TSTP Solution File: NUM924+6 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM924+6 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:10:15 EDT 2022
% Result : Unknown 8.12s 8.15s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM924+6 : TPTP v8.1.0. Released v5.3.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 10:01:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 8.06/8.07 ----- Otter 3.3f, August 2004 -----
% 8.06/8.07 The process was started by sandbox on n023.cluster.edu,
% 8.06/8.07 Wed Jul 27 10:01:18 2022
% 8.06/8.07 The command was "./otter". The process ID is 1906.
% 8.06/8.07
% 8.06/8.07 set(prolog_style_variables).
% 8.06/8.07 set(auto).
% 8.06/8.07 dependent: set(auto1).
% 8.06/8.07 dependent: set(process_input).
% 8.06/8.07 dependent: clear(print_kept).
% 8.06/8.07 dependent: clear(print_new_demod).
% 8.06/8.07 dependent: clear(print_back_demod).
% 8.06/8.07 dependent: clear(print_back_sub).
% 8.06/8.07 dependent: set(control_memory).
% 8.06/8.07 dependent: assign(max_mem, 12000).
% 8.06/8.07 dependent: assign(pick_given_ratio, 4).
% 8.06/8.07 dependent: assign(stats_level, 1).
% 8.06/8.07 dependent: assign(max_seconds, 10800).
% 8.06/8.07 clear(print_given).
% 8.06/8.07
% 8.06/8.07 formula_list(usable).
% 8.06/8.07 all A (A=A).
% 8.06/8.07 all B_1_1 B_2_1 X_a (ab_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)).
% 8.06/8.07 all B_1_1 B_2_1 X_a (ab_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)).
% 8.06/8.07 all B_1_1 B_2_1 X_a (ab_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)).
% 8.06/8.07 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)).
% 8.06/8.07 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)).
% 8.06/8.07 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)).
% 8.06/8.07 all X_a (zero_ne_q_one(X_a)->ti(X_a,one_one(X_a))=one_one(X_a)).
% 8.06/8.07 all X_a (power(X_a)->ti(X_a,one_one(X_a))=one_one(X_a)).
% 8.06/8.07 all B_1_1 B_2_1 X_a (semiring(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)).
% 8.06/8.07 all B_1_1 B_2_1 X_a (semiring(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)).
% 8.06/8.07 all B_1_1 B_2_1 X_a (semiring(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)).
% 8.06/8.07 all B_1_1 B_2_1 X_a (ab_group_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)).
% 8.06/8.07 all B_1_1 B_2_1 X_a (ab_group_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)).
% 8.06/8.07 all B_1_1 B_2_1 X_a (ab_group_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)).
% 8.06/8.07 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)).
% 8.06/8.07 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)).
% 8.06/8.07 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)).
% 8.06/8.07 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)).
% 8.06/8.07 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)).
% 8.06/8.07 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)).
% 8.06/8.07 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)).
% 8.06/8.07 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)).
% 8.06/8.07 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)).
% 8.06/8.07 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)).
% 8.06/8.07 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)).
% 8.06/8.07 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)).
% 8.06/8.07 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)).
% 8.06/8.07 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)).
% 8.06/8.07 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)).
% 8.06/8.07 all X_a (zero_ne_q_one(X_a)->ti(X_a,zero_zero(X_a))=zero_zero(X_a)).
% 8.06/8.07 all X_a (no_zero_divisors(X_a)->ti(X_a,zero_zero(X_a))=zero_zero(X_a)).
% 8.06/8.07 all X_a (mult_zero(X_a)->ti(X_a,zero_zero(X_a))=zero_zero(X_a)).
% 8.06/8.07 all X_a (linord219039673up_add(X_a)->ti(X_a,zero_zero(X_a))=zero_zero(X_a)).
% 8.06/8.07 all X_a (ti(X_a,undefined(X_a))=undefined(X_a)).
% 8.06/8.07 all B_1_1 B_2_1 B_3 (zcong(ti(int,B_1_1),B_2_1,B_3)<->zcong(B_1_1,B_2_1,B_3)).
% 8.06/8.07 all B_1_1 B_2_1 B_3 (zcong(B_1_1,ti(int,B_2_1),B_3)<->zcong(B_1_1,B_2_1,B_3)).
% 8.06/8.07 all B_1_1 B_2_1 B_3 (zcong(B_1_1,B_2_1,ti(int,B_3))<->zcong(B_1_1,B_2_1,B_3)).
% 8.06/8.07 all B_1_1 (zprime(ti(int,B_1_1))<->zprime(B_1_1)).
% 8.06/8.07 all B_1_1 (bit0(ti(int,B_1_1))=bit0(B_1_1)).
% 8.06/8.07 all B_1_1 (ti(int,bit0(B_1_1))=bit0(B_1_1)).
% 8.06/8.07 all B_1_1 (bit1(ti(int,B_1_1))=bit1(B_1_1)).
% 8.06/8.07 all B_1_1 (ti(int,bit1(B_1_1))=bit1(B_1_1)).
% 8.06/8.07 ti(int,min)=min.
% 8.06/8.07 ti(int,pls)=pls.
% 8.06/8.07 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)).
% 8.06/8.07 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)).
% 8.06/8.07 all B_1_1 B_2_1 X_a (order(X_a)-> (ord_less(X_a,ti(X_a,B_1_1),B_2_1)<->ord_less(X_a,B_1_1,B_2_1))).
% 8.06/8.07 all B_1_1 B_2_1 X_a (order(X_a)-> (ord_less(X_a,B_1_1,ti(X_a,B_2_1))<->ord_less(X_a,B_1_1,B_2_1))).
% 8.06/8.07 all B_1_1 B_2_1 X_a (order(X_a)-> (ord_less_e_q(X_a,ti(X_a,B_1_1),B_2_1)<->ord_less_e_q(X_a,B_1_1,B_2_1))).
% 8.06/8.07 all B_1_1 B_2_1 X_a (order(X_a)-> (ord_less_e_q(X_a,B_1_1,ti(X_a,B_2_1))<->ord_less_e_q(X_a,B_1_1,B_2_1))).
% 8.06/8.07 all B_1_1 B_2_1 X_a (power(X_a)->power_power(X_a,ti(X_a,B_1_1),B_2_1)=power_power(X_a,B_1_1,B_2_1)).
% 8.06/8.07 all B_1_1 B_2_1 X_a (power(X_a)->power_power(X_a,B_1_1,ti(nat,B_2_1))=power_power(X_a,B_1_1,B_2_1)).
% 8.06/8.07 all B_1_1 B_2_1 X_a (power(X_a)->ti(X_a,power_power(X_a,B_1_1,B_2_1))=power_power(X_a,B_1_1,B_2_1)).
% 8.06/8.07 all B_1_1 B_2_1 (legendre(ti(int,B_1_1),B_2_1)=legendre(B_1_1,B_2_1)).
% 8.06/8.07 all B_1_1 B_2_1 (legendre(B_1_1,ti(int,B_2_1))=legendre(B_1_1,B_2_1)).
% 8.06/8.07 all B_1_1 B_2_1 (ti(int,legendre(B_1_1,B_2_1))=legendre(B_1_1,B_2_1)).
% 8.06/8.07 all B_1_1 B_2_1 (quadRes(ti(int,B_1_1),B_2_1)<->quadRes(B_1_1,B_2_1)).
% 8.06/8.07 all B_1_1 B_2_1 (quadRes(B_1_1,ti(int,B_2_1))<->quadRes(B_1_1,B_2_1)).
% 8.06/8.07 all B_1_1 B_2_1 X_a (dvd(X_a)-> (dvd_dvd(X_a,ti(X_a,B_1_1),B_2_1)<->dvd_dvd(X_a,B_1_1,B_2_1))).
% 8.06/8.07 all B_1_1 B_2_1 X_a (dvd(X_a)-> (dvd_dvd(X_a,B_1_1,ti(X_a,B_2_1))<->dvd_dvd(X_a,B_1_1,B_2_1))).
% 8.06/8.07 all B_1_1 (twoSqu420862341sum2sq(ti(int,B_1_1))<->twoSqu420862341sum2sq(B_1_1)).
% 8.06/8.07 ti(int,m)=m.
% 8.06/8.07 ti(int,s1)=s1.
% 8.06/8.07 ti(int,s)=s.
% 8.06/8.07 ti(int,t)=t.
% 8.06/8.07 ord_less(int,t,zero_zero(int)).
% 8.06/8.07 ord_less(int,t,one_one(int)).
% 8.06/8.07 ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))).
% 8.06/8.07 plus_plus(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).
% 8.06/8.07 t=zero_zero(int)->plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))=zero_zero(int).
% 8.06/8.07 -ord_less_e_q(int,one_one(int),t).
% 8.06/8.07 ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 8.06/8.07 all X_a (linordered_idom(X_a)-> (all X Y (-ord_less(X_a,plus_plus(X_a,power_power(X_a,X,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X_a))))).
% 8.06/8.07 all X_a (linordered_idom(X_a)-> (all X_2 Y_2 (ord_less(X_a,zero_zero(X_a),plus_plus(X_a,power_power(X_a,X_2,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_2,number_number_of(nat,bit0(bit1(pls))))))<->ti(X_a,X_2)!=zero_zero(X_a)|ti(X_a,Y_2)!=zero_zero(X_a)))).
% 8.06/8.07 all X_a (linordered_idom(X_a)-> (all X_2 Y_2 (plus_plus(X_a,power_power(X_a,X_2,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_2,number_number_of(nat,bit0(bit1(pls)))))=zero_zero(X_a)<->ti(X_a,X_2)=zero_zero(X_a)&ti(X_a,Y_2)=zero_zero(X_a)))).
% 8.06/8.07 all X_a (linordered_idom(X_a)-> (all A_1 (-ord_less(X_a,power_power(X_a,A_1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X_a))))).
% 8.06/8.07 all X_a (linordered_idom(X_a)-> (all A_2 (ord_less(X_a,zero_zero(X_a),power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))))<->ti(X_a,A_2)!=zero_zero(X_a)))).
% 8.06/8.07 all X_a (semiring_1(X_a)->power_power(X_a,one_one(X_a),number_number_of(nat,bit0(bit1(pls))))=one_one(X_a)).
% 8.06/8.07 all X_a (semiring_1(X_a)->power_power(X_a,zero_zero(X_a),number_number_of(nat,bit0(bit1(pls))))=zero_zero(X_a)).
% 8.06/8.07 all X_a (ring_11004092258visors(X_a)-> (all A_2 (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)))).
% 8.06/8.07 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))))).
% 8.06/8.07 all X_a (number_ring(X_a)-> (all V (plus_plus(X_a,number_number_of(X_a,V),one_one(X_a))=number_number_of(X_a,plus_plus(int,V,bit1(pls)))))).
% 8.06/8.07 ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 8.06/8.07 -(all T_1 (plus_plus(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))).
% 8.06/8.07 zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 8.06/8.07 twoSqu420862341sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)).
% 8.06/8.07 all W ord_less_e_q(int,W,W).
% 8.06/8.07 all K (number_number_of(int,K)=ti(int,K)).
% 8.06/8.07 all Z W (times_times(int,Z,W)=times_times(int,W,Z)).
% 8.06/8.07 all Z W (ord_less_e_q(int,Z,W)|ord_less_e_q(int,W,Z)).
% 8.06/8.07 all V W (times_times(int,number_number_of(int,V),number_number_of(int,W))=number_number_of(int,times_times(int,V,W))).
% 8.06/8.07 all K_1 L_1 (ord_less_e_q(int,number_number_of(int,K_1),number_number_of(int,L_1))<->ord_less_e_q(int,K_1,L_1)).
% 8.06/8.07 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X_2 Y_2 (ord_less_e_q(X_a,number_number_of(X_a,X_2),number_number_of(X_a,Y_2))<->ord_less_e_q(int,X_2,Y_2)))).
% 8.06/8.07 all Z1 Z2 Z3 (times_times(int,times_times(int,Z1,Z2),Z3)=times_times(int,Z1,times_times(int,Z2,Z3))).
% 8.06/8.07 all K I J (ord_less_e_q(int,I,J)-> (ord_less_e_q(int,J,K)->ord_less_e_q(int,I,K))).
% 8.06/8.07 all Z W (ord_less_e_q(int,Z,W)-> (ord_less_e_q(int,W,Z)->ti(int,Z)=ti(int,W))).
% 8.06/8.07 all X Y Z (power_power(int,X,plus_plus(nat,Y,Z))=times_times(int,power_power(int,X,Y),power_power(int,X,Z))).
% 8.06/8.07 all K1 K2 (ord_less_e_q(int,bit1(K1),bit1(K2))<->ord_less_e_q(int,K1,K2)).
% 8.06/8.07 all K_1 L_1 (ord_less_e_q(int,bit1(K_1),bit1(L_1))<->ord_less_e_q(int,K_1,L_1)).
% 8.06/8.07 ord_less_e_q(int,pls,pls).
% 8.06/8.07 all K1 K2 (ord_less_e_q(int,bit0(K1),bit0(K2))<->ord_less_e_q(int,K1,K2)).
% 8.06/8.07 all K_1 L_1 (ord_less_e_q(int,bit0(K_1),bit0(L_1))<->ord_less_e_q(int,K_1,L_1)).
% 8.06/8.07 all Z_1 W_1 (ord_less(int,Z_1,W_1)<->ord_less_e_q(int,Z_1,W_1)&ti(int,Z_1)!=ti(int,W_1)).
% 8.06/8.07 all K I J (ord_less_e_q(int,I,J)->ord_less_e_q(int,plus_plus(int,K,I),plus_plus(int,K,J))).
% 8.06/8.07 all V_3 (number_number_of(nat,V_3)=zero_zero(nat)<->ord_less_e_q(int,V_3,pls)).
% 8.06/8.07 all V_3 (zero_zero(nat)=number_number_of(nat,V_3)<->ord_less_e_q(int,V_3,pls)).
% 8.06/8.07 all X_a (number_semiring(X_a)-> (all V_1 V (ord_less_e_q(int,pls,V)-> (ord_less_e_q(int,pls,V_1)->times_times(X_a,number_number_of(X_a,V),number_number_of(X_a,V_1))=number_number_of(X_a,times_times(int,V,V_1)))))).
% 8.06/8.07 all X_a (number_ring(X_a)-> (all V W Z (times_times(X_a,number_number_of(X_a,V),times_times(X_a,number_number_of(X_a,W),Z))=times_times(X_a,number_number_of(X_a,times_times(int,V,W)),Z)))).
% 8.06/8.07 all X_a (number_ring(X_a)-> (all V W (times_times(X_a,number_number_of(X_a,V),number_number_of(X_a,W))=number_number_of(X_a,times_times(int,V,W))))).
% 8.06/8.07 all X_a (number_ring(X_a)-> (all V W (number_number_of(X_a,times_times(int,V,W))=times_times(X_a,number_number_of(X_a,V),number_number_of(X_a,W))))).
% 8.06/8.07 all X_a (linord581940658strict(X_a)-> (all X_2 Y_2 (ord_less_e_q(X_a,plus_plus(X_a,times_times(X_a,X_2,X_2),times_times(X_a,Y_2,Y_2)),zero_zero(X_a))<->ti(X_a,X_2)=zero_zero(X_a)&ti(X_a,Y_2)=zero_zero(X_a)))).
% 8.06/8.07 all X_a (linordered_ring(X_a)-> (all X Y 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))))).
% 8.06/8.07 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X_2 (ord_less_e_q(X_a,number_number_of(X_a,X_2),zero_zero(X_a))<->ord_less_e_q(int,X_2,pls)))).
% 8.06/8.07 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Y_2 (ord_less_e_q(X_a,zero_zero(X_a),number_number_of(X_a,Y_2))<->ord_less_e_q(int,pls,Y_2)))).
% 8.06/8.07 all V_3 (ord_less(nat,zero_zero(nat),number_number_of(nat,V_3))<->ord_less(int,pls,V_3)).
% 8.06/8.07 all X_a (number(X_a)&linorder(X_a)-> (all V_3 W_1 (ord_less_e_q(X_a,number_number_of(X_a,V_3),number_number_of(X_a,W_1))<-> -ord_less(X_a,number_number_of(X_a,W_1),number_number_of(X_a,V_3))))).
% 8.06/8.07 all K_1 (ord_less_e_q(int,pls,bit1(K_1))<->ord_less_e_q(int,pls,K_1)).
% 8.06/8.07 all K1 K2 (ord_less_e_q(int,bit0(K1),bit1(K2))<->ord_less_e_q(int,K1,K2)).
% 8.06/8.07 all K_1 L_1 (ord_less_e_q(int,bit0(K_1),bit1(L_1))<->ord_less_e_q(int,K_1,L_1)).
% 8.06/8.07 all K_1 (ord_less_e_q(int,bit0(K_1),pls)<->ord_less_e_q(int,K_1,pls)).
% 8.06/8.07 all K_1 (ord_less_e_q(int,pls,bit0(K_1))<->ord_less_e_q(int,pls,K_1)).
% 8.06/8.07 all Z_2 Z W_2 W (ord_less(int,W_2,W)-> (ord_less_e_q(int,Z_2,Z)->ord_less(int,plus_plus(int,W_2,Z_2),plus_plus(int,W,Z)))).
% 8.06/8.07 number_number_of(nat,pls)=zero_zero(nat).
% 8.06/8.07 zero_zero(nat)=number_number_of(nat,pls).
% 8.06/8.07 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X_2 (ord_less_e_q(X_a,number_number_of(X_a,X_2),one_one(X_a))<->ord_less_e_q(int,X_2,bit1(pls))))).
% 8.06/8.07 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Y_2 (ord_less_e_q(X_a,one_one(X_a),number_number_of(X_a,Y_2))<->ord_less_e_q(int,bit1(pls),Y_2)))).
% 8.06/8.07 plus_plus(nat,one_one(nat),one_one(nat))=number_number_of(nat,bit0(bit1(pls))).
% 8.06/8.07 all W (times_times(int,pls,W)=pls).
% 8.06/8.07 all K L (times_times(int,bit0(K),L)=bit0(times_times(int,K,L))).
% 8.06/8.07 all K_1 L_1 (ord_less(int,number_number_of(int,K_1),number_number_of(int,L_1))<->ord_less(int,K_1,L_1)).
% 8.06/8.07 all Z (times_times(int,Z,one_one(int))=ti(int,Z)).
% 8.06/8.07 all Z (times_times(int,one_one(int),Z)=ti(int,Z)).
% 8.06/8.07 all V W (plus_plus(int,number_number_of(int,V),number_number_of(int,W))=number_number_of(int,plus_plus(int,V,W))).
% 8.06/8.07 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))).
% 8.06/8.07 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))).
% 8.06/8.07 all K_1 (ord_less_e_q(int,bit1(K_1),pls)<->ord_less(int,K_1,pls)).
% 8.06/8.07 all K_1 (ord_less(int,pls,bit1(K_1))<->ord_less_e_q(int,pls,K_1)).
% 8.06/8.07 all K1 K2 (ord_less_e_q(int,bit1(K1),bit0(K2))<->ord_less(int,K1,K2)).
% 8.06/8.07 all K_1 L_1 (ord_less_e_q(int,bit1(K_1),bit0(L_1))<->ord_less(int,K_1,L_1)).
% 8.06/8.07 all K1 K2 (ord_less(int,bit0(K1),bit1(K2))<->ord_less_e_q(int,K1,K2)).
% 8.06/8.07 all K_1 L_1 (ord_less(int,bit0(K_1),bit1(L_1))<->ord_less_e_q(int,K_1,L_1)).
% 8.06/8.07 all V_3 V_2 (ord_less(nat,number_number_of(nat,V_3),number_number_of(nat,V_2))<-> (ord_less(int,V_3,V_2)->ord_less(int,pls,V_2))&ord_less(int,V_3,V_2)).
% 8.06/8.07 all Z_1 (ord_less_e_q(int,one_one(int),Z_1)<->ord_less(int,zero_zero(int),Z_1)).
% 8.06/8.07 number_number_of(nat,bit1(pls))=one_one(nat).
% 8.06/8.07 one_one(nat)=number_number_of(nat,bit1(pls)).
% 8.06/8.07 all W Z (ord_less(int,W,Z)->ord_less_e_q(int,plus_plus(int,W,one_one(int)),Z)).
% 8.06/8.07 all W_1 Z_1 (ord_less_e_q(int,plus_plus(int,W_1,one_one(int)),Z_1)<->ord_less(int,W_1,Z_1)).
% 8.06/8.07 all W_1 Z_1 (ord_less(int,W_1,plus_plus(int,Z_1,one_one(int)))<->ord_less_e_q(int,W_1,Z_1)).
% 8.06/8.07 all X_a (number_semiring(X_a)-> (all V_1 V (ord_less_e_q(int,pls,V)-> (ord_less_e_q(int,pls,V_1)->plus_plus(X_a,number_number_of(X_a,V),number_number_of(X_a,V_1))=number_number_of(X_a,plus_plus(int,V,V_1)))))).
% 8.06/8.07 all V_1 V ((ord_less(int,V,pls)->plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1))=number_number_of(nat,V_1))& (-ord_less(int,V,pls)-> (ord_less(int,V_1,pls)->plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1))=number_number_of(nat,V))& (-ord_less(int,V_1,pls)->plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1))=number_number_of(nat,plus_plus(int,V,V_1))))).
% 8.06/8.07 all Z (ord_less_e_q(int,zero_zero(int),Z)->ord_less(int,zero_zero(int),plus_plus(int,one_one(int),Z))).
% 8.06/8.07 all X_a (number_ring(X_a)&ring_char_0(X_a)-> (all X_2 Y_2 (number_number_of(X_a,X_2)=number_number_of(X_a,Y_2)<->ti(int,X_2)=ti(int,Y_2)))).
% 8.06/8.07 all X_a (number(X_a)-> (all W_1 X_2 (number_number_of(X_a,W_1)=ti(X_a,X_2)<->ti(X_a,X_2)=number_number_of(X_a,W_1)))).
% 8.06/8.07 all K_1 L_1 (bit1(K_1)=bit1(L_1)<->ti(int,K_1)=ti(int,L_1)).
% 8.06/8.07 all K_1 L_1 (bit0(K_1)=bit0(L_1)<->ti(int,K_1)=ti(int,L_1)).
% 8.06/8.07 all X Y (ord_less(int,X,Y)|ti(int,X)=ti(int,Y)|ord_less(int,Y,X)).
% 8.06/8.07 all X_a (linord581940658strict(X_a)-> (all X_2 Y_2 (plus_plus(X_a,times_times(X_a,X_2,X_2),times_times(X_a,Y_2,Y_2))=zero_zero(X_a)<->ti(X_a,X_2)=zero_zero(X_a)&ti(X_a,Y_2)=zero_zero(X_a)))).
% 8.06/8.07 all X_b (number(X_b)&semiring(X_b)-> (all A_1 B V (times_times(X_b,plus_plus(X_b,A_1,B),number_number_of(X_b,V))=plus_plus(X_b,times_times(X_b,A_1,number_number_of(X_b,V)),times_times(X_b,B,number_number_of(X_b,V)))))).
% 8.06/8.07 all X_b (number(X_b)&semiring(X_b)-> (all V B C (times_times(X_b,number_number_of(X_b,V),plus_plus(X_b,B,C))=plus_plus(X_b,times_times(X_b,number_number_of(X_b,V),B),times_times(X_b,number_number_of(X_b,V),C))))).
% 8.06/8.07 all Z1 Z2 Z3 (plus_plus(int,plus_plus(int,Z1,Z2),Z3)=plus_plus(int,Z1,plus_plus(int,Z2,Z3))).
% 8.06/8.07 all X Y Z (plus_plus(int,X,plus_plus(int,Y,Z))=plus_plus(int,Y,plus_plus(int,X,Z))).
% 8.06/8.07 all Z W (plus_plus(int,Z,W)=plus_plus(int,W,Z)).
% 8.06/8.07 zero_zero(int)=number_number_of(int,pls).
% 8.06/8.07 all K I J (ord_less(int,I,J)-> (ord_less(int,zero_zero(int),K)->ord_less(int,times_times(int,K,I),times_times(int,K,J)))).
% 8.06/8.07 all X_a (linordered_semidom(X_a)-> (all X Y (power_power(X_a,X,number_number_of(nat,bit0(bit1(pls))))=power_power(X_a,Y,number_number_of(nat,bit0(bit1(pls))))-> (ord_less_e_q(X_a,zero_zero(X_a),X)-> (ord_less_e_q(X_a,zero_zero(X_a),Y)->ti(X_a,X)=ti(X_a,Y)))))).
% 8.06/8.07 all X_a (linordered_semidom(X_a)-> (all X Y (ord_less_e_q(X_a,power_power(X_a,X,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y,number_number_of(nat,bit0(bit1(pls)))))-> (ord_less_e_q(X_a,zero_zero(X_a),Y)->ord_less_e_q(X_a,X,Y))))).
% 8.06/8.07 all X_a (linordered_idom(X_a)-> (all A_1 ord_less_e_q(X_a,zero_zero(X_a),power_power(X_a,A_1,number_number_of(nat,bit0(bit1(pls))))))).
% 8.06/8.07 all X_a (linordered_semidom(X_a)-> (all X Y (ord_less(X_a,power_power(X_a,X,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y,number_number_of(nat,bit0(bit1(pls)))))-> (ord_less_e_q(X_a,zero_zero(X_a),Y)->ord_less(X_a,X,Y))))).
% 8.06/8.07 all X_a (linordered_idom(X_a)-> (all X_2 Y_2 (ord_less_e_q(X_a,plus_plus(X_a,power_power(X_a,X_2,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_2,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X_a))<->ti(X_a,X_2)=zero_zero(X_a)&ti(X_a,Y_2)=zero_zero(X_a)))).
% 8.06/8.07 all X_a (linordered_idom(X_a)-> (all X Y ord_less_e_q(X_a,zero_zero(X_a),plus_plus(X_a,power_power(X_a,X,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y,number_number_of(nat,bit0(bit1(pls)))))))).
% 8.06/8.07 all X_a (linord581940658strict(X_a)-> (all X_2 Y_2 (ord_less(X_a,zero_zero(X_a),plus_plus(X_a,times_times(X_a,X_2,X_2),times_times(X_a,Y_2,Y_2)))<->ti(X_a,X_2)!=zero_zero(X_a)|ti(X_a,Y_2)!=zero_zero(X_a)))).
% 8.06/8.07 all X_a (linordered_ring(X_a)-> (all X Y (-ord_less(X_a,plus_plus(X_a,times_times(X_a,X,X),times_times(X_a,Y,Y)),zero_zero(X_a))))).
% 8.06/8.07 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)))).
% 8.06/8.07 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)))).
% 8.06/8.07 one_one(int)=number_number_of(int,bit1(pls)).
% 8.06/8.07 all K L (times_times(int,bit1(K),L)=plus_plus(int,bit0(times_times(int,K,L)),L)).
% 8.06/8.07 all N_1 Ma (ord_less(int,zero_zero(int),Ma)-> (times_times(int,Ma,N_1)=one_one(int)<->ti(int,Ma)=one_one(int)&ti(int,N_1)=one_one(int))).
% 8.06/8.07 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)))).
% 8.06/8.07 all K (bit1(K)!=pls).
% 8.06/8.07 all L (pls!=bit1(L)).
% 8.06/8.07 all K L (bit1(K)!=bit0(L)).
% 8.06/8.07 all K L (bit0(K)!=bit1(L)).
% 8.06/8.07 all K_1 (bit0(K_1)=pls<->ti(int,K_1)=pls).
% 8.06/8.07 all L_1 (pls=bit0(L_1)<->pls=ti(int,L_1)).
