TSTP Solution File: NUM925+7 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM925+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n006.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 13:10:17 EDT 2022
% Result : Unknown 25.54s 25.38s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM925+7 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 09:50:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 25.45/25.29 ----- Otter 3.3f, August 2004 -----
% 25.45/25.29 The process was started by sandbox on n006.cluster.edu,
% 25.45/25.29 Wed Jul 27 09:50:47 2022
% 25.45/25.29 The command was "./otter". The process ID is 28639.
% 25.45/25.29
% 25.45/25.29 set(prolog_style_variables).
% 25.45/25.29 set(auto).
% 25.45/25.29 dependent: set(auto1).
% 25.45/25.29 dependent: set(process_input).
% 25.45/25.29 dependent: clear(print_kept).
% 25.45/25.29 dependent: clear(print_new_demod).
% 25.45/25.29 dependent: clear(print_back_demod).
% 25.45/25.29 dependent: clear(print_back_sub).
% 25.45/25.29 dependent: set(control_memory).
% 25.45/25.29 dependent: assign(max_mem, 12000).
% 25.45/25.29 dependent: assign(pick_given_ratio, 4).
% 25.45/25.29 dependent: assign(stats_level, 1).
% 25.45/25.29 dependent: assign(max_seconds, 10800).
% 25.45/25.29 clear(print_given).
% 25.45/25.29
% 25.45/25.29 formula_list(usable).
% 25.45/25.29 all A (A=A).
% 25.45/25.29 all B_1_1 X_a (ordere142940540dd_abs(X_a)->abs_abs(X_a,ti(X_a,B_1_1))=abs_abs(X_a,B_1_1)).
% 25.45/25.29 all B_1_1 X_a (ordere142940540dd_abs(X_a)->ti(X_a,abs_abs(X_a,B_1_1))=abs_abs(X_a,B_1_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (group_add(X_a)->minus_minus(X_a,ti(X_a,B_1_1),B_2_1)=minus_minus(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (group_add(X_a)->minus_minus(X_a,B_1_1,ti(X_a,B_2_1))=minus_minus(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (group_add(X_a)->ti(X_a,minus_minus(X_a,B_1_1,B_2_1))=minus_minus(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 (minus_minus(nat,ti(nat,B_1_1),B_2_1)=minus_minus(nat,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 (minus_minus(nat,B_1_1,ti(nat,B_2_1))=minus_minus(nat,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 (ti(nat,minus_minus(nat,B_1_1,B_2_1))=minus_minus(nat,B_1_1,B_2_1)).
% 25.45/25.29 all X_a (one(X_a)->ti(X_a,one_one(X_a))=one_one(X_a)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (monoid_add(X_a)->plus_plus(X_a,ti(X_a,B_1_1),B_2_1)=plus_plus(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (monoid_add(X_a)->plus_plus(X_a,B_1_1,ti(X_a,B_2_1))=plus_plus(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (monoid_add(X_a)->ti(X_a,plus_plus(X_a,B_1_1,B_2_1))=plus_plus(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (ab_semigroup_add(X_a)->plus_plus(X_a,ti(X_a,B_1_1),B_2_1)=plus_plus(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (ab_semigroup_add(X_a)->plus_plus(X_a,B_1_1,ti(X_a,B_2_1))=plus_plus(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (ab_semigroup_add(X_a)->ti(X_a,plus_plus(X_a,B_1_1,B_2_1))=plus_plus(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (cancel_semigroup_add(X_a)->plus_plus(X_a,ti(X_a,B_1_1),B_2_1)=plus_plus(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (cancel_semigroup_add(X_a)->plus_plus(X_a,B_1_1,ti(X_a,B_2_1))=plus_plus(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (cancel_semigroup_add(X_a)->ti(X_a,plus_plus(X_a,B_1_1,B_2_1))=plus_plus(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (dvd(X_a)->times_times(X_a,ti(X_a,B_1_1),B_2_1)=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (dvd(X_a)->times_times(X_a,B_1_1,ti(X_a,B_2_1))=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (dvd(X_a)->ti(X_a,times_times(X_a,B_1_1,B_2_1))=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (power(X_a)->times_times(X_a,ti(X_a,B_1_1),B_2_1)=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (power(X_a)->times_times(X_a,B_1_1,ti(X_a,B_2_1))=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (power(X_a)->ti(X_a,times_times(X_a,B_1_1,B_2_1))=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (semiring(X_a)->times_times(X_a,ti(X_a,B_1_1),B_2_1)=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (semiring(X_a)->times_times(X_a,B_1_1,ti(X_a,B_2_1))=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (semiring(X_a)->ti(X_a,times_times(X_a,B_1_1,B_2_1))=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (no_zero_divisors(X_a)->times_times(X_a,ti(X_a,B_1_1),B_2_1)=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (no_zero_divisors(X_a)->times_times(X_a,B_1_1,ti(X_a,B_2_1))=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (no_zero_divisors(X_a)->ti(X_a,times_times(X_a,B_1_1,B_2_1))=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (mult_zero(X_a)->times_times(X_a,ti(X_a,B_1_1),B_2_1)=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (mult_zero(X_a)->times_times(X_a,B_1_1,ti(X_a,B_2_1))=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (mult_zero(X_a)->ti(X_a,times_times(X_a,B_1_1,B_2_1))=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (ab_semigroup_mult(X_a)->times_times(X_a,ti(X_a,B_1_1),B_2_1)=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (ab_semigroup_mult(X_a)->times_times(X_a,B_1_1,ti(X_a,B_2_1))=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (ab_semigroup_mult(X_a)->ti(X_a,times_times(X_a,B_1_1,B_2_1))=times_times(X_a,B_1_1,B_2_1)).
% 25.45/25.29 all X_a (zero(X_a)->ti(X_a,zero_zero(X_a))=zero_zero(X_a)).
% 25.45/25.29 all X_a (ti(X_a,undefined(X_a))=undefined(X_a)).
% 25.45/25.29 all X_a B_1_1 B_2_1 B_3 (if(X_a,ti(bool,B_1_1),B_2_1,B_3)=if(X_a,B_1_1,B_2_1,B_3)).
% 25.45/25.29 all X_a B_1_1 B_2_1 B_3 (if(X_a,B_1_1,ti(X_a,B_2_1),B_3)=if(X_a,B_1_1,B_2_1,B_3)).
% 25.45/25.29 all X_a B_1_1 B_2_1 B_3 (if(X_a,B_1_1,B_2_1,ti(X_a,B_3))=if(X_a,B_1_1,B_2_1,B_3)).
% 25.45/25.29 all X_a B_1_1 B_2_1 B_3 (ti(X_a,if(X_a,B_1_1,B_2_1,B_3))=if(X_a,B_1_1,B_2_1,B_3)).
% 25.45/25.29 all B_1_1 B_2_1 (zcong(ti(int,B_1_1),B_2_1)=zcong(B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 (zcong(B_1_1,ti(int,B_2_1))=zcong(B_1_1,B_2_1)).
% 25.45/25.29 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)).
% 25.45/25.29 ti(fun(int,bool),zprime)=zprime.
% 25.45/25.29 all B_1_1 (bit0(ti(int,B_1_1))=bit0(B_1_1)).
% 25.45/25.29 all B_1_1 (ti(int,bit0(B_1_1))=bit0(B_1_1)).
% 25.45/25.29 all B_1_1 (bit1(ti(int,B_1_1))=bit1(B_1_1)).
% 25.45/25.29 all B_1_1 (ti(int,bit1(B_1_1))=bit1(B_1_1)).
% 25.45/25.29 ti(int,min)=min.
% 25.45/25.29 ti(int,pls)=pls.
% 25.45/25.29 all B_1_1 (nat_1(ti(int,B_1_1))=nat_1(B_1_1)).
% 25.45/25.29 all B_1_1 (ti(nat,nat_1(B_1_1))=nat_1(B_1_1)).
% 25.45/25.29 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)).
% 25.45/25.29 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)).
% 25.45/25.29 all B_1_1 (succ(ti(int,B_1_1))=succ(B_1_1)).
% 25.45/25.29 all B_1_1 (ti(int,succ(B_1_1))=succ(B_1_1)).
% 25.45/25.29 all X_a (semiring_1(X_a)->ti(fun(nat,X_a),semiring_1_of_nat(X_a))=semiring_1_of_nat(X_a)).
% 25.45/25.29 all X_a (order(X_a)->ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a)).
% 25.45/25.29 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)).
% 25.45/25.29 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)).
% 25.45/25.29 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)).
% 25.45/25.29 all B_1_1 B_2_1 (legendre(ti(int,B_1_1),B_2_1)=legendre(B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 (legendre(B_1_1,ti(int,B_2_1))=legendre(B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 (ti(int,legendre(B_1_1,B_2_1))=legendre(B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 (quadRes(ti(int,B_1_1))=quadRes(B_1_1)).
% 25.45/25.29 all B_1_1 (ti(fun(int,bool),quadRes(B_1_1))=quadRes(B_1_1)).
% 25.45/25.29 all X_a (dvd(X_a)->ti(fun(X_a,fun(X_a,bool)),dvd_dvd(X_a))=dvd_dvd(X_a)).
% 25.45/25.29 ti(fun(int,bool),twoSqu658283162sum2sq)=twoSqu658283162sum2sq.
% 25.45/25.29 ti(bool,fFalse)=fFalse.
% 25.45/25.29 ti(bool,fTrue)=fTrue.
% 25.45/25.29 all B_1_1 B_2_1 X_a (order(X_a)->hAPP(X_a,fun(X_a,bool),ti(fun(X_a,fun(X_a,bool)),B_1_1),B_2_1)=hAPP(X_a,fun(X_a,bool),B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (order(X_a)->hAPP(X_a,fun(X_a,bool),B_1_1,ti(X_a,B_2_1))=hAPP(X_a,fun(X_a,bool),B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (order(X_a)->ti(fun(X_a,bool),hAPP(X_a,fun(X_a,bool),B_1_1,B_2_1))=hAPP(X_a,fun(X_a,bool),B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (order(X_a)->hAPP(X_a,bool,ti(fun(X_a,bool),B_1_1),B_2_1)=hAPP(X_a,bool,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (order(X_a)->hAPP(X_a,bool,B_1_1,ti(X_a,B_2_1))=hAPP(X_a,bool,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (order(X_a)->ti(bool,hAPP(X_a,bool,B_1_1,B_2_1))=hAPP(X_a,bool,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (dvd(X_a)->hAPP(X_a,fun(X_a,bool),ti(fun(X_a,fun(X_a,bool)),B_1_1),B_2_1)=hAPP(X_a,fun(X_a,bool),B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (dvd(X_a)->hAPP(X_a,fun(X_a,bool),B_1_1,ti(X_a,B_2_1))=hAPP(X_a,fun(X_a,bool),B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (dvd(X_a)->ti(fun(X_a,bool),hAPP(X_a,fun(X_a,bool),B_1_1,B_2_1))=hAPP(X_a,fun(X_a,bool),B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (dvd(X_a)->hAPP(X_a,bool,ti(fun(X_a,bool),B_1_1),B_2_1)=hAPP(X_a,bool,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (dvd(X_a)->hAPP(X_a,bool,B_1_1,ti(X_a,B_2_1))=hAPP(X_a,bool,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (dvd(X_a)->ti(bool,hAPP(X_a,bool,B_1_1,B_2_1))=hAPP(X_a,bool,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (power(X_a)->hAPP(nat,X_a,ti(fun(nat,X_a),B_1_1),B_2_1)=hAPP(nat,X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (power(X_a)->hAPP(nat,X_a,B_1_1,ti(nat,B_2_1))=hAPP(nat,X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 B_2_1 X_a (power(X_a)->ti(X_a,hAPP(nat,X_a,B_1_1,B_2_1))=hAPP(nat,X_a,B_1_1,B_2_1)).
% 25.45/25.29 all B_1_1 (hBOOL(ti(bool,B_1_1))<->hBOOL(B_1_1)).
% 25.45/25.29 ti(int,m)=m.
% 25.45/25.29 ti(int,m1)=m1.
% 25.45/25.29 ti(nat,n)=n.
% 25.45/25.29 ti(int,s1)=s1.
% 25.45/25.29 ti(int,s)=s.
% 25.45/25.29 ti(int,t)=t.
% 25.45/25.29 ti(nat,tn)=tn.
% 25.45/25.29 ti(int,x)=x.
% 25.45/25.29 ti(int,y)=y.
% 25.45/25.29 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))).
% 25.45/25.29 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)).
% 25.45/25.29 all X_a (linordered_idom(X_a)-> (all Xa Ya (plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,bit0(bit1(pls)))))=zero_zero(X_a)<->ti(X_a,Xa)=zero_zero(X_a)&ti(X_a,Ya)=zero_zero(X_a)))).
% 25.45/25.29 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)).
% 25.45/25.29 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)).
% 25.45/25.29 all X_a (ring_11004092258visors(X_a)-> (all A_2 (hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(pls))))=zero_zero(X_a)<->ti(X_a,A_2)=zero_zero(X_a)))).
% 25.45/25.29 all X_a (number_ring(X_a)-> (all W (plus_plus(X_a,one_one(X_a),number_number_of(X_a,W))=number_number_of(X_a,plus_plus(int,bit1(pls),W))))).
% 25.45/25.29 all X_a (number_ring(X_a)-> (all V_1 (plus_plus(X_a,number_number_of(X_a,V_1),one_one(X_a))=number_number_of(X_a,plus_plus(int,V_1,bit1(pls)))))).
% 25.45/25.29 all X_a (number_ring(X_a)->plus_plus(X_a,one_one(X_a),one_one(X_a))=number_number_of(X_a,bit0(bit1(pls)))).
% 25.45/25.29 all X_a (number_semiring(X_a)->plus_plus(X_a,one_one(X_a),one_one(X_a))=number_number_of(X_a,bit0(bit1(pls)))).
% 25.45/25.29 all X (hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),number_number_of(nat,bit0(bit1(pls))))=hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit0(bit1(pls)))))).
% 25.45/25.29 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))))).
% 25.45/25.29 all X_a (number_ring(X_a)->one_one(X_a)=number_number_of(X_a,bit1(pls))).
% 25.45/25.29 all X_a (number_ring(X_a)->number_number_of(X_a,bit1(pls))=one_one(X_a)).
% 25.45/25.29 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),n)).
% 25.45/25.29 all X Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),Y))|ti(int,X)=ti(int,Y)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X))).
% 25.45/25.29 all K L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,K)),number_number_of(int,L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1))).
% 25.45/25.29 all V_1 W (plus_plus(int,number_number_of(int,V_1),number_number_of(int,W))=number_number_of(int,plus_plus(int,V_1,W))).
% 25.45/25.29 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Xa Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Xa)),number_number_of(X_a,Ya)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),Ya))))).
% 25.45/25.29 zero_zero(int)=number_number_of(int,pls).
% 25.45/25.29 all M N (hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),M)),N)=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,M),N))).
% 25.45/25.29 all M N (hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,M),N))=hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),M)),N)).
% 25.45/25.29 all M N Z (plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),M),plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),N),Z))=plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),plus_plus(nat,M,N)),Z)).
% 25.45/25.29 all M N (plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),M),hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,int,semiring_1_of_nat(int),plus_plus(nat,M,N))).
% 25.45/25.29 hAPP(nat,int,semiring_1_of_nat(int),one_one(nat))=one_one(int).
% 25.45/25.29 number_number_of(nat,pls)=zero_zero(nat).
% 25.45/25.29 zero_zero(nat)=number_number_of(nat,pls).
% 25.45/25.29 all Na (hAPP(nat,int,semiring_1_of_nat(int),Na)=zero_zero(int)<->Na=zero_zero(nat)).
% 25.45/25.29 hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat))=zero_zero(int).
% 25.45/25.29 plus_plus(nat,one_one(nat),one_one(nat))=number_number_of(nat,bit0(bit1(pls))).
% 25.45/25.29 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))).
% 25.45/25.29 all K L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit1(L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1))).
% 25.45/25.29 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)).
% 25.45/25.29 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))).
% 25.45/25.29 all K L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit0(L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1))).
% 25.45/25.29 all K_1 I_2 J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(int,I_2,K_1)),plus_plus(int,J_1,K_1)))).
% 25.45/25.29 all V_2 V_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->plus_plus(nat,number_number_of(nat,V_1),number_number_of(nat,V_2))=number_number_of(nat,V_2))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls))->plus_plus(nat,number_number_of(nat,V_1),number_number_of(nat,V_2))=number_number_of(nat,V_1))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls))->plus_plus(nat,number_number_of(nat,V_1),number_number_of(nat,V_2))=number_number_of(nat,plus_plus(int,V_1,V_2))))).
% 25.45/25.29 one_one(int)=number_number_of(int,bit1(pls)).
% 25.45/25.29 number_number_of(nat,bit1(pls))=one_one(nat).
% 25.45/25.29 one_one(nat)=number_number_of(nat,bit1(pls)).
% 25.45/25.29 all X_a (number_ring(X_a)&ring_char_0(X_a)-> (all Xa Ya (number_number_of(X_a,Xa)=number_number_of(X_a,Ya)<->ti(int,Xa)=ti(int,Ya)))).
% 25.45/25.29 all X_a (number(X_a)-> (all Wa Xa (number_number_of(X_a,Wa)=ti(X_a,Xa)<->ti(X_a,Xa)=number_number_of(X_a,Wa)))).
% 25.45/25.29 all K L_1 (bit1(K)=bit1(L_1)<->ti(int,K)=ti(int,L_1)).
% 25.45/25.29 all K L_1 (bit0(K)=bit0(L_1)<->ti(int,K)=ti(int,L_1)).
% 25.45/25.29 all X_a (linordered_idom(X_a)-> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_2,A_2)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a)))))).
% 25.45/25.29 all Z1 Z2 Z3 (plus_plus(int,plus_plus(int,Z1,Z2),Z3)=plus_plus(int,Z1,plus_plus(int,Z2,Z3))).
% 25.45/25.29 all X Y Z (plus_plus(int,X,plus_plus(int,Y,Z))=plus_plus(int,Y,plus_plus(int,X,Z))).
% 25.45/25.29 all Z W (plus_plus(int,Z,W)=plus_plus(int,W,Z)).
% 25.45/25.29 all Ma Na (hAPP(nat,int,semiring_1_of_nat(int),Ma)=hAPP(nat,int,semiring_1_of_nat(int),Na)<->Ma=Na).
% 25.45/25.29 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Xa)),zero_zero(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),pls))))).
% 25.45/25.29 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Ya (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,Ya)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Ya))))).
% 25.45/25.29 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))).
% 25.45/25.30 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))).
% 25.45/25.30 all K L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit0(L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1))).
% 25.45/25.30 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))).
% 25.45/25.30 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))).
% 25.45/25.30 all Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(Wa)),zero_zero(int)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int)))).
% 25.45/25.30 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))).
% 25.45/25.30 all Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(Wa)),zero_zero(int)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int)))).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))).
% 25.45/25.30 all Wa Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),plus_plus(int,Z_1,one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1))|ti(int,Wa)=ti(int,Z_1)).
% 25.45/25.30 all K_1 (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K_1)),zero_zero(int)))).
% 25.45/25.30 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Xa)),one_one(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),bit1(pls)))))).
% 25.45/25.30 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Ya (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,Ya)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(pls)),Ya))))).
% 25.45/25.30 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(int,plus_plus(int,one_one(int),Z_1),Z_1)),zero_zero(int)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),zero_zero(int)))).
% 25.45/25.30 all X_a (linord219039673up_add(X_a)-> (all A_2 (plus_plus(X_a,A_2,A_2)=zero_zero(X_a)<->ti(X_a,A_2)=zero_zero(X_a)))).
% 25.45/25.30 all K_1 (bit1(K_1)!=pls).
% 25.45/25.30 all L (pls!=bit1(L)).
% 25.45/25.30 all K_1 L (bit1(K_1)!=bit0(L)).
% 25.45/25.30 all K_1 L (bit0(K_1)!=bit1(L)).
% 25.45/25.30 all K (bit0(K)=pls<->ti(int,K)=pls).
% 25.45/25.30 all L_1 (pls=bit0(L_1)<->pls=ti(int,L_1)).
% 25.45/25.30 bit0(pls)=pls.
% 25.45/25.30 pls=zero_zero(int).
% 25.45/25.30 zero_zero(int)!=one_one(int).
% 25.45/25.30 all K_1 (plus_plus(int,K_1,pls)=ti(int,K_1)).
% 25.45/25.30 all K_1 (plus_plus(int,pls,K_1)=ti(int,K_1)).
% 25.45/25.30 all K_1 L (plus_plus(int,bit0(K_1),bit0(L))=bit0(plus_plus(int,K_1,L))).
% 25.45/25.30 all K_1 (bit0(K_1)=plus_plus(int,K_1,K_1)).
% 25.45/25.30 all Z (plus_plus(int,Z,zero_zero(int))=ti(int,Z)).
% 25.45/25.30 all Z (plus_plus(int,zero_zero(int),Z)=ti(int,Z)).
% 25.45/25.30 all X_a (number_semiring(X_a)->number_number_of(X_a,pls)=zero_zero(X_a)).
% 25.45/25.30 all X_a (number_ring(X_a)->number_number_of(X_a,pls)=zero_zero(X_a)).
% 25.45/25.30 all X_a (number_ring(X_a)->zero_zero(X_a)=number_number_of(X_a,pls)).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all A_1 (plus_plus(X_a,number_number_of(X_a,pls),A_1)=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all A_1 (plus_plus(X_a,A_1,number_number_of(X_a,pls))=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (power(X_a)&mult_zero(X_a)&no_zero_divisors(X_a)&zero_ne_q_one(X_a)-> (all A_2 Wa (hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,Wa))=zero_zero(X_a)<->ti(X_a,A_2)=zero_zero(X_a)&number_number_of(nat,Wa)!=zero_zero(nat)))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all V_1 W Z (plus_plus(X_a,number_number_of(X_a,V_1),plus_plus(X_a,number_number_of(X_a,W),Z))=plus_plus(X_a,number_number_of(X_a,plus_plus(int,V_1,W)),Z)))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all V_1 W (plus_plus(X_a,number_number_of(X_a,V_1),number_number_of(X_a,W))=number_number_of(X_a,plus_plus(int,V_1,W))))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all V_1 W (number_number_of(X_a,plus_plus(int,V_1,W))=plus_plus(X_a,number_number_of(X_a,V_1),number_number_of(X_a,W))))).
% 25.45/25.30 all K_1 L (plus_plus(int,bit1(K_1),bit0(L))=bit1(plus_plus(int,K_1,L))).
% 25.45/25.30 all K_1 L (plus_plus(int,bit0(K_1),bit1(L))=bit1(plus_plus(int,K_1,L))).
% 25.45/25.30 all K_1 (bit1(K_1)=plus_plus(int,plus_plus(int,one_one(int),K_1),K_1)).
% 25.45/25.30 all Z (plus_plus(int,plus_plus(int,one_one(int),Z),Z)!=zero_zero(int)).
% 25.45/25.30 all X_a (number_semiring(X_a)-> (all N (number_number_of(X_a,hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all A_2 (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_2),number_number_of(nat,bit0(bit1(pls))))))<->ti(X_a,A_2)!=zero_zero(X_a)))).
% 25.45/25.30 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)))))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all Xa Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,bit0(bit1(pls)))))))<->ti(X_a,Xa)!=zero_zero(X_a)|ti(X_a,Ya)!=zero_zero(X_a)))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all X Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(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),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(X_a)))))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all W (number_number_of(X_a,bit0(W))=plus_plus(X_a,plus_plus(X_a,zero_zero(X_a),number_number_of(X_a,W)),number_number_of(X_a,W))))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all W (number_number_of(X_a,bit1(W))=plus_plus(X_a,plus_plus(X_a,one_one(X_a),number_number_of(X_a,W)),number_number_of(X_a,W))))).
% 25.45/25.30 all X_a (number_semiring(X_a)->number_number_of(X_a,bit1(pls))=one_one(X_a)).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),m1),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))).
% 25.45/25.30 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)),hAPP(nat,X_a,power_power(X_a,number_number_of(X_a,bit0(bit1(pls)))),N))))).
% 25.45/25.30 number_number_of(int,bit0(bit1(pls)))=hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,bit0(bit1(pls)))).
% 25.45/25.30 number_number_of(int,bit1(bit1(pls)))=hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,bit1(bit1(pls)))).
% 25.45/25.30 all Xa Ya (plus_plus(real,hAPP(nat,real,power_power(real,Xa),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,real,power_power(real,Ya),number_number_of(nat,bit0(bit1(pls)))))=zero_zero(real)<->Xa=zero_zero(real)&Ya=zero_zero(real)).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all Na (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all N 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))->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))))))).
% 25.45/25.30 all X_a (power(X_a)&semiring_0(X_a)-> (all N ((N=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N)=one_one(X_a))& (N!=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N)=zero_zero(X_a))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all A_1 N N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_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(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_2)),hAPP(nat,X_a,power_power(X_a,A_1),N)))))))).
% 25.45/25.30 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)),plus_plus(X_a,one_one(X_a),one_one(X_a))))).
% 25.45/25.30 all P_1 K I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_1))-> (hBOOL(hAPP(int,bool,P_1,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,plus_plus(int,I,one_one(int)))))))->hBOOL(hAPP(int,bool,P_1,I_1))))).
% 25.45/25.30 zero_zero(int)=hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)).
% 25.45/25.30 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),tn)).
% 25.45/25.30 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))).
% 25.45/25.30 zero_zero(real)!=one_one(real).
% 25.45/25.30 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))).
% 25.45/25.30 all I_2 J_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,I_2,J_1)),I_2))).
% 25.45/25.30 all J_1 I_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,J_1,I_2)),I_2))).
% 25.45/25.30 all K_1 (number_number_of(int,K_1)=ti(int,K_1)).
% 25.45/25.30 all Ma Na (Ma!=Na<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma))).
% 25.45/25.30 all M N (plus_plus(nat,M,N)=plus_plus(nat,N,M)).
% 25.45/25.30 all X Y Z (plus_plus(nat,X,plus_plus(nat,Y,Z))=plus_plus(nat,Y,plus_plus(nat,X,Z))).
% 25.45/25.30 all M N K_1 (plus_plus(nat,plus_plus(nat,M,N),K_1)=plus_plus(nat,M,plus_plus(nat,N,K_1))).
% 25.45/25.30 all K Ma Na (plus_plus(nat,K,Ma)=plus_plus(nat,K,Na)<->Ma=Na).
% 25.45/25.30 all Ma K Na (plus_plus(nat,Ma,K)=plus_plus(nat,Na,K)<->Ma=Na).
% 25.45/25.30 all K Ma Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,K,Ma)),plus_plus(nat,K,Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))).
% 25.45/25.30 all X Y (X!=Y-> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X)))).
% 25.45/25.30 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))).
% 25.45/25.30 all N M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M))->M!=N).
% 25.45/25.30 all S_1 T_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S_1),T_2))->S_1!=T_2).
% 25.45/25.30 all M I_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),plus_plus(nat,J_1,M)))).
% 25.45/25.30 all M I_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),plus_plus(nat,M,J_1)))).
% 25.45/25.30 all K_1 I_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,I_2,K_1)),plus_plus(nat,J_1,K_1)))).
% 25.45/25.30 all K_1 L I_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,I_2,K_1)),plus_plus(nat,J_1,L))))).
% 25.45/25.30 all M N K_1 L (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L))-> (plus_plus(nat,M,L)=plus_plus(nat,K_1,N)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))).
% 25.45/25.30 all I_2 J_1 K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,I_2,J_1)),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1))).
% 25.45/25.30 all P_1 Ma Na ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma)))-> ((Ma=Na->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma)))-> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma))))).
% 25.45/25.30 all N (N!=zero_zero(nat)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))).
% 25.45/25.30 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))->N!=zero_zero(nat)).
% 25.45/25.30 all M N I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),I_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,I_2),M)),hAPP(nat,nat,power_power(nat,I_2),N)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))).
% 25.45/25.30 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))).
% 25.45/25.30 all Xa Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa))|Na=zero_zero(nat)).
% 25.45/25.30 all Ma Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),plus_plus(nat,Ma,Na)))<->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)),Na))).
% 25.45/25.30 all Na (Na!=zero_zero(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))).
% 25.45/25.30 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))).
% 25.45/25.30 all Xa Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na)))<->Na=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa))).
% 25.45/25.30 all Xa Ya (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya))).
% 25.45/25.30 all Xa Wa (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),number_number_of(nat,Wa))))<->number_number_of(nat,Wa)=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa))).
% 25.45/25.30 all Ma Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))).
% 25.45/25.30 all Va V_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,Va)),number_number_of(nat,V_3)))<-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Va),V_3))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_3)))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Va),V_3))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all X Y (ti(X_a,X)!=ti(X_a,Y)-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))).
% 25.45/25.30 all M N (plus_plus(nat,M,N)=M->N=zero_zero(nat)).
% 25.45/25.30 all Ma Na (plus_plus(nat,Ma,Na)=zero_zero(nat)<->Ma=zero_zero(nat)&Na=zero_zero(nat)).
% 25.45/25.30 all M (plus_plus(nat,M,zero_zero(nat))=M).
% 25.45/25.30 all N (plus_plus(nat,zero_zero(nat),N)=N).
% 25.45/25.30 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)))).
% 25.45/25.30 all X_a (semiring_char_0(X_a)-> (all Ma Na (hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)=hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)<->Ma=Na))).
% 25.45/25.30 all Xa Ya (hAPP(nat,int,semiring_1_of_nat(int),Xa)=hAPP(nat,int,semiring_1_of_nat(int),Ya)<->Xa=Ya).
% 25.45/25.30 all Xa Ya P_1 ((hBOOL(P_1)->hAPP(nat,int,semiring_1_of_nat(int),Xa)=hAPP(nat,int,semiring_1_of_nat(int),if(nat,P_1,Xa,Ya)))& (-hBOOL(P_1)->hAPP(nat,int,semiring_1_of_nat(int),Ya)=hAPP(nat,int,semiring_1_of_nat(int),if(nat,P_1,Xa,Ya)))).
% 25.45/25.30 all Va (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,Va)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Va))).
% 25.45/25.30 all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))).
% 25.45/25.30 all X_a (zero_ne_q_one(X_a)->one_one(X_a)!=zero_zero(X_a)).
% 25.45/25.30 all X_a (zero_ne_q_one(X_a)->zero_zero(X_a)!=one_one(X_a)).
% 25.45/25.30 all X_a (ring_11004092258visors(X_a)-> (all N A_1 (ti(X_a,A_1)!=zero_zero(X_a)->hAPP(nat,X_a,power_power(X_a,A_1),N)!=zero_zero(X_a)))).
% 25.45/25.30 all X_a (monoid_mult(X_a)-> (all N (hAPP(nat,X_a,power_power(X_a,one_one(X_a)),N)=one_one(X_a)))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all Ma Na (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all M N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))).
% 25.45/25.30 all X_a (semiring_1(X_a)-> (all M N (hAPP(nat,X_a,semiring_1_of_nat(X_a),plus_plus(nat,M,N))=plus_plus(X_a,hAPP(nat,X_a,semiring_1_of_nat(X_a),M),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))).
% 25.45/25.30 all X_a (semiring_1(X_a)->hAPP(nat,X_a,semiring_1_of_nat(X_a),one_one(nat))=one_one(X_a)).
% 25.45/25.30 all X_a (semiring_1(X_a)-> (all M N (hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,power_power(nat,M),N))=hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),N)))).
% 25.45/25.30 one_one(int)=hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)).
% 25.45/25.30 all X Y (plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X),hAPP(nat,int,semiring_1_of_nat(int),Y))=hAPP(nat,int,semiring_1_of_nat(int),plus_plus(nat,X,Y))).
% 25.45/25.30 all X N (hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X)),N)=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X),N))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all B_1 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_1),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),plus_plus(X_a,A_1,C))))))).
% 25.45/25.30 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)))).
% 25.45/25.30 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)))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all N 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)))))).
% 25.45/25.30 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),plus_plus(X_a,A_1,one_one(X_a)))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all Ma Na A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_2))-> (hAPP(nat,X_a,power_power(X_a,A_2),Ma)=hAPP(nat,X_a,power_power(X_a,A_2),Na)<->Ma=Na)))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all Xa Ya B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),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,B),Xa)),hAPP(nat,X_a,power_power(X_a,B),Ya)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all M N 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)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all A_1 N N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_2))-> (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)),hAPP(nat,X_a,power_power(X_a,A_1),N_2))))))).
% 25.45/25.30 all X_a (power(X_a)&mult_zero(X_a)&no_zero_divisors(X_a)&zero_ne_q_one(X_a)-> (all A_2 Na (hAPP(nat,X_a,power_power(X_a,A_2),Na)=zero_zero(X_a)<->ti(X_a,A_2)=zero_zero(X_a)&Na!=zero_zero(nat)))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all M (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),zero_zero(X_a)))))).
% 25.45/25.30 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)))).
% 25.45/25.30 all X_a (semiring_1(X_a)->hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat))=zero_zero(X_a)).
% 25.45/25.30 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,bit0(bit1(pls))))).
% 25.45/25.30 all K_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1))-> (exists N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))&ti(int,K_1)=hAPP(nat,int,semiring_1_of_nat(int),N_1)))).
% 25.45/25.30 all I_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))-> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2))&plus_plus(nat,I_2,K_2)=J_1))).
% 25.45/25.30 all Xa Na (hAPP(nat,nat,power_power(nat,Xa),Na)=one_one(nat)<->Xa=one_one(nat)|Na=zero_zero(nat)).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all X (hAPP(nat,X_a,power_power(X_a,X),zero_zero(nat))=one_one(X_a)))).
% 25.45/25.30 all X_a (linord219039673up_add(X_a)-> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),plus_plus(X_a,A_2,A_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))))).
% 25.45/25.30 all X_a (linord219039673up_add(X_a)-> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_2,A_2)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a)))))).
% 25.45/25.30 all X_a (ordere216010020id_add(X_a)-> (all B_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)),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),plus_plus(X_a,A_1,B_1))))))).
% 25.45/25.30 all X_a (ordere216010020id_add(X_a)-> (all B_1 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_1),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_1,B_1)),zero_zero(X_a))))))).
% 25.45/25.30 all X_a (zero(X_a)-> (all Xa (zero_zero(X_a)=ti(X_a,Xa)<->ti(X_a,Xa)=zero_zero(X_a)))).
% 25.45/25.30 all X_a (cancel_semigroup_add(X_a)-> (all B_1 A_1 C (plus_plus(X_a,B_1,A_1)=plus_plus(X_a,C,A_1)->ti(X_a,B_1)=ti(X_a,C)))).
% 25.45/25.30 all X_a (cancel146912293up_add(X_a)-> (all A_1 B_1 C (plus_plus(X_a,A_1,B_1)=plus_plus(X_a,A_1,C)->ti(X_a,B_1)=ti(X_a,C)))).
% 25.45/25.30 all X_a (cancel_semigroup_add(X_a)-> (all A_1 B_1 C (plus_plus(X_a,A_1,B_1)=plus_plus(X_a,A_1,C)->ti(X_a,B_1)=ti(X_a,C)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 B_1 C D_1 (plus_plus(X_a,plus_plus(X_a,A_1,B_1),plus_plus(X_a,C,D_1))=plus_plus(X_a,plus_plus(X_a,A_1,C),plus_plus(X_a,B_1,D_1))))).
% 25.45/25.30 all X_a (cancel_semigroup_add(X_a)-> (all B A_2 C_1 (plus_plus(X_a,B,A_2)=plus_plus(X_a,C_1,A_2)<->ti(X_a,B)=ti(X_a,C_1)))).
% 25.45/25.30 all X_a (cancel_semigroup_add(X_a)-> (all A_2 B C_1 (plus_plus(X_a,A_2,B)=plus_plus(X_a,A_2,C_1)<->ti(X_a,B)=ti(X_a,C_1)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 B_1 C (plus_plus(X_a,plus_plus(X_a,A_1,B_1),C)=plus_plus(X_a,plus_plus(X_a,A_1,C),B_1)))).
% 25.45/25.30 all X_a (ab_semigroup_add(X_a)-> (all A_1 B_1 C (plus_plus(X_a,plus_plus(X_a,A_1,B_1),C)=plus_plus(X_a,A_1,plus_plus(X_a,B_1,C))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 B_1 C (plus_plus(X_a,plus_plus(X_a,A_1,B_1),C)=plus_plus(X_a,A_1,plus_plus(X_a,B_1,C))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 C D_1 (plus_plus(X_a,A_1,plus_plus(X_a,C,D_1))=plus_plus(X_a,plus_plus(X_a,A_1,C),D_1)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 C D_1 (plus_plus(X_a,A_1,plus_plus(X_a,C,D_1))=plus_plus(X_a,C,plus_plus(X_a,A_1,D_1))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 C (plus_plus(X_a,A_1,C)=plus_plus(X_a,C,A_1)))).
% 25.45/25.30 all X_a (one(X_a)-> (all Xa (one_one(X_a)=ti(X_a,Xa)<->ti(X_a,Xa)=one_one(X_a)))).
% 25.45/25.30 all X_a (semiri456707255roduct(X_a)-> (all B A_2 (ti(X_a,B)=plus_plus(X_a,B,A_2)<->ti(X_a,A_2)=zero_zero(X_a)))).
% 25.45/25.30 all X_a (comm_monoid_add(X_a)-> (all A_1 (plus_plus(X_a,A_1,zero_zero(X_a))=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 (plus_plus(X_a,A_1,zero_zero(X_a))=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (monoid_add(X_a)-> (all A_1 (plus_plus(X_a,A_1,zero_zero(X_a))=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (linord219039673up_add(X_a)-> (all A_2 (zero_zero(X_a)=plus_plus(X_a,A_2,A_2)<->ti(X_a,A_2)=zero_zero(X_a)))).
% 25.45/25.30 all X_a (comm_monoid_add(X_a)-> (all A_1 (plus_plus(X_a,zero_zero(X_a),A_1)=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 (plus_plus(X_a,zero_zero(X_a),A_1)=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (monoid_add(X_a)-> (all A_1 (plus_plus(X_a,zero_zero(X_a),A_1)=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (ordere236663937imp_le(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,C,A_1)),plus_plus(X_a,C,B_1)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))))).
% 25.45/25.30 all X_a (ordere236663937imp_le(X_a)-> (all A_1 C B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_1,C)),plus_plus(X_a,B_1,C)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))))).
% 25.45/25.30 all X_a (ordere223160158up_add(X_a)-> (all C D_1 A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_1,C)),plus_plus(X_a,B_1,D_1))))))).
% 25.45/25.30 all X_a (ordere223160158up_add(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,C,A_1)),plus_plus(X_a,C,B_1)))))).
% 25.45/25.30 all X_a (ordere223160158up_add(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_1,C)),plus_plus(X_a,B_1,C)))))).
% 25.45/25.30 all X_a (ordere236663937imp_le(X_a)-> (all C_1 A_2 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,C_1,A_2)),plus_plus(X_a,C_1,B)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B))))).
% 25.45/25.30 all X_a (ordere236663937imp_le(X_a)-> (all A_2 C_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_2,C_1)),plus_plus(X_a,B,C_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all X (hAPP(nat,X_a,power_power(X_a,X),one_one(nat))=ti(X_a,X)))).
% 25.45/25.30 all Ma Na (hAPP(nat,nat,power_power(nat,Ma),Na)=zero_zero(nat)<->Na!=zero_zero(nat)&Ma=zero_zero(nat)).
% 25.45/25.30 all A_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))-> (exists X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1))&hAPP(nat,real,power_power(real,X_1),N)=A_1& (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1))&hAPP(nat,real,power_power(real,Y_1),N)=A_1->Y_1=X_1)))))).
% 25.45/25.30 all A_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))-> (exists R (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R))&hAPP(nat,real,power_power(real,R),N)=A_1)))).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),t)).
% 25.45/25.30 all V_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->plus_plus(nat,number_number_of(nat,V_1),one_one(nat))=one_one(nat))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->plus_plus(nat,number_number_of(nat,V_1),one_one(nat))=number_number_of(nat,succ(V_1)))).
% 25.45/25.30 all V_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->plus_plus(nat,one_one(nat),number_number_of(nat,V_1))=one_one(nat))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->plus_plus(nat,one_one(nat),number_number_of(nat,V_1))=number_number_of(nat,succ(V_1)))).
% 25.45/25.30 all A_1 B_1 (hAPP(nat,int,power_power(int,plus_plus(int,A_1,B_1)),number_number_of(nat,bit1(bit1(pls))))=plus_plus(int,plus_plus(int,plus_plus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit1(bit1(pls)))),times_times(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_1)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),A_1),hAPP(nat,int,power_power(int,B_1),number_number_of(nat,bit0(bit1(pls)))))),hAPP(nat,int,power_power(int,B_1),number_number_of(nat,bit1(bit1(pls)))))).
% 25.45/25.30 all A_1 B_1 (hAPP(nat,int,power_power(int,plus_plus(int,A_1,B_1)),number_number_of(nat,bit0(bit1(pls))))=plus_plus(int,plus_plus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),A_1),B_1)),hAPP(nat,int,power_power(int,B_1),number_number_of(nat,bit0(bit1(pls)))))).
% 25.45/25.30 tn=minus_minus(nat,nat_1(t),one_one(nat)).
% 25.45/25.30 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),minus_minus(nat,nat_1(t),one_one(nat)))).
% 25.45/25.30 all X_a (ordered_ab_group_add(X_a)-> (all A_2 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),minus_minus(X_a,A_2,B)),zero_zero(X_a)))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 B_1 (times_times(X_a,A_1,B_1)=times_times(X_a,B_1,A_1)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all Lx Rx Ry (times_times(X_a,Lx,times_times(X_a,Rx,Ry))=times_times(X_a,Rx,times_times(X_a,Lx,Ry))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all Lx Rx Ry (times_times(X_a,Lx,times_times(X_a,Rx,Ry))=times_times(X_a,times_times(X_a,Lx,Rx),Ry)))).
% 25.45/25.30 all X_a (ab_semigroup_mult(X_a)-> (all A_1 B_1 C (times_times(X_a,times_times(X_a,A_1,B_1),C)=times_times(X_a,A_1,times_times(X_a,B_1,C))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx (times_times(X_a,times_times(X_a,Lx,Ly),Rx)=times_times(X_a,Lx,times_times(X_a,Ly,Rx))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx (times_times(X_a,times_times(X_a,Lx,Ly),Rx)=times_times(X_a,times_times(X_a,Lx,Rx),Ly)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx Ry (times_times(X_a,times_times(X_a,Lx,Ly),times_times(X_a,Rx,Ry))=times_times(X_a,Lx,times_times(X_a,Ly,times_times(X_a,Rx,Ry)))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx Ry (times_times(X_a,times_times(X_a,Lx,Ly),times_times(X_a,Rx,Ry))=times_times(X_a,Rx,times_times(X_a,times_times(X_a,Lx,Ly),Ry))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx Ry (times_times(X_a,times_times(X_a,Lx,Ly),times_times(X_a,Rx,Ry))=times_times(X_a,times_times(X_a,Lx,Rx),times_times(X_a,Ly,Ry))))).
% 25.45/25.30 all X_a (ab_group_add(X_a)-> (all A_2 B C_1 D (minus_minus(X_a,A_2,B)=minus_minus(X_a,C_1,D)-> (ti(X_a,A_2)=ti(X_a,B)<->ti(X_a,C_1)=ti(X_a,D))))).
% 25.45/25.30 all X_a (ordered_ab_group_add(X_a)-> (all A_2 B C_1 D (minus_minus(X_a,A_2,B)=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_2),B))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),D)))))).
% 25.45/25.30 all X_a (number_semiring(X_a)-> (all V_2 V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_2))->times_times(X_a,number_number_of(X_a,V_1),number_number_of(X_a,V_2))=number_number_of(X_a,times_times(int,V_1,V_2)))))).
% 25.45/25.30 all W hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),W)).
% 25.45/25.30 all Z W (times_times(int,Z,W)=times_times(int,W,Z)).
% 25.45/25.30 all Z W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),W))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z))).
% 25.45/25.30 all Z1 Z2 Z3 (times_times(int,times_times(int,Z1,Z2),Z3)=times_times(int,Z1,times_times(int,Z2,Z3))).
% 25.45/25.30 all K_1 I_2 J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),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_2),K_1)))).
% 25.45/25.30 all Z W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),W))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z))->ti(int,Z)=ti(int,W))).
% 25.45/25.30 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Xa Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,Xa)),number_number_of(X_a,Ya)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),Ya))))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all V_1 W (number_number_of(X_a,times_times(int,V_1,W))=times_times(X_a,number_number_of(X_a,V_1),number_number_of(X_a,W))))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all V_1 W (times_times(X_a,number_number_of(X_a,V_1),number_number_of(X_a,W))=number_number_of(X_a,times_times(int,V_1,W))))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all V_1 W Z (times_times(X_a,number_number_of(X_a,V_1),times_times(X_a,number_number_of(X_a,W),Z))=times_times(X_a,number_number_of(X_a,times_times(int,V_1,W)),Z)))).
% 25.45/25.30 all Z_3 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_e_q(int),zero_zero(int)),Z_3))-> (nat_1(Z_1)=nat_1(Z_3)<->ti(int,Z_1)=ti(int,Z_3)))).
% 25.45/25.30 all X_b (number(X_b)&ring(X_b)-> (all V_1 B_1 C (times_times(X_b,number_number_of(X_b,V_1),minus_minus(X_b,B_1,C))=minus_minus(X_b,times_times(X_b,number_number_of(X_b,V_1),B_1),times_times(X_b,number_number_of(X_b,V_1),C))))).
% 25.45/25.30 all X_b (number(X_b)&ring(X_b)-> (all A_1 B_1 V_1 (times_times(X_b,minus_minus(X_b,A_1,B_1),number_number_of(X_b,V_1))=minus_minus(X_b,times_times(X_b,A_1,number_number_of(X_b,V_1)),times_times(X_b,B_1,number_number_of(X_b,V_1)))))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all V_1 W (number_number_of(X_a,minus_minus(int,V_1,W))=minus_minus(X_a,number_number_of(X_a,V_1),number_number_of(X_a,W))))).
% 25.45/25.30 all X_a (semiring_1(X_a)-> (all M N (hAPP(nat,X_a,semiring_1_of_nat(X_a),times_times(nat,M,N))=times_times(X_a,hAPP(nat,X_a,semiring_1_of_nat(X_a),M),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all Ma Na (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))))).
% 25.45/25.30 all I_2 J_1 K_1 (minus_minus(nat,minus_minus(nat,I_2,J_1),K_1)=minus_minus(nat,minus_minus(nat,I_2,K_1),J_1)).
% 25.45/25.30 all Xa Ya P_1 ((hBOOL(P_1)->nat_1(Xa)=nat_1(if(int,P_1,Xa,Ya)))& (-hBOOL(P_1)->nat_1(Ya)=nat_1(if(int,P_1,Xa,Ya)))).
% 25.45/25.30 all X_a (ordere453448008miring(X_a)-> (all B_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),B_1),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_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_1,B_1)),zero_zero(X_a)))))).
% 25.45/25.30 all X_a (ordered_ring(X_a)-> (all B_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)),B_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_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)),times_times(X_a,A_1,B_1)))))).
% 25.45/25.30 all X_a (ordered_semiring(X_a)-> (all C D_1 A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_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),times_times(X_a,A_1,C)),times_times(X_a,B_1,D_1))))))))).
% 25.45/25.30 all X_a (ordered_semiring(X_a)-> (all C D_1 A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_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)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_1,C)),times_times(X_a,B_1,D_1))))))))).
% 25.45/25.30 all X_a (ordered_ring(X_a)-> (all C B_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_1),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),times_times(X_a,C,A_1)),times_times(X_a,C,B_1))))))).
% 25.45/25.30 all X_a (ordered_ring(X_a)-> (all C B_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_1),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),times_times(X_a,A_1,C)),times_times(X_a,B_1,C))))))).
% 25.45/25.30 all X_a (ordere1490568538miring(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B_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),times_times(X_a,C,A_1)),times_times(X_a,C,B_1))))))).
% 25.45/25.30 all X_a (ordered_semiring(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B_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),times_times(X_a,C,A_1)),times_times(X_a,C,B_1))))))).
% 25.45/25.30 all X_a (ordered_semiring(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B_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),times_times(X_a,A_1,C)),times_times(X_a,B_1,C))))))).
% 25.45/25.30 all X_a (ordered_ring(X_a)-> (all B_1 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_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)),times_times(X_a,A_1,B_1))))))).
% 25.45/25.30 all X_a (ordere453448008miring(X_a)-> (all B_1 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_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_1,B_1)),zero_zero(X_a))))))).
% 25.45/25.30 all X_a (ordere453448008miring(X_a)-> (all B_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),B_1),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,B_1,A_1)),zero_zero(X_a))))))).
% 25.45/25.30 all X_a (ordere453448008miring(X_a)-> (all B_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),B_1),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_1,B_1)),zero_zero(X_a))))))).
% 25.45/25.30 all Ya Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Ya))-> (nat_1(Xa)=nat_1(Ya)<->ti(int,Xa)=ti(int,Ya)))).
% 25.45/25.30 all Y X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))-> (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)),times_times(int,X,Y))))).
% 25.45/25.30 all X_a (ordere453448008miring(X_a)-> (all B_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)),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),times_times(X_a,A_1,B_1))))))).
% 25.45/25.30 all X_a (ordered_ring(X_a)-> (all A_2 E_1 C_1 B D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)),plus_plus(X_a,times_times(X_a,B,E_1),D)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,times_times(X_a,minus_minus(X_a,A_2,B),E_1),C_1)),D))))).
% 25.45/25.30 all X_a (ring(X_a)-> (all A_2 E_1 C_1 B D (plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)=plus_plus(X_a,times_times(X_a,B,E_1),D)<->plus_plus(X_a,times_times(X_a,minus_minus(X_a,A_2,B),E_1),C_1)=ti(X_a,D)))).
% 25.45/25.30 all X_a (ordered_ring(X_a)-> (all A_2 E_1 C_1 B D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)),plus_plus(X_a,times_times(X_a,B,E_1),D)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),plus_plus(X_a,times_times(X_a,minus_minus(X_a,B,A_2),E_1),D)))))).
% 25.45/25.30 all X_a (ring(X_a)-> (all A_2 E_1 C_1 B D (plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)=plus_plus(X_a,times_times(X_a,B,E_1),D)<->ti(X_a,C_1)=plus_plus(X_a,times_times(X_a,minus_minus(X_a,B,A_2),E_1),D)))).
% 25.45/25.30 all X_a (ring(X_a)-> (all X Y A_1 B_1 (minus_minus(X_a,times_times(X_a,X,Y),times_times(X_a,A_1,B_1))=plus_plus(X_a,times_times(X_a,X,minus_minus(X_a,Y,B_1)),times_times(X_a,minus_minus(X_a,X,A_1),B_1))))).
% 25.45/25.30 all X_a (linord581940658strict(X_a)-> (all A_2 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_2,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)),A_2))&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_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))))).
% 25.45/25.30 all X_a (linord581940658strict(X_a)-> (all A_2 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),times_times(X_a,A_2,B)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_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),A_2),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)))))).
% 25.45/25.30 all P_1 ((all X1 hBOOL(hAPP(nat,bool,P_1,X1)))<-> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))->hBOOL(hAPP(nat,bool,P_1,nat_1(X_1)))))).
% 25.45/25.30 all P_1 ((exists X1 hBOOL(hAPP(nat,bool,P_1,X1)))<-> (exists X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))&hBOOL(hAPP(nat,bool,P_1,nat_1(X_1)))))).
% 25.45/25.30 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)),times_times(X_a,A_1,A_1))))).
% 25.45/25.30 all X_a (ordered_ring(X_a)-> (all A_2 E_1 C_1 B D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)),plus_plus(X_a,times_times(X_a,B,E_1),D)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,times_times(X_a,minus_minus(X_a,A_2,B),E_1),C_1)),D))))).
% 25.45/25.30 all X_a (ordered_ring(X_a)-> (all A_2 E_1 C_1 B D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)),plus_plus(X_a,times_times(X_a,B,E_1),D)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),plus_plus(X_a,times_times(X_a,minus_minus(X_a,B,A_2),E_1),D)))))).
% 25.45/25.30 all X_a (ring_1(X_a)-> (all X (minus_minus(X_a,times_times(X_a,X,X),one_one(X_a))=times_times(X_a,plus_plus(X_a,X,one_one(X_a)),minus_minus(X_a,X,one_one(X_a)))))).
% 25.45/25.30 all X_a (linord20386208strict(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,C,A_1)),times_times(X_a,C,B_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_e_q(X_a),A_1),B_1)))))).
% 25.45/25.30 all X_a (linord20386208strict(X_a)-> (all A_1 C B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_1,C)),times_times(X_a,B_1,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_1)))))).
% 25.45/25.30 all X_a (linord20386208strict(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,C,A_1)),times_times(X_a,C,B_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),A_1),B_1)))))).
% 25.45/25.30 all X_a (linordered_semiring(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,C,A_1)),times_times(X_a,C,B_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),A_1),B_1)))))).
% 25.45/25.30 all X_a (linord20386208strict(X_a)-> (all A_1 C B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_1,C)),times_times(X_a,B_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(X_a),A_1),B_1)))))).
% 25.45/25.30 all X_a (linordered_semiring(X_a)-> (all A_1 C B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_1,C)),times_times(X_a,B_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(X_a),A_1),B_1)))))).
% 25.45/25.30 all X_a (linord20386208strict(X_a)-> (all C D_1 A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_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)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_1,C)),times_times(X_a,B_1,D_1))))))))).
% 25.45/25.30 all X_a (linord20386208strict(X_a)-> (all C D_1 A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_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)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_1,C)),times_times(X_a,B_1,D_1))))))))).
% 25.45/25.30 all X_a (linord20386208strict(X_a)-> (all C D_1 A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_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)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_1,C)),times_times(X_a,B_1,D_1))))))))).
% 25.45/25.30 all X_a (linord20386208strict(X_a)-> (all C D_1 A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_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),times_times(X_a,A_1,C)),times_times(X_a,B_1,D_1))))))))).
% 25.45/25.30 all X_a (linord581940658strict(X_a)-> (all A_2 B 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),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_2)))))).
% 25.45/25.30 all X_a (linord581940658strict(X_a)-> (all A_2 B 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),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B)))))).
% 25.45/25.30 all X_a (linordered_ring(X_a)-> (all X Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),plus_plus(X_a,times_times(X_a,X,X),times_times(X_a,Y,Y)))))).
% 25.45/25.30 all X_a (linord581940658strict(X_a)-> (all Xa Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,times_times(X_a,Xa,Xa),times_times(X_a,Ya,Ya))),zero_zero(X_a)))<->ti(X_a,Xa)=zero_zero(X_a)&ti(X_a,Ya)=zero_zero(X_a)))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all Y 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))-> (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),times_times(X_a,X,Y)),X))))))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all Y 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))-> (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),times_times(X_a,Y,X)),X))))))).
% 25.45/25.30 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),zero_zero(int)))->nat_1(Z)=zero_zero(nat)).
% 25.45/25.30 all I_1 (nat_1(I_1)=zero_zero(nat)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),zero_zero(int)))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all A_1 N N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),N_2))-> (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)),hAPP(nat,X_a,power_power(X_a,A_1),N_2))))))).
% 25.45/25.30 all Z ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))->hAPP(nat,int,semiring_1_of_nat(int),nat_1(Z))=ti(int,Z))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))->hAPP(nat,int,semiring_1_of_nat(int),nat_1(Z))=zero_zero(int))).
% 25.45/25.30 all Ma Z_1 (hAPP(nat,int,semiring_1_of_nat(int),Ma)=ti(int,Z_1)<->Ma=nat_1(Z_1)&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1))).
% 25.45/25.30 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))->hAPP(nat,int,semiring_1_of_nat(int),nat_1(Z))=ti(int,Z)).
% 25.45/25.30 all X_a (group_add(X_a)-> (all A_2 B (minus_minus(X_a,A_2,B)=zero_zero(X_a)<->ti(X_a,A_2)=ti(X_a,B)))).
