tptp.int)) (let ((_let_1 (tptp.times_times_int C_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_2) tptp.zero_zero_int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_2)) (tptp.hAPP_int_int _let_1 B_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) A_2)))))) (forall ((B_9 tptp.real) (A_10 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real B_9) A_10))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_10)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_9)))))) (forall ((B_9 tptp.nat) (A_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat B_9) A_10))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_10)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_9)))))) (forall ((B_9 tptp.int) (A_10 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int B_9) A_10))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_10)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_9)))))) (forall ((A_9 tptp.real) (B_8 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real A_9) B_8))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_9)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_8)))))) (forall ((A_9 tptp.nat) (B_8 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat A_9) B_8))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_9)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_8)))))) (forall ((A_9 tptp.int) (B_8 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int A_9) B_8))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_9)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_8)))))) (forall ((B_7 tptp.real) (A_8 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_8)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_7) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real B_7) A_8)) tptp.zero_zero_real))))) (forall ((B_7 tptp.nat) (A_8 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_8)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_7) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat B_7) A_8)) tptp.zero_zero_nat))))) (forall ((B_7 tptp.int) (A_8 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_8)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_7) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int B_7) A_8)) tptp.zero_zero_int))))) (forall ((B_6 tptp.real) (A_7 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_7)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_6) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_7) B_6)) tptp.zero_zero_real))))) (forall ((B_6 tptp.nat) (A_7 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_7)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_6) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat A_7) B_6)) tptp.zero_zero_nat))))) (forall ((B_6 tptp.int) (A_7 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_7)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_6) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_7) B_6)) tptp.zero_zero_int))))) (forall ((B_5 tptp.real) (A_6 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_6)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_5)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real A_6) B_5))))))) (forall ((B_5 tptp.nat) (A_6 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_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_5)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat A_6) B_5))))))) (forall ((B_5 tptp.int) (A_6 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_6)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_5)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.times_times_int A_6) B_5))))))) (forall ((A_2 tptp.real) (B_2 tptp.real) (C_2 tptp.real)) (let ((_let_1 (tptp.times_times_real C_2))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_2)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_2)) (tptp.hAPP_real_real _let_1 B_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_2) B_2)))))) (forall ((A_2 tptp.int) (B_2 tptp.int) (C_2 tptp.int)) (let ((_let_1 (tptp.times_times_int C_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_2)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_2)) (tptp.hAPP_int_int _let_1 B_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) B_2)))))) (forall ((C_2 tptp.real) (A_2 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.times_times_real C_2))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_2)) (tptp.hAPP_real_real _let_1 B_2))) (or (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_2) B_2))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_2) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_2) A_2))))))) (forall ((C_2 tptp.int) (A_2 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.times_times_int C_2))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_2)) (tptp.hAPP_int_int _let_1 B_2))) (or (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) B_2))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_2) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) A_2))))))) (forall ((A_2 tptp.real) (C_2 tptp.real) (B_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_2) C_2)) (tptp.hAPP_real_real (tptp.times_times_real B_2) C_2))) (or (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_2) B_2))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_2) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_2) A_2)))))) (forall ((A_2 tptp.int) (C_2 tptp.int) (B_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_2) C_2)) (tptp.hAPP_int_int (tptp.times_times_int B_2) C_2))) (or (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) B_2))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_2) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) A_2)))))) (forall ((A_5 tptp.real)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real A_5) A_5)) tptp.zero_zero_real)))) (forall ((A_5 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.times_times_int A_5) A_5)) tptp.zero_zero_int)))) (forall ((B_4 tptp.nat) (C_1 tptp.nat) (A_4 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_4))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_4)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat A_4) C_1))))))) (forall ((B_4 tptp.int) (C_1 tptp.int) (A_4 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_4))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_4)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int A_4) C_1))))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B)) (or (= B tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A) B))))) (forall ((Ma tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) K)) (tptp.hAPP_nat_nat (tptp.times_times_nat N) K))) (or (= K tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) N))))) (forall ((X_2 tptp.real) (Y_2 tptp.real) (Z_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Z_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.times_times_real X_2) Z_1)) (tptp.hAPP_real_real (tptp.times_times_real Y_2) Z_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_2) Y_2))))) (forall ((X_2 tptp.real) (Y_2 tptp.real) (Z_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Z_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.times_times_real X_2) Z_1)) (tptp.hAPP_real_real (tptp.times_times_real Y_2) Z_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) Y_2))))) (forall ((X_2 tptp.real) (Y_2 tptp.real) (Z_1 tptp.real)) (let ((_let_1 (tptp.times_times_real Z_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Z_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 X_2)) (tptp.hAPP_real_real _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) Y_2)))))) (forall ((Y_1 tptp.real) (X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.times_times_real X_1) Y_1))))))) (forall ((X_1 tptp.real) (Y_1 tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.times_times_real Z))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Z)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 X_1)) (tptp.hAPP_real_real _let_1 Y_1))))))) (forall ((X_2 tptp.real) (Y_2 tptp.real)) (= (= (tptp.hAPP_real_real (tptp.plus_plus_real (tptp.hAPP_real_real (tptp.times_times_real X_2) X_2)) (tptp.hAPP_real_real (tptp.times_times_real Y_2) Y_2)) tptp.zero_zero_real) (and (= X_2 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat) (N_1 tptp.nat)) (=> (not (= N_1 tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.power_power_nat X_1) N_1)) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_1))))) (forall ((A tptp.nat) (N_1 tptp.nat) (B tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.power_power_nat A) N_1)) (tptp.hAPP_nat_nat (tptp.power_power_nat B) N_1))) (=> (not (= N_1 tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B))))) (forall ((X_2 tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.power_power_nat X_2) N) tptp.one_one_nat) (or (= X_2 tptp.one_one_nat) (= N tptp.zero_zero_nat)))) (forall ((X_1 tptp.nat) (Q_1 tptp.nat) (N_1 tptp.nat) (R_1 tptp.nat)) (=> (= X_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat Q_1) N_1)) R_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) R_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat R_1) N_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N_1) X_1))))))) (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.hAPP_nat_real (tptp.power_power_real (tptp.number267125858f_real (tptp.bit0 (tptp.bit1 tptp.pls)))) N_1)))) (forall ((A tptp.real) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (exists ((R_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) R_2)) (= (tptp.hAPP_nat_real (tptp.power_power_real R_2) N_1) A)))))) (forall ((A tptp.real) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (exists ((X tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.hAPP_nat_real (tptp.power_power_real X) N_1) A) (forall ((Y tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (= (tptp.hAPP_nat_real (tptp.power_power_real Y) N_1) A)) (= Y X)))))))) (forall ((N tptp.nat) (Ma tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Ma)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.times_times_nat N) Ma)) Ma)) (= N tptp.one_one_nat)))) (forall ((N tptp.nat) (Ma tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Ma)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) N)) Ma)) (= N tptp.one_one_nat)))) (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N_1))) (forall ((X_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) X_1))) (forall ((N_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) tptp.zero_zero_nat)))) (forall ((I_1 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.minus_minus_nat I_1))) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J_1)) K_1) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 K_1)) J_1)))) (forall ((W tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real W) W))) (forall ((Z tptp.real) (W tptp.real)) (or (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Z) W)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real W) Z)))) (forall ((K_1 tptp.real) (I_1 tptp.real) (J_1 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real I_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 J_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real J_1) K_1)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 K_1)))))) (forall ((Z tptp.real) (W tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Z) W)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real W) Z)) (= Z W)))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat tptp.zero_zero_nat) N_1) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) tptp.zero_zero_nat) M)) (forall ((M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) M) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1) tptp.zero_zero_nat) (=> (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat N_1) M) tptp.zero_zero_nat) (= M N_1)))) (forall ((P_2 tptp.fun_nat_fun_nat_bool) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool P_2 N) Ma)))) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N)) _let_1) (=> (=> (= Ma N) _let_1) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) Ma)) _let_1) _let_1))))) (forall ((S tptp.nat) (T tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat S) T)) (not (= S T)))) (forall ((N_1 tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) M)) (not (= M N_1)))) (forall ((N_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) N_1)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (not (= X_1 Y_1)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1))))) (forall ((Ma tptp.nat) (N tptp.nat)) (= (not (= Ma N)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) Ma))))) (forall ((N_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) N_1)))) (forall ((L tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.minus_minus_nat L))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 L)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 N_1)) (tptp.hAPP_nat_nat _let_1 M)))))))) (forall ((N_1 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J_1) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) N_1)) K_1)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) X_1)))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((Z tptp.nat) (X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Z))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1))) (let ((_let_3 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Y_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_3 X_1)))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_3 Z)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_1)))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Z)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_1)))))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B) A)))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((Z tptp.nat) (X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 X_1)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Z)) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Z) X_1))))))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B) A)))) (=> (= B C) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat C) A)))))))) (forall ((P_2 tptp.bool) (X_2 tptp.nat) (Y_2 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_2) Y_2)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_2) X_2)))) (=> (and _let_1 (not _let_2)) (=> (and _let_2 (not _let_1)) (tptp.hBOOL P_2)))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) X_1)))) (not (= Y_1 X_1)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) X_1)))) (not (= X_1 Y_1)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) X_1)))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_1)))) (=> (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) X_1)))) _let_1))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) X_1)))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) X_1)))) (not (= X_1 Y_1)))) (forall ((Z tptp.nat) (X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Z))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Y_1)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) Z)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_1)))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Z)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_1))))))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat C))) (=> (= A B) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B) C)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B)))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) C)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A)))))))) (forall ((Z tptp.nat) (X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) Z)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z)))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) X_1)) (= X_1 Y_1)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M) N_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N_1) M)) (= M N_1)))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B)) (=> (= B C) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C)))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (= A B) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B) C)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) C))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B)))) (=> _let_1 (=> (not (= A B)) (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B) A)))))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_1)))) (=> _let_1 (or (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_1) X_1)))) (= X_1 Y_1))))) (forall ((Y_2 tptp.nat) (X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_2) X_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (= X_1 Y_1) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_1)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B)))) (=> (not (= A B)) (=> _let_1 (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B) A)))))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (let ((_let_1 (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_2) X_2)))))) (= _let_1 _let_1))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_2) Y_2)))) (= (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_2) X_2)))) (and _let_1 (not (= X_2 Y_2)))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_2) Y_2)))) (= _let_1 (or (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_2) X_2)))) (= X_2 Y_2))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (= (= X_2 Y_2) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_2) X_2))))) (forall ((X_1 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) X_1)))) (not (and _let_1 (not _let_1))))) (forall ((N_1 tptp.nat) (K_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1))))))) (forall ((M tptp.nat) (N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) N_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) M))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat X_1))) (let ((_let_2 (tptp.plus_plus_nat Y_1))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Z)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Z)))))) (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat M))) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 N_1)) K_1) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) K_1))))) (forall ((K tptp.nat) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat K))) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 N)) (= Ma N)))) (forall ((Ma tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat Ma) K) (tptp.hAPP_nat_nat (tptp.plus_plus_nat N) K)) (= Ma N))) (forall ((M tptp.nat) (N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) N_1)) N_1) M)) (forall ((N_1 tptp.nat) (M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) M)) N_1) M)) (forall ((I_1 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.minus_minus_nat I_1))) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J_1)) K_1) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) K_1))))) (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat K_1))) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)))) (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) K_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) K_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1))) (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) N_1))) (forall ((M tptp.nat) (N_1 tptp.nat)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (= M N_1) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 K_1)))))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M)) (= M N_1)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) M))) (forall ((L tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.minus_minus_nat L))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 N_1)) (tptp.hAPP_nat_nat _let_1 M)))))) (forall ((L tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) L)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat N_1) L))))) (forall ((I_1 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.minus_minus_nat N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) N_1)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_1 I_1)) I_1)))) (forall ((N tptp.nat) (K tptp.nat) (Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (= (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat Ma) K) (tptp.hAPP_nat_nat (tptp.minus_minus_nat N) K)) (= Ma N)))))) (forall ((N_1 tptp.nat) (K_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.minus_minus_nat M))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N_1)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 K_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat N_1) K_1)) (tptp.hAPP_nat_nat _let_1 N_1))))))) (forall ((N tptp.nat) (K tptp.nat) (Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat Ma) K)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat N) K))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N))))))) (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat M))) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 N_1)) K_1) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat N_1) K_1))))) (forall ((M tptp.nat) (N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat M) N_1) (tptp.hAPP_nat_nat (tptp.times_times_nat N_1) M))) (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) K_1) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat M) K_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat N_1) K_1)))) (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat K_1))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N_1))))) (forall ((N_1 tptp.nat)) (=> (not (= N_1 tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1)) (not (= N_1 tptp.zero_zero_nat)))) (forall ((N_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) M)))))) (forall ((N tptp.nat) (Ma tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat (tptp.minus_minus_nat N) Ma))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) N_1) M) (= N_1 tptp.zero_zero_nat))) (forall ((Ma tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat Ma) N) tptp.zero_zero_nat) (and (= Ma tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) tptp.zero_zero_nat) M)) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat tptp.zero_zero_nat) N_1) N_1)) (forall ((N_1 tptp.nat) (M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat N_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) M)) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))) (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N_1))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1) tptp.zero_zero_nat))) (forall ((Ma tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat Ma) N) tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N)))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat tptp.zero_zero_nat) N_1) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((Ma tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) N) tptp.zero_zero_nat) (or (= Ma tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((K tptp.nat) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 N)) (or (= Ma N) (= K tptp.zero_zero_nat))))) (forall ((Ma tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) K) (tptp.hAPP_nat_nat (tptp.times_times_nat N) K)) (or (= Ma N) (= K tptp.zero_zero_nat)))) (forall ((I_1 tptp.nat) (J_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) J_1)) I_1)))) (forall ((J_1 tptp.nat) (I_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) I_1)) I_1)))) (forall ((K tptp.nat) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N))))) (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) M)))))) (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) J_1)))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) K_1))))) (forall ((K_1 tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_1) L)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) L)))))) (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat) (L tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_1) L)) (=> (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) L) (tptp.hAPP_nat_nat (tptp.plus_plus_nat K_1) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1))))) (forall ((I_1 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) J_1)) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) K_1)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1))) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) M))) (forall ((I_2 tptp.nat) (J_2 tptp.nat) (K tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) K))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_2) K)) J_2)))) (forall ((Ma tptp.nat) (N tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N)) (not (= Ma N))))) (forall ((Ma tptp.nat) (N tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N)) (= Ma N)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (=> (not (= M N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1))))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1)) (= M N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)))) (forall ((N tptp.nat) (K tptp.nat) (Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat Ma) K)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat N) K))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N))))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A) B)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C) A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat A) C)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat B) C)))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat N) K))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N))))) (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1))))))) (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M))))))) (forall ((N_1 tptp.nat) (M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) N_1)))) (forall ((N_1 tptp.nat) (M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) M)))) (forall ((Ma tptp.nat) (N tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N)) (exists ((K_2 tptp.nat)) (= N (tptp.hAPP_nat_nat (tptp.plus_plus_nat Ma) K_2))))) (forall ((K tptp.nat) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N))))) (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) M)))))) (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) J_1)))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) K_1))))) (forall ((K_1 tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) L)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) L)))))) (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) K_1)) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) N_1)))) (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) K_1)) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)))) (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) K_1)) N_1)) (not (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) N_1))))))) (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J_1)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat I_1) (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) K_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) K_1)) J_1)))) (forall ((J_2 tptp.nat) (K tptp.nat) (I_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) K)) I_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_2) (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_2) K))))) (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) M)) K_1))))) (forall ((N_1 tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat N_1) (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) M))) (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J_1)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) K_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J_1)) K_1))))) (forall ((I_2 tptp.nat) (K tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) K))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_2) K)) J_2))))) (forall ((N_1 tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) N_1) M))) (forall ((K tptp.nat) (I_2 tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_2)) (= (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) I_2) K) (= J_2 (tptp.hAPP_nat_nat (tptp.plus_plus_nat K) I_2))))) (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.plus_plus_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J_1)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J_1)) K_1) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) K_1)))))) (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J_1)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) K_1)) I_1) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) I_1)) K_1)))) (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J_1)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_1) I_1)) K_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) K_1)) I_1)))) (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) N_1)) K_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat M) K_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat N_1) K_1)))) (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat K_1))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) N_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N_1))))) (forall ((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_1 tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) L)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat J_1) L)))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 I_1)) (tptp.hAPP_nat_nat _let_1 J_1)))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat J_1) K_1))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.times_times_nat M))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_1 M)))))) (forall ((M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.hAPP_nat_nat (tptp.times_times_nat M) M)))) (forall ((Ma tptp.nat) (N tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) N) tptp.one_one_nat) (and (= Ma tptp.one_one_nat) (= N tptp.one_one_nat)))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat N_1) tptp.one_one_nat) N_1)) (forall ((Ma tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) N)) (and (= Ma tptp.one_one_nat) (= N tptp.one_one_nat)))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat tptp.one_one_nat) N_1) N_1)) (forall ((N_1 tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N_1) M)))))) (forall ((Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat Ma) N))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)))))) (forall ((P_2 tptp.fun_nat_bool) (A_2 tptp.nat) (B_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool P_2 (tptp.hAPP_nat_nat (tptp.minus_minus_nat A_2) B_2))) (and (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_2) B_2)) (tptp.hBOOL (tptp.hAPP_nat_bool P_2 tptp.zero_zero_nat))) (forall ((D_2 tptp.nat)) (=> (= A_2 (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_2) D_2)) (tptp.hBOOL (tptp.hAPP_nat_bool P_2 D_2))))))) (forall ((P_2 tptp.fun_nat_bool) (A_2 tptp.nat) (B_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool P_2 (tptp.hAPP_nat_nat (tptp.minus_minus_nat A_2) B_2))) (not (or (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_2) B_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool P_2 tptp.zero_zero_nat)))) (exists ((D_2 tptp.nat)) (and (= A_2 (tptp.hAPP_nat_nat (tptp.plus_plus_nat B_2) D_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool P_2 D_2))))))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 I_1)) (tptp.hAPP_nat_nat _let_1 J_1))))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat J_1) K_1)))))) (forall ((Ma tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) K)) (tptp.hAPP_nat_nat (tptp.times_times_nat N) K))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N))))) (forall ((K tptp.nat) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N)))))) (forall ((Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) N))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)))))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (= M (tptp.hAPP_nat_nat (tptp.times_times_nat M) N_1)) (or (= N_1 tptp.one_one_nat) (= M tptp.zero_zero_nat)))) (forall ((K_1 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_1) N_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) N_1))))) (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M) N_1)))))) (forall ((K tptp.nat) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N)))))) (forall ((Ma tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat Ma) K)) (tptp.hAPP_nat_nat (tptp.times_times_nat N) K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N))))) (forall ((N tptp.nat) (P_2 tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool P_2 tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_2 N)) (exists ((K_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_2) N)) (forall ((I tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) K_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool P_2 I))))) (tptp.hBOOL (tptp.hAPP_nat_bool P_2 (tptp.hAPP_nat_nat (tptp.plus_plus_nat K_2) tptp.one_one_nat)))))))) (forall ((U tptp.nat) (Ma tptp.nat) (N tptp.nat) (I_2 tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_2) U)) Ma)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_2) U)) N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) I_2)) U)) N)))))) (forall ((K tptp.nat) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 N)) (or (= K tptp.zero_zero_nat) (= Ma N))))) (forall ((I_1 tptp.nat) (U_1 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_1) U_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_1) U_1)) K_1)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) J_1)) U_1)) K_1))) (forall ((Ma tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 N)) (= Ma N))))) (forall ((Ma tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N)))))) (forall ((K tptp.nat) (Ma tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N))) (or (= K tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) N)))))) (forall ((Ma tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) N)))))) (forall ((Ma tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N)))))) (forall ((U tptp.nat) (Ma tptp.nat) (N tptp.nat) (J_2 tptp.nat) (I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_2) I_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_2) U)) Ma)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_2) U)) N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat I_2) J_2)) U)) Ma)) N))))) (forall ((U_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat) (J_1 tptp.nat) (I_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) I_1)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_1) U_1)) M)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_1) U_1)) N_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat I_1) J_1)) U_1)) M)) N_1)))) (forall ((U tptp.nat) (Ma tptp.nat) (N tptp.nat) (J_2 tptp.nat) (I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_2) I_2)) (= (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_2) U)) Ma) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_2) U)) N)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat I_2) J_2)) U)) Ma) N)))) (forall ((U tptp.nat) (Ma tptp.nat) (N tptp.nat) (I_2 tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_2) U)) Ma)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_2) U)) N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) I_2)) U)) N)))))) (forall ((U_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_1) U_1)) M)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_1) U_1)) N_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) I_1)) U_1)) N_1))))) (forall ((U tptp.nat) (Ma tptp.nat) (N tptp.nat) (I_2 tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_2)) (= (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_2) U)) Ma) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_2) U)) N)) (= Ma (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) I_2)) U)) N))))) (forall ((U tptp.nat) (Ma tptp.nat) (N tptp.nat) (J_2 tptp.nat) (I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_2) I_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_2) U)) Ma)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_2) U)) N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat I_2) J_2)) U)) Ma)) N))))) (forall ((N_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.number_number_of_int N_1))) (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.number_number_of_int (tptp.bit0 N_1)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.number_number_of_int (tptp.bit1 N_1)))))))) (forall ((X_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu820444569sum2sq X_2)) (exists ((A_3 tptp.int) (B_3 tptp.int)) (= (tptp.twoSqu949963151sum2sq (tptp.product_Pair_int_int A_3 B_3)) X_2)))) (forall ((P_5 tptp.bool) (P_2 tptp.bool) (X_2 tptp.int)) (let ((_let_1 (tptp.hBOOL P_5))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)))) (let ((_let_3 (tptp.hBOOL P_2))) (=> (=> _let_2 (= _let_3 _let_1)) (= (=> _let_2 _let_3) (=> _let_2 _let_1))))))) (forall ((P_5 tptp.bool) (P_2 tptp.bool) (X_2 tptp.int)) (let ((_let_1 (tptp.hBOOL P_5))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)))) (let ((_let_3 (tptp.hBOOL P_2))) (=> (=> _let_2 (= _let_3 _let_1)) (= (and _let_2 _let_3) (and _let_2 _let_1))))))) (forall ((Ma tptp.int) (Ta tptp.int) (K tptp.int)) (let ((_let_1 (tptp.times_times_int K))) (=> (not (= K tptp.zero_zero_int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Ma) Ta)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int _let_1 Ma)) (tptp.hAPP_int_int _let_1 Ta))))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_3 _let_2)) (forall ((K tptp.int) (P_2 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 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_2 X)) (tptp.hBOOL (tptp.hAPP_int_bool P_2 (tptp.hAPP_int_int (tptp.minus_minus_int X) D))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (forall ((X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_2 X)) (tptp.hBOOL (tptp.hAPP_int_bool P_2 (tptp.hAPP_int_int (tptp.minus_minus_int X) (tptp.hAPP_int_int (tptp.times_times_int K) D)))))))))) (forall ((K tptp.int) (P_2 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 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_2 X)) (tptp.hBOOL (tptp.hAPP_int_bool P_2 (tptp.hAPP_int_int (tptp.plus_plus_int X) D))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (forall ((X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_2 X)) (tptp.hBOOL (tptp.hAPP_int_bool P_2 (tptp.hAPP_int_int (tptp.plus_plus_int X) (tptp.hAPP_int_int (tptp.times_times_int K) D)))))))))) (forall ((A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A)) (exists ((P_4 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_4)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_4) A)))))) (forall ((A tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) M)) (exists ((X tptp.int)) (and (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 A X) M)) (forall ((Y tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A Y) M))) (= Y X))))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) (tptp.hAPP_int_int (tptp.minus_minus_int B) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) B)))) (forall ((P_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.zfact (tptp.hAPP_int_int (tptp.minus_minus_int P_1) tptp.one_one_int)) (tptp.number_number_of_int tptp.min)) P_1)))) (forall ((N_1 tptp.int)) (let ((_let_1 (tptp.zfact N_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int N_1) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.hAPP_int_int (tptp.times_times_int N_1) (tptp.zfact (tptp.hAPP_int_int (tptp.minus_minus_int N_1) tptp.one_one_int))))))))) (forall ((A tptp.int) (P_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int (tptp.bit1 (tptp.bit0 (tptp.bit1 tptp.pls))))) P_1)) (=> (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_1)) (= (tptp.inv P_1 (tptp.inv P_1 A)) A)))))) (forall ((J_1 tptp.int) (A tptp.int) (P_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_1)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A tptp.zero_zero_int) P_1))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 tptp.zero_zero_int) P_1))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.quadRes P_1) A))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 (tptp.hAPP_int_int (tptp.times_times_int A) (tptp.multInv P_1 J_1))) P_1))))))))) (forall ((J_1 tptp.int) (K_1 tptp.int) (A tptp.int) (P_1 tptp.int)) (let ((_let_1 (tptp.times_times_int (tptp.multInv P_1 J_1)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int J_1) K_1) A) P_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_1 J_1)) K_1) (tptp.hAPP_int_int _let_1 A)) P_1))))) (forall ((J_1 tptp.int) (A tptp.int) (P_1 tptp.int) (K_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.times_times_int A) (tptp.multInv P_1 K_1)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 _let_1) P_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int J_1) K_1) (tptp.hAPP_int_int (tptp.times_times_int _let_1) K_1)) P_1))))) (forall ((A tptp.int) (P_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) (tptp.hAPP_int_int (tptp.minus_minus_int P_1) tptp.one_one_int))) (not (= A (tptp.inv P_1 A))))))) (forall ((A tptp.int) (P_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) (tptp.hAPP_int_int (tptp.minus_minus_int P_1) tptp.one_one_int))) (not (= (tptp.inv P_1 A) tptp.one_one_int)))))) (forall ((A tptp.int) (P_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.minus_minus_int P_1) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) _let_1)) (not (= (tptp.inv P_1 A) _let_1))))))) (forall ((A tptp.int) (P_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) (tptp.hAPP_int_int (tptp.minus_minus_int P_1) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.inv P_1 A)))))))) (forall ((A tptp.int) (P_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.minus_minus_int P_1) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.inv P_1 A)) _let_1))))))) (forall ((X_1 tptp.int) (Y_1 tptp.int) (P_1 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_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 Y_1) P_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.multInv P_1 X_1) (tptp.multInv P_1 Y_1)) P_1))))) (forall ((A tptp.int) (P_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) (tptp.hAPP_int_int (tptp.minus_minus_int P_1) tptp.one_one_int))) (not (= (tptp.inv P_1 A) tptp.zero_zero_int)))))) (forall ((A tptp.int) (J_1 tptp.int) (K_1 tptp.int) (P_1 tptp.int)) (let ((_let_1 (tptp.times_times_int A))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 K_1) P_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int _let_1 (tptp.multInv P_1 J_1)) (tptp.hAPP_int_int _let_1 (tptp.multInv P_1 K_1))) P_1)))))) (forall ((Y_1 tptp.int) (X_1 tptp.int) (P_1 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_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_1))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong Y_1 tptp.zero_zero_int) P_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.multInv P_1 X_1) (tptp.multInv P_1 Y_1)) P_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 Y_1) P_1)))))))) (forall ((X_1 tptp.int) (P_1 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_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.multInv P_1 (tptp.multInv P_1 X_1)) X_1) P_1)))))) (forall ((X_1 tptp.int) (P_1 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_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_1))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.multInv P_1 X_1) tptp.zero_zero_int) P_1))))))) (forall ((A tptp.int) (P_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (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_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int