% 8.06/8.07 bit0(pls)=pls.
% 8.06/8.07 pls=zero_zero(int).
% 8.06/8.07 all K1 K2 (ord_less(int,bit1(K1),bit1(K2))<->ord_less(int,K1,K2)).
% 8.06/8.07 all K_1 L_1 (ord_less(int,bit1(K_1),bit1(L_1))<->ord_less(int,K_1,L_1)).
% 8.06/8.07 -ord_less(int,pls,pls).
% 8.06/8.07 all K1 K2 (ord_less(int,bit0(K1),bit0(K2))<->ord_less(int,K1,K2)).
% 8.06/8.07 all K_1 L_1 (ord_less(int,bit0(K_1),bit0(L_1))<->ord_less(int,K_1,L_1)).
% 8.06/8.07 zero_zero(int)!=one_one(int).
% 8.06/8.07 all K (plus_plus(int,K,pls)=ti(int,K)).
% 8.06/8.07 all K (plus_plus(int,pls,K)=ti(int,K)).
% 8.06/8.07 all K L (plus_plus(int,bit0(K),bit0(L))=bit0(plus_plus(int,K,L))).
% 8.06/8.07 all K (bit0(K)=plus_plus(int,K,K)).
% 8.06/8.07 all Z (plus_plus(int,Z,zero_zero(int))=ti(int,Z)).
% 8.06/8.07 all Z (plus_plus(int,zero_zero(int),Z)=ti(int,Z)).
% 8.06/8.07 all K I J (ord_less(int,I,J)->ord_less(int,plus_plus(int,I,K),plus_plus(int,J,K))).
% 8.06/8.07 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))))).
% 8.06/8.07 all X_a (monoid_mult(X_a)-> (all A_1 (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)))).
% 8.06/8.07 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)))).
% 8.06/8.07 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)))).
% 8.06/8.07 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)))).
% 8.06/8.07 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)))).
% 8.06/8.07 all X_a (monoid_mult(X_a)-> (all A_1 (power_power(X_a,A_1,number_number_of(nat,bit0(bit1(pls))))=times_times(X_a,A_1,A_1)))).
% 8.06/8.07 all X_a (linordered_idom(X_a)-> (all A_2 (ord_less(X_a,plus_plus(X_a,A_2,A_2),zero_zero(X_a))<->ord_less(X_a,A_2,zero_zero(X_a))))).
% 8.06/8.07 all X_a (number_semiring(X_a)->number_number_of(X_a,pls)=zero_zero(X_a)).
% 8.06/8.07 all X_a (number_ring(X_a)->number_number_of(X_a,pls)=zero_zero(X_a)).
% 8.06/8.07 all X_a (number_ring(X_a)->zero_zero(X_a)=number_number_of(X_a,pls)).
% 8.06/8.07 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)))).
% 8.06/8.07 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)))).
% 8.06/8.07 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X_2 Y_2 (ord_less(X_a,number_number_of(X_a,X_2),number_number_of(X_a,Y_2))<->ord_less(int,X_2,Y_2)))).
% 8.06/8.07 all X_a (number_ring(X_a)-> (all V W Z (plus_plus(X_a,number_number_of(X_a,V),plus_plus(X_a,number_number_of(X_a,W),Z))=plus_plus(X_a,number_number_of(X_a,plus_plus(int,V,W)),Z)))).
% 8.06/8.07 all X_a (number_ring(X_a)-> (all V W (plus_plus(X_a,number_number_of(X_a,V),number_number_of(X_a,W))=number_number_of(X_a,plus_plus(int,V,W))))).
% 8.06/8.07 all X_a (number_ring(X_a)-> (all V W (number_number_of(X_a,plus_plus(int,V,W))=plus_plus(X_a,number_number_of(X_a,V),number_number_of(X_a,W))))).
% 8.06/8.07 all K_1 (ord_less(int,bit1(K_1),pls)<->ord_less(int,K_1,pls)).
% 8.06/8.07 all K1 K2 (ord_less(int,bit1(K1),bit0(K2))<->ord_less(int,K1,K2)).
% 8.06/8.07 all K_1 L_1 (ord_less(int,bit1(K_1),bit0(L_1))<->ord_less(int,K_1,L_1)).
% 8.06/8.07 all W_1 (ord_less(int,bit1(W_1),zero_zero(int))<->ord_less(int,W_1,zero_zero(int))).
% 8.06/8.07 all K_1 (ord_less(int,bit0(K_1),pls)<->ord_less(int,K_1,pls)).
% 8.06/8.07 all K_1 (ord_less(int,pls,bit0(K_1))<->ord_less(int,pls,K_1)).
% 8.06/8.07 -ord_less(int,pls,zero_zero(int)).
% 8.06/8.07 all W_1 (ord_less(int,bit0(W_1),zero_zero(int))<->ord_less(int,W_1,zero_zero(int))).
% 8.06/8.07 all K L (plus_plus(int,bit1(K),bit0(L))=bit1(plus_plus(int,K,L))).
% 8.06/8.07 all K L (plus_plus(int,bit0(K),bit1(L))=bit1(plus_plus(int,K,L))).
% 8.06/8.07 ord_less(int,zero_zero(int),one_one(int)).
% 8.06/8.07 all K (bit1(K)=plus_plus(int,plus_plus(int,one_one(int),K),K)).
% 8.06/8.07 all Z (plus_plus(int,plus_plus(int,one_one(int),Z),Z)!=zero_zero(int)).
% 8.06/8.07 all W_1 Z_1 (ord_less(int,W_1,plus_plus(int,Z_1,one_one(int)))<->ord_less(int,W_1,Z_1)|ti(int,W_1)=ti(int,Z_1)).
% 8.06/8.07 all X_b (monoid_mult(X_b)&number(X_b)-> (all W (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))))).
% 8.06/8.07 all X_a (number_semiring(X_a)-> (all X Y (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,power_power(X_a,X,number_number_of(nat,bit0(bit1(pls)))),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))))).
% 8.06/8.07 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))))).
% 8.06/8.07 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))))).
% 8.06/8.07 all X_a (number_semiring(X_a)->number_number_of(X_a,bit1(pls))=one_one(X_a)).
% 8.06/8.07 all X_a (number_ring(X_a)->number_number_of(X_a,bit1(pls))=one_one(X_a)).
% 8.06/8.07 all X_a (number_ring(X_a)->one_one(X_a)=number_number_of(X_a,bit1(pls))).
% 8.06/8.07 all Z_1 (ord_less(int,plus_plus(int,plus_plus(int,one_one(int),Z_1),Z_1),zero_zero(int))<->ord_less(int,Z_1,zero_zero(int))).
% 8.06/8.07 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X_2 (ord_less(X_a,number_number_of(X_a,X_2),zero_zero(X_a))<->ord_less(int,X_2,pls)))).
% 8.06/8.07 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Y_2 (ord_less(X_a,zero_zero(X_a),number_number_of(X_a,Y_2))<->ord_less(int,pls,Y_2)))).
% 8.06/8.07 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)))).
% 8.06/8.07 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)))).
% 8.06/8.07 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X_2 (ord_less(X_a,number_number_of(X_a,X_2),one_one(X_a))<->ord_less(int,X_2,bit1(pls))))).
% 8.06/8.07 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Y_2 (ord_less(X_a,one_one(X_a),number_number_of(X_a,Y_2))<->ord_less(int,bit1(pls),Y_2)))).
% 8.06/8.07 dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))).
% 8.06/8.07 all A_1 B (power_power(int,plus_plus(int,A_1,B),number_number_of(nat,bit1(bit1(pls))))=plus_plus(int,plus_plus(int,plus_plus(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))),power_power(int,A_1,number_number_of(nat,bit0(bit1(pls))))),B)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),A_1),power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,B,number_number_of(nat,bit1(bit1(pls)))))).
% 8.06/8.07 all A_1 B (power_power(int,plus_plus(int,A_1,B),number_number_of(nat,bit0(bit1(pls))))=plus_plus(int,plus_plus(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)),power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))).
% 8.06/8.07 all X (ord_less_e_q(int,zero_zero(int),X)-> (ord_less(int,X,number_number_of(int,bit0(bit1(pls))))->ti(int,X)=zero_zero(int)|ti(int,X)=one_one(int))).
% 8.06/8.07 ord_less_e_q(int,zero_zero(int),s).
% 8.06/8.07 ord_less(int,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 8.06/8.07 zcong(s1,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 8.06/8.07 all A_1 (times_times(int,A_1,power_power(int,A_1,number_number_of(nat,bit0(bit1(pls)))))=power_power(int,A_1,number_number_of(nat,bit1(bit1(pls))))).
% 8.06/8.07 all X ord_less_e_q(int,X,power_power(int,X,number_number_of(nat,bit0(bit1(pls))))).
% 8.06/8.07 all R Q A_1 (ord_less(int,zero_zero(int),A_1)-> (ti(int,A_1)=plus_plus(int,R,times_times(int,A_1,Q))-> (ord_less(int,R,A_1)->ord_less_e_q(int,one_one(int),Q)))).
% 8.06/8.07 all R Q A_1 (ord_less(int,zero_zero(int),A_1)-> (ti(int,A_1)=plus_plus(int,R,times_times(int,A_1,Q))-> (ord_less_e_q(int,zero_zero(int),R)->ord_less_e_q(int,Q,one_one(int))))).
% 8.06/8.07 ord_less_e_q(int,zero_zero(int),number_number_of(int,bit0(bit1(pls)))).
% 8.06/8.07 all X_a (comm_semiring_1(X_a)-> (all X N (power_power(X_a,X,times_times(nat,number_number_of(nat,bit0(bit1(pls))),N))=times_times(X_a,power_power(X_a,X,N),power_power(X_a,X,N))))).
% 8.06/8.07 zcong(power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),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))).
% 8.06/8.07 exists X_1 (ord_less_e_q(int,zero_zero(int),X_1)&ord_less(int,X_1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))&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 (ord_less_e_q(int,zero_zero(int),Y_1)&ord_less(int,Y_1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))&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)))).
% 8.06/8.07 -(all S (-(ord_less_e_q(int,zero_zero(int),S)&ord_less(int,S,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))&zcong(s1,S,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))))).
% 8.06/8.07 zcong(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))).
% 8.06/8.08 all X_2 N_1 (ord_less(nat,zero_zero(nat),power_power(nat,X_2,N_1))<->N_1=zero_zero(nat)|ord_less(nat,zero_zero(nat),X_2)).
% 8.06/8.08 all A_1 N P (zprime(P)-> (dvd_dvd(int,P,power_power(int,A_1,N))->dvd_dvd(int,P,A_1))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all X P Q (power_power(X_a,power_power(X_a,X,P),Q)=power_power(X_a,X,times_times(nat,P,Q))))).
% 8.06/8.08 all N A_1 B P (zprime(P)-> (-dvd_dvd(int,P,B)-> (dvd_dvd(int,power_power(int,P,N),times_times(int,A_1,B))->dvd_dvd(int,power_power(int,P,N),A_1)))).
% 8.06/8.08 all N B A_1 P (zprime(P)-> (-dvd_dvd(int,P,A_1)-> (dvd_dvd(int,power_power(int,P,N),times_times(int,A_1,B))->dvd_dvd(int,power_power(int,P,N),B)))).
% 8.06/8.08 all X Y Z (power_power(int,power_power(int,X,Y),Z)=power_power(int,X,times_times(nat,Y,Z))).
% 8.06/8.08 all N M (ord_less(int,zero_zero(int),M)-> (ord_less(int,M,N)-> -dvd_dvd(int,N,M))).
% 8.06/8.08 all N M (ord_less_e_q(int,zero_zero(int),M)-> (ord_less_e_q(int,zero_zero(int),N)-> (dvd_dvd(int,M,N)-> (dvd_dvd(int,N,M)->ti(int,M)=ti(int,N))))).
% 8.06/8.08 all K M N (dvd_dvd(int,times_times(int,K,M),times_times(int,K,N))-> (ti(int,K)!=zero_zero(int)->dvd_dvd(int,M,N))).
% 8.06/8.08 all K_1 N_1 Ma (dvd_dvd(int,K_1,plus_plus(int,N_1,times_times(int,K_1,Ma)))<->dvd_dvd(int,K_1,N_1)).
% 8.06/8.08 all C_1 X_2 Ta A_2 D_1 (dvd_dvd(int,A_2,D_1)-> (dvd_dvd(int,A_2,plus_plus(int,X_2,Ta))<->dvd_dvd(int,A_2,plus_plus(int,plus_plus(int,X_2,times_times(int,C_1,D_1)),Ta)))).
% 8.06/8.08 zprime(number_number_of(int,bit0(bit1(pls)))).
% 8.06/8.08 all Z N (dvd_dvd(int,Z,N)-> (ord_less(int,zero_zero(int),N)->ord_less_e_q(int,Z,N))).
% 8.06/8.08 all Y X (twoSqu420862341sum2sq(X)-> (twoSqu420862341sum2sq(Y)->twoSqu420862341sum2sq(times_times(int,X,Y)))).
% 8.06/8.08 all V_3 V_2 (ord_less_e_q(nat,number_number_of(nat,V_3),number_number_of(nat,V_2))<-> (-ord_less_e_q(int,V_3,V_2)->ord_less_e_q(int,V_3,pls))).
% 8.06/8.08 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))))).
% 8.06/8.08 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))))).
% 8.06/8.08 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)))))).
% 8.06/8.08 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)))).
% 8.06/8.08 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))))).
% 8.06/8.08 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)))).
% 8.06/8.08 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))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all A_1 B (times_times(X_a,A_1,B)=times_times(X_a,B,A_1)))).
% 8.06/8.08 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)))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all A_1 C D (plus_plus(X_a,A_1,plus_plus(X_a,C,D))=plus_plus(X_a,C,plus_plus(X_a,A_1,D))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all A_1 C D (plus_plus(X_a,A_1,plus_plus(X_a,C,D))=plus_plus(X_a,plus_plus(X_a,A_1,C),D)))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (plus_plus(X_a,plus_plus(X_a,A_1,B),C)=plus_plus(X_a,A_1,plus_plus(X_a,B,C))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (plus_plus(X_a,plus_plus(X_a,A_1,B),C)=plus_plus(X_a,plus_plus(X_a,A_1,C),B)))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all A_1 B C D (plus_plus(X_a,plus_plus(X_a,A_1,B),plus_plus(X_a,C,D))=plus_plus(X_a,plus_plus(X_a,A_1,C),plus_plus(X_a,B,D))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all X (power_power(X_a,X,one_one(nat))=ti(X_a,X)))).
% 8.06/8.08 all X_2 W_1 (ord_less(nat,zero_zero(nat),power_power(nat,X_2,number_number_of(nat,W_1)))<->number_number_of(nat,W_1)=zero_zero(nat)|ord_less(nat,zero_zero(nat),X_2)).
% 8.06/8.08 all Z (times_times(nat,Z,number_number_of(nat,bit0(bit1(pls))))=plus_plus(nat,Z,Z)).
% 8.06/8.08 all Z (times_times(nat,number_number_of(nat,bit0(bit1(pls))),Z)=plus_plus(nat,Z,Z)).
% 8.06/8.08 all V_1 V ((ord_less(int,V,pls)->times_times(nat,number_number_of(nat,V),number_number_of(nat,V_1))=zero_zero(nat))& (-ord_less(int,V,pls)->times_times(nat,number_number_of(nat,V),number_number_of(nat,V_1))=number_number_of(nat,times_times(int,V,V_1)))).
% 8.06/8.08 all V_1 K V ((ord_less(int,V,pls)->times_times(nat,number_number_of(nat,V),times_times(nat,number_number_of(nat,V_1),K))=zero_zero(nat))& (-ord_less(int,V,pls)->times_times(nat,number_number_of(nat,V),times_times(nat,number_number_of(nat,V_1),K))=times_times(nat,number_number_of(nat,times_times(int,V,V_1)),K))).
% 8.06/8.08 all X_a (monoid_mult(X_a)-> (all A_1 N (power_power(X_a,A_1,times_times(nat,number_number_of(nat,bit0(bit1(pls))),N))=power_power(X_a,power_power(X_a,A_1,N),number_number_of(nat,bit0(bit1(pls))))))).
% 8.06/8.08 all X_a (linordered_idom(X_a)-> (all A_1 K (ord_less_e_q(X_a,power_power(X_a,A_1,times_times(nat,number_number_of(nat,bit0(bit1(pls))),K)),zero_zero(X_a))->ti(X_a,A_1)=zero_zero(X_a)))).
% 8.06/8.08 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)))).
% 8.06/8.08 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)))).
% 8.06/8.08 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)))).
% 8.06/8.08 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)))).
% 8.06/8.08 all X_a (semiri456707255roduct(X_a)-> (all B_1 A_2 (ti(X_a,B_1)=plus_plus(X_a,B_1,A_2)<->ti(X_a,A_2)=zero_zero(X_a)))).
% 8.06/8.08 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))))).
% 8.06/8.08 all X_a (semiri456707255roduct(X_a)-> (all C_1 D_1 A_2 B_1 (ti(X_a,A_2)!=ti(X_a,B_1)&ti(X_a,C_1)!=ti(X_a,D_1)<->plus_plus(X_a,times_times(X_a,A_2,C_1),times_times(X_a,B_1,D_1))!=plus_plus(X_a,times_times(X_a,A_2,D_1),times_times(X_a,B_1,C_1))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (times_times(X_a,plus_plus(X_a,A_1,B),C)=plus_plus(X_a,times_times(X_a,A_1,C),times_times(X_a,B,C))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all A_1 M B (plus_plus(X_a,times_times(X_a,A_1,M),times_times(X_a,B,M))=times_times(X_a,plus_plus(X_a,A_1,B),M)))).
% 8.06/8.08 all X_a (semiri456707255roduct(X_a)-> (all W_1 Y_2 X_2 Z_1 (plus_plus(X_a,times_times(X_a,W_1,Y_2),times_times(X_a,X_2,Z_1))=plus_plus(X_a,times_times(X_a,W_1,Z_1),times_times(X_a,X_2,Y_2))<->ti(X_a,W_1)=ti(X_a,X_2)|ti(X_a,Y_2)=ti(X_a,Z_1)))).
% 8.06/8.08 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)))).
% 8.06/8.08 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)))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all X Y Q (power_power(X_a,times_times(X_a,X,Y),Q)=times_times(X_a,power_power(X_a,X,Q),power_power(X_a,Y,Q))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all X P Q (times_times(X_a,power_power(X_a,X,P),power_power(X_a,X,Q))=power_power(X_a,X,plus_plus(nat,P,Q))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all X (power_power(X_a,X,zero_zero(nat))=one_one(X_a)))).
% 8.06/8.08 ord_less_e_q(int,zero_zero(int),zero_zero(int)).
% 8.06/8.08 all X_a (linordered_idom(X_a)-> (all A_1 N ord_less_e_q(X_a,zero_zero(X_a),power_power(X_a,A_1,times_times(nat,number_number_of(nat,bit0(bit1(pls))),N))))).
% 8.06/8.08 all X_a (semiri456707255roduct(X_a)-> (all C D A_1 B R (ti(X_a,R)!=zero_zero(X_a)-> (ti(X_a,A_1)=ti(X_a,B)&ti(X_a,C)!=ti(X_a,D)->plus_plus(X_a,A_1,times_times(X_a,R,C))!=plus_plus(X_a,B,times_times(X_a,R,D)))))).
% 8.06/8.08 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)))).
% 8.06/8.08 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)))).
% 8.06/8.08 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)))).
% 8.06/8.08 all X_a (power(X_a)&mult_zero(X_a)&no_zero_divisors(X_a)&zero_ne_q_one(X_a)-> (all A_2 W_1 (power_power(X_a,A_2,number_number_of(nat,W_1))=zero_zero(X_a)<->ti(X_a,A_2)=zero_zero(X_a)&number_number_of(nat,W_1)!=zero_zero(nat)))).
% 8.06/8.08 all B A_1 (ord_less(int,zero_zero(int),A_1)-> (ord_less(int,zero_zero(int),times_times(int,A_1,B))->ord_less(int,zero_zero(int),B))).
% 8.06/8.08 ord_less_e_q(int,zero_zero(int),one_one(int)).
% 8.06/8.08 all Y X (ord_less_e_q(int,zero_zero(int),X)-> (ord_less_e_q(int,zero_zero(int),Y)->ord_less_e_q(int,zero_zero(int),times_times(int,X,Y)))).
% 8.06/8.08 all Y X (ord_less_e_q(int,zero_zero(int),X)-> (ord_less_e_q(int,zero_zero(int),Y)->ord_less_e_q(int,zero_zero(int),plus_plus(int,X,Y)))).
% 8.06/8.08 all N X (ord_less_e_q(int,zero_zero(int),X)->ord_less_e_q(int,zero_zero(int),power_power(int,X,N))).
% 8.06/8.08 all X_a (power(X_a)&semiring_0(X_a)-> (all W ((number_number_of(nat,W)=zero_zero(nat)->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)->power_power(X_a,zero_zero(X_a),number_number_of(nat,W))=zero_zero(X_a))))).
% 8.06/8.08 ord_less_e_q(int,zero_zero(int),number_number_of(int,bit1(bit1(pls)))).
% 8.06/8.08 all B_2 Q_1 R_1 (ord_less_e_q(int,zero_zero(int),plus_plus(int,times_times(int,B_2,Q_1),R_1))-> (ord_less(int,R_1,B_2)-> (ord_less(int,zero_zero(int),B_2)->ord_less_e_q(int,zero_zero(int),Q_1)))).
% 8.06/8.08 all B_2 Q_1 R_1 (ord_less(int,plus_plus(int,times_times(int,B_2,Q_1),R_1),zero_zero(int))-> (ord_less_e_q(int,zero_zero(int),R_1)-> (ord_less(int,zero_zero(int),B_2)->ord_less_e_q(int,Q_1,zero_zero(int))))).
% 8.06/8.08 all B Q_1 R_1 Q R (ord_less_e_q(int,plus_plus(int,times_times(int,B,Q_1),R_1),plus_plus(int,times_times(int,B,Q),R))-> (ord_less_e_q(int,zero_zero(int),R_1)-> (ord_less(int,R_1,B)-> (ord_less(int,R,B)->ord_less_e_q(int,Q_1,Q))))).
% 8.06/8.08 all B Q R B_2 Q_1 R_1 (plus_plus(int,times_times(int,B,Q),R)=plus_plus(int,times_times(int,B_2,Q_1),R_1)-> (ord_less_e_q(int,zero_zero(int),plus_plus(int,times_times(int,B_2,Q_1),R_1))-> (ord_less(int,R_1,B_2)-> (ord_less_e_q(int,zero_zero(int),R)-> (ord_less(int,zero_zero(int),B_2)-> (ord_less_e_q(int,B_2,B)->ord_less_e_q(int,Q,Q_1))))))).
% 8.06/8.08 all B Q_1 R_1 Q R (ord_less_e_q(int,plus_plus(int,times_times(int,B,Q_1),R_1),plus_plus(int,times_times(int,B,Q),R))-> (ord_less_e_q(int,R,zero_zero(int))-> (ord_less(int,B,R)-> (ord_less(int,B,R_1)->ord_less_e_q(int,Q,Q_1))))).
% 8.06/8.08 all B Q R B_2 Q_1 R_1 (plus_plus(int,times_times(int,B,Q),R)=plus_plus(int,times_times(int,B_2,Q_1),R_1)-> (ord_less(int,plus_plus(int,times_times(int,B_2,Q_1),R_1),zero_zero(int))-> (ord_less(int,R,B)-> (ord_less_e_q(int,zero_zero(int),R_1)-> (ord_less(int,zero_zero(int),B_2)-> (ord_less_e_q(int,B_2,B)->ord_less_e_q(int,Q_1,Q))))))).
% 8.06/8.08 all X (power_power(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls))))=power_power(int,X,number_number_of(nat,bit0(bit0(bit1(pls)))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all X (times_times(X_a,X,X)=power_power(X_a,X,number_number_of(nat,bit0(bit1(pls))))))).
% 8.06/8.08 zcong(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))).
% 8.06/8.08 all Y X P (-zcong(X,zero_zero(int),P)-> (zcong(power_power(int,Y,number_number_of(nat,bit0(bit1(pls)))),X,P)-> -dvd_dvd(int,P,Y))).
% 8.06/8.08 all P_1 (zprime(P_1)<->ord_less(int,one_one(int),P_1)& (all M_1 (ord_less_e_q(int,zero_zero(int),M_1)&dvd_dvd(int,M_1,P_1)->ti(int,M_1)=one_one(int)|ti(int,M_1)=ti(int,P_1)))).
% 8.06/8.08 all P (zprime(P)-> (ti(int,P)!=number_number_of(int,bit0(bit1(pls)))-> (ti(int,P)!=number_number_of(int,bit1(bit1(pls)))->ord_less_e_q(int,number_number_of(int,bit1(bit0(bit1(pls)))),P)))).
% 8.06/8.08 ord_less(nat,zero_zero(nat),number_number_of(nat,bit0(bit1(pls)))).
% 8.06/8.08 -(all S1 (-zcong(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))))).
% 8.06/8.08 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).
% 8.06/8.08 bit1(min)=min.
% 8.06/8.08 all L_1 (min=bit1(L_1)<->min=ti(int,L_1)).
% 8.06/8.08 all K_1 (bit1(K_1)=min<->ti(int,K_1)=min).
% 8.06/8.08 min!=pls.
% 8.06/8.08 pls!=min.
% 8.06/8.08 all L (min!=bit0(L)).
% 8.06/8.08 all K (bit0(K)!=min).
% 8.06/8.08 -ord_less(int,min,min).
% 8.06/8.08 ord_less_e_q(int,min,min).
% 8.06/8.08 all K_1 (ord_less(int,bit1(K_1),min)<->ord_less(int,K_1,min)).
% 8.06/8.08 all K_1 (ord_less(int,min,bit1(K_1))<->ord_less(int,min,K_1)).
% 8.06/8.08 -ord_less(int,pls,min).
% 8.06/8.08 ord_less(int,min,pls).
% 8.06/8.08 all K_1 (ord_less(int,min,bit0(K_1))<->ord_less(int,min,K_1)).
% 8.06/8.08 ord_less(int,min,zero_zero(int)).
% 8.06/8.08 all K_1 (ord_less_e_q(int,min,bit1(K_1))<->ord_less_e_q(int,min,K_1)).
% 8.06/8.08 all K_1 (ord_less_e_q(int,bit1(K_1),min)<->ord_less_e_q(int,K_1,min)).
% 8.06/8.08 ord_less_e_q(int,min,pls).
% 8.06/8.08 -ord_less_e_q(int,pls,min).
% 8.06/8.08 all K_1 (ord_less_e_q(int,bit0(K_1),min)<->ord_less_e_q(int,K_1,min)).
% 8.06/8.08 number_number_of(int,pls)!=number_number_of(int,min).
% 8.06/8.08 all K_1 (ord_less(int,bit0(K_1),min)<->ord_less_e_q(int,K_1,min)).
% 8.06/8.08 all K_1 (ord_less_e_q(int,min,bit0(K_1))<->ord_less(int,min,K_1)).
% 8.06/8.08 all Ma N_1 (times_times(int,Ma,N_1)=one_one(int)<->ti(int,Ma)=one_one(int)&ti(int,N_1)=one_one(int)|ti(int,Ma)=number_number_of(int,min)&ti(int,N_1)=number_number_of(int,min)).
% 8.06/8.08 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)).
% 8.06/8.08 all A_2 B_1 Ma (zcong(A_2,B_1,Ma)<->zcong(B_1,A_2,Ma)).