% 25.45/25.30 all X_a (ab_group_add(X_a)-> (all A_2 B (ti(X_a,A_2)=ti(X_a,B)<->minus_minus(X_a,A_2,B)=zero_zero(X_a)))).
% 25.45/25.30 all X_a (group_add(X_a)-> (all A_1 (minus_minus(X_a,A_1,A_1)=zero_zero(X_a)))).
% 25.45/25.30 all X_a (group_add(X_a)-> (all A_1 (minus_minus(X_a,A_1,zero_zero(X_a))=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (ordered_ab_group_add(X_a)-> (all A_2 B C_1 D (minus_minus(X_a,A_2,B)=minus_minus(X_a,C_1,D)-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D)))))).
% 25.45/25.30 all X_a (ab_group_add(X_a)-> (all A_1 C B_1 D_1 (minus_minus(X_a,plus_plus(X_a,A_1,C),plus_plus(X_a,B_1,D_1))=plus_plus(X_a,minus_minus(X_a,A_1,B_1),minus_minus(X_a,C,D_1))))).
% 25.45/25.30 all X_a (group_add(X_a)-> (all A_1 B_1 (minus_minus(X_a,plus_plus(X_a,A_1,B_1),B_1)=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (group_add(X_a)-> (all A_1 B_1 (plus_plus(X_a,minus_minus(X_a,A_1,B_1),B_1)=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (mult_zero(X_a)-> (all A_1 (times_times(X_a,zero_zero(X_a),A_1)=zero_zero(X_a)))).
% 25.45/25.30 all X_a (mult_zero(X_a)-> (all A_1 (times_times(X_a,A_1,zero_zero(X_a))=zero_zero(X_a)))).
% 25.45/25.30 all X_a (ring_n68954251visors(X_a)-> (all A_2 B (times_times(X_a,A_2,B)=zero_zero(X_a)<->ti(X_a,A_2)=zero_zero(X_a)|ti(X_a,B)=zero_zero(X_a)))).
% 25.45/25.30 all X_a (no_zero_divisors(X_a)-> (all B_1 A_1 (ti(X_a,A_1)!=zero_zero(X_a)-> (ti(X_a,B_1)!=zero_zero(X_a)->times_times(X_a,A_1,B_1)!=zero_zero(X_a))))).
% 25.45/25.30 all X_a (no_zero_divisors(X_a)-> (all A_1 B_1 (times_times(X_a,A_1,B_1)=zero_zero(X_a)->ti(X_a,A_1)=zero_zero(X_a)|ti(X_a,B_1)=zero_zero(X_a)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 (times_times(X_a,A_1,zero_zero(X_a))=zero_zero(X_a)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 (times_times(X_a,zero_zero(X_a),A_1)=zero_zero(X_a)))).
% 25.45/25.30 all M N (minus_minus(nat,M,N)=zero_zero(nat)-> (minus_minus(nat,N,M)=zero_zero(nat)->M=N)).
% 25.45/25.30 all M (minus_minus(nat,M,M)=zero_zero(nat)).
% 25.45/25.30 all M (minus_minus(nat,M,zero_zero(nat))=M).
% 25.45/25.30 all N (minus_minus(nat,zero_zero(nat),N)=zero_zero(nat)).
% 25.45/25.30 all X_a (comm_semiring(X_a)-> (all A_1 B_1 C (times_times(X_a,plus_plus(X_a,A_1,B_1),C)=plus_plus(X_a,times_times(X_a,A_1,C),times_times(X_a,B_1,C))))).
% 25.45/25.30 all X_a (semiring(X_a)-> (all A_1 E B_1 C (plus_plus(X_a,times_times(X_a,A_1,E),plus_plus(X_a,times_times(X_a,B_1,E),C))=plus_plus(X_a,times_times(X_a,plus_plus(X_a,A_1,B_1),E),C)))).
% 25.45/25.30 all X_a (semiri456707255roduct(X_a)-> (all Wa Ya Xa Z_1 (plus_plus(X_a,times_times(X_a,Wa,Ya),times_times(X_a,Xa,Z_1))=plus_plus(X_a,times_times(X_a,Wa,Z_1),times_times(X_a,Xa,Ya))<->ti(X_a,Wa)=ti(X_a,Xa)|ti(X_a,Ya)=ti(X_a,Z_1)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 M B_1 (plus_plus(X_a,times_times(X_a,A_1,M),times_times(X_a,B_1,M))=times_times(X_a,plus_plus(X_a,A_1,B_1),M)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 B_1 C (times_times(X_a,plus_plus(X_a,A_1,B_1),C)=plus_plus(X_a,times_times(X_a,A_1,C),times_times(X_a,B_1,C))))).
% 25.45/25.30 all X_a (semiri456707255roduct(X_a)-> (all C_1 D A_2 B (ti(X_a,A_2)!=ti(X_a,B)&ti(X_a,C_1)!=ti(X_a,D)<->plus_plus(X_a,times_times(X_a,A_2,C_1),times_times(X_a,B,D))!=plus_plus(X_a,times_times(X_a,A_2,D),times_times(X_a,B,C_1))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all X Y Z (times_times(X_a,X,plus_plus(X_a,Y,Z))=plus_plus(X_a,times_times(X_a,X,Y),times_times(X_a,X,Z))))).
% 25.45/25.30 all N (nat_1(hAPP(nat,int,semiring_1_of_nat(int),N))=N).
% 25.45/25.30 all X_a (comm_monoid_mult(X_a)-> (all A_1 (times_times(X_a,A_1,one_one(X_a))=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 (times_times(X_a,A_1,one_one(X_a))=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (monoid_mult(X_a)-> (all A_1 (times_times(X_a,A_1,one_one(X_a))=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (comm_monoid_mult(X_a)-> (all A_1 (times_times(X_a,one_one(X_a),A_1)=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 (times_times(X_a,one_one(X_a),A_1)=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (monoid_mult(X_a)-> (all A_1 (times_times(X_a,one_one(X_a),A_1)=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (ordere236663937imp_le(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,C,A_1)),plus_plus(X_a,C,B_1)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B_1))))).
% 25.45/25.30 all X_a (ordere236663937imp_le(X_a)-> (all A_1 C B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,A_1,C)),plus_plus(X_a,B_1,C)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B_1))))).
% 25.45/25.30 all X_a (ordere779506340up_add(X_a)-> (all C D_1 A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,A_1,C)),plus_plus(X_a,B_1,D_1))))))).
% 25.45/25.30 all X_a (ordere779506340up_add(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,C,A_1)),plus_plus(X_a,C,B_1)))))).
% 25.45/25.30 all X_a (ordere779506340up_add(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,A_1,C)),plus_plus(X_a,B_1,C)))))).
% 25.45/25.30 all X_a (ordere236663937imp_le(X_a)-> (all C_1 A_2 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,C_1,A_2)),plus_plus(X_a,C_1,B)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B))))).
% 25.45/25.30 all X_a (ordere236663937imp_le(X_a)-> (all A_2 C_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,A_2,C_1)),plus_plus(X_a,B,C_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B))))).
% 25.45/25.30 all N 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),minus_minus(nat,J_1,N)),K_1))).
% 25.45/25.30 all L M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),minus_minus(nat,L,N)),minus_minus(nat,L,M))))).
% 25.45/25.30 all X_a (monoid_mult(X_a)-> (all A_1 N (times_times(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N),A_1)=times_times(X_a,A_1,hAPP(nat,X_a,power_power(X_a,A_1),N))))).
% 25.45/25.30 all X_a (comm_monoid_mult(X_a)-> (all A_1 B_1 N (hAPP(nat,X_a,power_power(X_a,times_times(X_a,A_1,B_1)),N)=times_times(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N),hAPP(nat,X_a,power_power(X_a,B_1),N))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all X Y Q (hAPP(nat,X_a,power_power(X_a,times_times(X_a,X,Y)),Q)=times_times(X_a,hAPP(nat,X_a,power_power(X_a,X),Q),hAPP(nat,X_a,power_power(X_a,Y),Q))))).
% 25.45/25.30 all M N (minus_minus(nat,plus_plus(nat,M,N),N)=M).
% 25.45/25.30 all N M (minus_minus(nat,plus_plus(nat,N,M),N)=M).
% 25.45/25.30 all I_2 J_1 K_1 (minus_minus(nat,minus_minus(nat,I_2,J_1),K_1)=minus_minus(nat,I_2,plus_plus(nat,J_1,K_1))).
% 25.45/25.30 all K_1 M N (minus_minus(nat,plus_plus(nat,K_1,M),plus_plus(nat,K_1,N))=minus_minus(nat,M,N)).
% 25.45/25.30 all M K_1 N (minus_minus(nat,plus_plus(nat,M,K_1),plus_plus(nat,N,K_1))=minus_minus(nat,M,N)).
% 25.45/25.30 all W (times_times(int,pls,W)=pls).
% 25.45/25.30 all K_1 L (times_times(int,bit0(K_1),L)=bit0(times_times(int,K_1,L))).
% 25.45/25.30 all K L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit1(L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L_1))).
% 25.45/25.30 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))).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),pls)).
% 25.45/25.30 all K L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit0(L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L_1))).
% 25.45/25.30 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))).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),zero_zero(int))).
% 25.45/25.30 all Z (times_times(int,one_one(int),Z)=ti(int,Z)).
% 25.45/25.30 all Z (times_times(int,Z,one_one(int))=ti(int,Z)).
% 25.45/25.30 all Z_1 Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),Wa))&ti(int,Z_1)!=ti(int,Wa)).
% 25.45/25.30 all W Z1 Z2 (times_times(int,W,plus_plus(int,Z1,Z2))=plus_plus(int,times_times(int,W,Z1),times_times(int,W,Z2))).
% 25.45/25.30 all Z1 Z2 W (times_times(int,plus_plus(int,Z1,Z2),W)=plus_plus(int,times_times(int,Z1,W),times_times(int,Z2,W))).
% 25.45/25.30 all K_1 I_2 J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),J_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),plus_plus(int,K_1,I_2)),plus_plus(int,K_1,J_1)))).
% 25.45/25.30 all V_1 W (times_times(int,number_number_of(int,V_1),number_number_of(int,W))=number_number_of(int,times_times(int,V_1,W))).
% 25.45/25.30 all K L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,K)),number_number_of(int,L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L_1))).
% 25.45/25.30 all X_a (linord1278240602ring_1(X_a)-> (all V_1 U_1 Y X A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),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_1))-> (plus_plus(X_a,U_1,V_1)=one_one(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,times_times(X_a,U_1,X),times_times(X_a,V_1,Y))),A_1))))))))).
% 25.45/25.30 all Ya Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Ya))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(Xa)),nat_1(Ya)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),Ya))))).
% 25.45/25.30 all Z_1 Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(Wa)),nat_1(Z_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1)))).
% 25.45/25.30 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Ya (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,Ya)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),Ya))))).
% 25.45/25.30 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,Xa)),zero_zero(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),pls))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all A_1 N N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),N_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),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_2)),hAPP(nat,X_a,power_power(X_a,A_1),N)))))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all Xa Ya B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B))-> (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),Xa)),hAPP(nat,X_a,power_power(X_a,B),Ya)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Xa),Ya)))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all M N 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)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N)))))).
% 25.45/25.30 all Ma Wa (Ma=nat_1(Wa)<-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa))->ti(int,Wa)=hAPP(nat,int,semiring_1_of_nat(int),Ma))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa))->Ma=zero_zero(nat))).
% 25.45/25.30 all Wa Ma (nat_1(Wa)=Ma<-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa))->ti(int,Wa)=hAPP(nat,int,semiring_1_of_nat(int),Ma))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa))->Ma=zero_zero(nat))).
% 25.45/25.30 all Y X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))->plus_plus(nat,nat_1(X),nat_1(Y))=nat_1(plus_plus(int,X,Y)))).
% 25.45/25.30 all Z_2 Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_2))->nat_1(plus_plus(int,Z,Z_2))=plus_plus(nat,nat_1(Z),nat_1(Z_2)))).
% 25.45/25.30 all Ma Va (hAPP(nat,int,semiring_1_of_nat(int),Ma)=number_number_of(int,Va)<->Ma=nat_1(number_number_of(int,Va))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,Va)))).
% 25.45/25.30 all N X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))->hAPP(nat,nat,power_power(nat,nat_1(X)),N)=nat_1(hAPP(nat,int,power_power(int,X),N))).
% 25.45/25.30 all N Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))->nat_1(hAPP(nat,int,power_power(int,Z),N))=hAPP(nat,nat,power_power(nat,nat_1(Z)),N)).
% 25.45/25.30 all X_a (linord626643107strict(X_a)-> (all V_1 U_1 Y X A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),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_1))-> (plus_plus(X_a,U_1,V_1)=one_one(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,times_times(X_a,U_1,X),times_times(X_a,V_1,Y))),A_1))))))))).
% 25.45/25.30 all Ma Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(Wa)),Ma))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),hAPP(nat,int,semiring_1_of_nat(int),Ma))))).
% 25.45/25.30 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Ya (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,Ya)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(pls)),Ya))))).
% 25.45/25.30 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,Xa)),one_one(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),bit1(pls)))))).
% 25.45/25.30 all X_a (monoid_mult(X_a)-> (all X N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))->times_times(X_a,hAPP(nat,X_a,power_power(X_a,X),minus_minus(nat,N,one_one(nat))),X)=hAPP(nat,X_a,power_power(X_a,X),N)))).
% 25.45/25.30 all X_a (ordered_ab_group_add(X_a)-> (all A_2 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),minus_minus(X_a,A_2,B)),zero_zero(X_a)))))).
% 25.45/25.30 zero_zero(nat)=nat_1(zero_zero(int)).
% 25.45/25.30 nat_1(zero_zero(int))=zero_zero(nat).
% 25.45/25.30 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),times_times(X_a,A_1,A_1)),zero_zero(X_a)))))).
% 25.45/25.30 all X_a (linord581940658strict(X_a)-> (all A_2 C_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_2,C_1)),times_times(X_a,B,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_2),B))|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),A_2))))).
% 25.45/25.30 all X_a (linord581940658strict(X_a)-> (all C_1 A_2 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))<->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_2),B))|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),A_2))))).
% 25.45/25.30 all X_a (linord581940658strict(X_a)-> (all A_2 B 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),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B)))))).
% 25.45/25.30 all X_a (linord20386208strict(X_a)-> (all B_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)),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),times_times(X_a,A_1,B_1))))))).
% 25.45/25.30 all X_a (linord20386208strict(X_a)-> (all B_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),B_1),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_1,B_1)),zero_zero(X_a))))))).
% 25.45/25.30 all X_a (linord20386208strict(X_a)-> (all B_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),B_1),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,B_1,A_1)),zero_zero(X_a))))))).
% 25.45/25.30 all X_a (linord20386208strict(X_a)-> (all A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),times_times(X_a,A_1,B_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_1)))))).
% 25.45/25.30 all X_a (linord20386208strict(X_a)-> (all B_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),times_times(X_a,B_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)),B_1)))))).
% 25.45/25.30 all X_a (linord581940658strict(X_a)-> (all A_2 B 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),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_2)))))).
% 25.45/25.30 all X_a (linord20386208strict(X_a)-> (all B_1 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_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_1,B_1)),zero_zero(X_a))))))).
% 25.45/25.30 all X_a (linord581940658strict(X_a)-> (all B_1 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_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)),times_times(X_a,A_1,B_1))))))).
% 25.45/25.30 all X_a (linord20386208strict(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_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),times_times(X_a,A_1,C)),times_times(X_a,B_1,C))))))).
% 25.45/25.30 all X_a (linord20386208strict(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_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),times_times(X_a,C,A_1)),times_times(X_a,C,B_1))))))).
% 25.45/25.30 all X_a (linord893533164strict(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_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),times_times(X_a,C,A_1)),times_times(X_a,C,B_1))))))).
% 25.45/25.30 all X_a (linord581940658strict(X_a)-> (all C B_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),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),times_times(X_a,A_1,C)),times_times(X_a,B_1,C))))))).
% 25.45/25.30 all X_a (linord581940658strict(X_a)-> (all C B_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),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),times_times(X_a,C,A_1)),times_times(X_a,C,B_1))))))).
% 25.45/25.30 all W (nat_1(number_number_of(int,W))=number_number_of(nat,W)).
% 25.45/25.30 all V_1 (number_number_of(nat,V_1)=nat_1(number_number_of(int,V_1))).
% 25.45/25.30 all X_a (linord581940658strict(X_a)-> (all Xa Ya (plus_plus(X_a,times_times(X_a,Xa,Xa),times_times(X_a,Ya,Ya))=zero_zero(X_a)<->ti(X_a,Xa)=zero_zero(X_a)&ti(X_a,Ya)=zero_zero(X_a)))).
% 25.45/25.30 all X_a (semiri456707255roduct(X_a)-> (all C D_1 A_1 B_1 R_1 (ti(X_a,R_1)!=zero_zero(X_a)-> (ti(X_a,A_1)=ti(X_a,B_1)&ti(X_a,C)!=ti(X_a,D_1)->plus_plus(X_a,A_1,times_times(X_a,R_1,C))!=plus_plus(X_a,B_1,times_times(X_a,R_1,D_1)))))).
% 25.45/25.30 one_one(nat)=nat_1(one_one(int)).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all N 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))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),times_times(X_a,M,N))))))).
% 25.45/25.30 all X_a (linord219039673up_add(X_a)-> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),plus_plus(X_a,A_2,A_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_2))))).
% 25.45/25.30 all X_a (linord219039673up_add(X_a)-> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,A_2,A_2)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),zero_zero(X_a)))))).
% 25.45/25.30 all X_a (ordere216010020id_add(X_a)-> (all B_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)),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),plus_plus(X_a,A_1,B_1))))))).
% 25.45/25.30 all X_a (ordere216010020id_add(X_a)-> (all Ya Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Xa))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Ya))-> (plus_plus(X_a,Xa,Ya)=zero_zero(X_a)<->ti(X_a,Xa)=zero_zero(X_a)&ti(X_a,Ya)=zero_zero(X_a)))))).
% 25.45/25.30 all X_a (ordere216010020id_add(X_a)-> (all B_1 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_1),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_1),plus_plus(X_a,A_1,C))))))).
% 25.45/25.30 all X_a (ordere216010020id_add(X_a)-> (all B_1 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_1),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_1),plus_plus(X_a,A_1,C))))))).
% 25.45/25.30 all X_a (ordere216010020id_add(X_a)-> (all B_1 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_1),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,A_1,B_1)),zero_zero(X_a))))))).
% 25.45/25.30 all X_a (ordere223160158up_add(X_a)-> (all C D_1 A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_1,C)),plus_plus(X_a,B_1,D_1))))))).
% 25.45/25.30 all X_a (ordere223160158up_add(X_a)-> (all C D_1 A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_1,C)),plus_plus(X_a,B_1,D_1))))))).
% 25.45/25.30 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)))).
% 25.45/25.30 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)))).
% 25.45/25.30 all X_b (number(X_b)&semiring(X_b)-> (all V_1 B_1 C (times_times(X_b,number_number_of(X_b,V_1),plus_plus(X_b,B_1,C))=plus_plus(X_b,times_times(X_b,number_number_of(X_b,V_1),B_1),times_times(X_b,number_number_of(X_b,V_1),C))))).
% 25.45/25.30 all X_b (number(X_b)&semiring(X_b)-> (all A_1 B_1 V_1 (times_times(X_b,plus_plus(X_b,A_1,B_1),number_number_of(X_b,V_1))=plus_plus(X_b,times_times(X_b,A_1,number_number_of(X_b,V_1)),times_times(X_b,B_1,number_number_of(X_b,V_1)))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all M (plus_plus(X_a,M,M)=times_times(X_a,plus_plus(X_a,one_one(X_a),one_one(X_a)),M)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all M A_1 (plus_plus(X_a,M,times_times(X_a,A_1,M))=times_times(X_a,plus_plus(X_a,A_1,one_one(X_a)),M)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 M (plus_plus(X_a,times_times(X_a,A_1,M),M)=times_times(X_a,plus_plus(X_a,A_1,one_one(X_a)),M)))).
% 25.45/25.30 all X_a (number(X_a)&linorder(X_a)-> (all Va Wa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,Va)),number_number_of(X_a,Wa)))<-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Wa)),number_number_of(X_a,Va)))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all N 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)))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all N A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B_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),hAPP(nat,X_a,power_power(X_a,A_1),N)),hAPP(nat,X_a,power_power(X_a,B_1),N))))))).
% 25.45/25.30 all Na Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),minus_minus(nat,Na,Ma)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))).
% 25.45/25.30 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))-> (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),minus_minus(nat,M,N)),M)))).
% 25.45/25.30 all N M (minus_minus(nat,N,plus_plus(nat,N,M))=zero_zero(nat)).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all N 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)))))).
% 25.45/25.30 all I_1 J K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),minus_minus(nat,J,K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,I_1,K)),J))).
% 25.45/25.30 all M N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))->plus_plus(nat,N,minus_minus(nat,M,N))=M).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all M 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,semiring_1_of_nat(X_a),M))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all N 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,semiring_1_of_nat(X_a),N))))).
% 25.45/25.30 all X_a (monoid_mult(X_a)-> (all A_1 M N (hAPP(nat,X_a,power_power(X_a,A_1),plus_plus(nat,M,N))=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))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all X P_2 Q (times_times(X_a,hAPP(nat,X_a,power_power(X_a,X),P_2),hAPP(nat,X_a,power_power(X_a,X),Q))=hAPP(nat,X_a,power_power(X_a,X),plus_plus(nat,P_2,Q))))).
% 25.45/25.30 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))).
% 25.45/25.30 all K L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit1(L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L_1))).
% 25.45/25.30 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))).
% 25.45/25.30 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))).
% 25.45/25.30 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))).
% 25.45/25.30 all B_1 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)),times_times(int,A_1,B_1)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)))).
% 25.45/25.30 all K_1 I_2 J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),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),times_times(int,K_1,I_2)),times_times(int,K_1,J_1))))).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),one_one(int))).
% 25.45/25.30 all Y X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))-> (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)),plus_plus(int,X,Y))))).
% 25.45/25.30 all X_a (semiring_1(X_a)-> (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))->hAPP(nat,X_a,semiring_1_of_nat(X_a),nat_1(times_times(int,number_number_of(int,bit0(bit1(pls))),X)))=plus_plus(X_a,hAPP(nat,X_a,semiring_1_of_nat(X_a),nat_1(X)),hAPP(nat,X_a,semiring_1_of_nat(X_a),nat_1(X)))))).
% 25.45/25.30 all Z_2 Z 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_2),Z))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(int,W_2,Z_2)),plus_plus(int,W,Z))))).
% 25.45/25.30 all Z hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Z))).
% 25.45/25.30 all P_1 ((exists 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,P_1,X_1))))<-> (exists X_1 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_1))))).
% 25.45/25.30 all P_1 ((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,P_1,X_1))))<-> (all X_1 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_1))))).
% 25.45/25.30 all N hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N))).
% 25.45/25.30 all N X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,power_power(int,X),N)))).
% 25.45/25.30 all Wa Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),Z_1))<-> (exists N_1 (ti(int,Z_1)=plus_plus(int,Wa,hAPP(nat,int,semiring_1_of_nat(int),N_1))))).
% 25.45/25.30 all X Y Z (hAPP(nat,int,power_power(int,X),plus_plus(nat,Y,Z))=times_times(int,hAPP(nat,int,power_power(int,X),Y),hAPP(nat,int,power_power(int,X),Z))).
% 25.45/25.30 all X_a (number_semiring(X_a)-> (all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))->plus_plus(X_a,one_one(X_a),number_number_of(X_a,V_1))=number_number_of(X_a,succ(V_1))))).
% 25.45/25.30 all X_a (number_semiring(X_a)-> (all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))->plus_plus(X_a,number_number_of(X_a,V_1),one_one(X_a))=number_number_of(X_a,succ(V_1))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all X N (hAPP(nat,X_a,power_power(X_a,X),times_times(nat,number_number_of(nat,bit0(bit1(pls))),N))=times_times(X_a,hAPP(nat,X_a,power_power(X_a,X),N),hAPP(nat,X_a,power_power(X_a,X),N))))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all V_1 W C (plus_plus(X_a,number_number_of(X_a,V_1),minus_minus(X_a,number_number_of(X_a,W),C))=minus_minus(X_a,number_number_of(X_a,plus_plus(int,V_1,W)),C)))).
% 25.45/25.30 all Wa Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(Wa)),nat_1(Z_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1)))).
% 25.45/25.30 all Wa Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(Wa)),nat_1(Z_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1))).
% 25.45/25.30 all X_a (linordered_ring(X_a)-> (all X Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,times_times(X_a,X,X),times_times(X_a,Y,Y))),zero_zero(X_a)))))).
% 25.45/25.30 all X_a (linord581940658strict(X_a)-> (all Xa Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),plus_plus(X_a,times_times(X_a,Xa,Xa),times_times(X_a,Ya,Ya))))<->ti(X_a,Xa)!=zero_zero(X_a)|ti(X_a,Ya)!=zero_zero(X_a)))).
% 25.45/25.30 all Ma Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),nat_1(Z_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),Z_1))).
% 25.45/25.30 all X_a (ordere216010020id_add(X_a)-> (all B_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_e_q(X_a),zero_zero(X_a)),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),plus_plus(X_a,A_1,B_1))))))).
% 25.45/25.30 all X_a (ordere216010020id_add(X_a)-> (all B_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(X_a),zero_zero(X_a)),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),plus_plus(X_a,A_1,B_1))))))).
% 25.45/25.30 all X_a (ordere216010020id_add(X_a)-> (all B_1 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_1),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),plus_plus(X_a,A_1,C))))))).
% 25.45/25.30 all X_a (ordere216010020id_add(X_a)-> (all B_1 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_1),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),plus_plus(X_a,A_1,C))))))).
% 25.45/25.30 all X_a (ordere216010020id_add(X_a)-> (all B_1 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_1),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_1,B_1)),zero_zero(X_a))))))).
% 25.45/25.30 all X_a (ordere216010020id_add(X_a)-> (all B_1 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_1),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_1,B_1)),zero_zero(X_a))))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all A_1 N B_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)),hAPP(nat,X_a,power_power(X_a,B_1),N)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all N 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)),times_times(X_a,A_1,hAPP(nat,X_a,power_power(X_a,A_1),N))))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all N 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)),times_times(X_a,A_1,hAPP(nat,X_a,power_power(X_a,A_1),N))))))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all A_1 (times_times(X_a,A_1,number_number_of(X_a,bit1(pls)))=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all A_1 (times_times(X_a,number_number_of(X_a,bit1(pls)),A_1)=ti(X_a,A_1)))).
% 25.45/25.30 all P_1 A_2 B (hBOOL(hAPP(nat,bool,P_1,minus_minus(nat,A_2,B)))<-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B))& -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| (exists D_3 (A_2=plus_plus(nat,B,D_3)& -hBOOL(hAPP(nat,bool,P_1,D_3)))))).
% 25.45/25.30 all P_1 A_2 B (hBOOL(hAPP(nat,bool,P_1,minus_minus(nat,A_2,B)))<-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B))->hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))))& (all D_3 (A_2=plus_plus(nat,B,D_3)->hBOOL(hAPP(nat,bool,P_1,D_3))))).
% 25.45/25.30 all Va (zero_zero(nat)=number_number_of(nat,Va)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls))).
% 25.45/25.30 all Va (number_number_of(nat,Va)=zero_zero(nat)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls))).
% 25.45/25.30 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))).
% 25.45/25.30 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))).
% 25.45/25.30 all K L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit1(L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L_1))).
% 25.45/25.30 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))).
% 25.45/25.30 all K L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit0(L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1))).
% 25.45/25.30 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))).
% 25.45/25.30 all K_1 L (times_times(int,bit1(K_1),L)=plus_plus(int,bit0(times_times(int,K_1,L)),L)).
% 25.45/25.30 all Na Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))-> (times_times(int,Ma,Na)=one_one(int)<->ti(int,Ma)=one_one(int)&ti(int,Na)=one_one(int))).
% 25.45/25.30 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_1))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1))).
% 25.45/25.30 all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)))<->Na=zero_zero(nat)).
% 25.45/25.30 succ(pls)=bit1(pls).
% 25.45/25.30 all K_1 (succ(bit0(K_1))=bit1(K_1)).
% 25.45/25.30 all K_1 (succ(bit1(K_1))=bit0(succ(K_1))).
% 25.45/25.30 all Wa Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),plus_plus(int,Z_1,one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),Z_1))).
% 25.45/25.30 all Wa Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),plus_plus(int,Wa,one_one(int))),Z_1))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1))).
% 25.45/25.30 all W Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),plus_plus(int,W,one_one(int))),Z))).
% 25.45/25.30 all K_1 (succ(K_1)=plus_plus(int,K_1,one_one(int))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all X Y (hAPP(nat,X_a,power_power(X_a,minus_minus(X_a,X,Y)),number_number_of(nat,bit0(bit1(pls))))=minus_minus(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),number_number_of(nat,bit0(bit1(pls))))),times_times(X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),X),Y))))).
% 25.45/25.30 all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),nat_1(Z_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1))).
% 25.45/25.30 number_number_of(nat,bit1(bit1(pls)))=nat_1(number_number_of(int,bit1(bit1(pls)))).
% 25.45/25.30 all P_1 I_1 (hBOOL(hAPP(nat,bool,P_1,nat_1(I_1)))<-> (all N_1 (ti(int,I_1)=hAPP(nat,int,semiring_1_of_nat(int),N_1)->hBOOL(hAPP(nat,bool,P_1,N_1))))& (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),zero_zero(int)))->hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all N 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),times_times(X_a,A_1,hAPP(nat,X_a,power_power(X_a,A_1),N))),hAPP(nat,X_a,power_power(X_a,A_1),N))))))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all W (times_times(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))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all A_1 N B_1 (hAPP(nat,X_a,power_power(X_a,A_1),N)=hAPP(nat,X_a,power_power(X_a,B_1),N)-> (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_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))->ti(X_a,A_1)=ti(X_a,B_1))))))).
% 25.45/25.30 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))))=times_times(X_a,times_times(X_a,A_1,A_1),A_1)))).
% 25.45/25.30 all X_a (number_semiring(X_a)-> (all V_2 V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_2))->plus_plus(X_a,number_number_of(X_a,V_1),number_number_of(X_a,V_2))=number_number_of(X_a,plus_plus(int,V_1,V_2)))))).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit1(bit1(pls))))).
% 25.45/25.30 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),Z)))).
% 25.45/25.30 all K_1 I_2 J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),times_times(int,hAPP(nat,int,semiring_1_of_nat(int),K_1),I_2)),times_times(int,hAPP(nat,int,semiring_1_of_nat(int),K_1),J_1))))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all K_1 (number_number_of(X_a,succ(K_1))=plus_plus(X_a,one_one(X_a),number_number_of(X_a,K_1))))).
% 25.45/25.30 all K_1 L (plus_plus(int,bit1(K_1),bit1(L))=bit0(plus_plus(int,K_1,succ(L)))).
% 25.45/25.30 number_number_of(nat,bit0(bit1(pls)))=nat_1(number_number_of(int,bit0(bit1(pls)))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all Z (times_times(X_a,Z,number_number_of(X_a,bit0(bit1(pls))))=plus_plus(X_a,Z,Z)))).
% 25.45/25.30 all X_a (number_semiring(X_a)-> (all Z (times_times(X_a,Z,number_number_of(X_a,bit0(bit1(pls))))=plus_plus(X_a,Z,Z)))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all Z (times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),Z)=plus_plus(X_a,Z,Z)))).
% 25.45/25.30 all X_a (number_semiring(X_a)-> (all Z (times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),Z)=plus_plus(X_a,Z,Z)))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all N A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_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(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))->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)),hAPP(nat,X_a,power_power(X_a,B_1),N)))))))).
% 25.45/25.30 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))))=times_times(X_a,A_1,A_1)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all X (times_times(X_a,X,X)=hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))))).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit0(bit1(pls))))).
% 25.45/25.30 all A_1 (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))))).
% 25.45/25.30 all X hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls)))))).
% 25.45/25.30 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))))=times_times(X_b,number_number_of(X_b,W),number_number_of(X_b,W))))).
% 25.45/25.30 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)))))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all X 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),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),Y)))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all X Y (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),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))-> (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)=ti(X_a,Y)))))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all V_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,V_1)))->hAPP(nat,X_a,semiring_1_of_nat(X_a),number_number_of(nat,V_1))=number_number_of(X_a,V_1))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,V_1)))->hAPP(nat,X_a,semiring_1_of_nat(X_a),number_number_of(nat,V_1))=zero_zero(X_a))))).
% 25.45/25.30 all X_a (number_semiring(X_a)-> (all X Y (hAPP(nat,X_a,power_power(X_a,plus_plus(X_a,X,Y)),number_number_of(nat,bit0(bit1(pls))))=plus_plus(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),number_number_of(nat,bit0(bit1(pls))))),times_times(X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),X),Y))))).
% 25.45/25.30 all X_a (linordered_semidom(X_a)-> (all X 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),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),Y)))))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all X Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(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),number_number_of(nat,bit0(bit1(pls))))))))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all Xa Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(X_a)))<->ti(X_a,Xa)=zero_zero(X_a)&ti(X_a,Ya)=zero_zero(X_a)))).
% 25.45/25.30 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),number_number_of(int,bit0(bit1(pls)))))->ti(int,X)=zero_zero(int)|ti(int,X)=one_one(int))).
% 25.45/25.30 all A_1 P_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_2))->hAPP(nat,int,power_power(int,A_1),nat_1(P_2))=times_times(int,A_1,hAPP(nat,int,power_power(int,A_1),minus_minus(nat,nat_1(P_2),one_one(nat))))).
% 25.45/25.30 all R_1 Q A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (ti(int,A_1)=plus_plus(int,R_1,times_times(int,A_1,Q))-> (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),one_one(int)))))).
% 25.45/25.30 all R_1 Q A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (ti(int,A_1)=plus_plus(int,R_1,times_times(int,A_1,Q))-> (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))))).
% 25.45/25.30 all X_a (power(X_a)-> (all M N ((N=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,M),N)=one_one(X_a))& (N!=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,M),N)=times_times(X_a,M,hAPP(nat,X_a,power_power(X_a,M),minus_minus(nat,N,one_one(nat)))))))).
% 25.45/25.30 -(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))-> -hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))))).
% 25.45/25.30 all B_2 Q_1 R_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),plus_plus(int,times_times(int,B_2,Q_1),R_2)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Q_1))))).
% 25.45/25.30 all B_2 Q_1 R_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(int,times_times(int,B_2,Q_1),R_2)),zero_zero(int)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),zero_zero(int)))))).
% 25.45/25.30 -hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)))))).
% 25.45/25.30 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N)).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),t),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.45/25.30 hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t))).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.45/25.30 hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))).
% 25.45/25.30 -(all X_1 Y_1 (plus_plus(int,hAPP(nat,int,power_power(int,X_1),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,int,power_power(int,Y_1),number_number_of(nat,bit0(bit1(pls)))))!=times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))).
% 25.45/25.30 plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),one_one(int))=times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t).
% 25.45/25.30 hBOOL(hAPP(int,bool,zprime,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.45/25.30 t=one_one(int)-> (exists X_1 Y_1 (plus_plus(int,hAPP(nat,int,power_power(int,X_1),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,int,power_power(int,Y_1),number_number_of(nat,bit0(bit1(pls)))))=plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.45/25.30 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),N)).
% 25.45/25.30 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),times_times(nat,M,M))).
% 25.45/25.30 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),times_times(nat,M,times_times(nat,M,M)))).
% 25.45/25.30 all M N (times_times(nat,M,N)=times_times(nat,N,M)).
% 25.45/25.30 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M))).
% 25.45/25.30 all M N K_1 (times_times(nat,times_times(nat,M,N),K_1)=times_times(nat,M,times_times(nat,N,K_1))).
% 25.45/25.30 all M N (M=N->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))).
% 25.45/25.30 all K_1 I_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),times_times(nat,I_2,K_1)),times_times(nat,J_1,K_1)))).
% 25.45/25.30 all K_1 I_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),times_times(nat,K_1,I_2)),times_times(nat,K_1,J_1)))).
% 25.45/25.30 all K_1 I_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),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_2),K_1)))).
% 25.45/25.30 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M))->M=N)).
% 25.45/25.30 all K_1 L I_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),times_times(nat,I_2,K_1)),times_times(nat,J_1,L))))).
% 25.45/25.30 all Xa Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),minus_minus(real,Xa,Ya)),zero_zero(real)))).
% 25.45/25.30 all Ma K Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),times_times(nat,Ma,K)),times_times(nat,Na,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),Na)))).
% 25.45/25.30 all K Ma Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),times_times(nat,K,Ma)),times_times(nat,K,Na)))<-> (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),Na)))).
% 25.45/25.30 all Xa Ya 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_e_q(real),times_times(real,Xa,Z_1)),times_times(real,Ya,Z_1)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya)))).
% 25.45/25.30 all Xa Ya 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_e_q(real),times_times(real,Z_1,Xa)),times_times(real,Z_1,Ya)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya)))).
% 25.45/25.30 all N M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M))->minus_minus(int,hAPP(nat,int,semiring_1_of_nat(int),M),hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,M,N))).
% 25.45/25.30 all K_1 (minus_minus(int,K_1,pls)=ti(int,K_1)).
% 25.45/25.30 all K_1 L (minus_minus(int,bit0(K_1),bit0(L))=bit0(minus_minus(int,K_1,L))).
% 25.45/25.30 all Z1 Z2 W (times_times(int,minus_minus(int,Z1,Z2),W)=minus_minus(int,times_times(int,Z1,W),times_times(int,Z2,W))).
% 25.45/25.30 all W Z1 Z2 (times_times(int,W,minus_minus(int,Z1,Z2))=minus_minus(int,times_times(int,W,Z1),times_times(int,W,Z2))).
% 25.45/25.30 all N (times_times(nat,zero_zero(nat),N)=zero_zero(nat)).
% 25.45/25.30 all M (times_times(nat,M,zero_zero(nat))=zero_zero(nat)).
% 25.45/25.30 all Ma Na (times_times(nat,Ma,Na)=zero_zero(nat)<->Ma=zero_zero(nat)|Na=zero_zero(nat)).
% 25.45/25.30 all K Ma Na (times_times(nat,K,Ma)=times_times(nat,K,Na)<->Ma=Na|K=zero_zero(nat)).
% 25.45/25.30 all Ma K Na (times_times(nat,Ma,K)=times_times(nat,Na,K)<->Ma=Na|K=zero_zero(nat)).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all X P_2 Q (hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,X),P_2)),Q)=hAPP(nat,X_a,power_power(X_a,X),times_times(nat,P_2,Q))))).
% 25.45/25.30 all X_a (monoid_mult(X_a)-> (all A_1 M N (hAPP(nat,X_a,power_power(X_a,A_1),times_times(nat,M,N))=hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,A_1),M)),N)))).
% 25.45/25.30 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N)).
% 25.45/25.30 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Na),zero_zero(nat)))<->Na=zero_zero(nat)).
% 25.45/25.30 all A_2 B C_1 (C_1!=zero_zero(real)-> (times_times(real,C_1,A_2)=times_times(real,C_1,B)<->A_2=B)).
% 25.45/25.30 all A_2 B C_1 (C_1!=zero_zero(real)-> (times_times(real,A_2,C_1)=times_times(real,B,C_1)<->A_2=B)).
% 25.45/25.30 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))|M=N->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))).
% 25.45/25.30 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))-> (M!=N->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))).
% 25.45/25.30 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))).
% 25.45/25.30 all Ma Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))|Ma=Na).
% 25.45/25.30 all Ma Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))&Ma!=Na).
% 25.45/25.30 all Xa Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya))&Xa!=Ya).
% 25.45/25.30 all Xa Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya))|Xa=Ya).
% 25.45/25.30 all M N K_1 (times_times(nat,plus_plus(nat,M,N),K_1)=plus_plus(nat,times_times(nat,M,K_1),times_times(nat,N,K_1))).
% 25.45/25.30 all K_1 M N (times_times(nat,K_1,plus_plus(nat,M,N))=plus_plus(nat,times_times(nat,K_1,M),times_times(nat,K_1,N))).
% 25.45/25.30 all M K_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,M,K_1)),N))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N)))).
% 25.45/25.30 all M K_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,M,K_1)),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))).
% 25.45/25.30 all M K_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,M,K_1)),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N))).
% 25.45/25.30 all K_1 L I_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,I_2,K_1)),plus_plus(nat,J_1,L))))).
% 25.45/25.30 all K_1 I_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,I_2,K_1)),plus_plus(nat,J_1,K_1)))).
% 25.45/25.30 all M I_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),plus_plus(nat,M,J_1)))).
% 25.45/25.30 all M I_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),plus_plus(nat,J_1,M)))).
% 25.45/25.30 all K Ma Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,K,Ma)),plus_plus(nat,K,Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))).
% 25.45/25.30 all Ma Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))<-> (exists K_2 (Na=plus_plus(nat,Ma,K_2)))).
% 25.45/25.30 all N M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),plus_plus(nat,N,M))).
% 25.45/25.30 all N M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),plus_plus(nat,M,N))).
% 25.45/25.30 all Na Ma (times_times(nat,Na,Ma)=one_one(nat)<->Na=one_one(nat)&Ma=one_one(nat)).
% 25.45/25.30 all Ma Na (times_times(nat,Ma,Na)=one_one(nat)<->Ma=one_one(nat)&Na=one_one(nat)).
% 25.45/25.30 all N (times_times(nat,N,one_one(nat))=N).
% 25.45/25.30 all Ma Na (one_one(nat)=times_times(nat,Ma,Na)<->Ma=one_one(nat)&Na=one_one(nat)).
% 25.45/25.30 all N (times_times(nat,one_one(nat),N)=N).
% 25.45/25.30 all M N K_1 (times_times(nat,minus_minus(nat,M,N),K_1)=minus_minus(nat,times_times(nat,M,K_1),times_times(nat,N,K_1))).
% 25.45/25.30 all K_1 M N (times_times(nat,K_1,minus_minus(nat,M,N))=minus_minus(nat,times_times(nat,K_1,M),times_times(nat,K_1,N))).
% 25.45/25.30 all Z (times_times(real,one_one(real),Z)=Z).
% 25.45/25.30 all Na 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),Na))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),minus_minus(nat,Ma,K)),minus_minus(nat,Na,K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))))).
% 25.45/25.30 all N 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))->minus_minus(nat,minus_minus(nat,M,K_1),minus_minus(nat,N,K_1))=minus_minus(nat,M,N))).
% 25.45/25.30 all Na 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),Na))-> (minus_minus(nat,Ma,K)=minus_minus(nat,Na,K)<->Ma=Na))).
% 25.45/25.30 all I_2 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),N))->minus_minus(nat,N,minus_minus(nat,N,I_2))=I_2).
% 25.45/25.30 all L M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),minus_minus(nat,M,L)),minus_minus(nat,N,L)))).
% 25.45/25.30 all L M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),minus_minus(nat,L,N)),minus_minus(nat,L,M)))).
% 25.45/25.30 all M N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),minus_minus(nat,M,N)),M)).
% 25.45/25.30 all Z1 Z2 W (times_times(real,plus_plus(real,Z1,Z2),W)=plus_plus(real,times_times(real,Z1,W),times_times(real,Z2,W))).
% 25.45/25.30 all X Y Z (hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X),Y)),Z)=hAPP(nat,int,power_power(int,X),times_times(nat,Y,Z))).
% 25.45/25.30 all Z X Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),plus_plus(real,Z,X)),plus_plus(real,Z,Y)))).
% 25.45/25.30 all K_1 L (minus_minus(int,bit1(K_1),bit1(L))=bit0(minus_minus(int,K_1,L))).
% 25.45/25.30 all K_1 L (minus_minus(int,bit1(K_1),bit0(L))=bit1(minus_minus(int,K_1,L))).
% 25.45/25.30 all L (minus_minus(int,pls,bit0(L))=bit0(minus_minus(int,pls,L))).
% 25.45/25.30 all A_1 X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),A_1))-> (ti(int,X)!=minus_minus(int,A_1,one_one(int))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),minus_minus(int,A_1,one_one(int))))))).
% 25.45/25.30 all K L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),minus_minus(int,K,L_1)),zero_zero(int)))).
% 25.45/25.30 all K_1 I_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),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),times_times(nat,K_1,I_2)),times_times(nat,K_1,J_1))))).
% 25.45/25.30 all K_1 I_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),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),times_times(nat,I_2,K_1)),times_times(nat,J_1,K_1))))).
% 25.45/25.30 all Ma K Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),times_times(nat,Ma,K)),times_times(nat,Na,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),Na))).
% 25.45/25.30 all K Ma Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),times_times(nat,K,Ma)),times_times(nat,K,Na)))<->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),Na))).
% 25.45/25.30 all Ma Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),times_times(nat,Ma,Na)))<->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)),Na))).
% 25.45/25.30 all Xa (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),times_times(real,Xa,Xa)))<->Xa=zero_zero(real)).
% 25.45/25.30 all X Y Z (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),times_times(real,Z,X)),times_times(real,Z,Y))))).
% 25.45/25.30 all Y X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X))-> (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)),times_times(real,X,Y))))).
% 25.45/25.30 all Xa Ya 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),times_times(real,Xa,Z_1)),times_times(real,Ya,Z_1)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya)))).
% 25.45/25.30 all M N (M=times_times(nat,M,N)->N=one_one(nat)|M=zero_zero(nat)).
% 25.45/25.30 all Ma Na (minus_minus(nat,Ma,Na)=zero_zero(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))).
% 25.45/25.30 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))->minus_minus(nat,M,N)=zero_zero(nat)).
% 25.45/25.30 all Xa Ya (plus_plus(real,times_times(real,Xa,Xa),times_times(real,Ya,Ya))=zero_zero(real)<->Xa=zero_zero(real)&Ya=zero_zero(real)).
% 25.45/25.30 all C A_1 B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B_1))-> (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),minus_minus(nat,A_1,C)),minus_minus(nat,B_1,C))))).
% 25.45/25.30 all Na 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),Na))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),minus_minus(nat,Ma,K)),minus_minus(nat,Na,K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))))).
% 25.45/25.30 all X Y (times_times(int,hAPP(nat,int,semiring_1_of_nat(int),X),hAPP(nat,int,semiring_1_of_nat(int),Y))=hAPP(nat,int,semiring_1_of_nat(int),times_times(nat,X,Y))).
% 25.45/25.30 all M N (times_times(int,hAPP(nat,int,semiring_1_of_nat(int),M),hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,int,semiring_1_of_nat(int),times_times(nat,M,N))).
% 25.45/25.30 all M N (hAPP(nat,int,semiring_1_of_nat(int),times_times(nat,M,N))=times_times(int,hAPP(nat,int,semiring_1_of_nat(int),M),hAPP(nat,int,semiring_1_of_nat(int),N))).
% 25.45/25.30 all I_2 K_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))->minus_minus(nat,I_2,minus_minus(nat,J_1,K_1))=minus_minus(nat,plus_plus(nat,I_2,K_1),J_1)).
% 25.45/25.30 all J K I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),minus_minus(nat,J,K)),I_1))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),plus_plus(nat,I_1,K)))).
% 25.45/25.30 all M K_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),minus_minus(nat,plus_plus(nat,N,M),K_1)))).
% 25.45/25.30 all N M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M))->plus_plus(nat,N,minus_minus(nat,M,N))=M).
% 25.45/25.30 all I_2 K_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))->plus_plus(nat,I_2,minus_minus(nat,J_1,K_1))=minus_minus(nat,plus_plus(nat,I_2,J_1),K_1)).
% 25.45/25.30 all I_1 K J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),minus_minus(nat,J,K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,I_1,K)),J)))).
% 25.45/25.30 all N M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M))->plus_plus(nat,minus_minus(nat,M,N),N)=M).
% 25.45/25.30 all K I_1 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J))-> (minus_minus(nat,J,I_1)=K<->J=plus_plus(nat,K,I_1))).
% 25.45/25.30 all I_2 K_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))->minus_minus(nat,plus_plus(nat,I_2,J_1),K_1)=plus_plus(nat,I_2,minus_minus(nat,J_1,K_1))).
% 25.45/25.30 all I_2 K_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))->plus_plus(nat,minus_minus(nat,J_1,K_1),I_2)=minus_minus(nat,plus_plus(nat,J_1,I_2),K_1)).
% 25.45/25.30 all I_2 K_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))->minus_minus(nat,plus_plus(nat,J_1,I_2),K_1)=plus_plus(nat,minus_minus(nat,J_1,K_1),I_2)).
% 25.45/25.30 all Xa Ya (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Xa),Ya))).
% 25.45/25.30 all Ma Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))).
% 25.45/25.30 all Y X (hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,X))-> (hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,Y))->hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,times_times(int,X,Y))))).
% 25.45/25.30 all Wa Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),minus_minus(int,Z_1,one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1))).
% 25.45/25.30 all Va V_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,Va)),number_number_of(nat,V_3)))<-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),V_3))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls)))).
% 25.45/25.30 all X_a (ring_1(X_a)-> (all N M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M))->hAPP(nat,X_a,semiring_1_of_nat(X_a),minus_minus(nat,M,N))=minus_minus(X_a,hAPP(nat,X_a,semiring_1_of_nat(X_a),M),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))).
% 25.45/25.30 all Ya Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Ya))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),nat_1(Xa)),nat_1(Ya)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),Ya))))).
% 25.45/25.30 all Z Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_2),Z))->nat_1(minus_minus(int,Z,Z_2))=minus_minus(nat,nat_1(Z),nat_1(Z_2)))).
% 25.45/25.30 all Z_2 Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))->nat_1(times_times(int,Z,Z_2))=times_times(nat,nat_1(Z),nat_1(Z_2))).
% 25.45/25.30 all Y X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))->times_times(nat,nat_1(X),nat_1(Y))=nat_1(times_times(int,X,Y)))).
% 25.45/25.30 all N M ((M=zero_zero(nat)->times_times(nat,M,N)=zero_zero(nat))& (M!=zero_zero(nat)->times_times(nat,M,N)=plus_plus(nat,N,times_times(nat,minus_minus(nat,M,one_one(nat)),N)))).
% 25.45/25.30 all Z_1 Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Wa))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),nat_1(Wa)),nat_1(Z_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),Z_1)))).
% 25.45/25.30 all P_2 M ((M=zero_zero(nat)->hAPP(nat,nat,power_power(nat,P_2),M)=one_one(nat))& (M!=zero_zero(nat)->hAPP(nat,nat,power_power(nat,P_2),M)=times_times(nat,P_2,hAPP(nat,nat,power_power(nat,P_2),minus_minus(nat,M,one_one(nat)))))).
% 25.45/25.30 all X_a (monoid_mult(X_a)-> (all A_1 N (hAPP(nat,X_a,power_power(X_a,A_1),times_times(nat,number_number_of(nat,bit0(bit1(pls))),N))=hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N)),number_number_of(nat,bit0(bit1(pls))))))).
% 25.45/25.30 all Z (times_times(nat,number_number_of(nat,bit0(bit1(pls))),Z)=plus_plus(nat,Z,Z)).
% 25.45/25.30 all Z (times_times(nat,Z,number_number_of(nat,bit0(bit1(pls))))=plus_plus(nat,Z,Z)).
% 25.45/25.30 all V_2 K_1 V_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->times_times(nat,number_number_of(nat,V_1),times_times(nat,number_number_of(nat,V_2),K_1))=zero_zero(nat))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->times_times(nat,number_number_of(nat,V_1),times_times(nat,number_number_of(nat,V_2),K_1))=times_times(nat,number_number_of(nat,times_times(int,V_1,V_2)),K_1))).
% 25.45/25.30 all V_2 V_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->times_times(nat,number_number_of(nat,V_1),number_number_of(nat,V_2))=zero_zero(nat))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->times_times(nat,number_number_of(nat,V_1),number_number_of(nat,V_2))=number_number_of(nat,times_times(int,V_1,V_2)))).
% 25.45/25.30 all X (times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),hAPP(nat,real,power_power(real,X),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,real,power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X)),number_number_of(nat,bit0(bit1(pls))))).
% 25.45/25.30 all N 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))).
% 25.45/25.30 all B_1 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_1),C))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),B_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_1),A_1)))).
% 25.45/25.30 all A_1 B_1 (times_times(int,plus_plus(int,A_1,B_1),minus_minus(int,A_1,B_1))=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_1),number_number_of(nat,bit0(bit1(pls)))))).
% 25.45/25.30 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),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)))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all A_1 N 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),times_times(nat,number_number_of(nat,bit0(bit1(pls))),N)))))).
% 25.45/25.30 all X Y (minus_minus(nat,hAPP(nat,nat,power_power(nat,X),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,nat,power_power(nat,Y),number_number_of(nat,bit0(bit1(pls)))))=times_times(nat,plus_plus(nat,X,Y),minus_minus(nat,X,Y))).
% 25.45/25.30 all A_1 B_1 (hAPP(nat,int,power_power(int,minus_minus(int,A_1,B_1)),number_number_of(nat,bit1(bit1(pls))))=minus_minus(int,plus_plus(int,minus_minus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit1(bit1(pls)))),times_times(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_1)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),A_1),hAPP(nat,int,power_power(int,B_1),number_number_of(nat,bit0(bit1(pls)))))),hAPP(nat,int,power_power(int,B_1),number_number_of(nat,bit1(bit1(pls)))))).
% 25.45/25.30 all A_1 B_1 (hAPP(nat,int,power_power(int,minus_minus(int,A_1,B_1)),number_number_of(nat,bit0(bit1(pls))))=plus_plus(int,minus_minus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),A_1),B_1)),hAPP(nat,int,power_power(int,B_1),number_number_of(nat,bit0(bit1(pls)))))).
% 25.45/25.30 all B_1 Q R_1 B_2 Q_1 R_2 (plus_plus(int,times_times(int,B_1,Q),R_1)=plus_plus(int,times_times(int,B_2,Q_1),R_2)-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(int,times_times(int,B_2,Q_1),R_2)),zero_zero(int)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),B_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q)))))))).
% 25.45/25.30 all B_1 Q_1 R_2 Q R_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),plus_plus(int,times_times(int,B_1,Q_1),R_2)),plus_plus(int,times_times(int,B_1,Q),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_1),R_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),R_2))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q),Q_1)))))).
% 25.45/25.30 all B_1 Q R_1 B_2 Q_1 R_2 (plus_plus(int,times_times(int,B_1,Q),R_1)=plus_plus(int,times_times(int,B_2,Q_1),R_2)-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),plus_plus(int,times_times(int,B_2,Q_1),R_2)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_2))-> (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_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),B_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q),Q_1)))))))).
% 25.45/25.30 all B_1 Q_1 R_2 Q R_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),plus_plus(int,times_times(int,B_1,Q_1),R_2)),plus_plus(int,times_times(int,B_1,Q),R_1)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q)))))).
% 25.45/25.30 plus_plus(int,hAPP(nat,int,power_power(int,x),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,int,power_power(int,y),number_number_of(nat,bit0(bit1(pls)))))=times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))).
% 25.45/25.30 all P_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_2))->minus_minus(nat,nat_1(P_2),number_number_of(nat,bit0(bit1(pls))))=nat_1(minus_minus(int,P_2,number_number_of(int,bit0(bit1(pls)))))).
% 25.45/25.30 all P_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),nat_1(minus_minus(int,P_2,number_number_of(int,bit0(bit1(pls)))))))).
% 25.45/25.30 -(all T_1 (plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),one_one(int))!=times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),T_1))).
% 25.45/25.30 all W hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),W)).
% 25.45/25.30 all Z W (times_times(real,Z,W)=times_times(real,W,Z)).
% 25.45/25.30 all Z W (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z),W))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),Z))).
% 25.45/25.30 all Z1 Z2 Z3 (times_times(real,times_times(real,Z1,Z2),Z3)=times_times(real,Z1,times_times(real,Z2,Z3))).
% 25.45/25.30 all K_1 I_2 J_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I_2),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_2),K_1)))).
