TSTP Solution File: NUM924+7 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM924+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:10:15 EDT 2022
% Result : Unknown 32.57s 32.39s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM924+7 : TPTP v8.1.0. Released v5.3.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 09:34:21 EDT 2022
% 0.13/0.33 % CPUTime :
% 32.46/32.32 ----- Otter 3.3f, August 2004 -----
% 32.46/32.32 The process was started by sandbox2 on n009.cluster.edu,
% 32.46/32.32 Wed Jul 27 09:34:21 2022
% 32.46/32.32 The command was "./otter". The process ID is 22169.
% 32.46/32.32
% 32.46/32.32 set(prolog_style_variables).
% 32.46/32.32 set(auto).
% 32.46/32.32 dependent: set(auto1).
% 32.46/32.32 dependent: set(process_input).
% 32.46/32.32 dependent: clear(print_kept).
% 32.46/32.32 dependent: clear(print_new_demod).
% 32.46/32.32 dependent: clear(print_back_demod).
% 32.46/32.32 dependent: clear(print_back_sub).
% 32.46/32.32 dependent: set(control_memory).
% 32.46/32.32 dependent: assign(max_mem, 12000).
% 32.46/32.32 dependent: assign(pick_given_ratio, 4).
% 32.46/32.32 dependent: assign(stats_level, 1).
% 32.46/32.32 dependent: assign(max_seconds, 10800).
% 32.46/32.32 clear(print_given).
% 32.46/32.32
% 32.46/32.32 formula_list(usable).
% 32.46/32.32 all A (A=A).
% 32.46/32.32 all X_b X_c X_a B_1_1 B_2_1 (combb(X_b,X_c,X_a,ti(fun(X_b,X_c),B_1_1),B_2_1)=combb(X_b,X_c,X_a,B_1_1,B_2_1)).
% 32.46/32.32 all X_b X_c X_a B_1_1 B_2_1 (combb(X_b,X_c,X_a,B_1_1,ti(fun(X_a,X_b),B_2_1))=combb(X_b,X_c,X_a,B_1_1,B_2_1)).
% 32.46/32.32 all X_a X_c X_b B_1_1 B_2_1 (ti(fun(X_a,X_c),combb(X_b,X_c,X_a,B_1_1,B_2_1))=combb(X_b,X_c,X_a,B_1_1,B_2_1)).
% 32.46/32.32 all X_a X_b X_c B_1_1 B_2_1 (combc(X_a,X_b,X_c,ti(fun(X_a,fun(X_b,X_c)),B_1_1),B_2_1)=combc(X_a,X_b,X_c,B_1_1,B_2_1)).
% 32.46/32.32 all X_a X_b X_c B_1_1 B_2_1 (combc(X_a,X_b,X_c,B_1_1,ti(X_b,B_2_1))=combc(X_a,X_b,X_c,B_1_1,B_2_1)).
% 32.46/32.32 all X_a X_c X_b B_1_1 B_2_1 (ti(fun(X_a,X_c),combc(X_a,X_b,X_c,B_1_1,B_2_1))=combc(X_a,X_b,X_c,B_1_1,B_2_1)).
% 32.46/32.32 all X_a X_b X_c B_1_1 B_2_1 (combs(X_a,X_b,X_c,ti(fun(X_a,fun(X_b,X_c)),B_1_1),B_2_1)=combs(X_a,X_b,X_c,B_1_1,B_2_1)).
% 32.46/32.32 all X_a X_b X_c B_1_1 B_2_1 (combs(X_a,X_b,X_c,B_1_1,ti(fun(X_a,X_b),B_2_1))=combs(X_a,X_b,X_c,B_1_1,B_2_1)).
% 32.46/32.32 all X_a X_c X_b B_1_1 B_2_1 (ti(fun(X_a,X_c),combs(X_a,X_b,X_c,B_1_1,B_2_1))=combs(X_a,X_b,X_c,B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 X_a (semiring_div(X_a)->div_mod(X_a,ti(X_a,B_1_1))=div_mod(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (semiring_div(X_a)->ti(fun(X_a,X_a),div_mod(X_a,B_1_1))=div_mod(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (group_add(X_a)->minus_minus(X_a,ti(X_a,B_1_1))=minus_minus(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (group_add(X_a)->ti(fun(X_a,X_a),minus_minus(X_a,B_1_1))=minus_minus(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 (minus_minus(nat,ti(nat,B_1_1))=minus_minus(nat,B_1_1)).
% 32.46/32.32 all B_1_1 (ti(fun(nat,nat),minus_minus(nat,B_1_1))=minus_minus(nat,B_1_1)).
% 32.46/32.32 all X_a (one(X_a)->ti(X_a,one_one(X_a))=one_one(X_a)).
% 32.46/32.32 all B_1_1 X_a (plus(X_a)&linorder(X_a)&dvd(X_a)->plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (plus(X_a)&linorder(X_a)&dvd(X_a)->ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (monoid_add(X_a)->plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (monoid_add(X_a)->ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (cancel_semigroup_add(X_a)->plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (cancel_semigroup_add(X_a)->ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (ab_semigroup_add(X_a)->plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (ab_semigroup_add(X_a)->ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (ab_semigroup_mult(X_a)->times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (ab_semigroup_mult(X_a)->ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (power(X_a)->times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (power(X_a)->ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (dvd(X_a)->times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (dvd(X_a)->ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (semiring(X_a)->times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (semiring(X_a)->ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (mult_zero(X_a)->times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (mult_zero(X_a)->ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (no_zero_divisors(X_a)->times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (no_zero_divisors(X_a)->ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1)).
% 32.46/32.32 all X_a (zero(X_a)->ti(X_a,zero_zero(X_a))=zero_zero(X_a)).
% 32.46/32.32 all X_a (ti(X_a,undefined(X_a))=undefined(X_a)).
% 32.46/32.32 all B_1_1 B_2_1 (multInv(ti(int,B_1_1),B_2_1)=multInv(B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 B_2_1 (multInv(B_1_1,ti(int,B_2_1))=multInv(B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 B_2_1 (ti(int,multInv(B_1_1,B_2_1))=multInv(B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 (d22set(ti(int,B_1_1))=d22set(B_1_1)).
% 32.46/32.32 all B_1_1 (ti(fun(int,bool),d22set(B_1_1))=d22set(B_1_1)).
% 32.46/32.32 all B_1_1 (zfact(ti(int,B_1_1))=zfact(B_1_1)).
% 32.46/32.32 all B_1_1 (ti(int,zfact(B_1_1))=zfact(B_1_1)).
% 32.46/32.32 all B_1_1 B_2_1 (zcong(ti(int,B_1_1),B_2_1)=zcong(B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 B_2_1 (zcong(B_1_1,ti(int,B_2_1))=zcong(B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 B_2_1 (ti(fun(int,bool),zcong(B_1_1,B_2_1))=zcong(B_1_1,B_2_1)).
% 32.46/32.32 ti(fun(int,bool),zprime)=zprime.
% 32.46/32.32 all B_1_1 (bit0(ti(int,B_1_1))=bit0(B_1_1)).
% 32.46/32.32 all B_1_1 (ti(int,bit0(B_1_1))=bit0(B_1_1)).
% 32.46/32.32 all B_1_1 (bit1(ti(int,B_1_1))=bit1(B_1_1)).
% 32.46/32.32 all B_1_1 (ti(int,bit1(B_1_1))=bit1(B_1_1)).
% 32.46/32.32 ti(int,min)=min.
% 32.46/32.32 ti(int,pls)=pls.
% 32.46/32.32 all B_1_1 X_a (number(X_a)->number_number_of(X_a,ti(int,B_1_1))=number_number_of(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (number(X_a)->ti(X_a,number_number_of(X_a,B_1_1))=number_number_of(X_a,B_1_1)).
% 32.46/32.32 all X_a (order(X_a)->ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a)).
% 32.46/32.32 all X_a (order(X_a)->ti(fun(X_a,fun(X_a,bool)),ord_less_e_q(X_a))=ord_less_e_q(X_a)).
% 32.46/32.32 all B_1_1 X_a (power(X_a)->power_power(X_a,ti(X_a,B_1_1))=power_power(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 X_a (power(X_a)->ti(fun(nat,X_a),power_power(X_a,B_1_1))=power_power(X_a,B_1_1)).
% 32.46/32.32 all B_1_1 B_2_1 (product_Pair(int,int,ti(int,B_1_1),B_2_1)=product_Pair(int,int,B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 B_2_1 (product_Pair(int,int,B_1_1,ti(int,B_2_1))=product_Pair(int,int,B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 B_2_1 (ti(product_prod(int,int),product_Pair(int,int,B_1_1,B_2_1))=product_Pair(int,int,B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 B_2_1 (legendre(ti(int,B_1_1),B_2_1)=legendre(B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 B_2_1 (legendre(B_1_1,ti(int,B_2_1))=legendre(B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 B_2_1 (ti(int,legendre(B_1_1,B_2_1))=legendre(B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 (quadRes(ti(int,B_1_1))=quadRes(B_1_1)).
% 32.46/32.32 all B_1_1 (ti(fun(int,bool),quadRes(B_1_1))=quadRes(B_1_1)).
% 32.46/32.32 all B_1_1 (sr(ti(int,B_1_1))=sr(B_1_1)).
% 32.46/32.32 all B_1_1 (ti(fun(int,bool),sr(B_1_1))=sr(B_1_1)).
% 32.46/32.32 all B_1_1 B_2_1 (standardRes(ti(int,B_1_1),B_2_1)=standardRes(B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 B_2_1 (standardRes(B_1_1,ti(int,B_2_1))=standardRes(B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 B_2_1 (ti(int,standardRes(B_1_1,B_2_1))=standardRes(B_1_1,B_2_1)).
% 32.46/32.32 all X_a (dvd(X_a)->ti(fun(X_a,fun(X_a,bool)),dvd_dvd(X_a))=dvd_dvd(X_a)).
% 32.46/32.32 all X_a B_1_1 (collect(X_a,ti(fun(X_a,bool),B_1_1))=collect(X_a,B_1_1)).
% 32.46/32.32 all X_a B_1_1 (ti(fun(X_a,bool),collect(X_a,B_1_1))=collect(X_a,B_1_1)).
% 32.46/32.32 ti(fun(int,bool),twoSqu658283162sum2sq)=twoSqu658283162sum2sq.
% 32.46/32.32 all B_1_1 (twoSqu1929807760sum2sq(ti(product_prod(int,int),B_1_1))=twoSqu1929807760sum2sq(B_1_1)).
% 32.46/32.32 all B_1_1 (ti(int,twoSqu1929807760sum2sq(B_1_1))=twoSqu1929807760sum2sq(B_1_1)).
% 32.46/32.32 all B_1_1 B_2_1 (inv(ti(int,B_1_1),B_2_1)=inv(B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 B_2_1 (inv(B_1_1,ti(int,B_2_1))=inv(B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 B_2_1 (ti(int,inv(B_1_1,B_2_1))=inv(B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 B_2_1 (wset(ti(int,B_1_1),B_2_1)=wset(B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 B_2_1 (wset(B_1_1,ti(int,B_2_1))=wset(B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 B_2_1 (ti(fun(int,bool),wset(B_1_1,B_2_1))=wset(B_1_1,B_2_1)).
% 32.46/32.32 ti(fun(bool,fun(bool,bool)),fconj)=fconj.
% 32.46/32.32 all X_a X_c B_1_1 B_2_1 (hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1)=hAPP(X_a,X_c,B_1_1,B_2_1)).
% 32.46/32.32 all X_a X_c B_1_1 B_2_1 (hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1))=hAPP(X_a,X_c,B_1_1,B_2_1)).
% 32.46/32.32 all X_c X_a B_1_1 B_2_1 (ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1))=hAPP(X_a,X_c,B_1_1,B_2_1)).
% 32.46/32.32 all B_1_1 (hBOOL(ti(bool,B_1_1))<->hBOOL(B_1_1)).
% 32.46/32.32 all X_a B_1_1 (member(X_a,ti(X_a,B_1_1))=member(X_a,B_1_1)).
% 32.46/32.32 all X_a B_1_1 (ti(fun(fun(X_a,bool),bool),member(X_a,B_1_1))=member(X_a,B_1_1)).
% 32.46/32.32 ti(int,m)=m.
% 32.46/32.32 ti(int,s1)=s1.
% 32.46/32.32 ti(int,s)=s.
% 32.46/32.32 ti(int,t)=t.
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),t),zero_zero(int))).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),t),one_one(int))).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)))).
% 32.46/32.32 hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))=hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t).
% 32.46/32.32 t=zero_zero(int)->hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))=zero_zero(int).
% 32.46/32.32 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),t)).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.46/32.32 all X_a (linordered_idom(X_a)-> (all X_1 Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(X_a)))))).
% 32.46/32.32 all X_a (linordered_idom(X_a)-> (all X Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))))<->ti(X_a,X)!=zero_zero(X_a)|ti(X_a,Y_1)!=zero_zero(X_a)))).
% 32.46/32.32 all X_a (linordered_idom(X_a)-> (all X Y_1 (hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))=zero_zero(X_a)<->ti(X_a,X)=zero_zero(X_a)&ti(X_a,Y_1)=zero_zero(X_a)))).
% 32.46/32.32 all X_a (linordered_idom(X_a)-> (all A_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls))))),zero_zero(X_a)))))).
% 32.46/32.32 all X_a (linordered_idom(X_a)-> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,bit0(bit1(pls))))))<->ti(X_a,A_3)!=zero_zero(X_a)))).
% 32.46/32.32 all X_a (semiring_1(X_a)->hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls))))=one_one(X_a)).
% 32.46/32.32 all X_a (semiring_1(X_a)->hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,bit0(bit1(pls))))=zero_zero(X_a)).
% 32.46/32.32 all X_a (ring_11004092258visors(X_a)-> (all A_3 (hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,bit0(bit1(pls))))=zero_zero(X_a)<->ti(X_a,A_3)=zero_zero(X_a)))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all W (hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,W))=number_number_of(X_a,hAPP(int,int,plus_plus(int,bit1(pls)),W))))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all V (hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),one_one(X_a))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V),bit1(pls)))))).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.46/32.32 -(all T_4 (hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))!=hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),T_4))).
% 32.46/32.32 hBOOL(hAPP(int,bool,zprime,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.46/32.32 hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))).
% 32.46/32.32 all W hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),W)).
% 32.46/32.32 all K_1 (number_number_of(int,K_1)=ti(int,K_1)).
% 32.46/32.32 all Z_1 W (hAPP(int,int,times_times(int,Z_1),W)=hAPP(int,int,times_times(int,W),Z_1)).
% 32.46/32.32 all Z_1 W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z_1))).
% 32.46/32.32 all V W (hAPP(int,int,times_times(int,number_number_of(int,V)),number_number_of(int,W))=number_number_of(int,hAPP(int,int,times_times(int,V),W))).
% 32.46/32.32 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,K)),number_number_of(int,L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L))).
% 32.46/32.32 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X)),number_number_of(X_a,Y_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X),Y_1))))).
% 32.46/32.32 all Z1 Z2 Z3 (hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,Z1),Z2)),Z3)=hAPP(int,int,times_times(int,Z1),hAPP(int,int,times_times(int,Z2),Z3))).
% 32.46/32.32 all K_1 I_1 J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),J_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),J_1),K_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),K_1)))).
% 32.46/32.32 all Z_1 W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z_1))->ti(int,Z_1)=ti(int,W))).
% 32.46/32.32 all X_1 Y Z_1 (hAPP(nat,int,power_power(int,X_1),hAPP(nat,nat,plus_plus(nat,Y),Z_1))=hAPP(int,int,times_times(int,hAPP(nat,int,power_power(int,X_1),Y)),hAPP(nat,int,power_power(int,X_1),Z_1))).
% 32.46/32.32 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K1)),bit1(K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2))).
% 32.46/32.32 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit1(L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L))).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),pls)).
% 32.46/32.32 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K1)),bit0(K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2))).
% 32.46/32.32 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit0(L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L))).
% 32.46/32.32 all Z_2 W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_2),W_1))&ti(int,Z_2)!=ti(int,W_1)).
% 32.46/32.32 all K_1 I_1 J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),J_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,K_1),I_1)),hAPP(int,int,plus_plus(int,K_1),J_1)))).
% 32.46/32.32 all V_3 (number_number_of(nat,V_3)=zero_zero(nat)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_3),pls))).
% 32.46/32.32 all V_3 (zero_zero(nat)=number_number_of(nat,V_3)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_3),pls))).
% 32.46/32.32 all X_a (number_semiring(X_a)-> (all V_1 V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))->hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,V)),number_number_of(X_a,V_1))=number_number_of(X_a,hAPP(int,int,times_times(int,V),V_1)))))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all V W Z_1 (hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,V)),hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,W)),Z_1))=hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,hAPP(int,int,times_times(int,V),W))),Z_1)))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all V W (hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,V)),number_number_of(X_a,W))=number_number_of(X_a,hAPP(int,int,times_times(int,V),W))))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all V W (number_number_of(X_a,hAPP(int,int,times_times(int,V),W))=hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,V)),number_number_of(X_a,W))))).
% 32.46/32.32 all X_a (linord581940658strict(X_a)-> (all X Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X),X)),hAPP(X_a,X_a,times_times(X_a,Y_1),Y_1))),zero_zero(X_a)))<->ti(X_a,X)=zero_zero(X_a)&ti(X_a,Y_1)=zero_zero(X_a)))).
% 32.46/32.32 all X_a (linordered_ring(X_a)-> (all X_1 Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),X_1)),hAPP(X_a,X_a,times_times(X_a,Y),Y)))))).
% 32.46/32.32 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X)),zero_zero(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X),pls))))).
% 32.46/32.32 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),number_number_of(X_a,Y_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),Y_1))))).
% 32.46/32.32 all V_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,V_3)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_3))).
% 32.46/32.32 all X_a (number(X_a)&linorder(X_a)-> (all V_3 W_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,V_3)),number_number_of(X_a,W_1)))<-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,W_1)),number_number_of(X_a,V_3)))))).
% 32.46/32.32 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit1(K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K))).
% 32.46/32.32 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K1)),bit1(K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2))).
% 32.46/32.32 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit1(L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L))).
% 32.46/32.32 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),pls))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),pls))).
% 32.46/32.32 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit0(K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K))).
% 32.46/32.32 all Z_3 Z_1 W_2 W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),W))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_3),Z_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,W_2),Z_3)),hAPP(int,int,plus_plus(int,W),Z_1))))).
% 32.46/32.32 number_number_of(nat,pls)=zero_zero(nat).
% 32.46/32.32 zero_zero(nat)=number_number_of(nat,pls).
% 32.46/32.32 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X)),one_one(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X),bit1(pls)))))).
% 32.46/32.32 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),number_number_of(X_a,Y_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(pls)),Y_1))))).
% 32.46/32.32 hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))=number_number_of(nat,bit0(bit1(pls))).
% 32.46/32.32 all W (hAPP(int,int,times_times(int,pls),W)=pls).
% 32.46/32.32 all K_1 L_1 (hAPP(int,int,times_times(int,bit0(K_1)),L_1)=bit0(hAPP(int,int,times_times(int,K_1),L_1))).
% 32.46/32.32 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,K)),number_number_of(int,L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))).
% 32.46/32.32 all Z_1 (hAPP(int,int,times_times(int,Z_1),one_one(int))=ti(int,Z_1)).
% 32.46/32.32 all Z_1 (hAPP(int,int,times_times(int,one_one(int)),Z_1)=ti(int,Z_1)).
% 32.46/32.32 all V W (hAPP(int,int,plus_plus(int,number_number_of(int,V)),number_number_of(int,W))=number_number_of(int,hAPP(int,int,plus_plus(int,V),W))).
% 32.46/32.32 all Z1 Z2 W (hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,Z1),Z2)),W)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,Z1),W)),hAPP(int,int,times_times(int,Z2),W))).
% 32.46/32.32 all W Z1 Z2 (hAPP(int,int,times_times(int,W),hAPP(int,int,plus_plus(int,Z1),Z2))=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,W),Z1)),hAPP(int,int,times_times(int,W),Z2))).
% 32.46/32.32 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),pls))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls))).
% 32.46/32.32 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit1(K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K))).
% 32.46/32.32 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K1)),bit0(K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2))).
% 32.46/32.32 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit0(L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))).
% 32.46/32.32 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K1)),bit1(K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2))).
% 32.46/32.32 all X_a X A_6 (hBOOL(hAPP(fun(X_a,bool),bool,member(X_a,X),A_6))<->hBOOL(hAPP(X_a,bool,A_6,X))).
% 32.46/32.32 all X_a P_1 (collect(X_a,P_1)=ti(fun(X_a,bool),P_1)).
% 32.46/32.32 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit1(L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L))).
% 32.46/32.32 all V_3 V_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,V_3)),number_number_of(nat,V_2)))<-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_3),V_2))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_2)))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_3),V_2))).
% 32.46/32.32 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_2))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2))).
% 32.46/32.32 number_number_of(nat,bit1(pls))=one_one(nat).
% 32.46/32.32 one_one(nat)=number_number_of(nat,bit1(pls)).
% 32.46/32.32 all W Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,W),one_one(int))),Z_1))).
% 32.46/32.32 all W_1 Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,W_1),one_one(int))),Z_2))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))).
% 32.46/32.32 all W_1 Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_2))).
% 32.46/32.32 all X_a (number_semiring(X_a)-> (all V_1 V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))->hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),number_number_of(X_a,V_1))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V),V_1)))))).
% 32.46/32.32 all V_1 V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=number_number_of(nat,V_1))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=number_number_of(nat,V))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=number_number_of(nat,hAPP(int,int,plus_plus(int,V),V_1))))).
% 32.46/32.32 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),Z_1)))).
% 32.46/32.32 all X_a (number_ring(X_a)&ring_char_0(X_a)-> (all X Y_1 (number_number_of(X_a,X)=number_number_of(X_a,Y_1)<->ti(int,X)=ti(int,Y_1)))).
% 32.46/32.32 all X_a (number(X_a)-> (all W_1 X (number_number_of(X_a,W_1)=ti(X_a,X)<->ti(X_a,X)=number_number_of(X_a,W_1)))).
% 32.46/32.32 all K L (bit1(K)=bit1(L)<->ti(int,K)=ti(int,L)).
% 32.46/32.32 all K L (bit0(K)=bit0(L)<->ti(int,K)=ti(int,L)).
% 32.46/32.32 all X_1 Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))|ti(int,X_1)=ti(int,Y)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1))).
% 32.46/32.32 all X_a (linord581940658strict(X_a)-> (all X Y_1 (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X),X)),hAPP(X_a,X_a,times_times(X_a,Y_1),Y_1))=zero_zero(X_a)<->ti(X_a,X)=zero_zero(X_a)&ti(X_a,Y_1)=zero_zero(X_a)))).
% 32.46/32.32 all X_b (number(X_b)&semiring(X_b)-> (all A_1 B V (hAPP(X_b,X_b,times_times(X_b,hAPP(X_b,X_b,plus_plus(X_b,A_1),B)),number_number_of(X_b,V))=hAPP(X_b,X_b,plus_plus(X_b,hAPP(X_b,X_b,times_times(X_b,A_1),number_number_of(X_b,V))),hAPP(X_b,X_b,times_times(X_b,B),number_number_of(X_b,V)))))).
% 32.46/32.32 all X_b (number(X_b)&semiring(X_b)-> (all V B C (hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),hAPP(X_b,X_b,plus_plus(X_b,B),C))=hAPP(X_b,X_b,plus_plus(X_b,hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),B)),hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),C))))).
% 32.46/32.32 all Z1 Z2 Z3 (hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,Z1),Z2)),Z3)=hAPP(int,int,plus_plus(int,Z1),hAPP(int,int,plus_plus(int,Z2),Z3))).
% 32.46/32.32 all X_1 Y Z_1 (hAPP(int,int,plus_plus(int,X_1),hAPP(int,int,plus_plus(int,Y),Z_1))=hAPP(int,int,plus_plus(int,Y),hAPP(int,int,plus_plus(int,X_1),Z_1))).
% 32.46/32.32 all Z_1 W (hAPP(int,int,plus_plus(int,Z_1),W)=hAPP(int,int,plus_plus(int,W),Z_1)).
% 32.46/32.32 zero_zero(int)=number_number_of(int,pls).
% 32.46/32.32 all K_1 I_1 J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,K_1),I_1)),hAPP(int,int,times_times(int,K_1),J_1))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all X_1 Y (hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))=hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,bit0(bit1(pls))))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))->ti(X_a,X_1)=ti(X_a,Y)))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,bit0(bit1(pls))))))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y)))))).
% 32.46/32.32 all X_a (linordered_idom(X_a)-> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls)))))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,bit0(bit1(pls))))))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)))))).
% 32.46/32.32 all X_a (linordered_idom(X_a)-> (all X Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(X_a)))<->ti(X_a,X)=zero_zero(X_a)&ti(X_a,Y_1)=zero_zero(X_a)))).
% 32.46/32.32 all X_a (linordered_idom(X_a)-> (all X_1 Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,bit0(bit1(pls))))))))).
% 32.46/32.32 all X_a (linord581940658strict(X_a)-> (all X Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X),X)),hAPP(X_a,X_a,times_times(X_a,Y_1),Y_1))))<->ti(X_a,X)!=zero_zero(X_a)|ti(X_a,Y_1)!=zero_zero(X_a)))).
% 32.46/32.32 all X_a (linordered_ring(X_a)-> (all X_1 Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),X_1)),hAPP(X_a,X_a,times_times(X_a,Y),Y))),zero_zero(X_a)))))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit1(pls))),A_1)=ti(X_a,A_1)))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,A_1),number_number_of(X_a,bit1(pls)))=ti(X_a,A_1)))).
% 32.46/32.32 one_one(int)=number_number_of(int,bit1(pls)).
% 32.46/32.32 all K_1 L_1 (hAPP(int,int,times_times(int,bit1(K_1)),L_1)=hAPP(int,int,plus_plus(int,bit0(hAPP(int,int,times_times(int,K_1),L_1))),L_1)).
% 32.46/32.32 all N Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))-> (hAPP(int,int,times_times(int,Ma),N)=one_one(int)<->ti(int,Ma)=one_one(int)&ti(int,N)=one_one(int))).
% 32.46/32.32 all X_a (linord219039673up_add(X_a)-> (all A_3 (hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)=zero_zero(X_a)<->ti(X_a,A_3)=zero_zero(X_a)))).
% 32.46/32.32 all K_1 (bit1(K_1)!=pls).
% 32.46/32.32 all L_1 (pls!=bit1(L_1)).
% 32.46/32.32 all K_1 L_1 (bit1(K_1)!=bit0(L_1)).
% 32.46/32.32 all K_1 L_1 (bit0(K_1)!=bit1(L_1)).
% 32.46/32.32 all K (bit0(K)=pls<->ti(int,K)=pls).
% 32.46/32.32 all L (pls=bit0(L)<->pls=ti(int,L)).
% 32.46/32.32 bit0(pls)=pls.
% 32.46/32.32 pls=zero_zero(int).
% 32.46/32.32 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K1)),bit1(K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2))).
% 32.46/32.32 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit1(L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))).
% 32.46/32.32 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)).
% 32.46/32.32 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K1)),bit0(K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2))).
% 32.46/32.32 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit0(L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))).
% 32.46/32.32 zero_zero(int)!=one_one(int).
% 32.46/32.32 all K_1 (hAPP(int,int,plus_plus(int,K_1),pls)=ti(int,K_1)).
% 32.46/32.32 all K_1 (hAPP(int,int,plus_plus(int,pls),K_1)=ti(int,K_1)).
% 32.46/32.32 all K_1 L_1 (hAPP(int,int,plus_plus(int,bit0(K_1)),bit0(L_1))=bit0(hAPP(int,int,plus_plus(int,K_1),L_1))).
% 32.46/32.32 all K_1 (bit0(K_1)=hAPP(int,int,plus_plus(int,K_1),K_1)).
% 32.46/32.32 all Z_1 (hAPP(int,int,plus_plus(int,Z_1),zero_zero(int))=ti(int,Z_1)).
% 32.46/32.32 all Z_1 (hAPP(int,int,plus_plus(int,zero_zero(int)),Z_1)=ti(int,Z_1)).
% 32.46/32.32 all K_1 I_1 J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,I_1),K_1)),hAPP(int,int,plus_plus(int,J_1),K_1)))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all W (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))),number_number_of(X_a,W))=number_number_of(X_a,bit0(W))))).
% 32.46/32.32 all X_a (monoid_mult(X_a)-> (all A_1 (hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit1(bit1(pls))))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),A_1)),A_1)))).
% 32.46/32.32 all X_a (number_semiring(X_a)-> (all Z_1 (hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls)))),Z_1)=hAPP(X_a,X_a,plus_plus(X_a,Z_1),Z_1)))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all Z_1 (hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls)))),Z_1)=hAPP(X_a,X_a,plus_plus(X_a,Z_1),Z_1)))).
% 32.46/32.32 all X_a (number_semiring(X_a)-> (all Z_1 (hAPP(X_a,X_a,times_times(X_a,Z_1),number_number_of(X_a,bit0(bit1(pls))))=hAPP(X_a,X_a,plus_plus(X_a,Z_1),Z_1)))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all Z_1 (hAPP(X_a,X_a,times_times(X_a,Z_1),number_number_of(X_a,bit0(bit1(pls))))=hAPP(X_a,X_a,plus_plus(X_a,Z_1),Z_1)))).
% 32.46/32.32 all X_a (monoid_mult(X_a)-> (all A_1 (hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls))))=hAPP(X_a,X_a,times_times(X_a,A_1),A_1)))).
% 32.46/32.32 all X_a (linordered_idom(X_a)-> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),zero_zero(X_a)))))).
% 32.46/32.32 all X_a (number_semiring(X_a)->number_number_of(X_a,pls)=zero_zero(X_a)).
% 32.46/32.32 all X_a (number_ring(X_a)->number_number_of(X_a,pls)=zero_zero(X_a)).
% 32.46/32.32 all X_a (number_ring(X_a)->zero_zero(X_a)=number_number_of(X_a,pls)).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,pls)),A_1)=ti(X_a,A_1)))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,A_1),number_number_of(X_a,pls))=ti(X_a,A_1)))).
% 32.46/32.32 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X)),number_number_of(X_a,Y_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),Y_1))))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all V W Z_1 (hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,W)),Z_1))=hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,hAPP(int,int,plus_plus(int,V),W))),Z_1)))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all V W (hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),number_number_of(X_a,W))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V),W))))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all V W (number_number_of(X_a,hAPP(int,int,plus_plus(int,V),W))=hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),number_number_of(X_a,W))))).
% 32.46/32.32 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),pls))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls))).
% 32.46/32.32 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K1)),bit0(K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2))).
% 32.46/32.32 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit0(L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))).
% 32.46/32.32 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(W_1)),zero_zero(int)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int)))).
% 32.46/32.32 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),pls))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls))).
% 32.46/32.32 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit0(K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K))).
% 32.46/32.32 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))).
% 32.46/32.32 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(W_1)),zero_zero(int)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int)))).
% 32.46/32.32 all K_1 L_1 (hAPP(int,int,plus_plus(int,bit1(K_1)),bit0(L_1))=bit1(hAPP(int,int,plus_plus(int,K_1),L_1))).
% 32.46/32.32 all K_1 L_1 (hAPP(int,int,plus_plus(int,bit0(K_1)),bit1(L_1))=bit1(hAPP(int,int,plus_plus(int,K_1),L_1))).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))).
% 32.46/32.32 all K_1 (bit1(K_1)=hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),K_1)),K_1)).
% 32.46/32.32 all Z_1 (hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_1)),Z_1)!=zero_zero(int)).
% 32.46/32.32 all W_1 Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))|ti(int,W_1)=ti(int,Z_2)).
% 32.46/32.32 all X_b (monoid_mult(X_b)&number(X_b)-> (all W (hAPP(nat,X_b,power_power(X_b,number_number_of(X_b,W)),number_number_of(nat,bit0(bit1(pls))))=hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,W)),number_number_of(X_b,W))))).
% 32.46/32.32 all X_a (number_semiring(X_a)-> (all X_1 Y (hAPP(nat,X_a,power_power(X_a,hAPP(X_a,X_a,plus_plus(X_a,X_1),Y)),number_number_of(nat,bit0(bit1(pls))))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,bit0(bit1(pls)))))),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls)))),X_1)),Y))))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all W (number_number_of(X_a,bit0(W))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),number_number_of(X_a,W))),number_number_of(X_a,W))))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all W (number_number_of(X_a,bit1(W))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,W))),number_number_of(X_a,W))))).
% 32.46/32.32 all X_a (number_semiring(X_a)->number_number_of(X_a,bit1(pls))=one_one(X_a)).
% 32.46/32.32 all X_a (number_ring(X_a)->number_number_of(X_a,bit1(pls))=one_one(X_a)).
% 32.46/32.32 all X_a (number_ring(X_a)->one_one(X_a)=number_number_of(X_a,bit1(pls))).
% 32.46/32.32 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_2)),Z_2)),zero_zero(int)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int)))).
% 32.46/32.32 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X)),zero_zero(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),pls))))).
% 32.46/32.32 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),number_number_of(X_a,Y_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Y_1))))).
% 32.46/32.32 all X_a (number_semiring(X_a)->hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))=number_number_of(X_a,bit0(bit1(pls)))).
% 32.46/32.32 all X_a (number_ring(X_a)->hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))=number_number_of(X_a,bit0(bit1(pls)))).
% 32.46/32.32 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X)),one_one(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),bit1(pls)))))).
% 32.46/32.32 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),number_number_of(X_a,Y_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(pls)),Y_1))))).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)))).
% 32.46/32.32 all A_1 B (hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,A_1),B)),number_number_of(nat,bit1(bit1(pls))))=hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit1(bit1(pls))))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit1(bit1(pls)))),hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))))),B))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit1(bit1(pls)))),A_1)),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls))))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit1(bit1(pls)))))).
% 32.46/32.32 all A_1 B (hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,A_1),B)),number_number_of(nat,bit0(bit1(pls))))=hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),A_1)),B))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls)))))).
% 32.46/32.32 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),number_number_of(int,bit0(bit1(pls)))))->ti(int,X_1)=zero_zero(int)|ti(int,X_1)=one_one(int))).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),s)).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),s),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.46/32.32 hBOOL(hAPP(int,bool,zcong(s1,s),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.46/32.32 all A_1 (hAPP(int,int,times_times(int,A_1),hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit1(bit1(pls))))).
% 32.46/32.32 all X_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_1),hAPP(nat,int,power_power(int,X_1),number_number_of(nat,bit0(bit1(pls)))))).
% 32.46/32.32 all R_1 Q_1 A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (ti(int,A_1)=hAPP(int,int,plus_plus(int,R_1),hAPP(int,int,times_times(int,A_1),Q_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),A_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Q_1))))).
% 32.46/32.32 all R_1 Q_1 A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (ti(int,A_1)=hAPP(int,int,plus_plus(int,R_1),hAPP(int,int,times_times(int,A_1),Q_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),one_one(int)))))).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit0(bit1(pls))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all X_1 N_1 (hAPP(nat,X_a,power_power(X_a,X_1),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1))=hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,X_1),N_1)),hAPP(nat,X_a,power_power(X_a,X_1),N_1))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all X_1 (hAPP(X_a,X_a,times_times(X_a,X_1),X_1)=hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))))).
% 32.46/32.32 hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,int,power_power(int,s1),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.46/32.32 exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_2))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))&hBOOL(hAPP(int,bool,zcong(s1,X_2),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))& (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y_2))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_2),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))&hBOOL(hAPP(int,bool,zcong(s1,Y_2),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))->ti(int,Y_2)=ti(int,X_2)))).
% 32.46/32.32 -(all S_1 (-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),S_1))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),S_1),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))&hBOOL(hAPP(int,bool,zcong(s1,S_1),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))))).
% 32.46/32.32 hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,s1),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.46/32.32 all X N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X),N)))<->N=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X))).
% 32.46/32.32 all A_1 N_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),hAPP(nat,int,power_power(int,A_1),N_1)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),A_1)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all X_1 P_3 Q_1 (hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,X_1),P_3)),Q_1)=hAPP(nat,X_a,power_power(X_a,X_1),hAPP(nat,nat,times_times(nat,P_3),Q_1))))).
% 32.46/32.32 all N_1 A_1 B P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),B))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_3),N_1)),hAPP(int,int,times_times(int,A_1),B)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_3),N_1)),A_1))))).
% 32.46/32.32 all N_1 B A_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_3),N_1)),hAPP(int,int,times_times(int,A_1),B)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_3),N_1)),B))))).
% 32.46/32.32 all X_1 Y Z_1 (hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X_1),Y)),Z_1)=hAPP(nat,int,power_power(int,X_1),hAPP(nat,nat,times_times(nat,Y),Z_1))).
% 32.46/32.32 all N_1 M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M),N_1))-> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),M)))).
% 32.46/32.32 all N_1 M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),N_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),M))->ti(int,M)=ti(int,N_1))))).
% 32.46/32.32 all K_1 M N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,times_times(int,K_1),M)),hAPP(int,int,times_times(int,K_1),N_1)))-> (ti(int,K_1)!=zero_zero(int)->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N_1)))).
% 32.46/32.32 all K N Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,plus_plus(int,N),hAPP(int,int,times_times(int,K),Ma))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N))).
% 32.46/32.32 all C_1 X Ta A_3 D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),D))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),hAPP(int,int,plus_plus(int,X),Ta)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X),hAPP(int,int,times_times(int,C_1),D))),Ta))))).
% 32.46/32.32 hBOOL(hAPP(int,bool,zprime,number_number_of(int,bit0(bit1(pls))))).
% 32.46/32.32 all Z_1 N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z_1),N_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),N_1)))).
% 32.46/32.32 all Y X_1 (hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,X_1))-> (hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,Y))->hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,hAPP(int,int,times_times(int,X_1),Y))))).
% 32.46/32.32 all V_3 V_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,V_3)),number_number_of(nat,V_2)))<-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_3),V_2))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_3),pls)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx Ry (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Rx)),hAPP(X_a,X_a,times_times(X_a,Ly),Ry))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx Ry (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,Rx),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),Ry))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx Ry (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,Lx),hAPP(X_a,X_a,times_times(X_a,Ly),hAPP(X_a,X_a,times_times(X_a,Rx),Ry)))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),Rx)=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Rx)),Ly)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),Rx)=hAPP(X_a,X_a,times_times(X_a,Lx),hAPP(X_a,X_a,times_times(X_a,Ly),Rx))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all Lx Rx Ry (hAPP(X_a,X_a,times_times(X_a,Lx),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Rx)),Ry)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all Lx Rx Ry (hAPP(X_a,X_a,times_times(X_a,Lx),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,Rx),hAPP(X_a,X_a,times_times(X_a,Lx),Ry))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 B (hAPP(X_a,X_a,times_times(X_a,A_1),B)=hAPP(X_a,X_a,times_times(X_a,B),A_1)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 C (hAPP(X_a,X_a,plus_plus(X_a,A_1),C)=hAPP(X_a,X_a,plus_plus(X_a,C),A_1)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 C D_2 (hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,C),D_2))=hAPP(X_a,X_a,plus_plus(X_a,C),hAPP(X_a,X_a,plus_plus(X_a,A_1),D_2))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 C D_2 (hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,C),D_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),D_2)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),B)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 B C D_2 (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),hAPP(X_a,X_a,plus_plus(X_a,C),D_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all X_1 (hAPP(nat,X_a,power_power(X_a,X_1),one_one(nat))=ti(X_a,X_1)))).
% 32.46/32.32 all X W_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X),number_number_of(nat,W_1))))<->number_number_of(nat,W_1)=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X))).
% 32.46/32.32 all Z_1 (hAPP(nat,nat,times_times(nat,Z_1),number_number_of(nat,bit0(bit1(pls))))=hAPP(nat,nat,plus_plus(nat,Z_1),Z_1)).
% 32.46/32.32 all Z_1 (hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),Z_1)=hAPP(nat,nat,plus_plus(nat,Z_1),Z_1)).
% 32.46/32.32 all V_1 V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,times_times(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=zero_zero(nat))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,times_times(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=number_number_of(nat,hAPP(int,int,times_times(int,V),V_1)))).
% 32.46/32.32 all V_1 K_1 V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,times_times(nat,number_number_of(nat,V)),hAPP(nat,nat,times_times(nat,number_number_of(nat,V_1)),K_1))=zero_zero(nat))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,times_times(nat,number_number_of(nat,V)),hAPP(nat,nat,times_times(nat,number_number_of(nat,V_1)),K_1))=hAPP(nat,nat,times_times(nat,number_number_of(nat,hAPP(int,int,times_times(int,V),V_1))),K_1))).
% 32.46/32.32 all X_a (monoid_mult(X_a)-> (all A_1 N_1 (hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1))=hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N_1)),number_number_of(nat,bit0(bit1(pls))))))).
% 32.46/32.32 all X_a (linordered_idom(X_a)-> (all A_1 K_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),K_1))),zero_zero(X_a)))->ti(X_a,A_1)=zero_zero(X_a)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,zero_zero(X_a)),A_1)=zero_zero(X_a)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a))=zero_zero(X_a)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1)))).
% 32.46/32.32 all X_a (semiri456707255roduct(X_a)-> (all B_2 A_3 (ti(X_a,B_2)=hAPP(X_a,X_a,plus_plus(X_a,B_2),A_3)<->ti(X_a,A_3)=zero_zero(X_a)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all X_1 Y Z_1 (hAPP(X_a,X_a,times_times(X_a,X_1),hAPP(X_a,X_a,plus_plus(X_a,Y),Z_1))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Y)),hAPP(X_a,X_a,times_times(X_a,X_1),Z_1))))).
% 32.46/32.32 all X_a (semiri456707255roduct(X_a)-> (all C_1 D A_3 B_2 (ti(X_a,A_3)!=ti(X_a,B_2)&ti(X_a,C_1)!=ti(X_a,D)<->hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),D))!=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),D)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 M B (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),M)),hAPP(X_a,X_a,times_times(X_a,B),M))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),M)))).
% 32.46/32.32 all X_a (semiri456707255roduct(X_a)-> (all W_1 Y_1 X Z_2 (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,W_1),Y_1)),hAPP(X_a,X_a,times_times(X_a,X),Z_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,W_1),Z_2)),hAPP(X_a,X_a,times_times(X_a,X),Y_1))<->ti(X_a,W_1)=ti(X_a,X)|ti(X_a,Y_1)=ti(X_a,Z_2)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,one_one(X_a)),A_1)=ti(X_a,A_1)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,A_1),one_one(X_a))=ti(X_a,A_1)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all X_1 Y Q_1 (hAPP(nat,X_a,power_power(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Y)),Q_1)=hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,X_1),Q_1)),hAPP(nat,X_a,power_power(X_a,Y),Q_1))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all X_1 P_3 Q_1 (hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,X_1),P_3)),hAPP(nat,X_a,power_power(X_a,X_1),Q_1))=hAPP(nat,X_a,power_power(X_a,X_1),hAPP(nat,nat,plus_plus(nat,P_3),Q_1))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all X_1 (hAPP(nat,X_a,power_power(X_a,X_1),zero_zero(nat))=one_one(X_a)))).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),zero_zero(int))).
% 32.46/32.32 all X_a (linordered_idom(X_a)-> (all A_1 N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1)))))).
% 32.46/32.32 all X_a (semiri456707255roduct(X_a)-> (all C D_2 A_1 B R_1 (ti(X_a,R_1)!=zero_zero(X_a)-> (ti(X_a,A_1)=ti(X_a,B)&ti(X_a,C)!=ti(X_a,D_2)->hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,times_times(X_a,R_1),C))!=hAPP(X_a,X_a,plus_plus(X_a,B),hAPP(X_a,X_a,times_times(X_a,R_1),D_2)))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all M (hAPP(X_a,X_a,plus_plus(X_a,M),M)=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))),M)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all M A_1 (hAPP(X_a,X_a,plus_plus(X_a,M),hAPP(X_a,X_a,times_times(X_a,A_1),M))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),one_one(X_a))),M)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 M (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),M)),M)=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),one_one(X_a))),M)))).
% 32.46/32.32 all X_a (power(X_a)&mult_zero(X_a)&no_zero_divisors(X_a)&zero_ne_q_one(X_a)-> (all A_3 W_1 (hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,W_1))=zero_zero(X_a)<->ti(X_a,A_3)=zero_zero(X_a)&number_number_of(nat,W_1)!=zero_zero(nat)))).
% 32.46/32.32 all B A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)))).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),one_one(int))).
% 32.46/32.32 all Y X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,times_times(int,X_1),Y))))).
% 32.46/32.32 all Y X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,X_1),Y))))).
% 32.46/32.32 all N_1 X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,power_power(int,X_1),N_1)))).
% 32.46/32.32 all X_a (power(X_a)&semiring_0(X_a)-> (all W ((number_number_of(nat,W)=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,W))=one_one(X_a))& (number_number_of(nat,W)!=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,W))=zero_zero(X_a))))).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit1(bit1(pls))))).
% 32.46/32.32 all B_3 Q_4 R_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Q_4))))).
% 32.46/32.32 all B_3 Q_4 R_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)),zero_zero(int)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_4),zero_zero(int)))))).
% 32.46/32.32 all B Q_4 R_3 Q_1 R_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_4)),R_3)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_1)),R_1)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_4),Q_1)))))).
% 32.46/32.32 all B Q_1 R_1 B_3 Q_4 R_3 (hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_1)),R_1)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_3),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q_4)))))))).
% 32.46/32.32 all B Q_4 R_3 Q_1 R_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_4)),R_3)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_1)),R_1)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_1),zero_zero(int)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_3))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q_4)))))).
% 32.46/32.32 all B Q_1 R_1 B_3 Q_4 R_3 (hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_1)),R_1)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)),zero_zero(int)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_3),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_4),Q_1)))))))).
% 32.46/32.32 all X_1 (hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X_1),number_number_of(nat,bit0(bit1(pls))))),number_number_of(nat,bit0(bit1(pls))))=hAPP(nat,int,power_power(int,X_1),number_number_of(nat,bit0(bit0(bit1(pls)))))).
% 32.46/32.32 hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.46/32.32 all Y X_1 P_3 (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))-> (hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,Y),number_number_of(nat,bit0(bit1(pls)))),X_1),P_3))-> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),Y)))).
% 32.46/32.32 all P_2 (hBOOL(hAPP(int,bool,zprime,P_2))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_2))& (all M_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M_2))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M_2),P_2))->ti(int,M_2)=one_one(int)|ti(int,M_2)=ti(int,P_2)))).
% 32.46/32.32 all P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (ti(int,P_3)!=number_number_of(int,bit0(bit1(pls)))-> (ti(int,P_3)!=number_number_of(int,bit1(bit1(pls)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),P_3))))).
% 32.46/32.32 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,bit0(bit1(pls))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,B),N_1)))))))).
% 32.46/32.32 all X_a (linord626643107strict(X_a)-> (all V U_1 Y X_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),U_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),V))-> (hAPP(X_a,X_a,plus_plus(X_a,U_1),V)=one_one(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,U_1),X_1)),hAPP(X_a,X_a,times_times(X_a,V),Y))),A_1))))))))).
% 32.46/32.32 all Y N_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),hAPP(nat,int,power_power(int,Y),N_1)))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),Y))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),zero_zero(X_a))))).
% 32.46/32.32 -(all S1 (-hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,S1),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))))).
% 32.46/32.32 legendre(number_number_of(int,min),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))=one_one(int).
% 32.46/32.32 all K (bit1(K)=min<->ti(int,K)=min).
% 32.46/32.32 all L (min=bit1(L)<->min=ti(int,L)).
% 32.46/32.32 bit1(min)=min.
% 32.46/32.32 pls!=min.
% 32.46/32.32 min!=pls.
% 32.46/32.32 all K_1 (bit0(K_1)!=min).
% 32.46/32.32 all L_1 (min!=bit0(L_1)).
% 32.46/32.32 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),min)).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),min)).
% 32.46/32.32 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),min))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),min))).
% 32.46/32.32 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit1(K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K))).
% 32.46/32.32 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),min)).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),pls)).
% 32.46/32.32 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit0(K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K))).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),zero_zero(int))).
% 32.46/32.32 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit1(K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),K))).
% 32.46/32.32 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),min))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min))).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),pls)).
% 32.46/32.32 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),min)).
% 32.46/32.32 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),min))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min))).
% 32.46/32.32 number_number_of(int,pls)!=number_number_of(int,min).
% 32.46/32.32 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),min))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min))).
% 32.46/32.32 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit0(K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K))).
% 32.46/32.32 all Ma N (hAPP(int,int,times_times(int,Ma),N)=one_one(int)<->ti(int,Ma)=one_one(int)&ti(int,N)=one_one(int)|ti(int,Ma)=number_number_of(int,min)&ti(int,N)=number_number_of(int,min)).
% 32.46/32.32 all M N_1 (hAPP(int,int,times_times(int,M),N_1)=one_one(int)->ti(int,M)=one_one(int)|ti(int,M)=number_number_of(int,min)).
% 32.46/32.32 all X_a (linordered_idom(X_a)-> (all X_1 Y (ti(X_a,X_1)!=ti(X_a,Y)-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),A_1)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)))))).
% 32.46/32.32 all A_3 B_2 Ma (hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))<->hBOOL(hAPP(int,bool,zcong(B_2,A_3),Ma))).
% 32.46/32.32 all K_1 M hBOOL(hAPP(int,bool,zcong(K_1,K_1),M)).
% 32.46/32.32 all D_2 C A_1 B M (hBOOL(hAPP(int,bool,zcong(A_1,B),M))-> (ti(int,B)=ti(int,C)-> (hBOOL(hAPP(int,bool,zcong(C,D_2),M))->hBOOL(hAPP(int,bool,zcong(A_1,D_2),M))))).
% 32.46/32.32 all C A_1 B M (hBOOL(hAPP(int,bool,zcong(A_1,B),M))-> (hBOOL(hAPP(int,bool,zcong(B,C),M))->hBOOL(hAPP(int,bool,zcong(A_1,C),M)))).
% 32.46/32.32 all X_1 P_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))-> (hBOOL(hAPP(int,bool,zcong(X_1,number_number_of(int,min)),P_3))-> -hBOOL(hAPP(int,bool,zcong(X_1,one_one(int)),P_3)))).