A) (tptp.inv P_1 A)) tptp.one_one_int) P_1)))))) (forall ((K_1 tptp.int) (A tptp.int) (J_1 tptp.int) (P_1 tptp.int)) (let ((_let_1 (tptp.multInv P_1 J_1))) (let ((_let_2 (tptp.times_times_int _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 tptp.zero_zero_int) P_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int _let_2 J_1)) K_1) (tptp.hAPP_int_int _let_2 A)) P_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong K_1 (tptp.hAPP_int_int (tptp.times_times_int A) _let_1)) P_1))))))))) (forall ((J_1 tptp.int) (A tptp.int) (K_1 tptp.int) (P_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.times_times_int J_1) K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong K_1 tptp.zero_zero_int) P_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong _let_1 (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.times_times_int A) (tptp.multInv P_1 K_1))) K_1)) P_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong _let_1 A) P_1)))))))) (forall ((A tptp.int) (J_1 tptp.int) (K_1 tptp.int) (P_1 tptp.int)) (let ((_let_1 (tptp.times_times_int A))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong K_1 tptp.zero_zero_int) P_1))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 tptp.zero_zero_int) P_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 (tptp.hAPP_int_int _let_1 (tptp.multInv P_1 K_1))) P_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong K_1 (tptp.hAPP_int_int _let_1 (tptp.multInv P_1 J_1))) P_1))))))))) (forall ((J_1 tptp.int) (K_1 tptp.int) (A tptp.int) (P_1 tptp.int)) (let ((_let_1 (tptp.times_times_int A))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A tptp.zero_zero_int) P_1))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong K_1 tptp.zero_zero_int) P_1))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 tptp.zero_zero_int) P_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int _let_1 (tptp.multInv P_1 J_1)) (tptp.hAPP_int_int _let_1 (tptp.multInv P_1 K_1))) P_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong J_1 K_1) P_1)))))))))) (forall ((X_1 tptp.int) (P_1 tptp.int)) (let ((_let_1 (tptp.multInv P_1 X_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.times_times_int X_1) _let_1)) (tptp.multInv P_1 _let_1)) X_1) P_1))))))) (forall ((X_1 tptp.int) (P_1 tptp.int)) (let ((_let_1 (tptp.multInv P_1 X_1))) (let ((_let_2 (tptp.multInv P_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) P_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong _let_2 (tptp.hAPP_int_int (tptp.times_times_int (tptp.hAPP_int_int (tptp.times_times_int X_1) _let_1)) _let_2)) P_1)))))))) (forall ((X_1 tptp.int) (P_1 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_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int (tptp.multInv P_1 X_1)) X_1) tptp.one_one_int) P_1)))))) (forall ((X_1 tptp.int) (P_1 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_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_1)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 tptp.zero_zero_int) P_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int X_1) (tptp.multInv P_1 X_1)) tptp.one_one_int) P_1)))))) (forall ((B_2 tptp.int) (A_2 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.wset A_2 P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int (tptp.bit1 (tptp.bit0 (tptp.bit1 tptp.pls))))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) (tptp.hAPP_int_int (tptp.minus_minus_int P_3) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.member_int B_2 _let_1)) (tptp.hBOOL (tptp.member_int (tptp.inv P_3 B_2) _let_1)))))))) (forall ((B_2 tptp.int) (A_2 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.wset A_2 P_3))) (let ((_let_2 (tptp.hAPP_int_int (tptp.minus_minus_int P_3) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int (tptp.bit1 (tptp.bit0 (tptp.bit1 tptp.pls))))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) _let_2)) (=> (tptp.hBOOL (tptp.member_int (tptp.inv P_3 B_2) _let_1)) (tptp.hBOOL (tptp.member_int B_2 _let_1))))))))))) (forall ((P_3 tptp.int) (A_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_2)) (tptp.hBOOL (tptp.member_int A_2 (tptp.wset A_2 P_3))))) (forall ((B_2 tptp.int) (P_3 tptp.int) (A_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_2)) (=> (tptp.hBOOL (tptp.member_int B_2 (tptp.wset (tptp.hAPP_int_int (tptp.minus_minus_int A_2) tptp.one_one_int) P_3))) (tptp.hBOOL (tptp.member_int B_2 (tptp.wset A_2 P_3)))))) (forall ((B_2 tptp.int) (A_2 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.minus_minus_int P_3) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) _let_1)) (=> (tptp.hBOOL (tptp.member_int B_2 (tptp.wset A_2 P_3))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) _let_1))))))) (forall ((B_2 tptp.int) (A_2 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) (tptp.hAPP_int_int (tptp.minus_minus_int P_3) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.member_int B_2 (tptp.wset A_2 P_3))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B_2)))))) (forall ((B_2 tptp.int) (P_3 tptp.int) (A_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_2)) (=> (not (tptp.hBOOL (tptp.member_int B_2 (tptp.wset (tptp.hAPP_int_int (tptp.minus_minus_int A_2) tptp.one_one_int) P_3)))) (=> (tptp.hBOOL (tptp.member_int B_2 (tptp.wset A_2 P_3))) (or (= B_2 A_2) (= B_2 (tptp.inv P_3 A_2))))))) (forall ((B_2 tptp.int) (A_2 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) (tptp.hAPP_int_int (tptp.minus_minus_int P_3) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) A_2)) (tptp.hBOOL (tptp.member_int B_2 (tptp.wset A_2 P_3)))))))) (forall ((P_2 tptp.fun_int_bool) (I_2 tptp.int) (K tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_2) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_2 K)) (=> (forall ((I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_2 I)) (tptp.hBOOL (tptp.hAPP_int_bool P_2 (tptp.hAPP_int_int (tptp.minus_minus_int I) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool P_2 I_2)))))) (forall ((P_2 tptp.fun_int_bool) (I_2 tptp.int) (K tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_2) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_2 (tptp.hAPP_int_int (tptp.minus_minus_int K) tptp.one_one_int))) (=> (forall ((I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_2 I)) (tptp.hBOOL (tptp.hAPP_int_bool P_2 (tptp.hAPP_int_int (tptp.minus_minus_int I) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool P_2 I_2)))))) (forall ((X_2 tptp.int) (P_2 tptp.fun_int_bool)) (=> (forall ((A_3 tptp.int)) (=> (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_3)) (tptp.hBOOL (tptp.hAPP_int_bool P_2 (tptp.hAPP_int_int (tptp.minus_minus_int A_3) tptp.one_one_int)))) (tptp.hBOOL (tptp.hAPP_int_bool P_2 A_3)))) (tptp.hBOOL (tptp.hAPP_int_bool P_2 X_2)))) (forall ((P_2 tptp.fun_int_bool) (K tptp.int) (I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) I_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_2 K)) (=> (forall ((I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) I)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_2 I)) (tptp.hBOOL (tptp.hAPP_int_bool P_2 (tptp.hAPP_int_int (tptp.plus_plus_int I) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool P_2 I_2)))))) (forall ((P_2 tptp.fun_int_bool) (K tptp.int) (I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) I_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_2 (tptp.hAPP_int_int (tptp.plus_plus_int K) tptp.one_one_int))) (=> (forall ((I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) I)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_2 I)) (tptp.hBOOL (tptp.hAPP_int_bool P_2 (tptp.hAPP_int_int (tptp.plus_plus_int I) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool P_2 I_2)))))) (forall ((Ma tptp.nat) (K tptp.nat) (F_1 tptp.fun_nat_nat)) (=> (forall ((M_2 tptp.nat) (N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat F_1 M_2)) (tptp.hAPP_nat_nat F_1 N_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat F_1 Ma)) K)) (tptp.hAPP_nat_nat F_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat Ma) K)))))) (forall ((P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.minus_minus_int P_3) (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (= (tptp.d22set _let_1) (tptp.wset _let_1 P_3))))) (forall ((N tptp.nat) (P_2 tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool P_2 tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_2 N)) (exists ((K_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) N)) (forall ((I tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) K_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool P_2 I))))) (tptp.hBOOL (tptp.hAPP_nat_bool P_2 K_2))))))) (forall ((B_2 tptp.int) (A_2 tptp.int)) (=> (tptp.hBOOL (tptp.member_int B_2 (tptp.d22set A_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) A_2)))) (forall ((A_2 tptp.int) (B_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) B_2)) (not (tptp.hBOOL (tptp.member_int B_2 (tptp.d22set A_2)))))) (forall ((B_2 tptp.int) (A_2 tptp.int)) (=> (tptp.hBOOL (tptp.member_int B_2 (tptp.d22set A_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B_2)))) (forall ((A_2 tptp.int) (B_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) A_2)) (tptp.hBOOL (tptp.member_int B_2 (tptp.d22set A_2)))))) (forall ((I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J_1)) (exists ((K_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_2)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) K_2) J_1))))) (forall ((A_2 tptp.int) (B_2 tptp.int) (N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.power_power_int A_2) N)) (tptp.hAPP_nat_int (tptp.power_power_int B_2) N))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_2) B_2))))) (forall ((A tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A)) (= A tptp.zero_zero_nat))) (forall ((A_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A_2)) (= A_2 tptp.zero_zero_nat))) (forall ((A_2 tptp.nat)) (= (not (= A_2 tptp.zero_zero_nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_2) tptp.zero_zero_nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A_2)))))) (forall ((A tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) tptp.zero_zero_nat))) (forall ((A tptp.nat)) (not (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))))) (forall ((A tptp.nat)) (not (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.one_one_nat) A)))))) (forall ((A tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.one_one_nat) A))) (forall ((A_2 tptp.nat)) (= (not (= A_2 tptp.one_one_nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.one_one_nat) A_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_2) tptp.one_one_nat)))))) (forall ((A_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_2) tptp.one_one_nat)) (= A_2 tptp.one_one_nat))) (forall ((A tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= A tptp.one_one_nat))) (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)))))) (forall ((A_2 tptp.nat) (B_2 tptp.nat) (N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.power_power_nat A_2) N)) (tptp.hAPP_nat_nat (tptp.power_power_nat B_2) N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_2) B_2))))) (forall ((A tptp.int) (N_1 tptp.nat) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.power_power_int A) N_1)) (tptp.hAPP_nat_int (tptp.power_power_int B) N_1))) (=> (not (= N_1 tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A) B))))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M) N_1)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (= N_1 tptp.zero_zero_nat)))) (forall ((N_1 tptp.nat) (M tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (=> (= (tptp.hAPP_nat_nat _let_1 N_1) (tptp.hAPP_nat_nat _let_1 M)) (= N_1 M))))) (forall ((P_3 tptp.int)) (= (tptp.sr P_3) (tptp.collect_int (tptp.cOMBS_int_bool_bool (tptp.cOMBB_1652995168ol_int tptp.fconj (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int)) (tptp.cOMBC_int_int_bool tptp.ord_less_int P_3))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.plus_plus_int tptp.one_one_int) (tptp.hAPP_int_int _let_1 B))) (tptp.hAPP_int_int _let_1 A)) (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.plus_plus_int B) tptp.one_one_int)) A))) tptp.one_one_int))))) (forall ((V tptp.int) (W tptp.int)) (let ((_let_1 (tptp.number_number_of_int W))) (let ((_let_2 (tptp.number_number_of_int V))) (let ((_let_3 (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))))) (let ((_let_4 (tptp.hAPP_int_int (tptp.div_mod_int (tptp.number_number_of_int (tptp.bit1 V))) (tptp.number_number_of_int (tptp.bit0 W))))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_1)))) (and (=> _let_5 (= _let_4 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_3 (tptp.hAPP_int_int (tptp.div_mod_int _let_2) _let_1))) tptp.one_one_int))) (=> (not _let_5) (= _let_4 (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int _let_3 (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1))) tptp.one_one_int)))))))))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.number_number_of_int X_2))) (let ((_let_2 (tptp.number_number_of_int Y_2))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int _let_1) _let_2)) (= (tptp.hAPP_int_int (tptp.div_mod_int _let_2) _let_1) tptp.zero_zero_int))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.div_mod_int A) B)))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.div_mod_int A) B)) B)))) (forall ((Y_1 tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.div_mod_int X_1) Y_1))))))) (forall ((K_1 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.div_mod_int M) K_1)) M)))) (forall ((Ma tptp.int) (D tptp.int)) (= (= (tptp.hAPP_int_int (tptp.div_mod_int Ma) D) tptp.zero_zero_int) (exists ((Q_2 tptp.int)) (= Ma (tptp.hAPP_int_int (tptp.times_times_int D) Q_2))))) (forall ((X_2 tptp.int) (N tptp.int) (Y_2 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.div_mod_int X_2) N) (tptp.hAPP_int_int (tptp.div_mod_int Y_2) N)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int N) (tptp.hAPP_int_int (tptp.minus_minus_int X_2) Y_2))))) (forall ((X_1 tptp.int) (M tptp.int) (Y_1 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.div_mod_int X_1) M) (tptp.hAPP_int_int (tptp.div_mod_int Y_1) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 Y_1) M)))) (forall ((X_1 tptp.int) (M tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 (tptp.hAPP_int_int (tptp.div_mod_int X_1) M)) M))) (forall ((A_2 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 B_2) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.div_mod_int A_2) Ma) (tptp.hAPP_int_int (tptp.div_mod_int B_2) Ma)) Ma)))) (forall ((K_1 tptp.int) (M tptp.int) (N_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.div_mod_int M) N_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)))))) (forall ((N_1 tptp.int) (F tptp.int) (M tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int F))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.div_mod_int M) N_1))))))) (forall ((X_1 tptp.int) (M tptp.int) (Y_1 tptp.nat)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_nat_int (tptp.power_power_int (tptp.hAPP_int_int (tptp.div_mod_int X_1) M)) Y_1)) M) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_nat_int (tptp.power_power_int X_1) Y_1)) M))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.times_times_int A))) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 B)) C) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int B) C))) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.times_times_int A))) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int B) C))) C) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 B)) C)))) (forall ((A tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A) A) tptp.zero_zero_int)) (forall ((B tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int tptp.zero_zero_int) B) tptp.zero_zero_int)) (forall ((X_1 tptp.int) (Y_1 tptp.int) (M tptp.int)) (let ((_let_1 (tptp.minus_minus_int X_1))) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int Y_1) M))) M) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 Y_1)) M)))) (forall ((X_1 tptp.int) (M tptp.int) (Y_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.minus_minus_int (tptp.hAPP_int_int (tptp.div_mod_int X_1) M)) Y_1)) M) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.minus_minus_int X_1) Y_1)) M))) (forall ((A tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A) (tptp.number_number_of_int tptp.min)) tptp.zero_zero_int)) (forall ((A tptp.int) (B tptp.int) (M tptp.int)) (let ((_let_1 (tptp.div_mod_int A))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int M) B)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 B)) M) (tptp.hAPP_int_int _let_1 M)))))) (forall ((A_2 tptp.int) (B_2 tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Ma)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong A_2 B_2) Ma)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_2) Ma) (tptp.hAPP_int_int (tptp.div_mod_int B_2) Ma))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.div_mod_int A) B))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.div_mod_int A) B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) B)))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) B)) (= (tptp.hAPP_int_int (tptp.div_mod_int A) B) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.div_mod_int A) B)) tptp.zero_zero_int)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.div_mod_int A) B))) (let ((_let_2 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_2 