% 25.45/25.30 all Z W (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z),W))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),Z))->Z=W)).
% 25.45/25.30 hBOOL(hAPP(int,bool,zprime,number_number_of(int,bit0(bit1(pls))))).
% 25.45/25.30 all A_1 B_1 C (minus_minus(int,A_1,B_1)=ti(int,C)->ti(int,A_1)=plus_plus(int,C,B_1)).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),one_one(int)))).
% 25.45/25.30 all X Y (hAPP(nat,real,power_power(real,plus_plus(real,X,Y)),number_number_of(nat,bit0(bit1(pls))))=plus_plus(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),number_number_of(nat,bit0(bit1(pls))))),times_times(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X),Y))).
% 25.45/25.30 minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min))=plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),one_one(int)).
% 25.45/25.30 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))))).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)))).
% 25.45/25.30 legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))=one_one(int).
% 25.45/25.30 all K_1 M N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),minus_minus(int,M,N)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),N))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),M)))).
% 25.45/25.30 all M N P_2 (hBOOL(hAPP(int,bool,zprime,P_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),times_times(int,M,N)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),N)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 B_1 C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),times_times(X_a,A_1,B_1)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B_1),C))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 B_1 C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),times_times(X_a,A_1,B_1)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C))))).
% 25.45/25.30 all X_a (dvd(X_a)-> (all A_1 B_1 K_1 (A_1=times_times(X_a,B_1,K_1)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B_1),A_1))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all C D_1 A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),D_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),times_times(X_a,A_1,C)),times_times(X_a,B_1,D_1))))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all B_1 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),times_times(X_a,B_1,C)))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),times_times(X_a,B_1,C)))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 B_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),times_times(X_a,B_1,A_1))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 B_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),times_times(X_a,A_1,B_1))))).
% 25.45/25.30 all X_a (comm_ring_1(X_a)-> (all Z X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Y))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Z))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),minus_minus(X_a,Y,Z))))))).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),min)).
% 25.45/25.30 all N M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),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),M))).
% 25.45/25.30 all A_1 N P_2 (hBOOL(hAPP(int,bool,zprime,P_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),hAPP(nat,int,power_power(int,A_1),N)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),A_1)))).
% 25.45/25.30 all X_a (idom(X_a)-> (all C_1 A_2 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))<->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_2),B))))).
% 25.45/25.30 all X_a (idom(X_a)-> (all A_2 C_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),times_times(X_a,A_2,C_1)),times_times(X_a,B,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_2),B))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all A_1 M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))->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)))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all N M X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Y))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),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),N)),hAPP(nat,X_a,power_power(X_a,Y),M))))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all M A_1 N B_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),N)),B_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))->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_1)))))).
% 25.45/25.30 all N 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))-> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),M)))).
% 25.45/25.30 all K_1 M N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),times_times(int,K_1,M)),times_times(int,K_1,N)))-> (ti(int,K_1)!=zero_zero(int)->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N)))).
% 25.45/25.30 all N 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))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),M))->ti(int,M)=ti(int,N))))).
% 25.45/25.30 all K Na Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),plus_plus(int,Na,times_times(int,K,Ma))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),Na))).
% 25.45/25.30 all C_1 Xa Ta A_2 D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),D))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),plus_plus(int,Xa,Ta)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),plus_plus(int,plus_plus(int,Xa,times_times(int,C_1,D)),Ta))))).
% 25.45/25.30 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))).
% 25.45/25.30 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))).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),pls)).
% 25.45/25.30 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),min)).
% 25.45/25.30 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))).
% 25.45/25.30 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))).
% 25.45/25.30 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))).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),zero_zero(int))).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),pls)).
% 25.45/25.30 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),min)).
% 25.45/25.30 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))).
% 25.45/25.30 number_number_of(int,pls)!=number_number_of(int,min).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B_1),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)))))).
% 25.45/25.30 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)))).
% 25.45/25.30 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),min)).
% 25.45/25.30 all L (min!=bit0(L)).
% 25.45/25.30 all K_1 (bit0(K_1)!=min).
% 25.45/25.30 min!=pls.
% 25.45/25.30 pls!=min.
% 25.45/25.30 bit1(min)=min.
% 25.45/25.30 all L_1 (min=bit1(L_1)<->min=ti(int,L_1)).
% 25.45/25.30 all K (bit1(K)=min<->ti(int,K)=min).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all N X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),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),N)),hAPP(nat,X_a,power_power(X_a,Y),N)))))).
% 25.45/25.30 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)))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all C A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B_1))-> (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),plus_plus(X_a,B_1,C))))))).
% 25.45/25.30 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)))).
% 25.45/25.30 succ(min)=pls.
% 25.45/25.30 all K_1 (minus_minus(int,K_1,min)=succ(K_1)).
% 25.45/25.30 all Z N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z),N))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),N)))).
% 25.45/25.30 all P_2 Y N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),Y))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),hAPP(nat,int,power_power(int,Y),N))))).
% 25.45/25.30 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))).
% 25.45/25.30 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))).
% 25.45/25.30 all L (minus_minus(int,pls,bit1(L))=bit1(minus_minus(int,min,L))).
% 25.45/25.30 all L (minus_minus(int,min,bit1(L))=bit0(minus_minus(int,min,L))).
% 25.45/25.30 all L (minus_minus(int,min,bit0(L))=bit1(minus_minus(int,min,L))).
% 25.45/25.30 all Ma Na (times_times(int,Ma,Na)=one_one(int)<->ti(int,Ma)=one_one(int)&ti(int,Na)=one_one(int)|ti(int,Ma)=number_number_of(int,min)&ti(int,Na)=number_number_of(int,min)).
% 25.45/25.30 all M N (times_times(int,M,N)=one_one(int)->ti(int,M)=one_one(int)|ti(int,M)=number_number_of(int,min)).
% 25.45/25.30 all N A_1 B_1 P_2 (hBOOL(hAPP(int,bool,zprime,P_2))-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),B_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_2),N)),times_times(int,A_1,B_1)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_2),N)),A_1))))).
% 25.45/25.30 all N B_1 A_1 P_2 (hBOOL(hAPP(int,bool,zprime,P_2))-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_2),N)),times_times(int,A_1,B_1)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_2),N)),B_1))))).
% 25.45/25.30 all X_a (comm_semiring_1(X_a)-> (all X N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|ti(X_a,X)=one_one(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),hAPP(nat,X_a,power_power(X_a,X),N)))))).
% 25.45/25.30 all Y N P_2 (hBOOL(hAPP(int,bool,zprime,P_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),hAPP(nat,int,power_power(int,Y),N)))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),Y))))).
% 25.45/25.30 all X_a (number_ring(X_a)-> (all N (hAPP(nat,X_a,power_power(X_a,number_number_of(X_a,min)),times_times(nat,number_number_of(nat,bit0(bit1(pls))),N))=one_one(X_a)))).
% 25.45/25.30 hBOOL(hAPP(int,bool,quadRes(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),number_number_of(int,min))).
% 25.45/25.30 hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.45/25.30 -hBOOL(hAPP(int,bool,quadRes(plus_plus(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),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))!=one_one(int).
% 25.45/25.30 hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,s1),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),s)).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),s),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.45/25.30 hBOOL(hAPP(int,bool,zcong(s1,s),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.45/25.30 -(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)),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))))).
% 25.45/25.30 all C A_1 B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),times_times(nat,A_1,C)),times_times(nat,B_1,C)))).
% 25.45/25.30 all C A_1 B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),times_times(nat,C,A_1)),times_times(nat,C,B_1)))).
% 25.45/25.30 all N 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))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),minus_minus(nat,M,N))))).
% 25.45/25.30 all Xa P_3 (hBOOL(hAPP(int,bool,zcong(Xa,zero_zero(int)),P_3))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),Xa))).
% 25.45/25.30 all A_2 Ma (hBOOL(hAPP(int,bool,zcong(A_2,zero_zero(int)),Ma))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),A_2))).
% 25.45/25.30 all N 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))-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),M)))).
% 25.45/25.30 all A_1 B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))->B_1=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A_1),B_1))).
% 25.45/25.30 all Ma K Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),times_times(nat,Ma,K)),times_times(nat,Na,K)))<->K=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),Na))).
% 25.45/25.30 all K_1 M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),minus_minus(nat,M,N)))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),M))))).
% 25.45/25.30 all K_1 M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),minus_minus(nat,M,N)))-> (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),M))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N))))).
% 25.45/25.30 all A_1 N B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,A_1),N)),hAPP(nat,nat,power_power(nat,B_1),N)))-> (N!=zero_zero(nat)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1)))).
% 25.45/25.30 all X Y N (N!=zero_zero(nat)-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,X),N)),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)))).
% 25.45/25.30 all Xa Ya (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))).
% 25.45/25.30 all Xa Ya (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya)))).
% 25.45/25.30 all N X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,X),N)),hAPP(nat,nat,power_power(nat,Y),N)))).
% 25.45/25.30 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),one_one(nat)))<->Ma=one_one(nat)).
% 25.45/25.30 all K Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),plus_plus(nat,Na,K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),Na))).
% 25.45/25.30 all B_1 D_1 A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),A_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),plus_plus(nat,A_1,B_1)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),B_1)))).
% 25.45/25.30 all M hBOOL(hAPP(int,bool,zcong(M,zero_zero(int)),M)).
% 25.45/25.30 all C A_1 B_1 M (hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))->hBOOL(hAPP(int,bool,zcong(plus_plus(int,A_1,C),plus_plus(int,B_1,C)),M))).
% 25.45/25.30 all D_1 C A_1 B_1 M (hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))-> (ti(int,B_1)=ti(int,C)-> (hBOOL(hAPP(int,bool,zcong(C,D_1),M))->hBOOL(hAPP(int,bool,zcong(A_1,D_1),M))))).
% 25.45/25.30 all Z X Y M (hBOOL(hAPP(int,bool,zcong(X,Y),M))->hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X),Z),hAPP(nat,int,power_power(int,Y),Z)),M))).
% 25.45/25.30 all M Y X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X))-> (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,Y),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),M))->ti(int,X)=ti(int,Y))))))).
% 25.45/25.30 all M X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M))-> -hBOOL(hAPP(int,bool,zcong(X,zero_zero(int)),M)))).
% 25.45/25.30 all C_1 D A_2 B Ma (hBOOL(hAPP(int,bool,zcong(A_2,B),Ma))-> (hBOOL(hAPP(int,bool,zcong(C_1,times_times(int,A_2,D)),Ma))<->hBOOL(hAPP(int,bool,zcong(C_1,times_times(int,B,D)),Ma)))).
% 25.45/25.30 all C_1 D A_2 B Ma (hBOOL(hAPP(int,bool,zcong(A_2,B),Ma))-> (hBOOL(hAPP(int,bool,zcong(C_1,times_times(int,D,A_2)),Ma))<->hBOOL(hAPP(int,bool,zcong(C_1,times_times(int,D,B)),Ma)))).
% 25.45/25.30 all M X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M))-> (hBOOL(hAPP(int,bool,zcong(X,zero_zero(int)),M))->ti(int,X)=zero_zero(int)))).
% 25.45/25.30 all Y X P_2 (hBOOL(hAPP(int,bool,zprime,P_2))-> (-hBOOL(hAPP(int,bool,zcong(X,zero_zero(int)),P_2))-> (-hBOOL(hAPP(int,bool,zcong(Y,zero_zero(int)),P_2))-> -hBOOL(hAPP(int,bool,zcong(times_times(int,X,Y),zero_zero(int)),P_2))))).
% 25.45/25.30 all K_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N)))).
% 25.45/25.30 all K_1 M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),times_times(nat,K_1,M)),times_times(nat,K_1,N)))-> (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)))).
% 25.45/25.30 all B_1 A_1 P_2 (hBOOL(hAPP(int,bool,zprime,P_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,zcong(times_times(int,A_1,B_1),zero_zero(int)),P_2))->hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_2))|hBOOL(hAPP(int,bool,zcong(B_1,zero_zero(int)),P_2))))).
% 25.45/25.30 all B_1 A_1 P_2 (hBOOL(hAPP(int,bool,zprime,P_2))-> (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_2))& -hBOOL(hAPP(int,bool,zcong(B_1,zero_zero(int)),P_2))-> -hBOOL(hAPP(int,bool,zcong(times_times(int,A_1,B_1),zero_zero(int)),P_2))))).
% 25.45/25.30 all X Q N R_1 (X=plus_plus(nat,times_times(nat,Q,N),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))-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),X))))).
% 25.45/25.30 all Na 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),times_times(nat,Ma,Na)),Ma))<->Na=one_one(nat))).
% 25.45/25.30 all Na 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),times_times(nat,Na,Ma)),Ma))<->Na=one_one(nat))).
% 25.45/25.30 all Ya Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Ya))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(Xa)),nat_1(Ya)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Xa),Ya))))).
% 25.45/25.30 all I_2 M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,I_2),M)),hAPP(nat,nat,power_power(nat,I_2),N)))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),I_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N)))).
% 25.45/25.30 all Z_1 Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(Z_1)),Ma))<-> (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),dvd_dvd(int),Z_1),hAPP(nat,int,semiring_1_of_nat(int),Ma))))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1))->Ma=zero_zero(nat))).
% 25.45/25.30 all X P_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_2))-> (hBOOL(hAPP(int,bool,zcong(X,number_number_of(int,min)),P_2))-> -hBOOL(hAPP(int,bool,zcong(X,one_one(int)),P_2)))).
% 25.45/25.30 all Y X P_2 (-hBOOL(hAPP(int,bool,zcong(X,zero_zero(int)),P_2))-> (hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,Y),number_number_of(nat,bit0(bit1(pls)))),X),P_2))-> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),Y)))).
% 25.45/25.30 all N M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),M))->M=zero_zero(nat)|M=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),times_times(nat,number_number_of(nat,bit0(bit1(pls))),N)),M))).
% 25.45/25.30 all M (hBOOL(hAPP(int,bool,zprime,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),M),one_one(int))))->legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),M),one_one(int)))=one_one(int)).
% 25.45/25.30 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))))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.45/25.30 exists 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),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))&hBOOL(hAPP(int,bool,zcong(s1,X_1),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))& (all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y_1))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_1),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))&hBOOL(hAPP(int,bool,zcong(s1,Y_1),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))->ti(int,Y_1)=ti(int,X_1)))).
% 25.45/25.30 all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),X)).
% 25.45/25.30 -(all S (-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),S))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),S),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))&hBOOL(hAPP(int,bool,zcong(s1,S),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))))).
% 25.45/25.30 all X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)))).
% 25.45/25.30 all Z X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z),X)))).
% 25.45/25.30 all A_1 B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B_1),A_1))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B_1),A_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1)))).
% 25.45/25.30 all Z X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z),X)))).
% 25.45/25.30 all C A_1 B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B_1),A_1))-> (B_1=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)))).
% 25.45/25.30 all P_1 Xa Ya (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))->hBOOL(P_1))).
% 25.45/25.30 all X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))->Y!=X).
% 25.45/25.30 all X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))->X!=Y).
% 25.45/25.30 all X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)))).
% 25.45/25.30 all X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))).
% 25.45/25.30 all X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)))).
% 25.45/25.30 all X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))->X!=Y).
% 25.45/25.30 all Z X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z),X)))).
% 25.45/25.30 all C A_1 B_1 (A_1=B_1-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B_1),C))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),B_1))->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)))).
% 25.45/25.30 all Z X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z)))).
% 25.45/25.30 all X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))->X=Y)).
% 25.45/25.30 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),M))->M=N)).
% 25.45/25.30 all C A_1 B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))-> (B_1=C->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)))).
% 25.45/25.30 all C A_1 B_1 (A_1=B_1-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B_1),C))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)))).
% 25.45/25.30 all A_1 B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))-> (A_1!=B_1->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B_1),A_1)))).
% 25.45/25.30 all X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))|X=Y).
% 25.45/25.30 all Ya Xa (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))<->Xa=Ya)).
% 25.45/25.30 all X Y (X=Y->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))).
% 25.45/25.30 all A_1 B_1 (A_1!=B_1-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B_1),A_1)))).
% 25.45/25.30 all Xa Ya (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa))).
% 25.45/25.30 all Xa Ya (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))&Xa!=Ya).
% 25.45/25.30 all Xa Ya (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa))|Xa=Ya).
% 25.45/25.30 all Xa Ya (Xa=Ya<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa))).
% 25.45/25.30 all X (-(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),X))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),X)))).
% 25.45/25.30 all Xa Ya (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa))<->Xa=Ya).
% 25.45/25.30 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))).
% 25.45/25.30 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))).
% 25.45/25.30 all N (hAPP(nat,int,power_power(int,number_number_of(int,min)),N)=one_one(int)|hAPP(nat,int,power_power(int,number_number_of(int,min)),N)=number_number_of(int,min)).
% 25.45/25.30 all A_1 P_2 ((hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_2))->legendre(A_1,P_2)=zero_zero(int))& (-hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_2))-> (hBOOL(hAPP(int,bool,quadRes(P_2),A_1))->legendre(A_1,P_2)=one_one(int))& (-hBOOL(hAPP(int,bool,quadRes(P_2),A_1))->legendre(A_1,P_2)=number_number_of(int,min)))).
% 25.45/25.30 all Ma Xa (hBOOL(hAPP(int,bool,quadRes(Ma),Xa))<-> (exists Y_1 hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,Y_1),number_number_of(nat,bit0(bit1(pls)))),Xa),Ma)))).
% 25.45/25.30 all X P_2 (hBOOL(hAPP(int,bool,zprime,P_2))-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),X))->hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X),nat_1(minus_minus(int,P_2,one_one(int)))),one_one(int)),P_2)))).
% 25.45/25.30 all A_1 P_2 (hBOOL(hAPP(int,bool,zprime,P_2))-> (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_2))-> (hBOOL(hAPP(int,bool,zcong(times_times(int,A_1,A_1),one_one(int)),P_2))->ti(int,A_1)=one_one(int)|ti(int,A_1)=minus_minus(int,P_2,one_one(int)))))).
% 25.45/25.30 all C A_1 B_1 M (hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))-> (hBOOL(hAPP(int,bool,zcong(B_1,C),M))->hBOOL(hAPP(int,bool,zcong(A_1,C),M)))).
% 25.45/25.30 all K_1 M hBOOL(hAPP(int,bool,zcong(K_1,K_1),M)).
% 25.45/25.30 all A_2 B Ma (hBOOL(hAPP(int,bool,zcong(A_2,B),Ma))<->hBOOL(hAPP(int,bool,zcong(B,A_2),Ma))).
% 25.45/25.30 all X_a (order(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))-> (ti(X_a,X)!=ti(X_a,Y)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))).
% 25.45/25.30 all A_2 B (hBOOL(hAPP(int,bool,zcong(A_2,B),zero_zero(int)))<->ti(int,A_2)=ti(int,B)).
% 25.45/25.30 all A_1 B_1 hBOOL(hAPP(int,bool,zcong(A_1,B_1),one_one(int))).
% 25.45/25.30 all A_1 M B_1 hBOOL(hAPP(int,bool,zcong(times_times(int,A_1,M),times_times(int,B_1,M)),M)).
% 25.45/25.30 all K_1 A_1 B_1 M (hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))->hBOOL(hAPP(int,bool,zcong(times_times(int,A_1,K_1),times_times(int,B_1,K_1)),M))).
% 25.45/25.30 all K_1 A_1 B_1 M (hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))->hBOOL(hAPP(int,bool,zcong(times_times(int,K_1,A_1),times_times(int,K_1,B_1)),M))).
% 25.45/25.30 all C D_1 A_1 B_1 M (hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))-> (hBOOL(hAPP(int,bool,zcong(C,D_1),M))->hBOOL(hAPP(int,bool,zcong(times_times(int,A_1,C),times_times(int,B_1,D_1)),M)))).
% 25.45/25.30 all C D_1 A_1 B_1 M (hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))-> (hBOOL(hAPP(int,bool,zcong(C,D_1),M))->hBOOL(hAPP(int,bool,zcong(plus_plus(int,A_1,C),plus_plus(int,B_1,D_1)),M)))).
% 25.45/25.30 all C D_1 A_1 B_1 M (hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))-> (hBOOL(hAPP(int,bool,zcong(C,D_1),M))->hBOOL(hAPP(int,bool,zcong(minus_minus(int,A_1,C),minus_minus(int,B_1,D_1)),M)))).
% 25.45/25.30 all B_1 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_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),A_1))-> -hBOOL(hAPP(int,bool,zcong(A_1,B_1),M)))))).
% 25.45/25.30 all A_1 R_1 B_1 M C D_1 N (plus_plus(int,times_times(int,minus_minus(int,A_1,times_times(int,R_1,B_1)),M),times_times(int,minus_minus(int,C,times_times(int,R_1,D_1)),N))=minus_minus(int,plus_plus(int,times_times(int,A_1,M),times_times(int,C,N)),times_times(int,R_1,plus_plus(int,times_times(int,B_1,M),times_times(int,D_1,N))))).
% 25.45/25.30 all A_2 B Ma (hBOOL(hAPP(int,bool,zcong(A_2,B),Ma))<-> (exists K_2 (ti(int,B)=plus_plus(int,A_2,times_times(int,Ma,K_2))))).
% 25.45/25.30 all A_2 B Ma (hBOOL(hAPP(int,bool,zcong(A_2,B),Ma))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),minus_minus(int,A_2,B)))).
% 25.45/25.30 all A_1 B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),minus_minus(int,B_1,one_one(int))))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B_1))).
% 25.45/25.30 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)))).
% 25.45/25.30 all B_1 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_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),M))-> (hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))->ti(int,A_1)=ti(int,B_1)))))).
% 25.45/25.30 all N P_2 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_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),times_times(int,M,N)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),N))))).
% 25.45/25.30 all P_3 (hBOOL(hAPP(int,bool,zprime,P_3))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_3))& (all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M_1))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M_1),P_3))->ti(int,M_1)=one_one(int)|ti(int,M_1)=ti(int,P_3)))).
% 25.45/25.30 all A_1 P_2 (hBOOL(hAPP(int,bool,zprime,P_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,zcong(times_times(int,A_1,A_1),one_one(int)),P_2))->hBOOL(hAPP(int,bool,zcong(A_1,one_one(int)),P_2))|hBOOL(hAPP(int,bool,zcong(A_1,minus_minus(int,P_2,one_one(int))),P_2))))).
% 25.45/25.30 all P_1 Xa Ya (hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,Xa,Ya))))<-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ya),Xa))->hBOOL(hAPP(int,bool,P_1,minus_minus(int,hAPP(nat,int,semiring_1_of_nat(int),Xa),hAPP(nat,int,semiring_1_of_nat(int),Ya)))))& (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya))->hBOOL(hAPP(int,bool,P_1,zero_zero(int))))).
% 25.45/25.30 all P_2 (hBOOL(hAPP(int,bool,zprime,P_2))-> (ti(int,P_2)!=number_number_of(int,bit0(bit1(pls)))-> (ti(int,P_2)!=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_2))))).
% 25.45/25.30 all P_4 P_1 Xa ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))-> (hBOOL(P_1)<->hBOOL(P_4)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))&hBOOL(P_1)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))&hBOOL(P_4))).
% 25.45/25.30 all P_4 P_1 Xa ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))-> (hBOOL(P_1)<->hBOOL(P_4)))-> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))->hBOOL(P_1))<-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))->hBOOL(P_4)))).
% 25.45/25.30 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),times_times(int,K,Ma)),times_times(int,K,Ta))))).
% 25.45/25.30 all X_a (dvd(X_a)&semiring_0(X_a)-> (all P_1 L_1 ((exists X_1 hBOOL(hAPP(X_a,bool,P_1,times_times(X_a,L_1,X_1))))<-> (exists X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L_1),plus_plus(X_a,X_1,zero_zero(X_a))))&hBOOL(hAPP(X_a,bool,P_1,X_1))))))).
% 25.45/25.30 all X_a (comm_ring(X_a)&dvd(X_a)-> (all Ta D D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),D_2))-> (all X_1 K_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),plus_plus(X_a,X_1,Ta)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),plus_plus(X_a,minus_minus(X_a,X_1,times_times(X_a,K_2,D_2)),Ta)))))))).
% 25.45/25.30 all X_a (comm_ring(X_a)&dvd(X_a)-> (all Ta D D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),D_2))-> (all X_1 K_2 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),plus_plus(X_a,X_1,Ta)))<-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),plus_plus(X_a,minus_minus(X_a,X_1,times_times(X_a,K_2,D_2)),Ta)))))))).
% 25.45/25.30 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,pls))).
% 25.45/25.30 all A_2 P_3 (hBOOL(hAPP(int,bool,zcong(times_times(int,A_2,minus_minus(int,P_3,one_one(int))),one_one(int)),P_3))<->hBOOL(hAPP(int,bool,zcong(A_2,minus_minus(int,P_3,one_one(int))),P_3))).
% 25.45/25.30 all Z X Y P_2 (hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X),Y),one_one(int)),P_2))->hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X),times_times(nat,Y,Z)),one_one(int)),P_2))).
% 25.45/25.30 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,N)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit0(N))))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit1(N))))).
% 25.45/25.30 -(all S W_1 (-(ti(int,W_1)=minus_minus(int,y,times_times(int,S,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,W_1))),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))))).
% 25.45/25.30 -(all R V (-(ti(int,V)=minus_minus(int,x,times_times(int,R,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,V))),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))))).
% 25.45/25.30 all D_1 I_2 (ti(int,I_2)!=zero_zero(int)-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),I_2))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),abs_abs(int,D_1)),abs_abs(int,I_2))))).
% 25.45/25.30 all W Z (nat_1(abs_abs(int,times_times(int,W,Z)))=times_times(nat,nat_1(abs_abs(int,W)),nat_1(abs_abs(int,Z)))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all L K_1 (abs_abs(X_a,L)=abs_abs(X_a,K_1)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L),K_1))))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all Ma K (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),abs_abs(X_a,Ma)),K))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),K))))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all Ma K (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),abs_abs(X_a,K)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),K))))).
% 25.45/25.30 all A_1 B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_1),B_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B_1),A_1))->abs_abs(int,A_1)=abs_abs(int,B_1))).
% 25.45/25.30 all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Xa),one_one(int)))<->abs_abs(int,Xa)=one_one(int)).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all Y X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X))->times_times(X_a,abs_abs(X_a,Y),X)=abs_abs(X_a,times_times(X_a,Y,X))))).
% 25.45/25.30 all X_a (ordered_ring_abs(X_a)-> (all B_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),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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_1),zero_zero(X_a))))->abs_abs(X_a,times_times(X_a,A_1,B_1))=times_times(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1))))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all A_1 N 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,abs_abs(X_a,A_1)),N))))).
% 25.45/25.30 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 B_1 C D_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),abs_abs(X_a,minus_minus(X_a,plus_plus(X_a,A_1,B_1),plus_plus(X_a,C,D_1)))),plus_plus(X_a,abs_abs(X_a,minus_minus(X_a,A_1,C)),abs_abs(X_a,minus_minus(X_a,B_1,D_1))))))).
% 25.45/25.30 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 B_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),abs_abs(X_a,minus_minus(X_a,A_1,B_1))),plus_plus(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1)))))).
% 25.45/25.30 all X_a (number_ring(X_a)&linordered_idom(X_a)->abs_abs(X_a,number_number_of(X_a,min))=one_one(X_a)).
% 25.45/25.30 all X_a (ordere142940540dd_abs(X_a)->abs_abs(X_a,zero_zero(X_a))=zero_zero(X_a)).
% 25.45/25.30 all X_a (ordere142940540dd_abs(X_a)-> (all A_2 (abs_abs(X_a,A_2)=zero_zero(X_a)<->ti(X_a,A_2)=zero_zero(X_a)))).
% 25.45/25.30 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 B_1 (abs_abs(X_a,plus_plus(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1)))=plus_plus(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1))))).
% 25.45/25.30 all X_a (linordered_idom(X_a)->abs_abs(X_a,one_one(X_a))=one_one(X_a)).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all A_1 N (abs_abs(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N))=hAPP(nat,X_a,power_power(X_a,abs_abs(X_a,A_1)),N)))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all N (abs_abs(X_a,hAPP(nat,X_a,semiring_1_of_nat(X_a),N))=hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))).
% 25.45/25.30 all M (abs_abs(int,hAPP(nat,int,semiring_1_of_nat(int),M))=hAPP(nat,int,semiring_1_of_nat(int),M)).
% 25.45/25.30 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 (abs_abs(X_a,abs_abs(X_a,A_1))=abs_abs(X_a,A_1)))).
% 25.45/25.30 all M N (abs_abs(int,times_times(int,M,N))=one_one(int)->abs_abs(int,M)=one_one(int)).
% 25.45/25.30 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 B_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),minus_minus(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1))),abs_abs(X_a,minus_minus(X_a,B_1,A_1)))))).
% 25.45/25.30 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 B_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),minus_minus(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1))),abs_abs(X_a,minus_minus(X_a,A_1,B_1)))))).
% 25.45/25.30 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 B_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),abs_abs(X_a,minus_minus(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1)))),abs_abs(X_a,minus_minus(X_a,A_1,B_1)))))).
% 25.45/25.30 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 B_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),abs_abs(X_a,plus_plus(X_a,A_1,B_1))),plus_plus(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1)))))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all B_1 D_1 A_1 C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),abs_abs(X_a,A_1)),C))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),abs_abs(X_a,B_1)),D_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1))),times_times(X_a,C,D_1))))))).
% 25.45/25.30 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))->abs_abs(X_a,A_1)=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (ordere142940540dd_abs(X_a)-> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),abs_abs(X_a,A_2)))<->ti(X_a,A_2)!=zero_zero(X_a)))).
% 25.45/25.30 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),abs_abs(X_a,A_1)),zero_zero(X_a)))))).
% 25.45/25.30 all X_a (ordere142940540dd_abs(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)),A_1))->abs_abs(X_a,A_1)=ti(X_a,A_1)))).
% 25.45/25.30 all X_a (ordere142940540dd_abs(X_a)-> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),abs_abs(X_a,A_2)),zero_zero(X_a)))<->ti(X_a,A_2)=zero_zero(X_a)))).
% 25.45/25.30 all X_a (ordere142940540dd_abs(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)),abs_abs(X_a,A_1))))).
% 25.45/25.30 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 B_1 (abs_abs(X_a,minus_minus(X_a,A_1,B_1))=abs_abs(X_a,minus_minus(X_a,B_1,A_1))))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all A_1 B_1 (abs_abs(X_a,times_times(X_a,A_1,B_1))=times_times(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1))))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all A_1 (times_times(X_a,abs_abs(X_a,A_1),abs_abs(X_a,A_1))=times_times(X_a,A_1,A_1)))).
% 25.45/25.30 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),abs_abs(X_a,A_1))))).
% 25.45/25.30 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),abs_abs(X_a,A_1)),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B_1))))).
% 25.45/25.30 all X N hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,power_power(int,abs_abs(int,X)),N))).
% 25.45/25.30 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),abs_abs(int,Z_1)),one_one(int)))<->ti(int,Z_1)=zero_zero(int)).
% 25.45/25.30 all Z_1 (abs_abs(int,Z_1)=one_one(int)<->ti(int,Z_1)=one_one(int)|ti(int,Z_1)=number_number_of(int,min)).
% 25.45/25.30 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all N (abs_abs(X_a,hAPP(nat,X_a,power_power(X_a,number_number_of(X_a,min)),N))=one_one(X_a)))).
% 25.45/25.30 all X (abs_abs(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit1(bit1(pls)))))=hAPP(nat,int,power_power(int,abs_abs(int,X)),number_number_of(nat,bit1(bit1(pls))))).
% 25.45/25.30 all Xa Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,power_power(int,abs_abs(int,Xa)),Na)))<->ti(int,Xa)!=zero_zero(int)|Na=zero_zero(nat)).
% 25.45/25.30 all Na Ma (ti(int,Ma)!=zero_zero(int)-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),times_times(int,Ma,Na)),Ma))<->abs_abs(int,Na)=one_one(int))).
% 25.45/25.30 all Ma Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),Z_1))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),nat_1(abs_abs(int,Z_1))))).
% 25.45/25.30 all Z_1 Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z_1),hAPP(nat,int,semiring_1_of_nat(int),Ma)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(abs_abs(int,Z_1))),Ma))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all A_1 (abs_abs(X_a,hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls))))))).
% 25.45/25.30 all X_a (linordered_idom(X_a)-> (all A_1 (hAPP(nat,X_a,power_power(X_a,abs_abs(X_a,A_1)),number_number_of(nat,bit0(bit1(pls))))=hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls))))))).
% 25.45/25.30 all A_1 (abs_abs(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,int,power_power(int,abs_abs(int,A_1)),number_number_of(nat,bit0(bit1(pls))))).
% 25.45/25.30 all A_2 B (hAPP(nat,int,power_power(int,A_2),number_number_of(nat,bit0(bit1(pls))))=hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls))))<->abs_abs(int,A_2)=abs_abs(int,B)).
% 25.45/25.30 all A_1 (hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls))))=one_one(int)->abs_abs(int,A_1)=one_one(int)).
% 25.45/25.30 all Z X D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),plus_plus(int,X,times_times(int,plus_plus(int,abs_abs(int,minus_minus(int,X,Z)),one_one(int)),D_1))))).
% 25.45/25.30 all X Z D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),minus_minus(int,X,times_times(int,plus_plus(int,abs_abs(int,minus_minus(int,X,Z)),one_one(int)),D_1))),Z))).
% 25.45/25.30 all Y X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X))-> (exists N_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,minus_minus(int,Y,times_times(int,N_1,X))))),X)))).
% 25.45/25.30 all K P_1 D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))-> ((all X_1 (hBOOL(hAPP(int,bool,P_1,X_1))->hBOOL(hAPP(int,bool,P_1,minus_minus(int,X_1,D)))))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))-> (all X_1 (hBOOL(hAPP(int,bool,P_1,X_1))->hBOOL(hAPP(int,bool,P_1,minus_minus(int,X_1,times_times(int,K,D))))))))).
% 25.45/25.30 all X (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),plus_plus(real,abs_abs(real,X),one_one(real))),X))).
% 25.45/25.30 all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),plus_plus(real,one_one(real),abs_abs(real,X)))).
% 25.45/25.30 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),abs_abs(real,X)),one_one(real)))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,power_power(real,X),number_number_of(nat,bit0(bit1(pls))))),one_one(real)))).
% 25.45/25.30 all Na P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))-> (hBOOL(hAPP(nat,bool,P_1,Na))-> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),Na))& (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,plus_plus(nat,K_2,one_one(nat)))))))).
% 25.45/25.30 all K P_1 D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))-> ((all X_1 (hBOOL(hAPP(int,bool,P_1,X_1))->hBOOL(hAPP(int,bool,P_1,plus_plus(int,X_1,D)))))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))-> (all X_1 (hBOOL(hAPP(int,bool,P_1,X_1))->hBOOL(hAPP(int,bool,P_1,plus_plus(int,X_1,times_times(int,K,D))))))))).
% 25.45/25.30 all U Ma Na J I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),I_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,times_times(nat,I_1,U),Ma)),plus_plus(nat,times_times(nat,J,U),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,times_times(nat,minus_minus(nat,I_1,J),U),Ma)),Na)))).
% 25.45/25.30 all U Ma Na I_1 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,times_times(nat,I_1,U),Ma)),plus_plus(nat,times_times(nat,J,U),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),plus_plus(nat,times_times(nat,minus_minus(nat,J,I_1),U),Na))))).
% 25.45/25.30 all K Ma Na (times_times(nat,K,Ma)=times_times(nat,K,Na)<->K=zero_zero(nat)|Ma=Na).
% 25.45/25.30 all I_2 U_1 J_1 K_1 (plus_plus(nat,times_times(nat,I_2,U_1),plus_plus(nat,times_times(nat,J_1,U_1),K_1))=plus_plus(nat,times_times(nat,plus_plus(nat,I_2,J_1),U_1),K_1)).
% 25.45/25.30 all Ma Na 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),times_times(nat,K,Ma)),times_times(nat,K,Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)))).
% 25.45/25.30 all Ma Na K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))-> (times_times(nat,K,Ma)=times_times(nat,K,Na)<->Ma=Na)).
% 25.45/25.30 all K Ma Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),times_times(nat,K,Ma)),times_times(nat,K,Na)))<->K=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),Na))).
% 25.45/25.31 all Ma Na 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),times_times(nat,K,Ma)),times_times(nat,K,Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),Na)))).
% 25.45/25.31 all Ma Na 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),times_times(nat,K,Ma)),times_times(nat,K,Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)))).
% 25.45/25.31 all U Ma Na J I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),I_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,times_times(nat,I_1,U),Ma)),plus_plus(nat,times_times(nat,J,U),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,times_times(nat,minus_minus(nat,I_1,J),U),Ma)),Na)))).
% 25.45/25.31 all U_1 M N J_1 I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),I_2))->minus_minus(nat,plus_plus(nat,times_times(nat,I_2,U_1),M),plus_plus(nat,times_times(nat,J_1,U_1),N))=minus_minus(nat,plus_plus(nat,times_times(nat,minus_minus(nat,I_2,J_1),U_1),M),N)).
% 25.45/25.31 all U Ma Na J I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),I_1))-> (plus_plus(nat,times_times(nat,I_1,U),Ma)=plus_plus(nat,times_times(nat,J,U),Na)<->plus_plus(nat,times_times(nat,minus_minus(nat,I_1,J),U),Ma)=Na)).
% 25.45/25.31 all U Ma Na I_1 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,times_times(nat,I_1,U),Ma)),plus_plus(nat,times_times(nat,J,U),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),plus_plus(nat,times_times(nat,minus_minus(nat,J,I_1),U),Na))))).
% 25.45/25.31 all U_1 M N I_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_1))->minus_minus(nat,plus_plus(nat,times_times(nat,I_2,U_1),M),plus_plus(nat,times_times(nat,J_1,U_1),N))=minus_minus(nat,M,plus_plus(nat,times_times(nat,minus_minus(nat,J_1,I_2),U_1),N))).
% 25.45/25.31 all U Ma Na I_1 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J))-> (plus_plus(nat,times_times(nat,I_1,U),Ma)=plus_plus(nat,times_times(nat,J,U),Na)<->Ma=plus_plus(nat,times_times(nat,minus_minus(nat,J,I_1),U),Na))).
% 25.45/25.31 all K F Na ((all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),Na))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),abs_abs(int,minus_minus(int,hAPP(nat,int,F,plus_plus(nat,I,one_one(nat))),hAPP(nat,int,F,I)))),one_one(int)))))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))-> (exists I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),Na))&hAPP(nat,int,F,I)=ti(int,K)))))).
% 25.45/25.31 all K F Na ((all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),Na))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),abs_abs(int,minus_minus(int,hAPP(nat,int,F,plus_plus(nat,I,one_one(nat))),hAPP(nat,int,F,I)))),one_one(int)))))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))-> (exists I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),Na))&hAPP(nat,int,F,I)=ti(int,K)))))).
% 25.45/25.31 semiri456707255roduct(int).
% 25.45/25.31 ordere223160158up_add(int).
% 25.45/25.31 ordere236663937imp_le(int).
% 25.45/25.31 linord893533164strict(int).
% 25.45/25.31 linord626643107strict(int).
% 25.45/25.31 linord20386208strict(int).
% 25.45/25.31 ordere779506340up_add(int).
% 25.45/25.31 ordere142940540dd_abs(int).
% 25.45/25.31 ordere216010020id_add(int).
% 25.45/25.31 linord219039673up_add(int).
% 25.45/25.31 cancel146912293up_add(int).
% 25.45/25.31 ring_11004092258visors(int).
% 25.45/25.31 ordere453448008miring(int).
% 25.45/25.31 linord581940658strict(int).
% 25.45/25.31 ring_n68954251visors(int).
% 25.45/25.31 ordere1490568538miring(int).
% 25.45/25.31 linord1278240602ring_1(int).
% 25.45/25.31 ordered_ab_group_add(int).
% 25.45/25.31 cancel_semigroup_add(int).
% 25.45/25.31 linordered_semiring(int).
% 25.45/25.31 linordered_semidom(int).
% 25.45/25.31 ab_semigroup_mult(int).
% 25.45/25.31 comm_monoid_mult(int).
% 25.45/25.31 ab_semigroup_add(int).
% 25.45/25.31 ordered_semiring(int).
% 25.45/25.31 ordered_ring_abs(int).
% 25.45/25.31 no_zero_divisors(int).
% 25.45/25.31 comm_monoid_add(int).
% 25.45/25.31 linordered_ring(int).
% 25.45/25.31 linordered_idom(int).
% 25.45/25.31 comm_semiring_1(int).
% 25.45/25.31 comm_semiring(int).
% 25.45/25.31 semiring_char_0(int).
% 25.45/25.31 number_semiring(int).
% 25.45/25.31 ab_group_add(int).
% 25.45/25.31 zero_ne_q_one(int).
% 25.45/25.31 ordered_ring(int).
% 25.45/25.31 linorder(int).
% 25.45/25.31 monoid_mult(int).
% 25.45/25.31 comm_ring_1(int).
% 25.45/25.31 monoid_add(int).
% 25.45/25.31 semiring_1(int).
% 25.45/25.31 semiring_0(int).
% 25.45/25.31 group_add(int).
% 25.45/25.31 mult_zero(int).
% 25.45/25.31 comm_ring(int).
% 25.45/25.31 order(int).
% 25.45/25.31 ring_char_0(int).
% 25.45/25.31 number_ring(int).
% 25.45/25.31 semiring(int).
% 25.45/25.31 ring_1(int).
% 25.45/25.31 power(int).
% 25.45/25.31 zero(int).
% 25.45/25.31 ring(int).
% 25.45/25.31 idom(int).
% 25.45/25.31 number(int).
% 25.45/25.31 one(int).
% 25.45/25.31 dvd(int).
% 25.45/25.31 semiri456707255roduct(nat).
% 25.45/25.31 ordere223160158up_add(nat).
% 25.45/25.31 ordere236663937imp_le(nat).
% 25.45/25.31 linord893533164strict(nat).
% 25.45/25.31 linord20386208strict(nat).
% 25.45/25.31 ordere779506340up_add(nat).
% 25.45/25.31 ordere216010020id_add(nat).
% 25.45/25.31 cancel146912293up_add(nat).
% 25.45/25.31 ordere453448008miring(nat).
% 25.45/25.31 ordere1490568538miring(nat).
% 25.45/25.31 cancel_semigroup_add(nat).
% 25.45/25.31 linordered_semiring(nat).
% 25.45/25.31 linordered_semidom(nat).
% 25.45/25.31 ab_semigroup_mult(nat).
% 25.45/25.31 comm_monoid_mult(nat).
% 25.45/25.31 ab_semigroup_add(nat).
% 25.45/25.31 ordered_semiring(nat).
% 25.45/25.31 no_zero_divisors(nat).
% 25.45/25.31 comm_monoid_add(nat).
% 25.45/25.31 comm_semiring_1(nat).
% 25.45/25.31 comm_semiring(nat).
% 25.45/25.31 semiring_char_0(nat).
% 25.45/25.31 number_semiring(nat).
% 25.45/25.31 zero_ne_q_one(nat).
% 25.45/25.31 linorder(nat).
% 25.45/25.31 monoid_mult(nat).
% 25.45/25.31 monoid_add(nat).
% 25.45/25.31 semiring_1(nat).
% 25.45/25.31 semiring_0(nat).
% 25.45/25.31 mult_zero(nat).
% 25.45/25.31 order(nat).
% 25.45/25.31 semiring(nat).
% 25.45/25.31 power(nat).
% 25.45/25.31 zero(nat).
% 25.45/25.31 number(nat).
% 25.45/25.31 one(nat).
% 25.45/25.31 dvd(nat).
% 25.45/25.31 order(bool).
% 25.45/25.31 semiri456707255roduct(real).
% 25.45/25.31 ordere223160158up_add(real).
% 25.45/25.31 ordere236663937imp_le(real).
% 25.45/25.31 linord893533164strict(real).
% 25.45/25.31 linord626643107strict(real).
% 25.45/25.31 linord20386208strict(real).
% 25.45/25.31 ordere779506340up_add(real).
% 25.45/25.31 ordere142940540dd_abs(real).
% 25.45/25.31 ordere216010020id_add(real).
% 25.45/25.31 linord219039673up_add(real).
% 25.45/25.31 cancel146912293up_add(real).
% 25.45/25.31 ring_11004092258visors(real).
% 25.45/25.31 ordere453448008miring(real).
% 25.45/25.31 linord581940658strict(real).
% 25.45/25.31 ring_n68954251visors(real).
% 25.45/25.31 ordere1490568538miring(real).
% 25.45/25.31 linord1278240602ring_1(real).
% 25.45/25.31 ordered_ab_group_add(real).
% 25.45/25.31 cancel_semigroup_add(real).
% 25.45/25.31 linordered_semiring(real).
% 25.45/25.31 linordered_semidom(real).
% 25.45/25.31 ab_semigroup_mult(real).
% 25.45/25.31 comm_monoid_mult(real).
% 25.45/25.31 ab_semigroup_add(real).
% 25.45/25.31 ordered_semiring(real).
% 25.45/25.31 ordered_ring_abs(real).
% 25.45/25.31 no_zero_divisors(real).
% 25.45/25.31 comm_monoid_add(real).
% 25.45/25.31 linordered_ring(real).
% 25.45/25.31 linordered_idom(real).
% 25.45/25.31 comm_semiring_1(real).
% 25.45/25.31 comm_semiring(real).
% 25.45/25.31 semiring_char_0(real).
% 25.45/25.31 number_semiring(real).
% 25.45/25.31 ab_group_add(real).
% 25.45/25.31 zero_ne_q_one(real).
% 25.45/25.31 ordered_ring(real).
% 25.45/25.31 linorder(real).
% 25.45/25.31 monoid_mult(real).
% 25.45/25.31 comm_ring_1(real).
% 25.45/25.31 monoid_add(real).
% 25.45/25.31 semiring_1(real).
% 25.45/25.31 semiring_0(real).
% 25.45/25.31 group_add(real).
% 25.45/25.31 mult_zero(real).
% 25.45/25.31 comm_ring(real).
% 25.45/25.31 order(real).
% 25.45/25.31 ring_char_0(real).
% 25.45/25.31 number_ring(real).
% 25.45/25.31 semiring(real).
% 25.45/25.31 ring_1(real).
% 25.45/25.31 power(real).
% 25.45/25.31 zero(real).
% 25.45/25.31 ring(real).
% 25.45/25.31 idom(real).
% 25.45/25.31 number(real).
% 25.45/25.31 one(real).
% 25.45/25.31 dvd(real).
% 25.45/25.31 all T A (ti(T,ti(T,A))=ti(T,A)).
% 25.45/25.31 all X_a X Y (if(X_a,fTrue,X,Y)=ti(X_a,X)).
% 25.45/25.31 all X_a X Y (if(X_a,fFalse,X,Y)=ti(X_a,Y)).
% 25.45/25.31 all P (ti(bool,P)=fTrue|ti(bool,P)=fFalse).
% 25.45/25.31 -(hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls))))!=zero_zero(int)).
% 25.45/25.31 end_of_list.
% 25.45/25.31
% 25.45/25.31 -------> usable clausifies to:
% 25.45/25.31
% 25.45/25.31 list(usable).
% 25.45/25.31 0 [] A=A.
% 25.45/25.31 0 [] -ordere142940540dd_abs(X_a)|abs_abs(X_a,ti(X_a,B_1_1))=abs_abs(X_a,B_1_1).
% 25.45/25.31 0 [] -ordere142940540dd_abs(X_a)|ti(X_a,abs_abs(X_a,B_1_1))=abs_abs(X_a,B_1_1).
% 25.45/25.31 0 [] -group_add(X_a)|minus_minus(X_a,ti(X_a,B_1_1),B_2_1)=minus_minus(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -group_add(X_a)|minus_minus(X_a,B_1_1,ti(X_a,B_2_1))=minus_minus(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -group_add(X_a)|ti(X_a,minus_minus(X_a,B_1_1,B_2_1))=minus_minus(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] minus_minus(nat,ti(nat,B_1_1),B_2_1)=minus_minus(nat,B_1_1,B_2_1).
% 25.45/25.31 0 [] minus_minus(nat,B_1_1,ti(nat,B_2_1))=minus_minus(nat,B_1_1,B_2_1).
% 25.45/25.31 0 [] ti(nat,minus_minus(nat,B_1_1,B_2_1))=minus_minus(nat,B_1_1,B_2_1).
% 25.45/25.31 0 [] -one(X_a)|ti(X_a,one_one(X_a))=one_one(X_a).
% 25.45/25.31 0 [] -monoid_add(X_a)|plus_plus(X_a,ti(X_a,B_1_1),B_2_1)=plus_plus(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -monoid_add(X_a)|plus_plus(X_a,B_1_1,ti(X_a,B_2_1))=plus_plus(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -monoid_add(X_a)|ti(X_a,plus_plus(X_a,B_1_1,B_2_1))=plus_plus(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -ab_semigroup_add(X_a)|plus_plus(X_a,ti(X_a,B_1_1),B_2_1)=plus_plus(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -ab_semigroup_add(X_a)|plus_plus(X_a,B_1_1,ti(X_a,B_2_1))=plus_plus(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -ab_semigroup_add(X_a)|ti(X_a,plus_plus(X_a,B_1_1,B_2_1))=plus_plus(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -cancel_semigroup_add(X_a)|plus_plus(X_a,ti(X_a,B_1_1),B_2_1)=plus_plus(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -cancel_semigroup_add(X_a)|plus_plus(X_a,B_1_1,ti(X_a,B_2_1))=plus_plus(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -cancel_semigroup_add(X_a)|ti(X_a,plus_plus(X_a,B_1_1,B_2_1))=plus_plus(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -dvd(X_a)|times_times(X_a,ti(X_a,B_1_1),B_2_1)=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -dvd(X_a)|times_times(X_a,B_1_1,ti(X_a,B_2_1))=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -dvd(X_a)|ti(X_a,times_times(X_a,B_1_1,B_2_1))=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -power(X_a)|times_times(X_a,ti(X_a,B_1_1),B_2_1)=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -power(X_a)|times_times(X_a,B_1_1,ti(X_a,B_2_1))=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -power(X_a)|ti(X_a,times_times(X_a,B_1_1,B_2_1))=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -semiring(X_a)|times_times(X_a,ti(X_a,B_1_1),B_2_1)=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -semiring(X_a)|times_times(X_a,B_1_1,ti(X_a,B_2_1))=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -semiring(X_a)|ti(X_a,times_times(X_a,B_1_1,B_2_1))=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -no_zero_divisors(X_a)|times_times(X_a,ti(X_a,B_1_1),B_2_1)=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -no_zero_divisors(X_a)|times_times(X_a,B_1_1,ti(X_a,B_2_1))=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -no_zero_divisors(X_a)|ti(X_a,times_times(X_a,B_1_1,B_2_1))=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -mult_zero(X_a)|times_times(X_a,ti(X_a,B_1_1),B_2_1)=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -mult_zero(X_a)|times_times(X_a,B_1_1,ti(X_a,B_2_1))=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -mult_zero(X_a)|ti(X_a,times_times(X_a,B_1_1,B_2_1))=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -ab_semigroup_mult(X_a)|times_times(X_a,ti(X_a,B_1_1),B_2_1)=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -ab_semigroup_mult(X_a)|times_times(X_a,B_1_1,ti(X_a,B_2_1))=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -ab_semigroup_mult(X_a)|ti(X_a,times_times(X_a,B_1_1,B_2_1))=times_times(X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -zero(X_a)|ti(X_a,zero_zero(X_a))=zero_zero(X_a).
% 25.45/25.31 0 [] ti(X_a,undefined(X_a))=undefined(X_a).
% 25.45/25.31 0 [] if(X_a,ti(bool,B_1_1),B_2_1,B_3)=if(X_a,B_1_1,B_2_1,B_3).
% 25.45/25.31 0 [] if(X_a,B_1_1,ti(X_a,B_2_1),B_3)=if(X_a,B_1_1,B_2_1,B_3).
% 25.45/25.31 0 [] if(X_a,B_1_1,B_2_1,ti(X_a,B_3))=if(X_a,B_1_1,B_2_1,B_3).
% 25.45/25.31 0 [] ti(X_a,if(X_a,B_1_1,B_2_1,B_3))=if(X_a,B_1_1,B_2_1,B_3).
% 25.45/25.31 0 [] zcong(ti(int,B_1_1),B_2_1)=zcong(B_1_1,B_2_1).
% 25.45/25.31 0 [] zcong(B_1_1,ti(int,B_2_1))=zcong(B_1_1,B_2_1).
% 25.45/25.31 0 [] ti(fun(int,bool),zcong(B_1_1,B_2_1))=zcong(B_1_1,B_2_1).
% 25.45/25.31 0 [] ti(fun(int,bool),zprime)=zprime.
% 25.45/25.31 0 [] bit0(ti(int,B_1_1))=bit0(B_1_1).
% 25.45/25.31 0 [] ti(int,bit0(B_1_1))=bit0(B_1_1).
% 25.45/25.31 0 [] bit1(ti(int,B_1_1))=bit1(B_1_1).
% 25.45/25.31 0 [] ti(int,bit1(B_1_1))=bit1(B_1_1).
% 25.45/25.31 0 [] ti(int,min)=min.
% 25.45/25.31 0 [] ti(int,pls)=pls.
% 25.45/25.31 0 [] nat_1(ti(int,B_1_1))=nat_1(B_1_1).
% 25.45/25.31 0 [] ti(nat,nat_1(B_1_1))=nat_1(B_1_1).
% 25.45/25.31 0 [] -number(X_a)|number_number_of(X_a,ti(int,B_1_1))=number_number_of(X_a,B_1_1).
% 25.45/25.31 0 [] -number(X_a)|ti(X_a,number_number_of(X_a,B_1_1))=number_number_of(X_a,B_1_1).
% 25.45/25.31 0 [] succ(ti(int,B_1_1))=succ(B_1_1).
% 25.45/25.31 0 [] ti(int,succ(B_1_1))=succ(B_1_1).
% 25.45/25.31 0 [] -semiring_1(X_a)|ti(fun(nat,X_a),semiring_1_of_nat(X_a))=semiring_1_of_nat(X_a).
% 25.45/25.31 0 [] -order(X_a)|ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a).
% 25.45/25.31 0 [] -order(X_a)|ti(fun(X_a,fun(X_a,bool)),ord_less_e_q(X_a))=ord_less_e_q(X_a).
% 25.45/25.31 0 [] -power(X_a)|power_power(X_a,ti(X_a,B_1_1))=power_power(X_a,B_1_1).
% 25.45/25.31 0 [] -power(X_a)|ti(fun(nat,X_a),power_power(X_a,B_1_1))=power_power(X_a,B_1_1).
% 25.45/25.31 0 [] legendre(ti(int,B_1_1),B_2_1)=legendre(B_1_1,B_2_1).
% 25.45/25.31 0 [] legendre(B_1_1,ti(int,B_2_1))=legendre(B_1_1,B_2_1).
% 25.45/25.31 0 [] ti(int,legendre(B_1_1,B_2_1))=legendre(B_1_1,B_2_1).
% 25.45/25.31 0 [] quadRes(ti(int,B_1_1))=quadRes(B_1_1).
% 25.45/25.31 0 [] ti(fun(int,bool),quadRes(B_1_1))=quadRes(B_1_1).
% 25.45/25.31 0 [] -dvd(X_a)|ti(fun(X_a,fun(X_a,bool)),dvd_dvd(X_a))=dvd_dvd(X_a).
% 25.45/25.31 0 [] ti(fun(int,bool),twoSqu658283162sum2sq)=twoSqu658283162sum2sq.
% 25.45/25.31 0 [] ti(bool,fFalse)=fFalse.
% 25.45/25.31 0 [] ti(bool,fTrue)=fTrue.
% 25.45/25.31 0 [] -order(X_a)|hAPP(X_a,fun(X_a,bool),ti(fun(X_a,fun(X_a,bool)),B_1_1),B_2_1)=hAPP(X_a,fun(X_a,bool),B_1_1,B_2_1).