% 32.46/32.32 all X_a (order(X_a)-> (all X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))-> (ti(X_a,X_1)!=ti(X_a,Y)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)))))).
% 32.46/32.32 all X_a (no_zero_divisors(X_a)-> (all A_1 B (hAPP(X_a,X_a,times_times(X_a,A_1),B)=zero_zero(X_a)->ti(X_a,A_1)=zero_zero(X_a)|ti(X_a,B)=zero_zero(X_a)))).
% 32.46/32.32 all X_a (no_zero_divisors(X_a)-> (all B A_1 (ti(X_a,A_1)!=zero_zero(X_a)-> (ti(X_a,B)!=zero_zero(X_a)->hAPP(X_a,X_a,times_times(X_a,A_1),B)!=zero_zero(X_a))))).
% 32.46/32.32 all X_a (ring_n68954251visors(X_a)-> (all A_3 B_2 (hAPP(X_a,X_a,times_times(X_a,A_3),B_2)=zero_zero(X_a)<->ti(X_a,A_3)=zero_zero(X_a)|ti(X_a,B_2)=zero_zero(X_a)))).
% 32.46/32.32 all X_a (mult_zero(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a))=zero_zero(X_a)))).
% 32.46/32.32 all X_a (mult_zero(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,zero_zero(X_a)),A_1)=zero_zero(X_a)))).
% 32.46/32.32 all X_a (zero_ne_q_one(X_a)->zero_zero(X_a)!=one_one(X_a)).
% 32.46/32.32 all X_a (zero_ne_q_one(X_a)->one_one(X_a)!=zero_zero(X_a)).
% 32.46/32.32 all X_a (semiring(X_a)-> (all A_1 E_1 B C (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),E_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B),E_1)),C))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),E_1)),C)))).
% 32.46/32.32 all X_a (comm_semiring(X_a)-> (all A_1 B C (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))))).
% 32.46/32.32 all X_a (ring_11004092258visors(X_a)-> (all N_1 A_1 (ti(X_a,A_1)!=zero_zero(X_a)->hAPP(nat,X_a,power_power(X_a,A_1),N_1)!=zero_zero(X_a)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),zero_zero(X_a)),A_1))->ti(X_a,A_1)=zero_zero(X_a)))).
% 32.46/32.32 all X_a (comm_monoid_mult(X_a)-> (all A_1 B N_1 (hAPP(nat,X_a,power_power(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),N_1)=hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,B),N_1))))).
% 32.46/32.32 all X_a (monoid_mult(X_a)-> (all A_1 N_1 (hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N_1)),A_1)=hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(nat,X_a,power_power(X_a,A_1),N_1))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,times_times(X_a,A_1),B))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,times_times(X_a,B),A_1))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,times_times(X_a,B),C)))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all B A_1 C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,times_times(X_a,B),C)))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),D_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))))))).
% 32.46/32.32 all X_a (dvd(X_a)-> (all A_1 B K_1 (A_1=hAPP(X_a,X_a,times_times(X_a,B),K_1)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),A_1))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),C))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C))))))).
% 32.46/32.32 all X_a (monoid_mult(X_a)-> (all N_1 (hAPP(nat,X_a,power_power(X_a,one_one(X_a)),N_1)=one_one(X_a)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),one_one(X_a)),A_1)))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all N_1 X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,X_1),N_1)),hAPP(nat,X_a,power_power(X_a,Y),N_1)))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all M A_1 N_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),B))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M)),B)))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all N_1 M X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,X_1),N_1)),hAPP(nat,X_a,power_power(X_a,Y),M))))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all A_1 M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))))).
% 32.46/32.32 all M N_1 I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),I_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,I_1),M)),hAPP(nat,nat,power_power(nat,I_1),N_1)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)))).
% 32.46/32.32 all X N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X))|N=zero_zero(nat)).
% 32.46/32.32 all X_a (monoid_mult(X_a)-> (all A_1 M N_1 (hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,times_times(nat,M),N_1))=hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,A_1),M)),N_1)))).
% 32.46/32.32 all B A_1 C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),C))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),A_1)))).
% 32.46/32.32 all X_a (monoid_mult(X_a)-> (all A_1 (hAPP(nat,X_a,power_power(X_a,A_1),one_one(nat))=ti(X_a,A_1)))).
% 32.46/32.32 all M hBOOL(hAPP(int,bool,zcong(M,zero_zero(int)),M)).
% 32.46/32.32 all A_3 B_2 (hBOOL(hAPP(int,bool,zcong(A_3,B_2),zero_zero(int)))<->ti(int,A_3)=ti(int,B_2)).
% 32.46/32.32 all A_1 B hBOOL(hAPP(int,bool,zcong(A_1,B),one_one(int))).
% 32.46/32.32 all A_1 M B hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),M),hAPP(int,int,times_times(int,B),M)),M)).
% 32.46/32.32 all C_1 D A_3 B_2 Ma (hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))-> (hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,A_3),D)),Ma))<->hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,B_2),D)),Ma)))).
% 32.46/32.32 all C_1 D A_3 B_2 Ma (hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))-> (hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,D),A_3)),Ma))<->hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,D),B_2)),Ma)))).
% 32.46/32.32 all K_1 A_1 B M (hBOOL(hAPP(int,bool,zcong(A_1,B),M))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),K_1),hAPP(int,int,times_times(int,B),K_1)),M))).
% 32.46/32.32 all K_1 A_1 B M (hBOOL(hAPP(int,bool,zcong(A_1,B),M))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,K_1),A_1),hAPP(int,int,times_times(int,K_1),B)),M))).
% 32.46/32.32 all C D_2 A_1 B M (hBOOL(hAPP(int,bool,zcong(A_1,B),M))-> (hBOOL(hAPP(int,bool,zcong(C,D_2),M))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),C),hAPP(int,int,times_times(int,B),D_2)),M)))).
% 32.46/32.32 all C D_2 A_1 B M (hBOOL(hAPP(int,bool,zcong(A_1,B),M))-> (hBOOL(hAPP(int,bool,zcong(C,D_2),M))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,plus_plus(int,A_1),C),hAPP(int,int,plus_plus(int,B),D_2)),M)))).
% 32.46/32.32 all C A_1 B M (hBOOL(hAPP(int,bool,zcong(A_1,B),M))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,plus_plus(int,A_1),C),hAPP(int,int,plus_plus(int,B),C)),M))).
% 32.46/32.32 all Z_1 X_1 Y M (hBOOL(hAPP(int,bool,zcong(X_1,Y),M))->hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X_1),Z_1),hAPP(nat,int,power_power(int,Y),Z_1)),M))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all N_1 (hAPP(nat,X_a,power_power(X_a,number_number_of(X_a,min)),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1))=one_one(X_a)))).
% 32.46/32.32 all X_a (ordere453448008miring(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a)))))).
% 32.46/32.32 all X_a (ordered_ring(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B)))))).
% 32.46/32.32 all X_a (ordered_semiring(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))))))))).
% 32.46/32.32 all X_a (ordered_semiring(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))))))))).
% 32.46/32.32 all X_a (ordered_ring(X_a)-> (all C B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))))))).
% 32.46/32.32 all X_a (ordered_ring(X_a)-> (all C B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))))))).
% 32.46/32.32 all X_a (ordere1490568538miring(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))))))).
% 32.46/32.32 all X_a (ordered_semiring(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))))))).
% 32.46/32.32 all X_a (ordered_semiring(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))))))).
% 32.46/32.32 all X_a (ordered_ring(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))))))).
% 32.46/32.32 all X_a (ordere453448008miring(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))))))).
% 32.46/32.32 all X_a (ordere453448008miring(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,B),A_1)),zero_zero(X_a))))))).
% 32.46/32.32 all X_a (ordere453448008miring(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))))))).
% 32.46/32.32 all X_a (ordere453448008miring(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))))))).
% 32.46/32.32 all X_a (linord581940658strict(X_a)-> (all A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a)))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_2))))).
% 32.46/32.32 all X_a (linord581940658strict(X_a)-> (all A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a)))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),zero_zero(X_a)))))).
% 32.46/32.32 all X_a (linordered_ring(X_a)-> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),A_1))))).
% 32.46/32.32 all X_a (linord581940658strict(X_a)-> (all C B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))))))).
% 32.46/32.32 all X_a (linord581940658strict(X_a)-> (all C B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))))))).
% 32.46/32.32 all X_a (linord893533164strict(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))))))).
% 32.46/32.32 all X_a (linord20386208strict(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))))))).
% 32.46/32.32 all X_a (linord20386208strict(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))))))).
% 32.46/32.32 all X_a (linord581940658strict(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))))))).
% 32.46/32.32 all X_a (linord20386208strict(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))))))).
% 32.46/32.32 all X_a (linord581940658strict(X_a)-> (all A_3 B_2 C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)))))).
% 32.46/32.32 all X_a (linord20386208strict(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,B),A_1)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)))))).
% 32.46/32.32 all X_a (linord20386208strict(X_a)-> (all A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)))))).
% 32.46/32.32 all X_a (linord20386208strict(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,B),A_1)),zero_zero(X_a))))))).
% 32.46/32.32 all X_a (linord20386208strict(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))))))).
% 32.46/32.32 all X_a (linord20386208strict(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))))))).
% 32.46/32.32 all X_a (linord581940658strict(X_a)-> (all A_3 B_2 C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)))))).
% 32.46/32.32 all X_a (linord581940658strict(X_a)-> (all C_1 A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3))))).
% 32.46/32.32 all X_a (linord581940658strict(X_a)-> (all A_3 C_1 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3))))).
% 32.46/32.32 all X_a (linordered_ring(X_a)-> (all A_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),A_1)),zero_zero(X_a)))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all B C A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),one_one(X_a)))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),zero_zero(X_a)))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a)))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a)))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,B),N_1))))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all N_1 M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,times_times(X_a,M),N_1))))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,plus_plus(X_a,A_1),one_one(X_a)))))).
% 32.46/32.32 all X_a (idom(X_a)-> (all C_1 A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))<->ti(X_a,C_1)=zero_zero(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2))))).
% 32.46/32.32 all X_a (idom(X_a)-> (all A_3 C_1 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))<->ti(X_a,C_1)=zero_zero(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all A_1 N_1 N_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),N_3))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,A_1),N_3))))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all Ma N A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_3))-> (hAPP(nat,X_a,power_power(X_a,A_3),Ma)=hAPP(nat,X_a,power_power(X_a,A_3),N)<->Ma=N)))).
% 32.46/32.32 all X_a (power(X_a)&mult_zero(X_a)&no_zero_divisors(X_a)&zero_ne_q_one(X_a)-> (all A_3 N (hAPP(nat,X_a,power_power(X_a,A_3),N)=zero_zero(X_a)<->ti(X_a,A_3)=zero_zero(X_a)&N!=zero_zero(nat)))).
% 32.46/32.32 all X_a (power(X_a)-> (all A_1 (hAPP(nat,X_a,power_power(X_a,A_1),zero_zero(nat))=one_one(X_a)))).
% 32.46/32.32 all X_a (monoid_mult(X_a)-> (all A_1 M N_1 (hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,plus_plus(nat,M),N_1))=hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,A_1),M)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))))).
% 32.46/32.32 all B M A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1))-> -hBOOL(hAPP(int,bool,zcong(A_1,B),M)))))).
% 32.46/32.32 all M X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),M))-> -hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),M)))).
% 32.46/32.32 all M Y X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Y))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))-> (hBOOL(hAPP(int,bool,zcong(X_1,Y),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),M))->ti(int,X_1)=ti(int,Y))))))).
% 32.46/32.32 all N_1 M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),M))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),M),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_1),M))).
% 32.46/32.32 all A_3 B_2 Ma (hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))<-> (exists K_2 (ti(int,B_2)=hAPP(int,int,plus_plus(int,A_3),hAPP(int,int,times_times(int,Ma),K_2))))).
% 32.46/32.32 all X P_2 (hBOOL(hAPP(int,bool,zcong(X,zero_zero(int)),P_2))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),X))).
% 32.46/32.32 all A_3 Ma (hBOOL(hAPP(int,bool,zcong(A_3,zero_zero(int)),Ma))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),A_3))).
% 32.46/32.32 all M N_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),hAPP(int,int,times_times(int,M),N_1)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),N_1)))).
% 32.46/32.32 all X_a (linord20386208strict(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B)))))).
% 32.46/32.32 all X_a (linord20386208strict(X_a)-> (all A_1 C B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B)))))).
% 32.46/32.32 all X_a (linord20386208strict(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))).
% 32.46/32.32 all X_a (linordered_semiring(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))).
% 32.46/32.32 all X_a (linord20386208strict(X_a)-> (all A_1 C B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))).
% 32.46/32.32 all X_a (linordered_semiring(X_a)-> (all A_1 C B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))).
% 32.46/32.32 all X_a (linord20386208strict(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))))))))).
% 32.46/32.32 all X_a (linord20386208strict(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))))))))).
% 32.46/32.32 all X_a (linord20386208strict(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))))))))).
% 32.46/32.32 all X_a (linord20386208strict(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))))))))).
% 32.46/32.32 all X_a (linord581940658strict(X_a)-> (all A_3 B_2 C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),A_3)))))).
% 32.46/32.32 all X_a (linord581940658strict(X_a)-> (all A_3 B_2 C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2)))))).
% 32.46/32.32 all X_a (linordered_idom(X_a)-> (all Y X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),one_one(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,Y),X_1)),X_1))))))).
% 32.46/32.32 all X_a (linordered_idom(X_a)-> (all Y X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),one_one(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,X_1),Y)),X_1))))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all A_1 N_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,B),N_1)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all A_1 N_1 N_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),N_3))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),one_one(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_3)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all M N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all X Y_1 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,B_2),X)),hAPP(nat,X_a,power_power(X_a,B_2),Y_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),Y_1)))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(nat,X_a,power_power(X_a,A_1),N_1))))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(nat,X_a,power_power(X_a,A_1),N_1))))))).
% 32.46/32.32 all X_a (power(X_a)&semiring_0(X_a)-> (all N_1 ((N_1=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N_1)=one_one(X_a))& (N_1!=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N_1)=zero_zero(X_a))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all A_1 N_1 N_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_3))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,A_1),N_3))))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all M N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all X Y_1 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,B_2),X)),hAPP(nat,X_a,power_power(X_a,B_2),Y_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y_1)))))).
% 32.46/32.32 all X_1 (hAPP(real,real,times_times(real,number_number_of(real,bit0(bit0(bit1(pls))))),hAPP(nat,real,power_power(real,X_1),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,real,power_power(real,hAPP(real,real,times_times(real,number_number_of(real,bit0(bit1(pls)))),X_1)),number_number_of(nat,bit0(bit1(pls))))).
% 32.46/32.32 all M X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),M))-> (hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),M))->ti(int,X_1)=zero_zero(int)))).
% 32.46/32.32 all M A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M))-> (hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),M))->ti(int,A_1)=zero_zero(int)))).
% 32.46/32.32 all B M A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),M))-> (hBOOL(hAPP(int,bool,zcong(A_1,B),M))->ti(int,A_1)=ti(int,B)))))).
% 32.46/32.32 all P_3 Y N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),Y))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),hAPP(nat,int,power_power(int,Y),N_1))))).
% 32.46/32.32 all Z_1 X_1 Y P_3 (hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X_1),Y),one_one(int)),P_3))->hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X_1),hAPP(nat,nat,times_times(nat,Y),Z_1)),one_one(int)),P_3))).
% 32.46/32.32 all Y X_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))-> (-hBOOL(hAPP(int,bool,zcong(Y,zero_zero(int)),P_3))-> -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,X_1),Y),zero_zero(int)),P_3))))).
% 32.46/32.32 all X_a (linord1278240602ring_1(X_a)-> (all V U_1 Y X_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),U_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),V))-> (hAPP(X_a,X_a,plus_plus(X_a,U_1),V)=one_one(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,U_1),X_1)),hAPP(X_a,X_a,times_times(X_a,V),Y))),A_1))))))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(nat,X_a,power_power(X_a,A_1),N_1))),hAPP(nat,X_a,power_power(X_a,A_1),N_1))))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all A_1 N_1 N_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_3))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_3)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all A_1 N_1 B (hAPP(nat,X_a,power_power(X_a,A_1),N_1)=hAPP(nat,X_a,power_power(X_a,B),N_1)-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->ti(X_a,A_1)=ti(X_a,B))))))).
% 32.46/32.32 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))))))).
% 32.46/32.32 all X_a (comm_semiring_1(X_a)-> (all X_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|ti(X_a,X_1)=one_one(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),hAPP(nat,X_a,power_power(X_a,X_1),N_1)))))).
% 32.46/32.32 all B A_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),B),zero_zero(int)),P_3))->hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,zcong(B,zero_zero(int)),P_3))))).
% 32.46/32.32 all B A_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (-hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_3))& -hBOOL(hAPP(int,bool,zcong(B,zero_zero(int)),P_3))-> -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),B),zero_zero(int)),P_3))))).
% 32.46/32.32 all N_1 P_3 M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M))-> (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),hAPP(int,int,times_times(int,M),N_1)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),N_1))))).
% 32.46/32.32 hBOOL(hAPP(int,bool,quadRes(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),number_number_of(int,min))).
% 32.46/32.32 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)))).
% 32.46/32.32 all J_1 K_1 M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),M))-> (hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,number_number_of(int,min)),J_1),hAPP(nat,int,power_power(int,number_number_of(int,min)),K_1)),M))->hAPP(nat,int,power_power(int,number_number_of(int,min)),J_1)=hAPP(nat,int,power_power(int,number_number_of(int,min)),K_1))).
% 32.46/32.32 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),M))-> -hBOOL(hAPP(int,bool,zcong(one_one(int),number_number_of(int,min)),M))).
% 32.46/32.32 hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min))=hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)).
% 32.46/32.32 -hBOOL(hAPP(int,bool,quadRes(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),number_number_of(int,min)))->legendre(number_number_of(int,min),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))!=one_one(int).
% 32.46/32.32 all X (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,times_times(real,X),X)))<->X=zero_zero(real)).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all V W (number_number_of(X_a,hAPP(int,int,minus_minus(int,V),W))=hAPP(X_a,X_a,minus_minus(X_a,number_number_of(X_a,V)),number_number_of(X_a,W))))).
% 32.46/32.32 all X_a (comm_ring_1(X_a)-> (all Z_1 X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Z_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),hAPP(X_a,X_a,minus_minus(X_a,Y),Z_1))))))).
% 32.46/32.32 all K_1 (hAPP(int,int,minus_minus(int,K_1),pls)=ti(int,K_1)).
% 32.46/32.32 all K_1 L_1 (hAPP(int,int,minus_minus(int,bit0(K_1)),bit0(L_1))=bit0(hAPP(int,int,minus_minus(int,K_1),L_1))).
% 32.46/32.32 all Z1 Z2 W (hAPP(int,int,times_times(int,hAPP(int,int,minus_minus(int,Z1),Z2)),W)=hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,Z1),W)),hAPP(int,int,times_times(int,Z2),W))).
% 32.46/32.32 all W Z1 Z2 (hAPP(int,int,times_times(int,W),hAPP(int,int,minus_minus(int,Z1),Z2))=hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,W),Z1)),hAPP(int,int,times_times(int,W),Z2))).
% 32.46/32.32 all A_1 B C (hAPP(int,int,minus_minus(int,A_1),B)=ti(int,C)->ti(int,A_1)=hAPP(int,int,plus_plus(int,C),B)).
% 32.46/32.32 all C D_2 A_1 B M (hBOOL(hAPP(int,bool,zcong(A_1,B),M))-> (hBOOL(hAPP(int,bool,zcong(C,D_2),M))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,minus_minus(int,A_1),C),hAPP(int,int,minus_minus(int,B),D_2)),M)))).
% 32.46/32.32 all K_1 M N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),hAPP(int,int,minus_minus(int,M),N_1)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),N_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),M)))).
% 32.46/32.32 all X_a (ring(X_a)-> (all A_3 E C_1 B_2 D (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)<->ti(X_a,C_1)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D)))).
% 32.46/32.32 all X_a (ring(X_a)-> (all A_3 E C_1 B_2 D (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)<->hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)=ti(X_a,D)))).
% 32.46/32.32 all X_b (number(X_b)&ring(X_b)-> (all V B C (hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),hAPP(X_b,X_b,minus_minus(X_b,B),C))=hAPP(X_b,X_b,minus_minus(X_b,hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),B)),hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),C))))).
% 32.46/32.32 all X_b (number(X_b)&ring(X_b)-> (all A_1 B V (hAPP(X_b,X_b,times_times(X_b,hAPP(X_b,X_b,minus_minus(X_b,A_1),B)),number_number_of(X_b,V))=hAPP(X_b,X_b,minus_minus(X_b,hAPP(X_b,X_b,times_times(X_b,A_1),number_number_of(X_b,V))),hAPP(X_b,X_b,times_times(X_b,B),number_number_of(X_b,V)))))).
% 32.46/32.32 all K_1 L_1 (hAPP(int,int,minus_minus(int,bit1(K_1)),bit0(L_1))=bit1(hAPP(int,int,minus_minus(int,K_1),L_1))).
% 32.46/32.32 all K_1 L_1 (hAPP(int,int,minus_minus(int,bit1(K_1)),bit1(L_1))=bit0(hAPP(int,int,minus_minus(int,K_1),L_1))).
% 32.46/32.32 all L_1 (hAPP(int,int,minus_minus(int,pls),bit0(L_1))=bit0(hAPP(int,int,minus_minus(int,pls),L_1))).
% 32.46/32.32 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,K),L)),zero_zero(int)))).
% 32.46/32.32 all A_1 R_1 B M C D_2 N_1 (hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,hAPP(int,int,minus_minus(int,A_1),hAPP(int,int,times_times(int,R_1),B))),M)),hAPP(int,int,times_times(int,hAPP(int,int,minus_minus(int,C),hAPP(int,int,times_times(int,R_1),D_2))),N_1))=hAPP(int,int,minus_minus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A_1),M)),hAPP(int,int,times_times(int,C),N_1))),hAPP(int,int,times_times(int,R_1),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),M)),hAPP(int,int,times_times(int,D_2),N_1))))).
% 32.46/32.32 all A_3 B_2 Ma (hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),hAPP(int,int,minus_minus(int,A_3),B_2)))).
% 32.46/32.32 all X_a (ordered_ring(X_a)-> (all A_3 E C_1 B_2 D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)),D))))).
% 32.46/32.32 all X_a (ordered_ring(X_a)-> (all A_3 E C_1 B_2 D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D)))))).
% 32.46/32.32 all X_a (ordered_ring(X_a)-> (all A_3 E C_1 B_2 D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D)))))).
% 32.46/32.32 all X_a (ordered_ring(X_a)-> (all A_3 E C_1 B_2 D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)),D))))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all V W C (hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),hAPP(X_a,X_a,minus_minus(X_a,number_number_of(X_a,W)),C))=hAPP(X_a,X_a,minus_minus(X_a,number_number_of(X_a,hAPP(int,int,plus_plus(int,V),W))),C)))).
% 32.46/32.32 all A_1 X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),A_1))-> (ti(int,X_1)!=hAPP(int,int,minus_minus(int,A_1),one_one(int))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),hAPP(int,int,minus_minus(int,A_1),one_one(int))))))).
% 32.46/32.32 all W_1 Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),hAPP(int,int,minus_minus(int,Z_2),one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))).
% 32.46/32.32 all L_1 (hAPP(int,int,minus_minus(int,pls),bit1(L_1))=bit1(hAPP(int,int,minus_minus(int,min),L_1))).
% 32.46/32.32 all L_1 (hAPP(int,int,minus_minus(int,min),bit0(L_1))=bit1(hAPP(int,int,minus_minus(int,min),L_1))).
% 32.46/32.32 all L_1 (hAPP(int,int,minus_minus(int,min),bit1(L_1))=bit0(hAPP(int,int,minus_minus(int,min),L_1))).
% 32.46/32.32 all A_3 P_2 (hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_3),hAPP(int,int,minus_minus(int,P_2),one_one(int))),one_one(int)),P_2))<->hBOOL(hAPP(int,bool,zcong(A_3,hAPP(int,int,minus_minus(int,P_2),one_one(int))),P_2))).
% 32.46/32.32 all I_1 M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,I_1),M)),hAPP(nat,nat,power_power(nat,I_1),N_1)))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),I_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)))).
% 32.46/32.32 all A_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_3))-> (hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),A_1),one_one(int)),P_3))->ti(int,A_1)=one_one(int)|ti(int,A_1)=hAPP(int,int,minus_minus(int,P_3),one_one(int)))))).
% 32.46/32.32 all A_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),A_1),one_one(int)),P_3))->hBOOL(hAPP(int,bool,zcong(A_1,one_one(int)),P_3))|hBOOL(hAPP(int,bool,zcong(A_1,hAPP(int,int,minus_minus(int,P_3),one_one(int))),P_3))))).
% 32.46/32.32 all A_1 B (hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,A_1),B)),hAPP(int,int,minus_minus(int,A_1),B))=hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls)))))).
% 32.46/32.32 all X_a (number_ring(X_a)-> (all X_1 Y (hAPP(nat,X_a,power_power(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),Y)),number_number_of(nat,bit0(bit1(pls))))=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,bit0(bit1(pls)))))),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls)))),X_1)),Y))))).
% 32.46/32.32 all A_1 B (hAPP(nat,int,power_power(int,hAPP(int,int,minus_minus(int,A_1),B)),number_number_of(nat,bit0(bit1(pls))))=hAPP(int,int,plus_plus(int,hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),A_1)),B))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls)))))).
% 32.46/32.32 all A_1 B (hAPP(nat,int,power_power(int,hAPP(int,int,minus_minus(int,A_1),B)),number_number_of(nat,bit1(bit1(pls))))=hAPP(int,int,minus_minus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit1(bit1(pls))))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit1(bit1(pls)))),hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))))),B))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit1(bit1(pls)))),A_1)),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls))))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit1(bit1(pls)))))).
% 32.46/32.32 all N_1 (hAPP(nat,int,power_power(int,number_number_of(int,min)),N_1)=one_one(int)|hAPP(nat,int,power_power(int,number_number_of(int,min)),N_1)=number_number_of(int,min)).
% 32.46/32.32 all M (hBOOL(hAPP(int,bool,zprime,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),M)),one_one(int))))->legendre(number_number_of(int,min),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),M)),one_one(int)))=one_one(int)).
% 32.46/32.32 all A_1 P_3 ((hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_3))->legendre(A_1,P_3)=zero_zero(int))& (-hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_3))-> (hBOOL(hAPP(int,bool,quadRes(P_3),A_1))->legendre(A_1,P_3)=one_one(int))& (-hBOOL(hAPP(int,bool,quadRes(P_3),A_1))->legendre(A_1,P_3)=number_number_of(int,min)))).
% 32.46/32.32 all Ma X (hBOOL(hAPP(int,bool,quadRes(Ma),X))<-> (exists Y_2 hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,Y_2),number_number_of(nat,bit0(bit1(pls)))),X),Ma)))).
% 32.46/32.32 all X_1 Y (hAPP(nat,real,power_power(real,hAPP(real,real,plus_plus(real,X_1),Y)),number_number_of(nat,bit0(bit1(pls))))=hAPP(real,real,plus_plus(real,hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,real,power_power(real,Y),number_number_of(nat,bit0(bit1(pls)))))),hAPP(real,real,times_times(real,hAPP(real,real,times_times(real,number_number_of(real,bit0(bit1(pls)))),X_1)),Y))).
% 32.46/32.32 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),M))->M=zero_zero(nat)|M=N_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1)),M))).
% 32.46/32.32 all X Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X))<->X=Y_1).
% 32.46/32.32 all B D_2 A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),A_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),hAPP(nat,nat,plus_plus(nat,A_1),B)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),B)))).
% 32.46/32.32 all C A_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,A_1),C)),hAPP(nat,nat,times_times(nat,B),C)))).
% 32.46/32.32 all C A_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,C),A_1)),hAPP(nat,nat,times_times(nat,C),B)))).
% 32.46/32.32 all N_1 X_1 Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,X_1),N_1)),hAPP(nat,nat,power_power(nat,Y),N_1)))).
% 32.46/32.32 all N_1 M ((M=zero_zero(nat)->hAPP(nat,nat,times_times(nat,M),N_1)=zero_zero(nat))& (M!=zero_zero(nat)->hAPP(nat,nat,times_times(nat,M),N_1)=hAPP(nat,nat,plus_plus(nat,N_1),hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,M),one_one(nat))),N_1)))).
% 32.46/32.32 all P_3 M ((M=zero_zero(nat)->hAPP(nat,nat,power_power(nat,P_3),M)=one_one(nat))& (M!=zero_zero(nat)->hAPP(nat,nat,power_power(nat,P_3),M)=hAPP(nat,nat,times_times(nat,P_3),hAPP(nat,nat,power_power(nat,P_3),hAPP(nat,nat,minus_minus(nat,M),one_one(nat)))))).
% 32.46/32.32 all X_1 Y (hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,power_power(nat,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,nat,power_power(nat,Y),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,nat,times_times(nat,hAPP(nat,nat,plus_plus(nat,X_1),Y)),hAPP(nat,nat,minus_minus(nat,X_1),Y))).
% 32.46/32.32 all A_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))->B=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A_1),B))).
% 32.46/32.32 all Ma K N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))<->K=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N))).
% 32.46/32.32 all N Ma (hAPP(nat,nat,times_times(nat,N),Ma)=one_one(nat)<->N=one_one(nat)&Ma=one_one(nat)).
% 32.46/32.32 all Ma N (hAPP(nat,nat,power_power(nat,Ma),N)=zero_zero(nat)<->N!=zero_zero(nat)&Ma=zero_zero(nat)).
% 32.46/32.32 all X_1 Y N_1 (N_1!=zero_zero(nat)-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,X_1),N_1)),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y)))).
% 32.46/32.32 all A_1 N_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,A_1),N_1)),hAPP(nat,nat,power_power(nat,B),N_1)))-> (N_1!=zero_zero(nat)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)))).
% 32.46/32.32 all X N (hAPP(nat,nat,power_power(nat,X),N)=one_one(nat)<->X=one_one(nat)|N=zero_zero(nat)).
% 32.46/32.32 all X_1 Q_1 N_1 R_1 (X_1=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,Q_1),N_1)),R_1)-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),R_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_1),N_1))-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),X_1))))).
% 32.46/32.32 all X Y_1 (hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,real,power_power(real,Y_1),number_number_of(nat,bit0(bit1(pls)))))=zero_zero(real)<->X=zero_zero(real)&Y_1=zero_zero(real)).
% 32.46/32.32 all A_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))-> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_2))&hAPP(nat,real,power_power(real,X_2),N_1)=A_1& (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_2))&hAPP(nat,real,power_power(real,Y_2),N_1)=A_1->Y_2=X_2)))))).
% 32.46/32.32 all A_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))-> (exists R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2))&hAPP(nat,real,power_power(real,R_2),N_1)=A_1)))).
% 32.46/32.32 all N Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,N),Ma)),Ma))<->N=one_one(nat))).
% 32.46/32.32 all X_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),X_1)).
% 32.46/32.32 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))).
% 32.46/32.32 all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N_1)).
% 32.46/32.32 all I_1 J_1 K_1 (hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,minus_minus(nat,I_1),J_1)),K_1)=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,minus_minus(nat,I_1),K_1)),J_1)).
% 32.46/32.32 all N_1 (hAPP(nat,nat,minus_minus(nat,zero_zero(nat)),N_1)=zero_zero(nat)).
% 32.46/32.32 all M (hAPP(nat,nat,minus_minus(nat,M),zero_zero(nat))=M).
% 32.46/32.32 all M (hAPP(nat,nat,minus_minus(nat,M),M)=zero_zero(nat)).
% 32.46/32.32 all M N_1 (hAPP(nat,nat,minus_minus(nat,M),N_1)=zero_zero(nat)-> (hAPP(nat,nat,minus_minus(nat,N_1),M)=zero_zero(nat)->M=N_1)).
% 32.46/32.32 zero_zero(real)!=one_one(real).
% 32.46/32.32 all X Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y_1))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,minus_minus(real,X),Y_1)),zero_zero(real)))).
% 32.46/32.32 all X Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y_1))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y_1))&X!=Y_1).
% 32.46/32.32 all X Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y_1))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y_1))|X=Y_1).
% 32.46/32.32 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))).
% 32.46/32.32 all Ma N (Ma!=N<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),Ma))).
% 32.46/32.32 all X_1 Y (X_1!=Y-> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X_1)))).
% 32.46/32.32 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))).
% 32.46/32.32 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M))->M!=N_1).
% 32.46/32.32 all S T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3))->S!=T_3).
% 32.46/32.32 all P_1 Ma N ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N),Ma)))-> ((Ma=N->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N),Ma)))-> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),Ma))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N),Ma)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N),Ma))))).
% 32.46/32.32 all N_1 J_1 K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,J_1),N_1)),K_1))).
% 32.46/32.32 all L_1 M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,L_1),N_1)),hAPP(nat,nat,minus_minus(nat,L_1),M))))).
% 32.46/32.32 all X_1 Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y)))).
% 32.46/32.32 all Z_1 X_1 Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X_1)))).
% 32.46/32.32 all A_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)))).
% 32.46/32.32 all Z_1 X_1 Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X_1)))).
% 32.46/32.32 all C A_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1))-> (B=C->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1)))).
% 32.46/32.32 all P_1 X Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))->hBOOL(P_1))).
% 32.46/32.32 all X_1 Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))->Y!=X_1).
% 32.46/32.32 all X_1 Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))->X_1!=Y).
% 32.46/32.32 all X_1 Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y)))).
% 32.46/32.32 all X_1 Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))).
% 32.46/32.32 all X_1 Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y)))).
% 32.46/32.32 all X_1 Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))->X_1!=Y).
% 32.46/32.32 all Z_1 X_1 Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X_1)))).
% 32.46/32.32 all C A_1 B (A_1=B-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),B))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1)))).
% 32.46/32.32 all N_1 K_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),M))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),hAPP(nat,nat,minus_minus(nat,M),N_1))))).
% 32.46/32.32 all Z_1 X_1 Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z_1)))).
% 32.46/32.32 all X_1 Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))->X_1=Y)).
% 32.46/32.32 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),M))->M=N_1)).
% 32.46/32.32 all C A_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))-> (B=C->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)))).
% 32.46/32.32 all C A_1 B (A_1=B-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)))).
% 32.46/32.32 all A_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))-> (A_1!=B->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)))).
% 32.46/32.32 all X_1 Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))|X_1=Y).
% 32.46/32.32 all Y_1 X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))<->X=Y_1)).
% 32.46/32.32 all X_1 Y (X_1=Y->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))).
% 32.46/32.32 all A_1 B (A_1!=B-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)))).
% 32.46/32.32 all X Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X))).
% 32.46/32.32 all X Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))&X!=Y_1).
% 32.46/32.32 all X Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X))|X=Y_1).
% 32.46/32.32 all X Y_1 (X=Y_1<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X))).
% 32.46/32.32 all X_1 (-(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),X_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),X_1)))).
% 32.46/32.32 all M N_1 (hAPP(nat,nat,plus_plus(nat,M),N_1)=hAPP(nat,nat,plus_plus(nat,N_1),M)).
% 32.46/32.32 all X_1 Y Z_1 (hAPP(nat,nat,plus_plus(nat,X_1),hAPP(nat,nat,plus_plus(nat,Y),Z_1))=hAPP(nat,nat,plus_plus(nat,Y),hAPP(nat,nat,plus_plus(nat,X_1),Z_1))).
% 32.46/32.32 all M N_1 K_1 (hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,plus_plus(nat,M),N_1)),K_1)=hAPP(nat,nat,plus_plus(nat,M),hAPP(nat,nat,plus_plus(nat,N_1),K_1))).
% 32.46/32.32 all K Ma N (hAPP(nat,nat,plus_plus(nat,K),Ma)=hAPP(nat,nat,plus_plus(nat,K),N)<->Ma=N).
% 32.46/32.32 all Ma K N (hAPP(nat,nat,plus_plus(nat,Ma),K)=hAPP(nat,nat,plus_plus(nat,N),K)<->Ma=N).
% 32.46/32.32 all M N_1 (hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,M),N_1)),N_1)=M).
% 32.46/32.32 all N_1 M (hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,N_1),M)),N_1)=M).
% 32.46/32.32 all I_1 J_1 K_1 (hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,minus_minus(nat,I_1),J_1)),K_1)=hAPP(nat,nat,minus_minus(nat,I_1),hAPP(nat,nat,plus_plus(nat,J_1),K_1))).
% 32.46/32.32 all K_1 M N_1 (hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,K_1),M)),hAPP(nat,nat,plus_plus(nat,K_1),N_1))=hAPP(nat,nat,minus_minus(nat,M),N_1)).
% 32.46/32.32 all M K_1 N_1 (hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,M),K_1)),hAPP(nat,nat,plus_plus(nat,N_1),K_1))=hAPP(nat,nat,minus_minus(nat,M),N_1)).
% 32.46/32.32 all Z1 Z2 Z3 (hAPP(real,real,times_times(real,hAPP(real,real,times_times(real,Z1),Z2)),Z3)=hAPP(real,real,times_times(real,Z1),hAPP(real,real,times_times(real,Z2),Z3))).
% 32.46/32.32 all Z_1 W (hAPP(real,real,times_times(real,Z_1),W)=hAPP(real,real,times_times(real,W),Z_1)).
% 32.46/32.32 all Z_1 (hAPP(real,real,times_times(real,one_one(real)),Z_1)=Z_1).
% 32.46/32.32 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->M=N_1)).
% 32.46/32.32 all K_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),K_1)))).
% 32.46/32.32 all M N_1 (M=N_1->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))).
% 32.46/32.32 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))).
% 32.46/32.32 all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),N_1)).
% 32.46/32.32 all N K Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,Ma),K)),hAPP(nat,nat,minus_minus(nat,N),K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))))).
% 32.46/32.32 all N_1 K_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))->hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,minus_minus(nat,M),K_1)),hAPP(nat,nat,minus_minus(nat,N_1),K_1))=hAPP(nat,nat,minus_minus(nat,M),N_1))).
% 32.46/32.32 all N K Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))-> (hAPP(nat,nat,minus_minus(nat,Ma),K)=hAPP(nat,nat,minus_minus(nat,N),K)<->Ma=N))).
% 32.46/32.32 all I_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),N_1))->hAPP(nat,nat,minus_minus(nat,N_1),hAPP(nat,nat,minus_minus(nat,N_1),I_1))=I_1).
% 32.46/32.32 all L_1 M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,M),L_1)),hAPP(nat,nat,minus_minus(nat,N_1),L_1)))).
% 32.46/32.32 all L_1 M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,L_1),N_1)),hAPP(nat,nat,minus_minus(nat,L_1),M)))).
% 32.46/32.32 all M N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,M),N_1)),M)).
% 32.46/32.32 all M N_1 (hAPP(nat,nat,times_times(nat,M),N_1)=hAPP(nat,nat,times_times(nat,N_1),M)).
% 32.46/32.32 all M N_1 K_1 (hAPP(nat,nat,times_times(nat,hAPP(nat,nat,times_times(nat,M),N_1)),K_1)=hAPP(nat,nat,times_times(nat,M),hAPP(nat,nat,times_times(nat,N_1),K_1))).
% 32.46/32.32 all K_1 M N_1 (hAPP(nat,nat,times_times(nat,K_1),hAPP(nat,nat,minus_minus(nat,M),N_1))=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,times_times(nat,K_1),M)),hAPP(nat,nat,times_times(nat,K_1),N_1))).
% 32.46/32.32 all M N_1 K_1 (hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),K_1)=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,times_times(nat,M),K_1)),hAPP(nat,nat,times_times(nat,N_1),K_1))).
% 32.46/32.32 all Z_1 X_1 Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),Y))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,plus_plus(real,Z_1),X_1)),hAPP(real,real,plus_plus(real,Z_1),Y)))).
% 32.46/32.32 all X_a (ab_group_add(X_a)-> (all A_1 C B D_2 (hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),hAPP(X_a,X_a,minus_minus(X_a,C),D_2))))).
% 32.46/32.32 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))).
% 32.46/32.32 all N (N!=zero_zero(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))).
% 32.46/32.32 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))).
% 32.46/32.32 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->N_1!=zero_zero(nat)).
% 32.46/32.32 all N_1 (N_1!=zero_zero(nat)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))).
% 32.46/32.32 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,M),N_1)),M)))).
% 32.46/32.32 all N Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,minus_minus(nat,N),Ma)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))).
% 32.46/32.32 all N_1 (hAPP(nat,nat,plus_plus(nat,zero_zero(nat)),N_1)=N_1).
% 32.46/32.32 all M (hAPP(nat,nat,plus_plus(nat,M),zero_zero(nat))=M).
% 32.46/32.32 all Ma N (hAPP(nat,nat,plus_plus(nat,Ma),N)=zero_zero(nat)<->Ma=zero_zero(nat)&N=zero_zero(nat)).
% 32.46/32.32 all M N_1 (hAPP(nat,nat,plus_plus(nat,M),N_1)=M->N_1=zero_zero(nat)).
% 32.46/32.32 all N_1 M (hAPP(nat,nat,minus_minus(nat,N_1),hAPP(nat,nat,plus_plus(nat,N_1),M))=zero_zero(nat)).
% 32.46/32.32 all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N_1)).
% 32.46/32.32 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),zero_zero(nat)))<->N=zero_zero(nat)).
% 32.46/32.32 all Ma N (hAPP(nat,nat,minus_minus(nat,Ma),N)=zero_zero(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))).
% 32.46/32.32 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))->hAPP(nat,nat,minus_minus(nat,M),N_1)=zero_zero(nat)).
% 32.46/32.32 all N_1 (hAPP(nat,nat,times_times(nat,zero_zero(nat)),N_1)=zero_zero(nat)).
% 32.46/32.32 all M (hAPP(nat,nat,times_times(nat,M),zero_zero(nat))=zero_zero(nat)).
% 32.46/32.32 all Ma N (hAPP(nat,nat,times_times(nat,Ma),N)=zero_zero(nat)<->Ma=zero_zero(nat)|N=zero_zero(nat)).
% 32.46/32.32 all K Ma N (hAPP(nat,nat,times_times(nat,K),Ma)=hAPP(nat,nat,times_times(nat,K),N)<->Ma=N|K=zero_zero(nat)).
% 32.46/32.32 all Ma K N (hAPP(nat,nat,times_times(nat,Ma),K)=hAPP(nat,nat,times_times(nat,N),K)<->Ma=N|K=zero_zero(nat)).
% 32.46/32.32 all A_3 B_2 C_1 (C_1!=zero_zero(real)-> (hAPP(real,real,times_times(real,C_1),A_3)=hAPP(real,real,times_times(real,C_1),B_2)<->A_3=B_2)).
% 32.46/32.32 all A_3 B_2 C_1 (C_1!=zero_zero(real)-> (hAPP(real,real,times_times(real,A_3),C_1)=hAPP(real,real,times_times(real,B_2),C_1)<->A_3=B_2)).
% 32.46/32.32 all I_1 J_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_1),J_1)),I_1))).
% 32.46/32.32 all J_1 I_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,J_1),I_1)),I_1))).
% 32.46/32.32 all K Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,K),Ma)),hAPP(nat,nat,plus_plus(nat,K),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))).
% 32.46/32.32 all M I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,plus_plus(nat,J_1),M)))).
% 32.46/32.32 all M I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,plus_plus(nat,M),J_1)))).
% 32.46/32.32 all K_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_1),K_1)),hAPP(nat,nat,plus_plus(nat,J_1),K_1)))).
% 32.46/32.32 all K_1 L_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_1),K_1)),hAPP(nat,nat,plus_plus(nat,J_1),L_1))))).
% 32.46/32.32 all M N_1 K_1 L_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_1))-> (hAPP(nat,nat,plus_plus(nat,M),L_1)=hAPP(nat,nat,plus_plus(nat,K_1),N_1)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)))).
% 32.46/32.32 all I_1 J_1 K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_1),J_1)),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K_1))).
% 32.46/32.32 all M N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->hAPP(nat,nat,plus_plus(nat,N_1),hAPP(nat,nat,minus_minus(nat,M),N_1))=M).
% 32.46/32.32 all I_2 J_2 K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,minus_minus(nat,J_2),K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),J_2))).
% 32.46/32.32 all Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))&Ma!=N).
% 32.46/32.32 all Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))|Ma=N).
% 32.46/32.32 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))).
% 32.46/32.32 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))-> (M!=N_1->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)))).
% 32.46/32.32 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|M=N_1->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))).
% 32.46/32.32 all C A_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),A_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,A_1),C)),hAPP(nat,nat,minus_minus(nat,B),C))))).
% 32.46/32.32 all N K Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,Ma),K)),hAPP(nat,nat,minus_minus(nat,N),K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))))).
% 32.46/32.32 all K N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,plus_plus(nat,N),K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),N))).
% 32.46/32.32 all K_1 M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),hAPP(nat,nat,minus_minus(nat,M),N_1)))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),M))))).
% 32.46/32.32 all K_1 M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),hAPP(nat,nat,minus_minus(nat,M),N_1)))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),M))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N_1))))).
% 32.46/32.32 all N_1 M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),hAPP(nat,nat,plus_plus(nat,M),N_1))).
% 32.46/32.32 all N_1 M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),hAPP(nat,nat,plus_plus(nat,N_1),M))).
% 32.46/32.32 all Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))<-> (exists K_2 (N=hAPP(nat,nat,plus_plus(nat,Ma),K_2)))).
% 32.46/32.32 all K Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,K),Ma)),hAPP(nat,nat,plus_plus(nat,K),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))).
% 32.46/32.32 all M I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),hAPP(nat,nat,plus_plus(nat,J_1),M)))).
% 32.46/32.32 all M I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),hAPP(nat,nat,plus_plus(nat,M),J_1)))).
% 32.46/32.32 all K_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_1),K_1)),hAPP(nat,nat,plus_plus(nat,J_1),K_1)))).
% 32.46/32.32 all K_1 L_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_1),K_1)),hAPP(nat,nat,plus_plus(nat,J_1),L_1))))).
% 32.46/32.32 all M K_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M),K_1)),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))).
% 32.46/32.32 all M K_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M),K_1)),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))).
% 32.46/32.32 all M K_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M),K_1)),N_1))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1)))).
% 32.46/32.32 all I_1 K_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))->hAPP(nat,nat,minus_minus(nat,I_1),hAPP(nat,nat,minus_minus(nat,J_1),K_1))=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,I_1),K_1)),J_1)).
% 32.46/32.32 all J_2 K I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,J_2),K)),I_2))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),hAPP(nat,nat,plus_plus(nat,I_2),K)))).
% 32.46/32.32 all M K_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,N_1),M)),K_1)))).
% 32.46/32.32 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hAPP(nat,nat,plus_plus(nat,N_1),hAPP(nat,nat,minus_minus(nat,M),N_1))=M).
% 32.46/32.32 all I_1 K_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))->hAPP(nat,nat,plus_plus(nat,I_1),hAPP(nat,nat,minus_minus(nat,J_1),K_1))=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,I_1),J_1)),K_1)).
% 32.46/32.32 all I_2 K J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),hAPP(nat,nat,minus_minus(nat,J_2),K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),J_2)))).
% 32.46/32.32 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),N_1)=M).
% 32.46/32.32 all K I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))-> (hAPP(nat,nat,minus_minus(nat,J_2),I_2)=K<->J_2=hAPP(nat,nat,plus_plus(nat,K),I_2))).
% 32.46/32.32 all I_1 K_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))->hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,I_1),J_1)),K_1)=hAPP(nat,nat,plus_plus(nat,I_1),hAPP(nat,nat,minus_minus(nat,J_1),K_1))).
% 32.46/32.32 all I_1 K_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))->hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,minus_minus(nat,J_1),K_1)),I_1)=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,J_1),I_1)),K_1)).
% 32.46/32.32 all I_1 K_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))->hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,J_1),I_1)),K_1)=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,minus_minus(nat,J_1),K_1)),I_1)).
% 32.46/32.32 all K_1 M N_1 (hAPP(nat,nat,times_times(nat,K_1),hAPP(nat,nat,plus_plus(nat,M),N_1))=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,K_1),M)),hAPP(nat,nat,times_times(nat,K_1),N_1))).
% 32.46/32.32 all M N_1 K_1 (hAPP(nat,nat,times_times(nat,hAPP(nat,nat,plus_plus(nat,M),N_1)),K_1)=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,M),K_1)),hAPP(nat,nat,times_times(nat,N_1),K_1))).
% 32.46/32.32 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),one_one(nat)))<->Ma=one_one(nat)).
% 32.46/32.32 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,times_times(nat,M),M))).
% 32.46/32.32 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,times_times(nat,M),hAPP(nat,nat,times_times(nat,M),M)))).
% 32.46/32.32 all K_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,I_1),K_1)),hAPP(nat,nat,times_times(nat,J_1),K_1)))).
% 32.46/32.32 all K_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K_1),I_1)),hAPP(nat,nat,times_times(nat,K_1),J_1)))).
% 32.46/32.32 all K_1 L_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,I_1),K_1)),hAPP(nat,nat,times_times(nat,J_1),L_1))))).
% 32.46/32.32 all N_1 (hAPP(nat,nat,times_times(nat,one_one(nat)),N_1)=N_1).
% 32.46/32.32 all Ma N (one_one(nat)=hAPP(nat,nat,times_times(nat,Ma),N)<->Ma=one_one(nat)&N=one_one(nat)).
% 32.46/32.32 all N_1 (hAPP(nat,nat,times_times(nat,N_1),one_one(nat))=N_1).
% 32.46/32.32 all Ma N (hAPP(nat,nat,times_times(nat,Ma),N)=one_one(nat)<->Ma=one_one(nat)&N=one_one(nat)).
% 32.46/32.32 all Z1 Z2 W (hAPP(real,real,times_times(real,hAPP(real,real,plus_plus(real,Z1),Z2)),W)=hAPP(real,real,plus_plus(real,hAPP(real,real,times_times(real,Z1),W)),hAPP(real,real,times_times(real,Z2),W))).