tptp.zero_zero_int)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int _let_1) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_2 _let_1))))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) A)) (= (tptp.hAPP_int_int (tptp.div_mod_int A) B) A)))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.plus_plus_int A) B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int _let_1) tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A) B) _let_1))))) (forall ((V tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.number_number_of_int (tptp.bit0 V))) (tptp.number_number_of_int (tptp.bit0 W))) (tptp.hAPP_int_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.number_number_of_int V)) (tptp.number_number_of_int W))))) (forall ((P_2 tptp.fun_int_bool) (N tptp.int) (K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool P_2 (tptp.hAPP_int_int (tptp.div_mod_int N) K))) (and (=> (= K tptp.zero_zero_int) (tptp.hBOOL (tptp.hAPP_int_bool P_2 N))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) K)) (forall ((I tptp.int) (J tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) J)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int J) K)) (= N (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int K) I)) J))) (tptp.hBOOL (tptp.hAPP_int_bool P_2 J))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) tptp.zero_zero_int)) (forall ((I tptp.int) (J tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) J)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int J) tptp.zero_zero_int)) (= N (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int K) I)) J))) (tptp.hBOOL (tptp.hAPP_int_bool P_2 J)))))))) (forall ((Q_1 tptp.int) (B tptp.int) (R_1 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 R_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_1) B)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B) (tptp.hAPP_int_int (tptp.div_mod_int Q_1) C))) R_1)))))))) (forall ((Q_1 tptp.int) (B tptp.int) (R_1 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.times_times_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_1) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int Q_1) C))) R_1)) (tptp.hAPP_int_int _let_1 C)))))))) (forall ((Q_1 tptp.int) (B tptp.int) (R_1 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.times_times_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) R_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int R_1) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 C)) (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int Q_1) C))) R_1)))))))) (forall ((Q_1 tptp.int) (B tptp.int) (R_1 tptp.int) (C tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) R_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int R_1) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B) (tptp.hAPP_int_int (tptp.div_mod_int Q_1) C))) R_1)) tptp.zero_zero_int)))))) (forall ((A_1 tptp.int) (B_1 tptp.int) (Q_3 tptp.int) (Y_1 tptp.int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_1)))) (=> (= A_1 (tptp.hAPP_int_int (tptp.plus_plus_int (tptp.hAPP_int_int (tptp.times_times_int B_1) Q_3)) Y_1)) (=> (and (=> _let_1 (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) B_1)))) (=> (not _let_1) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_1) Y_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_1) tptp.zero_zero_int))))) (=> (not (= B_1 tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_1) B_1) Y_1)))))) (forall ((X_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.div_mod_int X_2) (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))) (forall ((B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.number_number_of_int tptp.min)) B) (tptp.hAPP_int_int (tptp.minus_minus_int B) tptp.one_one_int)))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.plus_plus_int tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 B))) (tptp.hAPP_int_int _let_1 A)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int B) A)))))))) (forall ((M_1 tptp.int) (D_1 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.div_mod_int M_1) D_1) tptp.zero_zero_int) (exists ((Q_2 tptp.int)) (= M_1 (tptp.hAPP_int_int (tptp.times_times_int D_1) Q_2))))) (forall ((X_1 tptp.int) (Y_1 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int (tptp.bit0 (tptp.bit1 tptp.pls)))) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong (tptp.hAPP_int_int (tptp.times_times_int (tptp.standardRes M X_1)) (tptp.standardRes M Y_1)) (tptp.hAPP_int_int (tptp.times_times_int X_1) Y_1)) M)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1)) N_1)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1)) N_1)))) (forall ((Ma tptp.nat) (D tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.div_mod_nat Ma) D) tptp.zero_zero_nat) (exists ((Q_2 tptp.nat)) (= Ma (tptp.hAPP_nat_nat (tptp.times_times_nat D) Q_2))))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1))) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) N_1)))) (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1)))) (and (=> _let_2 (= _let_1 M)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) N_1))))))) (forall ((K_1 tptp.nat) (N_1 tptp.nat) (M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat K_1) N_1)) M)) N_1) (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1))) (forall ((N_1 tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N_1)) N_1)))) (forall ((M tptp.int) (X_1 tptp.int)) (= (tptp.standardRes M X_1) (tptp.hAPP_int_int (tptp.div_mod_int X_1) M))) (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1)) K_1) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.times_times_nat M) K_1)) (tptp.hAPP_nat_nat (tptp.times_times_nat N_1) K_1)))) (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat K_1))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1)) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N_1))))) (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1) M))) (forall ((M tptp.nat) (N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N_1)) M))) (forall ((Ma tptp.int) (X_2 tptp.int)) (= (= (tptp.standardRes Ma X_2) tptp.zero_zero_int) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_2 tptp.zero_zero_int) Ma)))) (forall ((X_2 tptp.int) (P_3 tptp.int)) (= (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_2 tptp.zero_zero_int) P_3))) (not (= (tptp.standardRes P_3 X_2) tptp.zero_zero_int)))) (forall ((X_1 tptp.int) (M tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X_1 (tptp.standardRes M X_1)) M))) (forall ((X_1 tptp.int) (P_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) P_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.standardRes P_1 X_1)) P_1)))) (forall ((X_2 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.member_int X_2 (tptp.sr P_3))) (= (tptp.standardRes P_3 X_2) X_2))) (forall ((P_2 tptp.fun_nat_bool) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (= K tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool P_2 (tptp.hAPP_nat_nat (tptp.div_mod_nat N) K))) (and (=> _let_1 (tptp.hBOOL (tptp.hAPP_nat_bool P_2 N))) (=> (not _let_1) (forall ((I tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J) K)) (=> (= N (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat K) I)) J)) (tptp.hBOOL (tptp.hAPP_nat_bool P_2 J)))))))))) (forall ((Q_1 tptp.nat) (R_1 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.times_times_nat B))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat R_1) B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat Q_1) C))) R_1)) (tptp.hAPP_nat_nat _let_1 C))))))) (forall ((X_1 tptp.int) (P_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) P_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.standardRes P_1 X_1))))) (forall ((X1 tptp.int) (X2 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.standardRes Ma X1) (tptp.standardRes Ma X2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.zcong X1 X2) Ma))))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((P tptp.fun_int_fun_int_bool) (Q tptp.int) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.cOMBC_int_int_bool P Q) R) (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P R) Q))) (forall ((P tptp.fun_in531499254l_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.cOMBS_int_bool_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_i68813070l_bool P R) (tptp.hAPP_int_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_i68813070l_bool (tptp.cOMBB_1652995168ol_int P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_int_bool Q R)))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.65/1.86  )
% 1.65/1.86  % SZS output end Proof for NUM926_3
% 1.65/1.86  % cvc5---1.0.5 exiting
% 1.65/1.86  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------