% 25.45/25.31 0 [] -order(X_a)|hAPP(X_a,fun(X_a,bool),B_1_1,ti(X_a,B_2_1))=hAPP(X_a,fun(X_a,bool),B_1_1,B_2_1).
% 25.45/25.31 0 [] -order(X_a)|ti(fun(X_a,bool),hAPP(X_a,fun(X_a,bool),B_1_1,B_2_1))=hAPP(X_a,fun(X_a,bool),B_1_1,B_2_1).
% 25.45/25.31 0 [] -order(X_a)|hAPP(X_a,bool,ti(fun(X_a,bool),B_1_1),B_2_1)=hAPP(X_a,bool,B_1_1,B_2_1).
% 25.45/25.31 0 [] -order(X_a)|hAPP(X_a,bool,B_1_1,ti(X_a,B_2_1))=hAPP(X_a,bool,B_1_1,B_2_1).
% 25.45/25.31 0 [] -order(X_a)|ti(bool,hAPP(X_a,bool,B_1_1,B_2_1))=hAPP(X_a,bool,B_1_1,B_2_1).
% 25.45/25.31 0 [] -dvd(X_a)|hAPP(X_a,fun(X_a,bool),ti(fun(X_a,fun(X_a,bool)),B_1_1),B_2_1)=hAPP(X_a,fun(X_a,bool),B_1_1,B_2_1).
% 25.45/25.31 0 [] -dvd(X_a)|hAPP(X_a,fun(X_a,bool),B_1_1,ti(X_a,B_2_1))=hAPP(X_a,fun(X_a,bool),B_1_1,B_2_1).
% 25.45/25.31 0 [] -dvd(X_a)|ti(fun(X_a,bool),hAPP(X_a,fun(X_a,bool),B_1_1,B_2_1))=hAPP(X_a,fun(X_a,bool),B_1_1,B_2_1).
% 25.45/25.31 0 [] -dvd(X_a)|hAPP(X_a,bool,ti(fun(X_a,bool),B_1_1),B_2_1)=hAPP(X_a,bool,B_1_1,B_2_1).
% 25.45/25.31 0 [] -dvd(X_a)|hAPP(X_a,bool,B_1_1,ti(X_a,B_2_1))=hAPP(X_a,bool,B_1_1,B_2_1).
% 25.45/25.31 0 [] -dvd(X_a)|ti(bool,hAPP(X_a,bool,B_1_1,B_2_1))=hAPP(X_a,bool,B_1_1,B_2_1).
% 25.45/25.31 0 [] -power(X_a)|hAPP(nat,X_a,ti(fun(nat,X_a),B_1_1),B_2_1)=hAPP(nat,X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -power(X_a)|hAPP(nat,X_a,B_1_1,ti(nat,B_2_1))=hAPP(nat,X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -power(X_a)|ti(X_a,hAPP(nat,X_a,B_1_1,B_2_1))=hAPP(nat,X_a,B_1_1,B_2_1).
% 25.45/25.31 0 [] -hBOOL(ti(bool,B_1_1))|hBOOL(B_1_1).
% 25.45/25.31 0 [] hBOOL(ti(bool,B_1_1))| -hBOOL(B_1_1).
% 25.45/25.31 0 [] ti(int,m)=m.
% 25.45/25.31 0 [] ti(int,m1)=m1.
% 25.45/25.31 0 [] ti(nat,n)=n.
% 25.45/25.31 0 [] ti(int,s1)=s1.
% 25.45/25.31 0 [] ti(int,s)=s.
% 25.45/25.31 0 [] ti(int,t)=t.
% 25.45/25.31 0 [] ti(nat,tn)=tn.
% 25.45/25.31 0 [] ti(int,x)=x.
% 25.45/25.31 0 [] ti(int,y)=y.
% 25.45/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))).
% 25.45/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)).
% 25.45/25.31 0 [] -linordered_idom(X_a)|plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(X_a)|ti(X_a,Xa)=zero_zero(X_a).
% 25.45/25.31 0 [] -linordered_idom(X_a)|plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(X_a)|ti(X_a,Ya)=zero_zero(X_a).
% 25.45/25.31 0 [] -linordered_idom(X_a)|plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,bit0(bit1(pls)))))=zero_zero(X_a)|ti(X_a,Xa)!=zero_zero(X_a)|ti(X_a,Ya)!=zero_zero(X_a).
% 25.45/25.31 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).
% 25.45/25.31 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).
% 25.45/25.31 0 [] -ring_11004092258visors(X_a)|hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(pls))))!=zero_zero(X_a)|ti(X_a,A_2)=zero_zero(X_a).
% 25.45/25.31 0 [] -ring_11004092258visors(X_a)|hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(pls))))=zero_zero(X_a)|ti(X_a,A_2)!=zero_zero(X_a).
% 25.45/25.31 0 [] -number_ring(X_a)|plus_plus(X_a,one_one(X_a),number_number_of(X_a,W))=number_number_of(X_a,plus_plus(int,bit1(pls),W)).
% 25.45/25.31 0 [] -number_ring(X_a)|plus_plus(X_a,number_number_of(X_a,V_1),one_one(X_a))=number_number_of(X_a,plus_plus(int,V_1,bit1(pls))).
% 25.45/25.31 0 [] -number_ring(X_a)|plus_plus(X_a,one_one(X_a),one_one(X_a))=number_number_of(X_a,bit0(bit1(pls))).
% 25.45/25.31 0 [] -number_semiring(X_a)|plus_plus(X_a,one_one(X_a),one_one(X_a))=number_number_of(X_a,bit0(bit1(pls))).
% 25.45/25.31 0 [] hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),number_number_of(nat,bit0(bit1(pls))))=hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit0(bit1(pls))))).
% 25.45/25.31 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).
% 25.45/25.31 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).
% 25.45/25.31 0 [] -number_ring(X_a)|one_one(X_a)=number_number_of(X_a,bit1(pls)).
% 25.45/25.31 0 [] -number_ring(X_a)|number_number_of(X_a,bit1(pls))=one_one(X_a).
% 25.45/25.31 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),n)).
% 25.45/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),Y))|ti(int,X)=ti(int,Y)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X)).
% 25.45/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,K)),number_number_of(int,L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1)).
% 25.45/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,K)),number_number_of(int,L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1)).
% 25.45/25.31 0 [] plus_plus(int,number_number_of(int,V_1),number_number_of(int,W))=number_number_of(int,plus_plus(int,V_1,W)).
% 25.45/25.31 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,Xa)),number_number_of(X_a,Ya)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),Ya)).
% 25.45/25.31 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,Xa)),number_number_of(X_a,Ya)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),Ya)).
% 25.45/25.31 0 [] zero_zero(int)=number_number_of(int,pls).
% 25.45/25.31 0 [] hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),M)),N)=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,M),N)).
% 25.45/25.31 0 [] hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,M),N))=hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),M)),N).
% 25.45/25.31 0 [] plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),M),plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),N),Z))=plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),plus_plus(nat,M,N)),Z).
% 25.45/25.31 0 [] plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),M),hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,int,semiring_1_of_nat(int),plus_plus(nat,M,N)).
% 25.45/25.31 0 [] hAPP(nat,int,semiring_1_of_nat(int),one_one(nat))=one_one(int).
% 25.45/25.31 0 [] number_number_of(nat,pls)=zero_zero(nat).
% 25.45/25.31 0 [] zero_zero(nat)=number_number_of(nat,pls).
% 25.45/25.31 0 [] hAPP(nat,int,semiring_1_of_nat(int),Na)!=zero_zero(int)|Na=zero_zero(nat).
% 25.45/25.31 0 [] hAPP(nat,int,semiring_1_of_nat(int),Na)=zero_zero(int)|Na!=zero_zero(nat).
% 25.45/25.31 0 [] hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat))=zero_zero(int).
% 25.45/25.31 0 [] plus_plus(nat,one_one(nat),one_one(nat))=number_number_of(nat,bit0(bit1(pls))).
% 25.45/25.31 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)).
% 25.45/25.31 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)).
% 25.45/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit1(L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1)).
% 25.45/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit1(L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1)).
% 25.45/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)).
% 25.45/25.31 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)).
% 25.45/25.31 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)).
% 25.45/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit0(L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1)).
% 25.45/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit0(L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1)).
% 25.45/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(int,I_2,K_1)),plus_plus(int,J_1,K_1))).
% 25.45/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|plus_plus(nat,number_number_of(nat,V_1),number_number_of(nat,V_2))=number_number_of(nat,V_2).
% 25.45/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls))|plus_plus(nat,number_number_of(nat,V_1),number_number_of(nat,V_2))=number_number_of(nat,V_1).
% 25.51/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls))|plus_plus(nat,number_number_of(nat,V_1),number_number_of(nat,V_2))=number_number_of(nat,plus_plus(int,V_1,V_2)).
% 25.51/25.31 0 [] one_one(int)=number_number_of(int,bit1(pls)).
% 25.51/25.31 0 [] number_number_of(nat,bit1(pls))=one_one(nat).
% 25.51/25.31 0 [] one_one(nat)=number_number_of(nat,bit1(pls)).
% 25.51/25.31 0 [] -number_ring(X_a)| -ring_char_0(X_a)|number_number_of(X_a,Xa)!=number_number_of(X_a,Ya)|ti(int,Xa)=ti(int,Ya).
% 25.51/25.31 0 [] -number_ring(X_a)| -ring_char_0(X_a)|number_number_of(X_a,Xa)=number_number_of(X_a,Ya)|ti(int,Xa)!=ti(int,Ya).
% 25.51/25.31 0 [] -number(X_a)|number_number_of(X_a,Wa)!=ti(X_a,Xa)|ti(X_a,Xa)=number_number_of(X_a,Wa).
% 25.51/25.31 0 [] -number(X_a)|number_number_of(X_a,Wa)=ti(X_a,Xa)|ti(X_a,Xa)!=number_number_of(X_a,Wa).
% 25.51/25.31 0 [] bit1(K)!=bit1(L_1)|ti(int,K)=ti(int,L_1).
% 25.51/25.31 0 [] bit1(K)=bit1(L_1)|ti(int,K)!=ti(int,L_1).
% 25.51/25.31 0 [] bit0(K)!=bit0(L_1)|ti(int,K)=ti(int,L_1).
% 25.51/25.31 0 [] bit0(K)=bit0(L_1)|ti(int,K)!=ti(int,L_1).
% 25.51/25.31 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_2,A_2)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))).
% 25.51/25.31 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_2,A_2)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))).
% 25.51/25.31 0 [] plus_plus(int,plus_plus(int,Z1,Z2),Z3)=plus_plus(int,Z1,plus_plus(int,Z2,Z3)).
% 25.51/25.31 0 [] plus_plus(int,X,plus_plus(int,Y,Z))=plus_plus(int,Y,plus_plus(int,X,Z)).
% 25.51/25.31 0 [] plus_plus(int,Z,W)=plus_plus(int,W,Z).
% 25.51/25.31 0 [] hAPP(nat,int,semiring_1_of_nat(int),Ma)!=hAPP(nat,int,semiring_1_of_nat(int),Na)|Ma=Na.
% 25.51/25.31 0 [] hAPP(nat,int,semiring_1_of_nat(int),Ma)=hAPP(nat,int,semiring_1_of_nat(int),Na)|Ma!=Na.
% 25.51/25.31 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,Xa)),zero_zero(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),pls)).
% 25.51/25.31 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,Xa)),zero_zero(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),pls)).
% 25.51/25.31 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,Ya)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Ya)).
% 25.51/25.31 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,Ya)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Ya)).
% 25.51/25.31 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)).
% 25.51/25.31 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)).
% 25.51/25.31 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)).
% 25.51/25.31 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)).
% 25.51/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit0(L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1)).
% 25.51/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit0(L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1)).
% 25.51/25.31 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)).
% 25.51/25.31 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)).
% 25.51/25.31 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)).
% 25.51/25.31 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)).
% 25.51/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(Wa)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int))).
% 25.51/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(Wa)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int))).
% 25.51/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))).
% 25.51/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(Wa)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int))).
% 25.51/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(Wa)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int))).
% 25.51/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))).
% 25.51/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),plus_plus(int,Z_1,one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1))|ti(int,Wa)=ti(int,Z_1).
% 25.51/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),plus_plus(int,Z_1,one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1)).
% 25.51/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),plus_plus(int,Z_1,one_one(int))))|ti(int,Wa)!=ti(int,Z_1).
% 25.51/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K_1)),zero_zero(int))).
% 25.51/25.31 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,Xa)),one_one(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),bit1(pls))).
% 25.51/25.31 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,Xa)),one_one(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),bit1(pls))).
% 25.51/25.31 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,Ya)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(pls)),Ya)).
% 25.51/25.31 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,Ya)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(pls)),Ya)).
% 25.51/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(int,plus_plus(int,one_one(int),Z_1),Z_1)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),zero_zero(int))).
% 25.51/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(int,plus_plus(int,one_one(int),Z_1),Z_1)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),zero_zero(int))).
% 25.51/25.31 0 [] -linord219039673up_add(X_a)|plus_plus(X_a,A_2,A_2)!=zero_zero(X_a)|ti(X_a,A_2)=zero_zero(X_a).
% 25.51/25.31 0 [] -linord219039673up_add(X_a)|plus_plus(X_a,A_2,A_2)=zero_zero(X_a)|ti(X_a,A_2)!=zero_zero(X_a).
% 25.51/25.31 0 [] bit1(K_1)!=pls.
% 25.51/25.31 0 [] pls!=bit1(L).
% 25.51/25.31 0 [] bit1(K_1)!=bit0(L).
% 25.51/25.31 0 [] bit0(K_1)!=bit1(L).
% 25.51/25.31 0 [] bit0(K)!=pls|ti(int,K)=pls.
% 25.51/25.31 0 [] bit0(K)=pls|ti(int,K)!=pls.
% 25.51/25.31 0 [] pls!=bit0(L_1)|pls=ti(int,L_1).
% 25.51/25.31 0 [] pls=bit0(L_1)|pls!=ti(int,L_1).
% 25.51/25.31 0 [] bit0(pls)=pls.
% 25.51/25.31 0 [] pls=zero_zero(int).
% 25.51/25.31 0 [] zero_zero(int)!=one_one(int).
% 25.51/25.31 0 [] plus_plus(int,K_1,pls)=ti(int,K_1).
% 25.51/25.31 0 [] plus_plus(int,pls,K_1)=ti(int,K_1).
% 25.51/25.31 0 [] plus_plus(int,bit0(K_1),bit0(L))=bit0(plus_plus(int,K_1,L)).
% 25.51/25.31 0 [] bit0(K_1)=plus_plus(int,K_1,K_1).
% 25.51/25.31 0 [] plus_plus(int,Z,zero_zero(int))=ti(int,Z).
% 25.51/25.31 0 [] plus_plus(int,zero_zero(int),Z)=ti(int,Z).
% 25.51/25.31 0 [] -number_semiring(X_a)|number_number_of(X_a,pls)=zero_zero(X_a).
% 25.51/25.31 0 [] -number_ring(X_a)|number_number_of(X_a,pls)=zero_zero(X_a).
% 25.51/25.31 0 [] -number_ring(X_a)|zero_zero(X_a)=number_number_of(X_a,pls).
% 25.51/25.31 0 [] -number_ring(X_a)|plus_plus(X_a,number_number_of(X_a,pls),A_1)=ti(X_a,A_1).
% 25.51/25.31 0 [] -number_ring(X_a)|plus_plus(X_a,A_1,number_number_of(X_a,pls))=ti(X_a,A_1).
% 25.51/25.31 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_2),number_number_of(nat,Wa))!=zero_zero(X_a)|ti(X_a,A_2)=zero_zero(X_a).
% 25.51/25.31 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_2),number_number_of(nat,Wa))!=zero_zero(X_a)|number_number_of(nat,Wa)!=zero_zero(nat).
% 25.51/25.31 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_2),number_number_of(nat,Wa))=zero_zero(X_a)|ti(X_a,A_2)!=zero_zero(X_a)|number_number_of(nat,Wa)=zero_zero(nat).
% 25.51/25.31 0 [] -number_ring(X_a)|plus_plus(X_a,number_number_of(X_a,V_1),plus_plus(X_a,number_number_of(X_a,W),Z))=plus_plus(X_a,number_number_of(X_a,plus_plus(int,V_1,W)),Z).
% 25.51/25.31 0 [] -number_ring(X_a)|plus_plus(X_a,number_number_of(X_a,V_1),number_number_of(X_a,W))=number_number_of(X_a,plus_plus(int,V_1,W)).
% 25.51/25.31 0 [] -number_ring(X_a)|number_number_of(X_a,plus_plus(int,V_1,W))=plus_plus(X_a,number_number_of(X_a,V_1),number_number_of(X_a,W)).
% 25.51/25.31 0 [] plus_plus(int,bit1(K_1),bit0(L))=bit1(plus_plus(int,K_1,L)).
% 25.51/25.31 0 [] plus_plus(int,bit0(K_1),bit1(L))=bit1(plus_plus(int,K_1,L)).
% 25.51/25.31 0 [] bit1(K_1)=plus_plus(int,plus_plus(int,one_one(int),K_1),K_1).
% 25.51/25.31 0 [] plus_plus(int,plus_plus(int,one_one(int),Z),Z)!=zero_zero(int).
% 25.51/25.31 0 [] -number_semiring(X_a)|number_number_of(X_a,hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,X_a,semiring_1_of_nat(X_a),N).
% 25.51/25.31 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_2),number_number_of(nat,bit0(bit1(pls))))))|ti(X_a,A_2)!=zero_zero(X_a).
% 25.51/25.31 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_2),number_number_of(nat,bit0(bit1(pls))))))|ti(X_a,A_2)=zero_zero(X_a).
% 25.51/25.31 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))).
% 25.51/25.31 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)),plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,bit0(bit1(pls)))))))|ti(X_a,Xa)!=zero_zero(X_a)|ti(X_a,Ya)!=zero_zero(X_a).
% 25.51/25.31 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)),plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,bit0(bit1(pls)))))))|ti(X_a,Xa)=zero_zero(X_a).
% 25.51/25.31 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)),plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,bit0(bit1(pls)))))))|ti(X_a,Ya)=zero_zero(X_a).
% 25.51/25.31 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(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),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(X_a))).
% 25.51/25.31 0 [] -number_ring(X_a)|number_number_of(X_a,bit0(W))=plus_plus(X_a,plus_plus(X_a,zero_zero(X_a),number_number_of(X_a,W)),number_number_of(X_a,W)).
% 25.51/25.31 0 [] -number_ring(X_a)|number_number_of(X_a,bit1(W))=plus_plus(X_a,plus_plus(X_a,one_one(X_a),number_number_of(X_a,W)),number_number_of(X_a,W)).
% 25.51/25.31 0 [] -number_semiring(X_a)|number_number_of(X_a,bit1(pls))=one_one(X_a).
% 25.51/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),m1),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))).
% 25.51/25.31 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),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)),hAPP(nat,X_a,power_power(X_a,number_number_of(X_a,bit0(bit1(pls)))),N))).
% 25.51/25.31 0 [] number_number_of(int,bit0(bit1(pls)))=hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,bit0(bit1(pls)))).
% 25.51/25.31 0 [] number_number_of(int,bit1(bit1(pls)))=hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,bit1(bit1(pls)))).
% 25.51/25.31 0 [] plus_plus(real,hAPP(nat,real,power_power(real,Xa),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,real,power_power(real,Ya),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(real)|Xa=zero_zero(real).
% 25.51/25.31 0 [] plus_plus(real,hAPP(nat,real,power_power(real,Xa),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,real,power_power(real,Ya),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(real)|Ya=zero_zero(real).
% 25.51/25.31 0 [] plus_plus(real,hAPP(nat,real,power_power(real,Xa),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,real,power_power(real,Ya),number_number_of(nat,bit0(bit1(pls)))))=zero_zero(real)|Xa!=zero_zero(real)|Ya!=zero_zero(real).
% 25.51/25.31 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(nat,X_a,semiring_1_of_nat(X_a),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)).
% 25.51/25.31 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(nat,X_a,semiring_1_of_nat(X_a),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)).
% 25.51/25.31 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))|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))).
% 25.51/25.31 0 [] -power(X_a)| -semiring_0(X_a)|N!=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N)=one_one(X_a).
% 25.51/25.31 0 [] -power(X_a)| -semiring_0(X_a)|N=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N)=zero_zero(X_a).
% 25.51/25.31 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_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(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_2)),hAPP(nat,X_a,power_power(X_a,A_1),N))).
% 25.51/25.31 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)),plus_plus(X_a,one_one(X_a),one_one(X_a)))).
% 25.51/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_1))| -hBOOL(hAPP(int,bool,P_1,plus_plus(int,K,one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f1(P_1,K,I_1)))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 25.51/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_1))| -hBOOL(hAPP(int,bool,P_1,plus_plus(int,K,one_one(int))))|hBOOL(hAPP(int,bool,P_1,$f1(P_1,K,I_1)))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 25.51/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_1))| -hBOOL(hAPP(int,bool,P_1,plus_plus(int,K,one_one(int))))| -hBOOL(hAPP(int,bool,P_1,plus_plus(int,$f1(P_1,K,I_1),one_one(int))))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 25.51/25.31 0 [] zero_zero(int)=hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)).
% 25.51/25.31 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),tn)).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))).
% 25.51/25.31 0 [] zero_zero(real)!=one_one(real).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,I_2,J_1)),I_2)).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,J_1,I_2)),I_2)).
% 25.51/25.31 0 [] number_number_of(int,K_1)=ti(int,K_1).
% 25.51/25.31 0 [] Ma=Na|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma)).
% 25.51/25.31 0 [] Ma!=Na| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)).
% 25.51/25.31 0 [] Ma!=Na| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma)).
% 25.51/25.31 0 [] plus_plus(nat,M,N)=plus_plus(nat,N,M).
% 25.51/25.31 0 [] plus_plus(nat,X,plus_plus(nat,Y,Z))=plus_plus(nat,Y,plus_plus(nat,X,Z)).
% 25.51/25.31 0 [] plus_plus(nat,plus_plus(nat,M,N),K_1)=plus_plus(nat,M,plus_plus(nat,N,K_1)).
% 25.51/25.31 0 [] plus_plus(nat,K,Ma)!=plus_plus(nat,K,Na)|Ma=Na.
% 25.51/25.31 0 [] plus_plus(nat,K,Ma)=plus_plus(nat,K,Na)|Ma!=Na.
% 25.51/25.31 0 [] plus_plus(nat,Ma,K)!=plus_plus(nat,Na,K)|Ma=Na.
% 25.51/25.31 0 [] plus_plus(nat,Ma,K)=plus_plus(nat,Na,K)|Ma!=Na.
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,K,Ma)),plus_plus(nat,K,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)).
% 25.51/25.31 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,K,Ma)),plus_plus(nat,K,Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)).
% 25.51/25.31 0 [] X=Y|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X)).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M))|M!=N.
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S_1),T_2))|S_1!=T_2.
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),plus_plus(nat,J_1,M))).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),plus_plus(nat,M,J_1))).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,I_2,K_1)),plus_plus(nat,J_1,K_1))).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,I_2,K_1)),plus_plus(nat,J_1,L))).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L))|plus_plus(nat,M,L)!=plus_plus(nat,K_1,N)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,I_2,J_1)),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1)).
% 25.51/25.31 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))|Ma=Na|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma)).
% 25.51/25.31 0 [] N=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))|N!=zero_zero(nat).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),I_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,I_2),M)),hAPP(nat,nat,power_power(nat,I_2),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa))|Na=zero_zero(nat).
% 25.51/25.31 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)).
% 25.51/25.31 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na)))|Na!=zero_zero(nat).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),plus_plus(nat,Ma,Na)))|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)),Na)).
% 25.51/25.31 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),plus_plus(nat,Ma,Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)).
% 25.51/25.31 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),plus_plus(nat,Ma,Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)).
% 25.51/25.31 0 [] Na=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)).
% 25.51/25.31 0 [] Na!=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na)))|Na=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)).
% 25.51/25.31 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na)))|Na!=zero_zero(nat).
% 25.51/25.31 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)).
% 25.51/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)).
% 25.51/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),number_number_of(nat,Wa))))|number_number_of(nat,Wa)=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)).
% 25.51/25.31 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),number_number_of(nat,Wa))))|number_number_of(nat,Wa)!=zero_zero(nat).
% 25.51/25.31 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),number_number_of(nat,Wa))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)).
% 25.51/25.31 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)).
% 25.51/25.31 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,Va)),number_number_of(nat,V_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Va),V_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_3)).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,Va)),number_number_of(nat,V_3)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Va),V_3)).
% 25.51/25.31 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,Va)),number_number_of(nat,V_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Va),V_3)).
% 25.51/25.31 0 [] -linordered_idom(X_a)|ti(X_a,X)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)).
% 25.51/25.31 0 [] plus_plus(nat,M,N)!=M|N=zero_zero(nat).
% 25.51/25.31 0 [] plus_plus(nat,Ma,Na)!=zero_zero(nat)|Ma=zero_zero(nat).
% 25.51/25.31 0 [] plus_plus(nat,Ma,Na)!=zero_zero(nat)|Na=zero_zero(nat).
% 25.51/25.31 0 [] plus_plus(nat,Ma,Na)=zero_zero(nat)|Ma!=zero_zero(nat)|Na!=zero_zero(nat).
% 25.51/25.31 0 [] plus_plus(nat,M,zero_zero(nat))=M.
% 25.51/25.31 0 [] plus_plus(nat,zero_zero(nat),N)=N.
% 25.51/25.31 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),one_one(nat))=ti(X_a,A_1).
% 25.51/25.31 0 [] -semiring_char_0(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)!=hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)|Ma=Na.
% 25.51/25.31 0 [] -semiring_char_0(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)=hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)|Ma!=Na.
% 25.51/25.31 0 [] hAPP(nat,int,semiring_1_of_nat(int),Xa)!=hAPP(nat,int,semiring_1_of_nat(int),Ya)|Xa=Ya.
% 25.51/25.31 0 [] hAPP(nat,int,semiring_1_of_nat(int),Xa)=hAPP(nat,int,semiring_1_of_nat(int),Ya)|Xa!=Ya.
% 25.51/25.31 0 [] -hBOOL(P_1)|hAPP(nat,int,semiring_1_of_nat(int),Xa)=hAPP(nat,int,semiring_1_of_nat(int),if(nat,P_1,Xa,Ya)).
% 25.51/25.31 0 [] hBOOL(P_1)|hAPP(nat,int,semiring_1_of_nat(int),Ya)=hAPP(nat,int,semiring_1_of_nat(int),if(nat,P_1,Xa,Ya)).
% 25.51/25.31 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,Va)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Va)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,Va)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Va)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)).
% 25.51/25.32 0 [] -zero_ne_q_one(X_a)|one_one(X_a)!=zero_zero(X_a).
% 25.51/25.32 0 [] -zero_ne_q_one(X_a)|zero_zero(X_a)!=one_one(X_a).
% 25.51/25.32 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)!=zero_zero(X_a).
% 25.51/25.32 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,one_one(X_a)),N)=one_one(X_a).
% 25.51/25.32 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,semiring_1_of_nat(X_a),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)).
% 25.51/25.32 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,semiring_1_of_nat(X_a),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)).
% 25.51/25.32 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))).
% 25.51/25.32 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,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)).
% 25.51/25.32 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),plus_plus(nat,M,N))=plus_plus(X_a,hAPP(nat,X_a,semiring_1_of_nat(X_a),M),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)).
% 25.51/25.32 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),one_one(nat))=one_one(X_a).
% 25.51/25.32 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,power_power(nat,M),N))=hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),N).
% 25.51/25.32 0 [] one_one(int)=hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)).
% 25.51/25.32 0 [] plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X),hAPP(nat,int,semiring_1_of_nat(int),Y))=hAPP(nat,int,semiring_1_of_nat(int),plus_plus(nat,X,Y)).
% 25.51/25.32 0 [] hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X)),N)=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X),N)).
% 25.51/25.32 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_1),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),plus_plus(X_a,A_1,C))).
% 25.51/25.32 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))).
% 25.51/25.32 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))).
% 25.51/25.32 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))).
% 25.51/25.32 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),plus_plus(X_a,A_1,one_one(X_a)))).
% 25.51/25.32 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_2))|hAPP(nat,X_a,power_power(X_a,A_2),Ma)!=hAPP(nat,X_a,power_power(X_a,A_2),Na)|Ma=Na.
% 25.51/25.32 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_2))|hAPP(nat,X_a,power_power(X_a,A_2),Ma)=hAPP(nat,X_a,power_power(X_a,A_2),Na)|Ma!=Na.
% 25.51/25.32 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))| -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),Xa)),hAPP(nat,X_a,power_power(X_a,B),Ya)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)).
% 25.51/25.32 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))|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),Xa)),hAPP(nat,X_a,power_power(X_a,B),Ya)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)).
% 25.51/25.32 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)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)).
% 25.51/25.32 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_2))| -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)),hAPP(nat,X_a,power_power(X_a,A_1),N_2))).
% 25.51/25.32 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_2),Na)!=zero_zero(X_a)|ti(X_a,A_2)=zero_zero(X_a).
% 25.51/25.32 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_2),Na)!=zero_zero(X_a)|Na!=zero_zero(nat).
% 25.51/25.32 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_2),Na)=zero_zero(X_a)|ti(X_a,A_2)!=zero_zero(X_a)|Na=zero_zero(nat).
% 25.51/25.32 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,semiring_1_of_nat(X_a),M)),zero_zero(X_a))).
% 25.51/25.32 0 [] -power(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),zero_zero(nat))=one_one(X_a).
% 25.51/25.32 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat))=zero_zero(X_a).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,bit0(bit1(pls))))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),$f2(K_1))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1))|ti(int,K_1)=hAPP(nat,int,semiring_1_of_nat(int),$f2(K_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),$f3(I_2,J_1))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))|plus_plus(nat,I_2,$f3(I_2,J_1))=J_1.
% 25.51/25.32 0 [] hAPP(nat,nat,power_power(nat,Xa),Na)!=one_one(nat)|Xa=one_one(nat)|Na=zero_zero(nat).
% 25.51/25.32 0 [] hAPP(nat,nat,power_power(nat,Xa),Na)=one_one(nat)|Xa!=one_one(nat).
% 25.51/25.32 0 [] hAPP(nat,nat,power_power(nat,Xa),Na)=one_one(nat)|Na!=zero_zero(nat).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,X),zero_zero(nat))=one_one(X_a).
% 25.51/25.32 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)),plus_plus(X_a,A_2,A_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)).
% 25.51/25.32 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)),plus_plus(X_a,A_2,A_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)).
% 25.51/25.32 0 [] -linord219039673up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_2,A_2)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))).
% 25.51/25.32 0 [] -linord219039673up_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_2,A_2)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))).
% 25.51/25.32 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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),plus_plus(X_a,A_1,B_1))).
% 25.51/25.32 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_1),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_1,B_1)),zero_zero(X_a))).
% 25.51/25.32 0 [] -zero(X_a)|zero_zero(X_a)!=ti(X_a,Xa)|ti(X_a,Xa)=zero_zero(X_a).
% 25.51/25.32 0 [] -zero(X_a)|zero_zero(X_a)=ti(X_a,Xa)|ti(X_a,Xa)!=zero_zero(X_a).
% 25.51/25.32 0 [] -cancel_semigroup_add(X_a)|plus_plus(X_a,B_1,A_1)!=plus_plus(X_a,C,A_1)|ti(X_a,B_1)=ti(X_a,C).
% 25.51/25.32 0 [] -cancel146912293up_add(X_a)|plus_plus(X_a,A_1,B_1)!=plus_plus(X_a,A_1,C)|ti(X_a,B_1)=ti(X_a,C).
% 25.51/25.32 0 [] -cancel_semigroup_add(X_a)|plus_plus(X_a,A_1,B_1)!=plus_plus(X_a,A_1,C)|ti(X_a,B_1)=ti(X_a,C).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,plus_plus(X_a,A_1,B_1),plus_plus(X_a,C,D_1))=plus_plus(X_a,plus_plus(X_a,A_1,C),plus_plus(X_a,B_1,D_1)).
% 25.51/25.32 0 [] -cancel_semigroup_add(X_a)|plus_plus(X_a,B,A_2)!=plus_plus(X_a,C_1,A_2)|ti(X_a,B)=ti(X_a,C_1).
% 25.51/25.32 0 [] -cancel_semigroup_add(X_a)|plus_plus(X_a,B,A_2)=plus_plus(X_a,C_1,A_2)|ti(X_a,B)!=ti(X_a,C_1).
% 25.51/25.32 0 [] -cancel_semigroup_add(X_a)|plus_plus(X_a,A_2,B)!=plus_plus(X_a,A_2,C_1)|ti(X_a,B)=ti(X_a,C_1).
% 25.51/25.32 0 [] -cancel_semigroup_add(X_a)|plus_plus(X_a,A_2,B)=plus_plus(X_a,A_2,C_1)|ti(X_a,B)!=ti(X_a,C_1).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,plus_plus(X_a,A_1,B_1),C)=plus_plus(X_a,plus_plus(X_a,A_1,C),B_1).
% 25.51/25.32 0 [] -ab_semigroup_add(X_a)|plus_plus(X_a,plus_plus(X_a,A_1,B_1),C)=plus_plus(X_a,A_1,plus_plus(X_a,B_1,C)).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,plus_plus(X_a,A_1,B_1),C)=plus_plus(X_a,A_1,plus_plus(X_a,B_1,C)).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,A_1,plus_plus(X_a,C,D_1))=plus_plus(X_a,plus_plus(X_a,A_1,C),D_1).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,A_1,plus_plus(X_a,C,D_1))=plus_plus(X_a,C,plus_plus(X_a,A_1,D_1)).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,A_1,C)=plus_plus(X_a,C,A_1).
% 25.51/25.32 0 [] -one(X_a)|one_one(X_a)!=ti(X_a,Xa)|ti(X_a,Xa)=one_one(X_a).
% 25.51/25.32 0 [] -one(X_a)|one_one(X_a)=ti(X_a,Xa)|ti(X_a,Xa)!=one_one(X_a).
% 25.51/25.32 0 [] -semiri456707255roduct(X_a)|ti(X_a,B)!=plus_plus(X_a,B,A_2)|ti(X_a,A_2)=zero_zero(X_a).
% 25.51/25.32 0 [] -semiri456707255roduct(X_a)|ti(X_a,B)=plus_plus(X_a,B,A_2)|ti(X_a,A_2)!=zero_zero(X_a).
% 25.51/25.32 0 [] -comm_monoid_add(X_a)|plus_plus(X_a,A_1,zero_zero(X_a))=ti(X_a,A_1).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,A_1,zero_zero(X_a))=ti(X_a,A_1).
% 25.51/25.32 0 [] -monoid_add(X_a)|plus_plus(X_a,A_1,zero_zero(X_a))=ti(X_a,A_1).
% 25.51/25.32 0 [] -linord219039673up_add(X_a)|zero_zero(X_a)!=plus_plus(X_a,A_2,A_2)|ti(X_a,A_2)=zero_zero(X_a).
% 25.51/25.32 0 [] -linord219039673up_add(X_a)|zero_zero(X_a)=plus_plus(X_a,A_2,A_2)|ti(X_a,A_2)!=zero_zero(X_a).
% 25.51/25.32 0 [] -comm_monoid_add(X_a)|plus_plus(X_a,zero_zero(X_a),A_1)=ti(X_a,A_1).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,zero_zero(X_a),A_1)=ti(X_a,A_1).
% 25.51/25.32 0 [] -monoid_add(X_a)|plus_plus(X_a,zero_zero(X_a),A_1)=ti(X_a,A_1).
% 25.51/25.32 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,C,A_1)),plus_plus(X_a,C,B_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)).
% 25.51/25.32 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_1,C)),plus_plus(X_a,B_1,C)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)).
% 25.51/25.32 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_1,C)),plus_plus(X_a,B_1,D_1))).
% 25.51/25.32 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,C,A_1)),plus_plus(X_a,C,B_1))).
% 25.51/25.32 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_1,C)),plus_plus(X_a,B_1,C))).
% 25.51/25.32 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,C_1,A_2)),plus_plus(X_a,C_1,B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B)).
% 25.51/25.32 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,C_1,A_2)),plus_plus(X_a,C_1,B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B)).
% 25.51/25.32 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_2,C_1)),plus_plus(X_a,B,C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B)).
% 25.51/25.32 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_2,C_1)),plus_plus(X_a,B,C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B)).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,X),one_one(nat))=ti(X_a,X).
% 25.51/25.32 0 [] hAPP(nat,nat,power_power(nat,Ma),Na)!=zero_zero(nat)|Na!=zero_zero(nat).
% 25.51/25.32 0 [] hAPP(nat,nat,power_power(nat,Ma),Na)!=zero_zero(nat)|Ma=zero_zero(nat).
% 25.51/25.32 0 [] hAPP(nat,nat,power_power(nat,Ma),Na)=zero_zero(nat)|Na=zero_zero(nat)|Ma!=zero_zero(nat).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))| -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))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))|hAPP(nat,real,power_power(real,$f4(A_1,N)),N)=A_1.
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1))|hAPP(nat,real,power_power(real,Y_1),N)!=A_1|Y_1=$f4(A_1,N).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))| -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)),$f5(A_1,N))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))|hAPP(nat,real,power_power(real,$f5(A_1,N)),N)=A_1.
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),t)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|plus_plus(nat,number_number_of(nat,V_1),one_one(nat))=one_one(nat).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|plus_plus(nat,number_number_of(nat,V_1),one_one(nat))=number_number_of(nat,succ(V_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|plus_plus(nat,one_one(nat),number_number_of(nat,V_1))=one_one(nat).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|plus_plus(nat,one_one(nat),number_number_of(nat,V_1))=number_number_of(nat,succ(V_1)).
% 25.51/25.32 0 [] hAPP(nat,int,power_power(int,plus_plus(int,A_1,B_1)),number_number_of(nat,bit1(bit1(pls))))=plus_plus(int,plus_plus(int,plus_plus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit1(bit1(pls)))),times_times(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_1)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),A_1),hAPP(nat,int,power_power(int,B_1),number_number_of(nat,bit0(bit1(pls)))))),hAPP(nat,int,power_power(int,B_1),number_number_of(nat,bit1(bit1(pls))))).
% 25.51/25.32 0 [] hAPP(nat,int,power_power(int,plus_plus(int,A_1,B_1)),number_number_of(nat,bit0(bit1(pls))))=plus_plus(int,plus_plus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),A_1),B_1)),hAPP(nat,int,power_power(int,B_1),number_number_of(nat,bit0(bit1(pls))))).
% 25.51/25.32 0 [] tn=minus_minus(nat,nat_1(t),one_one(nat)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),minus_minus(nat,nat_1(t),one_one(nat)))).
% 25.51/25.32 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_2),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),minus_minus(X_a,A_2,B)),zero_zero(X_a))).
% 25.51/25.32 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_2),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),minus_minus(X_a,A_2,B)),zero_zero(X_a))).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|times_times(X_a,A_1,B_1)=times_times(X_a,B_1,A_1).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|times_times(X_a,Lx,times_times(X_a,Rx,Ry))=times_times(X_a,Rx,times_times(X_a,Lx,Ry)).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|times_times(X_a,Lx,times_times(X_a,Rx,Ry))=times_times(X_a,times_times(X_a,Lx,Rx),Ry).
% 25.51/25.32 0 [] -ab_semigroup_mult(X_a)|times_times(X_a,times_times(X_a,A_1,B_1),C)=times_times(X_a,A_1,times_times(X_a,B_1,C)).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|times_times(X_a,times_times(X_a,Lx,Ly),Rx)=times_times(X_a,Lx,times_times(X_a,Ly,Rx)).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|times_times(X_a,times_times(X_a,Lx,Ly),Rx)=times_times(X_a,times_times(X_a,Lx,Rx),Ly).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|times_times(X_a,times_times(X_a,Lx,Ly),times_times(X_a,Rx,Ry))=times_times(X_a,Lx,times_times(X_a,Ly,times_times(X_a,Rx,Ry))).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|times_times(X_a,times_times(X_a,Lx,Ly),times_times(X_a,Rx,Ry))=times_times(X_a,Rx,times_times(X_a,times_times(X_a,Lx,Ly),Ry)).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|times_times(X_a,times_times(X_a,Lx,Ly),times_times(X_a,Rx,Ry))=times_times(X_a,times_times(X_a,Lx,Rx),times_times(X_a,Ly,Ry)).
% 25.51/25.32 0 [] -ab_group_add(X_a)|minus_minus(X_a,A_2,B)!=minus_minus(X_a,C_1,D)|ti(X_a,A_2)!=ti(X_a,B)|ti(X_a,C_1)=ti(X_a,D).
% 25.51/25.32 0 [] -ab_group_add(X_a)|minus_minus(X_a,A_2,B)!=minus_minus(X_a,C_1,D)|ti(X_a,A_2)=ti(X_a,B)|ti(X_a,C_1)!=ti(X_a,D).
% 25.51/25.32 0 [] -ordered_ab_group_add(X_a)|minus_minus(X_a,A_2,B)!=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_2),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),D)).
% 25.51/25.32 0 [] -ordered_ab_group_add(X_a)|minus_minus(X_a,A_2,B)!=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_2),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),D)).
% 25.51/25.32 0 [] -number_semiring(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_2))|times_times(X_a,number_number_of(X_a,V_1),number_number_of(X_a,V_2))=number_number_of(X_a,times_times(int,V_1,V_2)).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),W)).
% 25.51/25.32 0 [] times_times(int,Z,W)=times_times(int,W,Z).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),W))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z)).
% 25.51/25.32 0 [] times_times(int,times_times(int,Z1,Z2),Z3)=times_times(int,Z1,times_times(int,Z2,Z3)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),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_2),K_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),W))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z))|ti(int,Z)=ti(int,W).
% 25.51/25.32 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,Xa)),number_number_of(X_a,Ya)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),Ya)).
% 25.51/25.32 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,Xa)),number_number_of(X_a,Ya)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),Ya)).
% 25.51/25.32 0 [] -number_ring(X_a)|number_number_of(X_a,times_times(int,V_1,W))=times_times(X_a,number_number_of(X_a,V_1),number_number_of(X_a,W)).
% 25.51/25.32 0 [] -number_ring(X_a)|times_times(X_a,number_number_of(X_a,V_1),number_number_of(X_a,W))=number_number_of(X_a,times_times(int,V_1,W)).
% 25.51/25.32 0 [] -number_ring(X_a)|times_times(X_a,number_number_of(X_a,V_1),times_times(X_a,number_number_of(X_a,W),Z))=times_times(X_a,number_number_of(X_a,times_times(int,V_1,W)),Z).
% 25.51/25.32 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_e_q(int),zero_zero(int)),Z_3))|nat_1(Z_1)!=nat_1(Z_3)|ti(int,Z_1)=ti(int,Z_3).
% 25.51/25.32 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_e_q(int),zero_zero(int)),Z_3))|nat_1(Z_1)=nat_1(Z_3)|ti(int,Z_1)!=ti(int,Z_3).
% 25.51/25.32 0 [] -number(X_b)| -ring(X_b)|times_times(X_b,number_number_of(X_b,V_1),minus_minus(X_b,B_1,C))=minus_minus(X_b,times_times(X_b,number_number_of(X_b,V_1),B_1),times_times(X_b,number_number_of(X_b,V_1),C)).
% 25.51/25.32 0 [] -number(X_b)| -ring(X_b)|times_times(X_b,minus_minus(X_b,A_1,B_1),number_number_of(X_b,V_1))=minus_minus(X_b,times_times(X_b,A_1,number_number_of(X_b,V_1)),times_times(X_b,B_1,number_number_of(X_b,V_1))).
% 25.51/25.32 0 [] -number_ring(X_a)|number_number_of(X_a,minus_minus(int,V_1,W))=minus_minus(X_a,number_number_of(X_a,V_1),number_number_of(X_a,W)).
% 25.51/25.32 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),times_times(nat,M,N))=times_times(X_a,hAPP(nat,X_a,semiring_1_of_nat(X_a),M),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)).
% 25.51/25.32 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,semiring_1_of_nat(X_a),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)).
% 25.51/25.32 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,semiring_1_of_nat(X_a),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)).
% 25.51/25.32 0 [] minus_minus(nat,minus_minus(nat,I_2,J_1),K_1)=minus_minus(nat,minus_minus(nat,I_2,K_1),J_1).
% 25.51/25.32 0 [] -hBOOL(P_1)|nat_1(Xa)=nat_1(if(int,P_1,Xa,Ya)).
% 25.51/25.32 0 [] hBOOL(P_1)|nat_1(Ya)=nat_1(if(int,P_1,Xa,Ya)).
% 25.51/25.32 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_1),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_1,B_1)),zero_zero(X_a))).
% 25.51/25.32 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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_1,B_1)),zero_zero(X_a))).
% 25.51/25.32 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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),times_times(X_a,A_1,B_1))).
% 25.51/25.32 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_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)),times_times(X_a,A_1,B_1))).
% 25.51/25.32 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_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_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),times_times(X_a,A_1,C)),times_times(X_a,B_1,D_1))).
% 25.51/25.32 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_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_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)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_1,C)),times_times(X_a,B_1,D_1))).
% 25.51/25.32 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_1),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),times_times(X_a,C,A_1)),times_times(X_a,C,B_1))).
% 25.51/25.32 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_1),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),times_times(X_a,A_1,C)),times_times(X_a,B_1,C))).
% 25.51/25.32 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_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),times_times(X_a,C,A_1)),times_times(X_a,C,B_1))).
% 25.51/25.32 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_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),times_times(X_a,C,A_1)),times_times(X_a,C,B_1))).
% 25.51/25.32 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_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),times_times(X_a,A_1,C)),times_times(X_a,B_1,C))).
% 25.51/25.32 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_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)),times_times(X_a,A_1,B_1))).
% 25.51/25.32 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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_1,B_1)),zero_zero(X_a))).
% 25.51/25.32 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_1),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,B_1,A_1)),zero_zero(X_a))).
% 25.51/25.32 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_1),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_1,B_1)),zero_zero(X_a))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Ya))|nat_1(Xa)!=nat_1(Ya)|ti(int,Xa)=ti(int,Ya).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Ya))|nat_1(Xa)=nat_1(Ya)|ti(int,Xa)!=ti(int,Ya).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))| -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)),times_times(int,X,Y))).
% 25.51/25.32 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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),times_times(X_a,A_1,B_1))).
% 25.51/25.32 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)),plus_plus(X_a,times_times(X_a,B,E_1),D)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,times_times(X_a,minus_minus(X_a,A_2,B),E_1),C_1)),D)).
% 25.51/25.32 0 [] -ordered_ring(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)),plus_plus(X_a,times_times(X_a,B,E_1),D)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,times_times(X_a,minus_minus(X_a,A_2,B),E_1),C_1)),D)).
% 25.51/25.32 0 [] -ring(X_a)|plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)!=plus_plus(X_a,times_times(X_a,B,E_1),D)|plus_plus(X_a,times_times(X_a,minus_minus(X_a,A_2,B),E_1),C_1)=ti(X_a,D).
% 25.51/25.32 0 [] -ring(X_a)|plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)=plus_plus(X_a,times_times(X_a,B,E_1),D)|plus_plus(X_a,times_times(X_a,minus_minus(X_a,A_2,B),E_1),C_1)!=ti(X_a,D).
% 25.51/25.32 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)),plus_plus(X_a,times_times(X_a,B,E_1),D)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),plus_plus(X_a,times_times(X_a,minus_minus(X_a,B,A_2),E_1),D))).
% 25.51/25.32 0 [] -ordered_ring(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)),plus_plus(X_a,times_times(X_a,B,E_1),D)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),plus_plus(X_a,times_times(X_a,minus_minus(X_a,B,A_2),E_1),D))).
% 25.51/25.32 0 [] -ring(X_a)|plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)!=plus_plus(X_a,times_times(X_a,B,E_1),D)|ti(X_a,C_1)=plus_plus(X_a,times_times(X_a,minus_minus(X_a,B,A_2),E_1),D).
% 25.51/25.32 0 [] -ring(X_a)|plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)=plus_plus(X_a,times_times(X_a,B,E_1),D)|ti(X_a,C_1)!=plus_plus(X_a,times_times(X_a,minus_minus(X_a,B,A_2),E_1),D).
% 25.51/25.32 0 [] -ring(X_a)|minus_minus(X_a,times_times(X_a,X,Y),times_times(X_a,A_1,B_1))=plus_plus(X_a,times_times(X_a,X,minus_minus(X_a,Y,B_1)),times_times(X_a,minus_minus(X_a,X,A_1),B_1)).
% 25.51/25.32 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_2,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)),A_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),zero_zero(X_a))).
% 25.51/25.32 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_2,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)),A_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B)).
% 25.51/25.32 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_2,B)),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),A_2),zero_zero(X_a))).
% 25.51/25.32 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_2,B)),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)),B)).
% 25.51/25.32 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_2,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)),A_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a))).
% 25.51/25.32 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_2,B)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_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)).
% 25.51/25.32 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)),times_times(X_a,A_2,B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),zero_zero(X_a))).
% 25.51/25.32 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)),times_times(X_a,A_2,B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a))).
% 25.51/25.32 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)),times_times(X_a,A_2,B)))|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_2),zero_zero(X_a))).
% 25.51/25.32 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)),times_times(X_a,A_2,B)))|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),B),zero_zero(X_a))).
% 25.51/25.32 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)),times_times(X_a,A_2,B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B)).
% 25.51/25.32 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)),times_times(X_a,A_2,B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),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))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,P_1,$f6(P_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))|hBOOL(hAPP(nat,bool,P_1,nat_1(X_1))).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,P_1,X1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f7(P_1))).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,P_1,X1))| -hBOOL(hAPP(nat,bool,P_1,nat_1($f7(P_1)))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,P_1,X1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f8(P_1))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,P_1,X1))|hBOOL(hAPP(nat,bool,P_1,nat_1($f8(P_1)))).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,P_1,$f9(P_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))| -hBOOL(hAPP(nat,bool,P_1,nat_1(X_1))).
% 25.51/25.32 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)),times_times(X_a,A_1,A_1))).
% 25.51/25.32 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)),plus_plus(X_a,times_times(X_a,B,E_1),D)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,times_times(X_a,minus_minus(X_a,A_2,B),E_1),C_1)),D)).
% 25.51/25.32 0 [] -ordered_ring(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)),plus_plus(X_a,times_times(X_a,B,E_1),D)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,times_times(X_a,minus_minus(X_a,A_2,B),E_1),C_1)),D)).
% 25.51/25.32 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)),plus_plus(X_a,times_times(X_a,B,E_1),D)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),plus_plus(X_a,times_times(X_a,minus_minus(X_a,B,A_2),E_1),D))).
% 25.51/25.32 0 [] -ordered_ring(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,times_times(X_a,A_2,E_1),C_1)),plus_plus(X_a,times_times(X_a,B,E_1),D)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),plus_plus(X_a,times_times(X_a,minus_minus(X_a,B,A_2),E_1),D))).
% 25.51/25.32 0 [] -ring_1(X_a)|minus_minus(X_a,times_times(X_a,X,X),one_one(X_a))=times_times(X_a,plus_plus(X_a,X,one_one(X_a)),minus_minus(X_a,X,one_one(X_a))).
% 25.51/25.32 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,C,A_1)),times_times(X_a,C,B_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_e_q(X_a),A_1),B_1)).
% 25.51/25.32 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),times_times(X_a,A_1,C)),times_times(X_a,B_1,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_1)).
% 25.51/25.32 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,C,A_1)),times_times(X_a,C,B_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),A_1),B_1)).
% 25.51/25.32 0 [] -linordered_semiring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,C,A_1)),times_times(X_a,C,B_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),A_1),B_1)).
% 25.51/25.32 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_1,C)),times_times(X_a,B_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(X_a),A_1),B_1)).
% 25.51/25.32 0 [] -linordered_semiring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_1,C)),times_times(X_a,B_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(X_a),A_1),B_1)).
% 25.51/25.32 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_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_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)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_1,C)),times_times(X_a,B_1,D_1))).
% 25.51/25.32 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_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)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_1,C)),times_times(X_a,B_1,D_1))).
% 25.51/25.32 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_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)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_1,C)),times_times(X_a,B_1,D_1))).
% 25.51/25.32 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_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),times_times(X_a,A_1,C)),times_times(X_a,B_1,D_1))).
% 25.51/25.32 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),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_2)).
% 25.51/25.32 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),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_2)).
% 25.51/25.32 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),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B)).
% 25.51/25.32 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),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B)).
% 25.51/25.32 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)),plus_plus(X_a,times_times(X_a,X,X),times_times(X_a,Y,Y)))).
% 25.51/25.32 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,times_times(X_a,Xa,Xa),times_times(X_a,Ya,Ya))),zero_zero(X_a)))|ti(X_a,Xa)=zero_zero(X_a).
% 25.51/25.32 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,times_times(X_a,Xa,Xa),times_times(X_a,Ya,Ya))),zero_zero(X_a)))|ti(X_a,Ya)=zero_zero(X_a).
% 25.51/25.32 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,times_times(X_a,Xa,Xa),times_times(X_a,Ya,Ya))),zero_zero(X_a)))|ti(X_a,Xa)!=zero_zero(X_a)|ti(X_a,Ya)!=zero_zero(X_a).
% 25.51/25.32 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))| -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),times_times(X_a,X,Y)),X)).
% 25.51/25.32 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))| -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),times_times(X_a,Y,X)),X)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),zero_zero(int)))|nat_1(Z)=zero_zero(nat).
% 25.51/25.32 0 [] nat_1(I_1)!=zero_zero(nat)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),zero_zero(int))).
% 25.51/25.32 0 [] nat_1(I_1)=zero_zero(nat)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),zero_zero(int))).
% 25.51/25.32 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),N_2))| -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)),hAPP(nat,X_a,power_power(X_a,A_1),N_2))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))|hAPP(nat,int,semiring_1_of_nat(int),nat_1(Z))=ti(int,Z).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))|hAPP(nat,int,semiring_1_of_nat(int),nat_1(Z))=zero_zero(int).
% 25.51/25.32 0 [] hAPP(nat,int,semiring_1_of_nat(int),Ma)!=ti(int,Z_1)|Ma=nat_1(Z_1).
% 25.51/25.32 0 [] hAPP(nat,int,semiring_1_of_nat(int),Ma)!=ti(int,Z_1)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1)).
% 25.51/25.32 0 [] hAPP(nat,int,semiring_1_of_nat(int),Ma)=ti(int,Z_1)|Ma!=nat_1(Z_1)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))|hAPP(nat,int,semiring_1_of_nat(int),nat_1(Z))=ti(int,Z).
% 25.51/25.32 0 [] -group_add(X_a)|minus_minus(X_a,A_2,B)!=zero_zero(X_a)|ti(X_a,A_2)=ti(X_a,B).
% 25.51/25.32 0 [] -group_add(X_a)|minus_minus(X_a,A_2,B)=zero_zero(X_a)|ti(X_a,A_2)!=ti(X_a,B).
% 25.51/25.32 0 [] -ab_group_add(X_a)|ti(X_a,A_2)!=ti(X_a,B)|minus_minus(X_a,A_2,B)=zero_zero(X_a).
% 25.51/25.32 0 [] -ab_group_add(X_a)|ti(X_a,A_2)=ti(X_a,B)|minus_minus(X_a,A_2,B)!=zero_zero(X_a).
% 25.51/25.32 0 [] -group_add(X_a)|minus_minus(X_a,A_1,A_1)=zero_zero(X_a).
% 25.51/25.32 0 [] -group_add(X_a)|minus_minus(X_a,A_1,zero_zero(X_a))=ti(X_a,A_1).
% 25.51/25.32 0 [] -ordered_ab_group_add(X_a)|minus_minus(X_a,A_2,B)!=minus_minus(X_a,C_1,D)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D)).