% 32.46/32.33 all X_a (ring(X_a)-> (all X_1 Y A_1 B (hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Y)),hAPP(X_a,X_a,times_times(X_a,A_1),B))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),hAPP(X_a,X_a,minus_minus(X_a,Y),B))),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),A_1)),B))))).
% 32.46/32.33 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),M)))).
% 32.46/32.33 all Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,Ma),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))).
% 32.46/32.33 all P_1 A_3 B_2 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))<-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2))& -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| (exists D_4 (A_3=hAPP(nat,nat,plus_plus(nat,B_2),D_4)& -hBOOL(hAPP(nat,bool,P_1,D_4)))))).
% 32.46/32.33 all P_1 A_3 B_2 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))<-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2))->hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))))& (all D_4 (A_3=hAPP(nat,nat,plus_plus(nat,B_2),D_4)->hBOOL(hAPP(nat,bool,P_1,D_4))))).
% 32.46/32.33 all Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,times_times(nat,Ma),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))).
% 32.46/32.33 all K Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))).
% 32.46/32.33 all Ma K N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))).
% 32.46/32.33 all K_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,I_1),K_1)),hAPP(nat,nat,times_times(nat,J_1),K_1))))).
% 32.46/32.33 all K_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K_1),I_1)),hAPP(nat,nat,times_times(nat,K_1),J_1))))).
% 32.46/32.33 all X Y_1 Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,times_times(real,X),Z_2)),hAPP(real,real,times_times(real,Y_1),Z_2)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y_1)))).
% 32.46/32.33 all X Y_1 Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,times_times(real,Z_2),X)),hAPP(real,real,times_times(real,Z_2),Y_1)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y_1)))).
% 32.46/32.33 all X_1 Y Z_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_1))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,times_times(real,Z_1),X_1)),hAPP(real,real,times_times(real,Z_1),Y))))).
% 32.46/32.33 all Y X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,times_times(real,X_1),Y))))).
% 32.46/32.33 all X Y_1 Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,times_times(real,X),Z_2)),hAPP(real,real,times_times(real,Y_1),Z_2)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y_1)))).
% 32.46/32.33 all M N_1 (M=hAPP(nat,nat,times_times(nat,M),N_1)->N_1=one_one(nat)|M=zero_zero(nat)).
% 32.46/32.33 all X Y_1 (hAPP(real,real,plus_plus(real,hAPP(real,real,times_times(real,X),X)),hAPP(real,real,times_times(real,Y_1),Y_1))=zero_zero(real)<->X=zero_zero(real)&Y_1=zero_zero(real)).
% 32.46/32.33 all X_a (ring_1(X_a)-> (all X_1 (hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),X_1)),one_one(X_a))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,X_1),one_one(X_a))),hAPP(X_a,X_a,minus_minus(X_a,X_1),one_one(X_a)))))).
% 32.46/32.33 all K_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1)))).
% 32.46/32.33 all K_1 M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K_1),M)),hAPP(nat,nat,times_times(nat,K_1),N_1)))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N_1)))).
% 32.46/32.33 all K Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))<-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)))).
% 32.46/32.33 all Ma K N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))<-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)))).
% 32.46/32.33 all X_a (monoid_mult(X_a)-> (all X_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,X_1),hAPP(nat,nat,minus_minus(nat,N_1),one_one(nat)))),X_1)=hAPP(nat,X_a,power_power(X_a,X_1),N_1)))).
% 32.46/32.33 all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),one_one(real)),hAPP(nat,real,power_power(real,number_number_of(real,bit0(bit1(pls)))),N_1))).
% 32.46/32.33 all N Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,Ma),N)),Ma))<->N=one_one(nat))).
% 32.46/32.33 all X_a (power(X_a)-> (all M N_1 ((N_1=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,M),N_1)=one_one(X_a))& (N_1!=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,M),N_1)=hAPP(X_a,X_a,times_times(X_a,M),hAPP(nat,X_a,power_power(X_a,M),hAPP(nat,nat,minus_minus(nat,N_1),one_one(nat)))))))).
% 32.46/32.33 all N P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))-> (hBOOL(hAPP(nat,bool,P_1,N))-> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),N))& (all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),K_2))-> -hBOOL(hAPP(nat,bool,P_1,I))))&hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,plus_plus(nat,K_2),one_one(nat)))))))).
% 32.46/32.33 all U Ma N I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N))))).
% 32.46/32.33 all U Ma N J_2 I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)),N)))).
% 32.46/32.33 all W hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),W)).
% 32.46/32.33 all Z_1 W (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z_1),W))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),Z_1))).
% 32.46/32.33 all K_1 I_1 J_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I_1),J_1))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),J_1),K_1))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I_1),K_1)))).
% 32.46/32.33 all Z_1 W (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z_1),W))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),Z_1))->Z_1=W)).
% 32.46/32.33 all K Ma N (hAPP(nat,nat,times_times(nat,K),Ma)=hAPP(nat,nat,times_times(nat,K),N)<->K=zero_zero(nat)|Ma=N).
% 32.46/32.33 all I_1 U_1 J_1 K_1 (hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_1),U_1)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_1),U_1)),K_1))=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,plus_plus(nat,I_1),J_1)),U_1)),K_1)).
% 32.46/32.33 all Ma N K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)))).
% 32.46/32.33 all Ma N K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))-> (hAPP(nat,nat,times_times(nat,K),Ma)=hAPP(nat,nat,times_times(nat,K),N)<->Ma=N)).
% 32.46/32.33 all K Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))<->K=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N))).
% 32.46/32.33 all Ma N K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N)))).
% 32.46/32.33 all Ma N K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)))).
% 32.46/32.33 all U Ma N J_2 I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)),N)))).
% 32.46/32.33 all U_1 M N_1 J_1 I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),I_1))->hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_1),U_1)),M)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_1),U_1)),N_1))=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_1),J_1)),U_1)),M)),N_1)).
% 32.46/32.33 all U Ma N J_2 I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))-> (hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)<->hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)=N)).
% 32.46/32.33 all U Ma N I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N))))).
% 32.46/32.33 all U_1 M N_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))->hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_1),U_1)),M)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_1),U_1)),N_1))=hAPP(nat,nat,minus_minus(nat,M),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_1),I_1)),U_1)),N_1))).
% 32.46/32.33 all U Ma N I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))-> (hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)<->Ma=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N))).
% 32.46/32.33 all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,N_1)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit0(N_1))))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit1(N_1))))).
% 32.46/32.33 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))-> (exists P_5 (hBOOL(hAPP(int,bool,zprime,P_5))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),A_1))))).
% 32.46/32.33 all P_4 P_1 X ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))-> (hBOOL(P_1)<->hBOOL(P_4)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))&hBOOL(P_1)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))&hBOOL(P_4))).
% 32.46/32.33 all P_4 P_1 X ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))-> (hBOOL(P_1)<->hBOOL(P_4)))-> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))->hBOOL(P_1))<-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))->hBOOL(P_4)))).
% 32.46/32.33 all Ma Ta K (ti(int,K)!=zero_zero(int)-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),Ta))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,times_times(int,K),Ma)),hAPP(int,int,times_times(int,K),Ta))))).
% 32.46/32.33 all X_a (dvd(X_a)&semiring_0(X_a)-> (all P_1 L ((exists X_2 hBOOL(hAPP(X_a,bool,P_1,hAPP(X_a,X_a,times_times(X_a,L),X_2))))<-> (exists X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L),hAPP(X_a,X_a,plus_plus(X_a,X_2),zero_zero(X_a))))&hBOOL(hAPP(X_a,bool,P_1,X_2))))))).
% 32.46/32.33 all X_a (comm_ring(X_a)&dvd(X_a)-> (all Ta D D_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),D_3))-> (all X_2 K_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X_2),Ta)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_2),hAPP(X_a,X_a,times_times(X_a,K_2),D_3))),Ta)))))))).
% 32.46/32.33 all X_a (comm_ring(X_a)&dvd(X_a)-> (all Ta D D_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),D_3))-> (all X_2 K_2 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X_2),Ta)))<-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_2),hAPP(X_a,X_a,times_times(X_a,K_2),D_3))),Ta)))))))).
% 32.46/32.33 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,pls))).
% 32.46/32.33 all K P_1 D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))-> ((all X_2 (hBOOL(hAPP(int,bool,P_1,X_2))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,minus_minus(int,X_2),D)))))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))-> (all X_2 (hBOOL(hAPP(int,bool,P_1,X_2))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,minus_minus(int,X_2),hAPP(int,int,times_times(int,K),D))))))))).
% 32.46/32.33 all K P_1 D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))-> ((all X_2 (hBOOL(hAPP(int,bool,P_1,X_2))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,X_2),D)))))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))-> (all X_2 (hBOOL(hAPP(int,bool,P_1,X_2))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,X_2),hAPP(int,int,times_times(int,K),D))))))))).
% 32.46/32.33 all A_1 M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))-> (exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_2))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),M))&hBOOL(hAPP(int,bool,zcong(A_1,X_2),M))& (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y_2))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_2),M))&hBOOL(hAPP(int,bool,zcong(A_1,Y_2),M))->ti(int,Y_2)=ti(int,X_2)))))).
% 32.46/32.33 twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))=hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t).
% 32.46/32.33 all A_1 B P_3 Q_1 (hAPP(int,int,times_times(int,twoSqu1929807760sum2sq(product_Pair(int,int,A_1,B))),twoSqu1929807760sum2sq(product_Pair(int,int,P_3,Q_1)))=twoSqu1929807760sum2sq(product_Pair(int,int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A_1),P_3)),hAPP(int,int,times_times(int,B),Q_1)),hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,A_1),Q_1)),hAPP(int,int,times_times(int,B),P_3))))).
% 32.46/32.33 all X (hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,X))<-> (exists A_5 B_4 (twoSqu1929807760sum2sq(product_Pair(int,int,A_5,B_4))=ti(int,X)))).
% 32.46/32.33 all A_1 B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),hAPP(int,int,minus_minus(int,B),one_one(int))))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B))).
% 32.46/32.33 all P_3 (hBOOL(hAPP(int,bool,zprime,P_3))->hBOOL(hAPP(int,bool,zcong(zfact(hAPP(int,int,minus_minus(int,P_3),one_one(int))),number_number_of(int,min)),P_3))).
% 32.46/32.33 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))))))).
% 32.46/32.33 all X_a (zero(X_a)-> (all X (zero_zero(X_a)=ti(X_a,X)<->ti(X_a,X)=zero_zero(X_a)))).
% 32.46/32.33 all X_a (ab_semigroup_mult(X_a)-> (all A_1 B C (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,times_times(X_a,B),C))))).
% 32.46/32.33 all X_a (ab_semigroup_add(X_a)-> (all A_1 B C (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C))))).
% 32.46/32.33 all X_a (cancel_semigroup_add(X_a)-> (all A_3 B_2 C_1 (hAPP(X_a,X_a,plus_plus(X_a,A_3),B_2)=hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)<->ti(X_a,B_2)=ti(X_a,C_1)))).
% 32.46/32.33 all X_a (cancel_semigroup_add(X_a)-> (all B_2 A_3 C_1 (hAPP(X_a,X_a,plus_plus(X_a,B_2),A_3)=hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)<->ti(X_a,B_2)=ti(X_a,C_1)))).
% 32.46/32.33 all X_a (cancel_semigroup_add(X_a)-> (all A_1 B C (hAPP(X_a,X_a,plus_plus(X_a,A_1),B)=hAPP(X_a,X_a,plus_plus(X_a,A_1),C)->ti(X_a,B)=ti(X_a,C)))).
% 32.46/32.33 all X_a (cancel146912293up_add(X_a)-> (all A_1 B C (hAPP(X_a,X_a,plus_plus(X_a,A_1),B)=hAPP(X_a,X_a,plus_plus(X_a,A_1),C)->ti(X_a,B)=ti(X_a,C)))).
% 32.46/32.33 all X_a (cancel_semigroup_add(X_a)-> (all B A_1 C (hAPP(X_a,X_a,plus_plus(X_a,B),A_1)=hAPP(X_a,X_a,plus_plus(X_a,C),A_1)->ti(X_a,B)=ti(X_a,C)))).
% 32.46/32.33 all X_a (one(X_a)-> (all X (one_one(X_a)=ti(X_a,X)<->ti(X_a,X)=one_one(X_a)))).
% 32.46/32.33 all X_a (ab_group_add(X_a)-> (all A_3 B_2 C_1 D (hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)-> (ti(X_a,A_3)=ti(X_a,B_2)<->ti(X_a,C_1)=ti(X_a,D))))).
% 32.46/32.33 all X_a (monoid_add(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1)))).
% 32.46/32.33 all X_a (comm_monoid_add(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1)))).
% 32.46/32.33 all X_a (linord219039673up_add(X_a)-> (all A_3 (zero_zero(X_a)=hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)<->ti(X_a,A_3)=zero_zero(X_a)))).
% 32.46/32.33 all X_a (monoid_add(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1)))).
% 32.46/32.33 all X_a (comm_monoid_add(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1)))).
% 32.46/32.33 all X_a (ordere236663937imp_le(X_a)-> (all A_3 C_1 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B_2),C_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2))))).
% 32.46/32.33 all X_a (ordere236663937imp_le(X_a)-> (all C_1 A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2))))).
% 32.46/32.33 all X_a (ordere779506340up_add(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),C)))))).
% 32.46/32.33 all X_a (ordere779506340up_add(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C),B)))))).
% 32.46/32.33 all X_a (ordere779506340up_add(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))))))).
% 32.46/32.33 all X_a (ordere236663937imp_le(X_a)-> (all A_1 C B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),C)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))))).
% 32.46/32.33 all X_a (ordere236663937imp_le(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C),B)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))))).
% 32.46/32.33 all X_a (ordere236663937imp_le(X_a)-> (all A_3 C_1 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B_2),C_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))))).
% 32.46/32.33 all X_a (ordere236663937imp_le(X_a)-> (all C_1 A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))))).
% 32.46/32.33 all X_a (ordere223160158up_add(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),C)))))).
% 32.46/32.33 all X_a (ordere223160158up_add(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C),B)))))).
% 32.46/32.33 all X_a (ordere223160158up_add(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))))))).
% 32.46/32.33 all X_a (ordere236663937imp_le(X_a)-> (all A_1 C B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),C)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))).
% 32.46/32.33 all X_a (ordere236663937imp_le(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C),B)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))).
% 32.46/32.33 all X_a (group_add(X_a)-> (all A_3 B_2 (hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)=zero_zero(X_a)<->ti(X_a,A_3)=ti(X_a,B_2)))).
% 32.46/32.33 all X_a (ab_group_add(X_a)-> (all A_3 B_2 (ti(X_a,A_3)=ti(X_a,B_2)<->hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)=zero_zero(X_a)))).
% 32.46/32.33 all X_a (group_add(X_a)-> (all A_1 (hAPP(X_a,X_a,minus_minus(X_a,A_1),A_1)=zero_zero(X_a)))).
% 32.46/32.33 all X_a (group_add(X_a)-> (all A_1 (hAPP(X_a,X_a,minus_minus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1)))).
% 32.46/32.33 all X_a (ordered_ab_group_add(X_a)-> (all A_3 B_2 C_1 D (hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),D)))))).
% 32.46/32.33 all X_a (ordered_ab_group_add(X_a)-> (all A_3 B_2 C_1 D (hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D)))))).
% 32.46/32.33 all X_a (monoid_mult(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,one_one(X_a)),A_1)=ti(X_a,A_1)))).
% 32.46/32.33 all X_a (comm_monoid_mult(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,one_one(X_a)),A_1)=ti(X_a,A_1)))).
% 32.46/32.33 all X_a (monoid_mult(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,A_1),one_one(X_a))=ti(X_a,A_1)))).
% 32.46/32.33 all X_a (comm_monoid_mult(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,A_1),one_one(X_a))=ti(X_a,A_1)))).
% 32.46/32.33 all X_a (group_add(X_a)-> (all A_1 B (hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),B)=ti(X_a,A_1)))).
% 32.46/32.33 all X_a (group_add(X_a)-> (all A_1 B (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),B)=ti(X_a,A_1)))).
% 32.46/32.33 all X_a (linord219039673up_add(X_a)-> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))))).
% 32.46/32.33 all X_a (linord219039673up_add(X_a)-> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a)))))).
% 32.46/32.33 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))))))).
% 32.46/32.33 all X_a (ordere216010020id_add(X_a)-> (all Y_1 X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_1))-> (hAPP(X_a,X_a,plus_plus(X_a,X),Y_1)=zero_zero(X_a)<->ti(X_a,X)=zero_zero(X_a)&ti(X_a,Y_1)=zero_zero(X_a)))))).
% 32.46/32.33 all X_a (ordere216010020id_add(X_a)-> (all B C A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))))))).
% 32.46/32.33 all X_a (ordere216010020id_add(X_a)-> (all B A_1 C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))))))).
% 32.46/32.33 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))))))).
% 32.46/32.33 all X_a (linord219039673up_add(X_a)-> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_3))))).
% 32.46/32.33 all X_a (linord219039673up_add(X_a)-> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),zero_zero(X_a)))))).
% 32.46/32.33 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))))))).
% 32.46/32.33 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))))))).
% 32.46/32.33 all X_a (ordere223160158up_add(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))))))).
% 32.46/32.33 all X_a (ordere223160158up_add(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))))))).
% 32.46/32.33 all X_a (ordered_ab_group_add(X_a)-> (all A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),zero_zero(X_a)))))).
% 32.46/32.33 all X_a (ordered_ab_group_add(X_a)-> (all A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),zero_zero(X_a)))))).
% 32.46/32.33 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))))))).
% 32.46/32.33 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))))))).
% 32.46/32.33 all X_a (ordere216010020id_add(X_a)-> (all B C A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))))))).
% 32.46/32.33 all X_a (ordere216010020id_add(X_a)-> (all B C A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))))))).
% 32.46/32.33 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))))))).
% 32.46/32.33 all N_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_1),zero_zero(int)))->zfact(N_1)=one_one(int))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_1),zero_zero(int)))->zfact(N_1)=hAPP(int,int,times_times(int,N_1),zfact(hAPP(int,int,minus_minus(int,N_1),one_one(int)))))).
% 32.46/32.33 all A_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_3))->inv(P_3,inv(P_3,A_1))=ti(int,A_1))))).
% 32.46/32.33 all A_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_3),one_one(int))))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),inv(P_3,A_1)),hAPP(int,int,minus_minus(int,P_3),one_one(int))))))).
% 32.46/32.33 all A_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_3),one_one(int))))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),inv(P_3,A_1)))))).
% 32.46/32.33 all A_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_3),one_one(int))))->inv(P_3,A_1)!=hAPP(int,int,minus_minus(int,P_3),one_one(int))))).
% 32.46/32.33 all A_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_3),one_one(int))))->inv(P_3,A_1)!=one_one(int)))).
% 32.46/32.33 all A_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_3),one_one(int))))->ti(int,A_1)!=inv(P_3,A_1)))).
% 32.46/32.33 all A_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_3),one_one(int))))->inv(P_3,A_1)!=zero_zero(int)))).
% 32.46/32.33 all A_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_3))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),inv(P_3,A_1)),one_one(int)),P_3))))).
% 32.46/32.33 all B_2 A_3 P_2 (hBOOL(hAPP(int,bool,zprime,P_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),P_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_2),one_one(int))))-> (hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_2)))->hBOOL(hAPP(fun(int,bool),bool,member(int,inv(P_2,B_2)),wset(A_3,P_2))))))).
% 32.46/32.33 all B_2 A_3 P_2 (hBOOL(hAPP(int,bool,zprime,P_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),P_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_2),one_one(int))))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_2),hAPP(int,int,minus_minus(int,P_2),one_one(int))))-> (hBOOL(hAPP(fun(int,bool),bool,member(int,inv(P_2,B_2)),wset(A_3,P_2)))->hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_2))))))))).
% 32.46/32.33 all P_2 A_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_3))->hBOOL(hAPP(fun(int,bool),bool,member(int,A_3),wset(A_3,P_2)))).
% 32.46/32.33 all B_2 P_2 A_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_3))-> (hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(hAPP(int,int,minus_minus(int,A_3),one_one(int)),P_2)))->hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_2))))).
% 32.46/32.33 all B_2 A_3 P_2 (hBOOL(hAPP(int,bool,zprime,P_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_2),one_one(int))))-> (hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_2)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2))))).
% 32.46/32.33 all B_2 A_3 P_2 (hBOOL(hAPP(int,bool,zprime,P_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_2),one_one(int))))-> (hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_2)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_2),hAPP(int,int,minus_minus(int,P_2),one_one(int))))))).
% 32.46/32.33 all B_2 P_2 A_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_3))-> (-hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(hAPP(int,int,minus_minus(int,A_3),one_one(int)),P_2)))-> (hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_2)))->ti(int,B_2)=ti(int,A_3)|ti(int,B_2)=inv(P_2,A_3)))).
% 32.46/32.33 all B_2 A_3 P_2 (hBOOL(hAPP(int,bool,zprime,P_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_2),one_one(int))))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),A_3))->hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_2))))))).
% 32.46/32.33 all J_1 A_1 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))-> (-hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_3))-> (-hBOOL(hAPP(int,bool,zcong(J_1,zero_zero(int)),P_3))-> (-hBOOL(hAPP(int,bool,quadRes(P_3),A_1))-> -hBOOL(hAPP(int,bool,zcong(J_1,hAPP(int,int,times_times(int,A_1),multInv(P_3,J_1))),P_3))))))).
% 32.46/32.33 all P_1 I_2 K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),K))-> (hBOOL(hAPP(int,bool,P_1,K))-> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I),K))-> (hBOOL(hAPP(int,bool,P_1,I))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,minus_minus(int,I),one_one(int)))))))->hBOOL(hAPP(int,bool,P_1,I_2))))).
% 32.46/32.33 all J_1 A_1 P_3 K_1 (hBOOL(hAPP(int,bool,zcong(J_1,hAPP(int,int,times_times(int,A_1),multInv(P_3,K_1))),P_3))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,J_1),K_1),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,A_1),multInv(P_3,K_1))),K_1)),P_3))).
% 32.46/32.33 all J_1 K_1 A_1 P_3 (hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,J_1),K_1),A_1),P_3))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,multInv(P_3,J_1)),J_1)),K_1),hAPP(int,int,times_times(int,multInv(P_3,J_1)),A_1)),P_3))).
% 32.46/32.33 all X_1 Y P_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))-> (hBOOL(hAPP(int,bool,zcong(X_1,Y),P_3))->hBOOL(hAPP(int,bool,zcong(multInv(P_3,X_1),multInv(P_3,Y)),P_3)))).
% 32.46/32.33 all A_1 J_1 K_1 P_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))-> (hBOOL(hAPP(int,bool,zcong(J_1,K_1),P_3))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),multInv(P_3,J_1)),hAPP(int,int,times_times(int,A_1),multInv(P_3,K_1))),P_3)))).
% 32.46/32.33 all Y X_1 P_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))-> (hBOOL(hAPP(int,bool,zprime,P_3))-> (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))-> (-hBOOL(hAPP(int,bool,zcong(Y,zero_zero(int)),P_3))-> (hBOOL(hAPP(int,bool,zcong(multInv(P_3,X_1),multInv(P_3,Y)),P_3))->hBOOL(hAPP(int,bool,zcong(X_1,Y),P_3))))))).
% 32.46/32.33 all X_1 P_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))-> (hBOOL(hAPP(int,bool,zprime,P_3))-> (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))->hBOOL(hAPP(int,bool,zcong(multInv(P_3,multInv(P_3,X_1)),X_1),P_3))))).
% 32.46/32.33 all X_1 P_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))-> (hBOOL(hAPP(int,bool,zprime,P_3))-> (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))-> -hBOOL(hAPP(int,bool,zcong(multInv(P_3,X_1),zero_zero(int)),P_3))))).
% 32.46/32.33 all K_1 A_1 J_1 P_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))-> (hBOOL(hAPP(int,bool,zprime,P_3))-> (-hBOOL(hAPP(int,bool,zcong(J_1,zero_zero(int)),P_3))-> (hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,multInv(P_3,J_1)),J_1)),K_1),hAPP(int,int,times_times(int,multInv(P_3,J_1)),A_1)),P_3))->hBOOL(hAPP(int,bool,zcong(K_1,hAPP(int,int,times_times(int,A_1),multInv(P_3,J_1))),P_3)))))).
% 32.46/32.33 all J_1 A_1 K_1 P_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))-> (hBOOL(hAPP(int,bool,zprime,P_3))-> (-hBOOL(hAPP(int,bool,zcong(K_1,zero_zero(int)),P_3))-> (hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,J_1),K_1),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,A_1),multInv(P_3,K_1))),K_1)),P_3))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,J_1),K_1),A_1),P_3)))))).
% 32.46/32.33 all A_1 J_1 K_1 P_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))-> (hBOOL(hAPP(int,bool,zprime,P_3))-> (-hBOOL(hAPP(int,bool,zcong(K_1,zero_zero(int)),P_3))-> (-hBOOL(hAPP(int,bool,zcong(J_1,zero_zero(int)),P_3))-> (hBOOL(hAPP(int,bool,zcong(J_1,hAPP(int,int,times_times(int,A_1),multInv(P_3,K_1))),P_3))->hBOOL(hAPP(int,bool,zcong(K_1,hAPP(int,int,times_times(int,A_1),multInv(P_3,J_1))),P_3))))))).
% 32.46/32.33 all J_1 K_1 A_1 P_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))-> (hBOOL(hAPP(int,bool,zprime,P_3))-> (-hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_3))-> (-hBOOL(hAPP(int,bool,zcong(K_1,zero_zero(int)),P_3))-> (-hBOOL(hAPP(int,bool,zcong(J_1,zero_zero(int)),P_3))-> (hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),multInv(P_3,J_1)),hAPP(int,int,times_times(int,A_1),multInv(P_3,K_1))),P_3))->hBOOL(hAPP(int,bool,zcong(J_1,K_1),P_3)))))))).
% 32.46/32.33 all X_1 P_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))-> (hBOOL(hAPP(int,bool,zprime,P_3))-> (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,X_1),multInv(P_3,X_1))),multInv(P_3,multInv(P_3,X_1))),X_1),P_3))))).
% 32.46/32.33 all X_1 P_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))-> (hBOOL(hAPP(int,bool,zprime,P_3))-> (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))->hBOOL(hAPP(int,bool,zcong(multInv(P_3,multInv(P_3,X_1)),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,X_1),multInv(P_3,X_1))),multInv(P_3,multInv(P_3,X_1)))),P_3))))).
% 32.46/32.33 all X_1 P_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))-> (hBOOL(hAPP(int,bool,zprime,P_3))-> (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,multInv(P_3,X_1)),X_1),one_one(int)),P_3))))).
% 32.46/32.33 all X_1 P_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))-> (hBOOL(hAPP(int,bool,zprime,P_3))-> (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,X_1),multInv(P_3,X_1)),one_one(int)),P_3))))).
% 32.46/32.33 all X P_1 ((all A_5 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_5))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,minus_minus(int,A_5),one_one(int)))))->hBOOL(hAPP(int,bool,P_1,A_5))))->hBOOL(hAPP(int,bool,P_1,X))).
% 32.46/32.33 all P_1 I_2 K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),K))-> (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,minus_minus(int,K),one_one(int))))-> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),K))-> (hBOOL(hAPP(int,bool,P_1,I))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,minus_minus(int,I),one_one(int)))))))->hBOOL(hAPP(int,bool,P_1,I_2))))).
% 32.46/32.33 all P_1 K I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),I_2))-> (hBOOL(hAPP(int,bool,P_1,K))-> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),I))-> (hBOOL(hAPP(int,bool,P_1,I))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,I),one_one(int)))))))->hBOOL(hAPP(int,bool,P_1,I_2))))).
% 32.46/32.33 all P_1 K I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_2))-> (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,K),one_one(int))))-> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I))-> (hBOOL(hAPP(int,bool,P_1,I))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,I),one_one(int)))))))->hBOOL(hAPP(int,bool,P_1,I_2))))).
% 32.46/32.33 all Ma K F_1 ((all M_2 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F_1,M_2)),hAPP(nat,nat,F_1,N_2)))))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,F_1,Ma)),K)),hAPP(nat,nat,F_1,hAPP(nat,nat,plus_plus(nat,Ma),K))))).
% 32.46/32.33 all P_2 (hBOOL(hAPP(int,bool,zprime,P_2))->d22set(hAPP(int,int,minus_minus(int,P_2),number_number_of(int,bit0(bit1(pls)))))=wset(hAPP(int,int,minus_minus(int,P_2),number_number_of(int,bit0(bit1(pls)))),P_2)).
% 32.46/32.33 all A_3 B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),B_2))-> -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),d22set(A_3)))).
% 32.46/32.33 all B_2 A_3 (hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),d22set(A_3)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),A_3))).
% 32.46/32.33 all B_2 A_3 (hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),d22set(A_3)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2))).
% 32.46/32.33 all A_3 B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),A_3))->hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),d22set(A_3))))).
% 32.46/32.33 all N P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))-> (hBOOL(hAPP(nat,bool,P_1,N))-> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),N))& (all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_2))-> -hBOOL(hAPP(nat,bool,P_1,I))))&hBOOL(hAPP(nat,bool,P_1,K_2)))))).
% 32.46/32.33 all I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))-> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2))&hAPP(nat,nat,plus_plus(nat,I_1),K_2)=J_1))).
% 32.46/32.33 all X_a (plus(X_a)&linorder(X_a)&dvd(X_a)-> (all D Sa exists Z all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X_2),Sa)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X_2),Sa))))))).
% 32.46/32.33 all X_a (plus(X_a)&linorder(X_a)&dvd(X_a)-> (all D Sa exists Z all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X_2),Sa)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X_2),Sa))))))).
% 32.46/32.33 all X_a (plus(X_a)&linorder(X_a)&dvd(X_a)-> (all D Sa exists Z all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z))-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X_2),Sa)))<-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X_2),Sa))))))).
% 32.46/32.33 all X_a (plus(X_a)&linorder(X_a)&dvd(X_a)-> (all D Sa exists Z all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X_2))-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X_2),Sa)))<-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X_2),Sa))))))).
% 32.46/32.33 all A_3 B_2 N (N!=zero_zero(nat)-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A_3),N)),hAPP(nat,int,power_power(int,B_2),N)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),B_2)))).
% 32.46/32.33 all A_1 N_1 B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A_1),N_1)),hAPP(nat,int,power_power(int,B),N_1)))-> (N_1!=zero_zero(nat)->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_1),B)))).
% 32.46/32.33 all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_1))->A_1=zero_zero(nat)).
% 32.46/32.33 all A_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_3))<->A_3=zero_zero(nat)).
% 32.46/32.33 all A_3 (A_3!=zero_zero(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),zero_zero(nat)))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_3))).
% 32.46/32.33 all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),zero_zero(nat))).
% 32.46/32.33 all A_1 (-(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),zero_zero(nat))))).
% 32.46/32.33 all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),one_one(nat)))->A_1=one_one(nat)).
% 32.46/32.33 all A_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),one_one(nat)))<->A_3=one_one(nat)).
% 32.46/32.33 all A_3 (A_3!=one_one(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_3))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),one_one(nat)))).
% 32.46/32.33 all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_1)).
% 32.46/32.33 all A_1 (-(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),one_one(nat)))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_1)))).
% 32.46/32.33 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)))).
% 32.46/32.33 all A_3 B_2 N (N!=zero_zero(nat)-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,A_3),N)),hAPP(nat,nat,power_power(nat,B_2),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),B_2)))).
% 32.46/32.33 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|N_1=zero_zero(nat)).
% 32.46/32.33 all N_1 M K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))-> (hAPP(nat,nat,times_times(nat,K_1),N_1)=hAPP(nat,nat,times_times(nat,K_1),M)->N_1=M)).
% 32.46/32.33 all X_a (real_normed_algebra(X_a)-> (all X_1 Y A_1 B (hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Y)),hAPP(X_a,X_a,times_times(X_a,A_1),B))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),A_1)),hAPP(X_a,X_a,minus_minus(X_a,Y),B))),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),A_1)),B))),hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,minus_minus(X_a,Y),B)))))).
% 32.46/32.33 all P_2 (sr(P_2)=collect(int,combs(int,bool,bool,combb(bool,fun(bool,bool),int,fconj,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int))),combc(int,int,bool,ord_less(int),P_2)))).
% 32.46/32.33 all X_a (real_normed_algebra(X_a)-> (all B (hAPP(X_a,X_a,times_times(X_a,zero_zero(X_a)),B)=zero_zero(X_a)))).
% 32.46/32.33 all X_a (real_normed_algebra(X_a)-> (all Y (hAPP(X_a,X_a,times_times(X_a,zero_zero(X_a)),Y)=zero_zero(X_a)))).
% 32.46/32.33 all X_a (real_normed_algebra(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a))=zero_zero(X_a)))).
% 32.46/32.33 all X_a (real_normed_algebra(X_a)-> (all X_1 (hAPP(X_a,X_a,times_times(X_a,X_1),zero_zero(X_a))=zero_zero(X_a)))).
% 32.46/32.33 all X_a (real_normed_algebra(X_a)-> (all A_1 B B_3 (hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),B_3))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),hAPP(X_a,X_a,times_times(X_a,A_1),B_3))))).
% 32.46/32.33 all X_a (real_normed_algebra(X_a)-> (all Xa X_1 Y (hAPP(X_a,X_a,times_times(X_a,Xa),hAPP(X_a,X_a,plus_plus(X_a,X_1),Y))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,Xa),X_1)),hAPP(X_a,X_a,times_times(X_a,Xa),Y))))).
% 32.46/32.33 all X_a (real_normed_algebra(X_a)-> (all A_1 A_4 B (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),A_4)),B)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),hAPP(X_a,X_a,times_times(X_a,A_4),B))))).
% 32.46/32.33 all X_a (real_normed_algebra(X_a)-> (all X_1 Y Ya (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,X_1),Y)),Ya)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Ya)),hAPP(X_a,X_a,times_times(X_a,Y),Ya))))).
% 32.46/32.33 all X_a (real_normed_algebra(X_a)-> (all A_1 B B_3 (hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,minus_minus(X_a,B),B_3))=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),hAPP(X_a,X_a,times_times(X_a,A_1),B_3))))).
% 32.46/32.33 all X_a (real_normed_algebra(X_a)-> (all Xa X_1 Y (hAPP(X_a,X_a,times_times(X_a,Xa),hAPP(X_a,X_a,minus_minus(X_a,X_1),Y))=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,Xa),X_1)),hAPP(X_a,X_a,times_times(X_a,Xa),Y))))).
% 32.46/32.33 all X_a (real_normed_algebra(X_a)-> (all A_1 A_4 B (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),A_4)),B)=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),hAPP(X_a,X_a,times_times(X_a,A_4),B))))).
% 32.46/32.33 all X_a (real_normed_algebra(X_a)-> (all X_1 Y Ya (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),Y)),Ya)=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Ya)),hAPP(X_a,X_a,times_times(X_a,Y),Ya))))).
% 32.46/32.33 all V W ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,W)))->hAPP(int,int,div_mod(int,number_number_of(int,bit1(V))),number_number_of(int,bit0(W)))=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,number_number_of(int,V)),number_number_of(int,W)))),one_one(int)))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,W)))->hAPP(int,int,div_mod(int,number_number_of(int,bit1(V))),number_number_of(int,bit0(W)))=hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,hAPP(int,int,plus_plus(int,number_number_of(int,V)),one_one(int))),number_number_of(int,W)))),one_one(int)))).
% 32.46/32.33 all B A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),zero_zero(int)))->hAPP(int,int,div_mod(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),B))),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),A_1))=hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,hAPP(int,int,plus_plus(int,B),one_one(int))),A_1))),one_one(int))).
% 32.46/32.33 all X_a (semiring_div(X_a)&number(X_a)-> (all X Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),number_number_of(X_a,X)),number_number_of(X_a,Y_1)))<->hAPP(X_a,X_a,div_mod(X_a,number_number_of(X_a,Y_1)),number_number_of(X_a,X))=zero_zero(X_a)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all B B_3 A_1 C A_4 (hAPP(X_a,X_a,div_mod(X_a,A_1),C)=hAPP(X_a,X_a,div_mod(X_a,A_4),C)-> (hAPP(X_a,X_a,div_mod(X_a,B),C)=hAPP(X_a,X_a,div_mod(X_a,B_3),C)->hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_4),B_3)),C))))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 C B (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 C B (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),B)),C)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all C A_1 B (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))=hAPP(X_a,X_a,times_times(X_a,C),hAPP(X_a,X_a,div_mod(X_a,A_1),B))))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),hAPP(X_a,X_a,div_mod(X_a,B),C))),C)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,div_mod(X_a,B),C))),C)))).
% 32.46/32.33 all A_1 B C (hAPP(int,int,div_mod(int,hAPP(int,int,times_times(int,A_1),hAPP(int,int,div_mod(int,B),C))),C)=hAPP(int,int,div_mod(int,hAPP(int,int,times_times(int,A_1),B)),C)).
% 32.46/32.33 all A_1 B C (hAPP(int,int,div_mod(int,hAPP(int,int,times_times(int,A_1),B)),C)=hAPP(int,int,div_mod(int,hAPP(int,int,times_times(int,A_1),hAPP(int,int,div_mod(int,B),C))),C)).
% 32.46/32.33 all A_3 B_2 Ma (hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))<->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,div_mod(int,A_3),Ma),hAPP(int,int,div_mod(int,B_2),Ma)),Ma))).
% 32.46/32.33 all X_1 M Y (hAPP(int,int,div_mod(int,hAPP(nat,int,power_power(int,hAPP(int,int,div_mod(int,X_1),M)),Y)),M)=hAPP(int,int,div_mod(int,hAPP(nat,int,power_power(int,X_1),Y)),M)).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 B (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),B)),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B)))).
% 32.46/32.33 all X_1 M hBOOL(hAPP(int,bool,zcong(X_1,hAPP(int,int,div_mod(int,X_1),M)),M)).
% 32.46/32.33 all X_1 M Y (hAPP(int,int,div_mod(int,X_1),M)=hAPP(int,int,div_mod(int,Y),M)->hBOOL(hAPP(int,bool,zcong(X_1,Y),M))).
% 32.46/32.33 all N_1 F M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F),N_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F),hAPP(int,int,div_mod(int,M),N_1))))).
% 32.46/32.33 all K_1 M N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),hAPP(int,int,div_mod(int,M),N_1)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),N_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),M)))).
% 32.46/32.33 all A_1 (hAPP(int,int,div_mod(int,A_1),A_1)=zero_zero(int)).
% 32.46/32.33 all B (hAPP(int,int,div_mod(int,zero_zero(int)),B)=zero_zero(int)).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all Ma K N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),N))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),hAPP(X_a,X_a,div_mod(X_a,Ma),N)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),Ma)))))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 C B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),B))->hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,A_1),C)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all N_1 K_1 M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),M))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),N_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),hAPP(X_a,X_a,div_mod(X_a,M),N_1))))))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all K_1 M N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),hAPP(X_a,X_a,div_mod(X_a,M),N_1)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),N_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),M)))))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all B B_3 A_1 C A_4 (hAPP(X_a,X_a,div_mod(X_a,A_1),C)=hAPP(X_a,X_a,div_mod(X_a,A_4),C)-> (hAPP(X_a,X_a,div_mod(X_a,B),C)=hAPP(X_a,X_a,div_mod(X_a,B_3),C)->hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_4),B_3)),C))))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 C B (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,div_mod(X_a,B),C))),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),hAPP(X_a,X_a,div_mod(X_a,B),C))),C)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,div_mod(X_a,B),C))),C)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all B A_1 (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,B),A_1)),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 B (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 (hAPP(X_a,X_a,div_mod(X_a,A_1),A_1)=zero_zero(X_a)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 (hAPP(X_a,X_a,div_mod(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 (hAPP(X_a,X_a,div_mod(X_a,zero_zero(X_a)),A_1)=zero_zero(X_a)))).
% 32.46/32.33 all X N Y_1 (hAPP(int,int,div_mod(int,X),N)=hAPP(int,int,div_mod(int,Y_1),N)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),hAPP(int,int,minus_minus(int,X),Y_1)))).
% 32.46/32.33 all Ma D (hAPP(int,int,div_mod(int,Ma),D)=zero_zero(int)<-> (exists Q_2 (ti(int,Ma)=hAPP(int,int,times_times(int,D),Q_2)))).
% 32.46/32.33 all Y X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,div_mod(int,X_1),Y))))).
% 32.46/32.33 all K_1 M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,div_mod(int,M),K_1)),M))).
% 32.46/32.33 all A_1 B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,div_mod(int,A_1),B)),B))).
% 32.46/32.33 all A_1 B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,div_mod(int,A_1),B)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2))<->hAPP(X_a,X_a,div_mod(X_a,B_2),A_3)=zero_zero(X_a)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))->hAPP(X_a,X_a,div_mod(X_a,B),A_1)=zero_zero(X_a)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,times_times(X_a,B),C))),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 C B (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,times_times(X_a,C),B))),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 (hAPP(X_a,X_a,div_mod(X_a,A_1),one_one(X_a))=zero_zero(X_a)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all A_1 B (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),B)=zero_zero(X_a)))).
% 32.46/32.33 all X_a (semiring_div(X_a)-> (all B A_1 (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,B),A_1)),B)=zero_zero(X_a)))).
% 32.46/32.33 all X_a (ring_div(X_a)-> (all B B_3 A_1 C A_4 (hAPP(X_a,X_a,div_mod(X_a,A_1),C)=hAPP(X_a,X_a,div_mod(X_a,A_4),C)-> (hAPP(X_a,X_a,div_mod(X_a,B),C)=hAPP(X_a,X_a,div_mod(X_a,B_3),C)->hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_4),B_3)),C))))).
% 32.46/32.33 all X_1 M Y (hAPP(int,int,div_mod(int,hAPP(int,int,minus_minus(int,hAPP(int,int,div_mod(int,X_1),M)),Y)),M)=hAPP(int,int,div_mod(int,hAPP(int,int,minus_minus(int,X_1),Y)),M)).
% 32.46/32.33 all X_1 Y M (hAPP(int,int,div_mod(int,hAPP(int,int,minus_minus(int,X_1),hAPP(int,int,div_mod(int,Y),M))),M)=hAPP(int,int,div_mod(int,hAPP(int,int,minus_minus(int,X_1),Y)),M)).
% 32.46/32.33 all X_a (ring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),hAPP(X_a,X_a,div_mod(X_a,B),C))),C)))).
% 32.46/32.33 all X_a (ring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C)))).
% 32.46/32.33 all X_a (ring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),hAPP(X_a,X_a,div_mod(X_a,B),C))),C)))).
% 32.46/32.33 all X Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),number_number_of(int,X)),number_number_of(int,Y_1)))<->hAPP(int,int,div_mod(int,number_number_of(int,Y_1)),number_number_of(int,X))=zero_zero(int)).
% 32.46/32.33 all A_1 (hAPP(int,int,div_mod(int,A_1),number_number_of(int,min))=zero_zero(int)).
% 32.46/32.33 all A_1 B M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),B))->hAPP(int,int,div_mod(int,hAPP(int,int,div_mod(int,A_1),B)),M)=hAPP(int,int,div_mod(int,A_1),M))).
% 32.46/32.33 all A_3 B_2 Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))-> (hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))<->hAPP(int,int,div_mod(int,A_3),Ma)=hAPP(int,int,div_mod(int,B_2),Ma))).
% 32.46/32.33 all A_1 B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,div_mod(int,A_1),B)))).
% 32.46/32.33 all A_1 B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,div_mod(int,A_1),B)))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,div_mod(int,A_1),B)),B))).
% 32.46/32.33 all B A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B))->hAPP(int,int,div_mod(int,A_1),B)=ti(int,A_1))).
% 32.46/32.33 all A_1 B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,div_mod(int,A_1),B)),zero_zero(int)))).
% 32.46/32.33 all A_1 B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,div_mod(int,A_1),B)),zero_zero(int)))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,div_mod(int,A_1),B)))).
% 32.46/32.33 all B A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),zero_zero(int)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1))->hAPP(int,int,div_mod(int,A_1),B)=ti(int,A_1))).
% 32.46/32.33 all B A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,A_1),B)),zero_zero(int)))->hAPP(int,int,div_mod(int,A_1),B)=hAPP(int,int,plus_plus(int,A_1),B))).
% 32.46/32.33 all V W (hAPP(int,int,div_mod(int,number_number_of(int,bit0(V))),number_number_of(int,bit0(W)))=hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,number_number_of(int,V)),number_number_of(int,W)))).
% 32.46/32.33 all A_2 B_1 Q_3 Y (ti(int,A_2)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_1),Q_3)),Y)-> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),B_1)))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),Y))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Y),zero_zero(int))))-> (ti(int,B_1)!=zero_zero(int)->hAPP(int,int,div_mod(int,A_2),B_1)=ti(int,Y)))).
% 32.46/32.33 all Q_1 B R_1 C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_1),zero_zero(int)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),hAPP(int,int,div_mod(int,Q_1),C))),R_1)),zero_zero(int)))))).
% 32.46/32.33 all Q_1 B R_1 C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_1),zero_zero(int)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,B),C)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),hAPP(int,int,div_mod(int,Q_1),C))),R_1)))))).
% 32.46/32.33 all Q_1 B R_1 C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),hAPP(int,int,div_mod(int,Q_1),C))),R_1)),hAPP(int,int,times_times(int,B),C)))))).
% 32.46/32.33 all Q_1 B R_1 C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),hAPP(int,int,div_mod(int,Q_1),C))),R_1)))))).
% 32.46/32.33 all P_1 N K (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))<-> (ti(int,K)=zero_zero(int)->hBOOL(hAPP(int,bool,P_1,N)))& (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))-> (all I J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),J))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J),K))&ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),I)),J)->hBOOL(hAPP(int,bool,P_1,J)))))& (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int)))-> (all I J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),J))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),J),zero_zero(int)))&ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),I)),J)->hBOOL(hAPP(int,bool,P_1,J)))))).
% 32.46/32.33 all X (hAPP(int,int,div_mod(int,X),number_number_of(int,bit0(bit1(pls))))!=zero_zero(int)<->hAPP(int,int,div_mod(int,X),number_number_of(int,bit0(bit1(pls))))=one_one(int)).
% 32.46/32.33 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))->hAPP(int,int,div_mod(int,number_number_of(int,min)),B)=hAPP(int,int,minus_minus(int,B),one_one(int))).
% 32.46/32.33 all B A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A_1))->hAPP(int,int,div_mod(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),B))),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),A_1))=hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,B),A_1)))).
% 32.46/32.33 all M_1 D_1 (hAPP(int,int,div_mod(int,M_1),D_1)=zero_zero(int)-> (exists Q_2 (ti(int,M_1)=hAPP(int,int,times_times(int,D_1),Q_2)))).
% 32.46/32.33 all X_1 Y M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),M))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,standardRes(M,X_1)),standardRes(M,Y)),hAPP(int,int,times_times(int,X_1),Y)),M))).
% 32.46/32.33 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,div_mod(nat,M),N_1)),N_1))).
% 32.46/32.33 all K_1 M N_1 (hAPP(nat,nat,times_times(nat,K_1),hAPP(nat,nat,div_mod(nat,M),N_1))=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,times_times(nat,K_1),M)),hAPP(nat,nat,times_times(nat,K_1),N_1))).
% 32.46/32.33 all M N_1 K_1 (hAPP(nat,nat,times_times(nat,hAPP(nat,nat,div_mod(nat,M),N_1)),K_1)=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,times_times(nat,M),K_1)),hAPP(nat,nat,times_times(nat,N_1),K_1))).
% 32.46/32.33 all M X_1 (standardRes(M,X_1)=hAPP(int,int,div_mod(int,X_1),M)).
% 32.46/32.33 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->hAPP(nat,nat,div_mod(nat,M),N_1)=M).
% 32.46/32.33 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hAPP(nat,nat,div_mod(nat,M),N_1)=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),N_1)).
% 32.46/32.33 all K_1 N_1 M (hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,K_1),N_1)),M)),N_1)=hAPP(nat,nat,div_mod(nat,M),N_1)).
% 32.46/32.33 all M N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->hAPP(nat,nat,div_mod(nat,M),N_1)=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),N_1)).
% 32.46/32.33 all M N_1 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->hAPP(nat,nat,div_mod(nat,M),N_1)=M)& (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->hAPP(nat,nat,div_mod(nat,M),N_1)=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),N_1))).
% 32.54/32.34 all Ma D (hAPP(nat,nat,div_mod(nat,Ma),D)=zero_zero(nat)<-> (exists Q_2 (Ma=hAPP(nat,nat,times_times(nat,D),Q_2)))).
% 32.54/32.34 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,div_mod(nat,M),N_1)),N_1))).
% 32.54/32.34 all M N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,div_mod(nat,M),N_1)),M)).
% 32.54/32.34 all Ma X (standardRes(Ma,X)=zero_zero(int)<->hBOOL(hAPP(int,bool,zcong(X,zero_zero(int)),Ma))).
% 32.54/32.34 all X P_2 (-hBOOL(hAPP(int,bool,zcong(X,zero_zero(int)),P_2))<->standardRes(P_2,X)!=zero_zero(int)).
% 32.54/32.34 all X_1 M hBOOL(hAPP(int,bool,zcong(X_1,standardRes(M,X_1)),M)).
% 32.54/32.34 all X_1 P_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_3))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),standardRes(P_3,X_1)),P_3))).
% 32.54/32.34 all X P_2 (hBOOL(hAPP(fun(int,bool),bool,member(int,X),sr(P_2)))->standardRes(P_2,X)=ti(int,X)).
% 32.54/32.34 all P_1 N K (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,div_mod(nat,N),K)))<-> (K=zero_zero(nat)->hBOOL(hAPP(nat,bool,P_1,N)))& (K!=zero_zero(nat)-> (all I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K))-> (N=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,K),I)),J)->hBOOL(hAPP(nat,bool,P_1,J))))))).
% 32.54/32.34 all Q_1 R_1 B C (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_1),B))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,B),hAPP(nat,nat,div_mod(nat,Q_1),C))),R_1)),hAPP(nat,nat,times_times(nat,B),C))))).
% 32.54/32.34 all T_2 T_1 (order(T_1)->order(fun(T_2,T_1))).
% 32.54/32.34 semiri456707255roduct(int).