% 8.06/8.08 all K M zcong(K,K,M).
% 8.06/8.08 all C A_1 B M (zcong(A_1,B,M)-> (zcong(B,C,M)->zcong(A_1,C,M))).
% 8.06/8.08 all X_a (order(X_a)-> (all X Y (ord_less_e_q(X_a,X,Y)-> (ti(X_a,X)!=ti(X_a,Y)->ord_less(X_a,X,Y))))).
% 8.06/8.08 all B A_1 C (ord_less(int,A_1,C)-> (ord_less(int,B,C)->ord_less_e_q(int,A_1,B)|ord_less_e_q(int,B,A_1))).
% 8.06/8.08 all A_2 B_1 (zcong(A_2,B_1,zero_zero(int))<->ti(int,A_2)=ti(int,B_1)).
% 8.06/8.08 all A_1 B zcong(A_1,B,one_one(int)).
% 8.06/8.08 all A_1 M B zcong(times_times(int,A_1,M),times_times(int,B,M),M).
% 8.06/8.08 all K A_1 B M (zcong(A_1,B,M)->zcong(times_times(int,A_1,K),times_times(int,B,K),M)).
% 8.06/8.08 all K A_1 B M (zcong(A_1,B,M)->zcong(times_times(int,K,A_1),times_times(int,K,B),M)).
% 8.06/8.08 all C D A_1 B M (zcong(A_1,B,M)-> (zcong(C,D,M)->zcong(times_times(int,A_1,C),times_times(int,B,D),M))).
% 8.06/8.08 all C D A_1 B M (zcong(A_1,B,M)-> (zcong(C,D,M)->zcong(plus_plus(int,A_1,C),plus_plus(int,B,D),M))).
% 8.06/8.08 all X_a (number_ring(X_a)-> (all N (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)))).
% 8.06/8.08 all B M A_1 (ord_less(int,zero_zero(int),A_1)-> (ord_less(int,A_1,M)-> (ord_less(int,zero_zero(int),B)-> (ord_less(int,B,A_1)-> -zcong(A_1,B,M))))).
% 8.06/8.08 all A_2 B_1 Ma (zcong(A_2,B_1,Ma)<-> (exists K_2 (ti(int,B_1)=plus_plus(int,A_2,times_times(int,Ma,K_2))))).
% 8.06/8.08 all X (times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,X,number_number_of(nat,bit0(bit1(pls)))))=power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X),number_number_of(nat,bit0(bit1(pls))))).
% 8.06/8.08 all M A_1 (ord_less_e_q(int,zero_zero(int),A_1)-> (ord_less(int,A_1,M)-> (zcong(A_1,zero_zero(int),M)->ti(int,A_1)=zero_zero(int)))).
% 8.06/8.08 all B M A_1 (ord_less_e_q(int,zero_zero(int),A_1)-> (ord_less(int,A_1,M)-> (ord_less_e_q(int,zero_zero(int),B)-> (ord_less(int,B,M)-> (zcong(A_1,B,M)->ti(int,A_1)=ti(int,B)))))).
% 8.06/8.08 all Z X Y P (zcong(power_power(int,X,Y),one_one(int),P)->zcong(power_power(int,X,times_times(nat,Y,Z)),one_one(int),P)).
% 8.06/8.08 all N P M (ord_less_e_q(int,zero_zero(int),M)-> (zprime(P)-> (dvd_dvd(int,P,times_times(int,M,N))->dvd_dvd(int,P,M)|dvd_dvd(int,P,N)))).
% 8.06/8.08 quadRes(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),number_number_of(int,min)).
% 8.06/8.08 dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min))).
% 8.06/8.08 all J K M (ord_less(int,number_number_of(int,bit0(bit1(pls))),M)-> (zcong(power_power(int,number_number_of(int,min),J),power_power(int,number_number_of(int,min),K),M)->power_power(int,number_number_of(int,min),J)=power_power(int,number_number_of(int,min),K))).
% 8.06/8.08 all X P (ord_less(int,number_number_of(int,bit0(bit1(pls))),P)-> (zcong(X,number_number_of(int,min),P)-> -zcong(X,one_one(int),P))).
% 8.06/8.08 minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min))=plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)).
% 8.06/8.08 -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).
% 8.06/8.08 all X_2 (-ord_less(real,zero_zero(real),times_times(real,X_2,X_2))<->X_2=zero_zero(real)).
% 8.06/8.08 all C D A_1 B M (zcong(A_1,B,M)-> (zcong(C,D,M)->zcong(minus_minus(int,A_1,C),minus_minus(int,B,D),M))).
% 8.06/8.08 all K M N (dvd_dvd(int,K,minus_minus(int,M,N))-> (dvd_dvd(int,K,N)->dvd_dvd(int,K,M))).
% 8.06/8.08 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))).
% 8.06/8.08 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))).
% 8.06/8.08 all K L (minus_minus(int,bit0(K),bit0(L))=bit0(minus_minus(int,K,L))).
% 8.06/8.08 all K (minus_minus(int,K,pls)=ti(int,K)).
% 8.06/8.08 all A_1 B C (minus_minus(int,A_1,B)=ti(int,C)->ti(int,A_1)=plus_plus(int,C,B)).
% 8.06/8.08 all X_a (number_ring(X_a)-> (all V W (number_number_of(X_a,minus_minus(int,V,W))=minus_minus(X_a,number_number_of(X_a,V),number_number_of(X_a,W))))).
% 8.06/8.08 all X_b (number(X_b)&ring(X_b)-> (all V B C (times_times(X_b,number_number_of(X_b,V),minus_minus(X_b,B,C))=minus_minus(X_b,times_times(X_b,number_number_of(X_b,V),B),times_times(X_b,number_number_of(X_b,V),C))))).
% 8.06/8.08 all X_b (number(X_b)&ring(X_b)-> (all A_1 B V (times_times(X_b,minus_minus(X_b,A_1,B),number_number_of(X_b,V))=minus_minus(X_b,times_times(X_b,A_1,number_number_of(X_b,V)),times_times(X_b,B,number_number_of(X_b,V)))))).
% 8.06/8.08 all K L (minus_minus(int,bit1(K),bit0(L))=bit1(minus_minus(int,K,L))).
% 8.06/8.08 all K L (minus_minus(int,bit1(K),bit1(L))=bit0(minus_minus(int,K,L))).
% 8.06/8.08 all L (minus_minus(int,pls,bit0(L))=bit0(minus_minus(int,pls,L))).
% 8.06/8.08 all K_1 L_1 (ord_less(int,K_1,L_1)<->ord_less(int,minus_minus(int,K_1,L_1),zero_zero(int))).
% 8.06/8.08 all A_1 R B M C D N (plus_plus(int,times_times(int,minus_minus(int,A_1,times_times(int,R,B)),M),times_times(int,minus_minus(int,C,times_times(int,R,D)),N))=minus_minus(int,plus_plus(int,times_times(int,A_1,M),times_times(int,C,N)),times_times(int,R,plus_plus(int,times_times(int,B,M),times_times(int,D,N))))).
% 8.06/8.08 all A_2 B_1 Ma (zcong(A_2,B_1,Ma)<->dvd_dvd(int,Ma,minus_minus(int,A_2,B_1))).
% 8.06/8.08 all X_a (number_ring(X_a)-> (all V W C (plus_plus(X_a,number_number_of(X_a,V),minus_minus(X_a,number_number_of(X_a,W),C))=minus_minus(X_a,number_number_of(X_a,plus_plus(int,V,W)),C)))).
% 8.06/8.08 all A_1 X (ord_less(int,zero_zero(int),X)-> (ord_less(int,X,A_1)-> (ti(int,X)!=minus_minus(int,A_1,one_one(int))->ord_less(int,X,minus_minus(int,A_1,one_one(int)))))).
% 8.06/8.08 all W_1 Z_1 (ord_less_e_q(int,W_1,minus_minus(int,Z_1,one_one(int)))<->ord_less(int,W_1,Z_1)).
% 8.06/8.08 all L (minus_minus(int,pls,bit1(L))=bit1(minus_minus(int,min,L))).
% 8.06/8.08 all L (minus_minus(int,min,bit1(L))=bit0(minus_minus(int,min,L))).
% 8.06/8.08 all L (minus_minus(int,min,bit0(L))=bit1(minus_minus(int,min,L))).
% 8.06/8.08 all A_2 P_1 (zcong(times_times(int,A_2,minus_minus(int,P_1,one_one(int))),one_one(int),P_1)<->zcong(A_2,minus_minus(int,P_1,one_one(int)),P_1)).
% 8.06/8.08 all D C A_1 B M (zcong(A_1,B,M)-> (ti(int,B)=ti(int,C)-> (zcong(C,D,M)->zcong(A_1,D,M)))).
% 8.06/8.08 all A_1 P (zprime(P)-> (ord_less(int,zero_zero(int),A_1)-> (ord_less(int,A_1,P)-> (zcong(times_times(int,A_1,A_1),one_one(int),P)->ti(int,A_1)=one_one(int)|ti(int,A_1)=minus_minus(int,P,one_one(int)))))).
% 8.06/8.08 all A_1 P (zprime(P)-> (ord_less(int,zero_zero(int),A_1)-> (zcong(times_times(int,A_1,A_1),one_one(int),P)->zcong(A_1,one_one(int),P)|zcong(A_1,minus_minus(int,P,one_one(int)),P)))).
% 8.06/8.08 all A_1 B (times_times(int,plus_plus(int,A_1,B),minus_minus(int,A_1,B))=minus_minus(int,power_power(int,A_1,number_number_of(nat,bit0(bit1(pls)))),power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))).
% 8.06/8.08 all M zcong(M,zero_zero(int),M).
% 8.06/8.08 all C_1 D_1 A_2 B_1 Ma (zcong(A_2,B_1,Ma)-> (zcong(C_1,times_times(int,D_1,A_2),Ma)<->zcong(C_1,times_times(int,D_1,B_1),Ma))).
% 8.06/8.08 all C_1 D_1 A_2 B_1 Ma (zcong(A_2,B_1,Ma)-> (zcong(C_1,times_times(int,A_2,D_1),Ma)<->zcong(C_1,times_times(int,B_1,D_1),Ma))).
% 8.06/8.08 all C A_1 B M (zcong(A_1,B,M)->zcong(plus_plus(int,A_1,C),plus_plus(int,B,C),M)).
% 8.06/8.08 all Z X Y M (zcong(X,Y,M)->zcong(power_power(int,X,Z),power_power(int,Y,Z),M)).
% 8.06/8.08 all X_a (number_ring(X_a)-> (all X Y (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,power_power(X_a,X,number_number_of(nat,bit0(bit1(pls)))),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))))).
% 8.06/8.08 all A_1 B (power_power(int,minus_minus(int,A_1,B),number_number_of(nat,bit0(bit1(pls))))=plus_plus(int,minus_minus(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)),power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))).
% 8.06/8.08 all A_1 B (power_power(int,minus_minus(int,A_1,B),number_number_of(nat,bit1(bit1(pls))))=minus_minus(int,plus_plus(int,minus_minus(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))),power_power(int,A_1,number_number_of(nat,bit0(bit1(pls))))),B)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),A_1),power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,B,number_number_of(nat,bit1(bit1(pls)))))).
% 8.06/8.08 all M Y X (ord_less(int,zero_zero(int),X)-> (ord_less(int,zero_zero(int),Y)-> (ord_less(int,zero_zero(int),M)-> (zcong(X,Y,M)-> (ord_less(int,X,M)-> (ord_less(int,Y,M)->ti(int,X)=ti(int,Y))))))).
% 8.06/8.08 all M X (ord_less(int,zero_zero(int),X)-> (ord_less(int,X,M)-> -zcong(X,zero_zero(int),M))).
% 8.06/8.08 all N M (dvd_dvd(int,N,M)->ord_less_e_q(int,M,zero_zero(int))|ord_less_e_q(int,N,M)).
% 8.06/8.08 all A_2 Ma (zcong(A_2,zero_zero(int),Ma)<->dvd_dvd(int,Ma,A_2)).
% 8.06/8.08 all X_2 P_1 (zcong(X_2,zero_zero(int),P_1)<->dvd_dvd(int,P_1,X_2)).
% 8.06/8.08 all M N P (zprime(P)-> (dvd_dvd(int,P,times_times(int,M,N))->dvd_dvd(int,P,M)|dvd_dvd(int,P,N))).
% 8.06/8.08 all M X (ord_less_e_q(int,zero_zero(int),X)-> (ord_less(int,X,M)-> (zcong(X,zero_zero(int),M)->ti(int,X)=zero_zero(int)))).
% 8.06/8.08 all P Y N (ord_less(nat,zero_zero(nat),N)-> (dvd_dvd(int,P,Y)->dvd_dvd(int,P,power_power(int,Y,N)))).
% 8.06/8.08 all N (power_power(int,number_number_of(int,min),N)=one_one(int)|power_power(int,number_number_of(int,min),N)=number_number_of(int,min)).
% 8.06/8.08 all Y X P (zprime(P)-> (-zcong(X,zero_zero(int),P)-> (-zcong(Y,zero_zero(int),P)-> -zcong(times_times(int,X,Y),zero_zero(int),P)))).
% 8.06/8.08 all B A_1 P (zprime(P)-> (ord_less(int,zero_zero(int),A_1)-> (-zcong(A_1,zero_zero(int),P)& -zcong(B,zero_zero(int),P)-> -zcong(times_times(int,A_1,B),zero_zero(int),P)))).
% 8.06/8.08 all B A_1 P (zprime(P)-> (ord_less(int,zero_zero(int),A_1)-> (zcong(times_times(int,A_1,B),zero_zero(int),P)->zcong(A_1,zero_zero(int),P)|zcong(B,zero_zero(int),P)))).
% 8.06/8.08 all Y N P (zprime(P)-> (dvd_dvd(int,P,power_power(int,Y,N))-> (ord_less(nat,zero_zero(nat),N)->dvd_dvd(int,P,Y)))).
% 8.06/8.08 all M (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)).
% 8.06/8.08 all M (ord_less(int,number_number_of(int,bit0(bit1(pls))),M)-> -zcong(one_one(int),number_number_of(int,min),M)).
% 8.06/8.08 all A_1 P ((zcong(A_1,zero_zero(int),P)->legendre(A_1,P)=zero_zero(int))& (-zcong(A_1,zero_zero(int),P)-> (quadRes(P,A_1)->legendre(A_1,P)=one_one(int))& (-quadRes(P,A_1)->legendre(A_1,P)=number_number_of(int,min)))).
% 8.06/8.08 all Ma X_2 (quadRes(Ma,X_2)<-> (exists Y_1 zcong(power_power(int,Y_1,number_number_of(nat,bit0(bit1(pls)))),X_2,Ma))).
% 8.06/8.08 all X Y (power_power(real,plus_plus(real,X,Y),number_number_of(nat,bit0(bit1(pls))))=plus_plus(real,plus_plus(real,power_power(real,X,number_number_of(nat,bit0(bit1(pls)))),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))).
% 8.06/8.08 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)))).
% 8.06/8.08 all P M ((M=zero_zero(nat)->power_power(nat,P,M)=one_one(nat))& (M!=zero_zero(nat)->power_power(nat,P,M)=times_times(nat,P,power_power(nat,P,minus_minus(nat,M,one_one(nat)))))).
% 8.06/8.08 all X Y (minus_minus(nat,power_power(nat,X,number_number_of(nat,bit0(bit1(pls)))),power_power(nat,Y,number_number_of(nat,bit0(bit1(pls)))))=times_times(nat,plus_plus(nat,X,Y),minus_minus(nat,X,Y))).
% 8.06/8.08 all X_2 Y_2 (plus_plus(real,power_power(real,X_2,number_number_of(nat,bit0(bit1(pls)))),power_power(real,Y_2,number_number_of(nat,bit0(bit1(pls)))))=zero_zero(real)<->X_2=zero_zero(real)&Y_2=zero_zero(real)).
% 8.06/8.08 zero_zero(real)!=one_one(real).
% 8.06/8.08 all X_2 Y_2 (ord_less_e_q(real,X_2,Y_2)<->ord_less_e_q(real,minus_minus(real,X_2,Y_2),zero_zero(real))).
% 8.06/8.08 all X_2 Y_2 (ord_less(real,X_2,Y_2)<->ord_less_e_q(real,X_2,Y_2)&X_2!=Y_2).
% 8.06/8.08 all X_2 Y_2 (ord_less_e_q(real,X_2,Y_2)<->ord_less(real,X_2,Y_2)|X_2=Y_2).
% 8.06/8.08 all Z1 Z2 Z3 (times_times(real,times_times(real,Z1,Z2),Z3)=times_times(real,Z1,times_times(real,Z2,Z3))).
% 8.06/8.08 all Z W (times_times(real,Z,W)=times_times(real,W,Z)).
% 8.06/8.08 all Z (times_times(real,one_one(real),Z)=Z).
% 8.06/8.08 all Z X Y (ord_less_e_q(real,X,Y)->ord_less_e_q(real,plus_plus(real,Z,X),plus_plus(real,Z,Y))).
% 8.06/8.08 all X_a (ab_group_add(X_a)-> (all A_1 C B D (minus_minus(X_a,plus_plus(X_a,A_1,C),plus_plus(X_a,B,D))=plus_plus(X_a,minus_minus(X_a,A_1,B),minus_minus(X_a,C,D))))).
% 8.06/8.08 all A_2 B_1 C_1 (C_1!=zero_zero(real)-> (times_times(real,C_1,A_2)=times_times(real,C_1,B_1)<->A_2=B_1)).
% 8.06/8.08 all A_2 B_1 C_1 (C_1!=zero_zero(real)-> (times_times(real,A_2,C_1)=times_times(real,B_1,C_1)<->A_2=B_1)).
% 8.06/8.08 all N_1 Ma (times_times(nat,N_1,Ma)=one_one(nat)<->N_1=one_one(nat)&Ma=one_one(nat)).
% 8.06/8.08 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))).
% 8.06/8.08 all Ma N_1 (power_power(nat,Ma,N_1)=zero_zero(nat)<->N_1!=zero_zero(nat)&Ma=zero_zero(nat)).
% 8.06/8.08 all X_a (ring(X_a)-> (all X Y A_1 B (minus_minus(X_a,times_times(X_a,X,Y),times_times(X_a,A_1,B))=plus_plus(X_a,times_times(X_a,X,minus_minus(X_a,Y,B)),times_times(X_a,minus_minus(X_a,X,A_1),B))))).
% 8.06/8.08 all X_2 Y_2 Z_1 (ord_less(real,zero_zero(real),Z_1)-> (ord_less_e_q(real,times_times(real,X_2,Z_1),times_times(real,Y_2,Z_1))<->ord_less_e_q(real,X_2,Y_2))).
% 8.06/8.08 all X_2 Y_2 Z_1 (ord_less(real,zero_zero(real),Z_1)-> (ord_less_e_q(real,times_times(real,Z_1,X_2),times_times(real,Z_1,Y_2))<->ord_less_e_q(real,X_2,Y_2))).
% 8.06/8.08 all X Y Z (ord_less(real,zero_zero(real),Z)-> (ord_less(real,X,Y)->ord_less(real,times_times(real,Z,X),times_times(real,Z,Y)))).
% 8.06/8.08 all Y X (ord_less(real,zero_zero(real),X)-> (ord_less(real,zero_zero(real),Y)->ord_less(real,zero_zero(real),times_times(real,X,Y)))).
% 8.06/8.08 all X_2 Y_2 Z_1 (ord_less(real,zero_zero(real),Z_1)-> (ord_less(real,times_times(real,X_2,Z_1),times_times(real,Y_2,Z_1))<->ord_less(real,X_2,Y_2))).
% 8.06/8.08 all X_2 Y_2 (plus_plus(real,times_times(real,X_2,X_2),times_times(real,Y_2,Y_2))=zero_zero(real)<->X_2=zero_zero(real)&Y_2=zero_zero(real)).
% 8.06/8.08 all X_2 N_1 (power_power(nat,X_2,N_1)=one_one(nat)<->X_2=one_one(nat)|N_1=zero_zero(nat)).
% 8.06/8.08 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)))))).
% 8.06/8.08 all X_a (monoid_mult(X_a)-> (all X N (ord_less(nat,zero_zero(nat),N)->times_times(X_a,power_power(X_a,X,minus_minus(nat,N,one_one(nat))),X)=power_power(X_a,X,N)))).
% 8.06/8.08 all N ord_less_e_q(real,one_one(real),power_power(real,number_number_of(real,bit0(bit1(pls))),N)).
% 8.06/8.08 all X_a (power(X_a)-> (all M N ((N=zero_zero(nat)->power_power(X_a,M,N)=one_one(X_a))& (N!=zero_zero(nat)->power_power(X_a,M,N)=times_times(X_a,M,power_power(X_a,M,minus_minus(nat,N,one_one(nat)))))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all N A_1 B (ord_less(X_a,A_1,B)-> (ord_less_e_q(X_a,zero_zero(X_a),A_1)-> (ord_less(nat,zero_zero(nat),N)->ord_less(X_a,power_power(X_a,A_1,N),power_power(X_a,B,N))))))).
% 8.06/8.08 all W ord_less_e_q(real,W,W).
% 8.06/8.08 all Z W (ord_less_e_q(real,Z,W)|ord_less_e_q(real,W,Z)).
% 8.06/8.08 all K I J (ord_less_e_q(real,I,J)-> (ord_less_e_q(real,J,K)->ord_less_e_q(real,I,K))).
% 8.06/8.08 all Z W (ord_less_e_q(real,Z,W)-> (ord_less_e_q(real,W,Z)->Z=W)).
% 8.06/8.08 all X_a (ring_11004092258visors(X_a)-> (all N A_1 (ti(X_a,A_1)!=zero_zero(X_a)->power_power(X_a,A_1,N)!=zero_zero(X_a)))).
% 8.06/8.08 all X_a (comm_monoid_mult(X_a)-> (all A_1 B N (power_power(X_a,times_times(X_a,A_1,B),N)=times_times(X_a,power_power(X_a,A_1,N),power_power(X_a,B,N))))).
% 8.06/8.08 all X_a (monoid_mult(X_a)-> (all A_1 N (times_times(X_a,power_power(X_a,A_1,N),A_1)=times_times(X_a,A_1,power_power(X_a,A_1,N))))).
% 8.06/8.08 all X_a (monoid_mult(X_a)-> (all N (power_power(X_a,one_one(X_a),N)=one_one(X_a)))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all N X Y (dvd_dvd(X_a,X,Y)->dvd_dvd(X_a,power_power(X_a,X,N),power_power(X_a,Y,N))))).
% 8.06/8.08 all X_a (monoid_mult(X_a)-> (all A_1 M N (power_power(X_a,A_1,times_times(nat,M,N))=power_power(X_a,power_power(X_a,A_1,M),N)))).
% 8.06/8.08 all X_a (monoid_mult(X_a)-> (all A_1 (power_power(X_a,A_1,one_one(nat))=ti(X_a,A_1)))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all N A_1 B (ord_less_e_q(X_a,A_1,B)-> (ord_less_e_q(X_a,zero_zero(X_a),A_1)->ord_less_e_q(X_a,power_power(X_a,A_1,N),power_power(X_a,B,N)))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all N A_1 (ord_less_e_q(X_a,zero_zero(X_a),A_1)->ord_less_e_q(X_a,zero_zero(X_a),power_power(X_a,A_1,N))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all N A_1 (ord_less(X_a,zero_zero(X_a),A_1)->ord_less(X_a,zero_zero(X_a),power_power(X_a,A_1,N))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all N A_1 (ord_less_e_q(X_a,one_one(X_a),A_1)->ord_less_e_q(X_a,one_one(X_a),power_power(X_a,A_1,N))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all Ma N_1 A_2 (ord_less(X_a,one_one(X_a),A_2)-> (power_power(X_a,A_2,Ma)=power_power(X_a,A_2,N_1)<->Ma=N_1)))).
% 8.06/8.08 all X_a (power(X_a)&mult_zero(X_a)&no_zero_divisors(X_a)&zero_ne_q_one(X_a)-> (all A_2 N_1 (power_power(X_a,A_2,N_1)=zero_zero(X_a)<->ti(X_a,A_2)=zero_zero(X_a)&N_1!=zero_zero(nat)))).
% 8.06/8.08 all X_a (power(X_a)-> (all A_1 (power_power(X_a,A_1,zero_zero(nat))=one_one(X_a)))).
% 8.06/8.08 all X_a (monoid_mult(X_a)-> (all A_1 M N (power_power(X_a,A_1,plus_plus(nat,M,N))=times_times(X_a,power_power(X_a,A_1,M),power_power(X_a,A_1,N))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all M A_1 N B (dvd_dvd(X_a,power_power(X_a,A_1,N),B)-> (ord_less_e_q(nat,M,N)->dvd_dvd(X_a,power_power(X_a,A_1,M),B))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all N M X Y (dvd_dvd(X_a,X,Y)-> (ord_less_e_q(nat,N,M)->dvd_dvd(X_a,power_power(X_a,X,N),power_power(X_a,Y,M)))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all A_1 M N (ord_less_e_q(nat,M,N)->dvd_dvd(X_a,power_power(X_a,A_1,M),power_power(X_a,A_1,N))))).
% 8.06/8.08 all M N I (ord_less(nat,zero_zero(nat),I)-> (ord_less(nat,power_power(nat,I,M),power_power(nat,I,N))->ord_less(nat,M,N))).
% 8.06/8.08 all X_2 N_1 (ord_less(nat,zero_zero(nat),power_power(nat,X_2,N_1))<->ord_less(nat,zero_zero(nat),X_2)|N_1=zero_zero(nat)).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all A_1 N B (ord_less(X_a,power_power(X_a,A_1,N),power_power(X_a,B,N))-> (ord_less_e_q(X_a,zero_zero(X_a),B)->ord_less(X_a,A_1,B))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all N A_1 (ord_less(X_a,one_one(X_a),A_1)->ord_less(X_a,power_power(X_a,A_1,N),times_times(X_a,A_1,power_power(X_a,A_1,N)))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all N A_1 (ord_less(X_a,one_one(X_a),A_1)->ord_less(X_a,one_one(X_a),times_times(X_a,A_1,power_power(X_a,A_1,N)))))).