% 25.51/25.32 0 [] -ordered_ab_group_add(X_a)|minus_minus(X_a,A_2,B)!=minus_minus(X_a,C_1,D)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D)).
% 25.51/25.32 0 [] -ab_group_add(X_a)|minus_minus(X_a,plus_plus(X_a,A_1,C),plus_plus(X_a,B_1,D_1))=plus_plus(X_a,minus_minus(X_a,A_1,B_1),minus_minus(X_a,C,D_1)).
% 25.51/25.32 0 [] -group_add(X_a)|minus_minus(X_a,plus_plus(X_a,A_1,B_1),B_1)=ti(X_a,A_1).
% 25.51/25.32 0 [] -group_add(X_a)|plus_plus(X_a,minus_minus(X_a,A_1,B_1),B_1)=ti(X_a,A_1).
% 25.51/25.32 0 [] -mult_zero(X_a)|times_times(X_a,zero_zero(X_a),A_1)=zero_zero(X_a).
% 25.51/25.32 0 [] -mult_zero(X_a)|times_times(X_a,A_1,zero_zero(X_a))=zero_zero(X_a).
% 25.51/25.32 0 [] -ring_n68954251visors(X_a)|times_times(X_a,A_2,B)!=zero_zero(X_a)|ti(X_a,A_2)=zero_zero(X_a)|ti(X_a,B)=zero_zero(X_a).
% 25.51/25.32 0 [] -ring_n68954251visors(X_a)|times_times(X_a,A_2,B)=zero_zero(X_a)|ti(X_a,A_2)!=zero_zero(X_a).
% 25.51/25.32 0 [] -ring_n68954251visors(X_a)|times_times(X_a,A_2,B)=zero_zero(X_a)|ti(X_a,B)!=zero_zero(X_a).
% 25.51/25.32 0 [] -no_zero_divisors(X_a)|ti(X_a,A_1)=zero_zero(X_a)|ti(X_a,B_1)=zero_zero(X_a)|times_times(X_a,A_1,B_1)!=zero_zero(X_a).
% 25.51/25.32 0 [] -no_zero_divisors(X_a)|times_times(X_a,A_1,B_1)!=zero_zero(X_a)|ti(X_a,A_1)=zero_zero(X_a)|ti(X_a,B_1)=zero_zero(X_a).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|times_times(X_a,A_1,zero_zero(X_a))=zero_zero(X_a).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|times_times(X_a,zero_zero(X_a),A_1)=zero_zero(X_a).
% 25.51/25.32 0 [] minus_minus(nat,M,N)!=zero_zero(nat)|minus_minus(nat,N,M)!=zero_zero(nat)|M=N.
% 25.51/25.32 0 [] minus_minus(nat,M,M)=zero_zero(nat).
% 25.51/25.32 0 [] minus_minus(nat,M,zero_zero(nat))=M.
% 25.51/25.32 0 [] minus_minus(nat,zero_zero(nat),N)=zero_zero(nat).
% 25.51/25.32 0 [] -comm_semiring(X_a)|times_times(X_a,plus_plus(X_a,A_1,B_1),C)=plus_plus(X_a,times_times(X_a,A_1,C),times_times(X_a,B_1,C)).
% 25.51/25.32 0 [] -semiring(X_a)|plus_plus(X_a,times_times(X_a,A_1,E),plus_plus(X_a,times_times(X_a,B_1,E),C))=plus_plus(X_a,times_times(X_a,plus_plus(X_a,A_1,B_1),E),C).
% 25.51/25.32 0 [] -semiri456707255roduct(X_a)|plus_plus(X_a,times_times(X_a,Wa,Ya),times_times(X_a,Xa,Z_1))!=plus_plus(X_a,times_times(X_a,Wa,Z_1),times_times(X_a,Xa,Ya))|ti(X_a,Wa)=ti(X_a,Xa)|ti(X_a,Ya)=ti(X_a,Z_1).
% 25.51/25.32 0 [] -semiri456707255roduct(X_a)|plus_plus(X_a,times_times(X_a,Wa,Ya),times_times(X_a,Xa,Z_1))=plus_plus(X_a,times_times(X_a,Wa,Z_1),times_times(X_a,Xa,Ya))|ti(X_a,Wa)!=ti(X_a,Xa).
% 25.51/25.32 0 [] -semiri456707255roduct(X_a)|plus_plus(X_a,times_times(X_a,Wa,Ya),times_times(X_a,Xa,Z_1))=plus_plus(X_a,times_times(X_a,Wa,Z_1),times_times(X_a,Xa,Ya))|ti(X_a,Ya)!=ti(X_a,Z_1).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,times_times(X_a,A_1,M),times_times(X_a,B_1,M))=times_times(X_a,plus_plus(X_a,A_1,B_1),M).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|times_times(X_a,plus_plus(X_a,A_1,B_1),C)=plus_plus(X_a,times_times(X_a,A_1,C),times_times(X_a,B_1,C)).
% 25.51/25.32 0 [] -semiri456707255roduct(X_a)|ti(X_a,A_2)=ti(X_a,B)|ti(X_a,C_1)=ti(X_a,D)|plus_plus(X_a,times_times(X_a,A_2,C_1),times_times(X_a,B,D))!=plus_plus(X_a,times_times(X_a,A_2,D),times_times(X_a,B,C_1)).
% 25.51/25.32 0 [] -semiri456707255roduct(X_a)|ti(X_a,A_2)!=ti(X_a,B)|plus_plus(X_a,times_times(X_a,A_2,C_1),times_times(X_a,B,D))=plus_plus(X_a,times_times(X_a,A_2,D),times_times(X_a,B,C_1)).
% 25.51/25.32 0 [] -semiri456707255roduct(X_a)|ti(X_a,C_1)!=ti(X_a,D)|plus_plus(X_a,times_times(X_a,A_2,C_1),times_times(X_a,B,D))=plus_plus(X_a,times_times(X_a,A_2,D),times_times(X_a,B,C_1)).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|times_times(X_a,X,plus_plus(X_a,Y,Z))=plus_plus(X_a,times_times(X_a,X,Y),times_times(X_a,X,Z)).
% 25.51/25.32 0 [] nat_1(hAPP(nat,int,semiring_1_of_nat(int),N))=N.
% 25.51/25.32 0 [] -comm_monoid_mult(X_a)|times_times(X_a,A_1,one_one(X_a))=ti(X_a,A_1).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|times_times(X_a,A_1,one_one(X_a))=ti(X_a,A_1).
% 25.51/25.32 0 [] -monoid_mult(X_a)|times_times(X_a,A_1,one_one(X_a))=ti(X_a,A_1).
% 25.51/25.32 0 [] -comm_monoid_mult(X_a)|times_times(X_a,one_one(X_a),A_1)=ti(X_a,A_1).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|times_times(X_a,one_one(X_a),A_1)=ti(X_a,A_1).
% 25.51/25.32 0 [] -monoid_mult(X_a)|times_times(X_a,one_one(X_a),A_1)=ti(X_a,A_1).
% 25.51/25.32 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,C,A_1)),plus_plus(X_a,C,B_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B_1)).
% 25.51/25.32 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,A_1,C)),plus_plus(X_a,B_1,C)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B_1)).
% 25.51/25.32 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_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,A_1,C)),plus_plus(X_a,B_1,D_1))).
% 25.51/25.32 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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,C,A_1)),plus_plus(X_a,C,B_1))).
% 25.51/25.32 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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,A_1,C)),plus_plus(X_a,B_1,C))).
% 25.51/25.32 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,C_1,A_2)),plus_plus(X_a,C_1,B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B)).
% 25.51/25.32 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,C_1,A_2)),plus_plus(X_a,C_1,B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B)).
% 25.51/25.32 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,A_2,C_1)),plus_plus(X_a,B,C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B)).
% 25.51/25.32 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,A_2,C_1)),plus_plus(X_a,B,C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B)).
% 25.51/25.32 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),minus_minus(nat,J_1,N)),K_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),minus_minus(nat,L,N)),minus_minus(nat,L,M))).
% 25.51/25.32 0 [] -monoid_mult(X_a)|times_times(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N),A_1)=times_times(X_a,A_1,hAPP(nat,X_a,power_power(X_a,A_1),N)).
% 25.51/25.32 0 [] -comm_monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,times_times(X_a,A_1,B_1)),N)=times_times(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N),hAPP(nat,X_a,power_power(X_a,B_1),N)).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,times_times(X_a,X,Y)),Q)=times_times(X_a,hAPP(nat,X_a,power_power(X_a,X),Q),hAPP(nat,X_a,power_power(X_a,Y),Q)).
% 25.51/25.32 0 [] minus_minus(nat,plus_plus(nat,M,N),N)=M.
% 25.51/25.32 0 [] minus_minus(nat,plus_plus(nat,N,M),N)=M.
% 25.51/25.32 0 [] minus_minus(nat,minus_minus(nat,I_2,J_1),K_1)=minus_minus(nat,I_2,plus_plus(nat,J_1,K_1)).
% 25.51/25.32 0 [] minus_minus(nat,plus_plus(nat,K_1,M),plus_plus(nat,K_1,N))=minus_minus(nat,M,N).
% 25.51/25.32 0 [] minus_minus(nat,plus_plus(nat,M,K_1),plus_plus(nat,N,K_1))=minus_minus(nat,M,N).
% 25.51/25.32 0 [] times_times(int,pls,W)=pls.
% 25.51/25.32 0 [] times_times(int,bit0(K_1),L)=bit0(times_times(int,K_1,L)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit1(L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L_1)).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit1(L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L_1)).
% 25.51/25.32 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)).
% 25.51/25.32 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)).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),pls)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit0(L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L_1)).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit0(L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L_1)).
% 25.51/25.32 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)).
% 25.51/25.32 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)).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),zero_zero(int))).
% 25.51/25.32 0 [] times_times(int,one_one(int),Z)=ti(int,Z).
% 25.51/25.32 0 [] times_times(int,Z,one_one(int))=ti(int,Z).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),Wa)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))|ti(int,Z_1)!=ti(int,Wa).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),Wa))|ti(int,Z_1)=ti(int,Wa).
% 25.51/25.32 0 [] times_times(int,W,plus_plus(int,Z1,Z2))=plus_plus(int,times_times(int,W,Z1),times_times(int,W,Z2)).
% 25.51/25.32 0 [] times_times(int,plus_plus(int,Z1,Z2),W)=plus_plus(int,times_times(int,Z1,W),times_times(int,Z2,W)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),J_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),plus_plus(int,K_1,I_2)),plus_plus(int,K_1,J_1))).
% 25.51/25.32 0 [] times_times(int,number_number_of(int,V_1),number_number_of(int,W))=number_number_of(int,times_times(int,V_1,W)).
% 25.51/25.32 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_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L_1)).
% 25.51/25.32 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_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L_1)).
% 25.51/25.32 0 [] -linord1278240602ring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),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_1))|plus_plus(X_a,U_1,V_1)!=one_one(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,times_times(X_a,U_1,X),times_times(X_a,V_1,Y))),A_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Ya))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(Xa)),nat_1(Ya)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),Ya)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Ya))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(Xa)),nat_1(Ya)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),Ya)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(Wa)),nat_1(Z_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(Wa)),nat_1(Z_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1)).
% 25.51/25.32 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,Ya)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),Ya)).
% 25.51/25.32 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,Ya)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),Ya)).
% 25.51/25.32 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,Xa)),zero_zero(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),pls)).
% 25.51/25.32 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,Xa)),zero_zero(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),pls)).
% 25.51/25.32 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),N_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),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_2)),hAPP(nat,X_a,power_power(X_a,A_1),N))).
% 25.51/25.32 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))| -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),Xa)),hAPP(nat,X_a,power_power(X_a,B),Ya)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Xa),Ya)).
% 25.51/25.32 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))|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),Xa)),hAPP(nat,X_a,power_power(X_a,B),Ya)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Xa),Ya)).
% 25.51/25.32 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)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N)).
% 25.51/25.32 0 [] Ma!=nat_1(Wa)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa))|ti(int,Wa)=hAPP(nat,int,semiring_1_of_nat(int),Ma).
% 25.51/25.32 0 [] Ma!=nat_1(Wa)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa))|Ma=zero_zero(nat).
% 25.51/25.32 0 [] Ma=nat_1(Wa)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa))|Ma!=zero_zero(nat).
% 25.51/25.32 0 [] Ma=nat_1(Wa)|ti(int,Wa)!=hAPP(nat,int,semiring_1_of_nat(int),Ma)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa)).
% 25.51/25.32 0 [] Ma=nat_1(Wa)|ti(int,Wa)!=hAPP(nat,int,semiring_1_of_nat(int),Ma)|Ma!=zero_zero(nat).
% 25.51/25.32 0 [] nat_1(Wa)!=Ma| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa))|ti(int,Wa)=hAPP(nat,int,semiring_1_of_nat(int),Ma).
% 25.51/25.32 0 [] nat_1(Wa)!=Ma|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa))|Ma=zero_zero(nat).
% 25.51/25.32 0 [] nat_1(Wa)=Ma|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa))|Ma!=zero_zero(nat).
% 25.51/25.32 0 [] nat_1(Wa)=Ma|ti(int,Wa)!=hAPP(nat,int,semiring_1_of_nat(int),Ma)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa)).
% 25.51/25.32 0 [] nat_1(Wa)=Ma|ti(int,Wa)!=hAPP(nat,int,semiring_1_of_nat(int),Ma)|Ma!=zero_zero(nat).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))|plus_plus(nat,nat_1(X),nat_1(Y))=nat_1(plus_plus(int,X,Y)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_2))|nat_1(plus_plus(int,Z,Z_2))=plus_plus(nat,nat_1(Z),nat_1(Z_2)).
% 25.51/25.32 0 [] hAPP(nat,int,semiring_1_of_nat(int),Ma)!=number_number_of(int,Va)|Ma=nat_1(number_number_of(int,Va)).
% 25.51/25.32 0 [] hAPP(nat,int,semiring_1_of_nat(int),Ma)!=number_number_of(int,Va)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,Va))).
% 25.51/25.32 0 [] hAPP(nat,int,semiring_1_of_nat(int),Ma)=number_number_of(int,Va)|Ma!=nat_1(number_number_of(int,Va))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,Va))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))|hAPP(nat,nat,power_power(nat,nat_1(X)),N)=nat_1(hAPP(nat,int,power_power(int,X),N)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))|nat_1(hAPP(nat,int,power_power(int,Z),N))=hAPP(nat,nat,power_power(nat,nat_1(Z)),N).
% 25.51/25.32 0 [] -linord626643107strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),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_1))|plus_plus(X_a,U_1,V_1)!=one_one(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,times_times(X_a,U_1,X),times_times(X_a,V_1,Y))),A_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(Wa)),Ma))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),hAPP(nat,int,semiring_1_of_nat(int),Ma))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Wa))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(Wa)),Ma))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),hAPP(nat,int,semiring_1_of_nat(int),Ma))).
% 25.51/25.32 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,Ya)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(pls)),Ya)).
% 25.51/25.32 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,Ya)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(pls)),Ya)).
% 25.51/25.32 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,Xa)),one_one(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),bit1(pls))).
% 25.51/25.32 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,Xa)),one_one(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),bit1(pls))).
% 25.51/25.32 0 [] -monoid_mult(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|times_times(X_a,hAPP(nat,X_a,power_power(X_a,X),minus_minus(nat,N,one_one(nat))),X)=hAPP(nat,X_a,power_power(X_a,X),N).
% 25.51/25.32 0 [] -ordered_ab_group_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),minus_minus(X_a,A_2,B)),zero_zero(X_a))).
% 25.51/25.32 0 [] -ordered_ab_group_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),minus_minus(X_a,A_2,B)),zero_zero(X_a))).
% 25.51/25.32 0 [] zero_zero(nat)=nat_1(zero_zero(int)).
% 25.51/25.32 0 [] nat_1(zero_zero(int))=zero_zero(nat).
% 25.51/25.32 0 [] -linordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_1,A_1)),zero_zero(X_a))).
% 25.51/25.32 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_2,C_1)),times_times(X_a,B,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))).
% 25.51/25.32 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_2,C_1)),times_times(X_a,B,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),A_2)).
% 25.51/25.32 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_2,C_1)),times_times(X_a,B,C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))).
% 25.51/25.32 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_2,C_1)),times_times(X_a,B,C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_2)).
% 25.51/25.32 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_2,C_1)),times_times(X_a,B,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_2),B)).
% 25.51/25.32 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_2,C_1)),times_times(X_a,B,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),A_2)).
% 25.51/25.32 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))|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))).
% 25.51/25.32 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))|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),A_2)).
% 25.51/25.32 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))).
% 25.51/25.32 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_2)).
% 25.51/25.32 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))| -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_2),B)).
% 25.51/25.32 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))| -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),A_2)).
% 25.51/25.32 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),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B)).
% 25.51/25.32 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),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B)).
% 25.51/25.32 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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),times_times(X_a,A_1,B_1))).
% 25.51/25.32 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_1),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_1,B_1)),zero_zero(X_a))).
% 25.51/25.32 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_1),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,B_1,A_1)),zero_zero(X_a))).
% 25.51/25.32 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),times_times(X_a,A_1,B_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_1)).
% 25.51/25.32 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),times_times(X_a,B_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)),B_1)).
% 25.51/25.32 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),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_2)).
% 25.51/25.32 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),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_2)).
% 25.51/25.32 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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,A_1,B_1)),zero_zero(X_a))).
% 25.51/25.32 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_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)),times_times(X_a,A_1,B_1))).
% 25.51/25.32 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_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),times_times(X_a,A_1,C)),times_times(X_a,B_1,C))).
% 25.51/25.32 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_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),times_times(X_a,C,A_1)),times_times(X_a,C,B_1))).
% 25.51/25.32 0 [] -linord893533164strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_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),times_times(X_a,C,A_1)),times_times(X_a,C,B_1))).
% 25.51/25.32 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),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),times_times(X_a,A_1,C)),times_times(X_a,B_1,C))).
% 25.51/25.32 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),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),times_times(X_a,C,A_1)),times_times(X_a,C,B_1))).
% 25.51/25.32 0 [] nat_1(number_number_of(int,W))=number_number_of(nat,W).
% 25.51/25.32 0 [] number_number_of(nat,V_1)=nat_1(number_number_of(int,V_1)).
% 25.51/25.32 0 [] -linord581940658strict(X_a)|plus_plus(X_a,times_times(X_a,Xa,Xa),times_times(X_a,Ya,Ya))!=zero_zero(X_a)|ti(X_a,Xa)=zero_zero(X_a).
% 25.51/25.32 0 [] -linord581940658strict(X_a)|plus_plus(X_a,times_times(X_a,Xa,Xa),times_times(X_a,Ya,Ya))!=zero_zero(X_a)|ti(X_a,Ya)=zero_zero(X_a).
% 25.51/25.32 0 [] -linord581940658strict(X_a)|plus_plus(X_a,times_times(X_a,Xa,Xa),times_times(X_a,Ya,Ya))=zero_zero(X_a)|ti(X_a,Xa)!=zero_zero(X_a)|ti(X_a,Ya)!=zero_zero(X_a).
% 25.51/25.32 0 [] -semiri456707255roduct(X_a)|ti(X_a,R_1)=zero_zero(X_a)|ti(X_a,A_1)!=ti(X_a,B_1)|ti(X_a,C)=ti(X_a,D_1)|plus_plus(X_a,A_1,times_times(X_a,R_1,C))!=plus_plus(X_a,B_1,times_times(X_a,R_1,D_1)).
% 25.51/25.32 0 [] one_one(nat)=nat_1(one_one(int)).
% 25.51/25.32 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))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),times_times(X_a,M,N))).
% 25.51/25.32 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)),plus_plus(X_a,A_2,A_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_2)).
% 25.51/25.32 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)),plus_plus(X_a,A_2,A_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_2)).
% 25.51/25.32 0 [] -linord219039673up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,A_2,A_2)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),zero_zero(X_a))).
% 25.51/25.32 0 [] -linord219039673up_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,A_2,A_2)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),zero_zero(X_a))).
% 25.51/25.32 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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),plus_plus(X_a,A_1,B_1))).
% 25.51/25.32 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)),Xa))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Ya))|plus_plus(X_a,Xa,Ya)!=zero_zero(X_a)|ti(X_a,Xa)=zero_zero(X_a).
% 25.51/25.32 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)),Xa))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Ya))|plus_plus(X_a,Xa,Ya)!=zero_zero(X_a)|ti(X_a,Ya)=zero_zero(X_a).
% 25.51/25.32 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)),Xa))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Ya))|plus_plus(X_a,Xa,Ya)=zero_zero(X_a)|ti(X_a,Xa)!=zero_zero(X_a)|ti(X_a,Ya)!=zero_zero(X_a).
% 25.51/25.32 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_1),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_1),plus_plus(X_a,A_1,C))).
% 25.51/25.32 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_1),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_1),plus_plus(X_a,A_1,C))).
% 25.51/25.32 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_1),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,A_1,B_1)),zero_zero(X_a))).
% 25.51/25.32 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_1,C)),plus_plus(X_a,B_1,D_1))).
% 25.51/25.32 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_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_1,C)),plus_plus(X_a,B_1,D_1))).
% 25.51/25.32 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))).
% 25.51/25.32 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))).
% 25.51/25.32 0 [] -number(X_b)| -semiring(X_b)|times_times(X_b,number_number_of(X_b,V_1),plus_plus(X_b,B_1,C))=plus_plus(X_b,times_times(X_b,number_number_of(X_b,V_1),B_1),times_times(X_b,number_number_of(X_b,V_1),C)).
% 25.51/25.32 0 [] -number(X_b)| -semiring(X_b)|times_times(X_b,plus_plus(X_b,A_1,B_1),number_number_of(X_b,V_1))=plus_plus(X_b,times_times(X_b,A_1,number_number_of(X_b,V_1)),times_times(X_b,B_1,number_number_of(X_b,V_1))).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,M,M)=times_times(X_a,plus_plus(X_a,one_one(X_a),one_one(X_a)),M).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,M,times_times(X_a,A_1,M))=times_times(X_a,plus_plus(X_a,A_1,one_one(X_a)),M).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,times_times(X_a,A_1,M),M)=times_times(X_a,plus_plus(X_a,A_1,one_one(X_a)),M).
% 25.51/25.32 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,Va)),number_number_of(X_a,Wa)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Wa)),number_number_of(X_a,Va))).
% 25.51/25.32 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,Va)),number_number_of(X_a,Wa)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Wa)),number_number_of(X_a,Va))).
% 25.51/25.32 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))).
% 25.51/25.32 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_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),hAPP(nat,X_a,power_power(X_a,A_1),N)),hAPP(nat,X_a,power_power(X_a,B_1),N))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),minus_minus(nat,Na,Ma)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),minus_minus(nat,Na,Ma)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))| -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),minus_minus(nat,M,N)),M)).
% 25.51/25.32 0 [] minus_minus(nat,N,plus_plus(nat,N,M))=zero_zero(nat).
% 25.51/25.32 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))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),minus_minus(nat,J,K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,I_1,K)),J)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),minus_minus(nat,J,K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,I_1,K)),J)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))|plus_plus(nat,N,minus_minus(nat,M,N))=M.
% 25.51/25.32 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)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M))).
% 25.51/25.32 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)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))).
% 25.51/25.32 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),plus_plus(nat,M,N))=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)).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|times_times(X_a,hAPP(nat,X_a,power_power(X_a,X),P_2),hAPP(nat,X_a,power_power(X_a,X),Q))=hAPP(nat,X_a,power_power(X_a,X),plus_plus(nat,P_2,Q)).
% 25.51/25.32 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)).
% 25.51/25.32 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)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit1(L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L_1)).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit1(L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L_1)).
% 25.51/25.32 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)).
% 25.51/25.32 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)).
% 25.51/25.32 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)).
% 25.51/25.32 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)).
% 25.51/25.32 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)).
% 25.51/25.32 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)).
% 25.51/25.32 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)),times_times(int,A_1,B_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),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),times_times(int,K_1,I_2)),times_times(int,K_1,J_1))).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),one_one(int))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))| -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)),plus_plus(int,X,Y))).
% 25.51/25.32 0 [] -semiring_1(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))|hAPP(nat,X_a,semiring_1_of_nat(X_a),nat_1(times_times(int,number_number_of(int,bit0(bit1(pls))),X)))=plus_plus(X_a,hAPP(nat,X_a,semiring_1_of_nat(X_a),nat_1(X)),hAPP(nat,X_a,semiring_1_of_nat(X_a),nat_1(X))).
% 25.51/25.32 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_2),Z))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(int,W_2,Z_2)),plus_plus(int,W,Z))).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Z))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,P_1,X_1))|hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),$f10(P_1)))).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f11(P_1)))| -hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X2))).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,P_1,$f11(P_1)))| -hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X2))).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f12(P_1)))|hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_1))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,P_1,$f12(P_1)))|hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_1))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X3))|hBOOL(hAPP(int,bool,P_1,X3))| -hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),$f13(P_1)))).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,power_power(int,X),N))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),Z_1))|ti(int,Z_1)=plus_plus(int,Wa,hAPP(nat,int,semiring_1_of_nat(int),$f14(Wa,Z_1))).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),Z_1))|ti(int,Z_1)!=plus_plus(int,Wa,hAPP(nat,int,semiring_1_of_nat(int),N_1)).
% 25.51/25.32 0 [] hAPP(nat,int,power_power(int,X),plus_plus(nat,Y,Z))=times_times(int,hAPP(nat,int,power_power(int,X),Y),hAPP(nat,int,power_power(int,X),Z)).
% 25.51/25.32 0 [] -number_semiring(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))|plus_plus(X_a,one_one(X_a),number_number_of(X_a,V_1))=number_number_of(X_a,succ(V_1)).
% 25.51/25.32 0 [] -number_semiring(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))|plus_plus(X_a,number_number_of(X_a,V_1),one_one(X_a))=number_number_of(X_a,succ(V_1)).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,X),times_times(nat,number_number_of(nat,bit0(bit1(pls))),N))=times_times(X_a,hAPP(nat,X_a,power_power(X_a,X),N),hAPP(nat,X_a,power_power(X_a,X),N)).
% 25.51/25.32 0 [] -number_ring(X_a)|plus_plus(X_a,number_number_of(X_a,V_1),minus_minus(X_a,number_number_of(X_a,W),C))=minus_minus(X_a,number_number_of(X_a,plus_plus(int,V_1,W)),C).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(Wa)),nat_1(Z_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(Wa)),nat_1(Z_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(Wa)),nat_1(Z_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(Wa)),nat_1(Z_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(Wa)),nat_1(Z_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1)).
% 25.51/25.32 0 [] -linordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,times_times(X_a,X,X),times_times(X_a,Y,Y))),zero_zero(X_a))).
% 25.51/25.32 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),plus_plus(X_a,times_times(X_a,Xa,Xa),times_times(X_a,Ya,Ya))))|ti(X_a,Xa)!=zero_zero(X_a)|ti(X_a,Ya)!=zero_zero(X_a).
% 25.51/25.32 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),plus_plus(X_a,times_times(X_a,Xa,Xa),times_times(X_a,Ya,Ya))))|ti(X_a,Xa)=zero_zero(X_a).
% 25.51/25.32 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),plus_plus(X_a,times_times(X_a,Xa,Xa),times_times(X_a,Ya,Ya))))|ti(X_a,Ya)=zero_zero(X_a).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),nat_1(Z_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),Z_1)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),nat_1(Z_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),Z_1)).
% 25.51/25.32 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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),plus_plus(X_a,A_1,B_1))).
% 25.51/25.32 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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),plus_plus(X_a,A_1,B_1))).
% 25.51/25.32 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_1),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),plus_plus(X_a,A_1,C))).
% 25.51/25.32 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_1),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),plus_plus(X_a,A_1,C))).
% 25.51/25.32 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_1),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_1,B_1)),zero_zero(X_a))).
% 25.51/25.32 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_1),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),plus_plus(X_a,A_1,B_1)),zero_zero(X_a))).
% 25.51/25.32 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)),hAPP(nat,X_a,power_power(X_a,B_1),N)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)).
% 25.51/25.32 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)),times_times(X_a,A_1,hAPP(nat,X_a,power_power(X_a,A_1),N)))).
% 25.51/25.32 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)),times_times(X_a,A_1,hAPP(nat,X_a,power_power(X_a,A_1),N)))).
% 25.51/25.32 0 [] -number_ring(X_a)|times_times(X_a,A_1,number_number_of(X_a,bit1(pls)))=ti(X_a,A_1).
% 25.51/25.32 0 [] -number_ring(X_a)|times_times(X_a,number_number_of(X_a,bit1(pls)),A_1)=ti(X_a,A_1).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,P_1,minus_minus(nat,A_2,B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B))|hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,P_1,minus_minus(nat,A_2,B)))|A_2!=plus_plus(nat,B,D_3)|hBOOL(hAPP(nat,bool,P_1,D_3)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,P_1,minus_minus(nat,A_2,B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B))|A_2=plus_plus(nat,B,$f15(P_1,A_2,B)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,P_1,minus_minus(nat,A_2,B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B))| -hBOOL(hAPP(nat,bool,P_1,$f15(P_1,A_2,B))).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,P_1,minus_minus(nat,A_2,B)))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))|A_2=plus_plus(nat,B,$f15(P_1,A_2,B)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,P_1,minus_minus(nat,A_2,B)))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,$f15(P_1,A_2,B))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,P_1,minus_minus(nat,A_2,B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B))|hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,P_1,minus_minus(nat,A_2,B)))|A_2!=plus_plus(nat,B,D_3)|hBOOL(hAPP(nat,bool,P_1,D_3)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,P_1,minus_minus(nat,A_2,B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B))|A_2=plus_plus(nat,B,$f16(P_1,A_2,B)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,P_1,minus_minus(nat,A_2,B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B))| -hBOOL(hAPP(nat,bool,P_1,$f16(P_1,A_2,B))).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,P_1,minus_minus(nat,A_2,B)))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))|A_2=plus_plus(nat,B,$f16(P_1,A_2,B)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,P_1,minus_minus(nat,A_2,B)))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,$f16(P_1,A_2,B))).
% 25.51/25.32 0 [] zero_zero(nat)!=number_number_of(nat,Va)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls)).
% 25.51/25.32 0 [] zero_zero(nat)=number_number_of(nat,Va)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls)).
% 25.51/25.32 0 [] number_number_of(nat,Va)!=zero_zero(nat)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls)).
% 25.51/25.32 0 [] number_number_of(nat,Va)=zero_zero(nat)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls)).
% 25.51/25.32 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)).
% 25.51/25.32 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)).
% 25.51/25.32 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)).
% 25.51/25.32 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)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit1(L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L_1)).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit1(L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L_1)).
% 25.51/25.32 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)).
% 25.51/25.32 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)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit0(L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1)).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit0(L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1)).
% 25.51/25.32 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)).
% 25.51/25.32 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)).
% 25.51/25.32 0 [] times_times(int,bit1(K_1),L)=plus_plus(int,bit0(times_times(int,K_1,L)),L).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))|times_times(int,Ma,Na)!=one_one(int)|ti(int,Ma)=one_one(int).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))|times_times(int,Ma,Na)!=one_one(int)|ti(int,Na)=one_one(int).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))|times_times(int,Ma,Na)=one_one(int)|ti(int,Ma)!=one_one(int)|ti(int,Na)!=one_one(int).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)))|Na=zero_zero(nat).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)))|Na!=zero_zero(nat).
% 25.51/25.32 0 [] succ(pls)=bit1(pls).
% 25.51/25.32 0 [] succ(bit0(K_1))=bit1(K_1).
% 25.51/25.32 0 [] succ(bit1(K_1))=bit0(succ(K_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),plus_plus(int,Z_1,one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),Z_1)).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),plus_plus(int,Z_1,one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),Z_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),plus_plus(int,Wa,one_one(int))),Z_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1)).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),plus_plus(int,Wa,one_one(int))),Z_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),plus_plus(int,W,one_one(int))),Z)).
% 25.51/25.32 0 [] succ(K_1)=plus_plus(int,K_1,one_one(int)).
% 25.51/25.32 0 [] -number_ring(X_a)|hAPP(nat,X_a,power_power(X_a,minus_minus(X_a,X,Y)),number_number_of(nat,bit0(bit1(pls))))=minus_minus(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),number_number_of(nat,bit0(bit1(pls))))),times_times(X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),X),Y)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),nat_1(Z_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),nat_1(Z_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)).
% 25.51/25.32 0 [] number_number_of(nat,bit1(bit1(pls)))=nat_1(number_number_of(int,bit1(bit1(pls)))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,P_1,nat_1(I_1)))|ti(int,I_1)!=hAPP(nat,int,semiring_1_of_nat(int),N_1)|hBOOL(hAPP(nat,bool,P_1,N_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,P_1,nat_1(I_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),zero_zero(int)))|hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,P_1,nat_1(I_1)))|ti(int,I_1)=hAPP(nat,int,semiring_1_of_nat(int),$f17(P_1,I_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),zero_zero(int))).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,P_1,nat_1(I_1)))|ti(int,I_1)=hAPP(nat,int,semiring_1_of_nat(int),$f17(P_1,I_1))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,P_1,nat_1(I_1)))| -hBOOL(hAPP(nat,bool,P_1,$f17(P_1,I_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),zero_zero(int))).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,P_1,nat_1(I_1)))| -hBOOL(hAPP(nat,bool,P_1,$f17(P_1,I_1)))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))).
% 25.51/25.32 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),times_times(X_a,A_1,hAPP(nat,X_a,power_power(X_a,A_1),N))),hAPP(nat,X_a,power_power(X_a,A_1),N))).
% 25.51/25.32 0 [] -number_ring(X_a)|times_times(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)).
% 25.51/25.32 0 [] -linordered_semidom(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),N)!=hAPP(nat,X_a,power_power(X_a,B_1),N)| -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_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|ti(X_a,A_1)=ti(X_a,B_1).
% 25.51/25.32 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit1(bit1(pls))))=times_times(X_a,times_times(X_a,A_1,A_1),A_1).
% 25.51/25.32 0 [] -number_semiring(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_2))|plus_plus(X_a,number_number_of(X_a,V_1),number_number_of(X_a,V_2))=number_number_of(X_a,plus_plus(int,V_1,V_2)).
% 25.51/25.32 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))))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),Z))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),times_times(int,hAPP(nat,int,semiring_1_of_nat(int),K_1),I_2)),times_times(int,hAPP(nat,int,semiring_1_of_nat(int),K_1),J_1))).
% 25.51/25.32 0 [] -number_ring(X_a)|number_number_of(X_a,succ(K_1))=plus_plus(X_a,one_one(X_a),number_number_of(X_a,K_1)).
% 25.51/25.32 0 [] plus_plus(int,bit1(K_1),bit1(L))=bit0(plus_plus(int,K_1,succ(L))).
% 25.51/25.32 0 [] number_number_of(nat,bit0(bit1(pls)))=nat_1(number_number_of(int,bit0(bit1(pls)))).
% 25.51/25.32 0 [] -number_ring(X_a)|times_times(X_a,Z,number_number_of(X_a,bit0(bit1(pls))))=plus_plus(X_a,Z,Z).
% 25.51/25.32 0 [] -number_semiring(X_a)|times_times(X_a,Z,number_number_of(X_a,bit0(bit1(pls))))=plus_plus(X_a,Z,Z).
% 25.51/25.32 0 [] -number_ring(X_a)|times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),Z)=plus_plus(X_a,Z,Z).
% 25.51/25.32 0 [] -number_semiring(X_a)|times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),Z)=plus_plus(X_a,Z,Z).
% 25.51/25.32 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_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(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|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)),hAPP(nat,X_a,power_power(X_a,B_1),N))).
% 25.51/25.32 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls))))=times_times(X_a,A_1,A_1).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|times_times(X_a,X,X)=hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls)))).
% 25.51/25.32 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))))).
% 25.51/25.32 0 [] 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)))).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls)))))).
% 25.51/25.32 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))))=times_times(X_b,number_number_of(X_b,W),number_number_of(X_b,W)).
% 25.51/25.32 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)))))).
% 25.51/25.32 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),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),Y)).
% 25.51/25.32 0 [] -linordered_semidom(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),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))| -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)=ti(X_a,Y).
% 25.51/25.32 0 [] -number_ring(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,V_1)))|hAPP(nat,X_a,semiring_1_of_nat(X_a),number_number_of(nat,V_1))=number_number_of(X_a,V_1).
% 25.51/25.32 0 [] -number_ring(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,V_1)))|hAPP(nat,X_a,semiring_1_of_nat(X_a),number_number_of(nat,V_1))=zero_zero(X_a).
% 25.51/25.32 0 [] -number_semiring(X_a)|hAPP(nat,X_a,power_power(X_a,plus_plus(X_a,X,Y)),number_number_of(nat,bit0(bit1(pls))))=plus_plus(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),number_number_of(nat,bit0(bit1(pls))))),times_times(X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),X),Y)).
% 25.51/25.32 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),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),Y)).
% 25.51/25.32 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)),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),number_number_of(nat,bit0(bit1(pls))))))).
% 25.51/25.32 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(X_a)))|ti(X_a,Xa)=zero_zero(X_a).
% 25.51/25.32 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(X_a)))|ti(X_a,Ya)=zero_zero(X_a).
% 25.51/25.32 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(X_a)))|ti(X_a,Xa)!=zero_zero(X_a)|ti(X_a,Ya)!=zero_zero(X_a).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),number_number_of(int,bit0(bit1(pls)))))|ti(int,X)=zero_zero(int)|ti(int,X)=one_one(int).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_2))|hAPP(nat,int,power_power(int,A_1),nat_1(P_2))=times_times(int,A_1,hAPP(nat,int,power_power(int,A_1),minus_minus(nat,nat_1(P_2),one_one(nat)))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))|ti(int,A_1)!=plus_plus(int,R_1,times_times(int,A_1,Q))| -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),one_one(int))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))|ti(int,A_1)!=plus_plus(int,R_1,times_times(int,A_1,Q))| -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)).
% 25.51/25.32 0 [] -power(X_a)|N!=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,M),N)=one_one(X_a).
% 25.51/25.32 0 [] -power(X_a)|N=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,M),N)=times_times(X_a,M,hAPP(nat,X_a,power_power(X_a,M),minus_minus(nat,N,one_one(nat)))).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),plus_plus(int,times_times(int,B_2,Q_1),R_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Q_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(int,times_times(int,B_2,Q_1),R_2)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),zero_zero(int))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)))))).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N)).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),t),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t))).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))).
% 25.51/25.32 0 [] plus_plus(int,hAPP(nat,int,power_power(int,$c2),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,int,power_power(int,$c1),number_number_of(nat,bit0(bit1(pls)))))=times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))).
% 25.51/25.32 0 [] plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),one_one(int))=times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,zprime,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.51/25.32 0 [] t!=one_one(int)|plus_plus(int,hAPP(nat,int,power_power(int,$c4),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,int,power_power(int,$c3),number_number_of(nat,bit0(bit1(pls)))))=plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),N)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),times_times(nat,M,M))).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),times_times(nat,M,times_times(nat,M,M)))).
% 25.51/25.32 0 [] times_times(nat,M,N)=times_times(nat,N,M).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M)).
% 25.51/25.32 0 [] times_times(nat,times_times(nat,M,N),K_1)=times_times(nat,M,times_times(nat,N,K_1)).
% 25.51/25.32 0 [] M!=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),times_times(nat,I_2,K_1)),times_times(nat,J_1,K_1))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),times_times(nat,K_1,I_2)),times_times(nat,K_1,J_1))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),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_2),K_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M))|M=N.
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),times_times(nat,I_2,K_1)),times_times(nat,J_1,L))).
% 25.51/25.32 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),minus_minus(real,Xa,Ya)),zero_zero(real))).
% 25.51/25.32 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),minus_minus(real,Xa,Ya)),zero_zero(real))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),times_times(nat,Ma,K)),times_times(nat,Na,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),Na)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),times_times(nat,Ma,K)),times_times(nat,Na,K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),times_times(nat,Ma,K)),times_times(nat,Na,K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),times_times(nat,K,Ma)),times_times(nat,K,Na)))| -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),Na)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),times_times(nat,K,Ma)),times_times(nat,K,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),times_times(nat,K,Ma)),times_times(nat,K,Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)).
% 25.51/25.32 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_e_q(real),times_times(real,Xa,Z_1)),times_times(real,Ya,Z_1)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya)).
% 25.51/25.32 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_e_q(real),times_times(real,Xa,Z_1)),times_times(real,Ya,Z_1)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya)).
% 25.51/25.32 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_e_q(real),times_times(real,Z_1,Xa)),times_times(real,Z_1,Ya)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya)).
% 25.51/25.32 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_e_q(real),times_times(real,Z_1,Xa)),times_times(real,Z_1,Ya)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M))|minus_minus(int,hAPP(nat,int,semiring_1_of_nat(int),M),hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,M,N)).
% 25.51/25.32 0 [] minus_minus(int,K_1,pls)=ti(int,K_1).
% 25.51/25.32 0 [] minus_minus(int,bit0(K_1),bit0(L))=bit0(minus_minus(int,K_1,L)).
% 25.51/25.32 0 [] times_times(int,minus_minus(int,Z1,Z2),W)=minus_minus(int,times_times(int,Z1,W),times_times(int,Z2,W)).
% 25.51/25.32 0 [] times_times(int,W,minus_minus(int,Z1,Z2))=minus_minus(int,times_times(int,W,Z1),times_times(int,W,Z2)).
% 25.51/25.32 0 [] times_times(nat,zero_zero(nat),N)=zero_zero(nat).
% 25.51/25.32 0 [] times_times(nat,M,zero_zero(nat))=zero_zero(nat).
% 25.51/25.32 0 [] times_times(nat,Ma,Na)!=zero_zero(nat)|Ma=zero_zero(nat)|Na=zero_zero(nat).
% 25.51/25.32 0 [] times_times(nat,Ma,Na)=zero_zero(nat)|Ma!=zero_zero(nat).
% 25.51/25.32 0 [] times_times(nat,Ma,Na)=zero_zero(nat)|Na!=zero_zero(nat).
% 25.51/25.32 0 [] times_times(nat,K,Ma)!=times_times(nat,K,Na)|Ma=Na|K=zero_zero(nat).
% 25.51/25.32 0 [] times_times(nat,K,Ma)=times_times(nat,K,Na)|Ma!=Na.
% 25.51/25.32 0 [] times_times(nat,K,Ma)=times_times(nat,K,Na)|K!=zero_zero(nat).
% 25.51/25.32 0 [] times_times(nat,Ma,K)!=times_times(nat,Na,K)|Ma=Na|K=zero_zero(nat).
% 25.51/25.32 0 [] times_times(nat,Ma,K)=times_times(nat,Na,K)|Ma!=Na.
% 25.51/25.32 0 [] times_times(nat,Ma,K)=times_times(nat,Na,K)|K!=zero_zero(nat).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,X),P_2)),Q)=hAPP(nat,X_a,power_power(X_a,X),times_times(nat,P_2,Q)).
% 25.51/25.32 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),times_times(nat,M,N))=hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,A_1),M)),N).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Na),zero_zero(nat)))|Na=zero_zero(nat).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Na),zero_zero(nat)))|Na!=zero_zero(nat).
% 25.51/25.32 0 [] C_1=zero_zero(real)|times_times(real,C_1,A_2)!=times_times(real,C_1,B)|A_2=B.
% 25.51/25.32 0 [] C_1=zero_zero(real)|times_times(real,C_1,A_2)=times_times(real,C_1,B)|A_2!=B.
% 25.51/25.32 0 [] C_1=zero_zero(real)|times_times(real,A_2,C_1)!=times_times(real,B,C_1)|A_2=B.
% 25.51/25.32 0 [] C_1=zero_zero(real)|times_times(real,A_2,C_1)=times_times(real,B,C_1)|A_2!=B.
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N)).
% 25.51/25.32 0 [] M!=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))|M=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))|Ma=Na.
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))|Ma!=Na.
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))|Ma!=Na.
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))|Ma=Na.
% 25.51/25.32 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya)).
% 25.51/25.32 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya))|Xa!=Ya.
% 25.51/25.32 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya))|Xa=Ya.
% 25.51/25.32 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya))|Xa=Ya.
% 25.51/25.32 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya)).
% 25.51/25.32 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya))|Xa!=Ya.
% 25.51/25.32 0 [] times_times(nat,plus_plus(nat,M,N),K_1)=plus_plus(nat,times_times(nat,M,K_1),times_times(nat,N,K_1)).
% 25.51/25.32 0 [] times_times(nat,K_1,plus_plus(nat,M,N))=plus_plus(nat,times_times(nat,K_1,M),times_times(nat,K_1,N)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,M,K_1)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,M,K_1)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,M,K_1)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,M,K_1)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,I_2,K_1)),plus_plus(nat,J_1,L))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,I_2,K_1)),plus_plus(nat,J_1,K_1))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),plus_plus(nat,M,J_1))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),plus_plus(nat,J_1,M))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,K,Ma)),plus_plus(nat,K,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,K,Ma)),plus_plus(nat,K,Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))|Na=plus_plus(nat,Ma,$f18(Ma,Na)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))|Na!=plus_plus(nat,Ma,K_2).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),plus_plus(nat,N,M))).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),plus_plus(nat,M,N))).
% 25.51/25.32 0 [] times_times(nat,Na,Ma)!=one_one(nat)|Na=one_one(nat).
% 25.51/25.32 0 [] times_times(nat,Na,Ma)!=one_one(nat)|Ma=one_one(nat).
% 25.51/25.32 0 [] times_times(nat,Na,Ma)=one_one(nat)|Na!=one_one(nat)|Ma!=one_one(nat).
% 25.51/25.32 0 [] times_times(nat,Ma,Na)!=one_one(nat)|Ma=one_one(nat).
% 25.51/25.32 0 [] times_times(nat,Ma,Na)!=one_one(nat)|Na=one_one(nat).
% 25.51/25.32 0 [] times_times(nat,Ma,Na)=one_one(nat)|Ma!=one_one(nat)|Na!=one_one(nat).
% 25.51/25.32 0 [] times_times(nat,N,one_one(nat))=N.
% 25.51/25.32 0 [] one_one(nat)!=times_times(nat,Ma,Na)|Ma=one_one(nat).
% 25.51/25.32 0 [] one_one(nat)!=times_times(nat,Ma,Na)|Na=one_one(nat).
% 25.51/25.32 0 [] one_one(nat)=times_times(nat,Ma,Na)|Ma!=one_one(nat)|Na!=one_one(nat).
% 25.51/25.32 0 [] times_times(nat,one_one(nat),N)=N.
% 25.51/25.32 0 [] times_times(nat,minus_minus(nat,M,N),K_1)=minus_minus(nat,times_times(nat,M,K_1),times_times(nat,N,K_1)).
% 25.51/25.32 0 [] times_times(nat,K_1,minus_minus(nat,M,N))=minus_minus(nat,times_times(nat,K_1,M),times_times(nat,K_1,N)).
% 25.51/25.32 0 [] times_times(real,one_one(real),Z)=Z.
% 25.51/25.32 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),Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),minus_minus(nat,Ma,K)),minus_minus(nat,Na,K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)).
% 25.51/25.32 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),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),minus_minus(nat,Ma,K)),minus_minus(nat,Na,K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)).
% 25.51/25.32 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))|minus_minus(nat,minus_minus(nat,M,K_1),minus_minus(nat,N,K_1))=minus_minus(nat,M,N).
% 25.51/25.32 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),Na))|minus_minus(nat,Ma,K)!=minus_minus(nat,Na,K)|Ma=Na.
% 25.51/25.32 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),Na))|minus_minus(nat,Ma,K)=minus_minus(nat,Na,K)|Ma!=Na.
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),N))|minus_minus(nat,N,minus_minus(nat,N,I_2))=I_2.
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),minus_minus(nat,M,L)),minus_minus(nat,N,L))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),minus_minus(nat,L,N)),minus_minus(nat,L,M))).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),minus_minus(nat,M,N)),M)).
% 25.51/25.32 0 [] times_times(real,plus_plus(real,Z1,Z2),W)=plus_plus(real,times_times(real,Z1,W),times_times(real,Z2,W)).
% 25.51/25.32 0 [] hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X),Y)),Z)=hAPP(nat,int,power_power(int,X),times_times(nat,Y,Z)).
% 25.51/25.32 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),plus_plus(real,Z,X)),plus_plus(real,Z,Y))).
% 25.51/25.32 0 [] minus_minus(int,bit1(K_1),bit1(L))=bit0(minus_minus(int,K_1,L)).
% 25.51/25.32 0 [] minus_minus(int,bit1(K_1),bit0(L))=bit1(minus_minus(int,K_1,L)).
% 25.51/25.32 0 [] minus_minus(int,pls,bit0(L))=bit0(minus_minus(int,pls,L)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),A_1))|ti(int,X)=minus_minus(int,A_1,one_one(int))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),minus_minus(int,A_1,one_one(int)))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),minus_minus(int,K,L_1)),zero_zero(int))).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),minus_minus(int,K,L_1)),zero_zero(int))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),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),times_times(nat,K_1,I_2)),times_times(nat,K_1,J_1))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),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),times_times(nat,I_2,K_1)),times_times(nat,J_1,K_1))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),times_times(nat,Ma,K)),times_times(nat,Na,K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),times_times(nat,Ma,K)),times_times(nat,Na,K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),times_times(nat,Ma,K)),times_times(nat,Na,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),Na)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),times_times(nat,K,Ma)),times_times(nat,K,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),times_times(nat,K,Ma)),times_times(nat,K,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),times_times(nat,K,Ma)),times_times(nat,K,Na)))| -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),Na)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),times_times(nat,Ma,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),times_times(nat,Ma,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),times_times(nat,Ma,Na)))| -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)),Na)).
% 25.51/25.32 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),times_times(real,Xa,Xa)))|Xa=zero_zero(real).
% 25.51/25.32 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),times_times(real,Xa,Xa)))|Xa!=zero_zero(real).
% 25.51/25.32 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),times_times(real,Z,X)),times_times(real,Z,Y))).
% 25.51/25.32 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X))| -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)),times_times(real,X,Y))).
% 25.51/25.32 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),times_times(real,Xa,Z_1)),times_times(real,Ya,Z_1)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya)).
% 25.51/25.32 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),times_times(real,Xa,Z_1)),times_times(real,Ya,Z_1)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya)).
% 25.51/25.32 0 [] M!=times_times(nat,M,N)|N=one_one(nat)|M=zero_zero(nat).
% 25.51/25.32 0 [] minus_minus(nat,Ma,Na)!=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)).
% 25.51/25.32 0 [] minus_minus(nat,Ma,Na)=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))|minus_minus(nat,M,N)=zero_zero(nat).
% 25.51/25.32 0 [] plus_plus(real,times_times(real,Xa,Xa),times_times(real,Ya,Ya))!=zero_zero(real)|Xa=zero_zero(real).
% 25.51/25.32 0 [] plus_plus(real,times_times(real,Xa,Xa),times_times(real,Ya,Ya))!=zero_zero(real)|Ya=zero_zero(real).
% 25.51/25.32 0 [] plus_plus(real,times_times(real,Xa,Xa),times_times(real,Ya,Ya))=zero_zero(real)|Xa!=zero_zero(real)|Ya!=zero_zero(real).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B_1))| -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),minus_minus(nat,A_1,C)),minus_minus(nat,B_1,C))).
% 25.51/25.32 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),Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),minus_minus(nat,Ma,K)),minus_minus(nat,Na,K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)).
% 25.51/25.32 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),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),minus_minus(nat,Ma,K)),minus_minus(nat,Na,K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)).
% 25.51/25.32 0 [] times_times(int,hAPP(nat,int,semiring_1_of_nat(int),X),hAPP(nat,int,semiring_1_of_nat(int),Y))=hAPP(nat,int,semiring_1_of_nat(int),times_times(nat,X,Y)).
% 25.51/25.32 0 [] times_times(int,hAPP(nat,int,semiring_1_of_nat(int),M),hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,int,semiring_1_of_nat(int),times_times(nat,M,N)).
% 25.51/25.32 0 [] hAPP(nat,int,semiring_1_of_nat(int),times_times(nat,M,N))=times_times(int,hAPP(nat,int,semiring_1_of_nat(int),M),hAPP(nat,int,semiring_1_of_nat(int),N)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))|minus_minus(nat,I_2,minus_minus(nat,J_1,K_1))=minus_minus(nat,plus_plus(nat,I_2,K_1),J_1).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),minus_minus(nat,J,K)),I_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),plus_plus(nat,I_1,K))).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),minus_minus(nat,J,K)),I_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),plus_plus(nat,I_1,K))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),minus_minus(nat,plus_plus(nat,N,M),K_1))).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M))|plus_plus(nat,N,minus_minus(nat,M,N))=M.
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))|plus_plus(nat,I_2,minus_minus(nat,J_1,K_1))=minus_minus(nat,plus_plus(nat,I_2,J_1),K_1).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),minus_minus(nat,J,K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,I_1,K)),J)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),minus_minus(nat,J,K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,I_1,K)),J)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M))|plus_plus(nat,minus_minus(nat,M,N),N)=M.
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J))|minus_minus(nat,J,I_1)!=K|J=plus_plus(nat,K,I_1).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J))|minus_minus(nat,J,I_1)=K|J!=plus_plus(nat,K,I_1).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))|minus_minus(nat,plus_plus(nat,I_2,J_1),K_1)=plus_plus(nat,I_2,minus_minus(nat,J_1,K_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))|plus_plus(nat,minus_minus(nat,J_1,K_1),I_2)=minus_minus(nat,plus_plus(nat,J_1,I_2),K_1).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))|minus_minus(nat,plus_plus(nat,J_1,I_2),K_1)=plus_plus(nat,minus_minus(nat,J_1,K_1),I_2).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Xa),Ya)).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Xa),Ya)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,X))| -hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,Y))|hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,times_times(int,X,Y))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),minus_minus(int,Z_1,one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1)).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),minus_minus(int,Z_1,one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,Va)),number_number_of(nat,V_3)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),V_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,Va)),number_number_of(nat,V_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),V_3)).
% 25.51/25.32 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,Va)),number_number_of(nat,V_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls)).
% 25.51/25.32 0 [] -ring_1(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M))|hAPP(nat,X_a,semiring_1_of_nat(X_a),minus_minus(nat,M,N))=minus_minus(X_a,hAPP(nat,X_a,semiring_1_of_nat(X_a),M),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Ya))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),nat_1(Xa)),nat_1(Ya)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),Ya)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Ya))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),nat_1(Xa)),nat_1(Ya)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),Ya)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_2),Z))|nat_1(minus_minus(int,Z,Z_2))=minus_minus(nat,nat_1(Z),nat_1(Z_2)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))|nat_1(times_times(int,Z,Z_2))=times_times(nat,nat_1(Z),nat_1(Z_2)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))|times_times(nat,nat_1(X),nat_1(Y))=nat_1(times_times(int,X,Y)).
% 25.51/25.32 0 [] M!=zero_zero(nat)|times_times(nat,M,N)=zero_zero(nat).
% 25.51/25.32 0 [] M=zero_zero(nat)|times_times(nat,M,N)=plus_plus(nat,N,times_times(nat,minus_minus(nat,M,one_one(nat)),N)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Wa))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),nat_1(Wa)),nat_1(Z_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),Z_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Wa))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),nat_1(Wa)),nat_1(Z_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),Z_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),nat_1(Wa)),nat_1(Z_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),Z_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),nat_1(Wa)),nat_1(Z_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),Z_1)).
% 25.51/25.32 0 [] M!=zero_zero(nat)|hAPP(nat,nat,power_power(nat,P_2),M)=one_one(nat).
% 25.51/25.32 0 [] M=zero_zero(nat)|hAPP(nat,nat,power_power(nat,P_2),M)=times_times(nat,P_2,hAPP(nat,nat,power_power(nat,P_2),minus_minus(nat,M,one_one(nat)))).
% 25.51/25.32 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),times_times(nat,number_number_of(nat,bit0(bit1(pls))),N))=hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N)),number_number_of(nat,bit0(bit1(pls)))).