% 32.54/32.34 ordere223160158up_add(int).
% 32.54/32.34 ordere236663937imp_le(int).
% 32.54/32.34 linord893533164strict(int).
% 32.54/32.34 linord626643107strict(int).
% 32.54/32.34 linord20386208strict(int).
% 32.54/32.34 ordere779506340up_add(int).
% 32.54/32.34 ordere216010020id_add(int).
% 32.54/32.34 linord219039673up_add(int).
% 32.54/32.34 cancel146912293up_add(int).
% 32.54/32.34 ring_11004092258visors(int).
% 32.54/32.34 ordere453448008miring(int).
% 32.54/32.34 linord581940658strict(int).
% 32.54/32.34 ring_n68954251visors(int).
% 32.54/32.34 ordere1490568538miring(int).
% 32.54/32.34 linord1278240602ring_1(int).
% 32.54/32.34 ordered_ab_group_add(int).
% 32.54/32.34 cancel_semigroup_add(int).
% 32.54/32.34 linordered_semiring(int).
% 32.54/32.34 linordered_semidom(int).
% 32.54/32.34 ab_semigroup_mult(int).
% 32.54/32.34 comm_monoid_mult(int).
% 32.54/32.34 ab_semigroup_add(int).
% 32.54/32.34 ordered_semiring(int).
% 32.54/32.34 no_zero_divisors(int).
% 32.54/32.34 comm_monoid_add(int).
% 32.54/32.34 linordered_ring(int).
% 32.54/32.34 linordered_idom(int).
% 32.54/32.34 comm_semiring_1(int).
% 32.54/32.34 semiring_div(int).
% 32.54/32.34 comm_semiring(int).
% 32.54/32.34 number_semiring(int).
% 32.54/32.34 ab_group_add(int).
% 32.54/32.34 zero_ne_q_one(int).
% 32.54/32.34 ordered_ring(int).
% 32.54/32.34 linorder(int).
% 32.54/32.34 monoid_mult(int).
% 32.54/32.34 comm_ring_1(int).
% 32.54/32.34 monoid_add(int).
% 32.54/32.34 semiring_1(int).
% 32.54/32.34 semiring_0(int).
% 32.54/32.34 group_add(int).
% 32.54/32.34 ring_div(int).
% 32.54/32.34 mult_zero(int).
% 32.54/32.34 comm_ring(int).
% 32.54/32.34 order(int).
% 32.54/32.34 ring_char_0(int).
% 32.54/32.34 number_ring(int).
% 32.54/32.34 semiring(int).
% 32.54/32.34 ring_1(int).
% 32.54/32.34 power(int).
% 32.54/32.34 zero(int).
% 32.54/32.34 plus(int).
% 32.54/32.34 ring(int).
% 32.54/32.34 idom(int).
% 32.54/32.34 number(int).
% 32.54/32.34 one(int).
% 32.54/32.34 dvd(int).
% 32.54/32.34 semiri456707255roduct(nat).
% 32.54/32.34 ordere223160158up_add(nat).
% 32.54/32.34 ordere236663937imp_le(nat).
% 32.54/32.34 linord893533164strict(nat).
% 32.54/32.34 linord20386208strict(nat).
% 32.54/32.34 ordere779506340up_add(nat).
% 32.54/32.34 ordere216010020id_add(nat).
% 32.54/32.34 cancel146912293up_add(nat).
% 32.54/32.34 ordere453448008miring(nat).
% 32.54/32.34 ordere1490568538miring(nat).
% 32.54/32.34 cancel_semigroup_add(nat).
% 32.54/32.34 linordered_semiring(nat).
% 32.54/32.34 linordered_semidom(nat).
% 32.54/32.34 ab_semigroup_mult(nat).
% 32.54/32.34 comm_monoid_mult(nat).
% 32.54/32.34 ab_semigroup_add(nat).
% 32.54/32.34 ordered_semiring(nat).
% 32.54/32.34 no_zero_divisors(nat).
% 32.54/32.34 comm_monoid_add(nat).
% 32.54/32.34 comm_semiring_1(nat).
% 32.54/32.34 semiring_div(nat).
% 32.54/32.34 comm_semiring(nat).
% 32.54/32.34 number_semiring(nat).
% 32.54/32.34 zero_ne_q_one(nat).
% 32.54/32.34 linorder(nat).
% 32.54/32.34 monoid_mult(nat).
% 32.54/32.34 monoid_add(nat).
% 32.54/32.34 semiring_1(nat).
% 32.54/32.34 semiring_0(nat).
% 32.54/32.34 mult_zero(nat).
% 32.54/32.34 order(nat).
% 32.54/32.34 semiring(nat).
% 32.54/32.34 power(nat).
% 32.54/32.34 zero(nat).
% 32.54/32.34 plus(nat).
% 32.54/32.34 number(nat).
% 32.54/32.34 one(nat).
% 32.54/32.34 dvd(nat).
% 32.54/32.34 order(bool).
% 32.54/32.34 semiri456707255roduct(real).
% 32.54/32.34 ordere223160158up_add(real).
% 32.54/32.34 ordere236663937imp_le(real).
% 32.54/32.34 linord893533164strict(real).
% 32.54/32.34 linord626643107strict(real).
% 32.54/32.34 linord20386208strict(real).
% 32.54/32.34 ordere779506340up_add(real).
% 32.54/32.34 real_normed_algebra(real).
% 32.54/32.34 ordere216010020id_add(real).
% 32.54/32.34 linord219039673up_add(real).
% 32.54/32.34 cancel146912293up_add(real).
% 32.54/32.34 ring_11004092258visors(real).
% 32.54/32.34 ordere453448008miring(real).
% 32.54/32.34 linord581940658strict(real).
% 32.54/32.34 ring_n68954251visors(real).
% 32.54/32.34 ordere1490568538miring(real).
% 32.54/32.34 linord1278240602ring_1(real).
% 32.54/32.34 ordered_ab_group_add(real).
% 32.54/32.34 cancel_semigroup_add(real).
% 32.54/32.34 linordered_semiring(real).
% 32.54/32.34 linordered_semidom(real).
% 32.54/32.34 ab_semigroup_mult(real).
% 32.54/32.34 comm_monoid_mult(real).
% 32.54/32.34 ab_semigroup_add(real).
% 32.54/32.34 ordered_semiring(real).
% 32.54/32.34 no_zero_divisors(real).
% 32.54/32.34 comm_monoid_add(real).
% 32.54/32.34 linordered_ring(real).
% 32.54/32.34 linordered_idom(real).
% 32.54/32.34 comm_semiring_1(real).
% 32.54/32.34 comm_semiring(real).
% 32.54/32.34 number_semiring(real).
% 32.54/32.34 ab_group_add(real).
% 32.54/32.34 zero_ne_q_one(real).
% 32.54/32.34 ordered_ring(real).
% 32.54/32.34 linorder(real).
% 32.54/32.34 monoid_mult(real).
% 32.54/32.34 comm_ring_1(real).
% 32.54/32.34 monoid_add(real).
% 32.54/32.34 semiring_1(real).
% 32.54/32.34 semiring_0(real).
% 32.54/32.34 group_add(real).
% 32.54/32.34 mult_zero(real).
% 32.54/32.34 comm_ring(real).
% 32.54/32.34 order(real).
% 32.54/32.34 ring_char_0(real).
% 32.54/32.34 number_ring(real).
% 32.54/32.34 semiring(real).
% 32.54/32.34 ring_1(real).
% 32.54/32.34 power(real).
% 32.54/32.34 zero(real).
% 32.54/32.34 plus(real).
% 32.54/32.34 ring(real).
% 32.54/32.34 idom(real).
% 32.54/32.34 number(real).
% 32.54/32.34 one(real).
% 32.54/32.34 dvd(real).
% 32.54/32.34 all T A (ti(T,ti(T,A))=ti(T,A)).
% 32.54/32.34 all X_a X_c X_b P Q R (hAPP(X_a,X_c,combb(X_b,X_c,X_a,P,Q),R)=hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R))).
% 32.54/32.34 all X_a X_c X_b P Q R (hAPP(X_a,X_c,combc(X_a,X_b,X_c,P,Q),R)=hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)).
% 32.54/32.34 all X_a X_c X_b P Q R (hAPP(X_a,X_c,combs(X_a,X_b,X_c,P,Q),R)=hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R))).
% 32.54/32.34 all Q P (-hBOOL(P)| -hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))).
% 32.54/32.34 all P Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(P)).
% 32.54/32.34 all P Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(Q)).
% 32.54/32.34 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))).
% 32.54/32.34 end_of_list.
% 32.54/32.34
% 32.54/32.34 -------> usable clausifies to:
% 32.54/32.34
% 32.54/32.34 list(usable).
% 32.54/32.34 0 [] A=A.
% 32.54/32.34 0 [] combb(X_b,X_c,X_a,ti(fun(X_b,X_c),B_1_1),B_2_1)=combb(X_b,X_c,X_a,B_1_1,B_2_1).
% 32.54/32.34 0 [] combb(X_b,X_c,X_a,B_1_1,ti(fun(X_a,X_b),B_2_1))=combb(X_b,X_c,X_a,B_1_1,B_2_1).
% 32.54/32.34 0 [] ti(fun(X_a,X_c),combb(X_b,X_c,X_a,B_1_1,B_2_1))=combb(X_b,X_c,X_a,B_1_1,B_2_1).
% 32.54/32.34 0 [] combc(X_a,X_b,X_c,ti(fun(X_a,fun(X_b,X_c)),B_1_1),B_2_1)=combc(X_a,X_b,X_c,B_1_1,B_2_1).
% 32.54/32.34 0 [] combc(X_a,X_b,X_c,B_1_1,ti(X_b,B_2_1))=combc(X_a,X_b,X_c,B_1_1,B_2_1).
% 32.54/32.34 0 [] ti(fun(X_a,X_c),combc(X_a,X_b,X_c,B_1_1,B_2_1))=combc(X_a,X_b,X_c,B_1_1,B_2_1).
% 32.54/32.34 0 [] combs(X_a,X_b,X_c,ti(fun(X_a,fun(X_b,X_c)),B_1_1),B_2_1)=combs(X_a,X_b,X_c,B_1_1,B_2_1).
% 32.54/32.34 0 [] combs(X_a,X_b,X_c,B_1_1,ti(fun(X_a,X_b),B_2_1))=combs(X_a,X_b,X_c,B_1_1,B_2_1).
% 32.54/32.34 0 [] ti(fun(X_a,X_c),combs(X_a,X_b,X_c,B_1_1,B_2_1))=combs(X_a,X_b,X_c,B_1_1,B_2_1).
% 32.54/32.34 0 [] -semiring_div(X_a)|div_mod(X_a,ti(X_a,B_1_1))=div_mod(X_a,B_1_1).
% 32.54/32.34 0 [] -semiring_div(X_a)|ti(fun(X_a,X_a),div_mod(X_a,B_1_1))=div_mod(X_a,B_1_1).
% 32.54/32.34 0 [] -group_add(X_a)|minus_minus(X_a,ti(X_a,B_1_1))=minus_minus(X_a,B_1_1).
% 32.54/32.34 0 [] -group_add(X_a)|ti(fun(X_a,X_a),minus_minus(X_a,B_1_1))=minus_minus(X_a,B_1_1).
% 32.54/32.34 0 [] minus_minus(nat,ti(nat,B_1_1))=minus_minus(nat,B_1_1).
% 32.54/32.34 0 [] ti(fun(nat,nat),minus_minus(nat,B_1_1))=minus_minus(nat,B_1_1).
% 32.54/32.34 0 [] -one(X_a)|ti(X_a,one_one(X_a))=one_one(X_a).
% 32.54/32.34 0 [] -plus(X_a)| -linorder(X_a)| -dvd(X_a)|plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1).
% 32.54/32.34 0 [] -plus(X_a)| -linorder(X_a)| -dvd(X_a)|ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1).
% 32.54/32.34 0 [] -monoid_add(X_a)|plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1).
% 32.54/32.34 0 [] -monoid_add(X_a)|ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1).
% 32.54/32.34 0 [] -cancel_semigroup_add(X_a)|plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1).
% 32.54/32.34 0 [] -cancel_semigroup_add(X_a)|ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1).
% 32.54/32.34 0 [] -ab_semigroup_add(X_a)|plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1).
% 32.54/32.34 0 [] -ab_semigroup_add(X_a)|ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1).
% 32.54/32.34 0 [] -ab_semigroup_mult(X_a)|times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1).
% 32.54/32.34 0 [] -ab_semigroup_mult(X_a)|ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1).
% 32.54/32.34 0 [] -power(X_a)|times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1).
% 32.54/32.34 0 [] -power(X_a)|ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1).
% 32.54/32.34 0 [] -dvd(X_a)|times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1).
% 32.54/32.34 0 [] -dvd(X_a)|ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1).
% 32.54/32.34 0 [] -semiring(X_a)|times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1).
% 32.54/32.34 0 [] -semiring(X_a)|ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1).
% 32.54/32.34 0 [] -mult_zero(X_a)|times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1).
% 32.54/32.34 0 [] -mult_zero(X_a)|ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1).
% 32.54/32.34 0 [] -no_zero_divisors(X_a)|times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1).
% 32.54/32.34 0 [] -no_zero_divisors(X_a)|ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1).
% 32.54/32.34 0 [] -zero(X_a)|ti(X_a,zero_zero(X_a))=zero_zero(X_a).
% 32.54/32.34 0 [] ti(X_a,undefined(X_a))=undefined(X_a).
% 32.54/32.34 0 [] multInv(ti(int,B_1_1),B_2_1)=multInv(B_1_1,B_2_1).
% 32.54/32.34 0 [] multInv(B_1_1,ti(int,B_2_1))=multInv(B_1_1,B_2_1).
% 32.54/32.34 0 [] ti(int,multInv(B_1_1,B_2_1))=multInv(B_1_1,B_2_1).
% 32.54/32.34 0 [] d22set(ti(int,B_1_1))=d22set(B_1_1).
% 32.54/32.34 0 [] ti(fun(int,bool),d22set(B_1_1))=d22set(B_1_1).
% 32.54/32.34 0 [] zfact(ti(int,B_1_1))=zfact(B_1_1).
% 32.54/32.34 0 [] ti(int,zfact(B_1_1))=zfact(B_1_1).
% 32.54/32.34 0 [] zcong(ti(int,B_1_1),B_2_1)=zcong(B_1_1,B_2_1).
% 32.54/32.34 0 [] zcong(B_1_1,ti(int,B_2_1))=zcong(B_1_1,B_2_1).
% 32.54/32.34 0 [] ti(fun(int,bool),zcong(B_1_1,B_2_1))=zcong(B_1_1,B_2_1).
% 32.54/32.34 0 [] ti(fun(int,bool),zprime)=zprime.
% 32.54/32.34 0 [] bit0(ti(int,B_1_1))=bit0(B_1_1).
% 32.54/32.34 0 [] ti(int,bit0(B_1_1))=bit0(B_1_1).
% 32.54/32.34 0 [] bit1(ti(int,B_1_1))=bit1(B_1_1).
% 32.54/32.34 0 [] ti(int,bit1(B_1_1))=bit1(B_1_1).
% 32.54/32.34 0 [] ti(int,min)=min.
% 32.54/32.34 0 [] ti(int,pls)=pls.
% 32.54/32.34 0 [] -number(X_a)|number_number_of(X_a,ti(int,B_1_1))=number_number_of(X_a,B_1_1).
% 32.54/32.34 0 [] -number(X_a)|ti(X_a,number_number_of(X_a,B_1_1))=number_number_of(X_a,B_1_1).
% 32.54/32.34 0 [] -order(X_a)|ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a).
% 32.54/32.34 0 [] -order(X_a)|ti(fun(X_a,fun(X_a,bool)),ord_less_e_q(X_a))=ord_less_e_q(X_a).
% 32.54/32.34 0 [] -power(X_a)|power_power(X_a,ti(X_a,B_1_1))=power_power(X_a,B_1_1).
% 32.54/32.34 0 [] -power(X_a)|ti(fun(nat,X_a),power_power(X_a,B_1_1))=power_power(X_a,B_1_1).
% 32.54/32.34 0 [] product_Pair(int,int,ti(int,B_1_1),B_2_1)=product_Pair(int,int,B_1_1,B_2_1).
% 32.54/32.34 0 [] product_Pair(int,int,B_1_1,ti(int,B_2_1))=product_Pair(int,int,B_1_1,B_2_1).
% 32.54/32.34 0 [] ti(product_prod(int,int),product_Pair(int,int,B_1_1,B_2_1))=product_Pair(int,int,B_1_1,B_2_1).
% 32.54/32.34 0 [] legendre(ti(int,B_1_1),B_2_1)=legendre(B_1_1,B_2_1).
% 32.54/32.34 0 [] legendre(B_1_1,ti(int,B_2_1))=legendre(B_1_1,B_2_1).
% 32.54/32.34 0 [] ti(int,legendre(B_1_1,B_2_1))=legendre(B_1_1,B_2_1).
% 32.54/32.34 0 [] quadRes(ti(int,B_1_1))=quadRes(B_1_1).
% 32.54/32.34 0 [] ti(fun(int,bool),quadRes(B_1_1))=quadRes(B_1_1).
% 32.54/32.34 0 [] sr(ti(int,B_1_1))=sr(B_1_1).
% 32.54/32.34 0 [] ti(fun(int,bool),sr(B_1_1))=sr(B_1_1).
% 32.54/32.34 0 [] standardRes(ti(int,B_1_1),B_2_1)=standardRes(B_1_1,B_2_1).
% 32.54/32.34 0 [] standardRes(B_1_1,ti(int,B_2_1))=standardRes(B_1_1,B_2_1).
% 32.54/32.34 0 [] ti(int,standardRes(B_1_1,B_2_1))=standardRes(B_1_1,B_2_1).
% 32.54/32.34 0 [] -dvd(X_a)|ti(fun(X_a,fun(X_a,bool)),dvd_dvd(X_a))=dvd_dvd(X_a).
% 32.54/32.34 0 [] collect(X_a,ti(fun(X_a,bool),B_1_1))=collect(X_a,B_1_1).
% 32.54/32.34 0 [] ti(fun(X_a,bool),collect(X_a,B_1_1))=collect(X_a,B_1_1).
% 32.54/32.34 0 [] ti(fun(int,bool),twoSqu658283162sum2sq)=twoSqu658283162sum2sq.
% 32.54/32.34 0 [] twoSqu1929807760sum2sq(ti(product_prod(int,int),B_1_1))=twoSqu1929807760sum2sq(B_1_1).
% 32.54/32.34 0 [] ti(int,twoSqu1929807760sum2sq(B_1_1))=twoSqu1929807760sum2sq(B_1_1).
% 32.54/32.34 0 [] inv(ti(int,B_1_1),B_2_1)=inv(B_1_1,B_2_1).
% 32.54/32.34 0 [] inv(B_1_1,ti(int,B_2_1))=inv(B_1_1,B_2_1).
% 32.54/32.34 0 [] ti(int,inv(B_1_1,B_2_1))=inv(B_1_1,B_2_1).
% 32.54/32.34 0 [] wset(ti(int,B_1_1),B_2_1)=wset(B_1_1,B_2_1).
% 32.54/32.34 0 [] wset(B_1_1,ti(int,B_2_1))=wset(B_1_1,B_2_1).
% 32.54/32.34 0 [] ti(fun(int,bool),wset(B_1_1,B_2_1))=wset(B_1_1,B_2_1).
% 32.54/32.34 0 [] ti(fun(bool,fun(bool,bool)),fconj)=fconj.
% 32.54/32.34 0 [] hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1)=hAPP(X_a,X_c,B_1_1,B_2_1).
% 32.54/32.34 0 [] hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1))=hAPP(X_a,X_c,B_1_1,B_2_1).
% 32.54/32.34 0 [] ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1))=hAPP(X_a,X_c,B_1_1,B_2_1).
% 32.54/32.34 0 [] -hBOOL(ti(bool,B_1_1))|hBOOL(B_1_1).
% 32.54/32.34 0 [] hBOOL(ti(bool,B_1_1))| -hBOOL(B_1_1).
% 32.54/32.34 0 [] member(X_a,ti(X_a,B_1_1))=member(X_a,B_1_1).
% 32.54/32.34 0 [] ti(fun(fun(X_a,bool),bool),member(X_a,B_1_1))=member(X_a,B_1_1).
% 32.54/32.34 0 [] ti(int,m)=m.
% 32.54/32.34 0 [] ti(int,s1)=s1.
% 32.54/32.34 0 [] ti(int,s)=s.
% 32.54/32.34 0 [] ti(int,t)=t.
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),t),zero_zero(int))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),t),one_one(int))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)))).
% 32.54/32.34 0 [] hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))=hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t).
% 32.54/32.34 0 [] t!=zero_zero(int)|hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))=zero_zero(int).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),t)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.54/32.34 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(X_a))).
% 32.54/32.34 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))))|ti(X_a,X)!=zero_zero(X_a)|ti(X_a,Y_1)!=zero_zero(X_a).
% 32.54/32.34 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))))|ti(X_a,X)=zero_zero(X_a).
% 32.54/32.34 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))))|ti(X_a,Y_1)=zero_zero(X_a).
% 32.54/32.34 0 [] -linordered_idom(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(X_a)|ti(X_a,X)=zero_zero(X_a).
% 32.54/32.34 0 [] -linordered_idom(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(X_a)|ti(X_a,Y_1)=zero_zero(X_a).
% 32.54/32.34 0 [] -linordered_idom(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))=zero_zero(X_a)|ti(X_a,X)!=zero_zero(X_a)|ti(X_a,Y_1)!=zero_zero(X_a).
% 32.54/32.34 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls))))),zero_zero(X_a))).
% 32.54/32.34 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,bit0(bit1(pls))))))|ti(X_a,A_3)!=zero_zero(X_a).
% 32.54/32.34 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,bit0(bit1(pls))))))|ti(X_a,A_3)=zero_zero(X_a).
% 32.54/32.34 0 [] -semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls))))=one_one(X_a).
% 32.54/32.34 0 [] -semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,bit0(bit1(pls))))=zero_zero(X_a).
% 32.54/32.34 0 [] -ring_11004092258visors(X_a)|hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,bit0(bit1(pls))))!=zero_zero(X_a)|ti(X_a,A_3)=zero_zero(X_a).
% 32.54/32.34 0 [] -ring_11004092258visors(X_a)|hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,bit0(bit1(pls))))=zero_zero(X_a)|ti(X_a,A_3)!=zero_zero(X_a).
% 32.54/32.34 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,W))=number_number_of(X_a,hAPP(int,int,plus_plus(int,bit1(pls)),W)).
% 32.54/32.34 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),one_one(X_a))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V),bit1(pls))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.54/32.34 0 [] hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))=hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),$c1).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,zprime,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),W)).
% 32.54/32.34 0 [] number_number_of(int,K_1)=ti(int,K_1).
% 32.54/32.34 0 [] hAPP(int,int,times_times(int,Z_1),W)=hAPP(int,int,times_times(int,W),Z_1).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z_1)).
% 32.54/32.34 0 [] hAPP(int,int,times_times(int,number_number_of(int,V)),number_number_of(int,W))=number_number_of(int,hAPP(int,int,times_times(int,V),W)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,K)),number_number_of(int,L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,K)),number_number_of(int,L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X)),number_number_of(X_a,Y_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X),Y_1)).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X)),number_number_of(X_a,Y_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X),Y_1)).
% 32.54/32.34 0 [] hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,Z1),Z2)),Z3)=hAPP(int,int,times_times(int,Z1),hAPP(int,int,times_times(int,Z2),Z3)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),J_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),J_1),K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),K_1)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z_1))|ti(int,Z_1)=ti(int,W).
% 32.54/32.34 0 [] hAPP(nat,int,power_power(int,X_1),hAPP(nat,nat,plus_plus(nat,Y),Z_1))=hAPP(int,int,times_times(int,hAPP(nat,int,power_power(int,X_1),Y)),hAPP(nat,int,power_power(int,X_1),Z_1)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K1)),bit1(K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K1)),bit1(K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit1(L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit1(L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),pls)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K1)),bit0(K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K1)),bit0(K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit0(L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit0(L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_2),W_1)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))|ti(int,Z_2)!=ti(int,W_1).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_2),W_1))|ti(int,Z_2)=ti(int,W_1).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),J_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,K_1),I_1)),hAPP(int,int,plus_plus(int,K_1),J_1))).
% 32.54/32.34 0 [] number_number_of(nat,V_3)!=zero_zero(nat)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_3),pls)).
% 32.54/32.34 0 [] number_number_of(nat,V_3)=zero_zero(nat)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_3),pls)).
% 32.54/32.34 0 [] zero_zero(nat)!=number_number_of(nat,V_3)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_3),pls)).
% 32.54/32.34 0 [] zero_zero(nat)=number_number_of(nat,V_3)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_3),pls)).
% 32.54/32.34 0 [] -number_semiring(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))|hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,V)),number_number_of(X_a,V_1))=number_number_of(X_a,hAPP(int,int,times_times(int,V),V_1)).
% 32.54/32.34 0 [] -number_ring(X_a)|hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,V)),hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,W)),Z_1))=hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,hAPP(int,int,times_times(int,V),W))),Z_1).
% 32.54/32.34 0 [] -number_ring(X_a)|hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,V)),number_number_of(X_a,W))=number_number_of(X_a,hAPP(int,int,times_times(int,V),W)).
% 32.54/32.34 0 [] -number_ring(X_a)|number_number_of(X_a,hAPP(int,int,times_times(int,V),W))=hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,V)),number_number_of(X_a,W)).
% 32.54/32.34 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X),X)),hAPP(X_a,X_a,times_times(X_a,Y_1),Y_1))),zero_zero(X_a)))|ti(X_a,X)=zero_zero(X_a).
% 32.54/32.34 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X),X)),hAPP(X_a,X_a,times_times(X_a,Y_1),Y_1))),zero_zero(X_a)))|ti(X_a,Y_1)=zero_zero(X_a).
% 32.54/32.34 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X),X)),hAPP(X_a,X_a,times_times(X_a,Y_1),Y_1))),zero_zero(X_a)))|ti(X_a,X)!=zero_zero(X_a)|ti(X_a,Y_1)!=zero_zero(X_a).
% 32.54/32.34 0 [] -linordered_ring(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),X_1)),hAPP(X_a,X_a,times_times(X_a,Y),Y)))).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X)),zero_zero(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X),pls)).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X)),zero_zero(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X),pls)).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),number_number_of(X_a,Y_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),Y_1)).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),number_number_of(X_a,Y_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),Y_1)).
% 32.54/32.34 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,V_3)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_3)).
% 32.54/32.34 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,V_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_3)).
% 32.54/32.34 0 [] -number(X_a)| -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,V_3)),number_number_of(X_a,W_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,W_1)),number_number_of(X_a,V_3))).
% 32.54/32.34 0 [] -number(X_a)| -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,V_3)),number_number_of(X_a,W_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,W_1)),number_number_of(X_a,V_3))).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit1(K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit1(K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K1)),bit1(K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K1)),bit1(K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit1(L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit1(L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),pls)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),pls)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit0(K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit0(K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),W))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_3),Z_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,W_2),Z_3)),hAPP(int,int,plus_plus(int,W),Z_1))).
% 32.54/32.34 0 [] number_number_of(nat,pls)=zero_zero(nat).
% 32.54/32.34 0 [] zero_zero(nat)=number_number_of(nat,pls).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X)),one_one(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X),bit1(pls))).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X)),one_one(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X),bit1(pls))).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),number_number_of(X_a,Y_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(pls)),Y_1)).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),number_number_of(X_a,Y_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(pls)),Y_1)).
% 32.54/32.34 0 [] hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))=number_number_of(nat,bit0(bit1(pls))).
% 32.54/32.34 0 [] hAPP(int,int,times_times(int,pls),W)=pls.
% 32.54/32.34 0 [] hAPP(int,int,times_times(int,bit0(K_1)),L_1)=bit0(hAPP(int,int,times_times(int,K_1),L_1)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,K)),number_number_of(int,L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,K)),number_number_of(int,L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)).
% 32.54/32.34 0 [] hAPP(int,int,times_times(int,Z_1),one_one(int))=ti(int,Z_1).
% 32.54/32.34 0 [] hAPP(int,int,times_times(int,one_one(int)),Z_1)=ti(int,Z_1).
% 32.54/32.34 0 [] hAPP(int,int,plus_plus(int,number_number_of(int,V)),number_number_of(int,W))=number_number_of(int,hAPP(int,int,plus_plus(int,V),W)).
% 32.54/32.34 0 [] hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,Z1),Z2)),W)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,Z1),W)),hAPP(int,int,times_times(int,Z2),W)).
% 32.54/32.34 0 [] hAPP(int,int,times_times(int,W),hAPP(int,int,plus_plus(int,Z1),Z2))=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,W),Z1)),hAPP(int,int,times_times(int,W),Z2)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit1(K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit1(K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K1)),bit0(K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K1)),bit0(K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit0(L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit0(L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K1)),bit1(K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K1)),bit1(K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)).
% 32.54/32.34 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,member(X_a,X),A_6))|hBOOL(hAPP(X_a,bool,A_6,X)).
% 32.54/32.34 0 [] hBOOL(hAPP(fun(X_a,bool),bool,member(X_a,X),A_6))| -hBOOL(hAPP(X_a,bool,A_6,X)).
% 32.54/32.34 0 [] collect(X_a,P_1)=ti(fun(X_a,bool),P_1).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit1(L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit1(L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)).
% 32.54/32.34 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,V_3)),number_number_of(nat,V_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_3),V_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_2)).
% 32.54/32.34 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,V_3)),number_number_of(nat,V_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_3),V_2)).
% 32.54/32.34 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,V_3)),number_number_of(nat,V_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_3),V_2)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)).
% 32.54/32.34 0 [] number_number_of(nat,bit1(pls))=one_one(nat).
% 32.54/32.34 0 [] one_one(nat)=number_number_of(nat,bit1(pls)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,W),one_one(int))),Z_1)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,W_1),one_one(int))),Z_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,W_1),one_one(int))),Z_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_2)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_2)).
% 32.54/32.34 0 [] -number_semiring(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),number_number_of(X_a,V_1))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V),V_1)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=number_number_of(nat,V_1).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=number_number_of(nat,V).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=number_number_of(nat,hAPP(int,int,plus_plus(int,V),V_1)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),Z_1))).
% 32.54/32.34 0 [] -number_ring(X_a)| -ring_char_0(X_a)|number_number_of(X_a,X)!=number_number_of(X_a,Y_1)|ti(int,X)=ti(int,Y_1).
% 32.54/32.34 0 [] -number_ring(X_a)| -ring_char_0(X_a)|number_number_of(X_a,X)=number_number_of(X_a,Y_1)|ti(int,X)!=ti(int,Y_1).
% 32.54/32.34 0 [] -number(X_a)|number_number_of(X_a,W_1)!=ti(X_a,X)|ti(X_a,X)=number_number_of(X_a,W_1).
% 32.54/32.34 0 [] -number(X_a)|number_number_of(X_a,W_1)=ti(X_a,X)|ti(X_a,X)!=number_number_of(X_a,W_1).
% 32.54/32.34 0 [] bit1(K)!=bit1(L)|ti(int,K)=ti(int,L).
% 32.54/32.34 0 [] bit1(K)=bit1(L)|ti(int,K)!=ti(int,L).
% 32.54/32.34 0 [] bit0(K)!=bit0(L)|ti(int,K)=ti(int,L).
% 32.54/32.34 0 [] bit0(K)=bit0(L)|ti(int,K)!=ti(int,L).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))|ti(int,X_1)=ti(int,Y)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)).
% 32.54/32.34 0 [] -linord581940658strict(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X),X)),hAPP(X_a,X_a,times_times(X_a,Y_1),Y_1))!=zero_zero(X_a)|ti(X_a,X)=zero_zero(X_a).
% 32.54/32.34 0 [] -linord581940658strict(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X),X)),hAPP(X_a,X_a,times_times(X_a,Y_1),Y_1))!=zero_zero(X_a)|ti(X_a,Y_1)=zero_zero(X_a).
% 32.54/32.34 0 [] -linord581940658strict(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X),X)),hAPP(X_a,X_a,times_times(X_a,Y_1),Y_1))=zero_zero(X_a)|ti(X_a,X)!=zero_zero(X_a)|ti(X_a,Y_1)!=zero_zero(X_a).
% 32.54/32.34 0 [] -number(X_b)| -semiring(X_b)|hAPP(X_b,X_b,times_times(X_b,hAPP(X_b,X_b,plus_plus(X_b,A_1),B)),number_number_of(X_b,V))=hAPP(X_b,X_b,plus_plus(X_b,hAPP(X_b,X_b,times_times(X_b,A_1),number_number_of(X_b,V))),hAPP(X_b,X_b,times_times(X_b,B),number_number_of(X_b,V))).
% 32.54/32.34 0 [] -number(X_b)| -semiring(X_b)|hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),hAPP(X_b,X_b,plus_plus(X_b,B),C))=hAPP(X_b,X_b,plus_plus(X_b,hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),B)),hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),C)).
% 32.54/32.34 0 [] hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,Z1),Z2)),Z3)=hAPP(int,int,plus_plus(int,Z1),hAPP(int,int,plus_plus(int,Z2),Z3)).
% 32.54/32.34 0 [] hAPP(int,int,plus_plus(int,X_1),hAPP(int,int,plus_plus(int,Y),Z_1))=hAPP(int,int,plus_plus(int,Y),hAPP(int,int,plus_plus(int,X_1),Z_1)).
% 32.54/32.34 0 [] hAPP(int,int,plus_plus(int,Z_1),W)=hAPP(int,int,plus_plus(int,W),Z_1).
% 32.54/32.34 0 [] zero_zero(int)=number_number_of(int,pls).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,K_1),I_1)),hAPP(int,int,times_times(int,K_1),J_1))).
% 32.54/32.34 0 [] -linordered_semidom(X_a)|hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))!=hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,bit0(bit1(pls))))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))|ti(X_a,X_1)=ti(X_a,Y).
% 32.54/32.34 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,bit0(bit1(pls))))))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y)).
% 32.54/32.34 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls)))))).
% 32.54/32.34 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,bit0(bit1(pls))))))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)).
% 32.54/32.34 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(X_a)))|ti(X_a,X)=zero_zero(X_a).
% 32.54/32.34 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(X_a)))|ti(X_a,Y_1)=zero_zero(X_a).
% 32.54/32.34 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(X_a)))|ti(X_a,X)!=zero_zero(X_a)|ti(X_a,Y_1)!=zero_zero(X_a).
% 32.54/32.34 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,bit0(bit1(pls))))))).
% 32.54/32.34 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X),X)),hAPP(X_a,X_a,times_times(X_a,Y_1),Y_1))))|ti(X_a,X)!=zero_zero(X_a)|ti(X_a,Y_1)!=zero_zero(X_a).
% 32.54/32.34 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X),X)),hAPP(X_a,X_a,times_times(X_a,Y_1),Y_1))))|ti(X_a,X)=zero_zero(X_a).
% 32.54/32.34 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X),X)),hAPP(X_a,X_a,times_times(X_a,Y_1),Y_1))))|ti(X_a,Y_1)=zero_zero(X_a).
% 32.54/32.34 0 [] -linordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),X_1)),hAPP(X_a,X_a,times_times(X_a,Y),Y))),zero_zero(X_a))).
% 32.54/32.34 0 [] -number_ring(X_a)|hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit1(pls))),A_1)=ti(X_a,A_1).
% 32.54/32.34 0 [] -number_ring(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),number_number_of(X_a,bit1(pls)))=ti(X_a,A_1).
% 32.54/32.34 0 [] one_one(int)=number_number_of(int,bit1(pls)).
% 32.54/32.34 0 [] hAPP(int,int,times_times(int,bit1(K_1)),L_1)=hAPP(int,int,plus_plus(int,bit0(hAPP(int,int,times_times(int,K_1),L_1))),L_1).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))|hAPP(int,int,times_times(int,Ma),N)!=one_one(int)|ti(int,Ma)=one_one(int).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))|hAPP(int,int,times_times(int,Ma),N)!=one_one(int)|ti(int,N)=one_one(int).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))|hAPP(int,int,times_times(int,Ma),N)=one_one(int)|ti(int,Ma)!=one_one(int)|ti(int,N)!=one_one(int).
% 32.54/32.34 0 [] -linord219039673up_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)!=zero_zero(X_a)|ti(X_a,A_3)=zero_zero(X_a).
% 32.54/32.34 0 [] -linord219039673up_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)=zero_zero(X_a)|ti(X_a,A_3)!=zero_zero(X_a).
% 32.54/32.34 0 [] bit1(K_1)!=pls.
% 32.54/32.34 0 [] pls!=bit1(L_1).
% 32.54/32.34 0 [] bit1(K_1)!=bit0(L_1).
% 32.54/32.34 0 [] bit0(K_1)!=bit1(L_1).
% 32.54/32.34 0 [] bit0(K)!=pls|ti(int,K)=pls.
% 32.54/32.34 0 [] bit0(K)=pls|ti(int,K)!=pls.
% 32.54/32.34 0 [] pls!=bit0(L)|pls=ti(int,L).
% 32.54/32.34 0 [] pls=bit0(L)|pls!=ti(int,L).
% 32.54/32.34 0 [] bit0(pls)=pls.
% 32.54/32.34 0 [] pls=zero_zero(int).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K1)),bit1(K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K1)),bit1(K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit1(L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit1(L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K1)),bit0(K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K1)),bit0(K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit0(L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit0(L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)).
% 32.54/32.34 0 [] zero_zero(int)!=one_one(int).
% 32.54/32.34 0 [] hAPP(int,int,plus_plus(int,K_1),pls)=ti(int,K_1).
% 32.54/32.34 0 [] hAPP(int,int,plus_plus(int,pls),K_1)=ti(int,K_1).
% 32.54/32.34 0 [] hAPP(int,int,plus_plus(int,bit0(K_1)),bit0(L_1))=bit0(hAPP(int,int,plus_plus(int,K_1),L_1)).
% 32.54/32.34 0 [] bit0(K_1)=hAPP(int,int,plus_plus(int,K_1),K_1).
% 32.54/32.34 0 [] hAPP(int,int,plus_plus(int,Z_1),zero_zero(int))=ti(int,Z_1).
% 32.54/32.34 0 [] hAPP(int,int,plus_plus(int,zero_zero(int)),Z_1)=ti(int,Z_1).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,I_1),K_1)),hAPP(int,int,plus_plus(int,J_1),K_1))).
% 32.54/32.34 0 [] -number_ring(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))),number_number_of(X_a,W))=number_number_of(X_a,bit0(W)).
% 32.54/32.34 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit1(bit1(pls))))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),A_1)),A_1).
% 32.54/32.34 0 [] -number_semiring(X_a)|hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls)))),Z_1)=hAPP(X_a,X_a,plus_plus(X_a,Z_1),Z_1).
% 32.54/32.34 0 [] -number_ring(X_a)|hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls)))),Z_1)=hAPP(X_a,X_a,plus_plus(X_a,Z_1),Z_1).
% 32.54/32.34 0 [] -number_semiring(X_a)|hAPP(X_a,X_a,times_times(X_a,Z_1),number_number_of(X_a,bit0(bit1(pls))))=hAPP(X_a,X_a,plus_plus(X_a,Z_1),Z_1).
% 32.54/32.34 0 [] -number_ring(X_a)|hAPP(X_a,X_a,times_times(X_a,Z_1),number_number_of(X_a,bit0(bit1(pls))))=hAPP(X_a,X_a,plus_plus(X_a,Z_1),Z_1).
% 32.54/32.34 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls))))=hAPP(X_a,X_a,times_times(X_a,A_1),A_1).
% 32.54/32.34 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),zero_zero(X_a))).
% 32.54/32.34 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),zero_zero(X_a))).
% 32.54/32.34 0 [] -number_semiring(X_a)|number_number_of(X_a,pls)=zero_zero(X_a).
% 32.54/32.34 0 [] -number_ring(X_a)|number_number_of(X_a,pls)=zero_zero(X_a).
% 32.54/32.34 0 [] -number_ring(X_a)|zero_zero(X_a)=number_number_of(X_a,pls).
% 32.54/32.34 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,pls)),A_1)=ti(X_a,A_1).
% 32.54/32.34 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),number_number_of(X_a,pls))=ti(X_a,A_1).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X)),number_number_of(X_a,Y_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),Y_1)).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X)),number_number_of(X_a,Y_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),Y_1)).
% 32.54/32.34 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,W)),Z_1))=hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,hAPP(int,int,plus_plus(int,V),W))),Z_1).
% 32.54/32.34 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),number_number_of(X_a,W))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V),W)).
% 32.54/32.34 0 [] -number_ring(X_a)|number_number_of(X_a,hAPP(int,int,plus_plus(int,V),W))=hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),number_number_of(X_a,W)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K1)),bit0(K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K1)),bit0(K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit0(L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit0(L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(W_1)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(W_1)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int))).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit0(K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit0(K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(W_1)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(W_1)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int))).
% 32.54/32.34 0 [] hAPP(int,int,plus_plus(int,bit1(K_1)),bit0(L_1))=bit1(hAPP(int,int,plus_plus(int,K_1),L_1)).
% 32.54/32.34 0 [] hAPP(int,int,plus_plus(int,bit0(K_1)),bit1(L_1))=bit1(hAPP(int,int,plus_plus(int,K_1),L_1)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))).
% 32.54/32.34 0 [] bit1(K_1)=hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),K_1)),K_1).
% 32.54/32.34 0 [] hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_1)),Z_1)!=zero_zero(int).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))|ti(int,W_1)=ti(int,Z_2).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))|ti(int,W_1)!=ti(int,Z_2).
% 32.54/32.34 0 [] -monoid_mult(X_b)| -number(X_b)|hAPP(nat,X_b,power_power(X_b,number_number_of(X_b,W)),number_number_of(nat,bit0(bit1(pls))))=hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,W)),number_number_of(X_b,W)).
% 32.54/32.34 0 [] -number_semiring(X_a)|hAPP(nat,X_a,power_power(X_a,hAPP(X_a,X_a,plus_plus(X_a,X_1),Y)),number_number_of(nat,bit0(bit1(pls))))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,bit0(bit1(pls)))))),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls)))),X_1)),Y)).
% 32.54/32.34 0 [] -number_ring(X_a)|number_number_of(X_a,bit0(W))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),number_number_of(X_a,W))),number_number_of(X_a,W)).
% 32.54/32.34 0 [] -number_ring(X_a)|number_number_of(X_a,bit1(W))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,W))),number_number_of(X_a,W)).
% 32.54/32.34 0 [] -number_semiring(X_a)|number_number_of(X_a,bit1(pls))=one_one(X_a).
% 32.54/32.34 0 [] -number_ring(X_a)|number_number_of(X_a,bit1(pls))=one_one(X_a).
% 32.54/32.34 0 [] -number_ring(X_a)|one_one(X_a)=number_number_of(X_a,bit1(pls)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_2)),Z_2)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_2)),Z_2)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int))).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X)),zero_zero(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),pls)).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X)),zero_zero(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),pls)).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),number_number_of(X_a,Y_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Y_1)).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),number_number_of(X_a,Y_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Y_1)).
% 32.54/32.34 0 [] -number_semiring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))=number_number_of(X_a,bit0(bit1(pls))).
% 32.54/32.34 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))=number_number_of(X_a,bit0(bit1(pls))).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X)),one_one(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),bit1(pls))).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X)),one_one(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),bit1(pls))).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),number_number_of(X_a,Y_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(pls)),Y_1)).
% 32.54/32.34 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),number_number_of(X_a,Y_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(pls)),Y_1)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)))).
% 32.54/32.34 0 [] hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,A_1),B)),number_number_of(nat,bit1(bit1(pls))))=hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit1(bit1(pls))))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit1(bit1(pls)))),hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))))),B))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit1(bit1(pls)))),A_1)),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls))))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit1(bit1(pls))))).
% 32.54/32.34 0 [] hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,A_1),B)),number_number_of(nat,bit0(bit1(pls))))=hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),A_1)),B))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls))))).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),number_number_of(int,bit0(bit1(pls)))))|ti(int,X_1)=zero_zero(int)|ti(int,X_1)=one_one(int).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),s)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),s),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,zcong(s1,s),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.54/32.34 0 [] hAPP(int,int,times_times(int,A_1),hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit1(bit1(pls)))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_1),hAPP(nat,int,power_power(int,X_1),number_number_of(nat,bit0(bit1(pls)))))).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))|ti(int,A_1)!=hAPP(int,int,plus_plus(int,R_1),hAPP(int,int,times_times(int,A_1),Q_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),A_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Q_1)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))|ti(int,A_1)!=hAPP(int,int,plus_plus(int,R_1),hAPP(int,int,times_times(int,A_1),Q_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),one_one(int))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit0(bit1(pls))))).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,X_1),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1))=hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,X_1),N_1)),hAPP(nat,X_a,power_power(X_a,X_1),N_1)).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,X_1),X_1)=hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls)))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,int,power_power(int,s1),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$c2)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$c2),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,zcong(s1,$c2),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_2),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))| -hBOOL(hAPP(int,bool,zcong(s1,Y_2),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))|ti(int,Y_2)=ti(int,$c2).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$c3)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$c3),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,zcong(s1,$c3),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,s1),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.54/32.34 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X),N)))|N=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X)).
% 32.54/32.34 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X),N)))|N!=zero_zero(nat).
% 32.54/32.34 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),hAPP(nat,int,power_power(int,A_1),N_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),A_1)).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,X_1),P_3)),Q_1)=hAPP(nat,X_a,power_power(X_a,X_1),hAPP(nat,nat,times_times(nat,P_3),Q_1)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_3),N_1)),hAPP(int,int,times_times(int,A_1),B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_3),N_1)),A_1)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_3),N_1)),hAPP(int,int,times_times(int,A_1),B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_3),N_1)),B)).
% 32.54/32.34 0 [] hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X_1),Y)),Z_1)=hAPP(nat,int,power_power(int,X_1),hAPP(nat,nat,times_times(nat,Y),Z_1)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M),N_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),M)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),N_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),M))|ti(int,M)=ti(int,N_1).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,times_times(int,K_1),M)),hAPP(int,int,times_times(int,K_1),N_1)))|ti(int,K_1)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N_1)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,plus_plus(int,N),hAPP(int,int,times_times(int,K),Ma))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,plus_plus(int,N),hAPP(int,int,times_times(int,K),Ma))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),D))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),hAPP(int,int,plus_plus(int,X),Ta)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X),hAPP(int,int,times_times(int,C_1),D))),Ta))).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),D))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),hAPP(int,int,plus_plus(int,X),Ta)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X),hAPP(int,int,times_times(int,C_1),D))),Ta))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,zprime,number_number_of(int,bit0(bit1(pls))))).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z_1),N_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),N_1)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,X_1))| -hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,Y))|hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,hAPP(int,int,times_times(int,X_1),Y))).
% 32.54/32.34 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,V_3)),number_number_of(nat,V_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_3),V_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_3),pls)).
% 32.54/32.34 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,V_3)),number_number_of(nat,V_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_3),V_2)).
% 32.54/32.34 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,V_3)),number_number_of(nat,V_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_3),pls)).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Rx)),hAPP(X_a,X_a,times_times(X_a,Ly),Ry)).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,Rx),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),Ry)).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,Lx),hAPP(X_a,X_a,times_times(X_a,Ly),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),Rx)=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Rx)),Ly).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),Rx)=hAPP(X_a,X_a,times_times(X_a,Lx),hAPP(X_a,X_a,times_times(X_a,Ly),Rx)).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,Lx),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Rx)),Ry).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,Lx),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,Rx),hAPP(X_a,X_a,times_times(X_a,Lx),Ry)).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),B)=hAPP(X_a,X_a,times_times(X_a,B),A_1).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),C)=hAPP(X_a,X_a,plus_plus(X_a,C),A_1).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,C),D_2))=hAPP(X_a,X_a,plus_plus(X_a,C),hAPP(X_a,X_a,plus_plus(X_a,A_1),D_2)).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,C),D_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),D_2).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C)).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),B).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),hAPP(X_a,X_a,plus_plus(X_a,C),D_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2)).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,X_1),one_one(nat))=ti(X_a,X_1).
% 32.54/32.34 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X),number_number_of(nat,W_1))))|number_number_of(nat,W_1)=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X)).
% 32.54/32.34 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X),number_number_of(nat,W_1))))|number_number_of(nat,W_1)!=zero_zero(nat).
% 32.54/32.34 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X),number_number_of(nat,W_1))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X)).
% 32.54/32.34 0 [] hAPP(nat,nat,times_times(nat,Z_1),number_number_of(nat,bit0(bit1(pls))))=hAPP(nat,nat,plus_plus(nat,Z_1),Z_1).
% 32.54/32.34 0 [] hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),Z_1)=hAPP(nat,nat,plus_plus(nat,Z_1),Z_1).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,times_times(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=zero_zero(nat).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,times_times(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=number_number_of(nat,hAPP(int,int,times_times(int,V),V_1)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,times_times(nat,number_number_of(nat,V)),hAPP(nat,nat,times_times(nat,number_number_of(nat,V_1)),K_1))=zero_zero(nat).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,times_times(nat,number_number_of(nat,V)),hAPP(nat,nat,times_times(nat,number_number_of(nat,V_1)),K_1))=hAPP(nat,nat,times_times(nat,number_number_of(nat,hAPP(int,int,times_times(int,V),V_1))),K_1).
% 32.54/32.34 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1))=hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N_1)),number_number_of(nat,bit0(bit1(pls)))).
% 32.54/32.34 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),K_1))),zero_zero(X_a)))|ti(X_a,A_1)=zero_zero(X_a).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,zero_zero(X_a)),A_1)=zero_zero(X_a).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a))=zero_zero(X_a).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1).
% 32.54/32.34 0 [] -semiri456707255roduct(X_a)|ti(X_a,B_2)!=hAPP(X_a,X_a,plus_plus(X_a,B_2),A_3)|ti(X_a,A_3)=zero_zero(X_a).