% 8.06/8.08 all X_a (power(X_a)&semiring_0(X_a)-> (all N ((N=zero_zero(nat)->power_power(X_a,zero_zero(X_a),N)=one_one(X_a))& (N!=zero_zero(nat)->power_power(X_a,zero_zero(X_a),N)=zero_zero(X_a))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all A_1 N N_2 (ord_less(nat,N,N_2)-> (ord_less(X_a,one_one(X_a),A_1)->ord_less(X_a,power_power(X_a,A_1,N),power_power(X_a,A_1,N_2)))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all M N A_1 (ord_less(X_a,one_one(X_a),A_1)-> (ord_less(X_a,power_power(X_a,A_1,M),power_power(X_a,A_1,N))->ord_less(nat,M,N))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all X_2 Y_2 B_1 (ord_less(X_a,one_one(X_a),B_1)-> (ord_less(X_a,power_power(X_a,B_1,X_2),power_power(X_a,B_1,Y_2))<->ord_less(nat,X_2,Y_2))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all A_1 N N_2 (ord_less_e_q(nat,N,N_2)-> (ord_less_e_q(X_a,one_one(X_a),A_1)->ord_less_e_q(X_a,power_power(X_a,A_1,N),power_power(X_a,A_1,N_2)))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all N A_1 (ord_less(X_a,zero_zero(X_a),A_1)-> (ord_less(X_a,A_1,one_one(X_a))->ord_less(X_a,times_times(X_a,A_1,power_power(X_a,A_1,N)),power_power(X_a,A_1,N)))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all A_1 N N_2 (ord_less(nat,N,N_2)-> (ord_less(X_a,zero_zero(X_a),A_1)-> (ord_less(X_a,A_1,one_one(X_a))->ord_less(X_a,power_power(X_a,A_1,N_2),power_power(X_a,A_1,N))))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all A_1 N B (power_power(X_a,A_1,N)=power_power(X_a,B,N)-> (ord_less_e_q(X_a,zero_zero(X_a),A_1)-> (ord_less_e_q(X_a,zero_zero(X_a),B)-> (ord_less(nat,zero_zero(nat),N)->ti(X_a,A_1)=ti(X_a,B))))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all A_1 N N_2 (ord_less_e_q(nat,N,N_2)-> (ord_less_e_q(X_a,zero_zero(X_a),A_1)-> (ord_less_e_q(X_a,A_1,one_one(X_a))->ord_less_e_q(X_a,power_power(X_a,A_1,N_2),power_power(X_a,A_1,N))))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all M N A_1 (ord_less(X_a,one_one(X_a),A_1)-> (ord_less_e_q(X_a,power_power(X_a,A_1,M),power_power(X_a,A_1,N))->ord_less_e_q(nat,M,N))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all X_2 Y_2 B_1 (ord_less(X_a,one_one(X_a),B_1)-> (ord_less_e_q(X_a,power_power(X_a,B_1,X_2),power_power(X_a,B_1,Y_2))<->ord_less_e_q(nat,X_2,Y_2))))).
% 8.06/8.08 all X_a (linordered_semidom(X_a)-> (all N A_1 (ord_less(X_a,one_one(X_a),A_1)-> (ord_less(nat,zero_zero(nat),N)->ord_less(X_a,one_one(X_a),power_power(X_a,A_1,N)))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all X N (ord_less(nat,zero_zero(nat),N)|ti(X_a,X)=one_one(X_a)->dvd_dvd(X_a,X,power_power(X_a,X,N))))).
% 8.06/8.08 all X_a (linord626643107strict(X_a)-> (all V U Y X A_1 (ord_less(X_a,X,A_1)-> (ord_less(X_a,Y,A_1)-> (ord_less_e_q(X_a,zero_zero(X_a),U)-> (ord_less_e_q(X_a,zero_zero(X_a),V)-> (plus_plus(X_a,U,V)=one_one(X_a)->ord_less(X_a,plus_plus(X_a,times_times(X_a,U,X),times_times(X_a,V,Y)),A_1)))))))).
% 8.06/8.08 all A_1 N (ord_less(nat,zero_zero(nat),N)-> (ord_less(real,zero_zero(real),A_1)-> (exists X_1 (ord_less(real,zero_zero(real),X_1)&power_power(real,X_1,N)=A_1& (all Y_1 (ord_less(real,zero_zero(real),Y_1)&power_power(real,Y_1,N)=A_1->Y_1=X_1)))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all A_1 dvd_dvd(X_a,A_1,zero_zero(X_a)))).
% 8.06/8.08 all A_1 B (dvd_dvd(nat,A_1,B)->B=zero_zero(nat)|ord_less_e_q(nat,A_1,B)).
% 8.06/8.08 all N X Y (dvd_dvd(nat,X,Y)->dvd_dvd(nat,power_power(nat,X,N),power_power(nat,Y,N))).
% 8.06/8.08 all C A_1 B (dvd_dvd(nat,A_1,B)->dvd_dvd(nat,times_times(nat,C,A_1),times_times(nat,C,B))).
% 8.06/8.08 all C A_1 B (dvd_dvd(nat,A_1,B)->dvd_dvd(nat,times_times(nat,A_1,C),times_times(nat,B,C))).
% 8.06/8.08 all B D A_1 (dvd_dvd(nat,D,A_1)-> (dvd_dvd(nat,D,plus_plus(nat,A_1,B))->dvd_dvd(nat,D,B))).
% 8.06/8.08 all Ma K_1 N_1 (dvd_dvd(nat,times_times(nat,Ma,K_1),times_times(nat,N_1,K_1))<->K_1=zero_zero(nat)|dvd_dvd(nat,Ma,N_1)).
% 8.06/8.08 all A_1 N B (dvd_dvd(nat,power_power(nat,A_1,N),power_power(nat,B,N))-> (N!=zero_zero(nat)->dvd_dvd(nat,A_1,B))).
% 8.06/8.08 all X Y N (N!=zero_zero(nat)-> (dvd_dvd(nat,power_power(nat,X,N),Y)->dvd_dvd(nat,X,Y))).
% 8.06/8.08 all X_a (linordered_idom(X_a)-> (all X Y (ti(X_a,X)!=ti(X_a,Y)-> (-ord_less(X_a,X,Y)->ord_less(X_a,Y,X))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all C A_1 B (dvd_dvd(X_a,A_1,B)-> (dvd_dvd(X_a,B,C)->dvd_dvd(X_a,A_1,C))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all A_1 dvd_dvd(X_a,A_1,A_1))).
% 8.06/8.08 all X Q N R (X=plus_plus(nat,times_times(nat,Q,N),R)-> (ord_less(nat,zero_zero(nat),R)-> (ord_less(nat,R,N)-> -dvd_dvd(nat,N,X)))).
% 8.06/8.08 all I M N (dvd_dvd(nat,power_power(nat,I,M),power_power(nat,I,N))-> (ord_less(nat,one_one(nat),I)->ord_less_e_q(nat,M,N))).
% 8.06/8.08 all X_a (mult_zero(X_a)-> (all A_1 (times_times(X_a,zero_zero(X_a),A_1)=zero_zero(X_a)))).
% 8.06/8.08 all X_a (mult_zero(X_a)-> (all A_1 (times_times(X_a,A_1,zero_zero(X_a))=zero_zero(X_a)))).
% 8.06/8.08 all X_a (ring_n68954251visors(X_a)-> (all A_2 B_1 (times_times(X_a,A_2,B_1)=zero_zero(X_a)<->ti(X_a,A_2)=zero_zero(X_a)|ti(X_a,B_1)=zero_zero(X_a)))).
% 8.06/8.08 all X_a (no_zero_divisors(X_a)-> (all B A_1 (ti(X_a,A_1)!=zero_zero(X_a)-> (ti(X_a,B)!=zero_zero(X_a)->times_times(X_a,A_1,B)!=zero_zero(X_a))))).
% 8.06/8.08 all X_a (no_zero_divisors(X_a)-> (all A_1 B (times_times(X_a,A_1,B)=zero_zero(X_a)->ti(X_a,A_1)=zero_zero(X_a)|ti(X_a,B)=zero_zero(X_a)))).
% 8.06/8.08 all X_a (zero_ne_q_one(X_a)->one_one(X_a)!=zero_zero(X_a)).
% 8.06/8.08 all X_a (zero_ne_q_one(X_a)->zero_zero(X_a)!=one_one(X_a)).
% 8.06/8.08 all X_a (comm_semiring(X_a)-> (all A_1 B C (times_times(X_a,plus_plus(X_a,A_1,B),C)=plus_plus(X_a,times_times(X_a,A_1,C),times_times(X_a,B,C))))).
% 8.06/8.08 all X_a (semiring(X_a)-> (all A_1 E B C (plus_plus(X_a,times_times(X_a,A_1,E),plus_plus(X_a,times_times(X_a,B,E),C))=plus_plus(X_a,times_times(X_a,plus_plus(X_a,A_1,B),E),C)))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all A_1 (dvd_dvd(X_a,zero_zero(X_a),A_1)->ti(X_a,A_1)=zero_zero(X_a)))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (dvd_dvd(X_a,times_times(X_a,A_1,B),C)->dvd_dvd(X_a,B,C)))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (dvd_dvd(X_a,times_times(X_a,A_1,B),C)->dvd_dvd(X_a,A_1,C)))).
% 8.06/8.08 all X_a (dvd(X_a)-> (all A_1 B K (A_1=times_times(X_a,B,K)->dvd_dvd(X_a,B,A_1)))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all C D A_1 B (dvd_dvd(X_a,A_1,B)-> (dvd_dvd(X_a,C,D)->dvd_dvd(X_a,times_times(X_a,A_1,C),times_times(X_a,B,D)))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all B A_1 C (dvd_dvd(X_a,A_1,C)->dvd_dvd(X_a,A_1,times_times(X_a,B,C))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all C A_1 B (dvd_dvd(X_a,A_1,B)->dvd_dvd(X_a,A_1,times_times(X_a,B,C))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all A_1 B dvd_dvd(X_a,A_1,times_times(X_a,B,A_1)))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all A_1 B dvd_dvd(X_a,A_1,times_times(X_a,A_1,B)))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all C A_1 B (dvd_dvd(X_a,A_1,B)-> (dvd_dvd(X_a,A_1,C)->dvd_dvd(X_a,A_1,plus_plus(X_a,B,C)))))).
% 8.06/8.08 all X_a (comm_semiring_1(X_a)-> (all A_1 dvd_dvd(X_a,one_one(X_a),A_1))).
% 8.06/8.08 all X_a (comm_ring_1(X_a)-> (all Z X Y (dvd_dvd(X_a,X,Y)-> (dvd_dvd(X_a,X,Z)->dvd_dvd(X_a,X,minus_minus(X_a,Y,Z)))))).
% 8.06/8.08 all N M (dvd_dvd(nat,N,M)->M=zero_zero(nat)|M=N|ord_less_e_q(nat,times_times(nat,number_number_of(nat,bit0(bit1(pls))),N),M)).
% 8.06/8.08 all X_a (linordered_ring(X_a)-> (all A_1 ord_less_e_q(X_a,zero_zero(X_a),times_times(X_a,A_1,A_1)))).
% 8.06/8.08 all X_a (linord581940658strict(X_a)-> (all A_2 B_1 (ord_less_e_q(X_a,zero_zero(X_a),times_times(X_a,A_2,B_1))<->ord_less_e_q(X_a,zero_zero(X_a),A_2)&ord_less_e_q(X_a,zero_zero(X_a),B_1)|ord_less_e_q(X_a,A_2,zero_zero(X_a))&ord_less_e_q(X_a,B_1,zero_zero(X_a))))).
% 8.06/8.08 all X_a (linord581940658strict(X_a)-> (all A_2 B_1 (ord_less_e_q(X_a,times_times(X_a,A_2,B_1),zero_zero(X_a))<->ord_less_e_q(X_a,zero_zero(X_a),A_2)&ord_less_e_q(X_a,B_1,zero_zero(X_a))|ord_less_e_q(X_a,A_2,zero_zero(X_a))&ord_less_e_q(X_a,zero_zero(X_a),B_1)))).
% 8.06/8.08 all X_a (ordere453448008miring(X_a)-> (all B A_1 (ord_less_e_q(X_a,zero_zero(X_a),A_1)-> (ord_less_e_q(X_a,zero_zero(X_a),B)->ord_less_e_q(X_a,zero_zero(X_a),times_times(X_a,A_1,B)))))).
% 8.06/8.08 all X_a (ordere453448008miring(X_a)-> (all B A_1 (ord_less_e_q(X_a,zero_zero(X_a),A_1)-> (ord_less_e_q(X_a,B,zero_zero(X_a))->ord_less_e_q(X_a,times_times(X_a,A_1,B),zero_zero(X_a)))))).
% 8.06/8.08 all X_a (ordere453448008miring(X_a)-> (all B A_1 (ord_less_e_q(X_a,zero_zero(X_a),A_1)-> (ord_less_e_q(X_a,B,zero_zero(X_a))->ord_less_e_q(X_a,times_times(X_a,B,A_1),zero_zero(X_a)))))).
% 8.06/8.08 all X_a (ordere453448008miring(X_a)-> (all B A_1 (ord_less_e_q(X_a,A_1,zero_zero(X_a))-> (ord_less_e_q(X_a,zero_zero(X_a),B)->ord_less_e_q(X_a,times_times(X_a,A_1,B),zero_zero(X_a)))))).
% 8.06/8.08 all X_a (ordered_ring(X_a)-> (all B A_1 (ord_less_e_q(X_a,A_1,zero_zero(X_a))-> (ord_less_e_q(X_a,B,zero_zero(X_a))->ord_less_e_q(X_a,zero_zero(X_a),times_times(X_a,A_1,B)))))).
% 8.06/8.08 semiri456707255roduct(int).
% 8.06/8.08 linord626643107strict(int).
% 8.06/8.08 linord219039673up_add(int).
% 8.06/8.08 ring_11004092258visors(int).
% 8.06/8.08 ordere453448008miring(int).
% 8.06/8.08 linord581940658strict(int).
% 8.06/8.08 ring_n68954251visors(int).
% 8.06/8.08 linordered_semidom(int).
% 8.06/8.08 comm_monoid_mult(int).
% 8.06/8.08 no_zero_divisors(int).
% 8.06/8.08 linordered_ring(int).
% 8.06/8.08 linordered_idom(int).
% 8.06/8.08 comm_semiring_1(int).
% 8.06/8.08 comm_semiring(int).
% 8.06/8.08 number_semiring(int).
% 8.06/8.08 ab_group_add(int).
% 8.06/8.08 zero_ne_q_one(int).
% 8.06/8.08 ordered_ring(int).
% 8.06/8.08 linorder(int).
% 8.06/8.08 monoid_mult(int).
% 8.06/8.08 comm_ring_1(int).
% 8.06/8.08 semiring_1(int).
% 8.06/8.08 semiring_0(int).
% 8.06/8.08 mult_zero(int).
% 8.06/8.08 order(int).
% 8.06/8.08 ring_char_0(int).
% 8.06/8.08 number_ring(int).
% 8.06/8.08 semiring(int).
% 8.06/8.08 ring_1(int).
% 8.06/8.08 power(int).
% 8.06/8.08 ring(int).
% 8.06/8.08 number(int).
% 8.06/8.08 dvd(int).
% 8.06/8.08 semiri456707255roduct(nat).
% 8.06/8.08 ordere453448008miring(nat).
% 8.06/8.08 linordered_semidom(nat).
% 8.06/8.08 comm_monoid_mult(nat).
% 8.06/8.08 no_zero_divisors(nat).
% 8.06/8.08 comm_semiring_1(nat).
% 8.06/8.08 comm_semiring(nat).
% 8.06/8.08 number_semiring(nat).
% 8.06/8.08 zero_ne_q_one(nat).
% 8.06/8.08 linorder(nat).
% 8.06/8.08 monoid_mult(nat).
% 8.06/8.08 semiring_1(nat).
% 8.06/8.08 semiring_0(nat).
% 8.06/8.08 mult_zero(nat).
% 8.06/8.08 order(nat).
% 8.06/8.08 semiring(nat).
% 8.06/8.08 power(nat).
% 8.06/8.08 number(nat).
% 8.06/8.08 dvd(nat).
% 8.06/8.08 order(bool).
% 8.06/8.08 semiri456707255roduct(real).
% 8.06/8.08 linord626643107strict(real).
% 8.06/8.08 linord219039673up_add(real).
% 8.06/8.08 ring_11004092258visors(real).
% 8.06/8.08 ordere453448008miring(real).
% 8.06/8.08 linord581940658strict(real).
% 8.06/8.08 ring_n68954251visors(real).
% 8.06/8.08 linordered_semidom(real).
% 8.06/8.08 comm_monoid_mult(real).
% 8.06/8.08 no_zero_divisors(real).
% 8.06/8.08 linordered_ring(real).
% 8.06/8.08 linordered_idom(real).
% 8.06/8.08 comm_semiring_1(real).
% 8.06/8.08 comm_semiring(real).
% 8.06/8.08 number_semiring(real).
% 8.06/8.08 ab_group_add(real).
% 8.06/8.08 zero_ne_q_one(real).
% 8.06/8.08 ordered_ring(real).
% 8.06/8.08 linorder(real).
% 8.06/8.08 monoid_mult(real).
% 8.06/8.08 comm_ring_1(real).
% 8.06/8.08 semiring_1(real).
% 8.06/8.08 semiring_0(real).
% 8.06/8.08 mult_zero(real).
% 8.06/8.08 order(real).
% 8.06/8.08 ring_char_0(real).
% 8.06/8.08 number_ring(real).
% 8.06/8.08 semiring(real).
% 8.06/8.08 ring_1(real).
% 8.06/8.08 power(real).
% 8.06/8.08 ring(real).
% 8.06/8.08 number(real).
% 8.06/8.08 dvd(real).
% 8.06/8.08 all T A (ti(T,ti(T,A))=ti(T,A)).
% 8.06/8.08 -ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)).
% 8.06/8.08 end_of_list.
% 8.06/8.08
% 8.06/8.08 -------> usable clausifies to:
% 8.06/8.08
% 8.06/8.08 list(usable).
% 8.06/8.08 0 [] A=A.
% 8.06/8.08 0 [] -ab_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).
% 8.06/8.08 0 [] -ab_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).
% 8.06/8.08 0 [] -ab_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).
% 8.06/8.08 0 [] minus_minus(nat,ti(nat,B_1_1),B_2_1)=minus_minus(nat,B_1_1,B_2_1).
% 8.06/8.08 0 [] minus_minus(nat,B_1_1,ti(nat,B_2_1))=minus_minus(nat,B_1_1,B_2_1).
% 8.06/8.08 0 [] ti(nat,minus_minus(nat,B_1_1,B_2_1))=minus_minus(nat,B_1_1,B_2_1).
% 8.06/8.08 0 [] -zero_ne_q_one(X_a)|ti(X_a,one_one(X_a))=one_one(X_a).
% 8.06/8.08 0 [] -power(X_a)|ti(X_a,one_one(X_a))=one_one(X_a).
% 8.06/8.08 0 [] -semiring(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).
% 8.06/8.08 0 [] -semiring(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).
% 8.06/8.08 0 [] -semiring(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).
% 8.06/8.08 0 [] -ab_group_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).
% 8.06/8.08 0 [] -ab_group_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).
% 8.06/8.08 0 [] -ab_group_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).
% 8.06/8.08 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).
% 8.06/8.08 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).
% 8.06/8.08 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).
% 8.06/8.08 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).
% 8.06/8.08 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).
% 8.06/8.08 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).
% 8.06/8.08 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).
% 8.06/8.08 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).
% 8.06/8.08 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).
% 8.06/8.08 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).
% 8.06/8.08 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).
% 8.06/8.08 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).
% 8.06/8.08 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).
% 8.06/8.08 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).
% 8.06/8.08 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).
% 8.06/8.08 0 [] -zero_ne_q_one(X_a)|ti(X_a,zero_zero(X_a))=zero_zero(X_a).
% 8.06/8.08 0 [] -no_zero_divisors(X_a)|ti(X_a,zero_zero(X_a))=zero_zero(X_a).
% 8.06/8.08 0 [] -mult_zero(X_a)|ti(X_a,zero_zero(X_a))=zero_zero(X_a).
% 8.06/8.08 0 [] -linord219039673up_add(X_a)|ti(X_a,zero_zero(X_a))=zero_zero(X_a).
% 8.06/8.08 0 [] ti(X_a,undefined(X_a))=undefined(X_a).
% 8.06/8.08 0 [] -zcong(ti(int,B_1_1),B_2_1,B_3)|zcong(B_1_1,B_2_1,B_3).
% 8.06/8.08 0 [] zcong(ti(int,B_1_1),B_2_1,B_3)| -zcong(B_1_1,B_2_1,B_3).
% 8.06/8.08 0 [] -zcong(B_1_1,ti(int,B_2_1),B_3)|zcong(B_1_1,B_2_1,B_3).
% 8.06/8.08 0 [] zcong(B_1_1,ti(int,B_2_1),B_3)| -zcong(B_1_1,B_2_1,B_3).
% 8.06/8.08 0 [] -zcong(B_1_1,B_2_1,ti(int,B_3))|zcong(B_1_1,B_2_1,B_3).
% 8.06/8.08 0 [] zcong(B_1_1,B_2_1,ti(int,B_3))| -zcong(B_1_1,B_2_1,B_3).
% 8.06/8.08 0 [] -zprime(ti(int,B_1_1))|zprime(B_1_1).
% 8.06/8.08 0 [] zprime(ti(int,B_1_1))| -zprime(B_1_1).
% 8.06/8.08 0 [] bit0(ti(int,B_1_1))=bit0(B_1_1).
% 8.06/8.08 0 [] ti(int,bit0(B_1_1))=bit0(B_1_1).
% 8.06/8.08 0 [] bit1(ti(int,B_1_1))=bit1(B_1_1).
% 8.06/8.08 0 [] ti(int,bit1(B_1_1))=bit1(B_1_1).
% 8.06/8.08 0 [] ti(int,min)=min.
% 8.06/8.08 0 [] ti(int,pls)=pls.
% 8.06/8.08 0 [] -number(X_a)|number_number_of(X_a,ti(int,B_1_1))=number_number_of(X_a,B_1_1).
% 8.06/8.08 0 [] -number(X_a)|ti(X_a,number_number_of(X_a,B_1_1))=number_number_of(X_a,B_1_1).
% 8.06/8.08 0 [] -order(X_a)| -ord_less(X_a,ti(X_a,B_1_1),B_2_1)|ord_less(X_a,B_1_1,B_2_1).
% 8.06/8.08 0 [] -order(X_a)|ord_less(X_a,ti(X_a,B_1_1),B_2_1)| -ord_less(X_a,B_1_1,B_2_1).
% 8.06/8.08 0 [] -order(X_a)| -ord_less(X_a,B_1_1,ti(X_a,B_2_1))|ord_less(X_a,B_1_1,B_2_1).
% 8.06/8.08 0 [] -order(X_a)|ord_less(X_a,B_1_1,ti(X_a,B_2_1))| -ord_less(X_a,B_1_1,B_2_1).
% 8.06/8.08 0 [] -order(X_a)| -ord_less_e_q(X_a,ti(X_a,B_1_1),B_2_1)|ord_less_e_q(X_a,B_1_1,B_2_1).
% 8.06/8.08 0 [] -order(X_a)|ord_less_e_q(X_a,ti(X_a,B_1_1),B_2_1)| -ord_less_e_q(X_a,B_1_1,B_2_1).
% 8.06/8.08 0 [] -order(X_a)| -ord_less_e_q(X_a,B_1_1,ti(X_a,B_2_1))|ord_less_e_q(X_a,B_1_1,B_2_1).
% 8.06/8.08 0 [] -order(X_a)|ord_less_e_q(X_a,B_1_1,ti(X_a,B_2_1))| -ord_less_e_q(X_a,B_1_1,B_2_1).
% 8.06/8.08 0 [] -power(X_a)|power_power(X_a,ti(X_a,B_1_1),B_2_1)=power_power(X_a,B_1_1,B_2_1).
% 8.06/8.08 0 [] -power(X_a)|power_power(X_a,B_1_1,ti(nat,B_2_1))=power_power(X_a,B_1_1,B_2_1).
% 8.06/8.08 0 [] -power(X_a)|ti(X_a,power_power(X_a,B_1_1,B_2_1))=power_power(X_a,B_1_1,B_2_1).
% 8.06/8.08 0 [] legendre(ti(int,B_1_1),B_2_1)=legendre(B_1_1,B_2_1).
% 8.06/8.08 0 [] legendre(B_1_1,ti(int,B_2_1))=legendre(B_1_1,B_2_1).
% 8.06/8.08 0 [] ti(int,legendre(B_1_1,B_2_1))=legendre(B_1_1,B_2_1).
% 8.06/8.08 0 [] -quadRes(ti(int,B_1_1),B_2_1)|quadRes(B_1_1,B_2_1).
% 8.06/8.08 0 [] quadRes(ti(int,B_1_1),B_2_1)| -quadRes(B_1_1,B_2_1).
% 8.06/8.08 0 [] -quadRes(B_1_1,ti(int,B_2_1))|quadRes(B_1_1,B_2_1).
% 8.06/8.08 0 [] quadRes(B_1_1,ti(int,B_2_1))| -quadRes(B_1_1,B_2_1).
% 8.06/8.08 0 [] -dvd(X_a)| -dvd_dvd(X_a,ti(X_a,B_1_1),B_2_1)|dvd_dvd(X_a,B_1_1,B_2_1).
% 8.06/8.08 0 [] -dvd(X_a)|dvd_dvd(X_a,ti(X_a,B_1_1),B_2_1)| -dvd_dvd(X_a,B_1_1,B_2_1).
% 8.06/8.08 0 [] -dvd(X_a)| -dvd_dvd(X_a,B_1_1,ti(X_a,B_2_1))|dvd_dvd(X_a,B_1_1,B_2_1).
% 8.06/8.08 0 [] -dvd(X_a)|dvd_dvd(X_a,B_1_1,ti(X_a,B_2_1))| -dvd_dvd(X_a,B_1_1,B_2_1).
% 8.06/8.08 0 [] -twoSqu420862341sum2sq(ti(int,B_1_1))|twoSqu420862341sum2sq(B_1_1).
% 8.06/8.08 0 [] twoSqu420862341sum2sq(ti(int,B_1_1))| -twoSqu420862341sum2sq(B_1_1).
% 8.06/8.08 0 [] ti(int,m)=m.
% 8.06/8.08 0 [] ti(int,s1)=s1.
% 8.06/8.08 0 [] ti(int,s)=s.
% 8.06/8.08 0 [] ti(int,t)=t.
% 8.06/8.08 0 [] ord_less(int,t,zero_zero(int)).
% 8.06/8.08 0 [] ord_less(int,t,one_one(int)).
% 8.06/8.08 0 [] ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))).
% 8.06/8.08 0 [] plus_plus(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).
% 8.06/8.08 0 [] t!=zero_zero(int)|plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))=zero_zero(int).
% 8.06/8.08 0 [] -ord_less_e_q(int,one_one(int),t).
% 8.06/8.08 0 [] ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 8.06/8.08 0 [] -linordered_idom(X_a)| -ord_less(X_a,plus_plus(X_a,power_power(X_a,X,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X_a)).
% 8.06/8.08 0 [] -linordered_idom(X_a)| -ord_less(X_a,zero_zero(X_a),plus_plus(X_a,power_power(X_a,X_2,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_2,number_number_of(nat,bit0(bit1(pls))))))|ti(X_a,X_2)!=zero_zero(X_a)|ti(X_a,Y_2)!=zero_zero(X_a).
% 8.06/8.08 0 [] -linordered_idom(X_a)|ord_less(X_a,zero_zero(X_a),plus_plus(X_a,power_power(X_a,X_2,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_2,number_number_of(nat,bit0(bit1(pls))))))|ti(X_a,X_2)=zero_zero(X_a).
% 8.06/8.08 0 [] -linordered_idom(X_a)|ord_less(X_a,zero_zero(X_a),plus_plus(X_a,power_power(X_a,X_2,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_2,number_number_of(nat,bit0(bit1(pls))))))|ti(X_a,Y_2)=zero_zero(X_a).
% 8.06/8.08 0 [] -linordered_idom(X_a)|plus_plus(X_a,power_power(X_a,X_2,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_2,number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(X_a)|ti(X_a,X_2)=zero_zero(X_a).
% 8.06/8.08 0 [] -linordered_idom(X_a)|plus_plus(X_a,power_power(X_a,X_2,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_2,number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(X_a)|ti(X_a,Y_2)=zero_zero(X_a).
% 8.06/8.08 0 [] -linordered_idom(X_a)|plus_plus(X_a,power_power(X_a,X_2,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_2,number_number_of(nat,bit0(bit1(pls)))))=zero_zero(X_a)|ti(X_a,X_2)!=zero_zero(X_a)|ti(X_a,Y_2)!=zero_zero(X_a).