% 25.51/25.32 0 [] times_times(nat,number_number_of(nat,bit0(bit1(pls))),Z)=plus_plus(nat,Z,Z).
% 25.51/25.32 0 [] times_times(nat,Z,number_number_of(nat,bit0(bit1(pls))))=plus_plus(nat,Z,Z).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|times_times(nat,number_number_of(nat,V_1),times_times(nat,number_number_of(nat,V_2),K_1))=zero_zero(nat).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|times_times(nat,number_number_of(nat,V_1),times_times(nat,number_number_of(nat,V_2),K_1))=times_times(nat,number_number_of(nat,times_times(int,V_1,V_2)),K_1).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|times_times(nat,number_number_of(nat,V_1),number_number_of(nat,V_2))=zero_zero(nat).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|times_times(nat,number_number_of(nat,V_1),number_number_of(nat,V_2))=number_number_of(nat,times_times(int,V_1,V_2)).
% 25.51/25.32 0 [] times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),hAPP(nat,real,power_power(real,X),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,real,power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X)),number_number_of(nat,bit0(bit1(pls)))).
% 25.51/25.32 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))).
% 25.51/25.32 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_1),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),B_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_1),A_1)).
% 25.51/25.32 0 [] times_times(int,plus_plus(int,A_1,B_1),minus_minus(int,A_1,B_1))=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_1),number_number_of(nat,bit0(bit1(pls))))).
% 25.51/25.32 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),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).
% 25.51/25.32 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),times_times(nat,number_number_of(nat,bit0(bit1(pls))),N)))).
% 25.51/25.32 0 [] minus_minus(nat,hAPP(nat,nat,power_power(nat,X),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,nat,power_power(nat,Y),number_number_of(nat,bit0(bit1(pls)))))=times_times(nat,plus_plus(nat,X,Y),minus_minus(nat,X,Y)).
% 25.51/25.32 0 [] hAPP(nat,int,power_power(int,minus_minus(int,A_1,B_1)),number_number_of(nat,bit1(bit1(pls))))=minus_minus(int,plus_plus(int,minus_minus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit1(bit1(pls)))),times_times(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_1)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),A_1),hAPP(nat,int,power_power(int,B_1),number_number_of(nat,bit0(bit1(pls)))))),hAPP(nat,int,power_power(int,B_1),number_number_of(nat,bit1(bit1(pls))))).
% 25.51/25.32 0 [] hAPP(nat,int,power_power(int,minus_minus(int,A_1,B_1)),number_number_of(nat,bit0(bit1(pls))))=plus_plus(int,minus_minus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),A_1),B_1)),hAPP(nat,int,power_power(int,B_1),number_number_of(nat,bit0(bit1(pls))))).
% 25.51/25.32 0 [] plus_plus(int,times_times(int,B_1,Q),R_1)!=plus_plus(int,times_times(int,B_2,Q_1),R_2)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(int,times_times(int,B_2,Q_1),R_2)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),B_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),plus_plus(int,times_times(int,B_1,Q_1),R_2)),plus_plus(int,times_times(int,B_1,Q),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_1),R_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),R_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q),Q_1)).
% 25.51/25.32 0 [] plus_plus(int,times_times(int,B_1,Q),R_1)!=plus_plus(int,times_times(int,B_2,Q_1),R_2)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),plus_plus(int,times_times(int,B_2,Q_1),R_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_2))| -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_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),B_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q),Q_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),plus_plus(int,times_times(int,B_1,Q_1),R_2)),plus_plus(int,times_times(int,B_1,Q),R_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q)).
% 25.51/25.32 0 [] plus_plus(int,hAPP(nat,int,power_power(int,x),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,int,power_power(int,y),number_number_of(nat,bit0(bit1(pls)))))=times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_2))|minus_minus(nat,nat_1(P_2),number_number_of(nat,bit0(bit1(pls))))=nat_1(minus_minus(int,P_2,number_number_of(int,bit0(bit1(pls))))).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),nat_1(minus_minus(int,P_2,number_number_of(int,bit0(bit1(pls))))))).
% 25.51/25.32 0 [] plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),one_one(int))=times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),$c5).
% 25.51/25.32 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),W)).
% 25.51/25.32 0 [] times_times(real,Z,W)=times_times(real,W,Z).
% 25.51/25.32 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z),W))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),Z)).
% 25.51/25.32 0 [] times_times(real,times_times(real,Z1,Z2),Z3)=times_times(real,Z1,times_times(real,Z2,Z3)).
% 25.51/25.32 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I_2),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_2),K_1)).
% 25.51/25.32 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z),W))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),Z))|Z=W.
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,zprime,number_number_of(int,bit0(bit1(pls))))).
% 25.51/25.32 0 [] minus_minus(int,A_1,B_1)!=ti(int,C)|ti(int,A_1)=plus_plus(int,C,B_1).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),one_one(int)))).
% 25.51/25.32 0 [] hAPP(nat,real,power_power(real,plus_plus(real,X,Y)),number_number_of(nat,bit0(bit1(pls))))=plus_plus(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),number_number_of(nat,bit0(bit1(pls))))),times_times(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X),Y)).
% 25.51/25.32 0 [] minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min))=plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),one_one(int)).
% 25.51/25.32 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))).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)))).
% 25.51/25.32 0 [] legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))=one_one(int).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),minus_minus(int,M,N)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),M)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),times_times(int,M,N)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),N)).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),times_times(X_a,A_1,B_1)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B_1),C)).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),times_times(X_a,A_1,B_1)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)).
% 25.51/25.32 0 [] -dvd(X_a)|A_1!=times_times(X_a,B_1,K_1)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B_1),A_1)).
% 25.51/25.32 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_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),D_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),times_times(X_a,A_1,C)),times_times(X_a,B_1,D_1))).
% 25.51/25.32 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),times_times(X_a,B_1,C))).
% 25.51/25.32 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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),times_times(X_a,B_1,C))).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),times_times(X_a,B_1,A_1))).
% 25.51/25.32 0 [] -comm_semiring_1(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),times_times(X_a,A_1,B_1))).
% 25.51/25.32 0 [] -comm_ring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Z))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),minus_minus(X_a,Y,Z))).
% 25.51/25.32 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),min)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),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),M)).
% 25.51/25.32 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),hAPP(nat,int,power_power(int,A_1),N)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),A_1)).
% 25.51/25.32 0 [] -idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))|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_2),B)).
% 25.51/25.32 0 [] -idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))|ti(X_a,C_1)!=zero_zero(X_a).
% 25.51/25.32 0 [] -idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),times_times(X_a,C_1,A_2)),times_times(X_a,C_1,B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B)).
% 25.51/25.33 0 [] -idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),times_times(X_a,A_2,C_1)),times_times(X_a,B,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_2),B)).
% 25.51/25.33 0 [] -idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),times_times(X_a,A_2,C_1)),times_times(X_a,B,C_1)))|ti(X_a,C_1)!=zero_zero(X_a).
% 25.51/25.33 0 [] -idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),times_times(X_a,A_2,C_1)),times_times(X_a,B,C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B)).
% 25.51/25.33 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))|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))).
% 25.51/25.33 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Y))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),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),N)),hAPP(nat,X_a,power_power(X_a,Y),M))).
% 25.51/25.33 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)),B_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))|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_1)).
% 25.51/25.33 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))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),M)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),times_times(int,K_1,M)),times_times(int,K_1,N)))|ti(int,K_1)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N)).
% 25.51/25.33 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))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),M))|ti(int,M)=ti(int,N).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),plus_plus(int,Na,times_times(int,K,Ma))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),Na)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),plus_plus(int,Na,times_times(int,K,Ma))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),Na)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),D))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),plus_plus(int,Xa,Ta)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),plus_plus(int,plus_plus(int,Xa,times_times(int,C_1,D)),Ta))).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),D))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),plus_plus(int,Xa,Ta)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),plus_plus(int,plus_plus(int,Xa,times_times(int,C_1,D)),Ta))).
% 25.51/25.33 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)).
% 25.51/25.33 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)).
% 25.51/25.33 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)).
% 25.51/25.33 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)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),pls)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),min)).
% 25.51/25.33 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)).
% 25.51/25.33 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)).
% 25.51/25.33 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)).
% 25.51/25.33 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)).
% 25.51/25.33 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)).
% 25.51/25.33 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)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),zero_zero(int))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),pls)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),min)).
% 25.51/25.33 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)).
% 25.51/25.33 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)).
% 25.51/25.33 0 [] number_number_of(int,pls)!=number_number_of(int,min).
% 25.51/25.33 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_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B_1),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)).
% 25.51/25.33 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)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),min)).
% 25.51/25.33 0 [] min!=bit0(L).
% 25.51/25.33 0 [] bit0(K_1)!=min.
% 25.51/25.33 0 [] min!=pls.
% 25.51/25.33 0 [] pls!=min.
% 25.51/25.33 0 [] bit1(min)=min.
% 25.51/25.33 0 [] min!=bit1(L_1)|min=ti(int,L_1).
% 25.51/25.33 0 [] min=bit1(L_1)|min!=ti(int,L_1).
% 25.51/25.33 0 [] bit1(K)!=min|ti(int,K)=min.
% 25.51/25.33 0 [] bit1(K)=min|ti(int,K)!=min.
% 25.51/25.33 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),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),N)),hAPP(nat,X_a,power_power(X_a,Y),N))).
% 25.51/25.33 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)).
% 25.51/25.33 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_1))| -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),plus_plus(X_a,B_1,C))).
% 25.51/25.33 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).
% 25.51/25.33 0 [] succ(min)=pls.
% 25.51/25.33 0 [] minus_minus(int,K_1,min)=succ(K_1).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z),N))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),N)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),Y))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),hAPP(nat,int,power_power(int,Y),N))).
% 25.51/25.33 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)).
% 25.51/25.33 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)).
% 25.51/25.33 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)).
% 25.51/25.33 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)).
% 25.51/25.33 0 [] minus_minus(int,pls,bit1(L))=bit1(minus_minus(int,min,L)).
% 25.51/25.33 0 [] minus_minus(int,min,bit1(L))=bit0(minus_minus(int,min,L)).
% 25.51/25.33 0 [] minus_minus(int,min,bit0(L))=bit1(minus_minus(int,min,L)).
% 25.51/25.33 0 [] times_times(int,Ma,Na)!=one_one(int)|ti(int,Ma)=one_one(int)|ti(int,Ma)=number_number_of(int,min).
% 25.51/25.33 0 [] times_times(int,Ma,Na)!=one_one(int)|ti(int,Ma)=one_one(int)|ti(int,Na)=number_number_of(int,min).
% 25.51/25.33 0 [] times_times(int,Ma,Na)!=one_one(int)|ti(int,Na)=one_one(int)|ti(int,Ma)=number_number_of(int,min).
% 25.51/25.33 0 [] times_times(int,Ma,Na)!=one_one(int)|ti(int,Na)=one_one(int)|ti(int,Na)=number_number_of(int,min).
% 25.51/25.33 0 [] times_times(int,Ma,Na)=one_one(int)|ti(int,Ma)!=one_one(int)|ti(int,Na)!=one_one(int).
% 25.51/25.33 0 [] times_times(int,Ma,Na)=one_one(int)|ti(int,Ma)!=number_number_of(int,min)|ti(int,Na)!=number_number_of(int,min).
% 25.51/25.33 0 [] times_times(int,M,N)!=one_one(int)|ti(int,M)=one_one(int)|ti(int,M)=number_number_of(int,min).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),B_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_2),N)),times_times(int,A_1,B_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_2),N)),A_1)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_2),N)),times_times(int,A_1,B_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_2),N)),B_1)).
% 25.51/25.33 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),hAPP(nat,X_a,power_power(X_a,X),N))).
% 25.51/25.33 0 [] -comm_semiring_1(X_a)|ti(X_a,X)!=one_one(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),hAPP(nat,X_a,power_power(X_a,X),N))).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),hAPP(nat,int,power_power(int,Y),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),Y)).
% 25.51/25.33 0 [] -number_ring(X_a)|hAPP(nat,X_a,power_power(X_a,number_number_of(X_a,min)),times_times(nat,number_number_of(nat,bit0(bit1(pls))),N))=one_one(X_a).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,quadRes(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),number_number_of(int,min))).
% 25.51/25.33 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)),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,quadRes(plus_plus(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),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))!=one_one(int).
% 25.51/25.33 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)),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),s)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),s),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(s1,s),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,$c6),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),times_times(nat,A_1,C)),times_times(nat,B_1,C))).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),times_times(nat,C,A_1)),times_times(nat,C,B_1))).
% 25.51/25.33 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))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),minus_minus(nat,M,N))).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(Xa,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),Xa)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(Xa,zero_zero(int)),P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),Xa)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_2,zero_zero(int)),Ma))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),A_2)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(A_2,zero_zero(int)),Ma))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),A_2)).
% 25.51/25.33 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))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),M)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))|B_1=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A_1),B_1)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),times_times(nat,Ma,K)),times_times(nat,Na,K)))|K=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),Na)).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),times_times(nat,Ma,K)),times_times(nat,Na,K)))|K!=zero_zero(nat).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),times_times(nat,Ma,K)),times_times(nat,Na,K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),Na)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),minus_minus(nat,M,N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),M)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),minus_minus(nat,M,N)))| -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),M))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,A_1),N)),hAPP(nat,nat,power_power(nat,B_1),N)))|N=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1)).
% 25.51/25.33 0 [] N=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,X),N)),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya))).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya))).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,X),N)),hAPP(nat,nat,power_power(nat,Y),N))).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),one_one(nat)))|Ma=one_one(nat).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),one_one(nat)))|Ma!=one_one(nat).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),plus_plus(nat,Na,K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),Na)).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),plus_plus(nat,Na,K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),Na)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),A_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),plus_plus(nat,A_1,B_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),B_1)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(M,zero_zero(int)),M)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))|hBOOL(hAPP(int,bool,zcong(plus_plus(int,A_1,C),plus_plus(int,B_1,C)),M)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))|ti(int,B_1)!=ti(int,C)| -hBOOL(hAPP(int,bool,zcong(C,D_1),M))|hBOOL(hAPP(int,bool,zcong(A_1,D_1),M)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(X,Y),M))|hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X),Z),hAPP(nat,int,power_power(int,Y),Z)),M)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X))| -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,Y),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),M))|ti(int,X)=ti(int,Y).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M))| -hBOOL(hAPP(int,bool,zcong(X,zero_zero(int)),M)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_2,B),Ma))| -hBOOL(hAPP(int,bool,zcong(C_1,times_times(int,A_2,D)),Ma))|hBOOL(hAPP(int,bool,zcong(C_1,times_times(int,B,D)),Ma)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_2,B),Ma))|hBOOL(hAPP(int,bool,zcong(C_1,times_times(int,A_2,D)),Ma))| -hBOOL(hAPP(int,bool,zcong(C_1,times_times(int,B,D)),Ma)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_2,B),Ma))| -hBOOL(hAPP(int,bool,zcong(C_1,times_times(int,D,A_2)),Ma))|hBOOL(hAPP(int,bool,zcong(C_1,times_times(int,D,B)),Ma)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_2,B),Ma))|hBOOL(hAPP(int,bool,zcong(C_1,times_times(int,D,A_2)),Ma))| -hBOOL(hAPP(int,bool,zcong(C_1,times_times(int,D,B)),Ma)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M))| -hBOOL(hAPP(int,bool,zcong(X,zero_zero(int)),M))|ti(int,X)=zero_zero(int).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))|hBOOL(hAPP(int,bool,zcong(X,zero_zero(int)),P_2))|hBOOL(hAPP(int,bool,zcong(Y,zero_zero(int)),P_2))| -hBOOL(hAPP(int,bool,zcong(times_times(int,X,Y),zero_zero(int)),P_2)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),times_times(nat,K_1,M)),times_times(nat,K_1,N)))| -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)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,zcong(times_times(int,A_1,B_1),zero_zero(int)),P_2))|hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_2))|hBOOL(hAPP(int,bool,zcong(B_1,zero_zero(int)),P_2)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))| -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_2))|hBOOL(hAPP(int,bool,zcong(B_1,zero_zero(int)),P_2))| -hBOOL(hAPP(int,bool,zcong(times_times(int,A_1,B_1),zero_zero(int)),P_2)).
% 25.51/25.33 0 [] X!=plus_plus(nat,times_times(nat,Q,N),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))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),X)).
% 25.51/25.33 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),times_times(nat,Ma,Na)),Ma))|Na=one_one(nat).
% 25.51/25.33 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),times_times(nat,Ma,Na)),Ma))|Na!=one_one(nat).
% 25.51/25.33 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),times_times(nat,Na,Ma)),Ma))|Na=one_one(nat).
% 25.51/25.33 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),times_times(nat,Na,Ma)),Ma))|Na!=one_one(nat).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Ya))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(Xa)),nat_1(Ya)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Xa),Ya)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Ya))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(Xa)),nat_1(Ya)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Xa),Ya)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,I_2),M)),hAPP(nat,nat,power_power(nat,I_2),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),I_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(Z_1)),Ma))| -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),dvd_dvd(int),Z_1),hAPP(nat,int,semiring_1_of_nat(int),Ma))).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(Z_1)),Ma))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1))|Ma=zero_zero(nat).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(Z_1)),Ma))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1))|Ma!=zero_zero(nat).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(Z_1)),Ma))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z_1),hAPP(nat,int,semiring_1_of_nat(int),Ma)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1)).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(Z_1)),Ma))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z_1),hAPP(nat,int,semiring_1_of_nat(int),Ma)))|Ma!=zero_zero(nat).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_2))| -hBOOL(hAPP(int,bool,zcong(X,number_number_of(int,min)),P_2))| -hBOOL(hAPP(int,bool,zcong(X,one_one(int)),P_2)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(X,zero_zero(int)),P_2))| -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,Y),number_number_of(nat,bit0(bit1(pls)))),X),P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),Y)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),M))|M=zero_zero(nat)|M=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),times_times(nat,number_number_of(nat,bit0(bit1(pls))),N)),M)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zprime,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),M),one_one(int))))|legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),M),one_one(int)))=one_one(int).
% 25.51/25.33 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))))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$c7)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$c7),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(s1,$c7),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_1),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))| -hBOOL(hAPP(int,bool,zcong(s1,Y_1),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))|ti(int,Y_1)=ti(int,$c7).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),X)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$c8)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$c8),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(s1,$c8),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z),Y))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z),X)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z),X)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B_1),A_1))|B_1!=C|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B_1),A_1))|B_1!=C| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))|Y!=X.
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))|X!=Y.
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))|X!=Y.
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z),Y))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z),X)).
% 25.51/25.33 0 [] A_1!=B_1| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B_1),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),B_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)).
% 25.51/25.33 0 [] A_1!=B_1| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B_1),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),B_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))|X=Y.
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),M))|M=N.
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))|B_1!=C|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)).
% 25.51/25.33 0 [] A_1!=B_1| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B_1),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))|A_1=B_1| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B_1),A_1)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))|X=Y.
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))|Xa=Ya.
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))|Xa!=Ya.
% 25.51/25.33 0 [] X!=Y|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)).
% 25.51/25.33 0 [] A_1=B_1| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B_1),A_1)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa))|Xa!=Ya.
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))|Xa=Ya.
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa))|Xa=Ya.
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))|Xa!=Ya.
% 25.51/25.33 0 [] Xa!=Ya|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)).
% 25.51/25.33 0 [] Xa!=Ya|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa)).
% 25.51/25.33 0 [] Xa=Ya| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa))|Xa=Ya.
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya))|Xa!=Ya.
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa))|Xa!=Ya.
% 25.51/25.33 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).
% 25.51/25.33 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)).
% 25.51/25.33 0 [] hAPP(nat,int,power_power(int,number_number_of(int,min)),N)=one_one(int)|hAPP(nat,int,power_power(int,number_number_of(int,min)),N)=number_number_of(int,min).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_2))|legendre(A_1,P_2)=zero_zero(int).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_2))| -hBOOL(hAPP(int,bool,quadRes(P_2),A_1))|legendre(A_1,P_2)=one_one(int).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_2))|hBOOL(hAPP(int,bool,quadRes(P_2),A_1))|legendre(A_1,P_2)=number_number_of(int,min).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,quadRes(Ma),Xa))|hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,$f19(Ma,Xa)),number_number_of(nat,bit0(bit1(pls)))),Xa),Ma)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,quadRes(Ma),Xa))| -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,Y_1),number_number_of(nat,bit0(bit1(pls)))),Xa),Ma)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),X))|hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X),nat_1(minus_minus(int,P_2,one_one(int)))),one_one(int)),P_2)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))| -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_2))| -hBOOL(hAPP(int,bool,zcong(times_times(int,A_1,A_1),one_one(int)),P_2))|ti(int,A_1)=one_one(int)|ti(int,A_1)=minus_minus(int,P_2,one_one(int)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))| -hBOOL(hAPP(int,bool,zcong(B_1,C),M))|hBOOL(hAPP(int,bool,zcong(A_1,C),M)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(K_1,K_1),M)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_2,B),Ma))|hBOOL(hAPP(int,bool,zcong(B,A_2),Ma)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(A_2,B),Ma))| -hBOOL(hAPP(int,bool,zcong(B,A_2),Ma)).
% 25.51/25.33 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_2,B),zero_zero(int)))|ti(int,A_2)=ti(int,B).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(A_2,B),zero_zero(int)))|ti(int,A_2)!=ti(int,B).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(A_1,B_1),one_one(int))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(times_times(int,A_1,M),times_times(int,B_1,M)),M)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))|hBOOL(hAPP(int,bool,zcong(times_times(int,A_1,K_1),times_times(int,B_1,K_1)),M)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))|hBOOL(hAPP(int,bool,zcong(times_times(int,K_1,A_1),times_times(int,K_1,B_1)),M)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))| -hBOOL(hAPP(int,bool,zcong(C,D_1),M))|hBOOL(hAPP(int,bool,zcong(times_times(int,A_1,C),times_times(int,B_1,D_1)),M)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))| -hBOOL(hAPP(int,bool,zcong(C,D_1),M))|hBOOL(hAPP(int,bool,zcong(plus_plus(int,A_1,C),plus_plus(int,B_1,D_1)),M)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))| -hBOOL(hAPP(int,bool,zcong(C,D_1),M))|hBOOL(hAPP(int,bool,zcong(minus_minus(int,A_1,C),minus_minus(int,B_1,D_1)),M)).
% 25.51/25.33 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_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),A_1))| -hBOOL(hAPP(int,bool,zcong(A_1,B_1),M)).
% 25.51/25.33 0 [] plus_plus(int,times_times(int,minus_minus(int,A_1,times_times(int,R_1,B_1)),M),times_times(int,minus_minus(int,C,times_times(int,R_1,D_1)),N))=minus_minus(int,plus_plus(int,times_times(int,A_1,M),times_times(int,C,N)),times_times(int,R_1,plus_plus(int,times_times(int,B_1,M),times_times(int,D_1,N)))).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_2,B),Ma))|ti(int,B)=plus_plus(int,A_2,times_times(int,Ma,$f20(A_2,B,Ma))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(A_2,B),Ma))|ti(int,B)!=plus_plus(int,A_2,times_times(int,Ma,K_2)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(A_2,B),Ma))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),minus_minus(int,A_2,B))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(A_2,B),Ma))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),minus_minus(int,A_2,B))).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),minus_minus(int,B_1,one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B_1)).
% 25.51/25.33 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).
% 25.51/25.33 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_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),M))| -hBOOL(hAPP(int,bool,zcong(A_1,B_1),M))|ti(int,A_1)=ti(int,B_1).
% 25.51/25.33 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_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),times_times(int,M,N)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_2),N)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_3)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M_1),P_3))|ti(int,M_1)=one_one(int)|ti(int,M_1)=ti(int,P_3).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f21(P_3))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),$f21(P_3)),P_3)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_3))|ti(int,$f21(P_3))!=one_one(int).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_3))|ti(int,$f21(P_3))!=ti(int,P_3).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,zcong(times_times(int,A_1,A_1),one_one(int)),P_2))|hBOOL(hAPP(int,bool,zcong(A_1,one_one(int)),P_2))|hBOOL(hAPP(int,bool,zcong(A_1,minus_minus(int,P_2,one_one(int))),P_2)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,Xa,Ya))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ya),Xa))|hBOOL(hAPP(int,bool,P_1,minus_minus(int,hAPP(nat,int,semiring_1_of_nat(int),Xa),hAPP(nat,int,semiring_1_of_nat(int),Ya)))).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,Xa,Ya))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya))|hBOOL(hAPP(int,bool,P_1,zero_zero(int))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,Xa,Ya))))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ya),Xa))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,Xa,Ya))))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ya),Xa))| -hBOOL(hAPP(int,bool,P_1,zero_zero(int))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,Xa,Ya))))| -hBOOL(hAPP(int,bool,P_1,minus_minus(int,hAPP(nat,int,semiring_1_of_nat(int),Xa),hAPP(nat,int,semiring_1_of_nat(int),Ya))))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,Xa,Ya))))| -hBOOL(hAPP(int,bool,P_1,minus_minus(int,hAPP(nat,int,semiring_1_of_nat(int),Xa),hAPP(nat,int,semiring_1_of_nat(int),Ya))))| -hBOOL(hAPP(int,bool,P_1,zero_zero(int))).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zprime,P_2))|ti(int,P_2)=number_number_of(int,bit0(bit1(pls)))|ti(int,P_2)=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_2)).
% 25.51/25.33 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),times_times(int,K,Ma)),times_times(int,K,Ta))).
% 25.51/25.33 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),times_times(int,K,Ma)),times_times(int,K,Ta))).
% 25.51/25.33 0 [] -dvd(X_a)| -semiring_0(X_a)| -hBOOL(hAPP(X_a,bool,P_1,times_times(X_a,L_1,X_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L_1),plus_plus(X_a,$f22(X_a,P_1,L_1),zero_zero(X_a)))).
% 25.51/25.33 0 [] -dvd(X_a)| -semiring_0(X_a)| -hBOOL(hAPP(X_a,bool,P_1,times_times(X_a,L_1,X_1)))|hBOOL(hAPP(X_a,bool,P_1,$f22(X_a,P_1,L_1))).
% 25.51/25.33 0 [] -dvd(X_a)| -semiring_0(X_a)|hBOOL(hAPP(X_a,bool,P_1,times_times(X_a,L_1,$f23(X_a,P_1,L_1))))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L_1),plus_plus(X_a,X4,zero_zero(X_a))))| -hBOOL(hAPP(X_a,bool,P_1,X4)).
% 25.51/25.33 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_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),plus_plus(X_a,X_1,Ta)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),plus_plus(X_a,minus_minus(X_a,X_1,times_times(X_a,K_2,D_2)),Ta))).
% 25.51/25.33 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_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),plus_plus(X_a,X_1,Ta)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),plus_plus(X_a,minus_minus(X_a,X_1,times_times(X_a,K_2,D_2)),Ta))).
% 25.51/25.33 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_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),plus_plus(X_a,X_1,Ta)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),plus_plus(X_a,minus_minus(X_a,X_1,times_times(X_a,K_2,D_2)),Ta))).
% 25.51/25.33 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_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),plus_plus(X_a,X_1,Ta)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),plus_plus(X_a,minus_minus(X_a,X_1,times_times(X_a,K_2,D_2)),Ta))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,pls))).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(times_times(int,A_2,minus_minus(int,P_3,one_one(int))),one_one(int)),P_3))|hBOOL(hAPP(int,bool,zcong(A_2,minus_minus(int,P_3,one_one(int))),P_3)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,zcong(times_times(int,A_2,minus_minus(int,P_3,one_one(int))),one_one(int)),P_3))| -hBOOL(hAPP(int,bool,zcong(A_2,minus_minus(int,P_3,one_one(int))),P_3)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X),Y),one_one(int)),P_2))|hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X),times_times(nat,Y,Z)),one_one(int)),P_2)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,N)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit0(N)))).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,N)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit1(N)))).
% 25.51/25.33 0 [] ti(int,$c9)=minus_minus(int,y,times_times(int,$c10,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,$c9))),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))).
% 25.51/25.33 0 [] ti(int,$c11)=minus_minus(int,x,times_times(int,$c12,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,$c11))),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))).
% 25.51/25.33 0 [] ti(int,I_2)=zero_zero(int)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),I_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),abs_abs(int,D_1)),abs_abs(int,I_2))).
% 25.51/25.33 0 [] nat_1(abs_abs(int,times_times(int,W,Z)))=times_times(nat,nat_1(abs_abs(int,W)),nat_1(abs_abs(int,Z))).
% 25.51/25.33 0 [] -linordered_idom(X_a)|abs_abs(X_a,L)!=abs_abs(X_a,K_1)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L),K_1)).
% 25.51/25.33 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),abs_abs(X_a,Ma)),K))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),K)).
% 25.51/25.33 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),abs_abs(X_a,Ma)),K))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),K)).
% 25.51/25.33 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),abs_abs(X_a,K)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),K)).
% 25.51/25.33 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),abs_abs(X_a,K)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),K)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_1),B_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B_1),A_1))|abs_abs(int,A_1)=abs_abs(int,B_1).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Xa),one_one(int)))|abs_abs(int,Xa)=one_one(int).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Xa),one_one(int)))|abs_abs(int,Xa)!=one_one(int).
% 25.51/25.33 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))|times_times(X_a,abs_abs(X_a,Y),X)=abs_abs(X_a,times_times(X_a,Y,X)).
% 25.51/25.33 0 [] -ordered_ring_abs(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_1))|abs_abs(X_a,times_times(X_a,A_1,B_1))=times_times(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1)).
% 25.51/25.33 0 [] -ordered_ring_abs(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_1),zero_zero(X_a)))|abs_abs(X_a,times_times(X_a,A_1,B_1))=times_times(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1)).
% 25.51/25.33 0 [] -ordered_ring_abs(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_1))|abs_abs(X_a,times_times(X_a,A_1,B_1))=times_times(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1)).
% 25.51/25.33 0 [] -ordered_ring_abs(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_1),zero_zero(X_a)))|abs_abs(X_a,times_times(X_a,A_1,B_1))=times_times(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1)).
% 25.51/25.33 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,abs_abs(X_a,A_1)),N))).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),abs_abs(X_a,minus_minus(X_a,plus_plus(X_a,A_1,B_1),plus_plus(X_a,C,D_1)))),plus_plus(X_a,abs_abs(X_a,minus_minus(X_a,A_1,C)),abs_abs(X_a,minus_minus(X_a,B_1,D_1))))).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),abs_abs(X_a,minus_minus(X_a,A_1,B_1))),plus_plus(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1)))).
% 25.51/25.33 0 [] -number_ring(X_a)| -linordered_idom(X_a)|abs_abs(X_a,number_number_of(X_a,min))=one_one(X_a).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)|abs_abs(X_a,zero_zero(X_a))=zero_zero(X_a).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)|abs_abs(X_a,A_2)!=zero_zero(X_a)|ti(X_a,A_2)=zero_zero(X_a).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)|abs_abs(X_a,A_2)=zero_zero(X_a)|ti(X_a,A_2)!=zero_zero(X_a).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)|abs_abs(X_a,plus_plus(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1)))=plus_plus(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1)).
% 25.51/25.33 0 [] -linordered_idom(X_a)|abs_abs(X_a,one_one(X_a))=one_one(X_a).
% 25.51/25.33 0 [] -linordered_idom(X_a)|abs_abs(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N))=hAPP(nat,X_a,power_power(X_a,abs_abs(X_a,A_1)),N).
% 25.51/25.33 0 [] -linordered_idom(X_a)|abs_abs(X_a,hAPP(nat,X_a,semiring_1_of_nat(X_a),N))=hAPP(nat,X_a,semiring_1_of_nat(X_a),N).
% 25.51/25.33 0 [] abs_abs(int,hAPP(nat,int,semiring_1_of_nat(int),M))=hAPP(nat,int,semiring_1_of_nat(int),M).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)|abs_abs(X_a,abs_abs(X_a,A_1))=abs_abs(X_a,A_1).
% 25.51/25.33 0 [] abs_abs(int,times_times(int,M,N))!=one_one(int)|abs_abs(int,M)=one_one(int).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),minus_minus(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1))),abs_abs(X_a,minus_minus(X_a,B_1,A_1)))).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),minus_minus(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1))),abs_abs(X_a,minus_minus(X_a,A_1,B_1)))).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),abs_abs(X_a,minus_minus(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1)))),abs_abs(X_a,minus_minus(X_a,A_1,B_1)))).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),abs_abs(X_a,plus_plus(X_a,A_1,B_1))),plus_plus(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1)))).
% 25.51/25.33 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),abs_abs(X_a,A_1)),C))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),abs_abs(X_a,B_1)),D_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),times_times(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1))),times_times(X_a,C,D_1))).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))|abs_abs(X_a,A_1)=ti(X_a,A_1).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),abs_abs(X_a,A_2)))|ti(X_a,A_2)!=zero_zero(X_a).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),abs_abs(X_a,A_2)))|ti(X_a,A_2)=zero_zero(X_a).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),abs_abs(X_a,A_1)),zero_zero(X_a))).
% 25.51/25.33 0 [] -ordere142940540dd_abs(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))|abs_abs(X_a,A_1)=ti(X_a,A_1).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),abs_abs(X_a,A_2)),zero_zero(X_a)))|ti(X_a,A_2)=zero_zero(X_a).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),abs_abs(X_a,A_2)),zero_zero(X_a)))|ti(X_a,A_2)!=zero_zero(X_a).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),abs_abs(X_a,A_1))).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)|abs_abs(X_a,minus_minus(X_a,A_1,B_1))=abs_abs(X_a,minus_minus(X_a,B_1,A_1)).
% 25.51/25.33 0 [] -linordered_idom(X_a)|abs_abs(X_a,times_times(X_a,A_1,B_1))=times_times(X_a,abs_abs(X_a,A_1),abs_abs(X_a,B_1)).
% 25.51/25.33 0 [] -linordered_idom(X_a)|times_times(X_a,abs_abs(X_a,A_1),abs_abs(X_a,A_1))=times_times(X_a,A_1,A_1).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),abs_abs(X_a,A_1))).
% 25.51/25.33 0 [] -ordere142940540dd_abs(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),abs_abs(X_a,A_1)),B_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B_1)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,power_power(int,abs_abs(int,X)),N))).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),abs_abs(int,Z_1)),one_one(int)))|ti(int,Z_1)=zero_zero(int).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),abs_abs(int,Z_1)),one_one(int)))|ti(int,Z_1)!=zero_zero(int).
% 25.51/25.33 0 [] abs_abs(int,Z_1)!=one_one(int)|ti(int,Z_1)=one_one(int)|ti(int,Z_1)=number_number_of(int,min).
% 25.51/25.33 0 [] abs_abs(int,Z_1)=one_one(int)|ti(int,Z_1)!=one_one(int).
% 25.51/25.33 0 [] abs_abs(int,Z_1)=one_one(int)|ti(int,Z_1)!=number_number_of(int,min).
% 25.51/25.33 0 [] -number_ring(X_a)| -linordered_idom(X_a)|abs_abs(X_a,hAPP(nat,X_a,power_power(X_a,number_number_of(X_a,min)),N))=one_one(X_a).
% 25.51/25.33 0 [] abs_abs(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit1(bit1(pls)))))=hAPP(nat,int,power_power(int,abs_abs(int,X)),number_number_of(nat,bit1(bit1(pls)))).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,power_power(int,abs_abs(int,Xa)),Na)))|ti(int,Xa)!=zero_zero(int)|Na=zero_zero(nat).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,power_power(int,abs_abs(int,Xa)),Na)))|ti(int,Xa)=zero_zero(int).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,power_power(int,abs_abs(int,Xa)),Na)))|Na!=zero_zero(nat).
% 25.51/25.33 0 [] ti(int,Ma)=zero_zero(int)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),times_times(int,Ma,Na)),Ma))|abs_abs(int,Na)=one_one(int).
% 25.51/25.33 0 [] ti(int,Ma)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),times_times(int,Ma,Na)),Ma))|abs_abs(int,Na)!=one_one(int).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),Z_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),nat_1(abs_abs(int,Z_1)))).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),Z_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),nat_1(abs_abs(int,Z_1)))).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z_1),hAPP(nat,int,semiring_1_of_nat(int),Ma)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(abs_abs(int,Z_1))),Ma)).
% 25.51/25.33 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z_1),hAPP(nat,int,semiring_1_of_nat(int),Ma)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(abs_abs(int,Z_1))),Ma)).
% 25.51/25.33 0 [] -linordered_idom(X_a)|abs_abs(X_a,hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls)))).
% 25.51/25.33 0 [] -linordered_idom(X_a)|hAPP(nat,X_a,power_power(X_a,abs_abs(X_a,A_1)),number_number_of(nat,bit0(bit1(pls))))=hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls)))).
% 25.51/25.33 0 [] abs_abs(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,int,power_power(int,abs_abs(int,A_1)),number_number_of(nat,bit0(bit1(pls)))).
% 25.51/25.33 0 [] hAPP(nat,int,power_power(int,A_2),number_number_of(nat,bit0(bit1(pls))))!=hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls))))|abs_abs(int,A_2)=abs_abs(int,B).
% 25.51/25.33 0 [] hAPP(nat,int,power_power(int,A_2),number_number_of(nat,bit0(bit1(pls))))=hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls))))|abs_abs(int,A_2)!=abs_abs(int,B).
% 25.51/25.33 0 [] hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls))))!=one_one(int)|abs_abs(int,A_1)=one_one(int).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),plus_plus(int,X,times_times(int,plus_plus(int,abs_abs(int,minus_minus(int,X,Z)),one_one(int)),D_1)))).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),minus_minus(int,X,times_times(int,plus_plus(int,abs_abs(int,minus_minus(int,X,Z)),one_one(int)),D_1))),Z)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,minus_minus(int,Y,times_times(int,$f24(Y,X),X))))),X)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))|hBOOL(hAPP(int,bool,P_1,$f25(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_1))|hBOOL(hAPP(int,bool,P_1,minus_minus(int,X_1,times_times(int,K,D)))).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))| -hBOOL(hAPP(int,bool,P_1,minus_minus(int,$f25(K,P_1,D),D)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,P_1,X_1))|hBOOL(hAPP(int,bool,P_1,minus_minus(int,X_1,times_times(int,K,D)))).
% 25.51/25.33 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),plus_plus(real,abs_abs(real,X),one_one(real))),X)).
% 25.51/25.33 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),plus_plus(real,one_one(real),abs_abs(real,X)))).
% 25.51/25.33 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),abs_abs(real,X)),one_one(real)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,power_power(real,X),number_number_of(nat,bit0(bit1(pls))))),one_one(real))).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f26(Na,P_1)),Na)).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),$f26(Na,P_1)))| -hBOOL(hAPP(nat,bool,P_1,I)).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,Na))|hBOOL(hAPP(nat,bool,P_1,plus_plus(nat,$f26(Na,P_1),one_one(nat)))).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))|hBOOL(hAPP(int,bool,P_1,$f27(K,P_1,D)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,P_1,X_1))|hBOOL(hAPP(int,bool,P_1,plus_plus(int,X_1,times_times(int,K,D)))).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))| -hBOOL(hAPP(int,bool,P_1,plus_plus(int,$f27(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_1))|hBOOL(hAPP(int,bool,P_1,plus_plus(int,X_1,times_times(int,K,D)))).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),I_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,times_times(nat,I_1,U),Ma)),plus_plus(nat,times_times(nat,J,U),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,times_times(nat,minus_minus(nat,I_1,J),U),Ma)),Na)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),I_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,times_times(nat,I_1,U),Ma)),plus_plus(nat,times_times(nat,J,U),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,times_times(nat,minus_minus(nat,I_1,J),U),Ma)),Na)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,times_times(nat,I_1,U),Ma)),plus_plus(nat,times_times(nat,J,U),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),plus_plus(nat,times_times(nat,minus_minus(nat,J,I_1),U),Na))).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,times_times(nat,I_1,U),Ma)),plus_plus(nat,times_times(nat,J,U),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),plus_plus(nat,times_times(nat,minus_minus(nat,J,I_1),U),Na))).
% 25.51/25.33 0 [] times_times(nat,K,Ma)!=times_times(nat,K,Na)|K=zero_zero(nat)|Ma=Na.
% 25.51/25.33 0 [] times_times(nat,K,Ma)=times_times(nat,K,Na)|K!=zero_zero(nat).
% 25.51/25.33 0 [] times_times(nat,K,Ma)=times_times(nat,K,Na)|Ma!=Na.
% 25.51/25.33 0 [] plus_plus(nat,times_times(nat,I_2,U_1),plus_plus(nat,times_times(nat,J_1,U_1),K_1))=plus_plus(nat,times_times(nat,plus_plus(nat,I_2,J_1),U_1),K_1).
% 25.51/25.33 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),times_times(nat,K,Ma)),times_times(nat,K,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)).
% 25.51/25.33 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),times_times(nat,K,Ma)),times_times(nat,K,Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|times_times(nat,K,Ma)!=times_times(nat,K,Na)|Ma=Na.
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|times_times(nat,K,Ma)=times_times(nat,K,Na)|Ma!=Na.
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),times_times(nat,K,Ma)),times_times(nat,K,Na)))|K=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),Na)).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),times_times(nat,K,Ma)),times_times(nat,K,Na)))|K!=zero_zero(nat).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),times_times(nat,K,Ma)),times_times(nat,K,Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),Na)).
% 25.51/25.33 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),times_times(nat,K,Ma)),times_times(nat,K,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),Na)).
% 25.51/25.33 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),times_times(nat,K,Ma)),times_times(nat,K,Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),Na)).
% 25.51/25.33 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),times_times(nat,K,Ma)),times_times(nat,K,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)).
% 25.51/25.33 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),times_times(nat,K,Ma)),times_times(nat,K,Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),I_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,times_times(nat,I_1,U),Ma)),plus_plus(nat,times_times(nat,J,U),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,times_times(nat,minus_minus(nat,I_1,J),U),Ma)),Na)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),I_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,times_times(nat,I_1,U),Ma)),plus_plus(nat,times_times(nat,J,U),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,times_times(nat,minus_minus(nat,I_1,J),U),Ma)),Na)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),I_2))|minus_minus(nat,plus_plus(nat,times_times(nat,I_2,U_1),M),plus_plus(nat,times_times(nat,J_1,U_1),N))=minus_minus(nat,plus_plus(nat,times_times(nat,minus_minus(nat,I_2,J_1),U_1),M),N).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),I_1))|plus_plus(nat,times_times(nat,I_1,U),Ma)!=plus_plus(nat,times_times(nat,J,U),Na)|plus_plus(nat,times_times(nat,minus_minus(nat,I_1,J),U),Ma)=Na.
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),I_1))|plus_plus(nat,times_times(nat,I_1,U),Ma)=plus_plus(nat,times_times(nat,J,U),Na)|plus_plus(nat,times_times(nat,minus_minus(nat,I_1,J),U),Ma)!=Na.
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,times_times(nat,I_1,U),Ma)),plus_plus(nat,times_times(nat,J,U),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),plus_plus(nat,times_times(nat,minus_minus(nat,J,I_1),U),Na))).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),plus_plus(nat,times_times(nat,I_1,U),Ma)),plus_plus(nat,times_times(nat,J,U),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),plus_plus(nat,times_times(nat,minus_minus(nat,J,I_1),U),Na))).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_1))|minus_minus(nat,plus_plus(nat,times_times(nat,I_2,U_1),M),plus_plus(nat,times_times(nat,J_1,U_1),N))=minus_minus(nat,M,plus_plus(nat,times_times(nat,minus_minus(nat,J_1,I_2),U_1),N)).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J))|plus_plus(nat,times_times(nat,I_1,U),Ma)!=plus_plus(nat,times_times(nat,J,U),Na)|Ma=plus_plus(nat,times_times(nat,minus_minus(nat,J,I_1),U),Na).
% 25.51/25.33 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J))|plus_plus(nat,times_times(nat,I_1,U),Ma)=plus_plus(nat,times_times(nat,J,U),Na)|Ma!=plus_plus(nat,times_times(nat,minus_minus(nat,J,I_1),U),Na).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f28(K,F,Na)),Na))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f29(K,F,Na)),Na)).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f28(K,F,Na)),Na))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hAPP(nat,int,F,$f29(K,F,Na))=ti(int,K).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),abs_abs(int,minus_minus(int,hAPP(nat,int,F,plus_plus(nat,$f28(K,F,Na),one_one(nat))),hAPP(nat,int,F,$f28(K,F,Na))))),one_one(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f29(K,F,Na)),Na)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),abs_abs(int,minus_minus(int,hAPP(nat,int,F,plus_plus(nat,$f28(K,F,Na),one_one(nat))),hAPP(nat,int,F,$f28(K,F,Na))))),one_one(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hAPP(nat,int,F,$f29(K,F,Na))=ti(int,K).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f30(K,F,Na)),Na))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f31(K,F,Na)),Na)).
% 25.51/25.33 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f30(K,F,Na)),Na))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hAPP(nat,int,F,$f31(K,F,Na))=ti(int,K).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),abs_abs(int,minus_minus(int,hAPP(nat,int,F,plus_plus(nat,$f30(K,F,Na),one_one(nat))),hAPP(nat,int,F,$f30(K,F,Na))))),one_one(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f31(K,F,Na)),Na)).
% 25.51/25.33 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),abs_abs(int,minus_minus(int,hAPP(nat,int,F,plus_plus(nat,$f30(K,F,Na),one_one(nat))),hAPP(nat,int,F,$f30(K,F,Na))))),one_one(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hAPP(nat,int,F,$f31(K,F,Na))=ti(int,K).
% 25.51/25.33 0 [] semiri456707255roduct(int).
% 25.51/25.33 0 [] ordere223160158up_add(int).
% 25.51/25.33 0 [] ordere236663937imp_le(int).
% 25.51/25.33 0 [] linord893533164strict(int).
% 25.51/25.33 0 [] linord626643107strict(int).
% 25.51/25.33 0 [] linord20386208strict(int).
% 25.51/25.33 0 [] ordere779506340up_add(int).
% 25.51/25.33 0 [] ordere142940540dd_abs(int).
% 25.51/25.33 0 [] ordere216010020id_add(int).
% 25.51/25.33 0 [] linord219039673up_add(int).
% 25.51/25.33 0 [] cancel146912293up_add(int).
% 25.51/25.33 0 [] ring_11004092258visors(int).
% 25.51/25.33 0 [] ordere453448008miring(int).
% 25.51/25.33 0 [] linord581940658strict(int).
% 25.51/25.33 0 [] ring_n68954251visors(int).
% 25.51/25.33 0 [] ordere1490568538miring(int).
% 25.51/25.33 0 [] linord1278240602ring_1(int).
% 25.51/25.33 0 [] ordered_ab_group_add(int).
% 25.51/25.33 0 [] cancel_semigroup_add(int).
% 25.51/25.33 0 [] linordered_semiring(int).
% 25.51/25.33 0 [] linordered_semidom(int).
% 25.51/25.33 0 [] ab_semigroup_mult(int).
% 25.51/25.33 0 [] comm_monoid_mult(int).
% 25.51/25.33 0 [] ab_semigroup_add(int).
% 25.51/25.33 0 [] ordered_semiring(int).
% 25.51/25.33 0 [] ordered_ring_abs(int).
% 25.51/25.33 0 [] no_zero_divisors(int).
% 25.51/25.33 0 [] comm_monoid_add(int).
% 25.51/25.33 0 [] linordered_ring(int).
% 25.51/25.33 0 [] linordered_idom(int).
% 25.51/25.33 0 [] comm_semiring_1(int).
% 25.51/25.33 0 [] comm_semiring(int).
% 25.51/25.33 0 [] semiring_char_0(int).
% 25.51/25.33 0 [] number_semiring(int).
% 25.51/25.33 0 [] ab_group_add(int).
% 25.51/25.33 0 [] zero_ne_q_one(int).
% 25.51/25.33 0 [] ordered_ring(int).
% 25.51/25.33 0 [] linorder(int).
% 25.51/25.33 0 [] monoid_mult(int).
% 25.51/25.33 0 [] comm_ring_1(int).
% 25.51/25.33 0 [] monoid_add(int).
% 25.51/25.33 0 [] semiring_1(int).
% 25.51/25.33 0 [] semiring_0(int).
% 25.51/25.33 0 [] group_add(int).
% 25.51/25.33 0 [] mult_zero(int).
% 25.51/25.33 0 [] comm_ring(int).
% 25.51/25.33 0 [] order(int).
% 25.51/25.33 0 [] ring_char_0(int).
% 25.51/25.33 0 [] number_ring(int).
% 25.51/25.33 0 [] semiring(int).
% 25.51/25.33 0 [] ring_1(int).
% 25.51/25.33 0 [] power(int).
% 25.51/25.33 0 [] zero(int).
% 25.51/25.33 0 [] ring(int).
% 25.51/25.33 0 [] idom(int).
% 25.51/25.33 0 [] number(int).
% 25.51/25.33 0 [] one(int).
% 25.51/25.33 0 [] dvd(int).
% 25.51/25.33 0 [] semiri456707255roduct(nat).
% 25.51/25.33 0 [] ordere223160158up_add(nat).
% 25.51/25.33 0 [] ordere236663937imp_le(nat).
% 25.51/25.33 0 [] linord893533164strict(nat).
% 25.51/25.33 0 [] linord20386208strict(nat).
% 25.51/25.33 0 [] ordere779506340up_add(nat).
% 25.51/25.33 0 [] ordere216010020id_add(nat).
% 25.51/25.33 0 [] cancel146912293up_add(nat).
% 25.51/25.33 0 [] ordere453448008miring(nat).
% 25.51/25.33 0 [] ordere1490568538miring(nat).
% 25.51/25.33 0 [] cancel_semigroup_add(nat).
% 25.51/25.33 0 [] linordered_semiring(nat).
% 25.51/25.33 0 [] linordered_semidom(nat).
% 25.51/25.33 0 [] ab_semigroup_mult(nat).
% 25.51/25.33 0 [] comm_monoid_mult(nat).
% 25.51/25.33 0 [] ab_semigroup_add(nat).
% 25.51/25.33 0 [] ordered_semiring(nat).
% 25.51/25.33 0 [] no_zero_divisors(nat).
% 25.51/25.33 0 [] comm_monoid_add(nat).
% 25.51/25.33 0 [] comm_semiring_1(nat).
% 25.51/25.33 0 [] comm_semiring(nat).
% 25.51/25.33 0 [] semiring_char_0(nat).
% 25.51/25.33 0 [] number_semiring(nat).
% 25.51/25.33 0 [] zero_ne_q_one(nat).
% 25.51/25.33 0 [] linorder(nat).
% 25.51/25.33 0 [] monoid_mult(nat).
% 25.51/25.33 0 [] monoid_add(nat).
% 25.51/25.33 0 [] semiring_1(nat).
% 25.51/25.33 0 [] semiring_0(nat).
% 25.51/25.33 0 [] mult_zero(nat).
% 25.51/25.33 0 [] order(nat).
% 25.51/25.33 0 [] semiring(nat).
% 25.51/25.33 0 [] power(nat).
% 25.51/25.33 0 [] zero(nat).
% 25.51/25.33 0 [] number(nat).
% 25.51/25.33 0 [] one(nat).
% 25.51/25.33 0 [] dvd(nat).
% 25.51/25.33 0 [] order(bool).
% 25.51/25.33 0 [] semiri456707255roduct(real).
% 25.51/25.33 0 [] ordere223160158up_add(real).
% 25.51/25.33 0 [] ordere236663937imp_le(real).
% 25.51/25.33 0 [] linord893533164strict(real).
% 25.51/25.33 0 [] linord626643107strict(real).
% 25.51/25.33 0 [] linord20386208strict(real).
% 25.51/25.33 0 [] ordere779506340up_add(real).
% 25.51/25.33 0 [] ordere142940540dd_abs(real).
% 25.51/25.33 0 [] ordere216010020id_add(real).
% 25.51/25.33 0 [] linord219039673up_add(real).
% 25.51/25.33 0 [] cancel146912293up_add(real).
% 25.51/25.33 0 [] ring_11004092258visors(real).
% 25.51/25.33 0 [] ordere453448008miring(real).
% 25.51/25.33 0 [] linord581940658strict(real).
% 25.51/25.33 0 [] ring_n68954251visors(real).
% 25.51/25.33 0 [] ordere1490568538miring(real).
% 25.51/25.33 0 [] linord1278240602ring_1(real).
% 25.51/25.33 0 [] ordered_ab_group_add(real).
% 25.51/25.33 0 [] cancel_semigroup_add(real).
% 25.51/25.33 0 [] linordered_semiring(real).
% 25.51/25.33 0 [] linordered_semidom(real).
% 25.51/25.33 0 [] ab_semigroup_mult(real).
% 25.51/25.33 0 [] comm_monoid_mult(real).
% 25.51/25.33 0 [] ab_semigroup_add(real).
% 25.51/25.33 0 [] ordered_semiring(real).
% 25.51/25.33 0 [] ordered_ring_abs(real).
% 25.51/25.33 0 [] no_zero_divisors(real).
% 25.51/25.33 0 [] comm_monoid_add(real).
% 25.51/25.33 0 [] linordered_ring(real).
% 25.51/25.33 0 [] linordered_idom(real).
% 25.51/25.33 0 [] comm_semiring_1(real).
% 25.51/25.33 0 [] comm_semiring(real).
% 25.51/25.33 0 [] semiring_char_0(real).
% 25.51/25.33 0 [] number_semiring(real).
% 25.51/25.33 0 [] ab_group_add(real).
% 25.51/25.33 0 [] zero_ne_q_one(real).
% 25.51/25.33 0 [] ordered_ring(real).
% 25.51/25.33 0 [] linorder(real).
% 25.51/25.33 0 [] monoid_mult(real).
% 25.51/25.33 0 [] comm_ring_1(real).
% 25.51/25.33 0 [] monoid_add(real).
% 25.51/25.33 0 [] semiring_1(real).
% 25.51/25.33 0 [] semiring_0(real).
% 25.51/25.33 0 [] group_add(real).
% 25.51/25.33 0 [] mult_zero(real).
% 25.51/25.33 0 [] comm_ring(real).
% 25.51/25.33 0 [] order(real).
% 25.51/25.33 0 [] ring_char_0(real).
% 25.51/25.33 0 [] number_ring(real).
% 25.51/25.33 0 [] semiring(real).
% 25.51/25.33 0 [] ring_1(real).
% 25.51/25.33 0 [] power(real).
% 25.51/25.33 0 [] zero(real).
% 25.51/25.33 0 [] ring(real).
% 25.51/25.33 0 [] idom(real).
% 25.51/25.33 0 [] number(real).
% 25.51/25.33 0 [] one(real).
% 25.51/25.33 0 [] dvd(real).
% 25.51/25.33 0 [] ti(T,ti(T,A))=ti(T,A).
% 25.51/25.33 0 [] if(X_a,fTrue,X,Y)=ti(X_a,X).
% 25.51/25.33 0 [] if(X_a,fFalse,X,Y)=ti(X_a,Y).
% 25.51/25.33 0 [] ti(bool,P)=fTrue|ti(bool,P)=fFalse.
% 25.51/25.33 0 [] hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls))))=zero_zero(int).
% 25.51/25.33 end_of_list.
% 25.51/25.33
% 25.51/25.33 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 25.51/25.33
% 25.51/25.33 This ia a non-Horn set with equality. The strategy will be
% 25.51/25.33 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 25.51/25.33 deletion, with positive clauses in sos and nonpositive
% 25.51/25.33 clauses in usable.
% 25.51/25.33
% 25.51/25.33 dependent: set(knuth_bendix).
% 25.51/25.33 dependent: set(anl_eq).
% 25.51/25.33 dependent: set(para_from).
% 25.51/25.33 dependent: set(para_into).
% 25.51/25.33 dependent: clear(para_from_right).
% 25.51/25.33 dependent: clear(para_into_right).
% 25.51/25.33 dependent: set(para_from_vars).
% 25.51/25.33 dependent: set(eq_units_both_ways).