% 32.54/32.34 0 [] -semiri456707255roduct(X_a)|ti(X_a,B_2)=hAPP(X_a,X_a,plus_plus(X_a,B_2),A_3)|ti(X_a,A_3)!=zero_zero(X_a).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,X_1),hAPP(X_a,X_a,plus_plus(X_a,Y),Z_1))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Y)),hAPP(X_a,X_a,times_times(X_a,X_1),Z_1)).
% 32.54/32.34 0 [] -semiri456707255roduct(X_a)|ti(X_a,A_3)=ti(X_a,B_2)|ti(X_a,C_1)=ti(X_a,D)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),D))!=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),D)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)).
% 32.54/32.34 0 [] -semiri456707255roduct(X_a)|ti(X_a,A_3)!=ti(X_a,B_2)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),D))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),D)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)).
% 32.54/32.34 0 [] -semiri456707255roduct(X_a)|ti(X_a,C_1)!=ti(X_a,D)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),D))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),D)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C)).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),M)),hAPP(X_a,X_a,times_times(X_a,B),M))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),M).
% 32.54/32.34 0 [] -semiri456707255roduct(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,W_1),Y_1)),hAPP(X_a,X_a,times_times(X_a,X),Z_2))!=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,W_1),Z_2)),hAPP(X_a,X_a,times_times(X_a,X),Y_1))|ti(X_a,W_1)=ti(X_a,X)|ti(X_a,Y_1)=ti(X_a,Z_2).
% 32.54/32.34 0 [] -semiri456707255roduct(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,W_1),Y_1)),hAPP(X_a,X_a,times_times(X_a,X),Z_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,W_1),Z_2)),hAPP(X_a,X_a,times_times(X_a,X),Y_1))|ti(X_a,W_1)!=ti(X_a,X).
% 32.54/32.34 0 [] -semiri456707255roduct(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,W_1),Y_1)),hAPP(X_a,X_a,times_times(X_a,X),Z_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,W_1),Z_2)),hAPP(X_a,X_a,times_times(X_a,X),Y_1))|ti(X_a,Y_1)!=ti(X_a,Z_2).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,one_one(X_a)),A_1)=ti(X_a,A_1).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),one_one(X_a))=ti(X_a,A_1).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Y)),Q_1)=hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,X_1),Q_1)),hAPP(nat,X_a,power_power(X_a,Y),Q_1)).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,X_1),P_3)),hAPP(nat,X_a,power_power(X_a,X_1),Q_1))=hAPP(nat,X_a,power_power(X_a,X_1),hAPP(nat,nat,plus_plus(nat,P_3),Q_1)).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,X_1),zero_zero(nat))=one_one(X_a).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),zero_zero(int))).
% 32.54/32.34 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1)))).
% 32.54/32.34 0 [] -semiri456707255roduct(X_a)|ti(X_a,R_1)=zero_zero(X_a)|ti(X_a,A_1)!=ti(X_a,B)|ti(X_a,C)=ti(X_a,D_2)|hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,times_times(X_a,R_1),C))!=hAPP(X_a,X_a,plus_plus(X_a,B),hAPP(X_a,X_a,times_times(X_a,R_1),D_2)).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,M),M)=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))),M).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,M),hAPP(X_a,X_a,times_times(X_a,A_1),M))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),one_one(X_a))),M).
% 32.54/32.34 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),M)),M)=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),one_one(X_a))),M).
% 32.54/32.34 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,W_1))!=zero_zero(X_a)|ti(X_a,A_3)=zero_zero(X_a).
% 32.54/32.34 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,W_1))!=zero_zero(X_a)|number_number_of(nat,W_1)!=zero_zero(nat).
% 32.54/32.34 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,W_1))=zero_zero(X_a)|ti(X_a,A_3)!=zero_zero(X_a)|number_number_of(nat,W_1)=zero_zero(nat).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),one_one(int))).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,times_times(int,X_1),Y))).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,X_1),Y))).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,power_power(int,X_1),N_1))).
% 32.54/32.34 0 [] -power(X_a)| -semiring_0(X_a)|number_number_of(nat,W)!=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,W))=one_one(X_a).
% 32.54/32.34 0 [] -power(X_a)| -semiring_0(X_a)|number_number_of(nat,W)=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,W))=zero_zero(X_a).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit1(bit1(pls))))).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Q_4)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_4),zero_zero(int))).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_4)),R_3)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_1)),R_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_4),Q_1)).
% 32.54/32.34 0 [] hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_1)),R_1)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_3),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q_4)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_4)),R_3)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_1)),R_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_1),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q_4)).
% 32.54/32.34 0 [] hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_1)),R_1)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_3),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_4),Q_1)).
% 32.54/32.34 0 [] hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X_1),number_number_of(nat,bit0(bit1(pls))))),number_number_of(nat,bit0(bit1(pls))))=hAPP(nat,int,power_power(int,X_1),number_number_of(nat,bit0(bit0(bit1(pls))))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))| -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,Y),number_number_of(nat,bit0(bit1(pls)))),X_1),P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),Y)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_2)).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M_2),P_2))|ti(int,M_2)=one_one(int)|ti(int,M_2)=ti(int,P_2).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,zprime,P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f1(P_2))).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,zprime,P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),$f1(P_2)),P_2)).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,zprime,P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_2))|ti(int,$f1(P_2))!=one_one(int).
% 32.54/32.34 0 [] hBOOL(hAPP(int,bool,zprime,P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_2))|ti(int,$f1(P_2))!=ti(int,P_2).
% 32.54/32.34 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))|ti(int,P_3)=number_number_of(int,bit0(bit1(pls)))|ti(int,P_3)=number_number_of(int,bit1(bit1(pls)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),P_3)).
% 32.54/32.34 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,bit0(bit1(pls))))).
% 32.54/32.34 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,B),N_1))).
% 32.54/32.34 0 [] -linord626643107strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),U_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),V))|hAPP(X_a,X_a,plus_plus(X_a,U_1),V)!=one_one(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,U_1),X_1)),hAPP(X_a,X_a,times_times(X_a,V),Y))),A_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),hAPP(nat,int,power_power(int,Y),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),Y)).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),zero_zero(X_a))).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,$c4),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))).
% 32.54/32.35 0 [] legendre(number_number_of(int,min),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))=one_one(int).
% 32.54/32.35 0 [] bit1(K)!=min|ti(int,K)=min.
% 32.54/32.35 0 [] bit1(K)=min|ti(int,K)!=min.
% 32.54/32.35 0 [] min!=bit1(L)|min=ti(int,L).
% 32.54/32.35 0 [] min=bit1(L)|min!=ti(int,L).
% 32.54/32.35 0 [] bit1(min)=min.
% 32.54/32.35 0 [] pls!=min.
% 32.54/32.35 0 [] min!=pls.
% 32.54/32.35 0 [] bit0(K_1)!=min.
% 32.54/32.35 0 [] min!=bit0(L_1).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),min)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),min)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),min))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),min)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),min))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),min)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit1(K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit1(K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),min)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),pls)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit0(K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit0(K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),zero_zero(int))).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit1(K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),K)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit1(K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),K)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),min))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),min))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),pls)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),min)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),min))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),min))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min)).
% 32.54/32.35 0 [] number_number_of(int,pls)!=number_number_of(int,min).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),min))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),min))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit0(K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit0(K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)).
% 32.54/32.35 0 [] hAPP(int,int,times_times(int,Ma),N)!=one_one(int)|ti(int,Ma)=one_one(int)|ti(int,Ma)=number_number_of(int,min).
% 32.54/32.35 0 [] hAPP(int,int,times_times(int,Ma),N)!=one_one(int)|ti(int,Ma)=one_one(int)|ti(int,N)=number_number_of(int,min).
% 32.54/32.35 0 [] hAPP(int,int,times_times(int,Ma),N)!=one_one(int)|ti(int,N)=one_one(int)|ti(int,Ma)=number_number_of(int,min).
% 32.54/32.35 0 [] hAPP(int,int,times_times(int,Ma),N)!=one_one(int)|ti(int,N)=one_one(int)|ti(int,N)=number_number_of(int,min).
% 32.54/32.35 0 [] hAPP(int,int,times_times(int,Ma),N)=one_one(int)|ti(int,Ma)!=one_one(int)|ti(int,N)!=one_one(int).
% 32.54/32.35 0 [] hAPP(int,int,times_times(int,Ma),N)=one_one(int)|ti(int,Ma)!=number_number_of(int,min)|ti(int,N)!=number_number_of(int,min).
% 32.54/32.35 0 [] hAPP(int,int,times_times(int,M),N_1)!=one_one(int)|ti(int,M)=one_one(int)|ti(int,M)=number_number_of(int,min).
% 32.54/32.35 0 [] -linordered_idom(X_a)|ti(X_a,X_1)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),A_1)).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|hBOOL(hAPP(int,bool,zcong(B_2,A_3),Ma)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))| -hBOOL(hAPP(int,bool,zcong(B_2,A_3),Ma)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,zcong(K_1,K_1),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B),M))|ti(int,B)!=ti(int,C)| -hBOOL(hAPP(int,bool,zcong(C,D_2),M))|hBOOL(hAPP(int,bool,zcong(A_1,D_2),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B),M))| -hBOOL(hAPP(int,bool,zcong(B,C),M))|hBOOL(hAPP(int,bool,zcong(A_1,C),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))| -hBOOL(hAPP(int,bool,zcong(X_1,number_number_of(int,min)),P_3))| -hBOOL(hAPP(int,bool,zcong(X_1,one_one(int)),P_3)).
% 32.54/32.35 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))|ti(X_a,X_1)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)).
% 32.54/32.35 0 [] -no_zero_divisors(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),B)!=zero_zero(X_a)|ti(X_a,A_1)=zero_zero(X_a)|ti(X_a,B)=zero_zero(X_a).
% 32.54/32.35 0 [] -no_zero_divisors(X_a)|ti(X_a,A_1)=zero_zero(X_a)|ti(X_a,B)=zero_zero(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),B)!=zero_zero(X_a).
% 32.54/32.35 0 [] -ring_n68954251visors(X_a)|hAPP(X_a,X_a,times_times(X_a,A_3),B_2)!=zero_zero(X_a)|ti(X_a,A_3)=zero_zero(X_a)|ti(X_a,B_2)=zero_zero(X_a).
% 32.54/32.35 0 [] -ring_n68954251visors(X_a)|hAPP(X_a,X_a,times_times(X_a,A_3),B_2)=zero_zero(X_a)|ti(X_a,A_3)!=zero_zero(X_a).
% 32.54/32.35 0 [] -ring_n68954251visors(X_a)|hAPP(X_a,X_a,times_times(X_a,A_3),B_2)=zero_zero(X_a)|ti(X_a,B_2)!=zero_zero(X_a).
% 32.54/32.35 0 [] -mult_zero(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a))=zero_zero(X_a).
% 32.54/32.35 0 [] -mult_zero(X_a)|hAPP(X_a,X_a,times_times(X_a,zero_zero(X_a)),A_1)=zero_zero(X_a).
% 32.54/32.35 0 [] -zero_ne_q_one(X_a)|zero_zero(X_a)!=one_one(X_a).
% 32.54/32.35 0 [] -zero_ne_q_one(X_a)|one_one(X_a)!=zero_zero(X_a).
% 32.54/32.35 0 [] -semiring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),E_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B),E_1)),C))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),E_1)),C).
% 32.54/32.35 0 [] -comm_semiring(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C)).
% 32.54/32.35 0 [] -ring_11004092258visors(X_a)|ti(X_a,A_1)=zero_zero(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),N_1)!=zero_zero(X_a).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),zero_zero(X_a)),A_1))|ti(X_a,A_1)=zero_zero(X_a).
% 32.54/32.35 0 [] -comm_monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),N_1)=hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,B),N_1)).
% 32.54/32.35 0 [] -monoid_mult(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N_1)),A_1)=hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(nat,X_a,power_power(X_a,A_1),N_1)).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,times_times(X_a,A_1),B))).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,times_times(X_a,B),A_1))).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,times_times(X_a,B),C))).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,times_times(X_a,B),C))).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),D_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))).
% 32.54/32.35 0 [] -dvd(X_a)|A_1!=hAPP(X_a,X_a,times_times(X_a,B),K_1)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),A_1)).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),C)).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C))).
% 32.54/32.35 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,one_one(X_a)),N_1)=one_one(X_a).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),one_one(X_a)),A_1)).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,X_1),N_1)),hAPP(nat,X_a,power_power(X_a,Y),N_1))).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M)),B)).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,X_1),N_1)),hAPP(nat,X_a,power_power(X_a,Y),M))).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),I_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,I_1),M)),hAPP(nat,nat,power_power(nat,I_1),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X))|N=zero_zero(nat).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X),N)))|N!=zero_zero(nat).
% 32.54/32.35 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,times_times(nat,M),N_1))=hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,A_1),M)),N_1).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),A_1)).
% 32.54/32.35 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),one_one(nat))=ti(X_a,A_1).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,zcong(M,zero_zero(int)),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),zero_zero(int)))|ti(int,A_3)=ti(int,B_2).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,zcong(A_3,B_2),zero_zero(int)))|ti(int,A_3)!=ti(int,B_2).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,zcong(A_1,B),one_one(int))).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),M),hAPP(int,int,times_times(int,B),M)),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))| -hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,A_3),D)),Ma))|hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,B_2),D)),Ma)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,A_3),D)),Ma))| -hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,B_2),D)),Ma)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))| -hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,D),A_3)),Ma))|hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,D),B_2)),Ma)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,D),A_3)),Ma))| -hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,D),B_2)),Ma)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B),M))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),K_1),hAPP(int,int,times_times(int,B),K_1)),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B),M))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,K_1),A_1),hAPP(int,int,times_times(int,K_1),B)),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B),M))| -hBOOL(hAPP(int,bool,zcong(C,D_2),M))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),C),hAPP(int,int,times_times(int,B),D_2)),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B),M))| -hBOOL(hAPP(int,bool,zcong(C,D_2),M))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,plus_plus(int,A_1),C),hAPP(int,int,plus_plus(int,B),D_2)),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B),M))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,plus_plus(int,A_1),C),hAPP(int,int,plus_plus(int,B),C)),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(X_1,Y),M))|hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X_1),Z_1),hAPP(nat,int,power_power(int,Y),Z_1)),M)).
% 32.54/32.35 0 [] -number_ring(X_a)|hAPP(nat,X_a,power_power(X_a,number_number_of(X_a,min)),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1))=one_one(X_a).
% 32.54/32.35 0 [] -ordere453448008miring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))).
% 32.54/32.35 0 [] -ordere453448008miring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))).
% 32.54/32.35 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))).
% 32.54/32.35 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))).
% 32.54/32.35 0 [] -ordered_semiring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))).
% 32.54/32.35 0 [] -ordered_semiring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))).
% 32.54/32.35 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))).
% 32.54/32.35 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))).
% 32.54/32.35 0 [] -ordere1490568538miring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))).
% 32.54/32.35 0 [] -ordered_semiring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))).
% 32.54/32.35 0 [] -ordered_semiring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))).
% 32.54/32.35 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))).
% 32.54/32.35 0 [] -ordere453448008miring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))).
% 32.54/32.35 0 [] -ordere453448008miring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,B),A_1)),zero_zero(X_a))).
% 32.54/32.35 0 [] -ordere453448008miring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))).
% 32.54/32.35 0 [] -ordere453448008miring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_2)).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_2)).
% 32.54/32.35 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),zero_zero(X_a))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_2)).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),zero_zero(X_a))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),zero_zero(X_a))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_2)).
% 32.54/32.35 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),zero_zero(X_a))).
% 32.54/32.35 0 [] -linordered_ring(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),A_1))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))).
% 32.54/32.35 0 [] -linord893533164strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))).
% 32.54/32.35 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))).
% 32.54/32.35 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))).
% 32.54/32.35 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)).
% 32.54/32.35 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,B),A_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)).
% 32.54/32.35 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)).
% 32.54/32.35 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,B),A_1)),zero_zero(X_a))).
% 32.54/32.35 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))).
% 32.54/32.35 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)).
% 32.54/32.35 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)).
% 32.54/32.35 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)).
% 32.54/32.35 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)).
% 32.54/32.35 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)).
% 32.54/32.35 0 [] -linordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),A_1)),zero_zero(X_a))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),one_one(X_a))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),zero_zero(X_a))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,B),N_1))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,times_times(X_a,M),N_1))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,plus_plus(X_a,A_1),one_one(X_a)))).
% 32.54/32.35 0 [] -idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|ti(X_a,C_1)=zero_zero(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2)).
% 32.54/32.35 0 [] -idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|ti(X_a,C_1)!=zero_zero(X_a).
% 32.54/32.35 0 [] -idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2)).
% 32.54/32.35 0 [] -idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))|ti(X_a,C_1)=zero_zero(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2)).
% 32.54/32.35 0 [] -idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))|ti(X_a,C_1)!=zero_zero(X_a).
% 32.54/32.35 0 [] -idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2)).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),N_3))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,A_1),N_3))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_3))|hAPP(nat,X_a,power_power(X_a,A_3),Ma)!=hAPP(nat,X_a,power_power(X_a,A_3),N)|Ma=N.
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_3))|hAPP(nat,X_a,power_power(X_a,A_3),Ma)=hAPP(nat,X_a,power_power(X_a,A_3),N)|Ma!=N.
% 32.54/32.35 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_3),N)!=zero_zero(X_a)|ti(X_a,A_3)=zero_zero(X_a).
% 32.54/32.35 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_3),N)!=zero_zero(X_a)|N!=zero_zero(nat).
% 32.54/32.35 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_3),N)=zero_zero(X_a)|ti(X_a,A_3)!=zero_zero(X_a)|N=zero_zero(nat).
% 32.54/32.35 0 [] -power(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),zero_zero(nat))=one_one(X_a).
% 32.54/32.35 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,plus_plus(nat,M),N_1))=hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,A_1),M)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1))| -hBOOL(hAPP(int,bool,zcong(A_1,B),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),M))| -hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Y))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))| -hBOOL(hAPP(int,bool,zcong(X_1,Y),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),M))|ti(int,X_1)=ti(int,Y).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),M),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_1),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|ti(int,B_2)=hAPP(int,int,plus_plus(int,A_3),hAPP(int,int,times_times(int,Ma),$f2(A_3,B_2,Ma))).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|ti(int,B_2)!=hAPP(int,int,plus_plus(int,A_3),hAPP(int,int,times_times(int,Ma),K_2)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(X,zero_zero(int)),P_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),X)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,zcong(X,zero_zero(int)),P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),X)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,zero_zero(int)),Ma))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),A_3)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,zcong(A_3,zero_zero(int)),Ma))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),A_3)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),hAPP(int,int,times_times(int,M),N_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),N_1)).
% 32.54/32.35 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B)).
% 32.54/32.35 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B)).
% 32.54/32.35 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)).
% 32.54/32.35 0 [] -linordered_semiring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)).
% 32.54/32.35 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)).
% 32.54/32.35 0 [] -linordered_semiring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)).
% 32.54/32.35 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))).
% 32.54/32.35 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))).
% 32.54/32.35 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))).
% 32.54/32.35 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),A_3)).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),A_3)).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2)).
% 32.54/32.35 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2)).
% 32.54/32.35 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),one_one(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,Y),X_1)),X_1)).
% 32.54/32.35 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),one_one(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,X_1),Y)),X_1)).
% 32.54/32.35 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a)))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,B),N_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),N_3))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),one_one(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_3)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,B_2),X)),hAPP(nat,X_a,power_power(X_a,B_2),Y_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),Y_1)).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,B_2),X)),hAPP(nat,X_a,power_power(X_a,B_2),Y_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),Y_1)).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))).
% 32.54/32.35 0 [] -power(X_a)| -semiring_0(X_a)|N_1!=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N_1)=one_one(X_a).
% 32.54/32.35 0 [] -power(X_a)| -semiring_0(X_a)|N_1=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N_1)=zero_zero(X_a).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_3))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,A_1),N_3))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,B_2),X)),hAPP(nat,X_a,power_power(X_a,B_2),Y_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y_1)).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,B_2),X)),hAPP(nat,X_a,power_power(X_a,B_2),Y_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y_1)).
% 32.54/32.35 0 [] hAPP(real,real,times_times(real,number_number_of(real,bit0(bit0(bit1(pls))))),hAPP(nat,real,power_power(real,X_1),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,real,power_power(real,hAPP(real,real,times_times(real,number_number_of(real,bit0(bit1(pls)))),X_1)),number_number_of(nat,bit0(bit1(pls)))).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),M))| -hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),M))|ti(int,X_1)=zero_zero(int).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M))| -hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),M))|ti(int,A_1)=zero_zero(int).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),M))| -hBOOL(hAPP(int,bool,zcong(A_1,B),M))|ti(int,A_1)=ti(int,B).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),Y))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),hAPP(nat,int,power_power(int,Y),N_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X_1),Y),one_one(int)),P_3))|hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X_1),hAPP(nat,nat,times_times(nat,Y),Z_1)),one_one(int)),P_3)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))|hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,zcong(Y,zero_zero(int)),P_3))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,X_1),Y),zero_zero(int)),P_3)).
% 32.54/32.35 0 [] -linord1278240602ring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),U_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),V))|hAPP(X_a,X_a,plus_plus(X_a,U_1),V)!=one_one(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,U_1),X_1)),hAPP(X_a,X_a,times_times(X_a,V),Y))),A_1)).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(nat,X_a,power_power(X_a,A_1),N_1))),hAPP(nat,X_a,power_power(X_a,A_1),N_1))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_3))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_3)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))).
% 32.54/32.35 0 [] -linordered_semidom(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),N_1)!=hAPP(nat,X_a,power_power(X_a,B),N_1)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|ti(X_a,A_1)=ti(X_a,B).
% 32.54/32.35 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),hAPP(nat,X_a,power_power(X_a,X_1),N_1))).
% 32.54/32.35 0 [] -comm_semiring_1(X_a)|ti(X_a,X_1)!=one_one(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),hAPP(nat,X_a,power_power(X_a,X_1),N_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),B),zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,zcong(B,zero_zero(int)),P_3)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))|hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,zcong(B,zero_zero(int)),P_3))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),B),zero_zero(int)),P_3)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M))| -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),hAPP(int,int,times_times(int,M),N_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),N_1)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,quadRes(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),number_number_of(int,min))).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)))).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),M))| -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,number_number_of(int,min)),J_1),hAPP(nat,int,power_power(int,number_number_of(int,min)),K_1)),M))|hAPP(nat,int,power_power(int,number_number_of(int,min)),J_1)=hAPP(nat,int,power_power(int,number_number_of(int,min)),K_1).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),M))| -hBOOL(hAPP(int,bool,zcong(one_one(int),number_number_of(int,min)),M)).
% 32.54/32.35 0 [] hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min))=hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,quadRes(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),number_number_of(int,min)))|legendre(number_number_of(int,min),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))!=one_one(int).
% 32.54/32.35 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,times_times(real,X),X)))|X=zero_zero(real).
% 32.54/32.35 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,times_times(real,X),X)))|X!=zero_zero(real).
% 32.54/32.35 0 [] -number_ring(X_a)|number_number_of(X_a,hAPP(int,int,minus_minus(int,V),W))=hAPP(X_a,X_a,minus_minus(X_a,number_number_of(X_a,V)),number_number_of(X_a,W)).
% 32.54/32.35 0 [] -comm_ring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Z_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),hAPP(X_a,X_a,minus_minus(X_a,Y),Z_1))).
% 32.54/32.35 0 [] hAPP(int,int,minus_minus(int,K_1),pls)=ti(int,K_1).
% 32.54/32.35 0 [] hAPP(int,int,minus_minus(int,bit0(K_1)),bit0(L_1))=bit0(hAPP(int,int,minus_minus(int,K_1),L_1)).
% 32.54/32.35 0 [] hAPP(int,int,times_times(int,hAPP(int,int,minus_minus(int,Z1),Z2)),W)=hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,Z1),W)),hAPP(int,int,times_times(int,Z2),W)).
% 32.54/32.35 0 [] hAPP(int,int,times_times(int,W),hAPP(int,int,minus_minus(int,Z1),Z2))=hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,W),Z1)),hAPP(int,int,times_times(int,W),Z2)).
% 32.54/32.35 0 [] hAPP(int,int,minus_minus(int,A_1),B)!=ti(int,C)|ti(int,A_1)=hAPP(int,int,plus_plus(int,C),B).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B),M))| -hBOOL(hAPP(int,bool,zcong(C,D_2),M))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,minus_minus(int,A_1),C),hAPP(int,int,minus_minus(int,B),D_2)),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),hAPP(int,int,minus_minus(int,M),N_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),N_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),M)).
% 32.54/32.35 0 [] -ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)!=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)|ti(X_a,C_1)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D).
% 32.54/32.35 0 [] -ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)|ti(X_a,C_1)!=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D).
% 32.54/32.35 0 [] -ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)!=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)=ti(X_a,D).
% 32.54/32.35 0 [] -ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)!=ti(X_a,D).
% 32.54/32.35 0 [] -number(X_b)| -ring(X_b)|hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),hAPP(X_b,X_b,minus_minus(X_b,B),C))=hAPP(X_b,X_b,minus_minus(X_b,hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),B)),hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),C)).
% 32.54/32.35 0 [] -number(X_b)| -ring(X_b)|hAPP(X_b,X_b,times_times(X_b,hAPP(X_b,X_b,minus_minus(X_b,A_1),B)),number_number_of(X_b,V))=hAPP(X_b,X_b,minus_minus(X_b,hAPP(X_b,X_b,times_times(X_b,A_1),number_number_of(X_b,V))),hAPP(X_b,X_b,times_times(X_b,B),number_number_of(X_b,V))).
% 32.54/32.35 0 [] hAPP(int,int,minus_minus(int,bit1(K_1)),bit0(L_1))=bit1(hAPP(int,int,minus_minus(int,K_1),L_1)).
% 32.54/32.35 0 [] hAPP(int,int,minus_minus(int,bit1(K_1)),bit1(L_1))=bit0(hAPP(int,int,minus_minus(int,K_1),L_1)).
% 32.54/32.35 0 [] hAPP(int,int,minus_minus(int,pls),bit0(L_1))=bit0(hAPP(int,int,minus_minus(int,pls),L_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,K),L)),zero_zero(int))).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,K),L)),zero_zero(int))).
% 32.54/32.35 0 [] hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,hAPP(int,int,minus_minus(int,A_1),hAPP(int,int,times_times(int,R_1),B))),M)),hAPP(int,int,times_times(int,hAPP(int,int,minus_minus(int,C),hAPP(int,int,times_times(int,R_1),D_2))),N_1))=hAPP(int,int,minus_minus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A_1),M)),hAPP(int,int,times_times(int,C),N_1))),hAPP(int,int,times_times(int,R_1),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),M)),hAPP(int,int,times_times(int,D_2),N_1)))).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),hAPP(int,int,minus_minus(int,A_3),B_2))).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),hAPP(int,int,minus_minus(int,A_3),B_2))).
% 32.54/32.35 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)),D)).
% 32.54/32.35 0 [] -ordered_ring(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)),D)).
% 32.54/32.35 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D))).
% 32.54/32.35 0 [] -ordered_ring(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D))).
% 32.54/32.35 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D))).
% 32.54/32.35 0 [] -ordered_ring(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D))).
% 32.54/32.35 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)),D)).
% 32.54/32.35 0 [] -ordered_ring(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)),D)).
% 32.54/32.35 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),hAPP(X_a,X_a,minus_minus(X_a,number_number_of(X_a,W)),C))=hAPP(X_a,X_a,minus_minus(X_a,number_number_of(X_a,hAPP(int,int,plus_plus(int,V),W))),C).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),A_1))|ti(int,X_1)=hAPP(int,int,minus_minus(int,A_1),one_one(int))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),hAPP(int,int,minus_minus(int,A_1),one_one(int)))).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),hAPP(int,int,minus_minus(int,Z_2),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),hAPP(int,int,minus_minus(int,Z_2),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)).
% 32.54/32.35 0 [] hAPP(int,int,minus_minus(int,pls),bit1(L_1))=bit1(hAPP(int,int,minus_minus(int,min),L_1)).
% 32.54/32.35 0 [] hAPP(int,int,minus_minus(int,min),bit0(L_1))=bit1(hAPP(int,int,minus_minus(int,min),L_1)).
% 32.54/32.35 0 [] hAPP(int,int,minus_minus(int,min),bit1(L_1))=bit0(hAPP(int,int,minus_minus(int,min),L_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_3),hAPP(int,int,minus_minus(int,P_2),one_one(int))),one_one(int)),P_2))|hBOOL(hAPP(int,bool,zcong(A_3,hAPP(int,int,minus_minus(int,P_2),one_one(int))),P_2)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_3),hAPP(int,int,minus_minus(int,P_2),one_one(int))),one_one(int)),P_2))| -hBOOL(hAPP(int,bool,zcong(A_3,hAPP(int,int,minus_minus(int,P_2),one_one(int))),P_2)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,I_1),M)),hAPP(nat,nat,power_power(nat,I_1),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),I_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_3))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),A_1),one_one(int)),P_3))|ti(int,A_1)=one_one(int)|ti(int,A_1)=hAPP(int,int,minus_minus(int,P_3),one_one(int)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),A_1),one_one(int)),P_3))|hBOOL(hAPP(int,bool,zcong(A_1,one_one(int)),P_3))|hBOOL(hAPP(int,bool,zcong(A_1,hAPP(int,int,minus_minus(int,P_3),one_one(int))),P_3)).
% 32.54/32.35 0 [] hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,A_1),B)),hAPP(int,int,minus_minus(int,A_1),B))=hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls))))).
% 32.54/32.35 0 [] -number_ring(X_a)|hAPP(nat,X_a,power_power(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),Y)),number_number_of(nat,bit0(bit1(pls))))=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,bit0(bit1(pls)))))),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls)))),X_1)),Y)).
% 32.54/32.35 0 [] hAPP(nat,int,power_power(int,hAPP(int,int,minus_minus(int,A_1),B)),number_number_of(nat,bit0(bit1(pls))))=hAPP(int,int,plus_plus(int,hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),A_1)),B))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls))))).
% 32.54/32.35 0 [] hAPP(nat,int,power_power(int,hAPP(int,int,minus_minus(int,A_1),B)),number_number_of(nat,bit1(bit1(pls))))=hAPP(int,int,minus_minus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit1(bit1(pls))))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit1(bit1(pls)))),hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))))),B))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit1(bit1(pls)))),A_1)),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls))))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit1(bit1(pls))))).
% 32.54/32.35 0 [] hAPP(nat,int,power_power(int,number_number_of(int,min)),N_1)=one_one(int)|hAPP(nat,int,power_power(int,number_number_of(int,min)),N_1)=number_number_of(int,min).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zprime,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),M)),one_one(int))))|legendre(number_number_of(int,min),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),M)),one_one(int)))=one_one(int).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_3))|legendre(A_1,P_3)=zero_zero(int).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_3))| -hBOOL(hAPP(int,bool,quadRes(P_3),A_1))|legendre(A_1,P_3)=one_one(int).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,quadRes(P_3),A_1))|legendre(A_1,P_3)=number_number_of(int,min).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,quadRes(Ma),X))|hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,$f3(Ma,X)),number_number_of(nat,bit0(bit1(pls)))),X),Ma)).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,quadRes(Ma),X))| -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,Y_2),number_number_of(nat,bit0(bit1(pls)))),X),Ma)).
% 32.54/32.35 0 [] hAPP(nat,real,power_power(real,hAPP(real,real,plus_plus(real,X_1),Y)),number_number_of(nat,bit0(bit1(pls))))=hAPP(real,real,plus_plus(real,hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,real,power_power(real,Y),number_number_of(nat,bit0(bit1(pls)))))),hAPP(real,real,times_times(real,hAPP(real,real,times_times(real,number_number_of(real,bit0(bit1(pls)))),X_1)),Y)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),M))|M=zero_zero(nat)|M=N_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1)),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X))|X=Y_1.
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))|X!=Y_1.
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X))|X!=Y_1.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),A_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),hAPP(nat,nat,plus_plus(nat,A_1),B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),B)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,A_1),C)),hAPP(nat,nat,times_times(nat,B),C))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,C),A_1)),hAPP(nat,nat,times_times(nat,C),B))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,X_1),N_1)),hAPP(nat,nat,power_power(nat,Y),N_1))).
% 32.54/32.35 0 [] M!=zero_zero(nat)|hAPP(nat,nat,times_times(nat,M),N_1)=zero_zero(nat).
% 32.54/32.35 0 [] M=zero_zero(nat)|hAPP(nat,nat,times_times(nat,M),N_1)=hAPP(nat,nat,plus_plus(nat,N_1),hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,M),one_one(nat))),N_1)).
% 32.54/32.35 0 [] M!=zero_zero(nat)|hAPP(nat,nat,power_power(nat,P_3),M)=one_one(nat).
% 32.54/32.35 0 [] M=zero_zero(nat)|hAPP(nat,nat,power_power(nat,P_3),M)=hAPP(nat,nat,times_times(nat,P_3),hAPP(nat,nat,power_power(nat,P_3),hAPP(nat,nat,minus_minus(nat,M),one_one(nat)))).
% 32.54/32.35 0 [] hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,power_power(nat,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,nat,power_power(nat,Y),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,nat,times_times(nat,hAPP(nat,nat,plus_plus(nat,X_1),Y)),hAPP(nat,nat,minus_minus(nat,X_1),Y)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))|B=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A_1),B)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))|K=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))|K!=zero_zero(nat).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N)).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,N),Ma)!=one_one(nat)|N=one_one(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,N),Ma)!=one_one(nat)|Ma=one_one(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,N),Ma)=one_one(nat)|N!=one_one(nat)|Ma!=one_one(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,power_power(nat,Ma),N)!=zero_zero(nat)|N!=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,power_power(nat,Ma),N)!=zero_zero(nat)|Ma=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,power_power(nat,Ma),N)=zero_zero(nat)|N=zero_zero(nat)|Ma!=zero_zero(nat).
% 32.54/32.35 0 [] N_1=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,X_1),N_1)),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,A_1),N_1)),hAPP(nat,nat,power_power(nat,B),N_1)))|N_1=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)).
% 32.54/32.35 0 [] hAPP(nat,nat,power_power(nat,X),N)!=one_one(nat)|X=one_one(nat)|N=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,power_power(nat,X),N)=one_one(nat)|X!=one_one(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,power_power(nat,X),N)=one_one(nat)|N!=zero_zero(nat).
% 32.54/32.35 0 [] X_1!=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,Q_1),N_1)),R_1)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),R_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_1),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),X_1)).
% 32.54/32.35 0 [] hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,real,power_power(real,Y_1),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(real)|X=zero_zero(real).
% 32.54/32.35 0 [] hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,real,power_power(real,Y_1),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(real)|Y_1=zero_zero(real).
% 32.54/32.35 0 [] hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,real,power_power(real,Y_1),number_number_of(nat,bit0(bit1(pls)))))=zero_zero(real)|X!=zero_zero(real)|Y_1!=zero_zero(real).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),$f4(A_1,N_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))|hAPP(nat,real,power_power(real,$f4(A_1,N_1)),N_1)=A_1.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_2))|hAPP(nat,real,power_power(real,Y_2),N_1)!=A_1|Y_2=$f4(A_1,N_1).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),$f5(A_1,N_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))|hAPP(nat,real,power_power(real,$f5(A_1,N_1)),N_1)=A_1.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,N),Ma)),Ma))|N=one_one(nat).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,N),Ma)),Ma))|N!=one_one(nat).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),X_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N_1)).
% 32.54/32.35 0 [] hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,minus_minus(nat,I_1),J_1)),K_1)=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,minus_minus(nat,I_1),K_1)),J_1).
% 32.54/32.35 0 [] hAPP(nat,nat,minus_minus(nat,zero_zero(nat)),N_1)=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,minus_minus(nat,M),zero_zero(nat))=M.
% 32.54/32.35 0 [] hAPP(nat,nat,minus_minus(nat,M),M)=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,minus_minus(nat,M),N_1)!=zero_zero(nat)|hAPP(nat,nat,minus_minus(nat,N_1),M)!=zero_zero(nat)|M=N_1.
% 32.54/32.35 0 [] zero_zero(real)!=one_one(real).
% 32.54/32.35 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,minus_minus(real,X),Y_1)),zero_zero(real))).
% 32.54/32.35 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,minus_minus(real,X),Y_1)),zero_zero(real))).
% 32.54/32.35 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y_1))|X!=Y_1.
% 32.54/32.35 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y_1))|X=Y_1.
% 32.54/32.35 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y_1))|X=Y_1.
% 32.54/32.35 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y_1)).
% 32.54/32.35 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y_1))|X!=Y_1.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1)).
% 32.54/32.35 0 [] Ma=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),Ma)).
% 32.54/32.35 0 [] Ma!=N| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)).
% 32.54/32.35 0 [] Ma!=N| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),Ma)).
% 32.54/32.35 0 [] X_1=Y|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M))|M!=N_1.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3))|S!=T_3.
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))|Ma=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),Ma))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N),Ma)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,J_1),N_1)),K_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,L_1),N_1)),hAPP(nat,nat,minus_minus(nat,L_1),M))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),Y))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1))|B!=C|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1))|B!=C| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))|Y!=X_1.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))|X_1!=Y.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))|X_1!=Y.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),Y))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X_1)).
% 32.54/32.35 0 [] A_1!=B| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)).
% 32.54/32.35 0 [] A_1!=B| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),M))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),hAPP(nat,nat,minus_minus(nat,M),N_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))|X_1=Y.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),M))|M=N_1.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))|B!=C|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)).
% 32.54/32.35 0 [] A_1!=B| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))|A_1=B| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X_1))|X_1=Y.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))|X=Y_1.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))|X!=Y_1.
% 32.54/32.35 0 [] X_1!=Y|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y)).
% 32.54/32.35 0 [] A_1=B| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X))|X!=Y_1.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))|X=Y_1.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X))|X=Y_1.
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))|X!=Y_1.
% 32.54/32.35 0 [] X!=Y_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1)).
% 32.54/32.35 0 [] X!=Y_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X)).
% 32.54/32.35 0 [] X=Y_1| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X)).
% 32.54/32.35 0 [] hAPP(nat,nat,plus_plus(nat,M),N_1)=hAPP(nat,nat,plus_plus(nat,N_1),M).
% 32.54/32.35 0 [] hAPP(nat,nat,plus_plus(nat,X_1),hAPP(nat,nat,plus_plus(nat,Y),Z_1))=hAPP(nat,nat,plus_plus(nat,Y),hAPP(nat,nat,plus_plus(nat,X_1),Z_1)).
% 32.54/32.35 0 [] hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,plus_plus(nat,M),N_1)),K_1)=hAPP(nat,nat,plus_plus(nat,M),hAPP(nat,nat,plus_plus(nat,N_1),K_1)).
% 32.54/32.35 0 [] hAPP(nat,nat,plus_plus(nat,K),Ma)!=hAPP(nat,nat,plus_plus(nat,K),N)|Ma=N.
% 32.54/32.35 0 [] hAPP(nat,nat,plus_plus(nat,K),Ma)=hAPP(nat,nat,plus_plus(nat,K),N)|Ma!=N.
% 32.54/32.35 0 [] hAPP(nat,nat,plus_plus(nat,Ma),K)!=hAPP(nat,nat,plus_plus(nat,N),K)|Ma=N.
% 32.54/32.35 0 [] hAPP(nat,nat,plus_plus(nat,Ma),K)=hAPP(nat,nat,plus_plus(nat,N),K)|Ma!=N.
% 32.54/32.35 0 [] hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,M),N_1)),N_1)=M.
% 32.54/32.35 0 [] hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,N_1),M)),N_1)=M.
% 32.54/32.35 0 [] hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,minus_minus(nat,I_1),J_1)),K_1)=hAPP(nat,nat,minus_minus(nat,I_1),hAPP(nat,nat,plus_plus(nat,J_1),K_1)).
% 32.54/32.35 0 [] hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,K_1),M)),hAPP(nat,nat,plus_plus(nat,K_1),N_1))=hAPP(nat,nat,minus_minus(nat,M),N_1).
% 32.54/32.35 0 [] hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,M),K_1)),hAPP(nat,nat,plus_plus(nat,N_1),K_1))=hAPP(nat,nat,minus_minus(nat,M),N_1).
% 32.54/32.35 0 [] hAPP(real,real,times_times(real,hAPP(real,real,times_times(real,Z1),Z2)),Z3)=hAPP(real,real,times_times(real,Z1),hAPP(real,real,times_times(real,Z2),Z3)).
% 32.54/32.35 0 [] hAPP(real,real,times_times(real,Z_1),W)=hAPP(real,real,times_times(real,W),Z_1).
% 32.54/32.35 0 [] hAPP(real,real,times_times(real,one_one(real)),Z_1)=Z_1.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|M=N_1.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),K_1)).
% 32.54/32.35 0 [] M!=N_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,Ma),K)),hAPP(nat,nat,minus_minus(nat,N),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,Ma),K)),hAPP(nat,nat,minus_minus(nat,N),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))|hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,minus_minus(nat,M),K_1)),hAPP(nat,nat,minus_minus(nat,N_1),K_1))=hAPP(nat,nat,minus_minus(nat,M),N_1).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))|hAPP(nat,nat,minus_minus(nat,Ma),K)!=hAPP(nat,nat,minus_minus(nat,N),K)|Ma=N.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))|hAPP(nat,nat,minus_minus(nat,Ma),K)=hAPP(nat,nat,minus_minus(nat,N),K)|Ma!=N.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),N_1))|hAPP(nat,nat,minus_minus(nat,N_1),hAPP(nat,nat,minus_minus(nat,N_1),I_1))=I_1.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,M),L_1)),hAPP(nat,nat,minus_minus(nat,N_1),L_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,L_1),N_1)),hAPP(nat,nat,minus_minus(nat,L_1),M))).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,M),N_1)),M)).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,M),N_1)=hAPP(nat,nat,times_times(nat,N_1),M).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,hAPP(nat,nat,times_times(nat,M),N_1)),K_1)=hAPP(nat,nat,times_times(nat,M),hAPP(nat,nat,times_times(nat,N_1),K_1)).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,K_1),hAPP(nat,nat,minus_minus(nat,M),N_1))=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,times_times(nat,K_1),M)),hAPP(nat,nat,times_times(nat,K_1),N_1)).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),K_1)=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,times_times(nat,M),K_1)),hAPP(nat,nat,times_times(nat,N_1),K_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),Y))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,plus_plus(real,Z_1),X_1)),hAPP(real,real,plus_plus(real,Z_1),Y))).
% 32.54/32.35 0 [] -ab_group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),hAPP(X_a,X_a,minus_minus(X_a,C),D_2)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))).
% 32.54/32.35 0 [] N=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)).
% 32.54/32.35 0 [] N!=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|N_1!=zero_zero(nat).
% 32.54/32.35 0 [] N_1=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,M),N_1)),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,minus_minus(nat,N),Ma)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,minus_minus(nat,N),Ma)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)).
% 32.54/32.35 0 [] hAPP(nat,nat,plus_plus(nat,zero_zero(nat)),N_1)=N_1.
% 32.54/32.35 0 [] hAPP(nat,nat,plus_plus(nat,M),zero_zero(nat))=M.
% 32.54/32.35 0 [] hAPP(nat,nat,plus_plus(nat,Ma),N)!=zero_zero(nat)|Ma=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,plus_plus(nat,Ma),N)!=zero_zero(nat)|N=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,plus_plus(nat,Ma),N)=zero_zero(nat)|Ma!=zero_zero(nat)|N!=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,plus_plus(nat,M),N_1)!=M|N_1=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,minus_minus(nat,N_1),hAPP(nat,nat,plus_plus(nat,N_1),M))=zero_zero(nat).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),zero_zero(nat)))|N=zero_zero(nat).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),zero_zero(nat)))|N!=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,minus_minus(nat,Ma),N)!=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)).
% 32.54/32.35 0 [] hAPP(nat,nat,minus_minus(nat,Ma),N)=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|hAPP(nat,nat,minus_minus(nat,M),N_1)=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,zero_zero(nat)),N_1)=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,M),zero_zero(nat))=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,Ma),N)!=zero_zero(nat)|Ma=zero_zero(nat)|N=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,Ma),N)=zero_zero(nat)|Ma!=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,Ma),N)=zero_zero(nat)|N!=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,K),Ma)!=hAPP(nat,nat,times_times(nat,K),N)|Ma=N|K=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,K),Ma)=hAPP(nat,nat,times_times(nat,K),N)|Ma!=N.
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,K),Ma)=hAPP(nat,nat,times_times(nat,K),N)|K!=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,Ma),K)!=hAPP(nat,nat,times_times(nat,N),K)|Ma=N|K=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,Ma),K)=hAPP(nat,nat,times_times(nat,N),K)|Ma!=N.
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,Ma),K)=hAPP(nat,nat,times_times(nat,N),K)|K!=zero_zero(nat).
% 32.54/32.35 0 [] C_1=zero_zero(real)|hAPP(real,real,times_times(real,C_1),A_3)!=hAPP(real,real,times_times(real,C_1),B_2)|A_3=B_2.
% 32.54/32.35 0 [] C_1=zero_zero(real)|hAPP(real,real,times_times(real,C_1),A_3)=hAPP(real,real,times_times(real,C_1),B_2)|A_3!=B_2.
% 32.54/32.35 0 [] C_1=zero_zero(real)|hAPP(real,real,times_times(real,A_3),C_1)!=hAPP(real,real,times_times(real,B_2),C_1)|A_3=B_2.
% 32.54/32.35 0 [] C_1=zero_zero(real)|hAPP(real,real,times_times(real,A_3),C_1)=hAPP(real,real,times_times(real,B_2),C_1)|A_3!=B_2.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_1),J_1)),I_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,J_1),I_1)),I_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,K),Ma)),hAPP(nat,nat,plus_plus(nat,K),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,K),Ma)),hAPP(nat,nat,plus_plus(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,plus_plus(nat,J_1),M))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,plus_plus(nat,M),J_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_1),K_1)),hAPP(nat,nat,plus_plus(nat,J_1),K_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_1),K_1)),hAPP(nat,nat,plus_plus(nat,J_1),L_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_1))|hAPP(nat,nat,plus_plus(nat,M),L_1)!=hAPP(nat,nat,plus_plus(nat,K_1),N_1)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_1),J_1)),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K_1)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|hAPP(nat,nat,plus_plus(nat,N_1),hAPP(nat,nat,minus_minus(nat,M),N_1))=M.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,minus_minus(nat,J_2),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),J_2)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,minus_minus(nat,J_2),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),J_2)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))|Ma!=N.
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))|Ma=N.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))|Ma=N.
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))|Ma!=N.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|M=N_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)).
% 32.54/32.35 0 [] M!=N_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),A_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,A_1),C)),hAPP(nat,nat,minus_minus(nat,B),C))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,Ma),K)),hAPP(nat,nat,minus_minus(nat,N),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,Ma),K)),hAPP(nat,nat,minus_minus(nat,N),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,plus_plus(nat,N),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),N)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,plus_plus(nat,N),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),hAPP(nat,nat,minus_minus(nat,M),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),hAPP(nat,nat,minus_minus(nat,M),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),M))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N_1)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),hAPP(nat,nat,plus_plus(nat,M),N_1))).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),hAPP(nat,nat,plus_plus(nat,N_1),M))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))|N=hAPP(nat,nat,plus_plus(nat,Ma),$f6(Ma,N)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))|N!=hAPP(nat,nat,plus_plus(nat,Ma),K_2).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,K),Ma)),hAPP(nat,nat,plus_plus(nat,K),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,K),Ma)),hAPP(nat,nat,plus_plus(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),hAPP(nat,nat,plus_plus(nat,J_1),M))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),hAPP(nat,nat,plus_plus(nat,M),J_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_1),K_1)),hAPP(nat,nat,plus_plus(nat,J_1),K_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_1),K_1)),hAPP(nat,nat,plus_plus(nat,J_1),L_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M),K_1)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M),K_1)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M),K_1)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M),K_1)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))|hAPP(nat,nat,minus_minus(nat,I_1),hAPP(nat,nat,minus_minus(nat,J_1),K_1))=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,I_1),K_1)),J_1).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,J_2),K)),I_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),hAPP(nat,nat,plus_plus(nat,I_2),K))).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,J_2),K)),I_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),hAPP(nat,nat,plus_plus(nat,I_2),K))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,N_1),M)),K_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hAPP(nat,nat,plus_plus(nat,N_1),hAPP(nat,nat,minus_minus(nat,M),N_1))=M.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))|hAPP(nat,nat,plus_plus(nat,I_1),hAPP(nat,nat,minus_minus(nat,J_1),K_1))=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,I_1),J_1)),K_1).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),hAPP(nat,nat,minus_minus(nat,J_2),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),J_2)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),hAPP(nat,nat,minus_minus(nat,J_2),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),J_2)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),N_1)=M.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))|hAPP(nat,nat,minus_minus(nat,J_2),I_2)!=K|J_2=hAPP(nat,nat,plus_plus(nat,K),I_2).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))|hAPP(nat,nat,minus_minus(nat,J_2),I_2)=K|J_2!=hAPP(nat,nat,plus_plus(nat,K),I_2).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))|hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,I_1),J_1)),K_1)=hAPP(nat,nat,plus_plus(nat,I_1),hAPP(nat,nat,minus_minus(nat,J_1),K_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))|hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,minus_minus(nat,J_1),K_1)),I_1)=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,J_1),I_1)),K_1).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))|hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,J_1),I_1)),K_1)=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,minus_minus(nat,J_1),K_1)),I_1).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,K_1),hAPP(nat,nat,plus_plus(nat,M),N_1))=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,K_1),M)),hAPP(nat,nat,times_times(nat,K_1),N_1)).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,hAPP(nat,nat,plus_plus(nat,M),N_1)),K_1)=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,M),K_1)),hAPP(nat,nat,times_times(nat,N_1),K_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),one_one(nat)))|Ma=one_one(nat).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),one_one(nat)))|Ma!=one_one(nat).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,times_times(nat,M),M))).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,times_times(nat,M),hAPP(nat,nat,times_times(nat,M),M)))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,I_1),K_1)),hAPP(nat,nat,times_times(nat,J_1),K_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K_1),I_1)),hAPP(nat,nat,times_times(nat,K_1),J_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,I_1),K_1)),hAPP(nat,nat,times_times(nat,J_1),L_1))).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,one_one(nat)),N_1)=N_1.