% 8.06/8.08 0 [] -linordered_idom(X_a)| -ord_less(X_a,power_power(X_a,A_1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X_a)).
% 8.06/8.08 0 [] -linordered_idom(X_a)| -ord_less(X_a,zero_zero(X_a),power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))))|ti(X_a,A_2)!=zero_zero(X_a).
% 8.06/8.08 0 [] -linordered_idom(X_a)|ord_less(X_a,zero_zero(X_a),power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))))|ti(X_a,A_2)=zero_zero(X_a).
% 8.06/8.08 0 [] -semiring_1(X_a)|power_power(X_a,one_one(X_a),number_number_of(nat,bit0(bit1(pls))))=one_one(X_a).
% 8.06/8.08 0 [] -semiring_1(X_a)|power_power(X_a,zero_zero(X_a),number_number_of(nat,bit0(bit1(pls))))=zero_zero(X_a).
% 8.06/8.08 0 [] -ring_11004092258visors(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).
% 8.06/8.08 0 [] -ring_11004092258visors(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).
% 8.06/8.08 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)).
% 8.06/8.08 0 [] -number_ring(X_a)|plus_plus(X_a,number_number_of(X_a,V),one_one(X_a))=number_number_of(X_a,plus_plus(int,V,bit1(pls))).
% 8.06/8.08 0 [] ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 8.06/8.08 0 [] plus_plus(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)),$c1).
% 8.06/8.08 0 [] zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 8.06/8.08 0 [] twoSqu420862341sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)).
% 8.06/8.08 0 [] ord_less_e_q(int,W,W).
% 8.06/8.08 0 [] number_number_of(int,K)=ti(int,K).
% 8.06/8.08 0 [] times_times(int,Z,W)=times_times(int,W,Z).
% 8.06/8.08 0 [] ord_less_e_q(int,Z,W)|ord_less_e_q(int,W,Z).
% 8.06/8.08 0 [] times_times(int,number_number_of(int,V),number_number_of(int,W))=number_number_of(int,times_times(int,V,W)).
% 8.06/8.08 0 [] -ord_less_e_q(int,number_number_of(int,K_1),number_number_of(int,L_1))|ord_less_e_q(int,K_1,L_1).
% 8.06/8.08 0 [] ord_less_e_q(int,number_number_of(int,K_1),number_number_of(int,L_1))| -ord_less_e_q(int,K_1,L_1).
% 8.06/8.08 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -ord_less_e_q(X_a,number_number_of(X_a,X_2),number_number_of(X_a,Y_2))|ord_less_e_q(int,X_2,Y_2).
% 8.06/8.08 0 [] -number_ring(X_a)| -linordered_idom(X_a)|ord_less_e_q(X_a,number_number_of(X_a,X_2),number_number_of(X_a,Y_2))| -ord_less_e_q(int,X_2,Y_2).
% 8.06/8.08 0 [] times_times(int,times_times(int,Z1,Z2),Z3)=times_times(int,Z1,times_times(int,Z2,Z3)).
% 8.06/8.08 0 [] -ord_less_e_q(int,I,J)| -ord_less_e_q(int,J,K)|ord_less_e_q(int,I,K).
% 8.06/8.08 0 [] -ord_less_e_q(int,Z,W)| -ord_less_e_q(int,W,Z)|ti(int,Z)=ti(int,W).
% 8.06/8.08 0 [] power_power(int,X,plus_plus(nat,Y,Z))=times_times(int,power_power(int,X,Y),power_power(int,X,Z)).
% 8.06/8.08 0 [] -ord_less_e_q(int,bit1(K1),bit1(K2))|ord_less_e_q(int,K1,K2).
% 8.06/8.08 0 [] ord_less_e_q(int,bit1(K1),bit1(K2))| -ord_less_e_q(int,K1,K2).
% 8.06/8.08 0 [] -ord_less_e_q(int,bit1(K_1),bit1(L_1))|ord_less_e_q(int,K_1,L_1).
% 8.06/8.08 0 [] ord_less_e_q(int,bit1(K_1),bit1(L_1))| -ord_less_e_q(int,K_1,L_1).
% 8.06/8.08 0 [] ord_less_e_q(int,pls,pls).
% 8.06/8.08 0 [] -ord_less_e_q(int,bit0(K1),bit0(K2))|ord_less_e_q(int,K1,K2).
% 8.06/8.08 0 [] ord_less_e_q(int,bit0(K1),bit0(K2))| -ord_less_e_q(int,K1,K2).
% 8.06/8.08 0 [] -ord_less_e_q(int,bit0(K_1),bit0(L_1))|ord_less_e_q(int,K_1,L_1).
% 8.06/8.08 0 [] ord_less_e_q(int,bit0(K_1),bit0(L_1))| -ord_less_e_q(int,K_1,L_1).
% 8.06/8.08 0 [] -ord_less(int,Z_1,W_1)|ord_less_e_q(int,Z_1,W_1).
% 8.06/8.08 0 [] -ord_less(int,Z_1,W_1)|ti(int,Z_1)!=ti(int,W_1).
% 8.06/8.09 0 [] ord_less(int,Z_1,W_1)| -ord_less_e_q(int,Z_1,W_1)|ti(int,Z_1)=ti(int,W_1).
% 8.06/8.09 0 [] -ord_less_e_q(int,I,J)|ord_less_e_q(int,plus_plus(int,K,I),plus_plus(int,K,J)).
% 8.06/8.09 0 [] number_number_of(nat,V_3)!=zero_zero(nat)|ord_less_e_q(int,V_3,pls).
% 8.06/8.09 0 [] number_number_of(nat,V_3)=zero_zero(nat)| -ord_less_e_q(int,V_3,pls).
% 8.06/8.09 0 [] zero_zero(nat)!=number_number_of(nat,V_3)|ord_less_e_q(int,V_3,pls).
% 8.06/8.09 0 [] zero_zero(nat)=number_number_of(nat,V_3)| -ord_less_e_q(int,V_3,pls).
% 8.06/8.09 0 [] -number_semiring(X_a)| -ord_less_e_q(int,pls,V)| -ord_less_e_q(int,pls,V_1)|times_times(X_a,number_number_of(X_a,V),number_number_of(X_a,V_1))=number_number_of(X_a,times_times(int,V,V_1)).
% 8.06/8.09 0 [] -number_ring(X_a)|times_times(X_a,number_number_of(X_a,V),times_times(X_a,number_number_of(X_a,W),Z))=times_times(X_a,number_number_of(X_a,times_times(int,V,W)),Z).
% 8.06/8.09 0 [] -number_ring(X_a)|times_times(X_a,number_number_of(X_a,V),number_number_of(X_a,W))=number_number_of(X_a,times_times(int,V,W)).
% 8.06/8.09 0 [] -number_ring(X_a)|number_number_of(X_a,times_times(int,V,W))=times_times(X_a,number_number_of(X_a,V),number_number_of(X_a,W)).
% 8.06/8.09 0 [] -linord581940658strict(X_a)| -ord_less_e_q(X_a,plus_plus(X_a,times_times(X_a,X_2,X_2),times_times(X_a,Y_2,Y_2)),zero_zero(X_a))|ti(X_a,X_2)=zero_zero(X_a).
% 8.06/8.09 0 [] -linord581940658strict(X_a)| -ord_less_e_q(X_a,plus_plus(X_a,times_times(X_a,X_2,X_2),times_times(X_a,Y_2,Y_2)),zero_zero(X_a))|ti(X_a,Y_2)=zero_zero(X_a).
% 8.06/8.09 0 [] -linord581940658strict(X_a)|ord_less_e_q(X_a,plus_plus(X_a,times_times(X_a,X_2,X_2),times_times(X_a,Y_2,Y_2)),zero_zero(X_a))|ti(X_a,X_2)!=zero_zero(X_a)|ti(X_a,Y_2)!=zero_zero(X_a).
% 8.06/8.09 0 [] -linordered_ring(X_a)|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))).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -ord_less_e_q(X_a,number_number_of(X_a,X_2),zero_zero(X_a))|ord_less_e_q(int,X_2,pls).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)|ord_less_e_q(X_a,number_number_of(X_a,X_2),zero_zero(X_a))| -ord_less_e_q(int,X_2,pls).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -ord_less_e_q(X_a,zero_zero(X_a),number_number_of(X_a,Y_2))|ord_less_e_q(int,pls,Y_2).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)|ord_less_e_q(X_a,zero_zero(X_a),number_number_of(X_a,Y_2))| -ord_less_e_q(int,pls,Y_2).
% 8.06/8.09 0 [] -ord_less(nat,zero_zero(nat),number_number_of(nat,V_3))|ord_less(int,pls,V_3).
% 8.06/8.09 0 [] ord_less(nat,zero_zero(nat),number_number_of(nat,V_3))| -ord_less(int,pls,V_3).
% 8.06/8.09 0 [] -number(X_a)| -linorder(X_a)| -ord_less_e_q(X_a,number_number_of(X_a,V_3),number_number_of(X_a,W_1))| -ord_less(X_a,number_number_of(X_a,W_1),number_number_of(X_a,V_3)).
% 8.06/8.09 0 [] -number(X_a)| -linorder(X_a)|ord_less_e_q(X_a,number_number_of(X_a,V_3),number_number_of(X_a,W_1))|ord_less(X_a,number_number_of(X_a,W_1),number_number_of(X_a,V_3)).
% 8.06/8.09 0 [] -ord_less_e_q(int,pls,bit1(K_1))|ord_less_e_q(int,pls,K_1).
% 8.06/8.09 0 [] ord_less_e_q(int,pls,bit1(K_1))| -ord_less_e_q(int,pls,K_1).
% 8.06/8.09 0 [] -ord_less_e_q(int,bit0(K1),bit1(K2))|ord_less_e_q(int,K1,K2).
% 8.06/8.09 0 [] ord_less_e_q(int,bit0(K1),bit1(K2))| -ord_less_e_q(int,K1,K2).
% 8.06/8.09 0 [] -ord_less_e_q(int,bit0(K_1),bit1(L_1))|ord_less_e_q(int,K_1,L_1).
% 8.06/8.09 0 [] ord_less_e_q(int,bit0(K_1),bit1(L_1))| -ord_less_e_q(int,K_1,L_1).
% 8.06/8.09 0 [] -ord_less_e_q(int,bit0(K_1),pls)|ord_less_e_q(int,K_1,pls).
% 8.06/8.09 0 [] ord_less_e_q(int,bit0(K_1),pls)| -ord_less_e_q(int,K_1,pls).
% 8.06/8.09 0 [] -ord_less_e_q(int,pls,bit0(K_1))|ord_less_e_q(int,pls,K_1).
% 8.06/8.09 0 [] ord_less_e_q(int,pls,bit0(K_1))| -ord_less_e_q(int,pls,K_1).
% 8.06/8.09 0 [] -ord_less(int,W_2,W)| -ord_less_e_q(int,Z_2,Z)|ord_less(int,plus_plus(int,W_2,Z_2),plus_plus(int,W,Z)).
% 8.06/8.09 0 [] number_number_of(nat,pls)=zero_zero(nat).
% 8.06/8.09 0 [] zero_zero(nat)=number_number_of(nat,pls).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -ord_less_e_q(X_a,number_number_of(X_a,X_2),one_one(X_a))|ord_less_e_q(int,X_2,bit1(pls)).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)|ord_less_e_q(X_a,number_number_of(X_a,X_2),one_one(X_a))| -ord_less_e_q(int,X_2,bit1(pls)).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -ord_less_e_q(X_a,one_one(X_a),number_number_of(X_a,Y_2))|ord_less_e_q(int,bit1(pls),Y_2).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)|ord_less_e_q(X_a,one_one(X_a),number_number_of(X_a,Y_2))| -ord_less_e_q(int,bit1(pls),Y_2).
% 8.06/8.09 0 [] plus_plus(nat,one_one(nat),one_one(nat))=number_number_of(nat,bit0(bit1(pls))).
% 8.06/8.09 0 [] times_times(int,pls,W)=pls.
% 8.06/8.09 0 [] times_times(int,bit0(K),L)=bit0(times_times(int,K,L)).
% 8.06/8.09 0 [] -ord_less(int,number_number_of(int,K_1),number_number_of(int,L_1))|ord_less(int,K_1,L_1).
% 8.06/8.09 0 [] ord_less(int,number_number_of(int,K_1),number_number_of(int,L_1))| -ord_less(int,K_1,L_1).
% 8.06/8.09 0 [] times_times(int,Z,one_one(int))=ti(int,Z).
% 8.06/8.09 0 [] times_times(int,one_one(int),Z)=ti(int,Z).
% 8.06/8.09 0 [] plus_plus(int,number_number_of(int,V),number_number_of(int,W))=number_number_of(int,plus_plus(int,V,W)).
% 8.06/8.09 0 [] times_times(int,plus_plus(int,Z1,Z2),W)=plus_plus(int,times_times(int,Z1,W),times_times(int,Z2,W)).
% 8.06/8.09 0 [] times_times(int,W,plus_plus(int,Z1,Z2))=plus_plus(int,times_times(int,W,Z1),times_times(int,W,Z2)).
% 8.06/8.09 0 [] -ord_less_e_q(int,bit1(K_1),pls)|ord_less(int,K_1,pls).
% 8.06/8.09 0 [] ord_less_e_q(int,bit1(K_1),pls)| -ord_less(int,K_1,pls).
% 8.06/8.09 0 [] -ord_less(int,pls,bit1(K_1))|ord_less_e_q(int,pls,K_1).
% 8.06/8.09 0 [] ord_less(int,pls,bit1(K_1))| -ord_less_e_q(int,pls,K_1).
% 8.06/8.09 0 [] -ord_less_e_q(int,bit1(K1),bit0(K2))|ord_less(int,K1,K2).
% 8.06/8.09 0 [] ord_less_e_q(int,bit1(K1),bit0(K2))| -ord_less(int,K1,K2).
% 8.06/8.09 0 [] -ord_less_e_q(int,bit1(K_1),bit0(L_1))|ord_less(int,K_1,L_1).
% 8.06/8.09 0 [] ord_less_e_q(int,bit1(K_1),bit0(L_1))| -ord_less(int,K_1,L_1).
% 8.06/8.09 0 [] -ord_less(int,bit0(K1),bit1(K2))|ord_less_e_q(int,K1,K2).
% 8.06/8.09 0 [] ord_less(int,bit0(K1),bit1(K2))| -ord_less_e_q(int,K1,K2).
% 8.06/8.09 0 [] -ord_less(int,bit0(K_1),bit1(L_1))|ord_less_e_q(int,K_1,L_1).
% 8.06/8.09 0 [] ord_less(int,bit0(K_1),bit1(L_1))| -ord_less_e_q(int,K_1,L_1).
% 8.06/8.09 0 [] -ord_less(nat,number_number_of(nat,V_3),number_number_of(nat,V_2))| -ord_less(int,V_3,V_2)|ord_less(int,pls,V_2).
% 8.06/8.09 0 [] -ord_less(nat,number_number_of(nat,V_3),number_number_of(nat,V_2))|ord_less(int,V_3,V_2).
% 8.06/8.09 0 [] ord_less(nat,number_number_of(nat,V_3),number_number_of(nat,V_2))| -ord_less(int,pls,V_2)| -ord_less(int,V_3,V_2).
% 8.06/8.09 0 [] -ord_less_e_q(int,one_one(int),Z_1)|ord_less(int,zero_zero(int),Z_1).
% 8.06/8.09 0 [] ord_less_e_q(int,one_one(int),Z_1)| -ord_less(int,zero_zero(int),Z_1).
% 8.06/8.09 0 [] number_number_of(nat,bit1(pls))=one_one(nat).
% 8.06/8.09 0 [] one_one(nat)=number_number_of(nat,bit1(pls)).
% 8.06/8.09 0 [] -ord_less(int,W,Z)|ord_less_e_q(int,plus_plus(int,W,one_one(int)),Z).
% 8.06/8.09 0 [] -ord_less_e_q(int,plus_plus(int,W_1,one_one(int)),Z_1)|ord_less(int,W_1,Z_1).
% 8.06/8.09 0 [] ord_less_e_q(int,plus_plus(int,W_1,one_one(int)),Z_1)| -ord_less(int,W_1,Z_1).
% 8.06/8.09 0 [] -ord_less(int,W_1,plus_plus(int,Z_1,one_one(int)))|ord_less_e_q(int,W_1,Z_1).
% 8.06/8.09 0 [] ord_less(int,W_1,plus_plus(int,Z_1,one_one(int)))| -ord_less_e_q(int,W_1,Z_1).
% 8.06/8.09 0 [] -number_semiring(X_a)| -ord_less_e_q(int,pls,V)| -ord_less_e_q(int,pls,V_1)|plus_plus(X_a,number_number_of(X_a,V),number_number_of(X_a,V_1))=number_number_of(X_a,plus_plus(int,V,V_1)).
% 8.06/8.09 0 [] -ord_less(int,V,pls)|plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1))=number_number_of(nat,V_1).
% 8.06/8.09 0 [] ord_less(int,V,pls)| -ord_less(int,V_1,pls)|plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1))=number_number_of(nat,V).
% 8.06/8.09 0 [] ord_less(int,V,pls)|ord_less(int,V_1,pls)|plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1))=number_number_of(nat,plus_plus(int,V,V_1)).
% 8.06/8.09 0 [] -ord_less_e_q(int,zero_zero(int),Z)|ord_less(int,zero_zero(int),plus_plus(int,one_one(int),Z)).
% 8.06/8.09 0 [] -number_ring(X_a)| -ring_char_0(X_a)|number_number_of(X_a,X_2)!=number_number_of(X_a,Y_2)|ti(int,X_2)=ti(int,Y_2).
% 8.06/8.09 0 [] -number_ring(X_a)| -ring_char_0(X_a)|number_number_of(X_a,X_2)=number_number_of(X_a,Y_2)|ti(int,X_2)!=ti(int,Y_2).
% 8.06/8.09 0 [] -number(X_a)|number_number_of(X_a,W_1)!=ti(X_a,X_2)|ti(X_a,X_2)=number_number_of(X_a,W_1).
% 8.06/8.09 0 [] -number(X_a)|number_number_of(X_a,W_1)=ti(X_a,X_2)|ti(X_a,X_2)!=number_number_of(X_a,W_1).
% 8.06/8.09 0 [] bit1(K_1)!=bit1(L_1)|ti(int,K_1)=ti(int,L_1).
% 8.06/8.09 0 [] bit1(K_1)=bit1(L_1)|ti(int,K_1)!=ti(int,L_1).
% 8.06/8.09 0 [] bit0(K_1)!=bit0(L_1)|ti(int,K_1)=ti(int,L_1).
% 8.06/8.09 0 [] bit0(K_1)=bit0(L_1)|ti(int,K_1)!=ti(int,L_1).
% 8.06/8.09 0 [] ord_less(int,X,Y)|ti(int,X)=ti(int,Y)|ord_less(int,Y,X).
% 8.06/8.09 0 [] -linord581940658strict(X_a)|plus_plus(X_a,times_times(X_a,X_2,X_2),times_times(X_a,Y_2,Y_2))!=zero_zero(X_a)|ti(X_a,X_2)=zero_zero(X_a).
% 8.06/8.09 0 [] -linord581940658strict(X_a)|plus_plus(X_a,times_times(X_a,X_2,X_2),times_times(X_a,Y_2,Y_2))!=zero_zero(X_a)|ti(X_a,Y_2)=zero_zero(X_a).
% 8.06/8.09 0 [] -linord581940658strict(X_a)|plus_plus(X_a,times_times(X_a,X_2,X_2),times_times(X_a,Y_2,Y_2))=zero_zero(X_a)|ti(X_a,X_2)!=zero_zero(X_a)|ti(X_a,Y_2)!=zero_zero(X_a).
% 8.06/8.09 0 [] -number(X_b)| -semiring(X_b)|times_times(X_b,plus_plus(X_b,A_1,B),number_number_of(X_b,V))=plus_plus(X_b,times_times(X_b,A_1,number_number_of(X_b,V)),times_times(X_b,B,number_number_of(X_b,V))).
% 8.06/8.09 0 [] -number(X_b)| -semiring(X_b)|times_times(X_b,number_number_of(X_b,V),plus_plus(X_b,B,C))=plus_plus(X_b,times_times(X_b,number_number_of(X_b,V),B),times_times(X_b,number_number_of(X_b,V),C)).
% 8.06/8.09 0 [] plus_plus(int,plus_plus(int,Z1,Z2),Z3)=plus_plus(int,Z1,plus_plus(int,Z2,Z3)).
% 8.06/8.09 0 [] plus_plus(int,X,plus_plus(int,Y,Z))=plus_plus(int,Y,plus_plus(int,X,Z)).
% 8.06/8.09 0 [] plus_plus(int,Z,W)=plus_plus(int,W,Z).
% 8.06/8.09 0 [] zero_zero(int)=number_number_of(int,pls).
% 8.06/8.09 0 [] -ord_less(int,I,J)| -ord_less(int,zero_zero(int),K)|ord_less(int,times_times(int,K,I),times_times(int,K,J)).
% 8.06/8.09 0 [] -linordered_semidom(X_a)|power_power(X_a,X,number_number_of(nat,bit0(bit1(pls))))!=power_power(X_a,Y,number_number_of(nat,bit0(bit1(pls))))| -ord_less_e_q(X_a,zero_zero(X_a),X)| -ord_less_e_q(X_a,zero_zero(X_a),Y)|ti(X_a,X)=ti(X_a,Y).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less_e_q(X_a,power_power(X_a,X,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y,number_number_of(nat,bit0(bit1(pls)))))| -ord_less_e_q(X_a,zero_zero(X_a),Y)|ord_less_e_q(X_a,X,Y).
% 8.06/8.09 0 [] -linordered_idom(X_a)|ord_less_e_q(X_a,zero_zero(X_a),power_power(X_a,A_1,number_number_of(nat,bit0(bit1(pls))))).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(X_a,power_power(X_a,X,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y,number_number_of(nat,bit0(bit1(pls)))))| -ord_less_e_q(X_a,zero_zero(X_a),Y)|ord_less(X_a,X,Y).
% 8.06/8.09 0 [] -linordered_idom(X_a)| -ord_less_e_q(X_a,plus_plus(X_a,power_power(X_a,X_2,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_2,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X_a))|ti(X_a,X_2)=zero_zero(X_a).
% 8.06/8.09 0 [] -linordered_idom(X_a)| -ord_less_e_q(X_a,plus_plus(X_a,power_power(X_a,X_2,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_2,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X_a))|ti(X_a,Y_2)=zero_zero(X_a).
% 8.06/8.09 0 [] -linordered_idom(X_a)|ord_less_e_q(X_a,plus_plus(X_a,power_power(X_a,X_2,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_2,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X_a))|ti(X_a,X_2)!=zero_zero(X_a)|ti(X_a,Y_2)!=zero_zero(X_a).
% 8.06/8.09 0 [] -linordered_idom(X_a)|ord_less_e_q(X_a,zero_zero(X_a),plus_plus(X_a,power_power(X_a,X,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y,number_number_of(nat,bit0(bit1(pls)))))).
% 8.06/8.09 0 [] -linord581940658strict(X_a)| -ord_less(X_a,zero_zero(X_a),plus_plus(X_a,times_times(X_a,X_2,X_2),times_times(X_a,Y_2,Y_2)))|ti(X_a,X_2)!=zero_zero(X_a)|ti(X_a,Y_2)!=zero_zero(X_a).
% 8.06/8.09 0 [] -linord581940658strict(X_a)|ord_less(X_a,zero_zero(X_a),plus_plus(X_a,times_times(X_a,X_2,X_2),times_times(X_a,Y_2,Y_2)))|ti(X_a,X_2)=zero_zero(X_a).
% 8.06/8.09 0 [] -linord581940658strict(X_a)|ord_less(X_a,zero_zero(X_a),plus_plus(X_a,times_times(X_a,X_2,X_2),times_times(X_a,Y_2,Y_2)))|ti(X_a,Y_2)=zero_zero(X_a).
% 8.06/8.09 0 [] -linordered_ring(X_a)| -ord_less(X_a,plus_plus(X_a,times_times(X_a,X,X),times_times(X_a,Y,Y)),zero_zero(X_a)).
% 8.06/8.09 0 [] -number_ring(X_a)|times_times(X_a,number_number_of(X_a,bit1(pls)),A_1)=ti(X_a,A_1).
% 8.06/8.09 0 [] -number_ring(X_a)|times_times(X_a,A_1,number_number_of(X_a,bit1(pls)))=ti(X_a,A_1).
% 8.06/8.09 0 [] one_one(int)=number_number_of(int,bit1(pls)).
% 8.06/8.09 0 [] times_times(int,bit1(K),L)=plus_plus(int,bit0(times_times(int,K,L)),L).
% 8.06/8.09 0 [] -ord_less(int,zero_zero(int),Ma)|times_times(int,Ma,N_1)!=one_one(int)|ti(int,Ma)=one_one(int).
% 8.06/8.09 0 [] -ord_less(int,zero_zero(int),Ma)|times_times(int,Ma,N_1)!=one_one(int)|ti(int,N_1)=one_one(int).
% 8.06/8.09 0 [] -ord_less(int,zero_zero(int),Ma)|times_times(int,Ma,N_1)=one_one(int)|ti(int,Ma)!=one_one(int)|ti(int,N_1)!=one_one(int).
% 8.06/8.09 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).
% 8.06/8.09 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).
% 8.06/8.09 0 [] bit1(K)!=pls.
% 8.06/8.09 0 [] pls!=bit1(L).
% 8.06/8.09 0 [] bit1(K)!=bit0(L).
% 8.06/8.09 0 [] bit0(K)!=bit1(L).
% 8.06/8.09 0 [] bit0(K_1)!=pls|ti(int,K_1)=pls.
% 8.06/8.09 0 [] bit0(K_1)=pls|ti(int,K_1)!=pls.
% 8.06/8.09 0 [] pls!=bit0(L_1)|pls=ti(int,L_1).
% 8.06/8.09 0 [] pls=bit0(L_1)|pls!=ti(int,L_1).
% 8.06/8.09 0 [] bit0(pls)=pls.
% 8.06/8.09 0 [] pls=zero_zero(int).
% 8.06/8.09 0 [] -ord_less(int,bit1(K1),bit1(K2))|ord_less(int,K1,K2).
% 8.06/8.09 0 [] ord_less(int,bit1(K1),bit1(K2))| -ord_less(int,K1,K2).
% 8.06/8.09 0 [] -ord_less(int,bit1(K_1),bit1(L_1))|ord_less(int,K_1,L_1).
% 8.06/8.09 0 [] ord_less(int,bit1(K_1),bit1(L_1))| -ord_less(int,K_1,L_1).
% 8.06/8.09 0 [] -ord_less(int,pls,pls).
% 8.06/8.09 0 [] -ord_less(int,bit0(K1),bit0(K2))|ord_less(int,K1,K2).
% 8.06/8.09 0 [] ord_less(int,bit0(K1),bit0(K2))| -ord_less(int,K1,K2).
% 8.06/8.09 0 [] -ord_less(int,bit0(K_1),bit0(L_1))|ord_less(int,K_1,L_1).
% 8.06/8.09 0 [] ord_less(int,bit0(K_1),bit0(L_1))| -ord_less(int,K_1,L_1).
% 8.06/8.09 0 [] zero_zero(int)!=one_one(int).
% 8.06/8.09 0 [] plus_plus(int,K,pls)=ti(int,K).
% 8.06/8.09 0 [] plus_plus(int,pls,K)=ti(int,K).
% 8.06/8.09 0 [] plus_plus(int,bit0(K),bit0(L))=bit0(plus_plus(int,K,L)).