% 25.51/25.33 dependent: set(dynamic_demod_all).
% 25.51/25.33 dependent: set(dynamic_demod).
% 25.51/25.33 dependent: set(order_eq).
% 25.51/25.33 dependent: set(back_demod).
% 25.51/25.33 dependent: set(lrpo).
% 25.51/25.33 dependent: set(hyper_res).
% 25.51/25.33 dependent: set(unit_deletion).
% 25.51/25.33 dependent: set(factor).
% 25.51/25.33
% 25.51/25.33 ------------> process usable:
% 25.51/25.33 ** KEPT (pick-wt=11): 1 [] -ordere142940540dd_abs(A)|abs_abs(A,ti(A,B))=abs_abs(A,B).
% 25.51/25.33 ** KEPT (pick-wt=11): 2 [] -ordere142940540dd_abs(A)|ti(A,abs_abs(A,B))=abs_abs(A,B).
% 25.51/25.33 ** KEPT (pick-wt=13): 3 [] -group_add(A)|minus_minus(A,ti(A,B),C)=minus_minus(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 4 [] -group_add(A)|minus_minus(A,B,ti(A,C))=minus_minus(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 5 [] -group_add(A)|ti(A,minus_minus(A,B,C))=minus_minus(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=9): 6 [] -one(A)|ti(A,one_one(A))=one_one(A).
% 25.51/25.33 ** KEPT (pick-wt=13): 7 [] -monoid_add(A)|plus_plus(A,ti(A,B),C)=plus_plus(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 8 [] -monoid_add(A)|plus_plus(A,B,ti(A,C))=plus_plus(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 9 [] -monoid_add(A)|ti(A,plus_plus(A,B,C))=plus_plus(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 10 [] -ab_semigroup_add(A)|plus_plus(A,ti(A,B),C)=plus_plus(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 11 [] -ab_semigroup_add(A)|plus_plus(A,B,ti(A,C))=plus_plus(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 12 [] -ab_semigroup_add(A)|ti(A,plus_plus(A,B,C))=plus_plus(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 13 [] -cancel_semigroup_add(A)|plus_plus(A,ti(A,B),C)=plus_plus(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 14 [] -cancel_semigroup_add(A)|plus_plus(A,B,ti(A,C))=plus_plus(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 15 [] -cancel_semigroup_add(A)|ti(A,plus_plus(A,B,C))=plus_plus(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 16 [] -dvd(A)|times_times(A,ti(A,B),C)=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 17 [] -dvd(A)|times_times(A,B,ti(A,C))=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 18 [] -dvd(A)|ti(A,times_times(A,B,C))=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 19 [] -power(A)|times_times(A,ti(A,B),C)=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 20 [] -power(A)|times_times(A,B,ti(A,C))=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 21 [] -power(A)|ti(A,times_times(A,B,C))=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 22 [] -semiring(A)|times_times(A,ti(A,B),C)=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 23 [] -semiring(A)|times_times(A,B,ti(A,C))=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 24 [] -semiring(A)|ti(A,times_times(A,B,C))=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 25 [] -no_zero_divisors(A)|times_times(A,ti(A,B),C)=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 26 [] -no_zero_divisors(A)|times_times(A,B,ti(A,C))=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 27 [] -no_zero_divisors(A)|ti(A,times_times(A,B,C))=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 28 [] -mult_zero(A)|times_times(A,ti(A,B),C)=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 29 [] -mult_zero(A)|times_times(A,B,ti(A,C))=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 30 [] -mult_zero(A)|ti(A,times_times(A,B,C))=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 31 [] -ab_semigroup_mult(A)|times_times(A,ti(A,B),C)=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 32 [] -ab_semigroup_mult(A)|times_times(A,B,ti(A,C))=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=13): 33 [] -ab_semigroup_mult(A)|ti(A,times_times(A,B,C))=times_times(A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=9): 34 [] -zero(A)|ti(A,zero_zero(A))=zero_zero(A).
% 25.51/25.33 ** KEPT (pick-wt=11): 35 [] -number(A)|number_number_of(A,ti(int,B))=number_number_of(A,B).
% 25.51/25.33 ** KEPT (pick-wt=11): 36 [] -number(A)|ti(A,number_number_of(A,B))=number_number_of(A,B).
% 25.51/25.33 ** KEPT (pick-wt=11): 37 [] -semiring_1(A)|ti(fun(nat,A),semiring_1_of_nat(A))=semiring_1_of_nat(A).
% 25.51/25.33 ** KEPT (pick-wt=13): 38 [] -order(A)|ti(fun(A,fun(A,bool)),ord_less(A))=ord_less(A).
% 25.51/25.33 ** KEPT (pick-wt=13): 39 [] -order(A)|ti(fun(A,fun(A,bool)),ord_less_e_q(A))=ord_less_e_q(A).
% 25.51/25.33 ** KEPT (pick-wt=11): 40 [] -power(A)|power_power(A,ti(A,B))=power_power(A,B).
% 25.51/25.33 ** KEPT (pick-wt=13): 41 [] -power(A)|ti(fun(nat,A),power_power(A,B))=power_power(A,B).
% 25.51/25.33 ** KEPT (pick-wt=13): 42 [] -dvd(A)|ti(fun(A,fun(A,bool)),dvd_dvd(A))=dvd_dvd(A).
% 25.51/25.33 ** KEPT (pick-wt=23): 43 [] -order(A)|hAPP(A,fun(A,bool),ti(fun(A,fun(A,bool)),B),C)=hAPP(A,fun(A,bool),B,C).
% 25.51/25.33 ** KEPT (pick-wt=19): 44 [] -order(A)|hAPP(A,fun(A,bool),B,ti(A,C))=hAPP(A,fun(A,bool),B,C).
% 25.51/25.33 ** KEPT (pick-wt=21): 45 [] -order(A)|ti(fun(A,bool),hAPP(A,fun(A,bool),B,C))=hAPP(A,fun(A,bool),B,C).
% 25.51/25.33 ** KEPT (pick-wt=17): 46 [] -order(A)|hAPP(A,bool,ti(fun(A,bool),B),C)=hAPP(A,bool,B,C).
% 25.51/25.33 ** KEPT (pick-wt=15): 47 [] -order(A)|hAPP(A,bool,B,ti(A,C))=hAPP(A,bool,B,C).
% 25.51/25.33 ** KEPT (pick-wt=15): 48 [] -order(A)|ti(bool,hAPP(A,bool,B,C))=hAPP(A,bool,B,C).
% 25.51/25.33 ** KEPT (pick-wt=23): 49 [] -dvd(A)|hAPP(A,fun(A,bool),ti(fun(A,fun(A,bool)),B),C)=hAPP(A,fun(A,bool),B,C).
% 25.51/25.33 ** KEPT (pick-wt=19): 50 [] -dvd(A)|hAPP(A,fun(A,bool),B,ti(A,C))=hAPP(A,fun(A,bool),B,C).
% 25.51/25.33 ** KEPT (pick-wt=21): 51 [] -dvd(A)|ti(fun(A,bool),hAPP(A,fun(A,bool),B,C))=hAPP(A,fun(A,bool),B,C).
% 25.51/25.33 ** KEPT (pick-wt=17): 52 [] -dvd(A)|hAPP(A,bool,ti(fun(A,bool),B),C)=hAPP(A,bool,B,C).
% 25.51/25.33 ** KEPT (pick-wt=15): 53 [] -dvd(A)|hAPP(A,bool,B,ti(A,C))=hAPP(A,bool,B,C).
% 25.51/25.33 ** KEPT (pick-wt=15): 54 [] -dvd(A)|ti(bool,hAPP(A,bool,B,C))=hAPP(A,bool,B,C).
% 25.51/25.33 ** KEPT (pick-wt=17): 55 [] -power(A)|hAPP(nat,A,ti(fun(nat,A),B),C)=hAPP(nat,A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=15): 56 [] -power(A)|hAPP(nat,A,B,ti(nat,C))=hAPP(nat,A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=15): 57 [] -power(A)|ti(A,hAPP(nat,A,B,C))=hAPP(nat,A,B,C).
% 25.51/25.33 ** KEPT (pick-wt=6): 58 [] -hBOOL(ti(bool,A))|hBOOL(A).
% 25.51/25.33 ** KEPT (pick-wt=6): 59 [] hBOOL(ti(bool,A))| -hBOOL(A).
% 25.51/25.33 ** KEPT (pick-wt=35): 60 [] -linordered_idom(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).
% 25.51/25.33 ** KEPT (pick-wt=35): 61 [] -linordered_idom(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).
% 25.51/25.33 ** KEPT (pick-wt=41): 62 [] -linordered_idom(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).
% 25.51/25.33 ** KEPT (pick-wt=17): 63 [] -semiring_1(A)|hAPP(nat,A,power_power(A,one_one(A)),number_number_of(nat,bit0(bit1(pls))))=one_one(A).
% 25.51/25.33 ** KEPT (pick-wt=17): 64 [] -semiring_1(A)|hAPP(nat,A,power_power(A,zero_zero(A)),number_number_of(nat,bit0(bit1(pls))))=zero_zero(A).
% 25.51/25.33 ** KEPT (pick-wt=22): 65 [] -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).
% 25.51/25.33 ** KEPT (pick-wt=22): 66 [] -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).
% 25.51/25.33 ** KEPT (pick-wt=17): 67 [] -number_ring(A)|plus_plus(A,one_one(A),number_number_of(A,B))=number_number_of(A,plus_plus(int,bit1(pls),B)).
% 25.51/25.33 ** KEPT (pick-wt=17): 68 [] -number_ring(A)|plus_plus(A,number_number_of(A,B),one_one(A))=number_number_of(A,plus_plus(int,B,bit1(pls))).
% 25.51/25.33 ** KEPT (pick-wt=14): 69 [] -number_ring(A)|plus_plus(A,one_one(A),one_one(A))=number_number_of(A,bit0(bit1(pls))).
% 25.51/25.33 ** KEPT (pick-wt=14): 70 [] -number_semiring(A)|plus_plus(A,one_one(A),one_one(A))=number_number_of(A,bit0(bit1(pls))).
% 25.51/25.33 ** KEPT (pick-wt=23): 71 [] -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).
% 25.51/25.33 ** KEPT (pick-wt=23): 72 [] -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).
% 25.51/25.33 ** KEPT (pick-wt=9): 73 [] -number_ring(A)|one_one(A)=number_number_of(A,bit1(pls)).
% 25.51/25.33 Following clause subsumed by 73 during input processing: 0 [flip.2] -number_ring(A)|one_one(A)=number_number_of(A,bit1(pls)).
% 25.51/25.33 ** KEPT (pick-wt=30): 74 [] -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)).
% 25.51/25.33 ** KEPT (pick-wt=30): 75 [] 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)).
% 25.51/25.33 ** KEPT (pick-wt=34): 76 [] -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)).
% 25.51/25.33 ** KEPT (pick-wt=34): 77 [] -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)).
% 25.51/25.33 ** KEPT (pick-wt=13): 78 [] hAPP(nat,int,semiring_1_of_nat(int),A)!=zero_zero(int)|A=zero_zero(nat).
% 25.51/25.33 ** KEPT (pick-wt=13): 79 [] hAPP(nat,int,semiring_1_of_nat(int),A)=zero_zero(int)|A!=zero_zero(nat).
% 25.51/25.33 ** KEPT (pick-wt=28): 80 [] -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)).
% 25.51/25.33 ** KEPT (pick-wt=28): 81 [] 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)).
% 25.51/25.33 Following clause subsumed by 80 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)).
% 25.51/25.33 Following clause subsumed by 81 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)).
% 25.51/25.33 ** KEPT (pick-wt=13): 82 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)).
% 25.51/25.33 ** KEPT (pick-wt=28): 83 [] -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)).
% 25.51/25.33 ** KEPT (pick-wt=28): 84 [] 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)).
% 25.51/25.33 Following clause subsumed by 83 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)).
% 25.51/25.33 Following clause subsumed by 84 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)).
% 25.51/25.33 ** KEPT (pick-wt=32): 85 [] -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),plus_plus(int,A,C)),plus_plus(int,B,C))).
% 25.51/25.33 ** KEPT (pick-wt=25): 86 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls))|plus_plus(nat,number_number_of(nat,A),number_number_of(nat,B))=number_number_of(nat,B).
% 25.51/25.33 ** KEPT (pick-wt=38): 87 [] 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))|plus_plus(nat,number_number_of(nat,A),number_number_of(nat,B))=number_number_of(nat,A).
% 25.51/25.33 ** KEPT (pick-wt=18): 88 [] -number_ring(A)| -ring_char_0(A)|number_number_of(A,B)!=number_number_of(A,C)|ti(int,B)=ti(int,C).
% 25.51/25.33 ** KEPT (pick-wt=18): 89 [] -number_ring(A)| -ring_char_0(A)|number_number_of(A,B)=number_number_of(A,C)|ti(int,B)!=ti(int,C).
% 25.51/25.33 ** KEPT (pick-wt=16): 90 [] -number(A)|number_number_of(A,B)!=ti(A,C)|ti(A,C)=number_number_of(A,B).
% 25.51/25.33 ** KEPT (pick-wt=16): 91 [] -number(A)|number_number_of(A,B)=ti(A,C)|ti(A,C)!=number_number_of(A,B).
% 25.51/25.33 ** KEPT (pick-wt=12): 92 [] bit1(A)!=bit1(B)|ti(int,A)=ti(int,B).
% 25.51/25.33 ** KEPT (pick-wt=12): 93 [] bit1(A)=bit1(B)|ti(int,A)!=ti(int,B).
% 25.51/25.33 ** KEPT (pick-wt=12): 94 [] bit0(A)!=bit0(B)|ti(int,A)=ti(int,B).
% 25.51/25.33 ** KEPT (pick-wt=12): 95 [] bit0(A)=bit0(B)|ti(int,A)!=ti(int,B).
% 25.51/25.33 ** KEPT (pick-wt=33): 96 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))).
% 25.51/25.33 ** KEPT (pick-wt=33): 97 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))).
% 25.51/25.33 ** KEPT (pick-wt=16): 98 [] hAPP(nat,int,semiring_1_of_nat(int),A)!=hAPP(nat,int,semiring_1_of_nat(int),B)|A=B.
% 25.51/25.33 ** KEPT (pick-wt=16): 99 [] hAPP(nat,int,semiring_1_of_nat(int),A)=hAPP(nat,int,semiring_1_of_nat(int),B)|A!=B.
% 25.51/25.33 ** KEPT (pick-wt=33): 100 [] -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)).
% 25.51/25.33 ** KEPT (pick-wt=33): 101 [] -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)).
% 25.51/25.33 ** KEPT (pick-wt=33): 102 [] -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)).
% 25.51/25.33 ** KEPT (pick-wt=33): 103 [] -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)).
% 25.51/25.33 ** KEPT (pick-wt=27): 104 [] -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)).
% 25.51/25.33 ** KEPT (pick-wt=27): 105 [] 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)).
% 25.51/25.34 ** KEPT (pick-wt=28): 106 [] -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)).
% 25.51/25.34 ** KEPT (pick-wt=28): 107 [] 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)).
% 25.51/25.34 Following clause subsumed by 106 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)).
% 25.51/25.34 Following clause subsumed by 107 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)).
% 25.51/25.34 ** KEPT (pick-wt=27): 108 [] -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)).
% 25.51/25.34 ** KEPT (pick-wt=27): 109 [] 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)).
% 25.51/25.34 ** KEPT (pick-wt=27): 110 [] -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)).
% 25.51/25.34 ** KEPT (pick-wt=27): 111 [] 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)).
% 25.51/25.34 ** KEPT (pick-wt=29): 112 [] -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))).
% 25.51/25.34 ** KEPT (pick-wt=29): 113 [] 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))).
% 25.51/25.34 ** KEPT (pick-wt=14): 114 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))).
% 25.51/25.34 ** KEPT (pick-wt=29): 115 [] -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))).
% 25.51/25.34 ** KEPT (pick-wt=29): 116 [] 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))).
% 25.51/25.34 ** KEPT (pick-wt=37): 117 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),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).
% 25.51/25.34 ** KEPT (pick-wt=30): 118 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),plus_plus(int,B,one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 25.51/25.34 ** KEPT (pick-wt=24): 119 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),plus_plus(int,B,one_one(int))))|ti(int,A)!=ti(int,B).
% 25.51/25.34 ** KEPT (pick-wt=19): 120 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),zero_zero(int))).
% 25.51/25.34 ** KEPT (pick-wt=34): 121 [] -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))).
% 25.51/25.34 ** KEPT (pick-wt=34): 122 [] -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))).
% 25.51/25.34 ** KEPT (pick-wt=34): 123 [] -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)).
% 25.51/25.34 ** KEPT (pick-wt=34): 124 [] -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)).
% 25.51/25.34 ** KEPT (pick-wt=35): 125 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(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))).
% 25.51/25.34 ** KEPT (pick-wt=35): 126 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(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))).
% 25.51/25.34 ** KEPT (pick-wt=15): 127 [] -linord219039673up_add(A)|plus_plus(A,B,B)!=zero_zero(A)|ti(A,B)=zero_zero(A).
% 25.51/25.34 ** KEPT (pick-wt=15): 128 [] -linord219039673up_add(A)|plus_plus(A,B,B)=zero_zero(A)|ti(A,B)!=zero_zero(A).
% 25.51/25.34 ** KEPT (pick-wt=4): 129 [] bit1(A)!=pls.
% 25.51/25.34 Following clause subsumed by 129 during input processing: 0 [flip.1] bit1(A)!=pls.
% 25.51/25.34 ** KEPT (pick-wt=5): 130 [] bit1(A)!=bit0(B).
% 25.51/25.34 ** KEPT (pick-wt=5): 131 [] bit0(A)!=bit1(B).
% 25.51/25.34 ** KEPT (pick-wt=9): 132 [] bit0(A)!=pls|ti(int,A)=pls.
% 25.51/25.34 ** KEPT (pick-wt=9): 133 [] bit0(A)=pls|ti(int,A)!=pls.
% 25.51/25.34 Following clause subsumed by 132 during input processing: 0 [flip.1,flip.2] bit0(A)!=pls|ti(int,A)=pls.
% 25.51/25.34 Following clause subsumed by 133 during input processing: 0 [flip.1,flip.2] bit0(A)=pls|ti(int,A)!=pls.
% 25.51/25.34 ** KEPT (pick-wt=5): 134 [] zero_zero(int)!=one_one(int).
% 25.51/25.34 ** KEPT (pick-wt=8): 136 [copy,135,flip.2] -number_semiring(A)|zero_zero(A)=number_number_of(A,pls).
% 25.51/25.34 ** KEPT (pick-wt=8): 138 [copy,137,flip.2] -number_ring(A)|zero_zero(A)=number_number_of(A,pls).
% 25.51/25.34 Following clause subsumed by 138 during input processing: 0 [] -number_ring(A)|zero_zero(A)=number_number_of(A,pls).
% 25.51/25.34 ** KEPT (pick-wt=12): 140 [copy,139,flip.2] -number_ring(A)|ti(A,B)=plus_plus(A,number_number_of(A,pls),B).
% 25.51/25.34 ** KEPT (pick-wt=12): 142 [copy,141,flip.2] -number_ring(A)|ti(A,B)=plus_plus(A,B,number_number_of(A,pls)).
% 25.51/25.34 ** KEPT (pick-wt=26): 143 [] -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).
% 25.51/25.34 ** KEPT (pick-wt=26): 144 [] -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).
% 25.51/25.34 ** KEPT (pick-wt=32): 145 [] -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).
% 25.51/25.34 ** KEPT (pick-wt=23): 147 [copy,146,flip.2] -number_ring(A)|plus_plus(A,number_number_of(A,plus_plus(int,B,C)),D)=plus_plus(A,number_number_of(A,B),plus_plus(A,number_number_of(A,C),D)).
% 25.51/25.34 ** KEPT (pick-wt=17): 149 [copy,148,flip.2] -number_ring(A)|number_number_of(A,plus_plus(int,B,C))=plus_plus(A,number_number_of(A,B),number_number_of(A,C)).
% 25.51/25.34 Following clause subsumed by 149 during input processing: 0 [] -number_ring(A)|number_number_of(A,plus_plus(int,B,C))=plus_plus(A,number_number_of(A,B),number_number_of(A,C)).
% 25.51/25.34 ** KEPT (pick-wt=11): 150 [] plus_plus(int,plus_plus(int,one_one(int),A),A)!=zero_zero(int).
% 25.51/25.34 ** KEPT (pick-wt=17): 151 [] -number_semiring(A)|number_number_of(A,hAPP(nat,int,semiring_1_of_nat(int),B))=hAPP(nat,A,semiring_1_of_nat(A),B).
% 25.51/25.34 ** KEPT (pick-wt=32): 152 [] -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).
% 25.51/25.34 ** KEPT (pick-wt=32): 153 [] -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).
% 25.51/25.34 ** KEPT (pick-wt=26): 154 [] -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))).
% 25.51/25.34 ** KEPT (pick-wt=51): 155 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(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).
% 25.51/25.34 ** KEPT (pick-wt=45): 156 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(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).
% 25.51/25.34 ** KEPT (pick-wt=45): 157 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(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).
% 25.51/25.34 ** KEPT (pick-wt=39): 158 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))).
% 25.51/25.34 ** KEPT (pick-wt=19): 159 [] -number_ring(A)|number_number_of(A,bit0(B))=plus_plus(A,plus_plus(A,zero_zero(A),number_number_of(A,B)),number_number_of(A,B)).
% 25.51/25.34 ** KEPT (pick-wt=19): 160 [] -number_ring(A)|number_number_of(A,bit1(B))=plus_plus(A,plus_plus(A,one_one(A),number_number_of(A,B)),number_number_of(A,B)).
% 25.51/25.34 ** KEPT (pick-wt=9): 162 [copy,161,flip.2] -number_semiring(A)|one_one(A)=number_number_of(A,bit1(pls)).
% 25.51/25.34 ** KEPT (pick-wt=32): 163 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,power_power(A,number_number_of(A,bit0(bit1(pls)))),B))).
% 25.51/25.34 ** KEPT (pick-wt=31): 164 [] plus_plus(real,hAPP(nat,real,power_power(real,A),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,real,power_power(real,B),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(real)|A=zero_zero(real).
% 25.51/25.34 ** KEPT (pick-wt=31): 165 [] plus_plus(real,hAPP(nat,real,power_power(real,A),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,real,power_power(real,B),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(real)|B=zero_zero(real).
% 25.51/25.34 ** KEPT (pick-wt=35): 166 [] plus_plus(real,hAPP(nat,real,power_power(real,A),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,real,power_power(real,B),number_number_of(nat,bit0(bit1(pls)))))=zero_zero(real)|A!=zero_zero(real)|B!=zero_zero(real).
% 25.51/25.34 ** KEPT (pick-wt=35): 167 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)).
% 25.51/25.34 ** KEPT (pick-wt=35): 168 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)).
% 25.51/25.34 ** KEPT (pick-wt=50): 169 [] -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))).
% 25.51/25.34 ** KEPT (pick-wt=19): 170 [] -power(A)| -semiring_0(A)|B!=zero_zero(nat)|hAPP(nat,A,power_power(A,zero_zero(A)),B)=one_one(A).
% 25.51/25.34 ** KEPT (pick-wt=19): 171 [] -power(A)| -semiring_0(A)|B=zero_zero(nat)|hAPP(nat,A,power_power(A,zero_zero(A)),B)=zero_zero(A).
% 25.51/25.34 ** KEPT (pick-wt=68): 172 [] -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))).
% 25.51/25.34 ** KEPT (pick-wt=21): 173 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),plus_plus(A,one_one(A),one_one(A)))).
% 25.51/25.34 ** KEPT (pick-wt=45): 174 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,C,plus_plus(int,A,one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),$f1(C,A,B)))|hBOOL(hAPP(int,bool,C,B)).
% 25.51/25.34 ** KEPT (pick-wt=38): 175 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,C,plus_plus(int,A,one_one(int))))|hBOOL(hAPP(int,bool,C,$f1(C,A,B)))|hBOOL(hAPP(int,bool,C,B)).
% 25.51/25.34 ** KEPT (pick-wt=42): 176 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,C,plus_plus(int,A,one_one(int))))| -hBOOL(hAPP(int,bool,C,plus_plus(int,$f1(C,A,B),one_one(int))))|hBOOL(hAPP(int,bool,C,B)).
% 25.51/25.34 ** KEPT (pick-wt=14): 177 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))).
% 25.51/25.34 ** KEPT (pick-wt=5): 178 [] zero_zero(real)!=one_one(real).
% 25.51/25.34 ** KEPT (pick-wt=13): 179 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),A)).
% 25.51/25.34 ** KEPT (pick-wt=16): 180 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,A,B)),A)).
% 25.51/25.34 ** KEPT (pick-wt=16): 181 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,A,B)),B)).
% 25.51/25.34 ** KEPT (pick-wt=16): 182 [] A!=B| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).
% 25.51/25.34 ** KEPT (pick-wt=16): 183 [] A!=B| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)).
% 25.51/25.34 ** KEPT (pick-wt=12): 184 [] plus_plus(nat,A,B)!=plus_plus(nat,A,C)|B=C.
% 25.51/25.34 ** KEPT (pick-wt=12): 185 [] plus_plus(nat,A,B)=plus_plus(nat,A,C)|B!=C.
% 25.51/25.34 ** KEPT (pick-wt=12): 186 [] plus_plus(nat,A,B)!=plus_plus(nat,C,B)|A=C.
% 25.51/25.34 ** KEPT (pick-wt=12): 187 [] plus_plus(nat,A,B)=plus_plus(nat,C,B)|A!=C.
% 25.51/25.34 ** KEPT (pick-wt=32): 188 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,A,B)),plus_plus(nat,A,C)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).
% 25.51/25.34 ** KEPT (pick-wt=32): 189 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,A,B)),plus_plus(nat,A,C)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).
% 25.51/25.34 Following clause subsumed by 179 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),A)).
% 25.51/25.34 Following clause subsumed by 183 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|B!=A.
% 25.51/25.34 Following clause subsumed by 182 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|A!=B.
% 25.51/25.34 ** KEPT (pick-wt=29): 190 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),plus_plus(nat,B,C))).
% 25.51/25.34 ** KEPT (pick-wt=29): 191 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),plus_plus(nat,C,B))).
% 25.51/25.34 ** KEPT (pick-wt=32): 192 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,A,C)),plus_plus(nat,B,C))).
% 25.51/25.34 ** KEPT (pick-wt=45): 193 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,A,C)),plus_plus(nat,B,D))).
% 25.51/25.34 ** KEPT (pick-wt=35): 194 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|plus_plus(nat,C,B)!=plus_plus(nat,A,D)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)).
% 25.51/25.34 ** KEPT (pick-wt=29): 195 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,A,B)),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)).
% 25.51/25.34 ** KEPT (pick-wt=17): 196 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|B!=zero_zero(nat).
% 25.51/25.34 ** KEPT (pick-wt=52): 197 [] -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)).
% 25.51/25.34 Following clause subsumed by 177 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))).
% 25.51/25.34 ** KEPT (pick-wt=38): 198 [] -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).
% 25.51/25.34 ** KEPT (pick-wt=34): 199 [] 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)).
% 25.51/25.34 ** KEPT (pick-wt=24): 200 [] 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).
% 25.51/25.34 ** KEPT (pick-wt=45): 201 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),plus_plus(nat,A,B)))|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),zero_zero(nat)),B)).
% 25.51/25.34 Following clause subsumed by 190 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),plus_plus(nat,A,B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).
% 25.51/25.34 Following clause subsumed by 191 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),plus_plus(nat,A,B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)).
% 25.51/25.34 Following clause subsumed by 183 during input processing: 0 [] A!=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).
% 25.51/25.34 Following clause subsumed by 177 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))).
% 25.51/25.34 Following clause subsumed by 198 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)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).
% 25.51/25.34 Following clause subsumed by 200 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).
% 25.51/25.34 Following clause subsumed by 199 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)).
% 25.51/25.34 ** KEPT (pick-wt=36): 202 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).
% 25.51/25.34 ** KEPT (pick-wt=36): 203 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).
% 25.51/25.34 Following clause subsumed by 198 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)).
% 25.51/25.34 Following clause subsumed by 200 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).
% 25.51/25.34 Following clause subsumed by 199 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)).
% 25.51/25.34 Following clause subsumed by 202 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).
% 25.51/25.34 Following clause subsumed by 203 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).
% 25.51/25.34 ** KEPT (pick-wt=43): 204 [] -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)).
% 25.54/25.35 ** KEPT (pick-wt=30): 205 [] -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)).
% 25.54/25.35 ** KEPT (pick-wt=43): 206 [] 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)).
% 25.54/25.35 ** KEPT (pick-wt=35): 207 [] -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)).
% 25.54/25.35 ** KEPT (pick-wt=10): 208 [] plus_plus(nat,A,B)!=A|B=zero_zero(nat).
% 25.54/25.35 ** KEPT (pick-wt=11): 209 [] plus_plus(nat,A,B)!=zero_zero(nat)|A=zero_zero(nat).
% 25.54/25.35 ** KEPT (pick-wt=11): 210 [] plus_plus(nat,A,B)!=zero_zero(nat)|B=zero_zero(nat).
% 25.54/25.35 ** KEPT (pick-wt=15): 211 [] plus_plus(nat,A,B)=zero_zero(nat)|A!=zero_zero(nat)|B!=zero_zero(nat).
% 25.54/25.35 ** KEPT (pick-wt=14): 212 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,B),one_one(nat))=ti(A,B).
% 25.54/25.35 ** KEPT (pick-wt=18): 213 [] -semiring_char_0(A)|hAPP(nat,A,semiring_1_of_nat(A),B)!=hAPP(nat,A,semiring_1_of_nat(A),C)|B=C.
% 25.54/25.35 ** KEPT (pick-wt=18): 214 [] -semiring_char_0(A)|hAPP(nat,A,semiring_1_of_nat(A),B)=hAPP(nat,A,semiring_1_of_nat(A),C)|B!=C.
% 25.54/25.35 Following clause subsumed by 98 during input processing: 0 [] hAPP(nat,int,semiring_1_of_nat(int),A)!=hAPP(nat,int,semiring_1_of_nat(int),B)|A=B.
% 25.54/25.35 Following clause subsumed by 99 during input processing: 0 [] hAPP(nat,int,semiring_1_of_nat(int),A)=hAPP(nat,int,semiring_1_of_nat(int),B)|A!=B.
% 25.54/25.35 ** KEPT (pick-wt=19): 216 [copy,215,flip.2] -hBOOL(A)|hAPP(nat,int,semiring_1_of_nat(int),if(nat,A,B,C))=hAPP(nat,int,semiring_1_of_nat(int),B).
% 25.54/25.35 ** KEPT (pick-wt=29): 217 [] -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)).
% 25.54/25.35 ** KEPT (pick-wt=29): 218 [] 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)).
% 25.54/25.35 ** KEPT (pick-wt=33): 219 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).
% 25.54/25.35 ** KEPT (pick-wt=33): 220 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).
% 25.54/25.35 ** KEPT (pick-wt=7): 222 [copy,221,flip.2] -zero_ne_q_one(A)|zero_zero(A)!=one_one(A).
% 25.54/25.35 Following clause subsumed by 222 during input processing: 0 [] -zero_ne_q_one(A)|zero_zero(A)!=one_one(A).
% 25.54/25.35 ** KEPT (pick-wt=18): 223 [] -ring_11004092258visors(A)|ti(A,B)=zero_zero(A)|hAPP(nat,A,power_power(A,B),C)!=zero_zero(A).
% 25.54/25.35 ** KEPT (pick-wt=13): 224 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,one_one(A)),B)=one_one(A).
% 25.54/25.35 ** KEPT (pick-wt=38): 225 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).
% 25.54/25.35 ** KEPT (pick-wt=38): 226 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).
% 25.54/25.35 Following clause subsumed by 226 during input processing: 0 [] -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),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))).
% 25.54/25.35 Following clause subsumed by 225 during input processing: 0 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).
% 25.54/25.35 ** KEPT (pick-wt=26): 227 [] -semiring_1(A)|hAPP(nat,A,semiring_1_of_nat(A),plus_plus(nat,B,C))=plus_plus(A,hAPP(nat,A,semiring_1_of_nat(A),B),hAPP(nat,A,semiring_1_of_nat(A),C)).
% 25.54/25.35 ** KEPT (pick-wt=12): 228 [] -semiring_1(A)|hAPP(nat,A,semiring_1_of_nat(A),one_one(nat))=one_one(A).
% 25.54/25.35 ** KEPT (pick-wt=27): 229 [] -semiring_1(A)|hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,power_power(nat,B),C))=hAPP(nat,A,power_power(A,hAPP(nat,A,semiring_1_of_nat(A),B)),C).
% 25.54/25.35 ** KEPT (pick-wt=45): 230 [] -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),plus_plus(A,B,D))).
% 25.54/25.35 ** KEPT (pick-wt=17): 231 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),zero_zero(A))).
% 25.54/25.35 ** KEPT (pick-wt=17): 232 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),one_one(A))).
% 25.54/25.35 ** KEPT (pick-wt=36): 233 [] -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))).
% 25.54/25.35 ** KEPT (pick-wt=19): 234 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),plus_plus(A,B,one_one(A)))).
% 25.54/25.35 ** KEPT (pick-wt=34): 235 [] -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.
% 25.54/25.35 ** KEPT (pick-wt=34): 236 [] -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.
% 25.54/25.35 ** KEPT (pick-wt=54): 237 [] -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)).
% 25.54/25.35 ** KEPT (pick-wt=54): 238 [] -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)).
% 25.54/25.35 Following clause subsumed by 237 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)).
% 25.54/25.35 Following clause subsumed by 238 during input processing: 0 [] -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))).
% 25.54/25.35 ** KEPT (pick-wt=24): 239 [] -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).
% 25.54/25.35 ** KEPT (pick-wt=22): 240 [] -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).
% 25.54/25.35 ** KEPT (pick-wt=28): 241 [] -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).
% 25.54/25.35 ** KEPT (pick-wt=21): 242 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),zero_zero(A))).
% 25.54/25.35 ** KEPT (pick-wt=13): 243 [] -power(A)|hAPP(nat,A,power_power(A,B),zero_zero(nat))=one_one(A).
% 25.54/25.35 ** KEPT (pick-wt=12): 244 [] -semiring_1(A)|hAPP(nat,A,semiring_1_of_nat(A),zero_zero(nat))=zero_zero(A).
% 25.54/25.35 ** KEPT (pick-wt=29): 245 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),$f2(A))).
% 25.54/25.35 ** KEPT (pick-wt=25): 247 [copy,246,flip.2] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hAPP(nat,int,semiring_1_of_nat(int),$f2(A))=ti(int,A).
% 25.54/25.35 ** KEPT (pick-wt=29): 248 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),$f3(A,B))).
% 25.54/25.35 ** KEPT (pick-wt=21): 249 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|plus_plus(nat,A,$f3(A,B))=B.
% 25.54/25.35 ** KEPT (pick-wt=18): 250 [] hAPP(nat,nat,power_power(nat,A),B)!=one_one(nat)|A=one_one(nat)|B=zero_zero(nat).
% 25.54/25.35 ** KEPT (pick-wt=14): 251 [] hAPP(nat,nat,power_power(nat,A),B)=one_one(nat)|A!=one_one(nat).
% 25.54/25.35 ** KEPT (pick-wt=14): 252 [] hAPP(nat,nat,power_power(nat,A),B)=one_one(nat)|B!=zero_zero(nat).
% 25.54/25.35 ** KEPT (pick-wt=13): 253 [] -comm_semiring_1(A)|hAPP(nat,A,power_power(A,B),zero_zero(nat))=one_one(A).
% 25.54/25.35 ** KEPT (pick-wt=33): 254 [] -linord219039673up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),plus_plus(A,B,B)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)).
% 25.54/25.35 ** KEPT (pick-wt=33): 255 [] -linord219039673up_add(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),plus_plus(A,B,B)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)).
% 25.54/25.35 ** KEPT (pick-wt=33): 256 [] -linord219039673up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))).
% 25.54/25.35 ** KEPT (pick-wt=33): 257 [] -linord219039673up_add(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))).
% 25.54/25.35 ** KEPT (pick-wt=47): 258 [] -ordere216010020id_add(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)),plus_plus(A,B,C))).
% 25.54/25.35 ** KEPT (pick-wt=47): 259 [] -ordere216010020id_add(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),plus_plus(A,B,C)),zero_zero(A))).
% 25.54/25.35 ** KEPT (pick-wt=14): 260 [] -zero(A)|zero_zero(A)!=ti(A,B)|ti(A,B)=zero_zero(A).
% 25.54/25.35 ** KEPT (pick-wt=14): 261 [] -zero(A)|zero_zero(A)=ti(A,B)|ti(A,B)!=zero_zero(A).
% 25.54/25.35 ** KEPT (pick-wt=18): 262 [] -cancel_semigroup_add(A)|plus_plus(A,B,C)!=plus_plus(A,D,C)|ti(A,B)=ti(A,D).
% 25.54/25.35 ** KEPT (pick-wt=18): 263 [] -cancel146912293up_add(A)|plus_plus(A,B,C)!=plus_plus(A,B,D)|ti(A,C)=ti(A,D).
% 25.54/25.35 ** KEPT (pick-wt=18): 264 [] -cancel_semigroup_add(A)|plus_plus(A,B,C)!=plus_plus(A,B,D)|ti(A,C)=ti(A,D).
% 25.54/25.35 ** KEPT (pick-wt=23): 265 [] -comm_semiring_1(A)|plus_plus(A,plus_plus(A,B,C),plus_plus(A,D,E))=plus_plus(A,plus_plus(A,B,D),plus_plus(A,C,E)).
% 25.54/25.35 Following clause subsumed by 262 during input processing: 0 [] -cancel_semigroup_add(A)|plus_plus(A,B,C)!=plus_plus(A,D,C)|ti(A,B)=ti(A,D).
% 25.54/25.35 ** KEPT (pick-wt=18): 266 [] -cancel_semigroup_add(A)|plus_plus(A,B,C)=plus_plus(A,D,C)|ti(A,B)!=ti(A,D).
% 25.54/25.35 Following clause subsumed by 264 during input processing: 0 [] -cancel_semigroup_add(A)|plus_plus(A,B,C)!=plus_plus(A,B,D)|ti(A,C)=ti(A,D).
% 25.54/25.35 ** KEPT (pick-wt=18): 267 [] -cancel_semigroup_add(A)|plus_plus(A,B,C)=plus_plus(A,B,D)|ti(A,C)!=ti(A,D).
% 25.54/25.35 ** KEPT (pick-wt=17): 268 [] -comm_semiring_1(A)|plus_plus(A,plus_plus(A,B,C),D)=plus_plus(A,plus_plus(A,B,D),C).
% 25.54/25.35 ** KEPT (pick-wt=17): 269 [] -ab_semigroup_add(A)|plus_plus(A,plus_plus(A,B,C),D)=plus_plus(A,B,plus_plus(A,C,D)).
% 25.54/25.35 ** KEPT (pick-wt=17): 270 [] -comm_semiring_1(A)|plus_plus(A,plus_plus(A,B,C),D)=plus_plus(A,B,plus_plus(A,C,D)).
% 25.54/25.35 Following clause subsumed by 270 during input processing: 0 [flip.2] -comm_semiring_1(A)|plus_plus(A,plus_plus(A,B,C),D)=plus_plus(A,B,plus_plus(A,C,D)).
% 25.54/25.35 ** KEPT (pick-wt=17): 271 [] -comm_semiring_1(A)|plus_plus(A,B,plus_plus(A,C,D))=plus_plus(A,C,plus_plus(A,B,D)).
% 25.54/25.35 ** KEPT (pick-wt=11): 272 [] -comm_semiring_1(A)|plus_plus(A,B,C)=plus_plus(A,C,B).
% 25.54/25.35 ** KEPT (pick-wt=14): 273 [] -one(A)|one_one(A)!=ti(A,B)|ti(A,B)=one_one(A).
% 25.54/25.35 ** KEPT (pick-wt=14): 274 [] -one(A)|one_one(A)=ti(A,B)|ti(A,B)!=one_one(A).
% 25.54/25.35 ** KEPT (pick-wt=16): 275 [] -semiri456707255roduct(A)|ti(A,B)!=plus_plus(A,B,C)|ti(A,C)=zero_zero(A).
% 25.54/25.35 ** KEPT (pick-wt=16): 276 [] -semiri456707255roduct(A)|ti(A,B)=plus_plus(A,B,C)|ti(A,C)!=zero_zero(A).
% 25.54/25.35 ** KEPT (pick-wt=11): 277 [] -comm_monoid_add(A)|plus_plus(A,B,zero_zero(A))=ti(A,B).
% 25.54/25.35 ** KEPT (pick-wt=11): 278 [] -comm_semiring_1(A)|plus_plus(A,B,zero_zero(A))=ti(A,B).
% 25.54/25.35 ** KEPT (pick-wt=11): 279 [] -monoid_add(A)|plus_plus(A,B,zero_zero(A))=ti(A,B).
% 25.54/25.35 ** KEPT (pick-wt=15): 280 [] -linord219039673up_add(A)|zero_zero(A)!=plus_plus(A,B,B)|ti(A,B)=zero_zero(A).
% 25.54/25.35 ** KEPT (pick-wt=15): 281 [] -linord219039673up_add(A)|zero_zero(A)=plus_plus(A,B,B)|ti(A,B)!=zero_zero(A).
% 25.54/25.35 ** KEPT (pick-wt=11): 282 [] -comm_monoid_add(A)|plus_plus(A,zero_zero(A),B)=ti(A,B).
% 25.54/25.35 ** KEPT (pick-wt=11): 283 [] -comm_semiring_1(A)|plus_plus(A,zero_zero(A),B)=ti(A,B).
% 25.54/25.35 ** KEPT (pick-wt=11): 284 [] -monoid_add(A)|plus_plus(A,zero_zero(A),B)=ti(A,B).
% 25.54/25.35 ** KEPT (pick-wt=34): 285 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),plus_plus(A,B,C)),plus_plus(A,B,D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 25.54/25.35 ** KEPT (pick-wt=34): 286 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),plus_plus(A,B,C)),plus_plus(A,D,C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 25.54/25.35 ** KEPT (pick-wt=47): 287 [] -ordere223160158up_add(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),plus_plus(A,B,D)),plus_plus(A,C,E))).
% 25.54/25.35 ** KEPT (pick-wt=34): 288 [] -ordere223160158up_add(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),plus_plus(A,D,B)),plus_plus(A,D,C))).
% 25.54/25.35 ** KEPT (pick-wt=34): 289 [] -ordere223160158up_add(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),plus_plus(A,B,D)),plus_plus(A,C,D))).
% 25.54/25.35 Following clause subsumed by 285 during input processing: 0 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),plus_plus(A,B,C)),plus_plus(A,B,D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 25.54/25.35 ** KEPT (pick-wt=34): 290 [] -ordere236663937imp_le(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),plus_plus(A,B,C)),plus_plus(A,B,D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 25.54/25.35 Following clause subsumed by 286 during input processing: 0 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),plus_plus(A,B,C)),plus_plus(A,D,C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 25.54/25.35 ** KEPT (pick-wt=34): 291 [] -ordere236663937imp_le(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),plus_plus(A,B,C)),plus_plus(A,D,C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 25.54/25.35 ** KEPT (pick-wt=14): 292 [] -comm_semiring_1(A)|hAPP(nat,A,power_power(A,B),one_one(nat))=ti(A,B).
% 25.54/25.35 ** KEPT (pick-wt=14): 293 [] hAPP(nat,nat,power_power(nat,A),B)!=zero_zero(nat)|B!=zero_zero(nat).
% 25.54/25.35 ** KEPT (pick-wt=14): 294 [] hAPP(nat,nat,power_power(nat,A),B)!=zero_zero(nat)|A=zero_zero(nat).
% 25.54/25.35 ** KEPT (pick-wt=18): 295 [] hAPP(nat,nat,power_power(nat,A),B)=zero_zero(nat)|B=zero_zero(nat)|A!=zero_zero(nat).
% 25.54/25.35 ** KEPT (pick-wt=44): 296 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),$f4(B,A))).
% 25.54/25.35 ** KEPT (pick-wt=39): 297 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B))|hAPP(nat,real,power_power(real,$f4(B,A)),A)=B.
% 25.54/25.35 ** KEPT (pick-wt=56): 298 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C))|hAPP(nat,real,power_power(real,C),A)!=B|C=$f4(B,A).
% 25.54/25.35 ** KEPT (pick-wt=44): 299 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),$f5(B,A))).
% 25.54/25.35 ** KEPT (pick-wt=39): 300 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B))|hAPP(nat,real,power_power(real,$f5(B,A)),A)=B.
% 25.54/25.35 ** KEPT (pick-wt=23): 301 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls))|plus_plus(nat,number_number_of(nat,A),one_one(nat))=one_one(nat).
% 25.54/25.35 ** KEPT (pick-wt=23): 302 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls))|plus_plus(nat,one_one(nat),number_number_of(nat,A))=one_one(nat).
% 25.54/25.35 ** KEPT (pick-wt=32): 303 [] -ordered_ab_group_add(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),minus_minus(A,B,C)),zero_zero(A))).
% 25.54/25.35 ** KEPT (pick-wt=32): 304 [] -ordered_ab_group_add(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),minus_minus(A,B,C)),zero_zero(A))).
% 25.54/25.35 ** KEPT (pick-wt=11): 305 [] -comm_semiring_1(A)|times_times(A,B,C)=times_times(A,C,B).
% 25.54/25.35 ** KEPT (pick-wt=17): 306 [] -comm_semiring_1(A)|times_times(A,B,times_times(A,C,D))=times_times(A,C,times_times(A,B,D)).
% 25.54/25.35 ** KEPT (pick-wt=17): 308 [copy,307,flip.2] -comm_semiring_1(A)|times_times(A,times_times(A,B,C),D)=times_times(A,B,times_times(A,C,D)).
% 25.54/25.35 ** KEPT (pick-wt=17): 309 [] -ab_semigroup_mult(A)|times_times(A,times_times(A,B,C),D)=times_times(A,B,times_times(A,C,D)).
% 25.54/25.35 Following clause subsumed by 308 during input processing: 0 [] -comm_semiring_1(A)|times_times(A,times_times(A,B,C),D)=times_times(A,B,times_times(A,C,D)).
% 25.54/25.35 ** KEPT (pick-wt=17): 310 [] -comm_semiring_1(A)|times_times(A,times_times(A,B,C),D)=times_times(A,times_times(A,B,D),C).
% 25.54/25.35 Following clause subsumed by 308 during input processing: 0 [] -comm_semiring_1(A)|times_times(A,times_times(A,B,C),times_times(A,D,E))=times_times(A,B,times_times(A,C,times_times(A,D,E))).
% 25.54/25.35 Following clause subsumed by 306 during input processing: 0 [] -comm_semiring_1(A)|times_times(A,times_times(A,B,C),times_times(A,D,E))=times_times(A,D,times_times(A,times_times(A,B,C),E)).
% 25.54/25.35 ** KEPT (pick-wt=23): 311 [] -comm_semiring_1(A)|times_times(A,times_times(A,B,C),times_times(A,D,E))=times_times(A,times_times(A,B,D),times_times(A,C,E)).
% 25.54/25.35 ** KEPT (pick-wt=25): 312 [] -ab_group_add(A)|minus_minus(A,B,C)!=minus_minus(A,D,E)|ti(A,B)!=ti(A,C)|ti(A,D)=ti(A,E).
% 25.54/25.35 ** KEPT (pick-wt=25): 313 [] -ab_group_add(A)|minus_minus(A,B,C)!=minus_minus(A,D,E)|ti(A,B)=ti(A,C)|ti(A,D)!=ti(A,E).
% 25.54/25.35 ** KEPT (pick-wt=37): 314 [] -ordered_ab_group_add(A)|minus_minus(A,B,C)!=minus_minus(A,D,E)| -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)).
% 25.54/25.35 ** KEPT (pick-wt=37): 315 [] -ordered_ab_group_add(A)|minus_minus(A,B,C)!=minus_minus(A,D,E)|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)).
% 25.54/25.35 ** KEPT (pick-wt=43): 317 [copy,316,flip.4] -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))|number_number_of(A,times_times(int,B,C))=times_times(A,number_number_of(A,B),number_number_of(A,C)).
% 25.54/25.35 ** KEPT (pick-wt=39): 318 [] -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)).
% 25.54/25.35 ** KEPT (pick-wt=33): 319 [] -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).
% 25.54/25.35 ** KEPT (pick-wt=34): 320 [] -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)).
% 25.54/25.35 ** KEPT (pick-wt=34): 321 [] -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)).
% 25.54/25.35 ** KEPT (pick-wt=17): 322 [] -number_ring(A)|number_number_of(A,times_times(int,B,C))=times_times(A,number_number_of(A,B),number_number_of(A,C)).
% 25.54/25.35 Following clause subsumed by 322 during input processing: 0 [flip.2] -number_ring(A)|number_number_of(A,times_times(int,B,C))=times_times(A,number_number_of(A,B),number_number_of(A,C)).
% 25.54/25.35 ** KEPT (pick-wt=23): 324 [copy,323,flip.2] -number_ring(A)|times_times(A,number_number_of(A,times_times(int,B,C)),D)=times_times(A,number_number_of(A,B),times_times(A,number_number_of(A,C),D)).
% 25.54/25.35 ** KEPT (pick-wt=40): 325 [] -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))|nat_1(A)!=nat_1(B)|ti(int,A)=ti(int,B).
% 25.54/25.35 ** KEPT (pick-wt=40): 326 [] -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))|nat_1(A)=nat_1(B)|ti(int,A)!=ti(int,B).
% 25.54/25.35 ** KEPT (pick-wt=28): 327 [] -number(A)| -ring(A)|times_times(A,number_number_of(A,B),minus_minus(A,C,D))=minus_minus(A,times_times(A,number_number_of(A,B),C),times_times(A,number_number_of(A,B),D)).
% 25.54/25.35 ** KEPT (pick-wt=28): 328 [] -number(A)| -ring(A)|times_times(A,minus_minus(A,B,C),number_number_of(A,D))=minus_minus(A,times_times(A,B,number_number_of(A,D)),times_times(A,C,number_number_of(A,D))).
% 25.54/25.35 ** KEPT (pick-wt=17): 329 [] -number_ring(A)|number_number_of(A,minus_minus(int,B,C))=minus_minus(A,number_number_of(A,B),number_number_of(A,C)).
% 25.54/25.35 ** KEPT (pick-wt=26): 330 [] -semiring_1(A)|hAPP(nat,A,semiring_1_of_nat(A),times_times(nat,B,C))=times_times(A,hAPP(nat,A,semiring_1_of_nat(A),B),hAPP(nat,A,semiring_1_of_nat(A),C)).
% 25.54/25.35 ** KEPT (pick-wt=38): 331 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C)).
% 25.54/25.35 ** KEPT (pick-wt=38): 332 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C)).
% 25.54/25.35 ** KEPT (pick-wt=11): 334 [copy,333,flip.2] -hBOOL(A)|nat_1(if(int,A,B,C))=nat_1(B).
% 25.54/25.35 ** KEPT (pick-wt=47): 335 [] -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),times_times(A,B,C)),zero_zero(A))).
% 25.54/25.35 ** KEPT (pick-wt=47): 336 [] -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),times_times(A,B,C)),zero_zero(A))).
% 25.54/25.35 ** KEPT (pick-wt=47): 337 [] -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)),times_times(A,B,C))).
% 25.54/25.35 ** KEPT (pick-wt=47): 338 [] -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)),times_times(A,B,C))).
% 25.54/25.35 ** KEPT (pick-wt=75): 339 [] -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),times_times(A,B,D)),times_times(A,C,E))).
% 25.54/25.35 ** KEPT (pick-wt=75): 340 [] -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),times_times(A,B,D)),times_times(A,C,E))).
% 25.54/25.35 ** KEPT (pick-wt=48): 341 [] -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),times_times(A,D,C)),times_times(A,D,B))).
% 25.54/25.35 ** KEPT (pick-wt=48): 342 [] -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),times_times(A,C,D)),times_times(A,B,D))).
% 25.54/25.35 ** KEPT (pick-wt=48): 343 [] -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),times_times(A,D,B)),times_times(A,D,C))).
% 25.54/25.35 ** KEPT (pick-wt=48): 344 [] -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),times_times(A,D,B)),times_times(A,D,C))).
% 25.54/25.35 ** KEPT (pick-wt=48): 345 [] -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),times_times(A,B,D)),times_times(A,C,D))).
% 25.54/25.35 Following clause subsumed by 338 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)),times_times(A,B,C))).
% 25.54/25.35 Following clause subsumed by 336 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),times_times(A,B,C)),zero_zero(A))).
% 25.54/25.35 Following clause subsumed by 336 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),times_times(A,C,B)),zero_zero(A))).
% 25.54/25.35 Following clause subsumed by 335 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),times_times(A,B,C)),zero_zero(A))).
% 25.54/25.35 Following clause subsumed by 325 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_e_q(int),zero_zero(int)),B))|nat_1(A)!=nat_1(B)|ti(int,A)=ti(int,B).
% 25.54/25.35 Following clause subsumed by 326 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_e_q(int),zero_zero(int)),B))|nat_1(A)=nat_1(B)|ti(int,A)!=ti(int,B).
% 25.54/25.35 ** KEPT (pick-wt=45): 346 [] -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)),times_times(int,A,B))).
% 25.54/25.36 ** KEPT (pick-wt=47): 347 [] -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)),times_times(A,B,C))).
% 25.54/25.36 ** KEPT (pick-wt=49): 348 [] -ordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,times_times(A,B,C),D)),plus_plus(A,times_times(A,E,C),F)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,times_times(A,minus_minus(A,B,E),C),D)),F)).
% 25.54/25.36 ** KEPT (pick-wt=49): 349 [] -ordered_ring(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,times_times(A,B,C),D)),plus_plus(A,times_times(A,E,C),F)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,times_times(A,minus_minus(A,B,E),C),D)),F)).
% 25.54/25.36 ** KEPT (pick-wt=31): 350 [] -ring(A)|plus_plus(A,times_times(A,B,C),D)!=plus_plus(A,times_times(A,E,C),F)|plus_plus(A,times_times(A,minus_minus(A,B,E),C),D)=ti(A,F).
% 25.54/25.36 ** KEPT (pick-wt=31): 351 [] -ring(A)|plus_plus(A,times_times(A,B,C),D)=plus_plus(A,times_times(A,E,C),F)|plus_plus(A,times_times(A,minus_minus(A,B,E),C),D)!=ti(A,F).
% 25.54/25.36 ** KEPT (pick-wt=49): 352 [] -ordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,times_times(A,B,C),D)),plus_plus(A,times_times(A,E,C),F)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),plus_plus(A,times_times(A,minus_minus(A,E,B),C),F))).
% 25.54/25.36 ** KEPT (pick-wt=49): 353 [] -ordered_ring(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,times_times(A,B,C),D)),plus_plus(A,times_times(A,E,C),F)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),plus_plus(A,times_times(A,minus_minus(A,E,B),C),F))).
% 25.54/25.36 ** KEPT (pick-wt=31): 354 [] -ring(A)|plus_plus(A,times_times(A,B,C),D)!=plus_plus(A,times_times(A,E,C),F)|ti(A,D)=plus_plus(A,times_times(A,minus_minus(A,E,B),C),F).
% 25.54/25.36 ** KEPT (pick-wt=31): 355 [] -ring(A)|plus_plus(A,times_times(A,B,C),D)=plus_plus(A,times_times(A,E,C),F)|ti(A,D)!=plus_plus(A,times_times(A,minus_minus(A,E,B),C),F).
% 25.54/25.36 ** KEPT (pick-wt=29): 357 [copy,356,flip.2] -ring(A)|plus_plus(A,times_times(A,B,minus_minus(A,C,D)),times_times(A,minus_minus(A,B,E),D))=minus_minus(A,times_times(A,B,C),times_times(A,E,D)).