% 32.54/32.35 0 [] one_one(nat)!=hAPP(nat,nat,times_times(nat,Ma),N)|Ma=one_one(nat).
% 32.54/32.35 0 [] one_one(nat)!=hAPP(nat,nat,times_times(nat,Ma),N)|N=one_one(nat).
% 32.54/32.35 0 [] one_one(nat)=hAPP(nat,nat,times_times(nat,Ma),N)|Ma!=one_one(nat)|N!=one_one(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,N_1),one_one(nat))=N_1.
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,Ma),N)!=one_one(nat)|Ma=one_one(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,Ma),N)!=one_one(nat)|N=one_one(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,Ma),N)=one_one(nat)|Ma!=one_one(nat)|N!=one_one(nat).
% 32.54/32.35 0 [] hAPP(real,real,times_times(real,hAPP(real,real,plus_plus(real,Z1),Z2)),W)=hAPP(real,real,plus_plus(real,hAPP(real,real,times_times(real,Z1),W)),hAPP(real,real,times_times(real,Z2),W)).
% 32.54/32.35 0 [] -ring(X_a)|hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Y)),hAPP(X_a,X_a,times_times(X_a,A_1),B))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),hAPP(X_a,X_a,minus_minus(X_a,Y),B))),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),A_1)),B)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,Ma),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,Ma),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,Ma),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2))|hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))|A_3!=hAPP(nat,nat,plus_plus(nat,B_2),D_4)|hBOOL(hAPP(nat,bool,P_1,D_4)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2))|A_3=hAPP(nat,nat,plus_plus(nat,B_2),$f7(P_1,A_3,B_2)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2))| -hBOOL(hAPP(nat,bool,P_1,$f7(P_1,A_3,B_2))).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))|A_3=hAPP(nat,nat,plus_plus(nat,B_2),$f7(P_1,A_3,B_2)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,$f7(P_1,A_3,B_2))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2))|hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))|A_3!=hAPP(nat,nat,plus_plus(nat,B_2),D_4)|hBOOL(hAPP(nat,bool,P_1,D_4)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2))|A_3=hAPP(nat,nat,plus_plus(nat,B_2),$f8(P_1,A_3,B_2)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2))| -hBOOL(hAPP(nat,bool,P_1,$f8(P_1,A_3,B_2))).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))|A_3=hAPP(nat,nat,plus_plus(nat,B_2),$f8(P_1,A_3,B_2)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,$f8(P_1,A_3,B_2))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,times_times(nat,Ma),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,times_times(nat,Ma),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,times_times(nat,Ma),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,I_1),K_1)),hAPP(nat,nat,times_times(nat,J_1),K_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K_1),I_1)),hAPP(nat,nat,times_times(nat,K_1),J_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,times_times(real,X),Z_2)),hAPP(real,real,times_times(real,Y_1),Z_2)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,times_times(real,X),Z_2)),hAPP(real,real,times_times(real,Y_1),Z_2)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,times_times(real,Z_2),X)),hAPP(real,real,times_times(real,Z_2),Y_1)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,times_times(real,Z_2),X)),hAPP(real,real,times_times(real,Z_2),Y_1)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,times_times(real,Z_1),X_1)),hAPP(real,real,times_times(real,Z_1),Y))).
% 32.54/32.35 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,times_times(real,X_1),Y))).
% 32.54/32.35 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,times_times(real,X),Z_2)),hAPP(real,real,times_times(real,Y_1),Z_2)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,times_times(real,X),Z_2)),hAPP(real,real,times_times(real,Y_1),Z_2)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y_1)).
% 32.54/32.35 0 [] M!=hAPP(nat,nat,times_times(nat,M),N_1)|N_1=one_one(nat)|M=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(real,real,plus_plus(real,hAPP(real,real,times_times(real,X),X)),hAPP(real,real,times_times(real,Y_1),Y_1))!=zero_zero(real)|X=zero_zero(real).
% 32.54/32.35 0 [] hAPP(real,real,plus_plus(real,hAPP(real,real,times_times(real,X),X)),hAPP(real,real,times_times(real,Y_1),Y_1))!=zero_zero(real)|Y_1=zero_zero(real).
% 32.54/32.35 0 [] hAPP(real,real,plus_plus(real,hAPP(real,real,times_times(real,X),X)),hAPP(real,real,times_times(real,Y_1),Y_1))=zero_zero(real)|X!=zero_zero(real)|Y_1!=zero_zero(real).
% 32.54/32.35 0 [] -ring_1(X_a)|hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),X_1)),one_one(X_a))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,X_1),one_one(X_a))),hAPP(X_a,X_a,minus_minus(X_a,X_1),one_one(X_a))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K_1),M)),hAPP(nat,nat,times_times(nat,K_1),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)).
% 32.54/32.35 0 [] -monoid_mult(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,X_1),hAPP(nat,nat,minus_minus(nat,N_1),one_one(nat)))),X_1)=hAPP(nat,X_a,power_power(X_a,X_1),N_1).
% 32.54/32.35 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),one_one(real)),hAPP(nat,real,power_power(real,number_number_of(real,bit0(bit1(pls)))),N_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,Ma),N)),Ma))|N=one_one(nat).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,Ma),N)),Ma))|N!=one_one(nat).
% 32.54/32.35 0 [] -power(X_a)|N_1!=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,M),N_1)=one_one(X_a).
% 32.54/32.35 0 [] -power(X_a)|N_1=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,M),N_1)=hAPP(X_a,X_a,times_times(X_a,M),hAPP(nat,X_a,power_power(X_a,M),hAPP(nat,nat,minus_minus(nat,N_1),one_one(nat)))).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f9(N,P_1)),N)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),$f9(N,P_1)))| -hBOOL(hAPP(nat,bool,P_1,I)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,N))|hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,plus_plus(nat,$f9(N,P_1)),one_one(nat)))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)),N)).
% 32.54/32.35 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),W)).
% 32.54/32.35 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z_1),W))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),Z_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I_1),J_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),J_1),K_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I_1),K_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z_1),W))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),Z_1))|Z_1=W.
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,K),Ma)!=hAPP(nat,nat,times_times(nat,K),N)|K=zero_zero(nat)|Ma=N.
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,K),Ma)=hAPP(nat,nat,times_times(nat,K),N)|K!=zero_zero(nat).
% 32.54/32.35 0 [] hAPP(nat,nat,times_times(nat,K),Ma)=hAPP(nat,nat,times_times(nat,K),N)|Ma!=N.
% 32.54/32.35 0 [] hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_1),U_1)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_1),U_1)),K_1))=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,plus_plus(nat,I_1),J_1)),U_1)),K_1).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hAPP(nat,nat,times_times(nat,K),Ma)!=hAPP(nat,nat,times_times(nat,K),N)|Ma=N.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hAPP(nat,nat,times_times(nat,K),Ma)=hAPP(nat,nat,times_times(nat,K),N)|Ma!=N.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))|K=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N)).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))|K!=zero_zero(nat).
% 32.54/32.35 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)),N)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),I_1))|hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_1),U_1)),M)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_1),U_1)),N_1))=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_1),J_1)),U_1)),M)),N_1).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))|hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)!=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)|hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)=N.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))|hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)|hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)!=N.
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N))).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_1),U_1)),M)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_1),U_1)),N_1))=hAPP(nat,nat,minus_minus(nat,M),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_1),I_1)),U_1)),N_1)).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))|hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)!=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)|Ma=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N).
% 32.54/32.35 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))|hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)|Ma!=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,N_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit0(N_1)))).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,N_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit1(N_1)))).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))|hBOOL(hAPP(int,bool,zprime,$f10(A_1))).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),$f10(A_1)),A_1)).
% 32.54/32.35 0 [] ti(int,K)=zero_zero(int)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),Ta))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,times_times(int,K),Ma)),hAPP(int,int,times_times(int,K),Ta))).
% 32.54/32.35 0 [] ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),Ta))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,times_times(int,K),Ma)),hAPP(int,int,times_times(int,K),Ta))).
% 32.54/32.35 0 [] -dvd(X_a)| -semiring_0(X_a)| -hBOOL(hAPP(X_a,bool,P_1,hAPP(X_a,X_a,times_times(X_a,L),X_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L),hAPP(X_a,X_a,plus_plus(X_a,$f11(X_a,P_1,L)),zero_zero(X_a)))).
% 32.54/32.35 0 [] -dvd(X_a)| -semiring_0(X_a)| -hBOOL(hAPP(X_a,bool,P_1,hAPP(X_a,X_a,times_times(X_a,L),X_2)))|hBOOL(hAPP(X_a,bool,P_1,$f11(X_a,P_1,L))).
% 32.54/32.35 0 [] -dvd(X_a)| -semiring_0(X_a)|hBOOL(hAPP(X_a,bool,P_1,hAPP(X_a,X_a,times_times(X_a,L),$f12(X_a,P_1,L))))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L),hAPP(X_a,X_a,plus_plus(X_a,X1),zero_zero(X_a))))| -hBOOL(hAPP(X_a,bool,P_1,X1)).
% 32.54/32.35 0 [] -comm_ring(X_a)| -dvd(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),D_3))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X_2),Ta)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_2),hAPP(X_a,X_a,times_times(X_a,K_2),D_3))),Ta))).
% 32.54/32.35 0 [] -comm_ring(X_a)| -dvd(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),D_3))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X_2),Ta)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_2),hAPP(X_a,X_a,times_times(X_a,K_2),D_3))),Ta))).
% 32.54/32.35 0 [] -comm_ring(X_a)| -dvd(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),D_3))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X_2),Ta)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_2),hAPP(X_a,X_a,times_times(X_a,K_2),D_3))),Ta))).
% 32.54/32.35 0 [] -comm_ring(X_a)| -dvd(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),D_3))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X_2),Ta)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_2),hAPP(X_a,X_a,times_times(X_a,K_2),D_3))),Ta))).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,pls))).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))|hBOOL(hAPP(int,bool,P_1,$f13(K,P_1,D)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,P_1,X_2))|hBOOL(hAPP(int,bool,P_1,hAPP(int,int,minus_minus(int,X_2),hAPP(int,int,times_times(int,K),D)))).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,minus_minus(int,$f13(K,P_1,D)),D)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,P_1,X_2))|hBOOL(hAPP(int,bool,P_1,hAPP(int,int,minus_minus(int,X_2),hAPP(int,int,times_times(int,K),D)))).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))|hBOOL(hAPP(int,bool,P_1,$f14(K,P_1,D)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,P_1,X_2))|hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,X_2),hAPP(int,int,times_times(int,K),D)))).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,$f14(K,P_1,D)),D)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,P_1,X_2))|hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,X_2),hAPP(int,int,times_times(int,K),D)))).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f15(A_1,M))).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f15(A_1,M)),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))|hBOOL(hAPP(int,bool,zcong(A_1,$f15(A_1,M)),M)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_2),M))| -hBOOL(hAPP(int,bool,zcong(A_1,Y_2),M))|ti(int,Y_2)=ti(int,$f15(A_1,M)).
% 32.54/32.35 0 [] twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))=hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t).
% 32.54/32.35 0 [] hAPP(int,int,times_times(int,twoSqu1929807760sum2sq(product_Pair(int,int,A_1,B))),twoSqu1929807760sum2sq(product_Pair(int,int,P_3,Q_1)))=twoSqu1929807760sum2sq(product_Pair(int,int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A_1),P_3)),hAPP(int,int,times_times(int,B),Q_1)),hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,A_1),Q_1)),hAPP(int,int,times_times(int,B),P_3)))).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,X))|twoSqu1929807760sum2sq(product_Pair(int,int,$f17(X),$f16(X)))=ti(int,X).
% 32.54/32.35 0 [] hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,X))|twoSqu1929807760sum2sq(product_Pair(int,int,A_5,B_4))!=ti(int,X).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),hAPP(int,int,minus_minus(int,B),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)).
% 32.54/32.35 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))|hBOOL(hAPP(int,bool,zcong(zfact(hAPP(int,int,minus_minus(int,P_3),one_one(int))),number_number_of(int,min)),P_3)).
% 32.54/32.35 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))).
% 32.57/32.35 0 [] -zero(X_a)|zero_zero(X_a)!=ti(X_a,X)|ti(X_a,X)=zero_zero(X_a).
% 32.57/32.35 0 [] -zero(X_a)|zero_zero(X_a)=ti(X_a,X)|ti(X_a,X)!=zero_zero(X_a).
% 32.57/32.35 0 [] -ab_semigroup_mult(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,times_times(X_a,B),C)).
% 32.57/32.35 0 [] -ab_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C)).
% 32.57/32.35 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_3),B_2)!=hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)|ti(X_a,B_2)=ti(X_a,C_1).
% 32.57/32.35 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_3),B_2)=hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)|ti(X_a,B_2)!=ti(X_a,C_1).
% 32.57/32.35 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,B_2),A_3)!=hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)|ti(X_a,B_2)=ti(X_a,C_1).
% 32.57/32.35 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,B_2),A_3)=hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)|ti(X_a,B_2)!=ti(X_a,C_1).
% 32.57/32.35 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),B)!=hAPP(X_a,X_a,plus_plus(X_a,A_1),C)|ti(X_a,B)=ti(X_a,C).
% 32.57/32.35 0 [] -cancel146912293up_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),B)!=hAPP(X_a,X_a,plus_plus(X_a,A_1),C)|ti(X_a,B)=ti(X_a,C).
% 32.57/32.35 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,B),A_1)!=hAPP(X_a,X_a,plus_plus(X_a,C),A_1)|ti(X_a,B)=ti(X_a,C).
% 32.57/32.35 0 [] -one(X_a)|one_one(X_a)!=ti(X_a,X)|ti(X_a,X)=one_one(X_a).
% 32.57/32.35 0 [] -one(X_a)|one_one(X_a)=ti(X_a,X)|ti(X_a,X)!=one_one(X_a).
% 32.57/32.35 0 [] -ab_group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)!=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)|ti(X_a,A_3)!=ti(X_a,B_2)|ti(X_a,C_1)=ti(X_a,D).
% 32.57/32.35 0 [] -ab_group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)!=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)|ti(X_a,A_3)=ti(X_a,B_2)|ti(X_a,C_1)!=ti(X_a,D).
% 32.57/32.35 0 [] -monoid_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1).
% 32.57/32.35 0 [] -comm_monoid_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1).
% 32.57/32.35 0 [] -linord219039673up_add(X_a)|zero_zero(X_a)!=hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)|ti(X_a,A_3)=zero_zero(X_a).
% 32.57/32.35 0 [] -linord219039673up_add(X_a)|zero_zero(X_a)=hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)|ti(X_a,A_3)!=zero_zero(X_a).
% 32.57/32.35 0 [] -monoid_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1).
% 32.57/32.35 0 [] -comm_monoid_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1).
% 32.57/32.35 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B_2),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2)).
% 32.57/32.35 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B_2),C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2)).
% 32.57/32.35 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2)).
% 32.57/32.35 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2)).
% 32.57/32.35 0 [] -ordere779506340up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),C))).
% 32.57/32.35 0 [] -ordere779506340up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C),B))).
% 32.57/32.35 0 [] -ordere779506340up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))).
% 32.57/32.36 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),C)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B)).
% 32.57/32.36 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C),B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B)).
% 32.57/32.36 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B_2),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)).
% 32.57/32.36 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B_2),C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)).
% 32.57/32.36 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)).
% 32.57/32.36 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)).
% 32.57/32.36 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),C))).
% 32.57/32.36 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C),B))).
% 32.57/32.36 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))).
% 32.57/32.36 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),C)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)).
% 32.57/32.36 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C),B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)).
% 32.57/32.36 0 [] -group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)!=zero_zero(X_a)|ti(X_a,A_3)=ti(X_a,B_2).
% 32.57/32.36 0 [] -group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)=zero_zero(X_a)|ti(X_a,A_3)!=ti(X_a,B_2).
% 32.57/32.36 0 [] -ab_group_add(X_a)|ti(X_a,A_3)!=ti(X_a,B_2)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)=zero_zero(X_a).
% 32.57/32.36 0 [] -ab_group_add(X_a)|ti(X_a,A_3)=ti(X_a,B_2)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)!=zero_zero(X_a).
% 32.57/32.36 0 [] -group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_1),A_1)=zero_zero(X_a).
% 32.57/32.36 0 [] -group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1).
% 32.57/32.36 0 [] -ordered_ab_group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)!=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),D)).
% 32.57/32.36 0 [] -ordered_ab_group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)!=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),D)).
% 32.57/32.36 0 [] -ordered_ab_group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)!=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D)).
% 32.57/32.36 0 [] -ordered_ab_group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)!=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D)).
% 32.57/32.36 0 [] -monoid_mult(X_a)|hAPP(X_a,X_a,times_times(X_a,one_one(X_a)),A_1)=ti(X_a,A_1).
% 32.57/32.36 0 [] -comm_monoid_mult(X_a)|hAPP(X_a,X_a,times_times(X_a,one_one(X_a)),A_1)=ti(X_a,A_1).
% 32.57/32.36 0 [] -monoid_mult(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),one_one(X_a))=ti(X_a,A_1).
% 32.57/32.36 0 [] -comm_monoid_mult(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),one_one(X_a))=ti(X_a,A_1).
% 32.57/32.36 0 [] -group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),B)=ti(X_a,A_1).
% 32.57/32.36 0 [] -group_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),B)=ti(X_a,A_1).
% 32.57/32.36 0 [] -linord219039673up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3)).
% 32.57/32.36 0 [] -linord219039673up_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3)).
% 32.57/32.36 0 [] -linord219039673up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a))).
% 32.57/32.36 0 [] -linord219039673up_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a))).
% 32.57/32.36 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))).
% 32.57/32.36 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_1))|hAPP(X_a,X_a,plus_plus(X_a,X),Y_1)!=zero_zero(X_a)|ti(X_a,X)=zero_zero(X_a).
% 32.57/32.36 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_1))|hAPP(X_a,X_a,plus_plus(X_a,X),Y_1)!=zero_zero(X_a)|ti(X_a,Y_1)=zero_zero(X_a).
% 32.57/32.36 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_1))|hAPP(X_a,X_a,plus_plus(X_a,X),Y_1)=zero_zero(X_a)|ti(X_a,X)!=zero_zero(X_a)|ti(X_a,Y_1)!=zero_zero(X_a).
% 32.57/32.36 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))).
% 32.57/32.36 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))).
% 32.57/32.36 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))).
% 32.57/32.36 0 [] -linord219039673up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_3)).
% 32.57/32.36 0 [] -linord219039673up_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_3)).
% 32.57/32.36 0 [] -linord219039673up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),zero_zero(X_a))).
% 32.57/32.36 0 [] -linord219039673up_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),zero_zero(X_a))).
% 32.57/32.36 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))).
% 32.57/32.36 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))).
% 32.57/32.36 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))).
% 32.57/32.36 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))).
% 32.57/32.36 0 [] -ordered_ab_group_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),zero_zero(X_a))).
% 32.57/32.36 0 [] -ordered_ab_group_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),zero_zero(X_a))).
% 32.57/32.36 0 [] -ordered_ab_group_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),zero_zero(X_a))).
% 32.57/32.36 0 [] -ordered_ab_group_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),zero_zero(X_a))).
% 32.57/32.36 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))).
% 32.57/32.36 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))).
% 32.57/32.36 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))).
% 32.57/32.36 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))).
% 32.57/32.36 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_1),zero_zero(int)))|zfact(N_1)=one_one(int).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_1),zero_zero(int)))|zfact(N_1)=hAPP(int,int,times_times(int,N_1),zfact(hAPP(int,int,minus_minus(int,N_1),one_one(int)))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_3))|inv(P_3,inv(P_3,A_1))=ti(int,A_1).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_3),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),inv(P_3,A_1)),hAPP(int,int,minus_minus(int,P_3),one_one(int)))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_3),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),inv(P_3,A_1))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_3),one_one(int))))|inv(P_3,A_1)!=hAPP(int,int,minus_minus(int,P_3),one_one(int)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_3),one_one(int))))|inv(P_3,A_1)!=one_one(int).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_3),one_one(int))))|ti(int,A_1)!=inv(P_3,A_1).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_3),one_one(int))))|inv(P_3,A_1)!=zero_zero(int).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_3))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),inv(P_3,A_1)),one_one(int)),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_2),one_one(int))))| -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_2)))|hBOOL(hAPP(fun(int,bool),bool,member(int,inv(P_2,B_2)),wset(A_3,P_2))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_2),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_2),hAPP(int,int,minus_minus(int,P_2),one_one(int))))| -hBOOL(hAPP(fun(int,bool),bool,member(int,inv(P_2,B_2)),wset(A_3,P_2)))|hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_2))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_3))|hBOOL(hAPP(fun(int,bool),bool,member(int,A_3),wset(A_3,P_2))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_3))| -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(hAPP(int,int,minus_minus(int,A_3),one_one(int)),P_2)))|hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_2))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_2),one_one(int))))| -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_2),one_one(int))))| -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_2),hAPP(int,int,minus_minus(int,P_2),one_one(int)))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_3))|hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(hAPP(int,int,minus_minus(int,A_3),one_one(int)),P_2)))| -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_2)))|ti(int,B_2)=ti(int,A_3)|ti(int,B_2)=inv(P_2,A_3).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_2),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),A_3))|hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_2))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))|hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,zcong(J_1,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,quadRes(P_3),A_1))| -hBOOL(hAPP(int,bool,zcong(J_1,hAPP(int,int,times_times(int,A_1),multInv(P_3,J_1))),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),K))| -hBOOL(hAPP(int,bool,P_1,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f18(P_1,I_2,K)),K))|hBOOL(hAPP(int,bool,P_1,I_2)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),K))| -hBOOL(hAPP(int,bool,P_1,K))|hBOOL(hAPP(int,bool,P_1,$f18(P_1,I_2,K)))|hBOOL(hAPP(int,bool,P_1,I_2)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),K))| -hBOOL(hAPP(int,bool,P_1,K))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,minus_minus(int,$f18(P_1,I_2,K)),one_one(int))))|hBOOL(hAPP(int,bool,P_1,I_2)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zcong(J_1,hAPP(int,int,times_times(int,A_1),multInv(P_3,K_1))),P_3))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,J_1),K_1),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,A_1),multInv(P_3,K_1))),K_1)),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,J_1),K_1),A_1),P_3))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,multInv(P_3,J_1)),J_1)),K_1),hAPP(int,int,times_times(int,multInv(P_3,J_1)),A_1)),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))| -hBOOL(hAPP(int,bool,zcong(X_1,Y),P_3))|hBOOL(hAPP(int,bool,zcong(multInv(P_3,X_1),multInv(P_3,Y)),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))| -hBOOL(hAPP(int,bool,zcong(J_1,K_1),P_3))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),multInv(P_3,J_1)),hAPP(int,int,times_times(int,A_1),multInv(P_3,K_1))),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))| -hBOOL(hAPP(int,bool,zprime,P_3))|hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,zcong(Y,zero_zero(int)),P_3))| -hBOOL(hAPP(int,bool,zcong(multInv(P_3,X_1),multInv(P_3,Y)),P_3))|hBOOL(hAPP(int,bool,zcong(X_1,Y),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))| -hBOOL(hAPP(int,bool,zprime,P_3))|hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,zcong(multInv(P_3,multInv(P_3,X_1)),X_1),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))| -hBOOL(hAPP(int,bool,zprime,P_3))|hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))| -hBOOL(hAPP(int,bool,zcong(multInv(P_3,X_1),zero_zero(int)),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))| -hBOOL(hAPP(int,bool,zprime,P_3))|hBOOL(hAPP(int,bool,zcong(J_1,zero_zero(int)),P_3))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,multInv(P_3,J_1)),J_1)),K_1),hAPP(int,int,times_times(int,multInv(P_3,J_1)),A_1)),P_3))|hBOOL(hAPP(int,bool,zcong(K_1,hAPP(int,int,times_times(int,A_1),multInv(P_3,J_1))),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))| -hBOOL(hAPP(int,bool,zprime,P_3))|hBOOL(hAPP(int,bool,zcong(K_1,zero_zero(int)),P_3))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,J_1),K_1),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,A_1),multInv(P_3,K_1))),K_1)),P_3))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,J_1),K_1),A_1),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))| -hBOOL(hAPP(int,bool,zprime,P_3))|hBOOL(hAPP(int,bool,zcong(K_1,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,zcong(J_1,zero_zero(int)),P_3))| -hBOOL(hAPP(int,bool,zcong(J_1,hAPP(int,int,times_times(int,A_1),multInv(P_3,K_1))),P_3))|hBOOL(hAPP(int,bool,zcong(K_1,hAPP(int,int,times_times(int,A_1),multInv(P_3,J_1))),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))| -hBOOL(hAPP(int,bool,zprime,P_3))|hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,zcong(K_1,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,zcong(J_1,zero_zero(int)),P_3))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),multInv(P_3,J_1)),hAPP(int,int,times_times(int,A_1),multInv(P_3,K_1))),P_3))|hBOOL(hAPP(int,bool,zcong(J_1,K_1),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))| -hBOOL(hAPP(int,bool,zprime,P_3))|hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,X_1),multInv(P_3,X_1))),multInv(P_3,multInv(P_3,X_1))),X_1),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))| -hBOOL(hAPP(int,bool,zprime,P_3))|hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,zcong(multInv(P_3,multInv(P_3,X_1)),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,X_1),multInv(P_3,X_1))),multInv(P_3,multInv(P_3,X_1)))),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))| -hBOOL(hAPP(int,bool,zprime,P_3))|hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,multInv(P_3,X_1)),X_1),one_one(int)),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_3))| -hBOOL(hAPP(int,bool,zprime,P_3))|hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,X_1),multInv(P_3,X_1)),one_one(int)),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),$f19(X,P_1)))|hBOOL(hAPP(int,bool,P_1,hAPP(int,int,minus_minus(int,$f19(X,P_1)),one_one(int))))|hBOOL(hAPP(int,bool,P_1,X)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,P_1,$f19(X,P_1)))|hBOOL(hAPP(int,bool,P_1,X)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),K))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,minus_minus(int,K),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f20(P_1,I_2,K)),K))|hBOOL(hAPP(int,bool,P_1,I_2)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),K))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,minus_minus(int,K),one_one(int))))|hBOOL(hAPP(int,bool,P_1,$f20(P_1,I_2,K)))|hBOOL(hAPP(int,bool,P_1,I_2)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),K))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,minus_minus(int,K),one_one(int))))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,minus_minus(int,$f20(P_1,I_2,K)),one_one(int))))|hBOOL(hAPP(int,bool,P_1,I_2)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),I_2))| -hBOOL(hAPP(int,bool,P_1,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),$f21(P_1,K,I_2)))|hBOOL(hAPP(int,bool,P_1,I_2)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),I_2))| -hBOOL(hAPP(int,bool,P_1,K))|hBOOL(hAPP(int,bool,P_1,$f21(P_1,K,I_2)))|hBOOL(hAPP(int,bool,P_1,I_2)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),I_2))| -hBOOL(hAPP(int,bool,P_1,K))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,$f21(P_1,K,I_2)),one_one(int))))|hBOOL(hAPP(int,bool,P_1,I_2)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_2))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,K),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f22(P_1,K,I_2)))|hBOOL(hAPP(int,bool,P_1,I_2)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_2))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,K),one_one(int))))|hBOOL(hAPP(int,bool,P_1,$f22(P_1,K,I_2)))|hBOOL(hAPP(int,bool,P_1,I_2)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_2))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,K),one_one(int))))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,$f22(P_1,K,I_2)),one_one(int))))|hBOOL(hAPP(int,bool,P_1,I_2)).
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f24(Ma,K,F_1)),$f23(Ma,K,F_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,F_1,Ma)),K)),hAPP(nat,nat,F_1,hAPP(nat,nat,plus_plus(nat,Ma),K)))).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F_1,$f24(Ma,K,F_1))),hAPP(nat,nat,F_1,$f23(Ma,K,F_1))))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,F_1,Ma)),K)),hAPP(nat,nat,F_1,hAPP(nat,nat,plus_plus(nat,Ma),K)))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))|d22set(hAPP(int,int,minus_minus(int,P_2),number_number_of(int,bit0(bit1(pls)))))=wset(hAPP(int,int,minus_minus(int,P_2),number_number_of(int,bit0(bit1(pls)))),P_2).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),B_2))| -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),d22set(A_3))).
% 32.57/32.36 0 [] -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),d22set(A_3)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),A_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),d22set(A_3)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),A_3))|hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),d22set(A_3))).
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f25(N,P_1)),N)).
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),$f25(N,P_1)))| -hBOOL(hAPP(nat,bool,P_1,I)).
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,N))|hBOOL(hAPP(nat,bool,P_1,$f25(N,P_1))).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),$f26(I_1,J_1))).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))|hAPP(nat,nat,plus_plus(nat,I_1),$f26(I_1,J_1))=J_1.
% 32.57/32.36 0 [] N=zero_zero(nat)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A_3),N)),hAPP(nat,int,power_power(int,B_2),N)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),B_2)).
% 32.57/32.36 0 [] N=zero_zero(nat)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A_3),N)),hAPP(nat,int,power_power(int,B_2),N)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),B_2)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A_1),N_1)),hAPP(nat,int,power_power(int,B),N_1)))|N_1=zero_zero(nat)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_1),B)).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_1))|A_1=zero_zero(nat).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_3))|A_3=zero_zero(nat).
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_3))|A_3!=zero_zero(nat).
% 32.57/32.36 0 [] A_3=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),zero_zero(nat))).
% 32.57/32.36 0 [] A_3=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_3)).
% 32.57/32.36 0 [] A_3!=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),zero_zero(nat)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_3)).
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),zero_zero(nat))).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),zero_zero(nat))).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),one_one(nat)))|A_1=one_one(nat).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),one_one(nat)))|A_3=one_one(nat).
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),one_one(nat)))|A_3!=one_one(nat).
% 32.57/32.36 0 [] A_3=one_one(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_3)).
% 32.57/32.36 0 [] A_3=one_one(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),one_one(nat))).
% 32.57/32.36 0 [] A_3!=one_one(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_3))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),one_one(nat))).
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_1)).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),one_one(nat)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_1)).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)).
% 32.57/32.36 0 [] N=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,A_3),N)),hAPP(nat,nat,power_power(nat,B_2),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),B_2)).
% 32.57/32.36 0 [] N=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,A_3),N)),hAPP(nat,nat,power_power(nat,B_2),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),B_2)).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|N_1=zero_zero(nat).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))|hAPP(nat,nat,times_times(nat,K_1),N_1)!=hAPP(nat,nat,times_times(nat,K_1),M)|N_1=M.
% 32.57/32.36 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Y)),hAPP(X_a,X_a,times_times(X_a,A_1),B))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),A_1)),hAPP(X_a,X_a,minus_minus(X_a,Y),B))),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),A_1)),B))),hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,minus_minus(X_a,Y),B))).
% 32.57/32.36 0 [] sr(P_2)=collect(int,combs(int,bool,bool,combb(bool,fun(bool,bool),int,fconj,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int))),combc(int,int,bool,ord_less(int),P_2))).
% 32.57/32.36 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,zero_zero(X_a)),B)=zero_zero(X_a).
% 32.57/32.36 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,zero_zero(X_a)),Y)=zero_zero(X_a).
% 32.57/32.36 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a))=zero_zero(X_a).
% 32.57/32.36 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,X_1),zero_zero(X_a))=zero_zero(X_a).
% 32.57/32.36 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),B_3))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),hAPP(X_a,X_a,times_times(X_a,A_1),B_3)).
% 32.57/32.36 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,Xa),hAPP(X_a,X_a,plus_plus(X_a,X_1),Y))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,Xa),X_1)),hAPP(X_a,X_a,times_times(X_a,Xa),Y)).
% 32.57/32.36 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),A_4)),B)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),hAPP(X_a,X_a,times_times(X_a,A_4),B)).
% 32.57/32.36 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,X_1),Y)),Ya)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Ya)),hAPP(X_a,X_a,times_times(X_a,Y),Ya)).
% 32.57/32.36 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,minus_minus(X_a,B),B_3))=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),hAPP(X_a,X_a,times_times(X_a,A_1),B_3)).
% 32.57/32.36 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,Xa),hAPP(X_a,X_a,minus_minus(X_a,X_1),Y))=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,Xa),X_1)),hAPP(X_a,X_a,times_times(X_a,Xa),Y)).
% 32.57/32.36 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),A_4)),B)=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),hAPP(X_a,X_a,times_times(X_a,A_4),B)).
% 32.57/32.36 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),Y)),Ya)=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Ya)),hAPP(X_a,X_a,times_times(X_a,Y),Ya)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,W)))|hAPP(int,int,div_mod(int,number_number_of(int,bit1(V))),number_number_of(int,bit0(W)))=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,number_number_of(int,V)),number_number_of(int,W)))),one_one(int)).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,W)))|hAPP(int,int,div_mod(int,number_number_of(int,bit1(V))),number_number_of(int,bit0(W)))=hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,hAPP(int,int,plus_plus(int,number_number_of(int,V)),one_one(int))),number_number_of(int,W)))),one_one(int)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),zero_zero(int)))|hAPP(int,int,div_mod(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),B))),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),A_1))=hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,hAPP(int,int,plus_plus(int,B),one_one(int))),A_1))),one_one(int)).
% 32.57/32.36 0 [] -semiring_div(X_a)| -number(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),number_number_of(X_a,X)),number_number_of(X_a,Y_1)))|hAPP(X_a,X_a,div_mod(X_a,number_number_of(X_a,Y_1)),number_number_of(X_a,X))=zero_zero(X_a).
% 32.57/32.36 0 [] -semiring_div(X_a)| -number(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),number_number_of(X_a,X)),number_number_of(X_a,Y_1)))|hAPP(X_a,X_a,div_mod(X_a,number_number_of(X_a,Y_1)),number_number_of(X_a,X))!=zero_zero(X_a).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,A_1),C)!=hAPP(X_a,X_a,div_mod(X_a,A_4),C)|hAPP(X_a,X_a,div_mod(X_a,B),C)!=hAPP(X_a,X_a,div_mod(X_a,B_3),C)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_4),B_3)),C).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),B)),C).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))=hAPP(X_a,X_a,times_times(X_a,C),hAPP(X_a,X_a,div_mod(X_a,A_1),B)).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),hAPP(X_a,X_a,div_mod(X_a,B),C))),C).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,div_mod(X_a,B),C))),C).
% 32.57/32.36 0 [] hAPP(int,int,div_mod(int,hAPP(int,int,times_times(int,A_1),hAPP(int,int,div_mod(int,B),C))),C)=hAPP(int,int,div_mod(int,hAPP(int,int,times_times(int,A_1),B)),C).
% 32.57/32.36 0 [] hAPP(int,int,div_mod(int,hAPP(int,int,times_times(int,A_1),B)),C)=hAPP(int,int,div_mod(int,hAPP(int,int,times_times(int,A_1),hAPP(int,int,div_mod(int,B),C))),C).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,div_mod(int,A_3),Ma),hAPP(int,int,div_mod(int,B_2),Ma)),Ma)).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,div_mod(int,A_3),Ma),hAPP(int,int,div_mod(int,B_2),Ma)),Ma)).
% 32.57/32.36 0 [] hAPP(int,int,div_mod(int,hAPP(nat,int,power_power(int,hAPP(int,int,div_mod(int,X_1),M)),Y)),M)=hAPP(int,int,div_mod(int,hAPP(nat,int,power_power(int,X_1),Y)),M).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),B)),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,zcong(X_1,hAPP(int,int,div_mod(int,X_1),M)),M)).
% 32.57/32.36 0 [] hAPP(int,int,div_mod(int,X_1),M)!=hAPP(int,int,div_mod(int,Y),M)|hBOOL(hAPP(int,bool,zcong(X_1,Y),M)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F),N_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F),hAPP(int,int,div_mod(int,M),N_1))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),hAPP(int,int,div_mod(int,M),N_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),N_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),M)).
% 32.57/32.36 0 [] hAPP(int,int,div_mod(int,A_1),A_1)=zero_zero(int).
% 32.57/32.36 0 [] hAPP(int,int,div_mod(int,zero_zero(int)),B)=zero_zero(int).
% 32.57/32.36 0 [] -semiring_div(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),N))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),hAPP(X_a,X_a,div_mod(X_a,Ma),N)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),Ma)).
% 32.57/32.36 0 [] -semiring_div(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),N))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),hAPP(X_a,X_a,div_mod(X_a,Ma),N)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),Ma)).
% 32.57/32.36 0 [] -semiring_div(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),B))|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,A_1),C).
% 32.57/32.36 0 [] -semiring_div(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),M))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),N_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),hAPP(X_a,X_a,div_mod(X_a,M),N_1))).
% 32.57/32.36 0 [] -semiring_div(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),hAPP(X_a,X_a,div_mod(X_a,M),N_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),N_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),M)).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,A_1),C)!=hAPP(X_a,X_a,div_mod(X_a,A_4),C)|hAPP(X_a,X_a,div_mod(X_a,B),C)!=hAPP(X_a,X_a,div_mod(X_a,B_3),C)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_4),B_3)),C).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,div_mod(X_a,B),C))),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),hAPP(X_a,X_a,div_mod(X_a,B),C))),C).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,div_mod(X_a,B),C))),C).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,B),A_1)),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,A_1),A_1)=zero_zero(X_a).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,zero_zero(X_a)),A_1)=zero_zero(X_a).
% 32.57/32.36 0 [] hAPP(int,int,div_mod(int,X),N)!=hAPP(int,int,div_mod(int,Y_1),N)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),hAPP(int,int,minus_minus(int,X),Y_1))).
% 32.57/32.36 0 [] hAPP(int,int,div_mod(int,X),N)=hAPP(int,int,div_mod(int,Y_1),N)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),hAPP(int,int,minus_minus(int,X),Y_1))).
% 32.57/32.36 0 [] hAPP(int,int,div_mod(int,Ma),D)!=zero_zero(int)|ti(int,Ma)=hAPP(int,int,times_times(int,D),$f31(Ma,D)).
% 32.57/32.36 0 [] hAPP(int,int,div_mod(int,Ma),D)=zero_zero(int)|ti(int,Ma)!=hAPP(int,int,times_times(int,D),Q_2).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,div_mod(int,X_1),Y))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,div_mod(int,M),K_1)),M)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,div_mod(int,A_1),B)),B)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,div_mod(int,A_1),B))).
% 32.57/32.36 0 [] -semiring_div(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2))|hAPP(X_a,X_a,div_mod(X_a,B_2),A_3)=zero_zero(X_a).
% 32.57/32.36 0 [] -semiring_div(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2))|hAPP(X_a,X_a,div_mod(X_a,B_2),A_3)!=zero_zero(X_a).
% 32.57/32.36 0 [] -semiring_div(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))|hAPP(X_a,X_a,div_mod(X_a,B),A_1)=zero_zero(X_a).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,times_times(X_a,B),C))),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,times_times(X_a,C),B))),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,A_1),one_one(X_a))=zero_zero(X_a).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),B)=zero_zero(X_a).
% 32.57/32.36 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,B),A_1)),B)=zero_zero(X_a).
% 32.57/32.36 0 [] -ring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,A_1),C)!=hAPP(X_a,X_a,div_mod(X_a,A_4),C)|hAPP(X_a,X_a,div_mod(X_a,B),C)!=hAPP(X_a,X_a,div_mod(X_a,B_3),C)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_4),B_3)),C).
% 32.57/32.36 0 [] hAPP(int,int,div_mod(int,hAPP(int,int,minus_minus(int,hAPP(int,int,div_mod(int,X_1),M)),Y)),M)=hAPP(int,int,div_mod(int,hAPP(int,int,minus_minus(int,X_1),Y)),M).
% 32.57/32.36 0 [] hAPP(int,int,div_mod(int,hAPP(int,int,minus_minus(int,X_1),hAPP(int,int,div_mod(int,Y),M))),M)=hAPP(int,int,div_mod(int,hAPP(int,int,minus_minus(int,X_1),Y)),M).
% 32.57/32.36 0 [] -ring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),hAPP(X_a,X_a,div_mod(X_a,B),C))),C).
% 32.57/32.36 0 [] -ring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C).
% 32.57/32.36 0 [] -ring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),hAPP(X_a,X_a,div_mod(X_a,B),C))),C).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),number_number_of(int,X)),number_number_of(int,Y_1)))|hAPP(int,int,div_mod(int,number_number_of(int,Y_1)),number_number_of(int,X))=zero_zero(int).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),number_number_of(int,X)),number_number_of(int,Y_1)))|hAPP(int,int,div_mod(int,number_number_of(int,Y_1)),number_number_of(int,X))!=zero_zero(int).
% 32.57/32.36 0 [] hAPP(int,int,div_mod(int,A_1),number_number_of(int,min))=zero_zero(int).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),B))|hAPP(int,int,div_mod(int,hAPP(int,int,div_mod(int,A_1),B)),M)=hAPP(int,int,div_mod(int,A_1),M).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))| -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|hAPP(int,int,div_mod(int,A_3),Ma)=hAPP(int,int,div_mod(int,B_2),Ma).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))|hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|hAPP(int,int,div_mod(int,A_3),Ma)!=hAPP(int,int,div_mod(int,B_2),Ma).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,div_mod(int,A_1),B))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,div_mod(int,A_1),B))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,div_mod(int,A_1),B)),B)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B))|hAPP(int,int,div_mod(int,A_1),B)=ti(int,A_1).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,div_mod(int,A_1),B)),zero_zero(int))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,div_mod(int,A_1),B)),zero_zero(int))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,div_mod(int,A_1),B))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1))|hAPP(int,int,div_mod(int,A_1),B)=ti(int,A_1).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,A_1),B)),zero_zero(int)))|hAPP(int,int,div_mod(int,A_1),B)=hAPP(int,int,plus_plus(int,A_1),B).
% 32.57/32.36 0 [] hAPP(int,int,div_mod(int,number_number_of(int,bit0(V))),number_number_of(int,bit0(W)))=hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,number_number_of(int,V)),number_number_of(int,W))).
% 32.57/32.36 0 [] ti(int,A_2)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_1),Q_3)),Y)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),Y))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Y),zero_zero(int)))|ti(int,B_1)=zero_zero(int)|hAPP(int,int,div_mod(int,A_2),B_1)=ti(int,Y).
% 32.57/32.36 0 [] ti(int,A_2)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_1),Q_3)),Y)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),B_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1))|ti(int,B_1)=zero_zero(int)|hAPP(int,int,div_mod(int,A_2),B_1)=ti(int,Y).
% 32.57/32.36 0 [] ti(int,A_2)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_1),Q_3)),Y)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),B_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),Y))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Y),zero_zero(int)))|ti(int,B_1)=zero_zero(int)|hAPP(int,int,div_mod(int,A_2),B_1)=ti(int,Y).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_1),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),hAPP(int,int,div_mod(int,Q_1),C))),R_1)),zero_zero(int))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_1),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,B),C)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),hAPP(int,int,div_mod(int,Q_1),C))),R_1))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),hAPP(int,int,div_mod(int,Q_1),C))),R_1)),hAPP(int,int,times_times(int,B),C))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),hAPP(int,int,div_mod(int,Q_1),C))),R_1))).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)!=zero_zero(int)|hBOOL(hAPP(int,bool,P_1,N)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),J))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J),K))|ti(int,N)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),I)),J)|hBOOL(hAPP(int,bool,P_1,J)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),X3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X3),zero_zero(int)))|ti(int,N)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),X2)),X3)|hBOOL(hAPP(int,bool,P_1,X3)).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_1,N,K)),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_1,N,K))),$f34(P_1,N,K)).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,P_1,$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_1,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_1,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_1,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_1,N,K)),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_1,N,K)))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_1,N,K))),$f34(P_1,N,K)).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_1,N,K)))| -hBOOL(hAPP(int,bool,P_1,$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_1,N,K)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_1,N,K)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_1,N,K)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_1,N,K)),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_1,N,K)),K))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_1,N,K))),$f34(P_1,N,K)).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_1,N,K)),K))| -hBOOL(hAPP(int,bool,P_1,$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_1,N,K))),$f32(P_1,N,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_1,N,K))),$f32(P_1,N,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_1,N,K))),$f32(P_1,N,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_1,N,K)),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_1,N,K))),$f32(P_1,N,K))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_1,N,K))),$f34(P_1,N,K)).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_1,N,K))),$f32(P_1,N,K))| -hBOOL(hAPP(int,bool,P_1,$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)| -hBOOL(hAPP(int,bool,P_1,$f32(P_1,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)| -hBOOL(hAPP(int,bool,P_1,$f32(P_1,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)| -hBOOL(hAPP(int,bool,P_1,$f32(P_1,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_1,N,K)),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)| -hBOOL(hAPP(int,bool,P_1,$f32(P_1,N,K)))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_1,N,K))),$f34(P_1,N,K)).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)| -hBOOL(hAPP(int,bool,P_1,$f32(P_1,N,K)))| -hBOOL(hAPP(int,bool,P_1,$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_1,N,K)),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_1,N,K))),$f34(P_1,N,K)).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,P_1,$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_1,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_1,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_1,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_1,N,K)),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_1,N,K)))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_1,N,K))),$f34(P_1,N,K)).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_1,N,K)))| -hBOOL(hAPP(int,bool,P_1,$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_1,N,K)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_1,N,K)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_1,N,K)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_1,N,K)),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_1,N,K)),K))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_1,N,K))),$f34(P_1,N,K)).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_1,N,K)),K))| -hBOOL(hAPP(int,bool,P_1,$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_1,N,K))),$f32(P_1,N,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_1,N,K))),$f32(P_1,N,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_1,N,K))),$f32(P_1,N,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_1,N,K)),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_1,N,K))),$f32(P_1,N,K))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_1,N,K))),$f34(P_1,N,K)).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_1,N,K))),$f32(P_1,N,K))| -hBOOL(hAPP(int,bool,P_1,$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))| -hBOOL(hAPP(int,bool,P_1,$f32(P_1,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))| -hBOOL(hAPP(int,bool,P_1,$f32(P_1,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))| -hBOOL(hAPP(int,bool,P_1,$f32(P_1,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_1,N,K)),zero_zero(int))).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))| -hBOOL(hAPP(int,bool,P_1,$f32(P_1,N,K)))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_1,N,K))),$f34(P_1,N,K)).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_1,N))| -hBOOL(hAPP(int,bool,P_1,$f32(P_1,N,K)))| -hBOOL(hAPP(int,bool,P_1,$f34(P_1,N,K))).
% 32.57/32.36 0 [] hAPP(int,int,div_mod(int,X),number_number_of(int,bit0(bit1(pls))))=zero_zero(int)|hAPP(int,int,div_mod(int,X),number_number_of(int,bit0(bit1(pls))))=one_one(int).
% 32.57/32.36 0 [] hAPP(int,int,div_mod(int,X),number_number_of(int,bit0(bit1(pls))))!=zero_zero(int)|hAPP(int,int,div_mod(int,X),number_number_of(int,bit0(bit1(pls))))!=one_one(int).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))|hAPP(int,int,div_mod(int,number_number_of(int,min)),B)=hAPP(int,int,minus_minus(int,B),one_one(int)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A_1))|hAPP(int,int,div_mod(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),B))),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),A_1))=hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,B),A_1))).
% 32.57/32.36 0 [] hAPP(int,int,div_mod(int,M_1),D_1)!=zero_zero(int)|ti(int,M_1)=hAPP(int,int,times_times(int,D_1),$f36(M_1,D_1)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),M))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,standardRes(M,X_1)),standardRes(M,Y)),hAPP(int,int,times_times(int,X_1),Y)),M)).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,div_mod(nat,M),N_1)),N_1)).
% 32.57/32.36 0 [] hAPP(nat,nat,times_times(nat,K_1),hAPP(nat,nat,div_mod(nat,M),N_1))=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,times_times(nat,K_1),M)),hAPP(nat,nat,times_times(nat,K_1),N_1)).
% 32.57/32.36 0 [] hAPP(nat,nat,times_times(nat,hAPP(nat,nat,div_mod(nat,M),N_1)),K_1)=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,times_times(nat,M),K_1)),hAPP(nat,nat,times_times(nat,N_1),K_1)).
% 32.57/32.36 0 [] standardRes(M,X_1)=hAPP(int,int,div_mod(int,X_1),M).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|hAPP(nat,nat,div_mod(nat,M),N_1)=M.
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hAPP(nat,nat,div_mod(nat,M),N_1)=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),N_1).
% 32.57/32.36 0 [] hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,K_1),N_1)),M)),N_1)=hAPP(nat,nat,div_mod(nat,M),N_1).
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|hAPP(nat,nat,div_mod(nat,M),N_1)=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),N_1).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|hAPP(nat,nat,div_mod(nat,M),N_1)=M.
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|hAPP(nat,nat,div_mod(nat,M),N_1)=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),N_1).
% 32.57/32.36 0 [] hAPP(nat,nat,div_mod(nat,Ma),D)!=zero_zero(nat)|Ma=hAPP(nat,nat,times_times(nat,D),$f37(Ma,D)).
% 32.57/32.36 0 [] hAPP(nat,nat,div_mod(nat,Ma),D)=zero_zero(nat)|Ma!=hAPP(nat,nat,times_times(nat,D),Q_2).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,div_mod(nat,M),N_1)),N_1)).
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,div_mod(nat,M),N_1)),M)).
% 32.57/32.36 0 [] standardRes(Ma,X)!=zero_zero(int)|hBOOL(hAPP(int,bool,zcong(X,zero_zero(int)),Ma)).
% 32.57/32.36 0 [] standardRes(Ma,X)=zero_zero(int)| -hBOOL(hAPP(int,bool,zcong(X,zero_zero(int)),Ma)).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,zcong(X,zero_zero(int)),P_2))|standardRes(P_2,X)!=zero_zero(int).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,zcong(X,zero_zero(int)),P_2))|standardRes(P_2,X)=zero_zero(int).
% 32.57/32.36 0 [] hBOOL(hAPP(int,bool,zcong(X_1,standardRes(M,X_1)),M)).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),standardRes(P_3,X_1)),P_3)).