% 8.06/8.09 0 [] bit0(K)=plus_plus(int,K,K).
% 8.06/8.09 0 [] plus_plus(int,Z,zero_zero(int))=ti(int,Z).
% 8.06/8.09 0 [] plus_plus(int,zero_zero(int),Z)=ti(int,Z).
% 8.06/8.09 0 [] -ord_less(int,I,J)|ord_less(int,plus_plus(int,I,K),plus_plus(int,J,K)).
% 8.06/8.09 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)).
% 8.06/8.09 0 [] -monoid_mult(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).
% 8.06/8.09 0 [] -number_semiring(X_a)|times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),Z)=plus_plus(X_a,Z,Z).
% 8.06/8.09 0 [] -number_ring(X_a)|times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),Z)=plus_plus(X_a,Z,Z).
% 8.06/8.09 0 [] -number_semiring(X_a)|times_times(X_a,Z,number_number_of(X_a,bit0(bit1(pls))))=plus_plus(X_a,Z,Z).
% 8.06/8.09 0 [] -number_ring(X_a)|times_times(X_a,Z,number_number_of(X_a,bit0(bit1(pls))))=plus_plus(X_a,Z,Z).
% 8.06/8.09 0 [] -monoid_mult(X_a)|power_power(X_a,A_1,number_number_of(nat,bit0(bit1(pls))))=times_times(X_a,A_1,A_1).
% 8.06/8.09 0 [] -linordered_idom(X_a)| -ord_less(X_a,plus_plus(X_a,A_2,A_2),zero_zero(X_a))|ord_less(X_a,A_2,zero_zero(X_a)).
% 8.06/8.09 0 [] -linordered_idom(X_a)|ord_less(X_a,plus_plus(X_a,A_2,A_2),zero_zero(X_a))| -ord_less(X_a,A_2,zero_zero(X_a)).
% 8.06/8.09 0 [] -number_semiring(X_a)|number_number_of(X_a,pls)=zero_zero(X_a).
% 8.06/8.09 0 [] -number_ring(X_a)|number_number_of(X_a,pls)=zero_zero(X_a).
% 8.06/8.09 0 [] -number_ring(X_a)|zero_zero(X_a)=number_number_of(X_a,pls).
% 8.06/8.09 0 [] -number_ring(X_a)|plus_plus(X_a,number_number_of(X_a,pls),A_1)=ti(X_a,A_1).
% 8.06/8.09 0 [] -number_ring(X_a)|plus_plus(X_a,A_1,number_number_of(X_a,pls))=ti(X_a,A_1).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -ord_less(X_a,number_number_of(X_a,X_2),number_number_of(X_a,Y_2))|ord_less(int,X_2,Y_2).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)|ord_less(X_a,number_number_of(X_a,X_2),number_number_of(X_a,Y_2))| -ord_less(int,X_2,Y_2).
% 8.06/8.09 0 [] -number_ring(X_a)|plus_plus(X_a,number_number_of(X_a,V),plus_plus(X_a,number_number_of(X_a,W),Z))=plus_plus(X_a,number_number_of(X_a,plus_plus(int,V,W)),Z).
% 8.06/8.09 0 [] -number_ring(X_a)|plus_plus(X_a,number_number_of(X_a,V),number_number_of(X_a,W))=number_number_of(X_a,plus_plus(int,V,W)).
% 8.06/8.09 0 [] -number_ring(X_a)|number_number_of(X_a,plus_plus(int,V,W))=plus_plus(X_a,number_number_of(X_a,V),number_number_of(X_a,W)).
% 8.06/8.09 0 [] -ord_less(int,bit1(K_1),pls)|ord_less(int,K_1,pls).
% 8.06/8.09 0 [] ord_less(int,bit1(K_1),pls)| -ord_less(int,K_1,pls).
% 8.06/8.09 0 [] -ord_less(int,bit1(K1),bit0(K2))|ord_less(int,K1,K2).
% 8.06/8.09 0 [] ord_less(int,bit1(K1),bit0(K2))| -ord_less(int,K1,K2).
% 8.06/8.09 0 [] -ord_less(int,bit1(K_1),bit0(L_1))|ord_less(int,K_1,L_1).
% 8.06/8.09 0 [] ord_less(int,bit1(K_1),bit0(L_1))| -ord_less(int,K_1,L_1).
% 8.06/8.09 0 [] -ord_less(int,bit1(W_1),zero_zero(int))|ord_less(int,W_1,zero_zero(int)).
% 8.06/8.09 0 [] ord_less(int,bit1(W_1),zero_zero(int))| -ord_less(int,W_1,zero_zero(int)).
% 8.06/8.09 0 [] -ord_less(int,bit0(K_1),pls)|ord_less(int,K_1,pls).
% 8.06/8.09 0 [] ord_less(int,bit0(K_1),pls)| -ord_less(int,K_1,pls).
% 8.06/8.09 0 [] -ord_less(int,pls,bit0(K_1))|ord_less(int,pls,K_1).
% 8.06/8.09 0 [] ord_less(int,pls,bit0(K_1))| -ord_less(int,pls,K_1).
% 8.06/8.09 0 [] -ord_less(int,pls,zero_zero(int)).
% 8.06/8.09 0 [] -ord_less(int,bit0(W_1),zero_zero(int))|ord_less(int,W_1,zero_zero(int)).
% 8.06/8.09 0 [] ord_less(int,bit0(W_1),zero_zero(int))| -ord_less(int,W_1,zero_zero(int)).
% 8.06/8.09 0 [] plus_plus(int,bit1(K),bit0(L))=bit1(plus_plus(int,K,L)).
% 8.06/8.09 0 [] plus_plus(int,bit0(K),bit1(L))=bit1(plus_plus(int,K,L)).
% 8.06/8.09 0 [] ord_less(int,zero_zero(int),one_one(int)).
% 8.06/8.09 0 [] bit1(K)=plus_plus(int,plus_plus(int,one_one(int),K),K).
% 8.06/8.09 0 [] plus_plus(int,plus_plus(int,one_one(int),Z),Z)!=zero_zero(int).
% 8.06/8.09 0 [] -ord_less(int,W_1,plus_plus(int,Z_1,one_one(int)))|ord_less(int,W_1,Z_1)|ti(int,W_1)=ti(int,Z_1).
% 8.06/8.09 0 [] ord_less(int,W_1,plus_plus(int,Z_1,one_one(int)))| -ord_less(int,W_1,Z_1).
% 8.06/8.09 0 [] ord_less(int,W_1,plus_plus(int,Z_1,one_one(int)))|ti(int,W_1)!=ti(int,Z_1).
% 8.06/8.09 0 [] -monoid_mult(X_b)| -number(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)).
% 8.06/8.09 0 [] -number_semiring(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,power_power(X_a,X,number_number_of(nat,bit0(bit1(pls)))),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)).
% 8.06/8.09 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)).
% 8.06/8.09 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)).
% 8.06/8.09 0 [] -number_semiring(X_a)|number_number_of(X_a,bit1(pls))=one_one(X_a).
% 8.06/8.09 0 [] -number_ring(X_a)|number_number_of(X_a,bit1(pls))=one_one(X_a).
% 8.06/8.09 0 [] -number_ring(X_a)|one_one(X_a)=number_number_of(X_a,bit1(pls)).
% 8.06/8.09 0 [] -ord_less(int,plus_plus(int,plus_plus(int,one_one(int),Z_1),Z_1),zero_zero(int))|ord_less(int,Z_1,zero_zero(int)).
% 8.06/8.09 0 [] ord_less(int,plus_plus(int,plus_plus(int,one_one(int),Z_1),Z_1),zero_zero(int))| -ord_less(int,Z_1,zero_zero(int)).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -ord_less(X_a,number_number_of(X_a,X_2),zero_zero(X_a))|ord_less(int,X_2,pls).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)|ord_less(X_a,number_number_of(X_a,X_2),zero_zero(X_a))| -ord_less(int,X_2,pls).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -ord_less(X_a,zero_zero(X_a),number_number_of(X_a,Y_2))|ord_less(int,pls,Y_2).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)|ord_less(X_a,zero_zero(X_a),number_number_of(X_a,Y_2))| -ord_less(int,pls,Y_2).
% 8.06/8.09 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))).
% 8.06/8.09 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))).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -ord_less(X_a,number_number_of(X_a,X_2),one_one(X_a))|ord_less(int,X_2,bit1(pls)).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)|ord_less(X_a,number_number_of(X_a,X_2),one_one(X_a))| -ord_less(int,X_2,bit1(pls)).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -ord_less(X_a,one_one(X_a),number_number_of(X_a,Y_2))|ord_less(int,bit1(pls),Y_2).
% 8.06/8.09 0 [] -number_ring(X_a)| -linordered_idom(X_a)|ord_less(X_a,one_one(X_a),number_number_of(X_a,Y_2))| -ord_less(int,bit1(pls),Y_2).
% 8.06/8.09 0 [] dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))).
% 8.06/8.09 0 [] power_power(int,plus_plus(int,A_1,B),number_number_of(nat,bit1(bit1(pls))))=plus_plus(int,plus_plus(int,plus_plus(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))),power_power(int,A_1,number_number_of(nat,bit0(bit1(pls))))),B)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),A_1),power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,B,number_number_of(nat,bit1(bit1(pls))))).
% 8.06/8.09 0 [] power_power(int,plus_plus(int,A_1,B),number_number_of(nat,bit0(bit1(pls))))=plus_plus(int,plus_plus(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)),power_power(int,B,number_number_of(nat,bit0(bit1(pls))))).
% 8.06/8.09 0 [] -ord_less_e_q(int,zero_zero(int),X)| -ord_less(int,X,number_number_of(int,bit0(bit1(pls))))|ti(int,X)=zero_zero(int)|ti(int,X)=one_one(int).
% 8.06/8.09 0 [] ord_less_e_q(int,zero_zero(int),s).
% 8.06/8.09 0 [] ord_less(int,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 8.06/8.09 0 [] zcong(s1,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 8.06/8.09 0 [] times_times(int,A_1,power_power(int,A_1,number_number_of(nat,bit0(bit1(pls)))))=power_power(int,A_1,number_number_of(nat,bit1(bit1(pls)))).
% 8.06/8.09 0 [] ord_less_e_q(int,X,power_power(int,X,number_number_of(nat,bit0(bit1(pls))))).
% 8.06/8.09 0 [] -ord_less(int,zero_zero(int),A_1)|ti(int,A_1)!=plus_plus(int,R,times_times(int,A_1,Q))| -ord_less(int,R,A_1)|ord_less_e_q(int,one_one(int),Q).
% 8.06/8.09 0 [] -ord_less(int,zero_zero(int),A_1)|ti(int,A_1)!=plus_plus(int,R,times_times(int,A_1,Q))| -ord_less_e_q(int,zero_zero(int),R)|ord_less_e_q(int,Q,one_one(int)).
% 8.06/8.09 0 [] ord_less_e_q(int,zero_zero(int),number_number_of(int,bit0(bit1(pls)))).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|power_power(X_a,X,times_times(nat,number_number_of(nat,bit0(bit1(pls))),N))=times_times(X_a,power_power(X_a,X,N),power_power(X_a,X,N)).
% 8.06/8.09 0 [] zcong(power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),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))).
% 8.06/8.09 0 [] ord_less_e_q(int,zero_zero(int),$c2).
% 8.06/8.09 0 [] ord_less(int,$c2,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 8.06/8.09 0 [] zcong(s1,$c2,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 8.06/8.09 0 [] -ord_less_e_q(int,zero_zero(int),Y_1)| -ord_less(int,Y_1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))| -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,$c2).
% 8.06/8.09 0 [] ord_less_e_q(int,zero_zero(int),$c3).
% 8.06/8.09 0 [] ord_less(int,$c3,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 8.06/8.09 0 [] zcong(s1,$c3,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 8.06/8.09 0 [] zcong(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))).
% 8.06/8.09 0 [] -ord_less(nat,zero_zero(nat),power_power(nat,X_2,N_1))|N_1=zero_zero(nat)|ord_less(nat,zero_zero(nat),X_2).
% 8.06/8.09 0 [] ord_less(nat,zero_zero(nat),power_power(nat,X_2,N_1))|N_1!=zero_zero(nat).
% 8.06/8.09 0 [] ord_less(nat,zero_zero(nat),power_power(nat,X_2,N_1))| -ord_less(nat,zero_zero(nat),X_2).
% 8.06/8.09 0 [] -zprime(P)| -dvd_dvd(int,P,power_power(int,A_1,N))|dvd_dvd(int,P,A_1).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|power_power(X_a,power_power(X_a,X,P),Q)=power_power(X_a,X,times_times(nat,P,Q)).
% 8.06/8.09 0 [] -zprime(P)|dvd_dvd(int,P,B)| -dvd_dvd(int,power_power(int,P,N),times_times(int,A_1,B))|dvd_dvd(int,power_power(int,P,N),A_1).
% 8.06/8.09 0 [] -zprime(P)|dvd_dvd(int,P,A_1)| -dvd_dvd(int,power_power(int,P,N),times_times(int,A_1,B))|dvd_dvd(int,power_power(int,P,N),B).
% 8.06/8.09 0 [] power_power(int,power_power(int,X,Y),Z)=power_power(int,X,times_times(nat,Y,Z)).
% 8.06/8.09 0 [] -ord_less(int,zero_zero(int),M)| -ord_less(int,M,N)| -dvd_dvd(int,N,M).
% 8.06/8.09 0 [] -ord_less_e_q(int,zero_zero(int),M)| -ord_less_e_q(int,zero_zero(int),N)| -dvd_dvd(int,M,N)| -dvd_dvd(int,N,M)|ti(int,M)=ti(int,N).
% 8.06/8.09 0 [] -dvd_dvd(int,times_times(int,K,M),times_times(int,K,N))|ti(int,K)=zero_zero(int)|dvd_dvd(int,M,N).
% 8.06/8.09 0 [] -dvd_dvd(int,K_1,plus_plus(int,N_1,times_times(int,K_1,Ma)))|dvd_dvd(int,K_1,N_1).
% 8.06/8.09 0 [] dvd_dvd(int,K_1,plus_plus(int,N_1,times_times(int,K_1,Ma)))| -dvd_dvd(int,K_1,N_1).
% 8.06/8.09 0 [] -dvd_dvd(int,A_2,D_1)| -dvd_dvd(int,A_2,plus_plus(int,X_2,Ta))|dvd_dvd(int,A_2,plus_plus(int,plus_plus(int,X_2,times_times(int,C_1,D_1)),Ta)).
% 8.06/8.09 0 [] -dvd_dvd(int,A_2,D_1)|dvd_dvd(int,A_2,plus_plus(int,X_2,Ta))| -dvd_dvd(int,A_2,plus_plus(int,plus_plus(int,X_2,times_times(int,C_1,D_1)),Ta)).
% 8.06/8.09 0 [] zprime(number_number_of(int,bit0(bit1(pls)))).
% 8.06/8.09 0 [] -dvd_dvd(int,Z,N)| -ord_less(int,zero_zero(int),N)|ord_less_e_q(int,Z,N).
% 8.06/8.09 0 [] -twoSqu420862341sum2sq(X)| -twoSqu420862341sum2sq(Y)|twoSqu420862341sum2sq(times_times(int,X,Y)).
% 8.06/8.09 0 [] -ord_less_e_q(nat,number_number_of(nat,V_3),number_number_of(nat,V_2))|ord_less_e_q(int,V_3,V_2)|ord_less_e_q(int,V_3,pls).
% 8.06/8.09 0 [] ord_less_e_q(nat,number_number_of(nat,V_3),number_number_of(nat,V_2))| -ord_less_e_q(int,V_3,V_2).
% 8.06/8.09 0 [] ord_less_e_q(nat,number_number_of(nat,V_3),number_number_of(nat,V_2))| -ord_less_e_q(int,V_3,pls).
% 8.06/8.09 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)).
% 8.06/8.09 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)).
% 8.06/8.09 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))).
% 8.06/8.09 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).
% 8.06/8.09 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)).
% 8.06/8.09 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).
% 8.06/8.09 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)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|times_times(X_a,A_1,B)=times_times(X_a,B,A_1).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,A_1,C)=plus_plus(X_a,C,A_1).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,A_1,plus_plus(X_a,C,D))=plus_plus(X_a,C,plus_plus(X_a,A_1,D)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,A_1,plus_plus(X_a,C,D))=plus_plus(X_a,plus_plus(X_a,A_1,C),D).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,plus_plus(X_a,A_1,B),C)=plus_plus(X_a,A_1,plus_plus(X_a,B,C)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,plus_plus(X_a,A_1,B),C)=plus_plus(X_a,plus_plus(X_a,A_1,C),B).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,plus_plus(X_a,A_1,B),plus_plus(X_a,C,D))=plus_plus(X_a,plus_plus(X_a,A_1,C),plus_plus(X_a,B,D)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|power_power(X_a,X,one_one(nat))=ti(X_a,X).
% 8.06/8.09 0 [] -ord_less(nat,zero_zero(nat),power_power(nat,X_2,number_number_of(nat,W_1)))|number_number_of(nat,W_1)=zero_zero(nat)|ord_less(nat,zero_zero(nat),X_2).
% 8.06/8.09 0 [] ord_less(nat,zero_zero(nat),power_power(nat,X_2,number_number_of(nat,W_1)))|number_number_of(nat,W_1)!=zero_zero(nat).
% 8.06/8.09 0 [] ord_less(nat,zero_zero(nat),power_power(nat,X_2,number_number_of(nat,W_1)))| -ord_less(nat,zero_zero(nat),X_2).
% 8.06/8.09 0 [] times_times(nat,Z,number_number_of(nat,bit0(bit1(pls))))=plus_plus(nat,Z,Z).
% 8.06/8.09 0 [] times_times(nat,number_number_of(nat,bit0(bit1(pls))),Z)=plus_plus(nat,Z,Z).
% 8.06/8.09 0 [] -ord_less(int,V,pls)|times_times(nat,number_number_of(nat,V),number_number_of(nat,V_1))=zero_zero(nat).
% 8.06/8.09 0 [] ord_less(int,V,pls)|times_times(nat,number_number_of(nat,V),number_number_of(nat,V_1))=number_number_of(nat,times_times(int,V,V_1)).
% 8.06/8.09 0 [] -ord_less(int,V,pls)|times_times(nat,number_number_of(nat,V),times_times(nat,number_number_of(nat,V_1),K))=zero_zero(nat).
% 8.06/8.09 0 [] ord_less(int,V,pls)|times_times(nat,number_number_of(nat,V),times_times(nat,number_number_of(nat,V_1),K))=times_times(nat,number_number_of(nat,times_times(int,V,V_1)),K).
% 8.06/8.09 0 [] -monoid_mult(X_a)|power_power(X_a,A_1,times_times(nat,number_number_of(nat,bit0(bit1(pls))),N))=power_power(X_a,power_power(X_a,A_1,N),number_number_of(nat,bit0(bit1(pls)))).
% 8.06/8.09 0 [] -linordered_idom(X_a)| -ord_less_e_q(X_a,power_power(X_a,A_1,times_times(nat,number_number_of(nat,bit0(bit1(pls))),K)),zero_zero(X_a))|ti(X_a,A_1)=zero_zero(X_a).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|times_times(X_a,zero_zero(X_a),A_1)=zero_zero(X_a).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|times_times(X_a,A_1,zero_zero(X_a))=zero_zero(X_a).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,zero_zero(X_a),A_1)=ti(X_a,A_1).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,A_1,zero_zero(X_a))=ti(X_a,A_1).
% 8.06/8.09 0 [] -semiri456707255roduct(X_a)|ti(X_a,B_1)!=plus_plus(X_a,B_1,A_2)|ti(X_a,A_2)=zero_zero(X_a).
% 8.06/8.09 0 [] -semiri456707255roduct(X_a)|ti(X_a,B_1)=plus_plus(X_a,B_1,A_2)|ti(X_a,A_2)!=zero_zero(X_a).
% 8.06/8.09 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)).
% 8.06/8.09 0 [] -semiri456707255roduct(X_a)|ti(X_a,A_2)=ti(X_a,B_1)|ti(X_a,C_1)=ti(X_a,D_1)|plus_plus(X_a,times_times(X_a,A_2,C_1),times_times(X_a,B_1,D_1))!=plus_plus(X_a,times_times(X_a,A_2,D_1),times_times(X_a,B_1,C_1)).
% 8.06/8.09 0 [] -semiri456707255roduct(X_a)|ti(X_a,A_2)!=ti(X_a,B_1)|plus_plus(X_a,times_times(X_a,A_2,C_1),times_times(X_a,B_1,D_1))=plus_plus(X_a,times_times(X_a,A_2,D_1),times_times(X_a,B_1,C_1)).
% 8.06/8.09 0 [] -semiri456707255roduct(X_a)|ti(X_a,C_1)!=ti(X_a,D_1)|plus_plus(X_a,times_times(X_a,A_2,C_1),times_times(X_a,B_1,D_1))=plus_plus(X_a,times_times(X_a,A_2,D_1),times_times(X_a,B_1,C_1)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|times_times(X_a,plus_plus(X_a,A_1,B),C)=plus_plus(X_a,times_times(X_a,A_1,C),times_times(X_a,B,C)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,times_times(X_a,A_1,M),times_times(X_a,B,M))=times_times(X_a,plus_plus(X_a,A_1,B),M).
% 8.06/8.09 0 [] -semiri456707255roduct(X_a)|plus_plus(X_a,times_times(X_a,W_1,Y_2),times_times(X_a,X_2,Z_1))!=plus_plus(X_a,times_times(X_a,W_1,Z_1),times_times(X_a,X_2,Y_2))|ti(X_a,W_1)=ti(X_a,X_2)|ti(X_a,Y_2)=ti(X_a,Z_1).
% 8.06/8.09 0 [] -semiri456707255roduct(X_a)|plus_plus(X_a,times_times(X_a,W_1,Y_2),times_times(X_a,X_2,Z_1))=plus_plus(X_a,times_times(X_a,W_1,Z_1),times_times(X_a,X_2,Y_2))|ti(X_a,W_1)!=ti(X_a,X_2).
% 8.06/8.09 0 [] -semiri456707255roduct(X_a)|plus_plus(X_a,times_times(X_a,W_1,Y_2),times_times(X_a,X_2,Z_1))=plus_plus(X_a,times_times(X_a,W_1,Z_1),times_times(X_a,X_2,Y_2))|ti(X_a,Y_2)!=ti(X_a,Z_1).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|times_times(X_a,one_one(X_a),A_1)=ti(X_a,A_1).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|times_times(X_a,A_1,one_one(X_a))=ti(X_a,A_1).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|power_power(X_a,times_times(X_a,X,Y),Q)=times_times(X_a,power_power(X_a,X,Q),power_power(X_a,Y,Q)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|times_times(X_a,power_power(X_a,X,P),power_power(X_a,X,Q))=power_power(X_a,X,plus_plus(nat,P,Q)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|power_power(X_a,X,zero_zero(nat))=one_one(X_a).
% 8.06/8.09 0 [] ord_less_e_q(int,zero_zero(int),zero_zero(int)).
% 8.06/8.09 0 [] -linordered_idom(X_a)|ord_less_e_q(X_a,zero_zero(X_a),power_power(X_a,A_1,times_times(nat,number_number_of(nat,bit0(bit1(pls))),N))).
% 8.06/8.09 0 [] -semiri456707255roduct(X_a)|ti(X_a,R)=zero_zero(X_a)|ti(X_a,A_1)!=ti(X_a,B)|ti(X_a,C)=ti(X_a,D)|plus_plus(X_a,A_1,times_times(X_a,R,C))!=plus_plus(X_a,B,times_times(X_a,R,D)).
% 8.06/8.09 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).
% 8.06/8.09 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).
% 8.06/8.09 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).
% 8.06/8.09 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|power_power(X_a,A_2,number_number_of(nat,W_1))!=zero_zero(X_a)|ti(X_a,A_2)=zero_zero(X_a).
% 8.06/8.09 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|power_power(X_a,A_2,number_number_of(nat,W_1))!=zero_zero(X_a)|number_number_of(nat,W_1)!=zero_zero(nat).
% 8.06/8.09 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|power_power(X_a,A_2,number_number_of(nat,W_1))=zero_zero(X_a)|ti(X_a,A_2)!=zero_zero(X_a)|number_number_of(nat,W_1)=zero_zero(nat).
% 8.06/8.09 0 [] -ord_less(int,zero_zero(int),A_1)| -ord_less(int,zero_zero(int),times_times(int,A_1,B))|ord_less(int,zero_zero(int),B).
% 8.06/8.09 0 [] ord_less_e_q(int,zero_zero(int),one_one(int)).
% 8.06/8.09 0 [] -ord_less_e_q(int,zero_zero(int),X)| -ord_less_e_q(int,zero_zero(int),Y)|ord_less_e_q(int,zero_zero(int),times_times(int,X,Y)).
% 8.06/8.09 0 [] -ord_less_e_q(int,zero_zero(int),X)| -ord_less_e_q(int,zero_zero(int),Y)|ord_less_e_q(int,zero_zero(int),plus_plus(int,X,Y)).
% 8.06/8.09 0 [] -ord_less_e_q(int,zero_zero(int),X)|ord_less_e_q(int,zero_zero(int),power_power(int,X,N)).
% 8.06/8.09 0 [] -power(X_a)| -semiring_0(X_a)|number_number_of(nat,W)!=zero_zero(nat)|power_power(X_a,zero_zero(X_a),number_number_of(nat,W))=one_one(X_a).
% 8.06/8.09 0 [] -power(X_a)| -semiring_0(X_a)|number_number_of(nat,W)=zero_zero(nat)|power_power(X_a,zero_zero(X_a),number_number_of(nat,W))=zero_zero(X_a).
% 8.06/8.09 0 [] ord_less_e_q(int,zero_zero(int),number_number_of(int,bit1(bit1(pls)))).
% 8.06/8.09 0 [] -ord_less_e_q(int,zero_zero(int),plus_plus(int,times_times(int,B_2,Q_1),R_1))| -ord_less(int,R_1,B_2)| -ord_less(int,zero_zero(int),B_2)|ord_less_e_q(int,zero_zero(int),Q_1).
% 8.06/8.09 0 [] -ord_less(int,plus_plus(int,times_times(int,B_2,Q_1),R_1),zero_zero(int))| -ord_less_e_q(int,zero_zero(int),R_1)| -ord_less(int,zero_zero(int),B_2)|ord_less_e_q(int,Q_1,zero_zero(int)).
% 8.06/8.09 0 [] -ord_less_e_q(int,plus_plus(int,times_times(int,B,Q_1),R_1),plus_plus(int,times_times(int,B,Q),R))| -ord_less_e_q(int,zero_zero(int),R_1)| -ord_less(int,R_1,B)| -ord_less(int,R,B)|ord_less_e_q(int,Q_1,Q).
% 8.06/8.09 0 [] plus_plus(int,times_times(int,B,Q),R)!=plus_plus(int,times_times(int,B_2,Q_1),R_1)| -ord_less_e_q(int,zero_zero(int),plus_plus(int,times_times(int,B_2,Q_1),R_1))| -ord_less(int,R_1,B_2)| -ord_less_e_q(int,zero_zero(int),R)| -ord_less(int,zero_zero(int),B_2)| -ord_less_e_q(int,B_2,B)|ord_less_e_q(int,Q,Q_1).
% 8.06/8.09 0 [] -ord_less_e_q(int,plus_plus(int,times_times(int,B,Q_1),R_1),plus_plus(int,times_times(int,B,Q),R))| -ord_less_e_q(int,R,zero_zero(int))| -ord_less(int,B,R)| -ord_less(int,B,R_1)|ord_less_e_q(int,Q,Q_1).