% 25.54/25.36 ** KEPT (pick-wt=47): 358 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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))).
% 25.54/25.36 ** KEPT (pick-wt=47): 359 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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)).
% 25.54/25.36 ** KEPT (pick-wt=47): 360 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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))).
% 25.54/25.36 ** KEPT (pick-wt=47): 361 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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)).
% 25.54/25.36 ** KEPT (pick-wt=47): 362 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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))).
% 25.54/25.36 ** KEPT (pick-wt=47): 363 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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)).
% 25.54/25.36 ** KEPT (pick-wt=47): 364 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(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))).
% 25.54/25.36 ** KEPT (pick-wt=47): 365 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(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))).
% 25.54/25.36 ** KEPT (pick-wt=47): 366 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(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))).
% 25.54/25.36 ** KEPT (pick-wt=47): 367 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(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))).
% 25.54/25.36 ** KEPT (pick-wt=47): 368 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(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)).
% 25.54/25.36 ** KEPT (pick-wt=47): 369 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(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))).
% 25.54/25.36 ** KEPT (pick-wt=28): 370 [] -hBOOL(hAPP(nat,bool,A,$f6(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))|hBOOL(hAPP(nat,bool,A,nat_1(B))).
% 25.54/25.36 ** KEPT (pick-wt=14): 371 [] hBOOL(hAPP(nat,bool,A,B))| -hBOOL(hAPP(nat,bool,A,nat_1($f7(A)))).
% 25.54/25.36 ** KEPT (pick-wt=21): 372 [] -hBOOL(hAPP(nat,bool,A,B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f8(A))).
% 25.54/25.36 ** KEPT (pick-wt=14): 373 [] -hBOOL(hAPP(nat,bool,A,B))|hBOOL(hAPP(nat,bool,A,nat_1($f8(A)))).
% 25.54/25.36 ** KEPT (pick-wt=28): 374 [] hBOOL(hAPP(nat,bool,A,$f9(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))| -hBOOL(hAPP(nat,bool,A,nat_1(B))).
% 25.54/25.36 ** KEPT (pick-wt=19): 375 [] -linordered_ring(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),times_times(A,B,B))).
% 25.54/25.36 ** KEPT (pick-wt=49): 376 [] -ordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),plus_plus(A,times_times(A,B,C),D)),plus_plus(A,times_times(A,E,C),F)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),plus_plus(A,times_times(A,minus_minus(A,B,E),C),D)),F)).
% 25.54/25.36 ** KEPT (pick-wt=49): 377 [] -ordered_ring(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),plus_plus(A,times_times(A,B,C),D)),plus_plus(A,times_times(A,E,C),F)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),plus_plus(A,times_times(A,minus_minus(A,B,E),C),D)),F)).
% 25.54/25.36 ** KEPT (pick-wt=49): 378 [] -ordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),plus_plus(A,times_times(A,B,C),D)),plus_plus(A,times_times(A,E,C),F)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),plus_plus(A,times_times(A,minus_minus(A,E,B),C),F))).
% 25.54/25.36 ** KEPT (pick-wt=49): 379 [] -ordered_ring(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),plus_plus(A,times_times(A,B,C),D)),plus_plus(A,times_times(A,E,C),F)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),plus_plus(A,times_times(A,minus_minus(A,E,B),C),F))).
% 25.54/25.36 ** KEPT (pick-wt=23): 381 [copy,380,flip.2] -ring_1(A)|times_times(A,plus_plus(A,B,one_one(A)),minus_minus(A,B,one_one(A)))=minus_minus(A,times_times(A,B,B),one_one(A)).
% 25.54/25.36 ** KEPT (pick-wt=48): 382 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),times_times(A,B,C)),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)).
% 25.54/25.36 ** KEPT (pick-wt=48): 383 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),times_times(A,B,C)),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)).
% 25.54/25.36 ** KEPT (pick-wt=48): 384 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),times_times(A,B,C)),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)).
% 25.54/25.36 ** KEPT (pick-wt=48): 385 [] -linordered_semiring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),times_times(A,B,C)),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)).
% 25.54/25.36 ** KEPT (pick-wt=48): 386 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),times_times(A,B,C)),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)).
% 25.54/25.36 ** KEPT (pick-wt=48): 387 [] -linordered_semiring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),times_times(A,B,C)),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)).
% 25.54/25.36 ** KEPT (pick-wt=75): 388 [] -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),times_times(A,B,D)),times_times(A,C,E))).
% 25.54/25.36 ** KEPT (pick-wt=75): 389 [] -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),times_times(A,B,D)),times_times(A,C,E))).
% 25.54/25.36 ** KEPT (pick-wt=75): 390 [] -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),times_times(A,B,D)),times_times(A,C,E))).
% 25.54/25.36 ** KEPT (pick-wt=75): 391 [] -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),times_times(A,B,D)),times_times(A,C,E))).
% 25.54/25.36 ** KEPT (pick-wt=48): 392 [] -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),times_times(A,B,C)),times_times(A,B,D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),C)).
% 25.54/25.36 ** KEPT (pick-wt=48): 393 [] -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),times_times(A,B,C)),times_times(A,B,D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),C)).
% 25.54/25.36 ** KEPT (pick-wt=48): 394 [] -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),times_times(A,B,C)),times_times(A,B,D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D)).
% 25.54/25.36 ** KEPT (pick-wt=48): 395 [] -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),times_times(A,B,C)),times_times(A,B,D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D)).
% 25.54/25.36 ** KEPT (pick-wt=25): 396 [] -linordered_ring(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),plus_plus(A,times_times(A,B,B),times_times(A,C,C)))).
% 25.54/25.36 ** KEPT (pick-wt=31): 397 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,times_times(A,B,B),times_times(A,C,C))),zero_zero(A)))|ti(A,B)=zero_zero(A).
% 25.54/25.36 ** KEPT (pick-wt=31): 398 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,times_times(A,B,B),times_times(A,C,C))),zero_zero(A)))|ti(A,C)=zero_zero(A).
% 25.54/25.36 ** KEPT (pick-wt=37): 399 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,times_times(A,B,B),times_times(A,C,C))),zero_zero(A)))|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A).
% 25.54/25.36 ** KEPT (pick-wt=60): 400 [] -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),times_times(A,B,C)),B)).
% 25.54/25.36 ** KEPT (pick-wt=60): 401 [] -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),times_times(A,C,B)),B)).
% 25.54/25.36 ** KEPT (pick-wt=19): 402 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),zero_zero(int)))|nat_1(A)=zero_zero(nat).
% 25.54/25.36 ** KEPT (pick-wt=19): 403 [] nat_1(A)!=zero_zero(nat)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),zero_zero(int))).
% 25.54/25.36 Following clause subsumed by 402 during input processing: 0 [] nat_1(A)=zero_zero(nat)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),zero_zero(int))).
% 25.54/25.36 ** KEPT (pick-wt=54): 404 [] -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))).
% 25.54/25.36 ** KEPT (pick-wt=25): 405 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|hAPP(nat,int,semiring_1_of_nat(int),nat_1(A))=ti(int,A).
% 25.54/25.36 ** KEPT (pick-wt=14): 406 [] hAPP(nat,int,semiring_1_of_nat(int),A)!=ti(int,B)|A=nat_1(B).
% 25.54/25.36 ** KEPT (pick-wt=24): 407 [] hAPP(nat,int,semiring_1_of_nat(int),A)!=ti(int,B)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B)).
% 25.54/25.36 ** KEPT (pick-wt=28): 408 [] hAPP(nat,int,semiring_1_of_nat(int),A)=ti(int,B)|A!=nat_1(B)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B)).
% 25.54/25.36 Following clause subsumed by 405 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|hAPP(nat,int,semiring_1_of_nat(int),nat_1(A))=ti(int,A).
% 25.54/25.36 ** KEPT (pick-wt=16): 409 [] -group_add(A)|minus_minus(A,B,C)!=zero_zero(A)|ti(A,B)=ti(A,C).
% 25.54/25.36 ** KEPT (pick-wt=16): 410 [] -group_add(A)|minus_minus(A,B,C)=zero_zero(A)|ti(A,B)!=ti(A,C).
% 25.54/25.36 ** KEPT (pick-wt=16): 411 [] -ab_group_add(A)|ti(A,B)!=ti(A,C)|minus_minus(A,B,C)=zero_zero(A).
% 25.54/25.36 ** KEPT (pick-wt=16): 412 [] -ab_group_add(A)|ti(A,B)=ti(A,C)|minus_minus(A,B,C)!=zero_zero(A).
% 25.54/25.36 ** KEPT (pick-wt=9): 413 [] -group_add(A)|minus_minus(A,B,B)=zero_zero(A).
% 25.54/25.36 ** KEPT (pick-wt=11): 414 [] -group_add(A)|minus_minus(A,B,zero_zero(A))=ti(A,B).
% 25.54/25.36 ** KEPT (pick-wt=37): 415 [] -ordered_ab_group_add(A)|minus_minus(A,B,C)!=minus_minus(A,D,E)| -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)).
% 25.54/25.36 ** KEPT (pick-wt=37): 416 [] -ordered_ab_group_add(A)|minus_minus(A,B,C)!=minus_minus(A,D,E)|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)).
% 25.54/25.36 ** KEPT (pick-wt=23): 418 [copy,417,flip.2] -ab_group_add(A)|plus_plus(A,minus_minus(A,B,C),minus_minus(A,D,E))=minus_minus(A,plus_plus(A,B,D),plus_plus(A,C,E)).
% 25.54/25.36 ** KEPT (pick-wt=13): 419 [] -group_add(A)|minus_minus(A,plus_plus(A,B,C),C)=ti(A,B).
% 25.54/25.36 ** KEPT (pick-wt=13): 420 [] -group_add(A)|plus_plus(A,minus_minus(A,B,C),C)=ti(A,B).
% 25.54/25.36 ** KEPT (pick-wt=10): 421 [] -mult_zero(A)|times_times(A,zero_zero(A),B)=zero_zero(A).
% 25.54/25.36 ** KEPT (pick-wt=10): 422 [] -mult_zero(A)|times_times(A,B,zero_zero(A))=zero_zero(A).
% 25.54/25.36 ** KEPT (pick-wt=21): 423 [] -ring_n68954251visors(A)|times_times(A,B,C)!=zero_zero(A)|ti(A,B)=zero_zero(A)|ti(A,C)=zero_zero(A).
% 25.54/25.36 ** KEPT (pick-wt=15): 424 [] -ring_n68954251visors(A)|times_times(A,B,C)=zero_zero(A)|ti(A,B)!=zero_zero(A).
% 25.54/25.36 ** KEPT (pick-wt=15): 425 [] -ring_n68954251visors(A)|times_times(A,B,C)=zero_zero(A)|ti(A,C)!=zero_zero(A).
% 25.54/25.36 ** KEPT (pick-wt=21): 426 [] -no_zero_divisors(A)|ti(A,B)=zero_zero(A)|ti(A,C)=zero_zero(A)|times_times(A,B,C)!=zero_zero(A).
% 25.54/25.36 Following clause subsumed by 426 during input processing: 0 [] -no_zero_divisors(A)|times_times(A,B,C)!=zero_zero(A)|ti(A,B)=zero_zero(A)|ti(A,C)=zero_zero(A).
% 25.54/25.36 ** KEPT (pick-wt=10): 427 [] -comm_semiring_1(A)|times_times(A,B,zero_zero(A))=zero_zero(A).
% 25.54/25.36 ** KEPT (pick-wt=10): 428 [] -comm_semiring_1(A)|times_times(A,zero_zero(A),B)=zero_zero(A).
% 25.54/25.36 ** KEPT (pick-wt=17): 429 [] minus_minus(nat,A,B)!=zero_zero(nat)|minus_minus(nat,B,A)!=zero_zero(nat)|A=B.
% 25.54/25.36 ** KEPT (pick-wt=20): 430 [] -comm_semiring(A)|times_times(A,plus_plus(A,B,C),D)=plus_plus(A,times_times(A,B,D),times_times(A,C,D)).
% 25.54/25.36 ** KEPT (pick-wt=26): 432 [copy,431,flip.2] -semiring(A)|plus_plus(A,times_times(A,plus_plus(A,B,C),D),E)=plus_plus(A,times_times(A,B,D),plus_plus(A,times_times(A,C,D),E)).
% 25.54/25.36 ** KEPT (pick-wt=37): 433 [] -semiri456707255roduct(A)|plus_plus(A,times_times(A,B,C),times_times(A,D,E))!=plus_plus(A,times_times(A,B,E),times_times(A,D,C))|ti(A,B)=ti(A,D)|ti(A,C)=ti(A,E).
% 25.54/25.36 ** KEPT (pick-wt=30): 434 [] -semiri456707255roduct(A)|plus_plus(A,times_times(A,B,C),times_times(A,D,E))=plus_plus(A,times_times(A,B,E),times_times(A,D,C))|ti(A,B)!=ti(A,D).
% 25.54/25.36 ** KEPT (pick-wt=30): 435 [] -semiri456707255roduct(A)|plus_plus(A,times_times(A,B,C),times_times(A,D,E))=plus_plus(A,times_times(A,B,E),times_times(A,D,C))|ti(A,C)!=ti(A,E).
% 25.54/25.36 ** KEPT (pick-wt=20): 437 [copy,436,flip.2] -comm_semiring_1(A)|times_times(A,plus_plus(A,B,C),D)=plus_plus(A,times_times(A,B,D),times_times(A,C,D)).
% 25.54/25.36 Following clause subsumed by 437 during input processing: 0 [] -comm_semiring_1(A)|times_times(A,plus_plus(A,B,C),D)=plus_plus(A,times_times(A,B,D),times_times(A,C,D)).
% 25.54/25.36 Following clause subsumed by 433 during input processing: 0 [] -semiri456707255roduct(A)|ti(A,B)=ti(A,C)|ti(A,D)=ti(A,E)|plus_plus(A,times_times(A,B,D),times_times(A,C,E))!=plus_plus(A,times_times(A,B,E),times_times(A,C,D)).
% 25.54/25.36 Following clause subsumed by 434 during input processing: 0 [] -semiri456707255roduct(A)|ti(A,B)!=ti(A,C)|plus_plus(A,times_times(A,B,D),times_times(A,C,E))=plus_plus(A,times_times(A,B,E),times_times(A,C,D)).
% 25.54/25.36 Following clause subsumed by 435 during input processing: 0 [] -semiri456707255roduct(A)|ti(A,B)!=ti(A,C)|plus_plus(A,times_times(A,D,B),times_times(A,E,C))=plus_plus(A,times_times(A,D,C),times_times(A,E,B)).
% 25.54/25.36 ** KEPT (pick-wt=20): 438 [] -comm_semiring_1(A)|times_times(A,B,plus_plus(A,C,D))=plus_plus(A,times_times(A,B,C),times_times(A,B,D)).
% 25.54/25.36 ** KEPT (pick-wt=11): 439 [] -comm_monoid_mult(A)|times_times(A,B,one_one(A))=ti(A,B).
% 25.54/25.36 ** KEPT (pick-wt=11): 440 [] -comm_semiring_1(A)|times_times(A,B,one_one(A))=ti(A,B).
% 25.54/25.36 ** KEPT (pick-wt=11): 441 [] -monoid_mult(A)|times_times(A,B,one_one(A))=ti(A,B).
% 25.54/25.36 ** KEPT (pick-wt=11): 442 [] -comm_monoid_mult(A)|times_times(A,one_one(A),B)=ti(A,B).
% 25.54/25.36 ** KEPT (pick-wt=11): 443 [] -comm_semiring_1(A)|times_times(A,one_one(A),B)=ti(A,B).
% 25.54/25.36 ** KEPT (pick-wt=11): 444 [] -monoid_mult(A)|times_times(A,one_one(A),B)=ti(A,B).
% 25.54/25.36 ** KEPT (pick-wt=34): 445 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,B,C)),plus_plus(A,B,D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D)).
% 25.54/25.36 ** KEPT (pick-wt=34): 446 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,B,C)),plus_plus(A,D,C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),D)).
% 25.54/25.36 ** KEPT (pick-wt=47): 447 [] -ordere779506340up_add(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),plus_plus(A,B,D)),plus_plus(A,C,E))).
% 25.54/25.36 ** KEPT (pick-wt=34): 448 [] -ordere779506340up_add(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),plus_plus(A,D,B)),plus_plus(A,D,C))).
% 25.54/25.36 ** KEPT (pick-wt=34): 449 [] -ordere779506340up_add(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),plus_plus(A,B,D)),plus_plus(A,C,D))).
% 25.54/25.36 Following clause subsumed by 445 during input processing: 0 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,B,C)),plus_plus(A,B,D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D)).
% 25.54/25.36 ** KEPT (pick-wt=34): 450 [] -ordere236663937imp_le(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,B,C)),plus_plus(A,B,D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D)).
% 25.54/25.36 Following clause subsumed by 446 during input processing: 0 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,B,C)),plus_plus(A,D,C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),D)).
% 25.54/25.36 ** KEPT (pick-wt=34): 451 [] -ordere236663937imp_le(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,B,C)),plus_plus(A,D,C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),D)).
% 25.54/25.36 ** KEPT (pick-wt=29): 452 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),minus_minus(nat,A,C)),B)).
% 25.54/25.36 ** KEPT (pick-wt=45): 453 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),minus_minus(nat,C,B)),minus_minus(nat,C,A))).
% 25.54/25.36 ** KEPT (pick-wt=23): 454 [] -monoid_mult(A)|times_times(A,hAPP(nat,A,power_power(A,B),C),B)=times_times(A,B,hAPP(nat,A,power_power(A,B),C)).
% 25.54/25.36 ** KEPT (pick-wt=29): 455 [] -comm_monoid_mult(A)|hAPP(nat,A,power_power(A,times_times(A,B,C)),D)=times_times(A,hAPP(nat,A,power_power(A,B),D),hAPP(nat,A,power_power(A,C),D)).
% 25.54/25.36 ** KEPT (pick-wt=29): 456 [] -comm_semiring_1(A)|hAPP(nat,A,power_power(A,times_times(A,B,C)),D)=times_times(A,hAPP(nat,A,power_power(A,B),D),hAPP(nat,A,power_power(A,C),D)).
% 25.54/25.36 ** KEPT (pick-wt=28): 457 [] -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)).
% 25.54/25.36 ** KEPT (pick-wt=28): 458 [] 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)).
% 25.54/25.36 Following clause subsumed by 457 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)).
% 25.54/25.36 Following clause subsumed by 458 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)).
% 25.54/25.36 ** KEPT (pick-wt=28): 459 [] -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)).
% 25.54/25.36 ** KEPT (pick-wt=28): 460 [] 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)).
% 25.54/25.36 Following clause subsumed by 459 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)).
% 25.54/25.36 Following clause subsumed by 460 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)).
% 25.54/25.36 ** KEPT (pick-wt=26): 461 [] -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)).
% 25.54/25.36 ** KEPT (pick-wt=20): 462 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|ti(int,A)!=ti(int,B).
% 25.54/25.36 ** KEPT (pick-wt=33): 463 [] 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).
% 25.54/25.36 ** KEPT (pick-wt=32): 464 [] -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),plus_plus(int,C,A)),plus_plus(int,C,B))).
% 25.54/25.36 ** KEPT (pick-wt=30): 465 [] -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)).
% 25.54/25.36 ** KEPT (pick-wt=30): 466 [] 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)).
% 25.54/25.36 ** KEPT (pick-wt=85): 467 [] -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))|plus_plus(A,E,F)!=one_one(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,times_times(A,E,B),times_times(A,F,D))),C)).
% 25.54/25.36 ** KEPT (pick-wt=56): 468 [] -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(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(A)),nat_1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 25.54/25.36 ** KEPT (pick-wt=56): 469 [] -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(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(A)),nat_1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 25.54/25.36 ** KEPT (pick-wt=42): 470 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(A)),nat_1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 25.54/25.36 ** KEPT (pick-wt=42): 471 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(A)),nat_1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 25.54/25.36 ** KEPT (pick-wt=33): 472 [] -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)).
% 25.54/25.36 ** KEPT (pick-wt=33): 473 [] -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)).
% 25.54/25.36 ** KEPT (pick-wt=33): 474 [] -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)).
% 25.54/25.36 ** KEPT (pick-wt=33): 475 [] -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)).
% 25.54/25.36 ** KEPT (pick-wt=68): 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),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))).
% 25.54/25.36 ** KEPT (pick-wt=54): 477 [] -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)).
% 25.54/25.36 ** KEPT (pick-wt=54): 478 [] -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)).
% 25.54/25.36 Following clause subsumed by 477 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)).
% 25.54/25.36 ** KEPT (pick-wt=28): 479 [] A!=nat_1(B)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))|ti(int,B)=hAPP(nat,int,semiring_1_of_nat(int),A).
% 25.54/25.36 ** KEPT (pick-wt=22): 480 [] A!=nat_1(B)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))|A=zero_zero(nat).
% 25.54/25.36 ** KEPT (pick-wt=22): 481 [] A=nat_1(B)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))|A!=zero_zero(nat).
% 25.54/25.36 ** KEPT (pick-wt=28): 482 [] A=nat_1(B)|ti(int,B)!=hAPP(nat,int,semiring_1_of_nat(int),A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B)).
% 25.54/25.36 ** KEPT (pick-wt=18): 483 [] A=nat_1(B)|ti(int,B)!=hAPP(nat,int,semiring_1_of_nat(int),A)|A!=zero_zero(nat).
% 25.54/25.36 ** KEPT (pick-wt=28): 484 [] nat_1(A)!=B| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|ti(int,A)=hAPP(nat,int,semiring_1_of_nat(int),B).
% 25.54/25.36 ** KEPT (pick-wt=22): 485 [] nat_1(A)!=B|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|B=zero_zero(nat).
% 25.54/25.36 ** KEPT (pick-wt=22): 486 [] nat_1(A)=B|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|B!=zero_zero(nat).
% 25.54/25.36 ** KEPT (pick-wt=28): 487 [] nat_1(A)=B|ti(int,A)!=hAPP(nat,int,semiring_1_of_nat(int),B)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A)).
% 25.54/25.36 ** KEPT (pick-wt=18): 488 [] nat_1(A)=B|ti(int,A)!=hAPP(nat,int,semiring_1_of_nat(int),B)|B!=zero_zero(nat).
% 25.54/25.36 ** KEPT (pick-wt=40): 490 [copy,489,flip.3] -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))|nat_1(plus_plus(int,A,B))=plus_plus(nat,nat_1(A),nat_1(B)).
% 25.54/25.36 Following clause subsumed by 490 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_e_q(int),zero_zero(int)),B))|nat_1(plus_plus(int,A,B))=plus_plus(nat,nat_1(A),nat_1(B)).
% 25.54/25.36 ** KEPT (pick-wt=16): 491 [] hAPP(nat,int,semiring_1_of_nat(int),A)!=number_number_of(int,B)|A=nat_1(number_number_of(int,B)).
% 25.54/25.36 ** KEPT (pick-wt=26): 492 [] hAPP(nat,int,semiring_1_of_nat(int),A)!=number_number_of(int,B)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,B))).
% 25.54/25.36 ** KEPT (pick-wt=32): 493 [] hAPP(nat,int,semiring_1_of_nat(int),A)=number_number_of(int,B)|A!=nat_1(number_number_of(int,B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,B))).
% 25.54/25.36 ** KEPT (pick-wt=31): 495 [copy,494,flip.2] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|nat_1(hAPP(nat,int,power_power(int,A),B))=hAPP(nat,nat,power_power(nat,nat_1(A)),B).
% 25.54/25.36 Following clause subsumed by 495 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|nat_1(hAPP(nat,int,power_power(int,A),B))=hAPP(nat,nat,power_power(nat,nat_1(A)),B).
% 25.54/25.36 ** KEPT (pick-wt=85): 496 [] -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))|plus_plus(A,E,F)!=one_one(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),plus_plus(A,times_times(A,E,B),times_times(A,F,D))),C)).
% 25.54/25.36 ** KEPT (pick-wt=46): 497 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(A)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(nat,int,semiring_1_of_nat(int),B))).
% 25.54/25.36 ** KEPT (pick-wt=46): 498 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(A)),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(nat,int,semiring_1_of_nat(int),B))).
% 25.54/25.36 ** KEPT (pick-wt=34): 499 [] -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)).
% 25.54/25.36 ** KEPT (pick-wt=34): 500 [] -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)).
% 25.54/25.36 ** KEPT (pick-wt=34): 501 [] -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))).
% 25.54/25.36 ** KEPT (pick-wt=34): 502 [] -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))).
% 25.54/25.36 ** KEPT (pick-wt=38): 503 [] -monoid_mult(A)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B))|times_times(A,hAPP(nat,A,power_power(A,C),minus_minus(nat,B,one_one(nat))),C)=hAPP(nat,A,power_power(A,C),B).
% 25.54/25.36 ** KEPT (pick-wt=32): 504 [] -ordered_ab_group_add(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),minus_minus(A,B,C)),zero_zero(A))).
% 25.54/25.36 ** KEPT (pick-wt=32): 505 [] -ordered_ab_group_add(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),minus_minus(A,B,C)),zero_zero(A))).
% 25.54/25.36 ** KEPT (pick-wt=19): 506 [] -linordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),times_times(A,B,B)),zero_zero(A))).
% 25.54/25.36 ** KEPT (pick-wt=49): 507 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),times_times(A,B,C)),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))).
% 25.54/25.36 ** KEPT (pick-wt=48): 508 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),times_times(A,B,C)),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)).
% 25.54/25.36 ** KEPT (pick-wt=48): 509 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),times_times(A,B,C)),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))).
% 25.54/25.36 ** KEPT (pick-wt=47): 510 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),times_times(A,B,C)),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)).
% 25.54/25.36 ** KEPT (pick-wt=48): 511 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),times_times(A,B,C)),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)).
% 25.54/25.36 ** KEPT (pick-wt=48): 512 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),times_times(A,B,C)),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)).
% 25.54/25.36 ** KEPT (pick-wt=49): 513 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),times_times(A,B,C)),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))).
% 25.54/25.36 ** KEPT (pick-wt=48): 514 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),times_times(A,B,C)),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)).
% 25.54/25.36 ** KEPT (pick-wt=48): 515 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),times_times(A,B,C)),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))).
% 25.54/25.36 ** KEPT (pick-wt=47): 516 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),times_times(A,B,C)),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)).
% 25.54/25.36 ** KEPT (pick-wt=48): 517 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),times_times(A,B,C)),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)).
% 25.54/25.36 ** KEPT (pick-wt=48): 518 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),times_times(A,B,C)),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)).
% 25.54/25.36 ** KEPT (pick-wt=48): 519 [] -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),times_times(A,B,C)),times_times(A,B,D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 25.54/25.36 Following clause subsumed by 517 during input processing: 0 [] -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),times_times(A,B,C)),times_times(A,B,D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 25.54/25.36 ** KEPT (pick-wt=47): 520 [] -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)),times_times(A,B,C))).
% 25.54/25.36 ** KEPT (pick-wt=47): 521 [] -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),times_times(A,B,C)),zero_zero(A))).
% 25.54/25.36 ** KEPT (pick-wt=47): 522 [] -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),times_times(A,C,B)),zero_zero(A))).
% 25.54/25.36 ** KEPT (pick-wt=47): 523 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(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)).
% 25.54/25.36 ** KEPT (pick-wt=47): 524 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(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)).
% 25.54/25.36 ** KEPT (pick-wt=48): 525 [] -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),times_times(A,B,C)),times_times(A,B,D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)).
% 25.54/25.36 Following clause subsumed by 518 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),times_times(A,B,C)),times_times(A,B,D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)).
% 25.54/25.36 Following clause subsumed by 522 during input processing: 0 [] -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),times_times(A,B,C)),zero_zero(A))).
% 25.54/25.36 ** KEPT (pick-wt=47): 526 [] -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)),times_times(A,B,C))).
% 25.54/25.36 ** KEPT (pick-wt=48): 527 [] -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),times_times(A,B,D)),times_times(A,C,D))).
% 25.54/25.36 ** KEPT (pick-wt=48): 528 [] -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),times_times(A,D,B)),times_times(A,D,C))).
% 25.54/25.36 ** KEPT (pick-wt=48): 529 [] -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),times_times(A,D,B)),times_times(A,D,C))).
% 25.54/25.36 Following clause subsumed by 512 during input processing: 0 [] -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),times_times(A,C,D)),times_times(A,B,D))).
% 25.54/25.36 Following clause subsumed by 518 during input processing: 0 [] -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),times_times(A,D,C)),times_times(A,D,B))).
% 25.54/25.36 ** KEPT (pick-wt=21): 530 [] -linord581940658strict(A)|plus_plus(A,times_times(A,B,B),times_times(A,C,C))!=zero_zero(A)|ti(A,B)=zero_zero(A).
% 25.54/25.36 ** KEPT (pick-wt=21): 531 [] -linord581940658strict(A)|plus_plus(A,times_times(A,B,B),times_times(A,C,C))!=zero_zero(A)|ti(A,C)=zero_zero(A).
% 25.54/25.36 ** KEPT (pick-wt=27): 532 [] -linord581940658strict(A)|plus_plus(A,times_times(A,B,B),times_times(A,C,C))=zero_zero(A)|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A).
% 25.54/25.36 ** KEPT (pick-wt=37): 533 [] -semiri456707255roduct(A)|ti(A,B)=zero_zero(A)|ti(A,C)!=ti(A,D)|ti(A,E)=ti(A,F)|plus_plus(A,C,times_times(A,B,E))!=plus_plus(A,D,times_times(A,B,F)).
% 25.54/25.36 ** KEPT (pick-wt=47): 534 [] -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)),times_times(A,B,C))).
% 25.54/25.36 ** KEPT (pick-wt=33): 535 [] -linord219039673up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),plus_plus(A,B,B)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B)).
% 25.54/25.36 ** KEPT (pick-wt=33): 536 [] -linord219039673up_add(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),plus_plus(A,B,B)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B)).
% 25.54/25.36 ** KEPT (pick-wt=33): 537 [] -linord219039673up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,B,B)),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),zero_zero(A))).
% 25.54/25.36 ** KEPT (pick-wt=33): 538 [] -linord219039673up_add(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),plus_plus(A,B,B)),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),zero_zero(A))).
% 25.54/25.37 ** KEPT (pick-wt=47): 539 [] -ordere216010020id_add(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)),plus_plus(A,B,C))).
% 25.54/25.37 ** KEPT (pick-wt=43): 540 [] -ordere216010020id_add(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))|plus_plus(A,B,C)!=zero_zero(A)|ti(A,B)=zero_zero(A).
% 25.54/25.37 ** KEPT (pick-wt=43): 541 [] -ordere216010020id_add(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))|plus_plus(A,B,C)!=zero_zero(A)|ti(A,C)=zero_zero(A).
% 25.54/25.37 ** KEPT (pick-wt=49): 542 [] -ordere216010020id_add(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))|plus_plus(A,B,C)=zero_zero(A)|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A).
% 25.54/25.37 ** KEPT (pick-wt=45): 543 [] -ordere216010020id_add(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),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),plus_plus(A,B,D))).
% 25.54/25.37 ** KEPT (pick-wt=45): 544 [] -ordere216010020id_add(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),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),plus_plus(A,D,B))).
% 25.54/25.37 ** KEPT (pick-wt=47): 545 [] -ordere216010020id_add(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),plus_plus(A,B,C)),zero_zero(A))).
% 25.54/25.37 ** KEPT (pick-wt=47): 546 [] -ordere223160158up_add(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(A),plus_plus(A,B,D)),plus_plus(A,C,E))).
% 25.54/25.37 ** KEPT (pick-wt=47): 547 [] -ordere223160158up_add(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),plus_plus(A,B,D)),plus_plus(A,C,E))).
% 25.54/25.37 ** KEPT (pick-wt=17): 548 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),zero_zero(A))).
% 25.54/25.37 ** KEPT (pick-wt=17): 549 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),one_one(A))).
% 25.54/25.37 ** KEPT (pick-wt=28): 550 [] -number(A)| -semiring(A)|times_times(A,number_number_of(A,B),plus_plus(A,C,D))=plus_plus(A,times_times(A,number_number_of(A,B),C),times_times(A,number_number_of(A,B),D)).
% 25.54/25.37 ** KEPT (pick-wt=28): 551 [] -number(A)| -semiring(A)|times_times(A,plus_plus(A,B,C),number_number_of(A,D))=plus_plus(A,times_times(A,B,number_number_of(A,D)),times_times(A,C,number_number_of(A,D))).
% 25.54/25.37 ** KEPT (pick-wt=16): 553 [copy,552,flip.2] -comm_semiring_1(A)|times_times(A,plus_plus(A,one_one(A),one_one(A)),B)=plus_plus(A,B,B).
% 25.54/25.37 ** KEPT (pick-wt=18): 555 [copy,554,flip.2] -comm_semiring_1(A)|times_times(A,plus_plus(A,B,one_one(A)),C)=plus_plus(A,C,times_times(A,B,C)).
% 25.54/25.37 ** KEPT (pick-wt=18): 557 [copy,556,flip.2] -comm_semiring_1(A)|times_times(A,plus_plus(A,B,one_one(A)),C)=plus_plus(A,times_times(A,B,C),C).
% 25.54/25.37 ** KEPT (pick-wt=38): 558 [] -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))).
% 25.54/25.37 ** KEPT (pick-wt=38): 559 [] -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))).
% 25.54/25.37 ** KEPT (pick-wt=36): 560 [] -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))).
% 25.54/25.37 ** KEPT (pick-wt=54): 561 [] -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))).
% 25.54/25.37 ** KEPT (pick-wt=30): 562 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),minus_minus(nat,A,B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)).
% 25.54/25.37 ** KEPT (pick-wt=30): 563 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),minus_minus(nat,A,B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)).
% 25.54/25.37 ** KEPT (pick-wt=44): 564 [] -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),zero_zero(nat)),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),minus_minus(nat,B,A)),B)).
% 25.54/25.37 ** KEPT (pick-wt=36): 565 [] -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))).
% 25.54/25.37 ** KEPT (pick-wt=32): 566 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),minus_minus(nat,B,C)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,A,C)),B)).
% 25.54/25.37 ** KEPT (pick-wt=32): 567 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),minus_minus(nat,B,C)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,A,C)),B)).
% 25.54/25.37 ** KEPT (pick-wt=21): 568 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))).
% 25.54/25.37 Following clause subsumed by 568 during input processing: 0 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))).
% 25.54/25.37 ** KEPT (pick-wt=29): 570 [copy,569,flip.2] -monoid_mult(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),plus_plus(nat,C,D)).
% 25.54/25.37 ** KEPT (pick-wt=29): 571 [] -comm_semiring_1(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),plus_plus(nat,C,D)).
% 25.54/25.37 ** KEPT (pick-wt=27): 572 [] -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)).
% 25.54/25.37 ** KEPT (pick-wt=27): 573 [] 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)).
% 25.54/25.37 ** KEPT (pick-wt=28): 574 [] -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)).
% 25.54/25.37 ** KEPT (pick-wt=28): 575 [] 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)).
% 25.54/25.37 Following clause subsumed by 574 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)).
% 25.54/25.37 Following clause subsumed by 575 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)).
% 25.54/25.37 ** KEPT (pick-wt=27): 576 [] -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)).
% 25.54/25.37 ** KEPT (pick-wt=27): 577 [] 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)).
% 25.54/25.37 ** KEPT (pick-wt=27): 578 [] -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)).
% 25.54/25.37 ** KEPT (pick-wt=27): 579 [] 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)).
% 25.54/25.37 ** KEPT (pick-wt=45): 580 [] -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)),times_times(int,A,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)).
% 25.54/25.37 ** KEPT (pick-wt=46): 581 [] -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),times_times(int,C,A)),times_times(int,C,B))).
% 25.54/25.37 ** KEPT (pick-wt=45): 582 [] -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)),plus_plus(int,A,B))).
% 25.54/25.37 ** KEPT (pick-wt=47): 583 [] -semiring_1(A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))|hAPP(nat,A,semiring_1_of_nat(A),nat_1(times_times(int,number_number_of(int,bit0(bit1(pls))),B)))=plus_plus(A,hAPP(nat,A,semiring_1_of_nat(A),nat_1(B)),hAPP(nat,A,semiring_1_of_nat(A),nat_1(B))).
% 25.54/25.37 ** KEPT (pick-wt=45): 584 [] -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),plus_plus(int,A,C)),plus_plus(int,B,D))).
% 25.54/25.37 ** KEPT (pick-wt=32): 585 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,B,A))|hBOOL(hAPP(int,bool,B,hAPP(nat,int,semiring_1_of_nat(int),$f10(B)))).
% 25.54/25.37 ** KEPT (pick-wt=26): 586 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f11(A)))| -hBOOL(hAPP(int,bool,A,hAPP(nat,int,semiring_1_of_nat(int),B))).
% 25.54/25.37 ** KEPT (pick-wt=18): 587 [] hBOOL(hAPP(int,bool,A,$f11(A)))| -hBOOL(hAPP(int,bool,A,hAPP(nat,int,semiring_1_of_nat(int),B))).
% 25.54/25.37 ** KEPT (pick-wt=18): 588 [] -hBOOL(hAPP(int,bool,A,$f12(A)))|hBOOL(hAPP(int,bool,A,hAPP(nat,int,semiring_1_of_nat(int),B))).
% 25.54/25.37 ** KEPT (pick-wt=32): 589 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|hBOOL(hAPP(int,bool,B,A))| -hBOOL(hAPP(int,bool,B,hAPP(nat,int,semiring_1_of_nat(int),$f13(B)))).
% 25.54/25.37 ** KEPT (pick-wt=34): 590 [] -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))).
% 25.54/25.37 ** KEPT (pick-wt=28): 591 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))|ti(int,B)=plus_plus(int,A,hAPP(nat,int,semiring_1_of_nat(int),$f14(A,B))).
% 25.54/25.37 ** KEPT (pick-wt=26): 592 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))|ti(int,B)!=plus_plus(int,A,hAPP(nat,int,semiring_1_of_nat(int),C)).
% 25.54/25.37 ** KEPT (pick-wt=27): 593 [] -number_semiring(A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),B))|plus_plus(A,one_one(A),number_number_of(A,B))=number_number_of(A,succ(B)).
% 25.54/25.37 ** KEPT (pick-wt=27): 594 [] -number_semiring(A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),B))|plus_plus(A,number_number_of(A,B),one_one(A))=number_number_of(A,succ(B)).
% 25.54/25.37 ** KEPT (pick-wt=33): 595 [] -comm_semiring_1(A)|hAPP(nat,A,power_power(A,B),times_times(nat,number_number_of(nat,bit0(bit1(pls))),C))=times_times(A,hAPP(nat,A,power_power(A,B),C),hAPP(nat,A,power_power(A,B),C)).
% 25.54/25.37 ** KEPT (pick-wt=23): 596 [] -number_ring(A)|plus_plus(A,number_number_of(A,B),minus_minus(A,number_number_of(A,C),D))=minus_minus(A,number_number_of(A,plus_plus(int,B,C)),D).
% 25.54/25.37 ** KEPT (pick-wt=42): 597 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(B)),nat_1(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)).
% 25.54/25.37 ** KEPT (pick-wt=42): 598 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(B)),nat_1(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)).
% 25.54/25.37 ** KEPT (pick-wt=29): 599 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(A)),nat_1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)).
% 25.54/25.37 ** KEPT (pick-wt=28): 600 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(A)),nat_1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 25.54/25.37 Following clause subsumed by 598 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(A)),nat_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),A),B)).
% 25.54/25.37 ** KEPT (pick-wt=25): 601 [] -linordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),plus_plus(A,times_times(A,B,B),times_times(A,C,C))),zero_zero(A))).
% 25.54/25.37 ** KEPT (pick-wt=37): 602 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),plus_plus(A,times_times(A,B,B),times_times(A,C,C))))|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A).
% 25.54/25.37 ** KEPT (pick-wt=31): 603 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),plus_plus(A,times_times(A,B,B),times_times(A,C,C))))|ti(A,B)=zero_zero(A).
% 25.54/25.37 ** KEPT (pick-wt=31): 604 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),plus_plus(A,times_times(A,B,B),times_times(A,C,C))))|ti(A,C)=zero_zero(A).
% 25.54/25.37 ** KEPT (pick-wt=32): 605 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),nat_1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),B)).
% 25.54/25.37 ** KEPT (pick-wt=32): 606 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),nat_1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),B)).
% 25.54/25.37 ** KEPT (pick-wt=47): 607 [] -ordere216010020id_add(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),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),plus_plus(A,B,C))).
% 25.54/25.37 ** KEPT (pick-wt=47): 608 [] -ordere216010020id_add(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(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),plus_plus(A,B,C))).
% 25.54/25.37 ** KEPT (pick-wt=45): 609 [] -ordere216010020id_add(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),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),plus_plus(A,B,D))).
% 25.54/25.37 ** KEPT (pick-wt=45): 610 [] -ordere216010020id_add(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(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),plus_plus(A,B,D))).
% 25.54/25.37 ** KEPT (pick-wt=47): 611 [] -ordere216010020id_add(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),C),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),plus_plus(A,B,C)),zero_zero(A))).
% 25.54/25.37 ** KEPT (pick-wt=47): 612 [] -ordere216010020id_add(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(A),C),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),plus_plus(A,B,C)),zero_zero(A))).
% 25.54/25.37 ** KEPT (pick-wt=54): 613 [] -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)).
% 25.54/25.37 ** KEPT (pick-wt=39): 614 [] -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)),times_times(A,B,hAPP(nat,A,power_power(A,B),C)))).
% 25.54/25.37 ** KEPT (pick-wt=44): 615 [] -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)),times_times(A,B,hAPP(nat,A,power_power(A,B),C)))).
% 25.54/25.37 ** KEPT (pick-wt=13): 616 [] -number_ring(A)|times_times(A,B,number_number_of(A,bit1(pls)))=ti(A,B).
% 25.54/25.37 ** KEPT (pick-wt=13): 617 [] -number_ring(A)|times_times(A,number_number_of(A,bit1(pls)),B)=ti(A,B).
% 25.54/25.37 ** KEPT (pick-wt=29): 618 [] -hBOOL(hAPP(nat,bool,A,minus_minus(nat,B,C)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C))|hBOOL(hAPP(nat,bool,A,zero_zero(nat))).
% 25.54/25.37 ** KEPT (pick-wt=21): 619 [] -hBOOL(hAPP(nat,bool,A,minus_minus(nat,B,C)))|B!=plus_plus(nat,C,D)|hBOOL(hAPP(nat,bool,A,D)).
% 25.54/25.37 ** KEPT (pick-wt=31): 620 [] hBOOL(hAPP(nat,bool,A,minus_minus(nat,B,C)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C))| -hBOOL(hAPP(nat,bool,A,$f15(A,B,C))).
% 25.54/25.37 ** KEPT (pick-wt=25): 622 [copy,621,flip.3] hBOOL(hAPP(nat,bool,A,minus_minus(nat,B,C)))| -hBOOL(hAPP(nat,bool,A,zero_zero(nat)))|plus_plus(nat,C,$f15(A,B,C))=B.
% 25.54/25.37 ** KEPT (pick-wt=25): 623 [] hBOOL(hAPP(nat,bool,A,minus_minus(nat,B,C)))| -hBOOL(hAPP(nat,bool,A,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,A,$f15(A,B,C))).
% 25.54/25.37 Following clause subsumed by 618 during input processing: 0 [] -hBOOL(hAPP(nat,bool,A,minus_minus(nat,B,C)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C))|hBOOL(hAPP(nat,bool,A,zero_zero(nat))).
% 25.54/25.37 Following clause subsumed by 619 during input processing: 0 [] -hBOOL(hAPP(nat,bool,A,minus_minus(nat,B,C)))|B!=plus_plus(nat,C,D)|hBOOL(hAPP(nat,bool,A,D)).
% 25.54/25.37 ** KEPT (pick-wt=31): 624 [] hBOOL(hAPP(nat,bool,A,minus_minus(nat,B,C)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C))| -hBOOL(hAPP(nat,bool,A,$f16(A,B,C))).
% 25.54/25.37 ** KEPT (pick-wt=25): 626 [copy,625,flip.3] hBOOL(hAPP(nat,bool,A,minus_minus(nat,B,C)))| -hBOOL(hAPP(nat,bool,A,zero_zero(nat)))|plus_plus(nat,C,$f16(A,B,C))=B.
% 25.54/25.37 ** KEPT (pick-wt=25): 627 [] hBOOL(hAPP(nat,bool,A,minus_minus(nat,B,C)))| -hBOOL(hAPP(nat,bool,A,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,A,$f16(A,B,C))).
% 25.54/25.37 ** KEPT (pick-wt=19): 628 [] zero_zero(nat)!=number_number_of(nat,A)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)).
% 25.54/25.37 ** KEPT (pick-wt=19): 629 [] zero_zero(nat)=number_number_of(nat,A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)).
% 25.54/25.37 ** KEPT (pick-wt=19): 630 [] number_number_of(nat,A)!=zero_zero(nat)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)).
% 25.54/25.37 ** KEPT (pick-wt=19): 631 [] number_number_of(nat,A)=zero_zero(nat)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)).
% 25.54/25.37 ** KEPT (pick-wt=27): 632 [] -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)).
% 25.54/25.37 ** KEPT (pick-wt=27): 633 [] 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)).
% 25.54/25.37 ** KEPT (pick-wt=27): 634 [] -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)).
% 25.54/25.37 ** KEPT (pick-wt=27): 635 [] 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)).
% 25.54/25.37 ** KEPT (pick-wt=28): 636 [] -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)).
% 25.54/25.37 ** KEPT (pick-wt=28): 637 [] 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)).
% 25.54/25.37 Following clause subsumed by 636 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)).
% 25.54/25.37 Following clause subsumed by 637 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)).
% 25.54/25.37 ** KEPT (pick-wt=28): 638 [] -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)).
% 25.54/25.37 ** KEPT (pick-wt=28): 639 [] 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)).
% 25.54/25.37 Following clause subsumed by 638 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)).
% 25.54/25.37 Following clause subsumed by 639 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)).
% 25.54/25.37 ** KEPT (pick-wt=27): 640 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|times_times(int,A,B)!=one_one(int)|ti(int,A)=one_one(int).
% 25.54/25.37 ** KEPT (pick-wt=27): 641 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|times_times(int,A,B)!=one_one(int)|ti(int,B)=one_one(int).
% 25.54/25.37 ** KEPT (pick-wt=33): 642 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|times_times(int,A,B)=one_one(int)|ti(int,A)!=one_one(int)|ti(int,B)!=one_one(int).
% 25.54/25.37 ** KEPT (pick-wt=28): 643 [] -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)).
% 25.54/25.37 ** KEPT (pick-wt=28): 644 [] 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)).
% 25.54/25.37 ** KEPT (pick-wt=23): 645 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),A)),zero_zero(int)))|A=zero_zero(nat).
% 25.54/25.37 ** KEPT (pick-wt=23): 646 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),A)),zero_zero(int)))|A!=zero_zero(nat).
% 25.54/25.37 ** KEPT (pick-wt=30): 647 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),plus_plus(int,B,one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 25.54/25.37 ** KEPT (pick-wt=30): 648 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),plus_plus(int,B,one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 25.54/25.37 ** KEPT (pick-wt=30): 649 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),plus_plus(int,A,one_one(int))),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 25.54/25.37 ** KEPT (pick-wt=30): 650 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),plus_plus(int,A,one_one(int))),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 25.54/25.37 Following clause subsumed by 650 during input processing: 0 [] -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),plus_plus(int,A,one_one(int))),B)).
% 25.54/25.37 ** KEPT (pick-wt=54): 651 [] -number_ring(A)|hAPP(nat,A,power_power(A,minus_minus(A,B,C)),number_number_of(nat,bit0(bit1(pls))))=minus_minus(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))))),times_times(A,times_times(A,number_number_of(A,bit0(bit1(pls))),B),C)).
% 25.54/25.37 ** KEPT (pick-wt=29): 652 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),nat_1(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)).
% 25.54/25.37 ** KEPT (pick-wt=29): 653 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),nat_1(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)).
% 25.54/25.37 ** KEPT (pick-wt=23): 654 [] -hBOOL(hAPP(nat,bool,A,nat_1(B)))|ti(int,B)!=hAPP(nat,int,semiring_1_of_nat(int),C)|hBOOL(hAPP(nat,bool,A,C)).
% 25.54/25.37 ** KEPT (pick-wt=28): 655 [] -hBOOL(hAPP(nat,bool,A,nat_1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int)))|hBOOL(hAPP(nat,bool,A,zero_zero(nat))).
% 25.54/25.37 ** KEPT (pick-wt=26): 656 [] hBOOL(hAPP(nat,bool,A,nat_1(B)))|ti(int,B)=hAPP(nat,int,semiring_1_of_nat(int),$f17(A,B))| -hBOOL(hAPP(nat,bool,A,zero_zero(nat))).
% 25.54/25.37 ** KEPT (pick-wt=29): 657 [] hBOOL(hAPP(nat,bool,A,nat_1(B)))| -hBOOL(hAPP(nat,bool,A,$f17(A,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))).
% 25.54/25.37 ** KEPT (pick-wt=22): 658 [] hBOOL(hAPP(nat,bool,A,nat_1(B)))| -hBOOL(hAPP(nat,bool,A,$f17(A,B)))| -hBOOL(hAPP(nat,bool,A,zero_zero(nat))).
% 25.54/25.37 ** KEPT (pick-wt=58): 659 [] -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),times_times(A,B,hAPP(nat,A,power_power(A,B),C))),hAPP(nat,A,power_power(A,B),C))).
% 25.54/25.37 ** KEPT (pick-wt=18): 660 [] -number_ring(A)|times_times(A,plus_plus(A,one_one(A),one_one(A)),number_number_of(A,B))=number_number_of(A,bit0(B)).
% 25.54/25.37 ** KEPT (pick-wt=66): 661 [] -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).
% 25.54/25.37 ** KEPT (pick-wt=21): 662 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,bit1(bit1(pls))))=times_times(A,times_times(A,B,B),B).
% 25.54/25.37 ** KEPT (pick-wt=43): 664 [copy,663,flip.4] -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))|number_number_of(A,plus_plus(int,B,C))=plus_plus(A,number_number_of(A,B),number_number_of(A,C)).
% 25.54/25.37 ** KEPT (pick-wt=32): 665 [] -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)),plus_plus(int,one_one(int),A))).
% 25.54/25.37 ** KEPT (pick-wt=56): 666 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -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),ord_less(int),times_times(int,hAPP(nat,int,semiring_1_of_nat(int),C),A)),times_times(int,hAPP(nat,int,semiring_1_of_nat(int),C),B))).
% 25.54/25.37 ** KEPT (pick-wt=14): 667 [] -number_ring(A)|number_number_of(A,succ(B))=plus_plus(A,one_one(A),number_number_of(A,B)).
% 25.54/25.37 ** KEPT (pick-wt=15): 668 [] -number_ring(A)|times_times(A,B,number_number_of(A,bit0(bit1(pls))))=plus_plus(A,B,B).
% 25.54/25.37 ** KEPT (pick-wt=15): 669 [] -number_semiring(A)|times_times(A,B,number_number_of(A,bit0(bit1(pls))))=plus_plus(A,B,B).
% 25.54/25.37 ** KEPT (pick-wt=15): 670 [] -number_ring(A)|times_times(A,number_number_of(A,bit0(bit1(pls))),B)=plus_plus(A,B,B).
% 25.54/25.37 ** KEPT (pick-wt=15): 671 [] -number_semiring(A)|times_times(A,number_number_of(A,bit0(bit1(pls))),B)=plus_plus(A,B,B).
% 25.54/25.37 ** KEPT (pick-wt=68): 672 [] -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))).
% 25.54/25.37 ** KEPT (pick-wt=18): 673 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))=times_times(A,B,B).
% 25.54/25.37 ** KEPT (pick-wt=18): 675 [copy,674,flip.2] -comm_semiring_1(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))=times_times(A,B,B).
% 25.54/25.37 Following clause subsumed by 673 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))))=times_times(A,number_number_of(A,B),number_number_of(A,B)).
% 25.54/25.37 ** KEPT (pick-wt=26): 676 [] -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)))))).
% 25.54/25.37 ** KEPT (pick-wt=62): 677 [] -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)).
% 25.54/25.37 ** KEPT (pick-wt=60): 678 [] -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).
% 25.54/25.37 ** KEPT (pick-wt=30): 679 [] -number_ring(A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,B)))|hAPP(nat,A,semiring_1_of_nat(A),number_number_of(nat,B))=number_number_of(A,B).
% 25.54/25.37 ** KEPT (pick-wt=29): 680 [] -number_ring(A)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,B)))|hAPP(nat,A,semiring_1_of_nat(A),number_number_of(nat,B))=zero_zero(A).
% 25.54/25.37 ** KEPT (pick-wt=54): 681 [] -number_semiring(A)|hAPP(nat,A,power_power(A,plus_plus(A,B,C)),number_number_of(nat,bit0(bit1(pls))))=plus_plus(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))))),times_times(A,times_times(A,number_number_of(A,bit0(bit1(pls))),B),C)).
% 25.54/25.37 Following clause subsumed by 613 during input processing: 0 [] -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)).
% 25.54/25.37 ** KEPT (pick-wt=39): 682 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(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))))))).
% 25.54/25.37 ** KEPT (pick-wt=45): 683 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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).
% 25.54/25.37 ** KEPT (pick-wt=45): 684 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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).
% 25.54/25.37 ** KEPT (pick-wt=51): 685 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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).
% 25.54/25.37 ** KEPT (pick-wt=43): 686 [] -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).
% 25.54/25.37 ** KEPT (pick-wt=38): 688 [copy,687,flip.2] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|times_times(int,B,hAPP(nat,int,power_power(int,B),minus_minus(nat,nat_1(A),one_one(nat))))=hAPP(nat,int,power_power(int,B),nat_1(A)).
% 25.54/25.37 ** KEPT (pick-wt=53): 689 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|ti(int,A)!=plus_plus(int,B,times_times(int,A,C))| -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))).
% 25.54/25.37 ** KEPT (pick-wt=52): 690 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(
% 25.54/25.37 Search stopped in tp_alloc by max_mem option.
% 25.54/25.37 int)),A))|ti(int,A)!=plus_plus(int,B,times_times(int,A,C))| -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)).
% 25.54/25.37 ** KEPT (pick-wt=16): 691 [] -power(A)|B!=zero_zero(nat)|hAPP(nat,A,power_power(A,C),B)=one_one(A).
% 25.54/25.37 ** KEPT (pick-wt=28): 693 [copy,692,flip.3] -power(A)|B=zero_zero(nat)|times_times(A,C,hAPP(nat,A,power_power(A,C),minus_minus(nat,B,one_one(nat))))=hAPP(nat,A,power_power(A,C),B).
% 25.54/25.37 ** KEPT (pick-wt=61): 694 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),plus_plus(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)).
% 25.54/25.37 ** KEPT (pick-wt=62): 695 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),plus_plus(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))).
% 25.54/25.37
% 25.54/25.37 Search stopped in tp_alloc by max_mem option.
% 25.54/25.37
% 25.54/25.37 ============ end of search ============
% 25.54/25.37
% 25.54/25.37 -------------- statistics -------------
% 25.54/25.37 clauses given 0
% 25.54/25.37 clauses generated 0
% 25.54/25.37 clauses kept 664
% 25.54/25.37 clauses forward subsumed 84
% 25.54/25.37 clauses back subsumed 0
% 25.54/25.37 Kbytes malloced 11718
% 25.54/25.37
% 25.54/25.37 ----------- times (seconds) -----------
% 25.54/25.37 user CPU time 0.20 (0 hr, 0 min, 0 sec)
% 25.54/25.37 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 25.54/25.37 wall-clock time 25 (0 hr, 0 min, 25 sec)
% 25.54/25.37
% 25.54/25.37 Process 28639 finished Wed Jul 27 09:51:12 2022
% 25.54/25.37 Otter interrupted
% 25.54/25.37 PROOF NOT FOUND
%------------------------------------------------------------------------------