% 32.57/32.36 0 [] -hBOOL(hAPP(fun(int,bool),bool,member(int,X),sr(P_2)))|standardRes(P_2,X)=ti(int,X).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,div_mod(nat,N),K)))|K!=zero_zero(nat)|hBOOL(hAPP(nat,bool,P_1,N)).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,div_mod(nat,N),K)))|K=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K))|N!=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,K),I)),J)|hBOOL(hAPP(nat,bool,P_1,J)).
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,div_mod(nat,N),K)))|K=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f38(P_1,N,K)),K)).
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,div_mod(nat,N),K)))|K=zero_zero(nat)|N=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,K),$f39(P_1,N,K))),$f38(P_1,N,K)).
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,div_mod(nat,N),K)))|K=zero_zero(nat)| -hBOOL(hAPP(nat,bool,P_1,$f38(P_1,N,K))).
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,div_mod(nat,N),K)))| -hBOOL(hAPP(nat,bool,P_1,N))|K!=zero_zero(nat).
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,div_mod(nat,N),K)))| -hBOOL(hAPP(nat,bool,P_1,N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f38(P_1,N,K)),K)).
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,div_mod(nat,N),K)))| -hBOOL(hAPP(nat,bool,P_1,N))|N=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,K),$f39(P_1,N,K))),$f38(P_1,N,K)).
% 32.57/32.36 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,div_mod(nat,N),K)))| -hBOOL(hAPP(nat,bool,P_1,N))| -hBOOL(hAPP(nat,bool,P_1,$f38(P_1,N,K))).
% 32.57/32.36 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_1),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,B),hAPP(nat,nat,div_mod(nat,Q_1),C))),R_1)),hAPP(nat,nat,times_times(nat,B),C))).
% 32.57/32.36 0 [] -order(T_1)|order(fun(T_2,T_1)).
% 32.57/32.36 0 [] semiri456707255roduct(int).
% 32.57/32.36 0 [] ordere223160158up_add(int).
% 32.57/32.36 0 [] ordere236663937imp_le(int).
% 32.57/32.36 0 [] linord893533164strict(int).
% 32.57/32.36 0 [] linord626643107strict(int).
% 32.57/32.36 0 [] linord20386208strict(int).
% 32.57/32.36 0 [] ordere779506340up_add(int).
% 32.57/32.36 0 [] ordere216010020id_add(int).
% 32.57/32.36 0 [] linord219039673up_add(int).
% 32.57/32.36 0 [] cancel146912293up_add(int).
% 32.57/32.36 0 [] ring_11004092258visors(int).
% 32.57/32.36 0 [] ordere453448008miring(int).
% 32.57/32.36 0 [] linord581940658strict(int).
% 32.57/32.36 0 [] ring_n68954251visors(int).
% 32.57/32.36 0 [] ordere1490568538miring(int).
% 32.57/32.36 0 [] linord1278240602ring_1(int).
% 32.57/32.36 0 [] ordered_ab_group_add(int).
% 32.57/32.36 0 [] cancel_semigroup_add(int).
% 32.57/32.36 0 [] linordered_semiring(int).
% 32.57/32.36 0 [] linordered_semidom(int).
% 32.57/32.36 0 [] ab_semigroup_mult(int).
% 32.57/32.36 0 [] comm_monoid_mult(int).
% 32.57/32.36 0 [] ab_semigroup_add(int).
% 32.57/32.36 0 [] ordered_semiring(int).
% 32.57/32.36 0 [] no_zero_divisors(int).
% 32.57/32.36 0 [] comm_monoid_add(int).
% 32.57/32.36 0 [] linordered_ring(int).
% 32.57/32.36 0 [] linordered_idom(int).
% 32.57/32.36 0 [] comm_semiring_1(int).
% 32.57/32.36 0 [] semiring_div(int).
% 32.57/32.36 0 [] comm_semiring(int).
% 32.57/32.36 0 [] number_semiring(int).
% 32.57/32.36 0 [] ab_group_add(int).
% 32.57/32.36 0 [] zero_ne_q_one(int).
% 32.57/32.36 0 [] ordered_ring(int).
% 32.57/32.36 0 [] linorder(int).
% 32.57/32.36 0 [] monoid_mult(int).
% 32.57/32.36 0 [] comm_ring_1(int).
% 32.57/32.36 0 [] monoid_add(int).
% 32.57/32.36 0 [] semiring_1(int).
% 32.57/32.36 0 [] semiring_0(int).
% 32.57/32.36 0 [] group_add(int).
% 32.57/32.36 0 [] ring_div(int).
% 32.57/32.36 0 [] mult_zero(int).
% 32.57/32.36 0 [] comm_ring(int).
% 32.57/32.36 0 [] order(int).
% 32.57/32.36 0 [] ring_char_0(int).
% 32.57/32.36 0 [] number_ring(int).
% 32.57/32.36 0 [] semiring(int).
% 32.57/32.36 0 [] ring_1(int).
% 32.57/32.36 0 [] power(int).
% 32.57/32.36 0 [] zero(int).
% 32.57/32.36 0 [] plus(int).
% 32.57/32.36 0 [] ring(int).
% 32.57/32.36 0 [] idom(int).
% 32.57/32.36 0 [] number(int).
% 32.57/32.36 0 [] one(int).
% 32.57/32.36 0 [] dvd(int).
% 32.57/32.36 0 [] semiri456707255roduct(nat).
% 32.57/32.36 0 [] ordere223160158up_add(nat).
% 32.57/32.36 0 [] ordere236663937imp_le(nat).
% 32.57/32.36 0 [] linord893533164strict(nat).
% 32.57/32.36 0 [] linord20386208strict(nat).
% 32.57/32.36 0 [] ordere779506340up_add(nat).
% 32.57/32.36 0 [] ordere216010020id_add(nat).
% 32.57/32.36 0 [] cancel146912293up_add(nat).
% 32.57/32.36 0 [] ordere453448008miring(nat).
% 32.57/32.36 0 [] ordere1490568538miring(nat).
% 32.57/32.36 0 [] cancel_semigroup_add(nat).
% 32.57/32.36 0 [] linordered_semiring(nat).
% 32.57/32.36 0 [] linordered_semidom(nat).
% 32.57/32.36 0 [] ab_semigroup_mult(nat).
% 32.57/32.36 0 [] comm_monoid_mult(nat).
% 32.57/32.36 0 [] ab_semigroup_add(nat).
% 32.57/32.36 0 [] ordered_semiring(nat).
% 32.57/32.36 0 [] no_zero_divisors(nat).
% 32.57/32.36 0 [] comm_monoid_add(nat).
% 32.57/32.36 0 [] comm_semiring_1(nat).
% 32.57/32.36 0 [] semiring_div(nat).
% 32.57/32.36 0 [] comm_semiring(nat).
% 32.57/32.36 0 [] number_semiring(nat).
% 32.57/32.36 0 [] zero_ne_q_one(nat).
% 32.57/32.36 0 [] linorder(nat).
% 32.57/32.36 0 [] monoid_mult(nat).
% 32.57/32.36 0 [] monoid_add(nat).
% 32.57/32.36 0 [] semiring_1(nat).
% 32.57/32.36 0 [] semiring_0(nat).
% 32.57/32.36 0 [] mult_zero(nat).
% 32.57/32.36 0 [] order(nat).
% 32.57/32.36 0 [] semiring(nat).
% 32.57/32.36 0 [] power(nat).
% 32.57/32.36 0 [] zero(nat).
% 32.57/32.36 0 [] plus(nat).
% 32.57/32.36 0 [] number(nat).
% 32.57/32.36 0 [] one(nat).
% 32.57/32.36 0 [] dvd(nat).
% 32.57/32.36 0 [] order(bool).
% 32.57/32.36 0 [] semiri456707255roduct(real).
% 32.57/32.36 0 [] ordere223160158up_add(real).
% 32.57/32.36 0 [] ordere236663937imp_le(real).
% 32.57/32.36 0 [] linord893533164strict(real).
% 32.57/32.36 0 [] linord626643107strict(real).
% 32.57/32.36 0 [] linord20386208strict(real).
% 32.57/32.36 0 [] ordere779506340up_add(real).
% 32.57/32.36 0 [] real_normed_algebra(real).
% 32.57/32.36 0 [] ordere216010020id_add(real).
% 32.57/32.36 0 [] linord219039673up_add(real).
% 32.57/32.36 0 [] cancel146912293up_add(real).
% 32.57/32.36 0 [] ring_11004092258visors(real).
% 32.57/32.36 0 [] ordere453448008miring(real).
% 32.57/32.36 0 [] linord581940658strict(real).
% 32.57/32.36 0 [] ring_n68954251visors(real).
% 32.57/32.36 0 [] ordere1490568538miring(real).
% 32.57/32.36 0 [] linord1278240602ring_1(real).
% 32.57/32.36 0 [] ordered_ab_group_add(real).
% 32.57/32.36 0 [] cancel_semigroup_add(real).
% 32.57/32.36 0 [] linordered_semiring(real).
% 32.57/32.36 0 [] linordered_semidom(real).
% 32.57/32.36 0 [] ab_semigroup_mult(real).
% 32.57/32.36 0 [] comm_monoid_mult(real).
% 32.57/32.36 0 [] ab_semigroup_add(real).
% 32.57/32.36 0 [] ordered_semiring(real).
% 32.57/32.36 0 [] no_zero_divisors(real).
% 32.57/32.36 0 [] comm_monoid_add(real).
% 32.57/32.36 0 [] linordered_ring(real).
% 32.57/32.36 0 [] linordered_idom(real).
% 32.57/32.36 0 [] comm_semiring_1(real).
% 32.57/32.36 0 [] comm_semiring(real).
% 32.57/32.36 0 [] number_semiring(real).
% 32.57/32.36 0 [] ab_group_add(real).
% 32.57/32.36 0 [] zero_ne_q_one(real).
% 32.57/32.36 0 [] ordered_ring(real).
% 32.57/32.36 0 [] linorder(real).
% 32.57/32.36 0 [] monoid_mult(real).
% 32.57/32.36 0 [] comm_ring_1(real).
% 32.57/32.36 0 [] monoid_add(real).
% 32.57/32.36 0 [] semiring_1(real).
% 32.57/32.36 0 [] semiring_0(real).
% 32.57/32.36 0 [] group_add(real).
% 32.57/32.36 0 [] mult_zero(real).
% 32.57/32.36 0 [] comm_ring(real).
% 32.57/32.36 0 [] order(real).
% 32.57/32.36 0 [] ring_char_0(real).
% 32.57/32.36 0 [] number_ring(real).
% 32.57/32.36 0 [] semiring(real).
% 32.57/32.36 0 [] ring_1(real).
% 32.57/32.36 0 [] power(real).
% 32.57/32.36 0 [] zero(real).
% 32.57/32.36 0 [] plus(real).
% 32.57/32.36 0 [] ring(real).
% 32.57/32.36 0 [] idom(real).
% 32.57/32.36 0 [] number(real).
% 32.57/32.36 0 [] one(real).
% 32.57/32.36 0 [] dvd(real).
% 32.57/32.36 0 [] ti(T,ti(T,A))=ti(T,A).
% 32.57/32.36 0 [] hAPP(X_a,X_c,combb(X_b,X_c,X_a,P,Q),R)=hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R)).
% 32.57/32.36 0 [] hAPP(X_a,X_c,combc(X_a,X_b,X_c,P,Q),R)=hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q).
% 32.57/32.36 0 [] hAPP(X_a,X_c,combs(X_a,X_b,X_c,P,Q),R)=hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R)).
% 32.57/32.36 0 [] -hBOOL(P)| -hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)).
% 32.57/32.36 0 [] -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(P).
% 32.57/32.36 0 [] -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(Q).
% 32.57/32.36 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))).
% 32.57/32.36 end_of_list.
% 32.57/32.36
% 32.57/32.36 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 32.57/32.36
% 32.57/32.36 This ia a non-Horn set with equality. The strategy will be
% 32.57/32.36 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 32.57/32.36 deletion, with positive clauses in sos and nonpositive
% 32.57/32.36 clauses in usable.
% 32.57/32.36
% 32.57/32.36 dependent: set(knuth_bendix).
% 32.57/32.36 dependent: set(anl_eq).
% 32.57/32.36 dependent: set(para_from).
% 32.57/32.36 dependent: set(para_into).
% 32.57/32.36 dependent: clear(para_from_right).
% 32.57/32.36 dependent: clear(para_into_right).
% 32.57/32.36 dependent: set(para_from_vars).
% 32.57/32.36 dependent: set(eq_units_both_ways).
% 32.57/32.36 dependent: set(dynamic_demod_all).
% 32.57/32.36 dependent: set(dynamic_demod).
% 32.57/32.36 dependent: set(order_eq).
% 32.57/32.36 dependent: set(back_demod).
% 32.57/32.36 dependent: set(lrpo).
% 32.57/32.36 dependent: set(hyper_res).
% 32.57/32.36 dependent: set(unit_deletion).
% 32.57/32.36 dependent: set(factor).
% 32.57/32.36
% 32.57/32.36 ------------> process usable:
% 32.57/32.36 ** KEPT (pick-wt=11): 1 [] -semiring_div(A)|div_mod(A,ti(A,B))=div_mod(A,B).
% 32.57/32.36 ** KEPT (pick-wt=13): 2 [] -semiring_div(A)|ti(fun(A,A),div_mod(A,B))=div_mod(A,B).
% 32.57/32.36 ** KEPT (pick-wt=11): 3 [] -group_add(A)|minus_minus(A,ti(A,B))=minus_minus(A,B).
% 32.57/32.36 ** KEPT (pick-wt=13): 4 [] -group_add(A)|ti(fun(A,A),minus_minus(A,B))=minus_minus(A,B).
% 32.57/32.36 ** KEPT (pick-wt=9): 5 [] -one(A)|ti(A,one_one(A))=one_one(A).
% 32.57/32.36 ** KEPT (pick-wt=15): 6 [] -plus(A)| -linorder(A)| -dvd(A)|plus_plus(A,ti(A,B))=plus_plus(A,B).
% 32.57/32.36 ** KEPT (pick-wt=17): 7 [] -plus(A)| -linorder(A)| -dvd(A)|ti(fun(A,A),plus_plus(A,B))=plus_plus(A,B).
% 32.57/32.36 ** KEPT (pick-wt=11): 8 [] -monoid_add(A)|plus_plus(A,ti(A,B))=plus_plus(A,B).
% 32.57/32.36 ** KEPT (pick-wt=13): 9 [] -monoid_add(A)|ti(fun(A,A),plus_plus(A,B))=plus_plus(A,B).
% 32.57/32.36 ** KEPT (pick-wt=11): 10 [] -cancel_semigroup_add(A)|plus_plus(A,ti(A,B))=plus_plus(A,B).
% 32.57/32.36 ** KEPT (pick-wt=13): 11 [] -cancel_semigroup_add(A)|ti(fun(A,A),plus_plus(A,B))=plus_plus(A,B).
% 32.57/32.36 ** KEPT (pick-wt=11): 12 [] -ab_semigroup_add(A)|plus_plus(A,ti(A,B))=plus_plus(A,B).
% 32.57/32.36 ** KEPT (pick-wt=13): 13 [] -ab_semigroup_add(A)|ti(fun(A,A),plus_plus(A,B))=plus_plus(A,B).
% 32.57/32.36 ** KEPT (pick-wt=11): 14 [] -ab_semigroup_mult(A)|times_times(A,ti(A,B))=times_times(A,B).
% 32.57/32.36 ** KEPT (pick-wt=13): 15 [] -ab_semigroup_mult(A)|ti(fun(A,A),times_times(A,B))=times_times(A,B).
% 32.57/32.36 ** KEPT (pick-wt=11): 16 [] -power(A)|times_times(A,ti(A,B))=times_times(A,B).
% 32.57/32.36 ** KEPT (pick-wt=13): 17 [] -power(A)|ti(fun(A,A),times_times(A,B))=times_times(A,B).
% 32.57/32.36 ** KEPT (pick-wt=11): 18 [] -dvd(A)|times_times(A,ti(A,B))=times_times(A,B).
% 32.57/32.36 ** KEPT (pick-wt=13): 19 [] -dvd(A)|ti(fun(A,A),times_times(A,B))=times_times(A,B).
% 32.57/32.36 ** KEPT (pick-wt=11): 20 [] -semiring(A)|times_times(A,ti(A,B))=times_times(A,B).
% 32.57/32.36 ** KEPT (pick-wt=13): 21 [] -semiring(A)|ti(fun(A,A),times_times(A,B))=times_times(A,B).
% 32.57/32.36 ** KEPT (pick-wt=11): 22 [] -mult_zero(A)|times_times(A,ti(A,B))=times_times(A,B).
% 32.57/32.36 ** KEPT (pick-wt=13): 23 [] -mult_zero(A)|ti(fun(A,A),times_times(A,B))=times_times(A,B).
% 32.57/32.36 ** KEPT (pick-wt=11): 24 [] -no_zero_divisors(A)|times_times(A,ti(A,B))=times_times(A,B).
% 32.57/32.36 ** KEPT (pick-wt=13): 25 [] -no_zero_divisors(A)|ti(fun(A,A),times_times(A,B))=times_times(A,B).
% 32.57/32.36 ** KEPT (pick-wt=9): 26 [] -zero(A)|ti(A,zero_zero(A))=zero_zero(A).
% 32.57/32.36 ** KEPT (pick-wt=11): 27 [] -number(A)|number_number_of(A,ti(int,B))=number_number_of(A,B).
% 32.57/32.36 ** KEPT (pick-wt=11): 28 [] -number(A)|ti(A,number_number_of(A,B))=number_number_of(A,B).
% 32.57/32.36 ** KEPT (pick-wt=13): 29 [] -order(A)|ti(fun(A,fun(A,bool)),ord_less(A))=ord_less(A).
% 32.57/32.36 ** KEPT (pick-wt=13): 30 [] -order(A)|ti(fun(A,fun(A,bool)),ord_less_e_q(A))=ord_less_e_q(A).
% 32.57/32.36 ** KEPT (pick-wt=11): 31 [] -power(A)|power_power(A,ti(A,B))=power_power(A,B).
% 32.57/32.36 ** KEPT (pick-wt=13): 32 [] -power(A)|ti(fun(nat,A),power_power(A,B))=power_power(A,B).
% 32.57/32.36 ** KEPT (pick-wt=13): 33 [] -dvd(A)|ti(fun(A,fun(A,bool)),dvd_dvd(A))=dvd_dvd(A).
% 32.57/32.36 ** KEPT (pick-wt=6): 34 [] -hBOOL(ti(bool,A))|hBOOL(A).
% 32.57/32.36 ** KEPT (pick-wt=6): 35 [] hBOOL(ti(bool,A))| -hBOOL(A).
% 32.57/32.36 ** KEPT (pick-wt=25): 37 [copy,36,flip.1,flip.2] zero_zero(int)!=t|zero_zero(int)=hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)).
% 32.57/32.36 ** KEPT (pick-wt=14): 38 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),t)).
% 32.57/32.36 ** KEPT (pick-wt=42): 39 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(A))).
% 32.57/32.36 ** KEPT (pick-wt=54): 40 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))))|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A).
% 32.57/32.36 ** KEPT (pick-wt=48): 41 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))))|ti(A,B)=zero_zero(A).
% 32.57/32.36 ** KEPT (pick-wt=48): 42 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))))|ti(A,C)=zero_zero(A).
% 32.57/32.36 ** KEPT (pick-wt=38): 43 [] -linordered_idom(A)|hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(A)|ti(A,B)=zero_zero(A).
% 32.57/32.36 ** KEPT (pick-wt=38): 44 [] -linordered_idom(A)|hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(A)|ti(A,C)=zero_zero(A).
% 32.57/32.36 ** KEPT (pick-wt=44): 45 [] -linordered_idom(A)|hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))=zero_zero(A)|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A).
% 32.57/32.36 ** KEPT (pick-wt=26): 46 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),zero_zero(A))).
% 32.57/32.36 ** KEPT (pick-wt=32): 47 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))))|ti(A,B)!=zero_zero(A).
% 32.57/32.36 ** KEPT (pick-wt=32): 48 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))))|ti(A,B)=zero_zero(A).
% 32.57/32.36 ** KEPT (pick-wt=17): 49 [] -semiring_1(A)|hAPP(nat,A,power_power(A,one_one(A)),number_number_of(nat,bit0(bit1(pls))))=one_one(A).
% 32.57/32.36 ** KEPT (pick-wt=17): 50 [] -semiring_1(A)|hAPP(nat,A,power_power(A,zero_zero(A)),number_number_of(nat,bit0(bit1(pls))))=zero_zero(A).
% 32.57/32.36 ** KEPT (pick-wt=22): 51 [] -ring_11004092258visors(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))!=zero_zero(A)|ti(A,B)=zero_zero(A).
% 32.57/32.36 ** KEPT (pick-wt=22): 52 [] -ring_11004092258visors(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))=zero_zero(A)|ti(A,B)!=zero_zero(A).
% 32.57/32.36 ** KEPT (pick-wt=23): 53 [] -number_ring(A)|hAPP(A,A,plus_plus(A,one_one(A)),number_number_of(A,B))=number_number_of(A,hAPP(int,int,plus_plus(int,bit1(pls)),B)).
% 32.57/32.36 ** KEPT (pick-wt=23): 54 [] -number_ring(A)|hAPP(A,A,plus_plus(A,number_number_of(A,B)),one_one(A))=number_number_of(A,hAPP(int,int,plus_plus(int,B),bit1(pls))).
% 32.57/32.36 ** KEPT (pick-wt=30): 55 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,A)),number_number_of(int,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.36 ** KEPT (pick-wt=30): 56 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,A)),number_number_of(int,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.36 ** KEPT (pick-wt=34): 57 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),number_number_of(A,C)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),C)).
% 32.57/32.36 ** KEPT (pick-wt=34): 58 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),number_number_of(A,C)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),C)).
% 32.57/32.36 ** KEPT (pick-wt=39): 59 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),C)).
% 32.57/32.36 ** KEPT (pick-wt=33): 60 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),A))|ti(int,A)=ti(int,B).
% 32.57/32.36 ** KEPT (pick-wt=28): 61 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),bit1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.36 ** KEPT (pick-wt=28): 62 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),bit1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.36 Following clause subsumed by 61 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),bit1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.36 Following clause subsumed by 62 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),bit1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.36 ** KEPT (pick-wt=28): 63 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),bit0(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.36 ** KEPT (pick-wt=28): 64 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),bit0(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.36 Following clause subsumed by 63 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),bit0(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.36 Following clause subsumed by 64 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),bit0(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.36 ** KEPT (pick-wt=26): 65 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.36 ** KEPT (pick-wt=20): 66 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|ti(int,A)!=ti(int,B).
% 32.57/32.36 ** KEPT (pick-wt=33): 67 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))|ti(int,A)=ti(int,B).
% 32.57/32.36 ** KEPT (pick-wt=38): 68 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,C),A)),hAPP(int,int,plus_plus(int,C),B))).
% 32.57/32.36 ** KEPT (pick-wt=19): 69 [] number_number_of(nat,A)!=zero_zero(nat)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)).
% 32.57/32.36 ** KEPT (pick-wt=19): 70 [] number_number_of(nat,A)=zero_zero(nat)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)).
% 32.57/32.36 ** KEPT (pick-wt=19): 71 [] zero_zero(nat)!=number_number_of(nat,A)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)).
% 32.57/32.36 ** KEPT (pick-wt=19): 72 [] zero_zero(nat)=number_number_of(nat,A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)).
% 32.57/32.36 ** KEPT (pick-wt=49): 73 [] -number_semiring(A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),C))|hAPP(A,A,times_times(A,number_number_of(A,B)),number_number_of(A,C))=number_number_of(A,hAPP(int,int,times_times(int,B),C)).
% 32.57/32.36 ** KEPT (pick-wt=35): 75 [copy,74,flip.2] -number_ring(A)|hAPP(A,A,times_times(A,number_number_of(A,hAPP(int,int,times_times(int,B),C))),D)=hAPP(A,A,times_times(A,number_number_of(A,B)),hAPP(A,A,times_times(A,number_number_of(A,C)),D)).
% 32.57/32.36 ** KEPT (pick-wt=23): 76 [] -number_ring(A)|hAPP(A,A,times_times(A,number_number_of(A,B)),number_number_of(A,C))=number_number_of(A,hAPP(int,int,times_times(int,B),C)).
% 32.57/32.36 ** KEPT (pick-wt=23): 77 [] -number_ring(A)|number_number_of(A,hAPP(int,int,times_times(int,B),C))=hAPP(A,A,times_times(A,number_number_of(A,B)),number_number_of(A,C)).
% 32.57/32.36 ** KEPT (pick-wt=40): 78 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))),zero_zero(A)))|ti(A,B)=zero_zero(A).
% 32.57/32.36 ** KEPT (pick-wt=40): 79 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))),zero_zero(A)))|ti(A,C)=zero_zero(A).
% 32.57/32.36 ** KEPT (pick-wt=46): 80 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))),zero_zero(A)))|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A).
% 32.57/32.36 ** KEPT (pick-wt=34): 81 [] -linordered_ring(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C)))).
% 32.57/32.36 ** KEPT (pick-wt=33): 82 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),zero_zero(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),pls)).
% 32.57/32.36 ** KEPT (pick-wt=33): 83 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),zero_zero(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),pls)).
% 32.57/32.36 ** KEPT (pick-wt=33): 84 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),number_number_of(A,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),B)).
% 32.57/32.36 ** KEPT (pick-wt=33): 85 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),number_number_of(A,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),B)).
% 32.57/32.36 ** KEPT (pick-wt=29): 86 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)).
% 32.57/32.37 ** KEPT (pick-wt=29): 87 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)).
% 32.57/32.37 ** KEPT (pick-wt=38): 88 [] -number(A)| -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),number_number_of(A,C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,C)),number_number_of(A,B))).
% 32.57/32.37 ** KEPT (pick-wt=38): 89 [] -number(A)| -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),number_number_of(A,C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,C)),number_number_of(A,B))).
% 32.57/32.37 ** KEPT (pick-wt=27): 90 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit1(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)).
% 32.57/32.37 ** KEPT (pick-wt=27): 91 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit1(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)).
% 32.57/32.37 ** KEPT (pick-wt=28): 92 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),bit1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=28): 93 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),bit1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.37 Following clause subsumed by 92 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),bit1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.37 Following clause subsumed by 93 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),bit1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=27): 94 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)).
% 32.57/32.37 ** KEPT (pick-wt=27): 95 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)).
% 32.57/32.37 ** KEPT (pick-wt=27): 96 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit0(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)).
% 32.57/32.37 ** KEPT (pick-wt=27): 97 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit0(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)).
% 32.57/32.37 ** KEPT (pick-wt=51): 98 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),C),D))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,A),C)),hAPP(int,int,plus_plus(int,B),D))).
% 32.57/32.37 ** KEPT (pick-wt=34): 99 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),one_one(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),bit1(pls))).
% 32.57/32.37 ** KEPT (pick-wt=34): 100 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),one_one(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),bit1(pls))).
% 32.57/32.37 ** KEPT (pick-wt=34): 101 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),number_number_of(A,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(pls)),B)).
% 32.57/32.37 ** KEPT (pick-wt=34): 102 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),number_number_of(A,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(pls)),B)).
% 32.57/32.37 ** KEPT (pick-wt=30): 103 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,A)),number_number_of(int,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=30): 104 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,A)),number_number_of(int,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=27): 105 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)).
% 32.57/32.37 ** KEPT (pick-wt=27): 106 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)).
% 32.57/32.37 ** KEPT (pick-wt=27): 107 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit1(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)).
% 32.57/32.37 ** KEPT (pick-wt=27): 108 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit1(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)).
% 32.57/32.37 ** KEPT (pick-wt=28): 109 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),bit0(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=28): 110 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),bit0(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 Following clause subsumed by 109 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),bit0(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 Following clause subsumed by 110 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),bit0(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=28): 111 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),bit1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=28): 112 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),bit1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=16): 113 [] -hBOOL(hAPP(fun(A,bool),bool,member(A,B),C))|hBOOL(hAPP(A,bool,C,B)).
% 32.57/32.37 ** KEPT (pick-wt=16): 114 [] hBOOL(hAPP(fun(A,bool),bool,member(A,B),C))| -hBOOL(hAPP(A,bool,C,B)).
% 32.57/32.37 Following clause subsumed by 111 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),bit1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.37 Following clause subsumed by 112 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),bit1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=43): 115 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,A)),number_number_of(nat,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)).
% 32.57/32.37 ** KEPT (pick-wt=30): 116 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,A)),number_number_of(nat,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=43): 117 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,A)),number_number_of(nat,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=28): 118 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)).
% 32.57/32.37 ** KEPT (pick-wt=28): 119 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)).
% 32.57/32.37 ** KEPT (pick-wt=33): 120 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,A),one_one(int))),B)).
% 32.57/32.37 ** KEPT (pick-wt=33): 121 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,A),one_one(int))),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 Following clause subsumed by 120 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,A),one_one(int))),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=33): 122 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,B),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=33): 123 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,B),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=49): 124 [] -number_semiring(A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),C))|hAPP(A,A,plus_plus(A,number_number_of(A,B)),number_number_of(A,C))=number_number_of(A,hAPP(int,int,plus_plus(int,B),C)).
% 32.57/32.37 ** KEPT (pick-wt=28): 125 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,A)),number_number_of(nat,B))=number_number_of(nat,B).
% 32.57/32.37 ** KEPT (pick-wt=41): 126 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,A)),number_number_of(nat,B))=number_number_of(nat,A).
% 32.57/32.37 ** KEPT (pick-wt=35): 127 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),A))).
% 32.57/32.37 ** KEPT (pick-wt=18): 128 [] -number_ring(A)| -ring_char_0(A)|number_number_of(A,B)!=number_number_of(A,C)|ti(int,B)=ti(int,C).
% 32.57/32.37 ** KEPT (pick-wt=18): 129 [] -number_ring(A)| -ring_char_0(A)|number_number_of(A,B)=number_number_of(A,C)|ti(int,B)!=ti(int,C).
% 32.57/32.37 ** KEPT (pick-wt=16): 130 [] -number(A)|number_number_of(A,B)!=ti(A,C)|ti(A,C)=number_number_of(A,B).
% 32.57/32.37 ** KEPT (pick-wt=16): 131 [] -number(A)|number_number_of(A,B)=ti(A,C)|ti(A,C)!=number_number_of(A,B).
% 32.57/32.37 ** KEPT (pick-wt=12): 132 [] bit1(A)!=bit1(B)|ti(int,A)=ti(int,B).
% 32.57/32.37 ** KEPT (pick-wt=12): 133 [] bit1(A)=bit1(B)|ti(int,A)!=ti(int,B).
% 32.57/32.37 ** KEPT (pick-wt=12): 134 [] bit0(A)!=bit0(B)|ti(int,A)=ti(int,B).
% 32.57/32.37 ** KEPT (pick-wt=12): 135 [] bit0(A)=bit0(B)|ti(int,A)!=ti(int,B).
% 32.57/32.37 ** KEPT (pick-wt=30): 136 [] -linord581940658strict(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))!=zero_zero(A)|ti(A,B)=zero_zero(A).
% 32.57/32.37 ** KEPT (pick-wt=30): 137 [] -linord581940658strict(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))!=zero_zero(A)|ti(A,C)=zero_zero(A).
% 32.57/32.37 ** KEPT (pick-wt=36): 138 [] -linord581940658strict(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))=zero_zero(A)|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A).
% 32.57/32.37 ** KEPT (pick-wt=43): 139 [] -number(A)| -semiring(A)|hAPP(A,A,times_times(A,hAPP(A,A,plus_plus(A,B),C)),number_number_of(A,D))=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),number_number_of(A,D))),hAPP(A,A,times_times(A,C),number_number_of(A,D))).
% 32.57/32.37 ** KEPT (pick-wt=43): 141 [copy,140,flip.3] -number(A)| -semiring(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,number_number_of(A,B)),C)),hAPP(A,A,times_times(A,number_number_of(A,B)),D))=hAPP(A,A,times_times(A,number_number_of(A,B)),hAPP(A,A,plus_plus(A,C),D)).
% 32.57/32.37 ** KEPT (pick-wt=52): 142 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,C),A)),hAPP(int,int,times_times(int,C),B))).
% 32.57/32.37 ** KEPT (pick-wt=60): 143 [] -linordered_semidom(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))!=hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls))))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|ti(A,B)=ti(A,C).
% 32.57/32.37 ** KEPT (pick-wt=62): 144 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls))))))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C)).
% 32.57/32.37 ** KEPT (pick-wt=26): 145 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls)))))).
% 32.57/32.37 ** KEPT (pick-wt=62): 146 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls))))))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)).
% 32.57/32.37 ** KEPT (pick-wt=48): 147 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(A)))|ti(A,B)=zero_zero(A).
% 32.57/32.37 ** KEPT (pick-wt=48): 148 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(A)))|ti(A,C)=zero_zero(A).
% 32.57/32.37 ** KEPT (pick-wt=54): 149 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(A)))|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A).
% 32.57/32.37 ** KEPT (pick-wt=42): 150 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls))))))).
% 32.57/32.37 ** KEPT (pick-wt=46): 151 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))))|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A).
% 32.57/32.37 ** KEPT (pick-wt=40): 152 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))))|ti(A,B)=zero_zero(A).
% 32.57/32.37 ** KEPT (pick-wt=40): 153 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))))|ti(A,C)=zero_zero(A).
% 32.57/32.37 ** KEPT (pick-wt=34): 154 [] -linordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))),zero_zero(A))).
% 32.57/32.37 ** KEPT (pick-wt=16): 155 [] -number_ring(A)|hAPP(A,A,times_times(A,number_number_of(A,bit1(pls))),B)=ti(A,B).
% 32.57/32.37 ** KEPT (pick-wt=16): 156 [] -number_ring(A)|hAPP(A,A,times_times(A,B),number_number_of(A,bit1(pls)))=ti(A,B).
% 32.57/32.37 ** KEPT (pick-wt=30): 157 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hAPP(int,int,times_times(int,A),B)!=one_one(int)|ti(int,A)=one_one(int).
% 32.57/32.37 ** KEPT (pick-wt=30): 158 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hAPP(int,int,times_times(int,A),B)!=one_one(int)|ti(int,B)=one_one(int).
% 32.57/32.37 ** KEPT (pick-wt=36): 159 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hAPP(int,int,times_times(int,A),B)=one_one(int)|ti(int,A)!=one_one(int)|ti(int,B)!=one_one(int).
% 32.57/32.37 ** KEPT (pick-wt=18): 160 [] -linord219039673up_add(A)|hAPP(A,A,plus_plus(A,B),B)!=zero_zero(A)|ti(A,B)=zero_zero(A).
% 32.57/32.37 ** KEPT (pick-wt=18): 161 [] -linord219039673up_add(A)|hAPP(A,A,plus_plus(A,B),B)=zero_zero(A)|ti(A,B)!=zero_zero(A).
% 32.57/32.37 ** KEPT (pick-wt=4): 162 [] bit1(A)!=pls.
% 32.57/32.37 Following clause subsumed by 162 during input processing: 0 [flip.1] bit1(A)!=pls.
% 32.57/32.37 ** KEPT (pick-wt=5): 163 [] bit1(A)!=bit0(B).
% 32.57/32.37 ** KEPT (pick-wt=5): 164 [] bit0(A)!=bit1(B).
% 32.57/32.37 ** KEPT (pick-wt=9): 165 [] bit0(A)!=pls|ti(int,A)=pls.
% 32.57/32.37 ** KEPT (pick-wt=9): 166 [] bit0(A)=pls|ti(int,A)!=pls.
% 32.57/32.37 Following clause subsumed by 165 during input processing: 0 [flip.1,flip.2] bit0(A)!=pls|ti(int,A)=pls.
% 32.57/32.37 Following clause subsumed by 166 during input processing: 0 [flip.1,flip.2] bit0(A)=pls|ti(int,A)!=pls.
% 32.57/32.37 ** KEPT (pick-wt=28): 167 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),bit1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=28): 168 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),bit1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 Following clause subsumed by 167 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),bit1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 Following clause subsumed by 168 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),bit1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=13): 169 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)).
% 32.57/32.37 ** KEPT (pick-wt=28): 170 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),bit0(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=28): 171 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),bit0(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 Following clause subsumed by 170 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),bit0(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 Following clause subsumed by 171 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),bit0(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=5): 172 [] zero_zero(int)!=one_one(int).
% 32.57/32.37 ** KEPT (pick-wt=38): 173 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,A),C)),hAPP(int,int,plus_plus(int,B),C))).
% 32.57/32.37 ** KEPT (pick-wt=24): 174 [] -number_ring(A)|hAPP(A,A,times_times(A,hAPP(A,A,plus_plus(A,one_one(A)),one_one(A))),number_number_of(A,B))=number_number_of(A,bit0(B)).
% 32.57/32.37 ** KEPT (pick-wt=27): 175 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,bit1(bit1(pls))))=hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),B)),B).
% 32.57/32.37 ** KEPT (pick-wt=21): 176 [] -number_semiring(A)|hAPP(A,A,times_times(A,number_number_of(A,bit0(bit1(pls)))),B)=hAPP(A,A,plus_plus(A,B),B).
% 32.57/32.37 ** KEPT (pick-wt=21): 177 [] -number_ring(A)|hAPP(A,A,times_times(A,number_number_of(A,bit0(bit1(pls)))),B)=hAPP(A,A,plus_plus(A,B),B).
% 32.57/32.37 ** KEPT (pick-wt=21): 178 [] -number_semiring(A)|hAPP(A,A,times_times(A,B),number_number_of(A,bit0(bit1(pls))))=hAPP(A,A,plus_plus(A,B),B).
% 32.57/32.37 ** KEPT (pick-wt=21): 179 [] -number_ring(A)|hAPP(A,A,times_times(A,B),number_number_of(A,bit0(bit1(pls))))=hAPP(A,A,plus_plus(A,B),B).
% 32.57/32.37 ** KEPT (pick-wt=21): 180 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))=hAPP(A,A,times_times(A,B),B).
% 32.57/32.37 ** KEPT (pick-wt=36): 181 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),B)),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))).
% 32.57/32.37 ** KEPT (pick-wt=36): 182 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),B)),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))).
% 32.57/32.37 ** KEPT (pick-wt=8): 184 [copy,183,flip.2] -number_semiring(A)|zero_zero(A)=number_number_of(A,pls).
% 32.57/32.37 ** KEPT (pick-wt=8): 186 [copy,185,flip.2] -number_ring(A)|zero_zero(A)=number_number_of(A,pls).
% 32.57/32.37 Following clause subsumed by 186 during input processing: 0 [] -number_ring(A)|zero_zero(A)=number_number_of(A,pls).
% 32.57/32.37 ** KEPT (pick-wt=15): 188 [copy,187,flip.2] -number_ring(A)|ti(A,B)=hAPP(A,A,plus_plus(A,number_number_of(A,pls)),B).
% 32.57/32.37 ** KEPT (pick-wt=15): 190 [copy,189,flip.2] -number_ring(A)|ti(A,B)=hAPP(A,A,plus_plus(A,B),number_number_of(A,pls)).
% 32.57/32.37 ** KEPT (pick-wt=34): 191 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),number_number_of(A,C)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)).
% 32.57/32.37 ** KEPT (pick-wt=34): 192 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),number_number_of(A,C)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)).
% 32.57/32.37 ** KEPT (pick-wt=35): 194 [copy,193,flip.2] -number_ring(A)|hAPP(A,A,plus_plus(A,number_number_of(A,hAPP(int,int,plus_plus(int,B),C))),D)=hAPP(A,A,plus_plus(A,number_number_of(A,B)),hAPP(A,A,plus_plus(A,number_number_of(A,C)),D)).
% 32.57/32.37 ** KEPT (pick-wt=23): 195 [] -number_ring(A)|hAPP(A,A,plus_plus(A,number_number_of(A,B)),number_number_of(A,C))=number_number_of(A,hAPP(int,int,plus_plus(int,B),C)).
% 32.57/32.37 ** KEPT (pick-wt=23): 196 [] -number_ring(A)|number_number_of(A,hAPP(int,int,plus_plus(int,B),C))=hAPP(A,A,plus_plus(A,number_number_of(A,B)),number_number_of(A,C)).
% 32.57/32.37 ** KEPT (pick-wt=27): 197 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)).
% 32.57/32.37 ** KEPT (pick-wt=27): 198 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)).
% 32.57/32.37 ** KEPT (pick-wt=28): 199 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),bit0(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=28): 200 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),bit0(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 Following clause subsumed by 199 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),bit0(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 Following clause subsumed by 200 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),bit0(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=29): 201 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).
% 32.57/32.37 ** KEPT (pick-wt=29): 202 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).
% 32.57/32.37 ** KEPT (pick-wt=27): 203 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)).
% 32.57/32.37 ** KEPT (pick-wt=27): 204 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)).
% 32.57/32.37 ** KEPT (pick-wt=27): 205 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit0(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)).
% 32.57/32.37 ** KEPT (pick-wt=27): 206 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit0(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)).
% 32.57/32.37 ** KEPT (pick-wt=14): 207 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))).
% 32.57/32.37 ** KEPT (pick-wt=29): 208 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).
% 32.57/32.37 ** KEPT (pick-wt=29): 209 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).
% 32.57/32.37 ** KEPT (pick-wt=17): 210 [] hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),A)),A)!=zero_zero(int).
% 32.57/32.37 ** KEPT (pick-wt=40): 211 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,B),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|ti(int,A)=ti(int,B).
% 32.57/32.37 ** KEPT (pick-wt=33): 212 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,B),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=27): 213 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,B),one_one(int))))|ti(int,A)!=ti(int,B).
% 32.57/32.37 Following clause subsumed by 180 during input processing: 0 [] -monoid_mult(A)| -number(A)|hAPP(nat,A,power_power(A,number_number_of(A,B)),number_number_of(nat,bit0(bit1(pls))))=hAPP(A,A,times_times(A,number_number_of(A,B)),number_number_of(A,B)).
% 32.57/32.37 ** KEPT (pick-wt=69): 214 [] -number_semiring(A)|hAPP(nat,A,power_power(A,hAPP(A,A,plus_plus(A,B),C)),number_number_of(nat,bit0(bit1(pls))))=hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))),hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,number_number_of(A,bit0(bit1(pls)))),B)),C)).
% 32.57/32.37 ** KEPT (pick-wt=25): 215 [] -number_ring(A)|number_number_of(A,bit0(B))=hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,zero_zero(A)),number_number_of(A,B))),number_number_of(A,B)).
% 32.57/32.37 ** KEPT (pick-wt=25): 216 [] -number_ring(A)|number_number_of(A,bit1(B))=hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,one_one(A)),number_number_of(A,B))),number_number_of(A,B)).
% 32.57/32.37 ** KEPT (pick-wt=9): 218 [copy,217,flip.2] -number_semiring(A)|one_one(A)=number_number_of(A,bit1(pls)).
% 32.57/32.37 ** KEPT (pick-wt=9): 220 [copy,219,flip.2] -number_ring(A)|one_one(A)=number_number_of(A,bit1(pls)).
% 32.57/32.37 Following clause subsumed by 220 during input processing: 0 [] -number_ring(A)|one_one(A)=number_number_of(A,bit1(pls)).
% 32.57/32.37 ** KEPT (pick-wt=41): 221 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),A)),A)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).
% 32.57/32.37 ** KEPT (pick-wt=41): 222 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),A)),A)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).
% 32.57/32.37 ** KEPT (pick-wt=33): 223 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),zero_zero(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)).
% 32.57/32.37 ** KEPT (pick-wt=33): 224 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),zero_zero(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)).
% 32.57/32.37 ** KEPT (pick-wt=33): 225 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),number_number_of(A,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)).
% 32.57/32.37 ** KEPT (pick-wt=33): 226 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),number_number_of(A,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)).
% 32.57/32.37 ** KEPT (pick-wt=17): 227 [] -number_semiring(A)|hAPP(A,A,plus_plus(A,one_one(A)),one_one(A))=number_number_of(A,bit0(bit1(pls))).
% 32.57/32.37 ** KEPT (pick-wt=17): 228 [] -number_ring(A)|hAPP(A,A,plus_plus(A,one_one(A)),one_one(A))=number_number_of(A,bit0(bit1(pls))).
% 32.57/32.37 ** KEPT (pick-wt=34): 229 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),one_one(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),bit1(pls))).
% 32.57/32.37 ** KEPT (pick-wt=34): 230 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),one_one(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),bit1(pls))).
% 32.57/32.37 ** KEPT (pick-wt=34): 231 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),number_number_of(A,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(pls)),B)).
% 32.57/32.37 ** KEPT (pick-wt=34): 232 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),number_number_of(A,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(pls)),B)).
% 32.57/32.37 ** KEPT (pick-wt=43): 233 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),number_number_of(int,bit0(bit1(pls)))))|ti(int,A)=zero_zero(int)|ti(int,A)=one_one(int).
% 32.57/32.37 ** KEPT (pick-wt=58): 235 [copy,234,flip.2] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hAPP(int,int,plus_plus(int,B),hAPP(int,int,times_times(int,A),C))!=ti(int,A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),C)).
% 32.57/32.37 ** KEPT (pick-wt=59): 237 [copy,236,flip.2] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hAPP(int,int,plus_plus(int,B),hAPP(int,int,times_times(int,A),C))!=ti(int,A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),C),one_one(int))).
% 32.57/32.37 ** KEPT (pick-wt=39): 238 [] -comm_semiring_1(A)|hAPP(nat,A,power_power(A,B),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),C))=hAPP(A,A,times_times(A,hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),C)).
% 32.57/32.37 ** KEPT (pick-wt=21): 239 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,B),B)=hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls)))).
% 32.57/32.37 ** KEPT (pick-wt=78): 240 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))| -hBOOL(hAPP(int,bool,zcong(s1,A),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))|ti(int,A)=ti(int,$c2).
% 32.57/32.37 ** KEPT (pick-wt=38): 241 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))|B=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).
% 32.57/32.37 ** KEPT (pick-wt=24): 242 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))|B!=zero_zero(nat).
% 32.57/32.37 ** KEPT (pick-wt=34): 243 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).
% 32.57/32.37 ** KEPT (pick-wt=38): 244 [] -hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(nat,int,power_power(int,B),C)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=29): 245 [] -comm_semiring_1(A)|hAPP(nat,A,power_power(A,hAPP(nat,A,power_power(A,B),C)),D)=hAPP(nat,A,power_power(A,B),hAPP(nat,nat,times_times(nat,C),D)).
% 32.57/32.37 ** KEPT (pick-wt=63): 246 [] -hBOOL(hAPP(int,bool,zprime,A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A),C)),hAPP(int,int,times_times(int,D),B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A),C)),D)).
% 32.57/32.37 ** KEPT (pick-wt=63): 247 [] -hBOOL(hAPP(int,bool,zprime,A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A),C)),hAPP(int,int,times_times(int,B),D)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A),C)),D)).
% 32.57/32.37 ** KEPT (pick-wt=40): 248 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A)).
% 32.57/32.37 ** KEPT (pick-wt=61): 249 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A))|ti(int,A)=ti(int,B).
% 32.57/32.37 ** KEPT (pick-wt=44): 250 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,times_times(int,A),B)),hAPP(int,int,times_times(int,A),C)))|ti(int,A)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)).
% 32.57/32.37 ** KEPT (pick-wt=38): 251 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,plus_plus(int,B),hAPP(int,int,times_times(int,A),C))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=38): 252 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,plus_plus(int,B),hAPP(int,int,times_times(int,A),C))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=63): 253 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,plus_plus(int,C),D)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,C),hAPP(int,int,times_times(int,E),B))),D))).
% 32.57/32.37 ** KEPT (pick-wt=63): 254 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,plus_plus(int,C),D)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,C),hAPP(int,int,times_times(int,E),B))),D))).
% 32.57/32.37 ** KEPT (pick-wt=40): 255 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=24): 256 [] -hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,A))| -hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,B))|hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,hAPP(int,int,times_times(int,A),B))).
% 32.57/32.37 ** KEPT (pick-wt=43): 257 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,A)),number_number_of(nat,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)).
% 32.57/32.37 ** KEPT (pick-wt=30): 258 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,A)),number_number_of(nat,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.37 ** KEPT (pick-wt=30): 259 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,A)),number_number_of(nat,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)).
% 32.57/32.37 ** KEPT (pick-wt=41): 260 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),E))=hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),E)).
% 32.57/32.37 ** KEPT (pick-wt=41): 261 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),E))=hAPP(A,A,times_times(A,D),hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),C)),E)).
% 32.57/32.37 ** KEPT (pick-wt=41): 262 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),E))=hAPP(A,A,times_times(A,B),hAPP(A,A,times_times(A,C),hAPP(A,A,times_times(A,D),E))).
% 32.57/32.37 ** KEPT (pick-wt=29): 263 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),C)),D)=hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),D)),C).
% 32.57/32.37 ** KEPT (pick-wt=29): 264 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),C)),D)=hAPP(A,A,times_times(A,B),hAPP(A,A,times_times(A,C),D)).
% 32.57/32.37 Following clause subsumed by 264 during input processing: 0 [flip.2] -comm_semiring_1(A)|hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),C)),D)=hAPP(A,A,times_times(A,B),hAPP(A,A,times_times(A,C),D)).
% 32.57/32.37 ** KEPT (pick-wt=29): 265 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,B),hAPP(A,A,times_times(A,C),D))=hAPP(A,A,times_times(A,C),hAPP(A,A,times_times(A,B),D)).
% 32.57/32.37 ** KEPT (pick-wt=17): 266 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,B),C)=hAPP(A,A,times_times(A,C),B).
% 32.57/32.37 ** KEPT (pick-wt=17): 267 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,B),C)=hAPP(A,A,plus_plus(A,C),B).
% 32.57/32.37 ** KEPT (pick-wt=29): 268 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,B),hAPP(A,A,plus_plus(A,C),D))=hAPP(A,A,plus_plus(A,C),hAPP(A,A,plus_plus(A,B),D)).
% 32.57/32.37 ** KEPT (pick-wt=29): 270 [copy,269,flip.2] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),D)=hAPP(A,A,plus_plus(A,B),hAPP(A,A,plus_plus(A,C),D)).
% 32.57/32.37 Following clause subsumed by 270 during input processing: 0 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),D)=hAPP(A,A,plus_plus(A,B),hAPP(A,A,plus_plus(A,C),D)).