% 8.06/8.09 0 [] plus_plus(int,times_times(int,B,Q),R)!=plus_plus(int,times_times(int,B_2,Q_1),R_1)| -ord_less(int,plus_plus(int,times_times(int,B_2,Q_1),R_1),zero_zero(int))| -ord_less(int,R,B)| -ord_less_e_q(int,zero_zero(int),R_1)| -ord_less(int,zero_zero(int),B_2)| -ord_less_e_q(int,B_2,B)|ord_less_e_q(int,Q_1,Q).
% 8.06/8.09 0 [] power_power(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls))))=power_power(int,X,number_number_of(nat,bit0(bit0(bit1(pls))))).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|times_times(X_a,X,X)=power_power(X_a,X,number_number_of(nat,bit0(bit1(pls)))).
% 8.06/8.09 0 [] zcong(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))).
% 8.06/8.09 0 [] zcong(X,zero_zero(int),P)| -zcong(power_power(int,Y,number_number_of(nat,bit0(bit1(pls)))),X,P)| -dvd_dvd(int,P,Y).
% 8.06/8.09 0 [] -zprime(P_1)|ord_less(int,one_one(int),P_1).
% 8.06/8.09 0 [] -zprime(P_1)| -ord_less_e_q(int,zero_zero(int),M_1)| -dvd_dvd(int,M_1,P_1)|ti(int,M_1)=one_one(int)|ti(int,M_1)=ti(int,P_1).
% 8.06/8.09 0 [] zprime(P_1)| -ord_less(int,one_one(int),P_1)|ord_less_e_q(int,zero_zero(int),$f1(P_1)).
% 8.06/8.09 0 [] zprime(P_1)| -ord_less(int,one_one(int),P_1)|dvd_dvd(int,$f1(P_1),P_1).
% 8.06/8.09 0 [] zprime(P_1)| -ord_less(int,one_one(int),P_1)|ti(int,$f1(P_1))!=one_one(int).
% 8.06/8.09 0 [] zprime(P_1)| -ord_less(int,one_one(int),P_1)|ti(int,$f1(P_1))!=ti(int,P_1).
% 8.06/8.09 0 [] -zprime(P)|ti(int,P)=number_number_of(int,bit0(bit1(pls)))|ti(int,P)=number_number_of(int,bit1(bit1(pls)))|ord_less_e_q(int,number_number_of(int,bit1(bit0(bit1(pls)))),P).
% 8.06/8.09 0 [] ord_less(nat,zero_zero(nat),number_number_of(nat,bit0(bit1(pls)))).
% 8.06/8.09 0 [] zcong(power_power(int,$c4,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))).
% 8.06/8.09 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).
% 8.06/8.09 0 [] bit1(min)=min.
% 8.06/8.09 0 [] min!=bit1(L_1)|min=ti(int,L_1).
% 8.06/8.09 0 [] min=bit1(L_1)|min!=ti(int,L_1).
% 8.06/8.09 0 [] bit1(K_1)!=min|ti(int,K_1)=min.
% 8.06/8.09 0 [] bit1(K_1)=min|ti(int,K_1)!=min.
% 8.06/8.09 0 [] min!=pls.
% 8.06/8.09 0 [] pls!=min.
% 8.06/8.09 0 [] min!=bit0(L).
% 8.06/8.09 0 [] bit0(K)!=min.
% 8.06/8.09 0 [] -ord_less(int,min,min).
% 8.06/8.09 0 [] ord_less_e_q(int,min,min).
% 8.06/8.09 0 [] -ord_less(int,bit1(K_1),min)|ord_less(int,K_1,min).
% 8.06/8.09 0 [] ord_less(int,bit1(K_1),min)| -ord_less(int,K_1,min).
% 8.06/8.09 0 [] -ord_less(int,min,bit1(K_1))|ord_less(int,min,K_1).
% 8.06/8.09 0 [] ord_less(int,min,bit1(K_1))| -ord_less(int,min,K_1).
% 8.06/8.09 0 [] -ord_less(int,pls,min).
% 8.06/8.09 0 [] ord_less(int,min,pls).
% 8.06/8.09 0 [] -ord_less(int,min,bit0(K_1))|ord_less(int,min,K_1).
% 8.06/8.09 0 [] ord_less(int,min,bit0(K_1))| -ord_less(int,min,K_1).
% 8.06/8.09 0 [] ord_less(int,min,zero_zero(int)).
% 8.06/8.09 0 [] -ord_less_e_q(int,min,bit1(K_1))|ord_less_e_q(int,min,K_1).
% 8.06/8.09 0 [] ord_less_e_q(int,min,bit1(K_1))| -ord_less_e_q(int,min,K_1).
% 8.06/8.09 0 [] -ord_less_e_q(int,bit1(K_1),min)|ord_less_e_q(int,K_1,min).
% 8.06/8.09 0 [] ord_less_e_q(int,bit1(K_1),min)| -ord_less_e_q(int,K_1,min).
% 8.06/8.09 0 [] ord_less_e_q(int,min,pls).
% 8.06/8.09 0 [] -ord_less_e_q(int,pls,min).
% 8.06/8.09 0 [] -ord_less_e_q(int,bit0(K_1),min)|ord_less_e_q(int,K_1,min).
% 8.06/8.09 0 [] ord_less_e_q(int,bit0(K_1),min)| -ord_less_e_q(int,K_1,min).
% 8.06/8.09 0 [] number_number_of(int,pls)!=number_number_of(int,min).
% 8.06/8.09 0 [] -ord_less(int,bit0(K_1),min)|ord_less_e_q(int,K_1,min).
% 8.06/8.09 0 [] ord_less(int,bit0(K_1),min)| -ord_less_e_q(int,K_1,min).
% 8.06/8.09 0 [] -ord_less_e_q(int,min,bit0(K_1))|ord_less(int,min,K_1).
% 8.06/8.09 0 [] ord_less_e_q(int,min,bit0(K_1))| -ord_less(int,min,K_1).
% 8.06/8.09 0 [] times_times(int,Ma,N_1)!=one_one(int)|ti(int,Ma)=one_one(int)|ti(int,Ma)=number_number_of(int,min).
% 8.06/8.09 0 [] times_times(int,Ma,N_1)!=one_one(int)|ti(int,Ma)=one_one(int)|ti(int,N_1)=number_number_of(int,min).
% 8.06/8.09 0 [] times_times(int,Ma,N_1)!=one_one(int)|ti(int,N_1)=one_one(int)|ti(int,Ma)=number_number_of(int,min).
% 8.06/8.09 0 [] times_times(int,Ma,N_1)!=one_one(int)|ti(int,N_1)=one_one(int)|ti(int,N_1)=number_number_of(int,min).
% 8.06/8.09 0 [] times_times(int,Ma,N_1)=one_one(int)|ti(int,Ma)!=one_one(int)|ti(int,N_1)!=one_one(int).
% 8.06/8.09 0 [] times_times(int,Ma,N_1)=one_one(int)|ti(int,Ma)!=number_number_of(int,min)|ti(int,N_1)!=number_number_of(int,min).
% 8.06/8.09 0 [] times_times(int,M,N)!=one_one(int)|ti(int,M)=one_one(int)|ti(int,M)=number_number_of(int,min).
% 8.06/8.09 0 [] -zcong(A_2,B_1,Ma)|zcong(B_1,A_2,Ma).
% 8.06/8.09 0 [] zcong(A_2,B_1,Ma)| -zcong(B_1,A_2,Ma).
% 8.06/8.09 0 [] zcong(K,K,M).
% 8.06/8.09 0 [] -zcong(A_1,B,M)| -zcong(B,C,M)|zcong(A_1,C,M).
% 8.06/8.09 0 [] -order(X_a)| -ord_less_e_q(X_a,X,Y)|ti(X_a,X)=ti(X_a,Y)|ord_less(X_a,X,Y).
% 8.06/8.09 0 [] -ord_less(int,A_1,C)| -ord_less(int,B,C)|ord_less_e_q(int,A_1,B)|ord_less_e_q(int,B,A_1).
% 8.06/8.09 0 [] -zcong(A_2,B_1,zero_zero(int))|ti(int,A_2)=ti(int,B_1).
% 8.06/8.09 0 [] zcong(A_2,B_1,zero_zero(int))|ti(int,A_2)!=ti(int,B_1).
% 8.06/8.09 0 [] zcong(A_1,B,one_one(int)).
% 8.06/8.09 0 [] zcong(times_times(int,A_1,M),times_times(int,B,M),M).
% 8.06/8.09 0 [] -zcong(A_1,B,M)|zcong(times_times(int,A_1,K),times_times(int,B,K),M).
% 8.06/8.09 0 [] -zcong(A_1,B,M)|zcong(times_times(int,K,A_1),times_times(int,K,B),M).
% 8.06/8.09 0 [] -zcong(A_1,B,M)| -zcong(C,D,M)|zcong(times_times(int,A_1,C),times_times(int,B,D),M).
% 8.06/8.09 0 [] -zcong(A_1,B,M)| -zcong(C,D,M)|zcong(plus_plus(int,A_1,C),plus_plus(int,B,D),M).
% 8.06/8.09 0 [] -number_ring(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).
% 8.06/8.09 0 [] -ord_less(int,zero_zero(int),A_1)| -ord_less(int,A_1,M)| -ord_less(int,zero_zero(int),B)| -ord_less(int,B,A_1)| -zcong(A_1,B,M).
% 8.06/8.09 0 [] -zcong(A_2,B_1,Ma)|ti(int,B_1)=plus_plus(int,A_2,times_times(int,Ma,$f2(A_2,B_1,Ma))).
% 8.06/8.09 0 [] zcong(A_2,B_1,Ma)|ti(int,B_1)!=plus_plus(int,A_2,times_times(int,Ma,K_2)).
% 8.06/8.09 0 [] times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,X,number_number_of(nat,bit0(bit1(pls)))))=power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X),number_number_of(nat,bit0(bit1(pls)))).
% 8.06/8.09 0 [] -ord_less_e_q(int,zero_zero(int),A_1)| -ord_less(int,A_1,M)| -zcong(A_1,zero_zero(int),M)|ti(int,A_1)=zero_zero(int).
% 8.06/8.09 0 [] -ord_less_e_q(int,zero_zero(int),A_1)| -ord_less(int,A_1,M)| -ord_less_e_q(int,zero_zero(int),B)| -ord_less(int,B,M)| -zcong(A_1,B,M)|ti(int,A_1)=ti(int,B).
% 8.06/8.09 0 [] -zcong(power_power(int,X,Y),one_one(int),P)|zcong(power_power(int,X,times_times(nat,Y,Z)),one_one(int),P).
% 8.06/8.09 0 [] -ord_less_e_q(int,zero_zero(int),M)| -zprime(P)| -dvd_dvd(int,P,times_times(int,M,N))|dvd_dvd(int,P,M)|dvd_dvd(int,P,N).
% 8.06/8.09 0 [] quadRes(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),number_number_of(int,min)).
% 8.06/8.09 0 [] dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min))).
% 8.06/8.09 0 [] -ord_less(int,number_number_of(int,bit0(bit1(pls))),M)| -zcong(power_power(int,number_number_of(int,min),J),power_power(int,number_number_of(int,min),K),M)|power_power(int,number_number_of(int,min),J)=power_power(int,number_number_of(int,min),K).
% 8.06/8.09 0 [] -ord_less(int,number_number_of(int,bit0(bit1(pls))),P)| -zcong(X,number_number_of(int,min),P)| -zcong(X,one_one(int),P).
% 8.06/8.09 0 [] minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min))=plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)).
% 8.06/8.09 0 [] 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).
% 8.06/8.09 0 [] ord_less(real,zero_zero(real),times_times(real,X_2,X_2))|X_2=zero_zero(real).
% 8.06/8.09 0 [] -ord_less(real,zero_zero(real),times_times(real,X_2,X_2))|X_2!=zero_zero(real).
% 8.06/8.09 0 [] -zcong(A_1,B,M)| -zcong(C,D,M)|zcong(minus_minus(int,A_1,C),minus_minus(int,B,D),M).
% 8.06/8.09 0 [] -dvd_dvd(int,K,minus_minus(int,M,N))| -dvd_dvd(int,K,N)|dvd_dvd(int,K,M).
% 8.06/8.09 0 [] times_times(int,W,minus_minus(int,Z1,Z2))=minus_minus(int,times_times(int,W,Z1),times_times(int,W,Z2)).
% 8.06/8.09 0 [] times_times(int,minus_minus(int,Z1,Z2),W)=minus_minus(int,times_times(int,Z1,W),times_times(int,Z2,W)).
% 8.06/8.09 0 [] minus_minus(int,bit0(K),bit0(L))=bit0(minus_minus(int,K,L)).
% 8.06/8.09 0 [] minus_minus(int,K,pls)=ti(int,K).
% 8.06/8.09 0 [] minus_minus(int,A_1,B)!=ti(int,C)|ti(int,A_1)=plus_plus(int,C,B).
% 8.06/8.09 0 [] -number_ring(X_a)|number_number_of(X_a,minus_minus(int,V,W))=minus_minus(X_a,number_number_of(X_a,V),number_number_of(X_a,W)).
% 8.06/8.09 0 [] -number(X_b)| -ring(X_b)|times_times(X_b,number_number_of(X_b,V),minus_minus(X_b,B,C))=minus_minus(X_b,times_times(X_b,number_number_of(X_b,V),B),times_times(X_b,number_number_of(X_b,V),C)).
% 8.06/8.09 0 [] -number(X_b)| -ring(X_b)|times_times(X_b,minus_minus(X_b,A_1,B),number_number_of(X_b,V))=minus_minus(X_b,times_times(X_b,A_1,number_number_of(X_b,V)),times_times(X_b,B,number_number_of(X_b,V))).
% 8.06/8.09 0 [] minus_minus(int,bit1(K),bit0(L))=bit1(minus_minus(int,K,L)).
% 8.06/8.09 0 [] minus_minus(int,bit1(K),bit1(L))=bit0(minus_minus(int,K,L)).
% 8.06/8.09 0 [] minus_minus(int,pls,bit0(L))=bit0(minus_minus(int,pls,L)).
% 8.06/8.09 0 [] -ord_less(int,K_1,L_1)|ord_less(int,minus_minus(int,K_1,L_1),zero_zero(int)).
% 8.06/8.09 0 [] ord_less(int,K_1,L_1)| -ord_less(int,minus_minus(int,K_1,L_1),zero_zero(int)).
% 8.06/8.09 0 [] plus_plus(int,times_times(int,minus_minus(int,A_1,times_times(int,R,B)),M),times_times(int,minus_minus(int,C,times_times(int,R,D)),N))=minus_minus(int,plus_plus(int,times_times(int,A_1,M),times_times(int,C,N)),times_times(int,R,plus_plus(int,times_times(int,B,M),times_times(int,D,N)))).
% 8.06/8.09 0 [] -zcong(A_2,B_1,Ma)|dvd_dvd(int,Ma,minus_minus(int,A_2,B_1)).
% 8.06/8.09 0 [] zcong(A_2,B_1,Ma)| -dvd_dvd(int,Ma,minus_minus(int,A_2,B_1)).
% 8.06/8.09 0 [] -number_ring(X_a)|plus_plus(X_a,number_number_of(X_a,V),minus_minus(X_a,number_number_of(X_a,W),C))=minus_minus(X_a,number_number_of(X_a,plus_plus(int,V,W)),C).
% 8.06/8.09 0 [] -ord_less(int,zero_zero(int),X)| -ord_less(int,X,A_1)|ti(int,X)=minus_minus(int,A_1,one_one(int))|ord_less(int,X,minus_minus(int,A_1,one_one(int))).
% 8.06/8.09 0 [] -ord_less_e_q(int,W_1,minus_minus(int,Z_1,one_one(int)))|ord_less(int,W_1,Z_1).
% 8.06/8.09 0 [] ord_less_e_q(int,W_1,minus_minus(int,Z_1,one_one(int)))| -ord_less(int,W_1,Z_1).
% 8.06/8.09 0 [] minus_minus(int,pls,bit1(L))=bit1(minus_minus(int,min,L)).
% 8.06/8.09 0 [] minus_minus(int,min,bit1(L))=bit0(minus_minus(int,min,L)).
% 8.06/8.09 0 [] minus_minus(int,min,bit0(L))=bit1(minus_minus(int,min,L)).
% 8.06/8.09 0 [] -zcong(times_times(int,A_2,minus_minus(int,P_1,one_one(int))),one_one(int),P_1)|zcong(A_2,minus_minus(int,P_1,one_one(int)),P_1).
% 8.06/8.09 0 [] zcong(times_times(int,A_2,minus_minus(int,P_1,one_one(int))),one_one(int),P_1)| -zcong(A_2,minus_minus(int,P_1,one_one(int)),P_1).
% 8.06/8.09 0 [] -zcong(A_1,B,M)|ti(int,B)!=ti(int,C)| -zcong(C,D,M)|zcong(A_1,D,M).
% 8.06/8.09 0 [] -zprime(P)| -ord_less(int,zero_zero(int),A_1)| -ord_less(int,A_1,P)| -zcong(times_times(int,A_1,A_1),one_one(int),P)|ti(int,A_1)=one_one(int)|ti(int,A_1)=minus_minus(int,P,one_one(int)).
% 8.06/8.09 0 [] -zprime(P)| -ord_less(int,zero_zero(int),A_1)| -zcong(times_times(int,A_1,A_1),one_one(int),P)|zcong(A_1,one_one(int),P)|zcong(A_1,minus_minus(int,P,one_one(int)),P).
% 8.06/8.09 0 [] times_times(int,plus_plus(int,A_1,B),minus_minus(int,A_1,B))=minus_minus(int,power_power(int,A_1,number_number_of(nat,bit0(bit1(pls)))),power_power(int,B,number_number_of(nat,bit0(bit1(pls))))).
% 8.06/8.09 0 [] zcong(M,zero_zero(int),M).
% 8.06/8.09 0 [] -zcong(A_2,B_1,Ma)| -zcong(C_1,times_times(int,D_1,A_2),Ma)|zcong(C_1,times_times(int,D_1,B_1),Ma).
% 8.06/8.09 0 [] -zcong(A_2,B_1,Ma)|zcong(C_1,times_times(int,D_1,A_2),Ma)| -zcong(C_1,times_times(int,D_1,B_1),Ma).
% 8.06/8.09 0 [] -zcong(A_2,B_1,Ma)| -zcong(C_1,times_times(int,A_2,D_1),Ma)|zcong(C_1,times_times(int,B_1,D_1),Ma).
% 8.06/8.09 0 [] -zcong(A_2,B_1,Ma)|zcong(C_1,times_times(int,A_2,D_1),Ma)| -zcong(C_1,times_times(int,B_1,D_1),Ma).
% 8.06/8.09 0 [] -zcong(A_1,B,M)|zcong(plus_plus(int,A_1,C),plus_plus(int,B,C),M).
% 8.06/8.09 0 [] -zcong(X,Y,M)|zcong(power_power(int,X,Z),power_power(int,Y,Z),M).
% 8.06/8.09 0 [] -number_ring(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,power_power(X_a,X,number_number_of(nat,bit0(bit1(pls)))),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)).
% 8.06/8.09 0 [] power_power(int,minus_minus(int,A_1,B),number_number_of(nat,bit0(bit1(pls))))=plus_plus(int,minus_minus(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)),power_power(int,B,number_number_of(nat,bit0(bit1(pls))))).
% 8.06/8.09 0 [] power_power(int,minus_minus(int,A_1,B),number_number_of(nat,bit1(bit1(pls))))=minus_minus(int,plus_plus(int,minus_minus(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))),power_power(int,A_1,number_number_of(nat,bit0(bit1(pls))))),B)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),A_1),power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,B,number_number_of(nat,bit1(bit1(pls))))).
% 8.06/8.09 0 [] -ord_less(int,zero_zero(int),X)| -ord_less(int,zero_zero(int),Y)| -ord_less(int,zero_zero(int),M)| -zcong(X,Y,M)| -ord_less(int,X,M)| -ord_less(int,Y,M)|ti(int,X)=ti(int,Y).
% 8.06/8.09 0 [] -ord_less(int,zero_zero(int),X)| -ord_less(int,X,M)| -zcong(X,zero_zero(int),M).
% 8.06/8.09 0 [] -dvd_dvd(int,N,M)|ord_less_e_q(int,M,zero_zero(int))|ord_less_e_q(int,N,M).
% 8.06/8.09 0 [] -zcong(A_2,zero_zero(int),Ma)|dvd_dvd(int,Ma,A_2).
% 8.06/8.09 0 [] zcong(A_2,zero_zero(int),Ma)| -dvd_dvd(int,Ma,A_2).
% 8.06/8.09 0 [] -zcong(X_2,zero_zero(int),P_1)|dvd_dvd(int,P_1,X_2).
% 8.06/8.09 0 [] zcong(X_2,zero_zero(int),P_1)| -dvd_dvd(int,P_1,X_2).
% 8.06/8.09 0 [] -zprime(P)| -dvd_dvd(int,P,times_times(int,M,N))|dvd_dvd(int,P,M)|dvd_dvd(int,P,N).
% 8.06/8.09 0 [] -ord_less_e_q(int,zero_zero(int),X)| -ord_less(int,X,M)| -zcong(X,zero_zero(int),M)|ti(int,X)=zero_zero(int).
% 8.06/8.09 0 [] -ord_less(nat,zero_zero(nat),N)| -dvd_dvd(int,P,Y)|dvd_dvd(int,P,power_power(int,Y,N)).
% 8.06/8.09 0 [] power_power(int,number_number_of(int,min),N)=one_one(int)|power_power(int,number_number_of(int,min),N)=number_number_of(int,min).
% 8.06/8.09 0 [] -zprime(P)|zcong(X,zero_zero(int),P)|zcong(Y,zero_zero(int),P)| -zcong(times_times(int,X,Y),zero_zero(int),P).
% 8.06/8.09 0 [] -zprime(P)| -ord_less(int,zero_zero(int),A_1)|zcong(A_1,zero_zero(int),P)|zcong(B,zero_zero(int),P)| -zcong(times_times(int,A_1,B),zero_zero(int),P).
% 8.06/8.09 0 [] -zprime(P)| -ord_less(int,zero_zero(int),A_1)| -zcong(times_times(int,A_1,B),zero_zero(int),P)|zcong(A_1,zero_zero(int),P)|zcong(B,zero_zero(int),P).
% 8.06/8.09 0 [] -zprime(P)| -dvd_dvd(int,P,power_power(int,Y,N))| -ord_less(nat,zero_zero(nat),N)|dvd_dvd(int,P,Y).
% 8.06/8.09 0 [] -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).
% 8.06/8.09 0 [] -ord_less(int,number_number_of(int,bit0(bit1(pls))),M)| -zcong(one_one(int),number_number_of(int,min),M).
% 8.06/8.09 0 [] -zcong(A_1,zero_zero(int),P)|legendre(A_1,P)=zero_zero(int).
% 8.06/8.09 0 [] zcong(A_1,zero_zero(int),P)| -quadRes(P,A_1)|legendre(A_1,P)=one_one(int).
% 8.06/8.09 0 [] zcong(A_1,zero_zero(int),P)|quadRes(P,A_1)|legendre(A_1,P)=number_number_of(int,min).
% 8.06/8.09 0 [] -quadRes(Ma,X_2)|zcong(power_power(int,$f3(Ma,X_2),number_number_of(nat,bit0(bit1(pls)))),X_2,Ma).
% 8.06/8.09 0 [] quadRes(Ma,X_2)| -zcong(power_power(int,Y_1,number_number_of(nat,bit0(bit1(pls)))),X_2,Ma).
% 8.06/8.09 0 [] power_power(real,plus_plus(real,X,Y),number_number_of(nat,bit0(bit1(pls))))=plus_plus(real,plus_plus(real,power_power(real,X,number_number_of(nat,bit0(bit1(pls)))),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)).
% 8.06/8.09 0 [] M!=zero_zero(nat)|times_times(nat,M,N)=zero_zero(nat).
% 8.06/8.09 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)).
% 8.06/8.09 0 [] M!=zero_zero(nat)|power_power(nat,P,M)=one_one(nat).
% 8.06/8.09 0 [] M=zero_zero(nat)|power_power(nat,P,M)=times_times(nat,P,power_power(nat,P,minus_minus(nat,M,one_one(nat)))).
% 8.06/8.09 0 [] minus_minus(nat,power_power(nat,X,number_number_of(nat,bit0(bit1(pls)))),power_power(nat,Y,number_number_of(nat,bit0(bit1(pls)))))=times_times(nat,plus_plus(nat,X,Y),minus_minus(nat,X,Y)).
% 8.06/8.09 0 [] plus_plus(real,power_power(real,X_2,number_number_of(nat,bit0(bit1(pls)))),power_power(real,Y_2,number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(real)|X_2=zero_zero(real).
% 8.06/8.09 0 [] plus_plus(real,power_power(real,X_2,number_number_of(nat,bit0(bit1(pls)))),power_power(real,Y_2,number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(real)|Y_2=zero_zero(real).
% 8.06/8.09 0 [] plus_plus(real,power_power(real,X_2,number_number_of(nat,bit0(bit1(pls)))),power_power(real,Y_2,number_number_of(nat,bit0(bit1(pls)))))=zero_zero(real)|X_2!=zero_zero(real)|Y_2!=zero_zero(real).
% 8.06/8.09 0 [] zero_zero(real)!=one_one(real).
% 8.06/8.09 0 [] -ord_less_e_q(real,X_2,Y_2)|ord_less_e_q(real,minus_minus(real,X_2,Y_2),zero_zero(real)).
% 8.06/8.09 0 [] ord_less_e_q(real,X_2,Y_2)| -ord_less_e_q(real,minus_minus(real,X_2,Y_2),zero_zero(real)).
% 8.06/8.09 0 [] -ord_less(real,X_2,Y_2)|ord_less_e_q(real,X_2,Y_2).
% 8.06/8.09 0 [] -ord_less(real,X_2,Y_2)|X_2!=Y_2.
% 8.06/8.09 0 [] ord_less(real,X_2,Y_2)| -ord_less_e_q(real,X_2,Y_2)|X_2=Y_2.
% 8.06/8.09 0 [] -ord_less_e_q(real,X_2,Y_2)|ord_less(real,X_2,Y_2)|X_2=Y_2.
% 8.06/8.09 0 [] ord_less_e_q(real,X_2,Y_2)| -ord_less(real,X_2,Y_2).
% 8.06/8.09 0 [] ord_less_e_q(real,X_2,Y_2)|X_2!=Y_2.
% 8.06/8.09 0 [] times_times(real,times_times(real,Z1,Z2),Z3)=times_times(real,Z1,times_times(real,Z2,Z3)).
% 8.06/8.09 0 [] times_times(real,Z,W)=times_times(real,W,Z).
% 8.06/8.09 0 [] times_times(real,one_one(real),Z)=Z.
% 8.06/8.09 0 [] -ord_less_e_q(real,X,Y)|ord_less_e_q(real,plus_plus(real,Z,X),plus_plus(real,Z,Y)).
% 8.06/8.09 0 [] -ab_group_add(X_a)|minus_minus(X_a,plus_plus(X_a,A_1,C),plus_plus(X_a,B,D))=plus_plus(X_a,minus_minus(X_a,A_1,B),minus_minus(X_a,C,D)).
% 8.06/8.09 0 [] C_1=zero_zero(real)|times_times(real,C_1,A_2)!=times_times(real,C_1,B_1)|A_2=B_1.