% 32.57/32.37 ** KEPT (pick-wt=29): 271 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),D)=hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),D)),C).
% 32.57/32.37 ** KEPT (pick-wt=41): 272 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,D),E))=hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),E)).
% 32.57/32.37 ** KEPT (pick-wt=14): 273 [] -comm_semiring_1(A)|hAPP(nat,A,power_power(A,B),one_one(nat))=ti(A,B).
% 32.57/32.37 Following clause subsumed by 241 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),number_number_of(nat,B))))|number_number_of(nat,B)=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).
% 32.57/32.37 Following clause subsumed by 242 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),number_number_of(nat,B))))|number_number_of(nat,B)!=zero_zero(nat).
% 32.57/32.37 Following clause subsumed by 243 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),number_number_of(nat,B))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).
% 32.57/32.37 ** KEPT (pick-wt=27): 274 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls))|hAPP(nat,nat,times_times(nat,number_number_of(nat,A)),number_number_of(nat,B))=zero_zero(nat).
% 32.57/32.37 ** KEPT (pick-wt=33): 275 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls))|hAPP(nat,nat,times_times(nat,number_number_of(nat,A)),hAPP(nat,nat,times_times(nat,number_number_of(nat,B)),C))=zero_zero(nat).
% 32.57/32.37 ** KEPT (pick-wt=37): 276 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,B),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),C))=hAPP(nat,A,power_power(A,hAPP(nat,A,power_power(A,B),C)),number_number_of(nat,bit0(bit1(pls)))).
% 32.57/32.37 ** KEPT (pick-wt=38): 277 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,B),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),C))),zero_zero(A)))|ti(A,B)=zero_zero(A).
% 32.57/32.37 ** KEPT (pick-wt=13): 278 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,zero_zero(A)),B)=zero_zero(A).
% 32.57/32.37 ** KEPT (pick-wt=13): 279 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,B),zero_zero(A))=zero_zero(A).
% 32.57/32.37 ** KEPT (pick-wt=14): 280 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,zero_zero(A)),B)=ti(A,B).
% 32.57/32.37 ** KEPT (pick-wt=14): 281 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,B),zero_zero(A))=ti(A,B).
% 32.57/32.37 ** KEPT (pick-wt=19): 282 [] -semiri456707255roduct(A)|ti(A,B)!=hAPP(A,A,plus_plus(A,B),C)|ti(A,C)=zero_zero(A).
% 32.57/32.37 ** KEPT (pick-wt=19): 283 [] -semiri456707255roduct(A)|ti(A,B)=hAPP(A,A,plus_plus(A,B),C)|ti(A,C)!=zero_zero(A).
% 32.57/32.37 ** KEPT (pick-wt=35): 285 [copy,284,flip.2] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D))=hAPP(A,A,times_times(A,B),hAPP(A,A,plus_plus(A,C),D)).
% 32.57/32.37 ** KEPT (pick-wt=55): 286 [] -semiri456707255roduct(A)|ti(A,B)=ti(A,C)|ti(A,D)=ti(A,E)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),E))!=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),E)),hAPP(A,A,times_times(A,C),D)).
% 32.57/32.38 ** KEPT (pick-wt=48): 287 [] -semiri456707255roduct(A)|ti(A,B)!=ti(A,C)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),E))=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),E)),hAPP(A,A,times_times(A,C),D)).
% 32.57/32.38 ** KEPT (pick-wt=48): 288 [] -semiri456707255roduct(A)|ti(A,B)!=ti(A,C)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,D),B)),hAPP(A,A,times_times(A,E),C))=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,D),C)),hAPP(A,A,times_times(A,E),B)).
% 32.57/32.38 ** KEPT (pick-wt=35): 289 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,hAPP(A,A,plus_plus(A,B),C)),D)=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),D)).
% 32.57/32.38 ** KEPT (pick-wt=35): 290 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),C))=hAPP(A,A,times_times(A,hAPP(A,A,plus_plus(A,B),D)),C).
% 32.57/32.38 Following clause subsumed by 286 during input processing: 0 [] -semiri456707255roduct(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),E))!=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),E)),hAPP(A,A,times_times(A,D),C))|ti(A,B)=ti(A,D)|ti(A,C)=ti(A,E).
% 32.57/32.38 Following clause subsumed by 287 during input processing: 0 [] -semiri456707255roduct(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),E))=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),E)),hAPP(A,A,times_times(A,D),C))|ti(A,B)!=ti(A,D).
% 32.57/32.38 Following clause subsumed by 288 during input processing: 0 [] -semiri456707255roduct(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),E))=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),E)),hAPP(A,A,times_times(A,D),C))|ti(A,C)!=ti(A,E).
% 32.57/32.38 ** KEPT (pick-wt=14): 291 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,one_one(A)),B)=ti(A,B).
% 32.57/32.38 ** KEPT (pick-wt=14): 292 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,B),one_one(A))=ti(A,B).
% 32.57/32.38 ** KEPT (pick-wt=35): 293 [] -comm_semiring_1(A)|hAPP(nat,A,power_power(A,hAPP(A,A,times_times(A,B),C)),D)=hAPP(A,A,times_times(A,hAPP(nat,A,power_power(A,B),D)),hAPP(nat,A,power_power(A,C),D)).
% 32.57/32.38 ** KEPT (pick-wt=35): 294 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D))=hAPP(nat,A,power_power(A,B),hAPP(nat,nat,plus_plus(nat,C),D)).
% 32.57/32.38 ** KEPT (pick-wt=13): 295 [] -comm_semiring_1(A)|hAPP(nat,A,power_power(A,B),zero_zero(nat))=one_one(A).
% 32.57/32.38 ** KEPT (pick-wt=32): 296 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),C)))).
% 32.57/32.38 ** KEPT (pick-wt=49): 297 [] -semiri456707255roduct(A)|ti(A,B)=zero_zero(A)|ti(A,C)!=ti(A,D)|ti(A,E)=ti(A,F)|hAPP(A,A,plus_plus(A,C),hAPP(A,A,times_times(A,B),E))!=hAPP(A,A,plus_plus(A,D),hAPP(A,A,times_times(A,B),F)).
% 32.57/32.38 ** KEPT (pick-wt=25): 298 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,B),B)=hAPP(A,A,times_times(A,hAPP(A,A,plus_plus(A,one_one(A)),one_one(A))),B).
% 32.57/32.38 ** KEPT (pick-wt=30): 299 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,B),hAPP(A,A,times_times(A,C),B))=hAPP(A,A,times_times(A,hAPP(A,A,plus_plus(A,C),one_one(A))),B).
% 32.57/32.38 ** KEPT (pick-wt=30): 300 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),C)=hAPP(A,A,times_times(A,hAPP(A,A,plus_plus(A,B),one_one(A))),C).
% 32.57/32.38 ** KEPT (pick-wt=26): 301 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,C))!=zero_zero(A)|ti(A,B)=zero_zero(A).
% 32.57/32.38 ** KEPT (pick-wt=26): 302 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,C))!=zero_zero(A)|number_number_of(nat,C)!=zero_zero(nat).
% 32.57/32.38 ** KEPT (pick-wt=32): 303 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,C))=zero_zero(A)|ti(A,B)!=zero_zero(A)|number_number_of(nat,C)=zero_zero(nat).
% 32.57/32.38 ** KEPT (pick-wt=48): 304 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A),B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)).
% 32.57/32.38 ** KEPT (pick-wt=48): 305 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,times_times(int,A),B))).
% 32.57/32.38 ** KEPT (pick-wt=48): 306 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,A),B))).
% 32.57/32.38 ** KEPT (pick-wt=34): 307 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,power_power(int,A),B))).
% 32.57/32.38 ** KEPT (pick-wt=23): 308 [] -power(A)| -semiring_0(A)|number_number_of(nat,B)!=zero_zero(nat)|hAPP(nat,A,power_power(A,zero_zero(A)),number_number_of(nat,B))=one_one(A).
% 32.57/32.38 ** KEPT (pick-wt=23): 309 [] -power(A)| -semiring_0(A)|number_number_of(nat,B)=zero_zero(nat)|hAPP(nat,A,power_power(A,zero_zero(A)),number_number_of(nat,B))=zero_zero(A).
% 32.57/32.38 ** KEPT (pick-wt=67): 310 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A),B)),C)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B)).
% 32.57/32.38 ** KEPT (pick-wt=68): 311 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A),B)),C)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),zero_zero(int))).
% 32.57/32.38 ** KEPT (pick-wt=90): 312 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A),B)),C)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A),D)),E)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),E),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),D)).
% 32.57/32.38 ** KEPT (pick-wt=120): 313 [] hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A),B)),C)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,D),E)),F)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,D),E)),F)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),F),D))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),D),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),E)).
% 32.57/32.38 ** KEPT (pick-wt=90): 314 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A),B)),C)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A),D)),E)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),E),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),E))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),D),B)).
% 32.57/32.38 ** KEPT (pick-wt=120): 315 [] hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A),B)),C)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,D),E)),F)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,D),E)),F)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),F))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),D),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),E),B)).
% 32.57/32.38 ** KEPT (pick-wt=40): 316 [] hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B))| -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,C),number_number_of(nat,bit0(bit1(pls)))),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)).
% 32.57/32.38 ** KEPT (pick-wt=20): 317 [] -hBOOL(hAPP(int,bool,zprime,A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)).
% 32.57/32.38 ** KEPT (pick-wt=46): 318 [] -hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A))|ti(int,B)=one_one(int)|ti(int,B)=ti(int,A).
% 32.57/32.38 ** KEPT (pick-wt=35): 319 [] hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f1(A))).
% 32.57/32.38 ** KEPT (pick-wt=34): 320 [] hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),$f1(A)),A)).
% 32.57/32.38 ** KEPT (pick-wt=27): 321 [] hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A))|ti(int,$f1(A))!=one_one(int).
% 32.57/32.38 ** KEPT (pick-wt=28): 322 [] hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A))|ti(int,$f1(A))!=ti(int,A).
% 32.57/32.38 ** KEPT (pick-wt=42): 323 [] -hBOOL(hAPP(int,bool,zprime,A))|ti(int,A)=number_number_of(int,bit0(bit1(pls)))|ti(int,A)=number_number_of(int,bit1(bit1(pls)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),A)).
% 32.57/32.38 ** KEPT (pick-wt=68): 324 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),D)),hAPP(nat,A,power_power(A,C),D))).
% 32.57/32.38 ** KEPT (pick-wt=97): 325 [] -linord626643107strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),E))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),F))|hAPP(A,A,plus_plus(A,E),F)!=one_one(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,E),B)),hAPP(A,A,times_times(A,F),D))),C)).
% 32.57/32.38 Following clause subsumed by 244 during input processing: 0 [] -hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(nat,int,power_power(int,B),C)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)).
% 32.57/32.38 ** KEPT (pick-wt=16): 326 [] -comm_semiring_1(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=9): 327 [] bit1(A)!=min|ti(int,A)=min.
% 32.57/32.38 ** KEPT (pick-wt=9): 328 [] bit1(A)=min|ti(int,A)!=min.
% 32.57/32.38 Following clause subsumed by 327 during input processing: 0 [flip.1,flip.2] bit1(A)!=min|ti(int,A)=min.
% 32.57/32.38 Following clause subsumed by 328 during input processing: 0 [flip.1,flip.2] bit1(A)=min|ti(int,A)!=min.
% 32.57/32.38 ** KEPT (pick-wt=3): 329 [] pls!=min.
% 32.57/32.38 Following clause subsumed by 329 during input processing: 0 [flip.1] pls!=min.
% 32.57/32.38 ** KEPT (pick-wt=4): 330 [] bit0(A)!=min.
% 32.57/32.38 Following clause subsumed by 330 during input processing: 0 [flip.1] bit0(A)!=min.
% 32.57/32.38 ** KEPT (pick-wt=13): 331 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),min)).
% 32.57/32.38 ** KEPT (pick-wt=27): 332 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),min))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),min)).
% 32.57/32.38 ** KEPT (pick-wt=27): 333 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),min))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),min)).
% 32.57/32.38 ** KEPT (pick-wt=27): 334 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit1(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),A)).
% 32.57/32.38 ** KEPT (pick-wt=27): 335 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit1(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),A)).
% 32.57/32.38 ** KEPT (pick-wt=13): 336 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),min)).
% 32.57/32.38 ** KEPT (pick-wt=27): 337 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit0(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),A)).
% 32.57/32.38 ** KEPT (pick-wt=27): 338 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit0(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),A)).
% 32.57/32.38 ** KEPT (pick-wt=27): 339 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit1(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),A)).
% 32.57/32.38 ** KEPT (pick-wt=27): 340 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit1(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),A)).
% 32.57/32.38 ** KEPT (pick-wt=27): 341 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),min))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),min)).
% 32.57/32.38 ** KEPT (pick-wt=27): 342 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),min))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),min)).
% 32.57/32.38 ** KEPT (pick-wt=13): 343 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),min)).
% 32.57/32.38 ** KEPT (pick-wt=27): 344 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),min))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),min)).
% 32.57/32.38 ** KEPT (pick-wt=27): 345 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),min))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),min)).
% 32.57/32.38 ** KEPT (pick-wt=7): 346 [] number_number_of(int,pls)!=number_number_of(int,min).
% 32.57/32.38 ** KEPT (pick-wt=27): 347 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),min))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),min)).
% 32.57/32.38 ** KEPT (pick-wt=27): 348 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),min))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),min)).
% 32.57/32.38 ** KEPT (pick-wt=27): 349 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit0(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),A)).
% 32.57/32.38 ** KEPT (pick-wt=27): 350 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit0(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),A)).
% 32.57/32.38 ** KEPT (pick-wt=23): 351 [] hAPP(int,int,times_times(int,A),B)!=one_one(int)|ti(int,A)=one_one(int)|ti(int,A)=number_number_of(int,min).
% 32.57/32.38 ** KEPT (pick-wt=23): 352 [] hAPP(int,int,times_times(int,A),B)!=one_one(int)|ti(int,A)=one_one(int)|ti(int,B)=number_number_of(int,min).
% 32.57/32.38 ** KEPT (pick-wt=23): 353 [] hAPP(int,int,times_times(int,A),B)!=one_one(int)|ti(int,B)=one_one(int)|ti(int,A)=number_number_of(int,min).
% 32.57/32.38 ** KEPT (pick-wt=23): 354 [] hAPP(int,int,times_times(int,A),B)!=one_one(int)|ti(int,B)=one_one(int)|ti(int,B)=number_number_of(int,min).
% 32.57/32.38 ** KEPT (pick-wt=22): 355 [] hAPP(int,int,times_times(int,A),B)=one_one(int)|ti(int,A)!=one_one(int)|ti(int,B)!=one_one(int).
% 32.57/32.38 ** KEPT (pick-wt=24): 356 [] hAPP(int,int,times_times(int,A),B)=one_one(int)|ti(int,A)!=number_number_of(int,min)|ti(int,B)!=number_number_of(int,min).
% 32.57/32.38 Following clause subsumed by 351 during input processing: 0 [] hAPP(int,int,times_times(int,A),B)!=one_one(int)|ti(int,A)=one_one(int)|ti(int,A)=number_number_of(int,min).
% 32.57/32.38 ** KEPT (pick-wt=35): 357 [] -linordered_idom(A)|ti(A,B)=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 32.57/32.38 ** KEPT (pick-wt=15): 358 [] -comm_semiring_1(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),B)).
% 32.57/32.38 ** KEPT (pick-wt=41): 359 [] -comm_semiring_1(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)).
% 32.57/32.38 ** KEPT (pick-wt=16): 360 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|hBOOL(hAPP(int,bool,zcong(B,A),C)).
% 32.57/32.38 Following clause subsumed by 360 during input processing: 0 [] hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,zcong(B,A),C)).
% 32.57/32.38 ** KEPT (pick-wt=31): 361 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|ti(int,B)!=ti(int,D)| -hBOOL(hAPP(int,bool,zcong(D,E),C))|hBOOL(hAPP(int,bool,zcong(A,E),C)).
% 32.57/32.38 ** KEPT (pick-wt=24): 362 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,zcong(B,D),C))|hBOOL(hAPP(int,bool,zcong(A,D),C)).
% 32.57/32.38 ** KEPT (pick-wt=36): 363 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),A))| -hBOOL(hAPP(int,bool,zcong(B,number_number_of(int,min)),A))| -hBOOL(hAPP(int,bool,zcong(B,one_one(int)),A)).
% 32.57/32.38 ** KEPT (pick-wt=35): 364 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|ti(A,B)=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)).
% 32.57/32.38 ** KEPT (pick-wt=24): 365 [] -no_zero_divisors(A)|hAPP(A,A,times_times(A,B),C)!=zero_zero(A)|ti(A,B)=zero_zero(A)|ti(A,C)=zero_zero(A).
% 32.57/32.38 Following clause subsumed by 365 during input processing: 0 [] -no_zero_divisors(A)|ti(A,B)=zero_zero(A)|ti(A,C)=zero_zero(A)|hAPP(A,A,times_times(A,B),C)!=zero_zero(A).
% 32.57/32.38 ** KEPT (pick-wt=24): 366 [] -ring_n68954251visors(A)|hAPP(A,A,times_times(A,B),C)!=zero_zero(A)|ti(A,B)=zero_zero(A)|ti(A,C)=zero_zero(A).
% 32.57/32.38 ** KEPT (pick-wt=18): 367 [] -ring_n68954251visors(A)|hAPP(A,A,times_times(A,B),C)=zero_zero(A)|ti(A,B)!=zero_zero(A).
% 32.57/32.38 ** KEPT (pick-wt=18): 368 [] -ring_n68954251visors(A)|hAPP(A,A,times_times(A,B),C)=zero_zero(A)|ti(A,C)!=zero_zero(A).
% 32.57/32.38 ** KEPT (pick-wt=13): 369 [] -mult_zero(A)|hAPP(A,A,times_times(A,B),zero_zero(A))=zero_zero(A).
% 32.57/32.38 ** KEPT (pick-wt=13): 370 [] -mult_zero(A)|hAPP(A,A,times_times(A,zero_zero(A)),B)=zero_zero(A).
% 32.57/32.38 ** KEPT (pick-wt=7): 371 [] -zero_ne_q_one(A)|zero_zero(A)!=one_one(A).
% 32.57/32.38 Following clause subsumed by 371 during input processing: 0 [flip.2] -zero_ne_q_one(A)|zero_zero(A)!=one_one(A).
% 32.57/32.38 ** KEPT (pick-wt=47): 373 [copy,372,flip.2] -semiring(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,hAPP(A,A,plus_plus(A,B),C)),D)),E)=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),D)),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,C),D)),E)).
% 32.57/32.38 ** KEPT (pick-wt=35): 374 [] -comm_semiring(A)|hAPP(A,A,times_times(A,hAPP(A,A,plus_plus(A,B),C)),D)=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),D)).
% 32.57/32.38 ** KEPT (pick-wt=18): 375 [] -ring_11004092258visors(A)|ti(A,B)=zero_zero(A)|hAPP(nat,A,power_power(A,B),C)!=zero_zero(A).
% 32.57/32.38 ** KEPT (pick-wt=22): 376 [] -comm_semiring_1(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),zero_zero(A)),B))|ti(A,B)=zero_zero(A).
% 32.57/32.38 ** KEPT (pick-wt=35): 377 [] -comm_monoid_mult(A)|hAPP(nat,A,power_power(A,hAPP(A,A,times_times(A,B),C)),D)=hAPP(A,A,times_times(A,hAPP(nat,A,power_power(A,B),D)),hAPP(nat,A,power_power(A,C),D)).
% 32.57/32.38 ** KEPT (pick-wt=29): 378 [] -monoid_mult(A)|hAPP(A,A,times_times(A,hAPP(nat,A,power_power(A,B),C)),B)=hAPP(A,A,times_times(A,B),hAPP(nat,A,power_power(A,B),C)).
% 32.57/32.38 ** KEPT (pick-wt=21): 379 [] -comm_semiring_1(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,times_times(A,B),C))).
% 32.57/32.38 ** KEPT (pick-wt=21): 380 [] -comm_semiring_1(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,times_times(A,C),B))).
% 32.57/32.38 ** KEPT (pick-wt=34): 381 [] -comm_semiring_1(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,times_times(A,C),D))).
% 32.57/32.38 ** KEPT (pick-wt=34): 382 [] -comm_semiring_1(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,times_times(A,D),C))).
% 32.57/32.38 ** KEPT (pick-wt=53): 383 [] -comm_semiring_1(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),D),E))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),E))).
% 32.57/32.38 ** KEPT (pick-wt=24): 384 [] -dvd(A)|B!=hAPP(A,A,times_times(A,C),D)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),B)).
% 32.57/32.38 ** KEPT (pick-wt=34): 385 [] -comm_semiring_1(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,times_times(A,B),C)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)).
% 32.57/32.38 ** KEPT (pick-wt=34): 386 [] -comm_semiring_1(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,times_times(A,B),C)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)).
% 32.57/32.38 ** KEPT (pick-wt=47): 387 [] -comm_semiring_1(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,plus_plus(A,C),D))).
% 32.57/32.38 ** KEPT (pick-wt=13): 388 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,one_one(A)),B)=one_one(A).
% 32.57/32.38 ** KEPT (pick-wt=16): 389 [] -comm_semiring_1(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),one_one(A)),B)).
% 32.57/32.38 ** KEPT (pick-wt=40): 390 [] -comm_semiring_1(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,power_power(A,B),D)),hAPP(nat,A,power_power(A,C),D))).
% 32.57/32.38 ** KEPT (pick-wt=53): 391 [] -comm_semiring_1(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,power_power(A,B),C)),D))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),E),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,power_power(A,B),E)),D)).
% 32.57/32.38 ** KEPT (pick-wt=53): 392 [] -comm_semiring_1(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),D),E))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,power_power(A,B),D)),hAPP(nat,A,power_power(A,C),E))).
% 32.57/32.38 ** KEPT (pick-wt=40): 393 [] -comm_semiring_1(A)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,power_power(A,D),B)),hAPP(nat,A,power_power(A,D),C))).
% 32.57/32.38 ** KEPT (pick-wt=52): 394 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,A),B)),hAPP(nat,nat,power_power(nat,A),C)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).
% 32.57/32.38 Following clause subsumed by 241 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))|B=zero_zero(nat).
% 32.57/32.38 Following clause subsumed by 243 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).
% 32.57/32.38 Following clause subsumed by 242 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))|B!=zero_zero(nat).
% 32.57/32.38 ** KEPT (pick-wt=29): 395 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,B),hAPP(nat,nat,times_times(nat,C),D))=hAPP(nat,A,power_power(A,hAPP(nat,A,power_power(A,B),C)),D).
% 32.57/32.38 ** KEPT (pick-wt=52): 396 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),C),A)).
% 32.57/32.38 ** KEPT (pick-wt=14): 397 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,B),one_one(nat))=ti(A,B).
% 32.57/32.38 ** KEPT (pick-wt=16): 398 [] -hBOOL(hAPP(int,bool,zcong(A,B),zero_zero(int)))|ti(int,A)=ti(int,B).
% 32.57/32.38 ** KEPT (pick-wt=16): 399 [] hBOOL(hAPP(int,bool,zcong(A,B),zero_zero(int)))|ti(int,A)!=ti(int,B).
% 32.57/32.38 ** KEPT (pick-wt=36): 400 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,zcong(D,hAPP(int,int,times_times(int,A),E)),C))|hBOOL(hAPP(int,bool,zcong(D,hAPP(int,int,times_times(int,B),E)),C)).
% 32.57/32.38 ** KEPT (pick-wt=36): 401 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|hBOOL(hAPP(int,bool,zcong(D,hAPP(int,int,times_times(int,A),E)),C))| -hBOOL(hAPP(int,bool,zcong(D,hAPP(int,int,times_times(int,B),E)),C)).
% 32.57/32.38 ** KEPT (pick-wt=36): 402 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,zcong(D,hAPP(int,int,times_times(int,E),A)),C))|hBOOL(hAPP(int,bool,zcong(D,hAPP(int,int,times_times(int,E),B)),C)).
% 32.57/32.38 ** KEPT (pick-wt=36): 403 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|hBOOL(hAPP(int,bool,zcong(D,hAPP(int,int,times_times(int,E),A)),C))| -hBOOL(hAPP(int,bool,zcong(D,hAPP(int,int,times_times(int,E),B)),C)).
% 32.57/32.38 ** KEPT (pick-wt=28): 404 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A),D),hAPP(int,int,times_times(int,B),D)),C)).
% 32.57/32.38 ** KEPT (pick-wt=28): 405 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,D),A),hAPP(int,int,times_times(int,D),B)),C)).
% 32.57/32.38 ** KEPT (pick-wt=36): 406 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,zcong(D,E),C))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A),D),hAPP(int,int,times_times(int,B),E)),C)).
% 32.57/32.38 ** KEPT (pick-wt=36): 407 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,zcong(D,E),C))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,plus_plus(int,A),D),hAPP(int,int,plus_plus(int,B),E)),C)).
% 32.57/32.38 ** KEPT (pick-wt=28): 408 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,plus_plus(int,A),D),hAPP(int,int,plus_plus(int,B),D)),C)).
% 32.57/32.38 ** KEPT (pick-wt=28): 409 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,A),D),hAPP(nat,int,power_power(int,B),D)),C)).
% 32.57/32.38 ** KEPT (pick-wt=24): 410 [] -number_ring(A)|hAPP(nat,A,power_power(A,number_number_of(A,min)),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),B))=one_one(A).
% 32.57/32.38 ** KEPT (pick-wt=50): 411 [] -ordere453448008miring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),C)),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=50): 412 [] -ordere453448008miring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),C)),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=50): 413 [] -ordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,times_times(A,B),C))).
% 32.57/32.38 ** KEPT (pick-wt=50): 414 [] -ordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,times_times(A,B),C))).
% 32.57/32.38 ** KEPT (pick-wt=81): 415 [] -ordered_semiring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),E))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),E))).
% 32.57/32.38 ** KEPT (pick-wt=81): 416 [] -ordered_semiring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),E))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),E))).
% 32.57/32.38 ** KEPT (pick-wt=54): 417 [] -ordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,D),C)),hAPP(A,A,times_times(A,D),B))).
% 32.57/32.38 ** KEPT (pick-wt=54): 418 [] -ordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,C),D)),hAPP(A,A,times_times(A,B),D))).
% 32.57/32.38 ** KEPT (pick-wt=54): 419 [] -ordere1490568538miring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,D),B)),hAPP(A,A,times_times(A,D),C))).
% 32.57/32.38 ** KEPT (pick-wt=54): 420 [] -ordered_semiring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,D),B)),hAPP(A,A,times_times(A,D),C))).
% 32.57/32.38 ** KEPT (pick-wt=54): 421 [] -ordered_semiring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),D))).
% 32.57/32.38 Following clause subsumed by 414 during input processing: 0 [] -ordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,times_times(A,B),C))).
% 32.57/32.38 Following clause subsumed by 412 during input processing: 0 [] -ordere453448008miring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),C)),zero_zero(A))).
% 32.57/32.38 Following clause subsumed by 412 during input processing: 0 [] -ordere453448008miring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,C),B)),zero_zero(A))).
% 32.57/32.38 Following clause subsumed by 411 during input processing: 0 [] -ordere453448008miring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),C)),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=50): 422 [] -ordere453448008miring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,times_times(A,B),C))).
% 32.57/32.38 ** KEPT (pick-wt=50): 423 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),C)),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=50): 424 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),C)),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C)).
% 32.57/32.38 ** KEPT (pick-wt=50): 425 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),C)),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=50): 426 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),C)),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C)).
% 32.57/32.38 ** KEPT (pick-wt=50): 427 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),C)),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=50): 428 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),C)),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C)).
% 32.57/32.38 ** KEPT (pick-wt=50): 429 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,times_times(A,B),C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=50): 430 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,times_times(A,B),C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=50): 431 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,times_times(A,B),C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=50): 432 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,times_times(A,B),C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=50): 433 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,times_times(A,B),C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C)).
% 32.57/32.38 ** KEPT (pick-wt=50): 434 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,times_times(A,B),C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=22): 435 [] -linordered_ring(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,times_times(A,B),B))).
% 32.57/32.38 ** KEPT (pick-wt=54): 436 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,D),C)),hAPP(A,A,times_times(A,D),B))).
% 32.57/32.38 ** KEPT (pick-wt=54): 437 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,C),D)),hAPP(A,A,times_times(A,B),D))).
% 32.57/32.38 ** KEPT (pick-wt=54): 438 [] -linord893533164strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,D),B)),hAPP(A,A,times_times(A,D),C))).
% 32.57/32.38 ** KEPT (pick-wt=54): 439 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,D),B)),hAPP(A,A,times_times(A,D),C))).
% 32.57/32.38 ** KEPT (pick-wt=54): 440 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),D))).
% 32.57/32.38 ** KEPT (pick-wt=50): 441 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,times_times(A,B),C))).
% 32.57/32.38 ** KEPT (pick-wt=50): 442 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=54): 443 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)).
% 32.57/32.38 Following clause subsumed by 436 during input processing: 0 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)).
% 32.57/32.38 ** KEPT (pick-wt=50): 444 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,times_times(A,B),C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)).
% 32.57/32.38 ** KEPT (pick-wt=50): 445 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,times_times(A,B),C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)).
% 32.57/32.38 Following clause subsumed by 442 during input processing: 0 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,C),B)),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=50): 446 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=50): 447 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,times_times(A,B),C))).
% 32.57/32.38 ** KEPT (pick-wt=54): 448 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 32.57/32.38 ** KEPT (pick-wt=54): 449 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 32.57/32.38 ** KEPT (pick-wt=55): 450 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=54): 451 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)).
% 32.57/32.38 ** KEPT (pick-wt=54): 452 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=53): 453 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)).
% 32.57/32.38 Following clause subsumed by 449 during input processing: 0 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 32.57/32.38 Following clause subsumed by 436 during input processing: 0 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)).
% 32.57/32.38 ** KEPT (pick-wt=55): 454 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=54): 455 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)).
% 32.57/32.38 ** KEPT (pick-wt=54): 456 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=53): 457 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)).
% 32.57/32.38 ** KEPT (pick-wt=54): 458 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 32.57/32.38 Following clause subsumed by 437 during input processing: 0 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)).
% 32.57/32.38 ** KEPT (pick-wt=22): 459 [] -linordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),B)),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=48): 460 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,plus_plus(A,B),D))).
% 32.57/32.38 ** KEPT (pick-wt=17): 461 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),one_one(A))).
% 32.57/32.38 ** KEPT (pick-wt=17): 462 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=17): 463 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),one_one(A))).
% 32.57/32.38 ** KEPT (pick-wt=17): 464 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),zero_zero(A))).
% 32.57/32.38 ** KEPT (pick-wt=54): 465 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,B),D)),hAPP(nat,A,power_power(A,C),D))).
% 32.57/32.38 ** KEPT (pick-wt=36): 466 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),C))).
% 32.57/32.38 ** KEPT (pick-wt=50): 467 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,times_times(A,B),C))).
% 32.57/32.38 ** KEPT (pick-wt=36): 468 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),C))).
% 32.57/32.38 ** KEPT (pick-wt=22): 469 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,plus_plus(A,B),one_one(A)))).
% 32.57/32.38 ** KEPT (pick-wt=46): 470 [] -idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))|ti(A,B)=zero_zero(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)).
% 32.57/32.38 ** KEPT (pick-wt=33): 471 [] -idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))|ti(A,B)!=zero_zero(A).
% 32.57/32.38 ** KEPT (pick-wt=40): 472 [] -idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)).
% 32.57/32.38 ** KEPT (pick-wt=46): 473 [] -idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),C)))|ti(A,C)=zero_zero(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)).
% 32.57/32.38 ** KEPT (pick-wt=33): 474 [] -idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),C)))|ti(A,C)!=zero_zero(A).
% 32.57/32.38 ** KEPT (pick-wt=40): 475 [] -idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)).
% 32.57/32.38 ** KEPT (pick-wt=54): 476 [] -linordered_semidom(A)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,D),B)),hAPP(nat,A,power_power(A,D),C))).
% 32.57/32.38 ** KEPT (pick-wt=36): 477 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),hAPP(nat,A,power_power(A,B),C))).
% 32.57/32.38 ** KEPT (pick-wt=34): 478 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))|hAPP(nat,A,power_power(A,B),C)!=hAPP(nat,A,power_power(A,B),D)|C=D.
% 32.57/32.38 ** KEPT (pick-wt=34): 479 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))|hAPP(nat,A,power_power(A,B),C)=hAPP(nat,A,power_power(A,B),D)|C!=D.
% 32.57/32.38 ** KEPT (pick-wt=24): 480 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),C)!=zero_zero(A)|ti(A,B)=zero_zero(A).
% 32.57/32.38 ** KEPT (pick-wt=22): 481 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),C)!=zero_zero(A)|C!=zero_zero(nat).
% 32.57/32.38 ** KEPT (pick-wt=28): 482 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),C)=zero_zero(A)|ti(A,B)!=zero_zero(A)|C=zero_zero(nat).
% 32.57/32.38 ** KEPT (pick-wt=13): 483 [] -power(A)|hAPP(nat,A,power_power(A,B),zero_zero(nat))=one_one(A).
% 32.57/32.38 ** KEPT (pick-wt=35): 484 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,B),hAPP(nat,nat,plus_plus(nat,C),D))=hAPP(A,A,times_times(A,hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)).
% 32.57/32.38 ** KEPT (pick-wt=62): 485 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),A))| -hBOOL(hAPP(int,bool,zcong(A,C),B)).
% 32.57/32.39 ** KEPT (pick-wt=36): 486 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B)).
% 32.57/32.39 ** KEPT (pick-wt=83): 487 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C))|ti(int,A)=ti(int,B).
% 32.57/32.39 ** KEPT (pick-wt=40): 488 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 32.57/32.39 ** KEPT (pick-wt=28): 489 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|ti(int,B)=hAPP(int,int,plus_plus(int,A),hAPP(int,int,times_times(int,C),$f2(A,B,C))).
% 32.57/32.39 ** KEPT (pick-wt=25): 490 [] hBOOL(hAPP(int,bool,zcong(A,B),C))|ti(int,B)!=hAPP(int,int,plus_plus(int,A),hAPP(int,int,times_times(int,C),D)).
% 32.57/32.39 ** KEPT (pick-wt=22): 491 [] -hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A)).
% 32.57/32.39 ** KEPT (pick-wt=22): 492 [] hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A)).
% 32.57/32.39 Following clause subsumed by 491 during input processing: 0 [] -hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A)).
% 32.57/32.39 Following clause subsumed by 492 during input processing: 0 [] hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A)).
% 32.57/32.39 ** KEPT (pick-wt=51): 493 [] -hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,times_times(int,B),C)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)).
% 32.57/32.39 ** KEPT (pick-wt=54): 494 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D)).
% 32.57/32.39 ** KEPT (pick-wt=54): 495 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),D)).
% 32.57/32.39 ** KEPT (pick-wt=54): 496 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 32.57/32.39 ** KEPT (pick-wt=54): 497 [] -linordered_semiring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 32.57/32.39 ** KEPT (pick-wt=54): 498 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 32.57/32.39 ** KEPT (pick-wt=54): 499 [] -linordered_semiring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 32.57/32.39 ** KEPT (pick-wt=81): 500 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),E))).
% 32.57/32.39 ** KEPT (pick-wt=81): 501 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),E))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),E))).
% 32.57/32.39 ** KEPT (pick-wt=81): 502 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),E))).
% 32.57/32.39 ** KEPT (pick-wt=81): 503 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),E))).
% 32.57/32.39 ** KEPT (pick-wt=54): 504 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),C)).
% 32.57/32.39 ** KEPT (pick-wt=54): 505 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),C)).
% 32.57/32.39 ** KEPT (pick-wt=54): 506 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D)).
% 32.57/32.39 ** KEPT (pick-wt=54): 507 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D)).
% 32.57/32.39 ** KEPT (pick-wt=63): 508 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),one_one(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,C),B)),B)).
% 32.57/32.39 ** KEPT (pick-wt=63): 509 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),one_one(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,times_times(A,B),C)),B)).
% 32.57/32.39 ** KEPT (pick-wt=24): 510 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,one_one(A)),one_one(A)))).
% 32.57/32.39 ** KEPT (pick-wt=54): 511 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,D),C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 32.57/32.39 ** KEPT (pick-wt=68): 512 [] -linordered_semidom(A)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),D))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),one_one(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,D),C)),hAPP(nat,A,power_power(A,D),B))).
% 32.57/32.39 ** KEPT (pick-wt=54): 513 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),D)).
% 32.57/32.39 Following clause subsumed by 513 during input processing: 0 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),D)).
% 32.57/32.39 ** KEPT (pick-wt=54): 514 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),D)).
% 32.57/32.39 ** KEPT (pick-wt=47): 515 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),C)),hAPP(A,A,times_times(A,B),hAPP(nat,A,power_power(A,B),C)))).
% 32.57/32.39 ** KEPT (pick-wt=42): 516 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,times_times(A,B),hAPP(nat,A,power_power(A,B),C)))).
% 32.57/32.39 ** KEPT (pick-wt=19): 517 [] -power(A)| -semiring_0(A)|B!=zero_zero(nat)|hAPP(nat,A,power_power(A,zero_zero(A)),B)=one_one(A).
% 32.57/32.39 ** KEPT (pick-wt=19): 518 [] -power(A)| -semiring_0(A)|B=zero_zero(nat)|hAPP(nat,A,power_power(A,zero_zero(A)),B)=zero_zero(A).
% 32.57/32.39 ** KEPT (pick-wt=54): 519 [] -linordered_semidom(A)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,D),B)),hAPP(nat,A,power_power(A,D),C))).
% 32.57/32.39 ** KEPT (pick-wt=54): 520 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)).
% 32.57/32.39 Following clause subsumed by 520 during input processing: 0 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)).
% 32.57/32.39 Following clause subsumed by 519 during input processing: 0 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)).
% 32.57/32.39 ** KEPT (pick-wt=42): 521 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B))|ti(int,A)=zero_zero(int).
% 32.57/32.39 Following clause subsumed by 521 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B))|ti(int,A)=zero_zero(int).
% 32.57/32.39 ** KEPT (pick-wt=69): 522 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B))| -hBOOL(hAPP(int,bool,zcong(A,C),B))|ti(int,A)=ti(int,C).
% 32.57/32.39 ** KEPT (pick-wt=46): 523 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),hAPP(nat,int,power_power(int,C),A))).
% 32.57/32.39 ** KEPT (pick-wt=36): 524 [] -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,A),B),one_one(int)),C))|hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,A),hAPP(nat,nat,times_times(nat,B),D)),one_one(int)),C)).
% 32.57/32.39 ** KEPT (pick-wt=39): 525 [] -hBOOL(hAPP(int,bool,zprime,A))|hBOOL(hAPP(int,bool,zcong(B,zero_zero(int)),A))|hBOOL(hAPP(int,bool,zcong(C,zero_zero(int)),A))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,B),C),zero_zero(int)),A)).
% 32.57/32.39 ** KEPT (pick-wt=97): 526 [] -linord1278240602ring_1(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),E))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),F))|hAPP(A,A,plus_plus(A,E),F)!=one_one(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,E),B)),hAPP(A,A,times_times(A,F),D))),C)).
% 32.57/32.39 ** KEPT (pick-wt=61): 527 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),hAPP(nat,A,power_power(A,B),C))),hAPP(nat,A,power_power(A,B),C))).
% 32.57/32.39 ** KEPT (pick-wt=68): 528 [] -linordered_semidom(A)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),one_one(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,D),C)),hAPP(nat,A,power_power(A,D),B))).
% 32.57/32.39 ** KEPT (pick-wt=66): 529 [] -linordered_semidom(A)|hAPP(nat,A,power_power(A,B),C)!=hAPP(nat,A,power_power(A,D),C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),D))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C))|ti(A,B)=ti(A,D).
% 32.57/32.39 ** KEPT (pick-wt=50): 530 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(nat,A,power_power(A,B),C))).
% 32.57/32.39 ** KEPT (pick-wt=35): 531 [] -comm_semiring_1(A)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),hAPP(nat,A,power_power(A,C),B))).
% 32.57/32.39 ** KEPT (pick-wt=27): 532 [] -comm_semiring_1(A)|ti(A,B)!=one_one(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(nat,A,power_power(A,B),C))).
% 32.57/32.39 Following clause subsumed by 525 during input processing: 0 [] -hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,B),C),zero_zero(int)),A))|hBOOL(hAPP(int,bool,zcong(B,zero_zero(int)),A))|hBOOL(hAPP(int,bool,zcong(C,zero_zero(int)),A)).
% 32.57/32.39 Following clause subsumed by 525 during input processing: 0 [] -hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,zcong(B,zero_zero(int)),A))|hBOOL(hAPP(int,bool,zcong(C,zero_zero(int)),A))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,B),C),zero_zero(int)),A)).
% 32.57/32.39 Following clause subsumed by 493 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,zprime,B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),hAPP(int,int,times_times(int,A),C)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)).
% 32.57/32.39 ** KEPT (pick-wt=60): 533 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),A))| -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,number_number_of(int,min)),B),hAPP(nat,int,power_power(int,number_number_of(int,min)),C)),A))|hAPP(nat,int,power_power(int,number_number_of(int,min)),B)=hAPP(nat,int,power_power(int,number_number_of(int,min)),C).
% 32.57/32.39 ** KEPT (pick-wt=28): 534 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),A))| -hBOOL(hAPP(int,bool,zcong(one_one(int),number_number_of(int,min)),A)).
% 32.57/32.39 ** KEPT (pick-wt=53): 535 [] hBOOL(hAPP(int,bool,quadRes(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),number_number_of(int,min)))|legendre(number_number_of(int,min),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))!=one_one(int).
% 32.57/32.39 ** KEPT (pick-wt=24): 536 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,times_times(real,A),A)))|A!=zero_zero(real).
% 32.57/32.39 ** KEPT (pick-wt=23): 537 [] -number_ring(A)|number_number_of(A,hAPP(int,int,minus_minus(int,B),C))=hAPP(A,A,minus_minus(A,number_number_of(A,B)),number_number_of(A,C)).
% 32.57/32.39 ** KEPT (pick-wt=47): 538 [] -comm_ring_1(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,minus_minus(A,C),D))).
% 32.57/32.39 ** KEPT (pick-wt=22): 539 [] hAPP(int,int,minus_minus(int,A),B)!=ti(int,C)|ti(int,A)=hAPP(int,int,plus_plus(int,C),B).
% 32.57/32.39 ** KEPT (pick-wt=36): 540 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,zcong(D,E),C))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,minus_minus(int,A),D),hAPP(int,int,minus_minus(int,B),E)),C)).
% 32.57/32.39 ** KEPT (pick-wt=45): 541 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,minus_minus(int,B),C)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)).
% 32.57/32.39 ** KEPT (pick-wt=52): 542 [] -ring(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),D)!=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,E),C)),F)|ti(A,D)=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,hAPP(A,A,minus_minus(A,E),B)),C)),F).
% 32.57/32.39 ** KEPT (pick-wt=52): 543 [] -ring(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),D)=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,E),C)),F)|ti(A,D)!=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,hAPP(A,A,minus_minus(A,E),B)),C)),F).
% 32.57/32.39 ** KEPT (pick-wt=52): 544 [] -ring(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),D)!=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,E),C)),F)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,hAPP(A,A,minus_minus(A,B),E)),C)),D)=ti(A,F).
% 32.57/32.39 ** KEPT (pick-wt=52): 545 [] -ring(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),D)=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,E),C)),F)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,hAPP(A,A,minus_minus(A,B),E)),C)),D)!=ti(A,F).
% 32.57/32.39 ** KEPT (pick-wt=43): 547 [copy,546,flip.3] -number(A)| -ring(A)|hAPP(A,A,minus_minus(A,hAPP(A,A,times_times(A,number_number_of(A,B)),C)),hAPP(A,A,times_times(A,number_number_of(A,B)),D))=hAPP(A,A,times_times(A,number_number_of(A,B)),hAPP(A,A,minus_minus(A,C),D)).
% 32.57/32.39 ** KEPT (pick-wt=43): 548 [] -number(A)| -ring(A)|hAPP(A,A,times_times(A,hAPP(A,A,minus_minus(A,B),C)),number_number_of(A,D))=hAPP(A,A,minus_minus(A,hAPP(A,A,times_times(A,B),number_number_of(A,D))),hAPP(A,A,times_times(A,C),number_number_of(A,D))).
% 32.57/32.39 ** KEPT (pick-wt=33): 549 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,A),B)),zero_zero(int))).
% 32.57/32.39 ** KEPT (pick-wt=33): 550 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,A),B)),zero_zero(int))).
% 32.57/32.39 ** KEPT (pick-wt=27): 551 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),C),hAPP(int,int,minus_minus(int,A),B))).
% 32.57/32.39 ** KEPT (pick-wt=27): 552 [] hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),C),hAPP(int,int,minus_minus(int,A),B))).
% 32.57/32.39 ** KEPT (pick-wt=70): 553 [] -ordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),D)),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,E),C)),F)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,hAPP(A,A,minus_minus(A,B),E)),C)),D)),F)).
% 32.57/32.39 ** KEPT (pick-wt=70): 554 [] -ordered_ring(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),D)),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,E),C)),F)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,hAPP(A,A,minus_minus(A,B),E)),C)),D)),F)).
% 32.57/32.39 ** KEPT (pick-wt=70): 555 [] -ordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),D)),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,E),C)),F)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,hAPP(A,A,minus_minus(A,E),B)),C)),F))).
% 32.57/32.39 ** KEPT (pick-wt=70): 556 [] -ordered_ring(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),D)),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,E),C)),F)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,hAPP(A,A,minus_minus(A,E),B)),C)),F))).
% 32.57/32.39 ** KEPT (pick-wt=70): 557 [] -ordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),D)),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,E),C)),F)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,hAPP(A,A,minus_minus(A,E),B)),C)),F))).
% 32.57/32.39 ** KEPT (pick-wt=70): 558 [] -ordered_ring(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),D)),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,E),C)),F)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,hAPP(A,A,minus_minus(A,E),B)),C)),F))).
% 32.57/32.39 ** KEPT (pick-wt=70): 559 [] -ordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),D)),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,E),C)),F)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,hAPP(A,A,minus_minus(A,B),E)),C)),D)),F)).
% 32.57/32.39 ** KEPT (pick-wt=70): 560 [] -ordered_ring(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),D)),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,E),C)),F)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,hAPP(A,A,minus_minus(A,B),E)),C)),D)),F)).
% 32.57/32.39 ** KEPT (pick-wt=35): 561 [] -number_ring(A)|hAPP(A,A,plus_plus(A,number_number_of(A,B)),hAPP(A,A,minus_minus(A,number_number_of(A,C)),D))=hAPP(A,A,minus_minus(A,number_number_of(A,hAPP(int,int,plus_plus(int,B),C))),D).
% 32.57/32.39 ** KEPT (pick-wt=59): 562 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|ti(int,A)=hAPP(int,int,minus_minus(int,B),one_one(int))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,minus_minus(int,B),one_one(int)))).
% 32.57/32.39 ** KEPT (pick-wt=33): 563 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),hAPP(int,int,minus_minus(int,B),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.39 ** KEPT (pick-wt=33): 564 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool)
% 32.57/32.39 Search stopped in tp_alloc by max_mem option.
% 32.57/32.39 ,ord_less_e_q(int),A),hAPP(int,int,minus_minus(int,B),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 32.57/32.39 ** KEPT (pick-wt=37): 565 [] -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A),hAPP(int,int,minus_minus(int,B),one_one(int))),one_one(int)),B))|hBOOL(hAPP(int,bool,zcong(A,hAPP(int,int,minus_minus(int,B),one_one(int))),B)).
% 32.57/32.39 ** KEPT (pick-wt=37): 566 [] hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A),hAPP(int,int,minus_minus(int,B),one_one(int))),one_one(int)),B))| -hBOOL(hAPP(int,bool,zcong(A,hAPP(int,int,minus_minus(int,B),one_one(int))),B)).
% 32.57/32.39 ** KEPT (pick-wt=52): 567 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,A),B)),hAPP(nat,nat,power_power(nat,A),C)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C)).
% 32.57/32.39 ** KEPT (pick-wt=66): 568 [] -hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,B),B),one_one(int)),A))|ti(int,B)=one_one(int)|ti(int,B)=hAPP(int,int,minus_minus(int,A),one_one(int)).
% 32.57/32.39 ** KEPT (pick-wt=59): 569 [] -hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,B),B),one_one(int)),A))|hBOOL(hAPP(int,bool,zcong(B,one_one(int)),A))|hBOOL(hAPP(int,bool,zcong(B,hAPP(int,int,minus_minus(int,A),one_one(int))),A)).
% 32.57/32.39 ** KEPT (pick-wt=69): 570 [] -number_ring(A)|hAPP(nat,A,power_power(A,hAPP(A,A,minus_minus(A,B),C)),number_number_of(nat,bit0(bit1(pls))))=hAPP(A,A,minus_minus(A,hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))),hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,number_number_of(A,bit0(bit1(pls)))),B)),C)).
% 32.57/32.39
% 32.57/32.39 Search stopped in tp_alloc by max_mem option.
% 32.57/32.39
% 32.57/32.39 ============ end of search ============
% 32.57/32.39
% 32.57/32.39 -------------- statistics -------------
% 32.57/32.39 clauses given 0
% 32.57/32.39 clauses generated 0
% 32.57/32.39 clauses kept 554
% 32.57/32.39 clauses forward subsumed 61
% 32.57/32.39 clauses back subsumed 0
% 32.57/32.39 Kbytes malloced 11718
% 32.57/32.39
% 32.57/32.39 ----------- times (seconds) -----------
% 32.57/32.39 user CPU time 0.23 (0 hr, 0 min, 0 sec)
% 32.57/32.39 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 32.57/32.39 wall-clock time 32 (0 hr, 0 min, 32 sec)
% 32.57/32.39
% 32.57/32.39 Process 22169 finished Wed Jul 27 09:34:53 2022
% 32.57/32.39 Otter interrupted
% 32.57/32.39 PROOF NOT FOUND
%------------------------------------------------------------------------------