% 8.06/8.09 0 [] C_1=zero_zero(real)|times_times(real,C_1,A_2)=times_times(real,C_1,B_1)|A_2!=B_1.
% 8.06/8.09 0 [] C_1=zero_zero(real)|times_times(real,A_2,C_1)!=times_times(real,B_1,C_1)|A_2=B_1.
% 8.06/8.09 0 [] C_1=zero_zero(real)|times_times(real,A_2,C_1)=times_times(real,B_1,C_1)|A_2!=B_1.
% 8.06/8.09 0 [] times_times(nat,N_1,Ma)!=one_one(nat)|N_1=one_one(nat).
% 8.06/8.09 0 [] times_times(nat,N_1,Ma)!=one_one(nat)|Ma=one_one(nat).
% 8.06/8.09 0 [] times_times(nat,N_1,Ma)=one_one(nat)|N_1!=one_one(nat)|Ma!=one_one(nat).
% 8.06/8.09 0 [] times_times(real,plus_plus(real,Z1,Z2),W)=plus_plus(real,times_times(real,Z1,W),times_times(real,Z2,W)).
% 8.06/8.09 0 [] power_power(nat,Ma,N_1)!=zero_zero(nat)|N_1!=zero_zero(nat).
% 8.06/8.09 0 [] power_power(nat,Ma,N_1)!=zero_zero(nat)|Ma=zero_zero(nat).
% 8.06/8.09 0 [] power_power(nat,Ma,N_1)=zero_zero(nat)|N_1=zero_zero(nat)|Ma!=zero_zero(nat).
% 8.06/8.09 0 [] -ring(X_a)|minus_minus(X_a,times_times(X_a,X,Y),times_times(X_a,A_1,B))=plus_plus(X_a,times_times(X_a,X,minus_minus(X_a,Y,B)),times_times(X_a,minus_minus(X_a,X,A_1),B)).
% 8.06/8.09 0 [] -ord_less(real,zero_zero(real),Z_1)| -ord_less_e_q(real,times_times(real,X_2,Z_1),times_times(real,Y_2,Z_1))|ord_less_e_q(real,X_2,Y_2).
% 8.06/8.09 0 [] -ord_less(real,zero_zero(real),Z_1)|ord_less_e_q(real,times_times(real,X_2,Z_1),times_times(real,Y_2,Z_1))| -ord_less_e_q(real,X_2,Y_2).
% 8.06/8.09 0 [] -ord_less(real,zero_zero(real),Z_1)| -ord_less_e_q(real,times_times(real,Z_1,X_2),times_times(real,Z_1,Y_2))|ord_less_e_q(real,X_2,Y_2).
% 8.06/8.09 0 [] -ord_less(real,zero_zero(real),Z_1)|ord_less_e_q(real,times_times(real,Z_1,X_2),times_times(real,Z_1,Y_2))| -ord_less_e_q(real,X_2,Y_2).
% 8.06/8.09 0 [] -ord_less(real,zero_zero(real),Z)| -ord_less(real,X,Y)|ord_less(real,times_times(real,Z,X),times_times(real,Z,Y)).
% 8.06/8.09 0 [] -ord_less(real,zero_zero(real),X)| -ord_less(real,zero_zero(real),Y)|ord_less(real,zero_zero(real),times_times(real,X,Y)).
% 8.06/8.09 0 [] -ord_less(real,zero_zero(real),Z_1)| -ord_less(real,times_times(real,X_2,Z_1),times_times(real,Y_2,Z_1))|ord_less(real,X_2,Y_2).
% 8.06/8.09 0 [] -ord_less(real,zero_zero(real),Z_1)|ord_less(real,times_times(real,X_2,Z_1),times_times(real,Y_2,Z_1))| -ord_less(real,X_2,Y_2).
% 8.06/8.09 0 [] plus_plus(real,times_times(real,X_2,X_2),times_times(real,Y_2,Y_2))!=zero_zero(real)|X_2=zero_zero(real).
% 8.06/8.09 0 [] plus_plus(real,times_times(real,X_2,X_2),times_times(real,Y_2,Y_2))!=zero_zero(real)|Y_2=zero_zero(real).
% 8.06/8.09 0 [] plus_plus(real,times_times(real,X_2,X_2),times_times(real,Y_2,Y_2))=zero_zero(real)|X_2!=zero_zero(real)|Y_2!=zero_zero(real).
% 8.06/8.09 0 [] power_power(nat,X_2,N_1)!=one_one(nat)|X_2=one_one(nat)|N_1=zero_zero(nat).
% 8.06/8.09 0 [] power_power(nat,X_2,N_1)=one_one(nat)|X_2!=one_one(nat).
% 8.06/8.09 0 [] power_power(nat,X_2,N_1)=one_one(nat)|N_1!=zero_zero(nat).
% 8.06/8.09 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))).
% 8.06/8.09 0 [] -monoid_mult(X_a)| -ord_less(nat,zero_zero(nat),N)|times_times(X_a,power_power(X_a,X,minus_minus(nat,N,one_one(nat))),X)=power_power(X_a,X,N).
% 8.06/8.09 0 [] ord_less_e_q(real,one_one(real),power_power(real,number_number_of(real,bit0(bit1(pls))),N)).
% 8.06/8.09 0 [] -power(X_a)|N!=zero_zero(nat)|power_power(X_a,M,N)=one_one(X_a).
% 8.06/8.09 0 [] -power(X_a)|N=zero_zero(nat)|power_power(X_a,M,N)=times_times(X_a,M,power_power(X_a,M,minus_minus(nat,N,one_one(nat)))).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(X_a,A_1,B)| -ord_less_e_q(X_a,zero_zero(X_a),A_1)| -ord_less(nat,zero_zero(nat),N)|ord_less(X_a,power_power(X_a,A_1,N),power_power(X_a,B,N)).
% 8.06/8.09 0 [] ord_less_e_q(real,W,W).
% 8.06/8.09 0 [] ord_less_e_q(real,Z,W)|ord_less_e_q(real,W,Z).
% 8.06/8.09 0 [] -ord_less_e_q(real,I,J)| -ord_less_e_q(real,J,K)|ord_less_e_q(real,I,K).
% 8.06/8.09 0 [] -ord_less_e_q(real,Z,W)| -ord_less_e_q(real,W,Z)|Z=W.
% 8.06/8.09 0 [] -ring_11004092258visors(X_a)|ti(X_a,A_1)=zero_zero(X_a)|power_power(X_a,A_1,N)!=zero_zero(X_a).
% 8.06/8.09 0 [] -comm_monoid_mult(X_a)|power_power(X_a,times_times(X_a,A_1,B),N)=times_times(X_a,power_power(X_a,A_1,N),power_power(X_a,B,N)).
% 8.06/8.09 0 [] -monoid_mult(X_a)|times_times(X_a,power_power(X_a,A_1,N),A_1)=times_times(X_a,A_1,power_power(X_a,A_1,N)).
% 8.06/8.09 0 [] -monoid_mult(X_a)|power_power(X_a,one_one(X_a),N)=one_one(X_a).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)| -dvd_dvd(X_a,X,Y)|dvd_dvd(X_a,power_power(X_a,X,N),power_power(X_a,Y,N)).
% 8.06/8.09 0 [] -monoid_mult(X_a)|power_power(X_a,A_1,times_times(nat,M,N))=power_power(X_a,power_power(X_a,A_1,M),N).
% 8.06/8.09 0 [] -monoid_mult(X_a)|power_power(X_a,A_1,one_one(nat))=ti(X_a,A_1).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less_e_q(X_a,A_1,B)| -ord_less_e_q(X_a,zero_zero(X_a),A_1)|ord_less_e_q(X_a,power_power(X_a,A_1,N),power_power(X_a,B,N)).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less_e_q(X_a,zero_zero(X_a),A_1)|ord_less_e_q(X_a,zero_zero(X_a),power_power(X_a,A_1,N)).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(X_a,zero_zero(X_a),A_1)|ord_less(X_a,zero_zero(X_a),power_power(X_a,A_1,N)).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less_e_q(X_a,one_one(X_a),A_1)|ord_less_e_q(X_a,one_one(X_a),power_power(X_a,A_1,N)).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(X_a,one_one(X_a),A_2)|power_power(X_a,A_2,Ma)!=power_power(X_a,A_2,N_1)|Ma=N_1.
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(X_a,one_one(X_a),A_2)|power_power(X_a,A_2,Ma)=power_power(X_a,A_2,N_1)|Ma!=N_1.
% 8.06/8.09 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|power_power(X_a,A_2,N_1)!=zero_zero(X_a)|ti(X_a,A_2)=zero_zero(X_a).
% 8.06/8.09 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|power_power(X_a,A_2,N_1)!=zero_zero(X_a)|N_1!=zero_zero(nat).
% 8.06/8.09 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|power_power(X_a,A_2,N_1)=zero_zero(X_a)|ti(X_a,A_2)!=zero_zero(X_a)|N_1=zero_zero(nat).
% 8.06/8.09 0 [] -power(X_a)|power_power(X_a,A_1,zero_zero(nat))=one_one(X_a).
% 8.06/8.09 0 [] -monoid_mult(X_a)|power_power(X_a,A_1,plus_plus(nat,M,N))=times_times(X_a,power_power(X_a,A_1,M),power_power(X_a,A_1,N)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)| -dvd_dvd(X_a,power_power(X_a,A_1,N),B)| -ord_less_e_q(nat,M,N)|dvd_dvd(X_a,power_power(X_a,A_1,M),B).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)| -dvd_dvd(X_a,X,Y)| -ord_less_e_q(nat,N,M)|dvd_dvd(X_a,power_power(X_a,X,N),power_power(X_a,Y,M)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)| -ord_less_e_q(nat,M,N)|dvd_dvd(X_a,power_power(X_a,A_1,M),power_power(X_a,A_1,N)).
% 8.06/8.09 0 [] -ord_less(nat,zero_zero(nat),I)| -ord_less(nat,power_power(nat,I,M),power_power(nat,I,N))|ord_less(nat,M,N).
% 8.06/8.09 0 [] -ord_less(nat,zero_zero(nat),power_power(nat,X_2,N_1))|ord_less(nat,zero_zero(nat),X_2)|N_1=zero_zero(nat).
% 8.06/8.09 0 [] ord_less(nat,zero_zero(nat),power_power(nat,X_2,N_1))| -ord_less(nat,zero_zero(nat),X_2).
% 8.06/8.09 0 [] ord_less(nat,zero_zero(nat),power_power(nat,X_2,N_1))|N_1!=zero_zero(nat).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(X_a,power_power(X_a,A_1,N),power_power(X_a,B,N))| -ord_less_e_q(X_a,zero_zero(X_a),B)|ord_less(X_a,A_1,B).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(X_a,one_one(X_a),A_1)|ord_less(X_a,power_power(X_a,A_1,N),times_times(X_a,A_1,power_power(X_a,A_1,N))).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(X_a,one_one(X_a),A_1)|ord_less(X_a,one_one(X_a),times_times(X_a,A_1,power_power(X_a,A_1,N))).
% 8.06/8.09 0 [] -power(X_a)| -semiring_0(X_a)|N!=zero_zero(nat)|power_power(X_a,zero_zero(X_a),N)=one_one(X_a).
% 8.06/8.09 0 [] -power(X_a)| -semiring_0(X_a)|N=zero_zero(nat)|power_power(X_a,zero_zero(X_a),N)=zero_zero(X_a).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(nat,N,N_2)| -ord_less(X_a,one_one(X_a),A_1)|ord_less(X_a,power_power(X_a,A_1,N),power_power(X_a,A_1,N_2)).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(X_a,one_one(X_a),A_1)| -ord_less(X_a,power_power(X_a,A_1,M),power_power(X_a,A_1,N))|ord_less(nat,M,N).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(X_a,one_one(X_a),B_1)| -ord_less(X_a,power_power(X_a,B_1,X_2),power_power(X_a,B_1,Y_2))|ord_less(nat,X_2,Y_2).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(X_a,one_one(X_a),B_1)|ord_less(X_a,power_power(X_a,B_1,X_2),power_power(X_a,B_1,Y_2))| -ord_less(nat,X_2,Y_2).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less_e_q(nat,N,N_2)| -ord_less_e_q(X_a,one_one(X_a),A_1)|ord_less_e_q(X_a,power_power(X_a,A_1,N),power_power(X_a,A_1,N_2)).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(X_a,zero_zero(X_a),A_1)| -ord_less(X_a,A_1,one_one(X_a))|ord_less(X_a,times_times(X_a,A_1,power_power(X_a,A_1,N)),power_power(X_a,A_1,N)).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(nat,N,N_2)| -ord_less(X_a,zero_zero(X_a),A_1)| -ord_less(X_a,A_1,one_one(X_a))|ord_less(X_a,power_power(X_a,A_1,N_2),power_power(X_a,A_1,N)).
% 8.06/8.09 0 [] -linordered_semidom(X_a)|power_power(X_a,A_1,N)!=power_power(X_a,B,N)| -ord_less_e_q(X_a,zero_zero(X_a),A_1)| -ord_less_e_q(X_a,zero_zero(X_a),B)| -ord_less(nat,zero_zero(nat),N)|ti(X_a,A_1)=ti(X_a,B).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less_e_q(nat,N,N_2)| -ord_less_e_q(X_a,zero_zero(X_a),A_1)| -ord_less_e_q(X_a,A_1,one_one(X_a))|ord_less_e_q(X_a,power_power(X_a,A_1,N_2),power_power(X_a,A_1,N)).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(X_a,one_one(X_a),A_1)| -ord_less_e_q(X_a,power_power(X_a,A_1,M),power_power(X_a,A_1,N))|ord_less_e_q(nat,M,N).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(X_a,one_one(X_a),B_1)| -ord_less_e_q(X_a,power_power(X_a,B_1,X_2),power_power(X_a,B_1,Y_2))|ord_less_e_q(nat,X_2,Y_2).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(X_a,one_one(X_a),B_1)|ord_less_e_q(X_a,power_power(X_a,B_1,X_2),power_power(X_a,B_1,Y_2))| -ord_less_e_q(nat,X_2,Y_2).
% 8.06/8.09 0 [] -linordered_semidom(X_a)| -ord_less(X_a,one_one(X_a),A_1)| -ord_less(nat,zero_zero(nat),N)|ord_less(X_a,one_one(X_a),power_power(X_a,A_1,N)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)| -ord_less(nat,zero_zero(nat),N)|dvd_dvd(X_a,X,power_power(X_a,X,N)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|ti(X_a,X)!=one_one(X_a)|dvd_dvd(X_a,X,power_power(X_a,X,N)).
% 8.06/8.09 0 [] -linord626643107strict(X_a)| -ord_less(X_a,X,A_1)| -ord_less(X_a,Y,A_1)| -ord_less_e_q(X_a,zero_zero(X_a),U)| -ord_less_e_q(X_a,zero_zero(X_a),V)|plus_plus(X_a,U,V)!=one_one(X_a)|ord_less(X_a,plus_plus(X_a,times_times(X_a,U,X),times_times(X_a,V,Y)),A_1).
% 8.06/8.09 0 [] -ord_less(nat,zero_zero(nat),N)| -ord_less(real,zero_zero(real),A_1)|ord_less(real,zero_zero(real),$f4(A_1,N)).
% 8.06/8.09 0 [] -ord_less(nat,zero_zero(nat),N)| -ord_less(real,zero_zero(real),A_1)|power_power(real,$f4(A_1,N),N)=A_1.
% 8.06/8.09 0 [] -ord_less(nat,zero_zero(nat),N)| -ord_less(real,zero_zero(real),A_1)| -ord_less(real,zero_zero(real),Y_1)|power_power(real,Y_1,N)!=A_1|Y_1=$f4(A_1,N).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|dvd_dvd(X_a,A_1,zero_zero(X_a)).
% 8.06/8.09 0 [] -dvd_dvd(nat,A_1,B)|B=zero_zero(nat)|ord_less_e_q(nat,A_1,B).
% 8.06/8.09 0 [] -dvd_dvd(nat,X,Y)|dvd_dvd(nat,power_power(nat,X,N),power_power(nat,Y,N)).
% 8.06/8.09 0 [] -dvd_dvd(nat,A_1,B)|dvd_dvd(nat,times_times(nat,C,A_1),times_times(nat,C,B)).
% 8.06/8.09 0 [] -dvd_dvd(nat,A_1,B)|dvd_dvd(nat,times_times(nat,A_1,C),times_times(nat,B,C)).
% 8.06/8.09 0 [] -dvd_dvd(nat,D,A_1)| -dvd_dvd(nat,D,plus_plus(nat,A_1,B))|dvd_dvd(nat,D,B).
% 8.06/8.09 0 [] -dvd_dvd(nat,times_times(nat,Ma,K_1),times_times(nat,N_1,K_1))|K_1=zero_zero(nat)|dvd_dvd(nat,Ma,N_1).
% 8.06/8.09 0 [] dvd_dvd(nat,times_times(nat,Ma,K_1),times_times(nat,N_1,K_1))|K_1!=zero_zero(nat).
% 8.06/8.09 0 [] dvd_dvd(nat,times_times(nat,Ma,K_1),times_times(nat,N_1,K_1))| -dvd_dvd(nat,Ma,N_1).
% 8.06/8.09 0 [] -dvd_dvd(nat,power_power(nat,A_1,N),power_power(nat,B,N))|N=zero_zero(nat)|dvd_dvd(nat,A_1,B).
% 8.06/8.09 0 [] N=zero_zero(nat)| -dvd_dvd(nat,power_power(nat,X,N),Y)|dvd_dvd(nat,X,Y).
% 8.06/8.09 0 [] -linordered_idom(X_a)|ti(X_a,X)=ti(X_a,Y)|ord_less(X_a,X,Y)|ord_less(X_a,Y,X).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)| -dvd_dvd(X_a,A_1,B)| -dvd_dvd(X_a,B,C)|dvd_dvd(X_a,A_1,C).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|dvd_dvd(X_a,A_1,A_1).
% 8.06/8.09 0 [] X!=plus_plus(nat,times_times(nat,Q,N),R)| -ord_less(nat,zero_zero(nat),R)| -ord_less(nat,R,N)| -dvd_dvd(nat,N,X).
% 8.06/8.09 0 [] -dvd_dvd(nat,power_power(nat,I,M),power_power(nat,I,N))| -ord_less(nat,one_one(nat),I)|ord_less_e_q(nat,M,N).
% 8.06/8.09 0 [] -mult_zero(X_a)|times_times(X_a,zero_zero(X_a),A_1)=zero_zero(X_a).
% 8.06/8.09 0 [] -mult_zero(X_a)|times_times(X_a,A_1,zero_zero(X_a))=zero_zero(X_a).
% 8.06/8.09 0 [] -ring_n68954251visors(X_a)|times_times(X_a,A_2,B_1)!=zero_zero(X_a)|ti(X_a,A_2)=zero_zero(X_a)|ti(X_a,B_1)=zero_zero(X_a).
% 8.06/8.09 0 [] -ring_n68954251visors(X_a)|times_times(X_a,A_2,B_1)=zero_zero(X_a)|ti(X_a,A_2)!=zero_zero(X_a).
% 8.06/8.09 0 [] -ring_n68954251visors(X_a)|times_times(X_a,A_2,B_1)=zero_zero(X_a)|ti(X_a,B_1)!=zero_zero(X_a).
% 8.06/8.09 0 [] -no_zero_divisors(X_a)|ti(X_a,A_1)=zero_zero(X_a)|ti(X_a,B)=zero_zero(X_a)|times_times(X_a,A_1,B)!=zero_zero(X_a).
% 8.06/8.09 0 [] -no_zero_divisors(X_a)|times_times(X_a,A_1,B)!=zero_zero(X_a)|ti(X_a,A_1)=zero_zero(X_a)|ti(X_a,B)=zero_zero(X_a).
% 8.06/8.09 0 [] -zero_ne_q_one(X_a)|one_one(X_a)!=zero_zero(X_a).
% 8.06/8.09 0 [] -zero_ne_q_one(X_a)|zero_zero(X_a)!=one_one(X_a).
% 8.06/8.09 0 [] -comm_semiring(X_a)|times_times(X_a,plus_plus(X_a,A_1,B),C)=plus_plus(X_a,times_times(X_a,A_1,C),times_times(X_a,B,C)).
% 8.06/8.09 0 [] -semiring(X_a)|plus_plus(X_a,times_times(X_a,A_1,E),plus_plus(X_a,times_times(X_a,B,E),C))=plus_plus(X_a,times_times(X_a,plus_plus(X_a,A_1,B),E),C).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)| -dvd_dvd(X_a,zero_zero(X_a),A_1)|ti(X_a,A_1)=zero_zero(X_a).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)| -dvd_dvd(X_a,times_times(X_a,A_1,B),C)|dvd_dvd(X_a,B,C).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)| -dvd_dvd(X_a,times_times(X_a,A_1,B),C)|dvd_dvd(X_a,A_1,C).
% 8.06/8.09 0 [] -dvd(X_a)|A_1!=times_times(X_a,B,K)|dvd_dvd(X_a,B,A_1).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)| -dvd_dvd(X_a,A_1,B)| -dvd_dvd(X_a,C,D)|dvd_dvd(X_a,times_times(X_a,A_1,C),times_times(X_a,B,D)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)| -dvd_dvd(X_a,A_1,C)|dvd_dvd(X_a,A_1,times_times(X_a,B,C)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)| -dvd_dvd(X_a,A_1,B)|dvd_dvd(X_a,A_1,times_times(X_a,B,C)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|dvd_dvd(X_a,A_1,times_times(X_a,B,A_1)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|dvd_dvd(X_a,A_1,times_times(X_a,A_1,B)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)| -dvd_dvd(X_a,A_1,B)| -dvd_dvd(X_a,A_1,C)|dvd_dvd(X_a,A_1,plus_plus(X_a,B,C)).
% 8.06/8.09 0 [] -comm_semiring_1(X_a)|dvd_dvd(X_a,one_one(X_a),A_1).
% 8.06/8.09 0 [] -comm_ring_1(X_a)| -dvd_dvd(X_a,X,Y)| -dvd_dvd(X_a,X,Z)|dvd_dvd(X_a,X,minus_minus(X_a,Y,Z)).
% 8.09/8.09 0 [] -dvd_dvd(nat,N,M)|M=zero_zero(nat)|M=N|ord_less_e_q(nat,times_times(nat,number_number_of(nat,bit0(bit1(pls))),N),M).
% 8.09/8.09 0 [] -linordered_ring(X_a)|ord_less_e_q(X_a,zero_zero(X_a),times_times(X_a,A_1,A_1)).
% 8.09/8.09 0 [] -linord581940658strict(X_a)| -ord_less_e_q(X_a,zero_zero(X_a),times_times(X_a,A_2,B_1))|ord_less_e_q(X_a,zero_zero(X_a),A_2)|ord_less_e_q(X_a,A_2,zero_zero(X_a)).
% 8.09/8.09 0 [] -linord581940658strict(X_a)| -ord_less_e_q(X_a,zero_zero(X_a),times_times(X_a,A_2,B_1))|ord_less_e_q(X_a,zero_zero(X_a),A_2)|ord_less_e_q(X_a,B_1,zero_zero(X_a)).
% 8.09/8.09 0 [] -linord581940658strict(X_a)| -ord_less_e_q(X_a,zero_zero(X_a),times_times(X_a,A_2,B_1))|ord_less_e_q(X_a,zero_zero(X_a),B_1)|ord_less_e_q(X_a,A_2,zero_zero(X_a)).
% 8.09/8.09 0 [] -linord581940658strict(X_a)| -ord_less_e_q(X_a,zero_zero(X_a),times_times(X_a,A_2,B_1))|ord_less_e_q(X_a,zero_zero(X_a),B_1)|ord_less_e_q(X_a,B_1,zero_zero(X_a)).
% 8.09/8.09 0 [] -linord581940658strict(X_a)|ord_less_e_q(X_a,zero_zero(X_a),times_times(X_a,A_2,B_1))| -ord_less_e_q(X_a,zero_zero(X_a),A_2)| -ord_less_e_q(X_a,zero_zero(X_a),B_1).
% 8.09/8.09 0 [] -linord581940658strict(X_a)|ord_less_e_q(X_a,zero_zero(X_a),times_times(X_a,A_2,B_1))| -ord_less_e_q(X_a,A_2,zero_zero(X_a))| -ord_less_e_q(X_a,B_1,zero_zero(X_a)).
% 8.09/8.09 0 [] -linord581940658strict(X_a)| -ord_less_e_q(X_a,times_times(X_a,A_2,B_1),zero_zero(X_a))|ord_less_e_q(X_a,zero_zero(X_a),A_2)|ord_less_e_q(X_a,A_2,zero_zero(X_a)).
% 8.09/8.09 0 [] -linord581940658strict(X_a)| -ord_less_e_q(X_a,times_times(X_a,A_2,B_1),zero_zero(X_a))|ord_less_e_q(X_a,zero_zero(X_a),A_2)|ord_less_e_q(X_a,zero_zero(X_a),B_1).
% 8.09/8.09 0 [] -linord581940658strict(X_a)| -ord_less_e_q(X_a,times_times(X_a,A_2,B_1),zero_zero(X_a))|ord_less_e_q(X_a,B_1,zero_zero(X_a))|ord_less_e_q(X_a,A_2,zero_zero(X_a)).
% 8.09/8.09 0 [] -linord581940658strict(X_a)| -ord_less_e_q(X_a,times_times(X_a,A_2,B_1),zero_zero(X_a))|ord_less_e_q(X_a,B_1,zero_zero(X_a))|ord_less_e_q(X_a,zero_zero(X_a),B_1).
% 8.09/8.09 0 [] -linord581940658strict(X_a)|ord_less_e_q(X_a,times_times(X_a,A_2,B_1),zero_zero(X_a))| -ord_less_e_q(X_a,zero_zero(X_a),A_2)| -ord_less_e_q(X_a,B_1,zero_zero(X_a)).
% 8.09/8.09 0 [] -linord581940658strict(X_a)|ord_less_e_q(X_a,times_times(X_a,A_2,B_1),zero_zero(X_a))| -ord_less_e_q(X_a,A_2,zero_zero(X_a))| -ord_less_e_q(X_a,zero_zero(X_a),B_1).
% 8.09/8.09 0 [] -ordere453448008miring(X_a)| -ord_less_e_q(X_a,zero_zero(X_a),A_1)| -ord_less_e_q(X_a,zero_zero(X_a),B)|ord_less_e_q(X_a,zero_zero(X_a),times_times(X_a,A_1,B)).
% 8.09/8.09 0 [] -ordere453448008miring(X_a)| -ord_less_e_q(X_a,zero_zero(X_a),A_1)| -ord_less_e_q(X_a,B,zero_zero(X_a))|ord_less_e_q(X_a,times_times(X_a,A_1,B),zero_zero(X_a)).
% 8.09/8.09 0 [] -ordere453448008miring(X_a)| -ord_less_e_q(X_a,zero_zero(X_a),A_1)| -ord_less_e_q(X_a,B,zero_zero(X_a))|ord_less_e_q(X_a,times_times(X_a,B,A_1),zero_zero(X_a)).
% 8.09/8.09 0 [] -ordere453448008miring(X_a)| -ord_less_e_q(X_a,A_1,zero_zero(X_a))| -ord_less_e_q(X_a,zero_zero(X_a),B)|ord_less_e_q(X_a,times_times(X_a,A_1,B),zero_zero(X_a)).
% 8.09/8.09 0 [] -ordered_ring(X_a)| -ord_less_e_q(X_a,A_1,zero_zero(X_a))| -ord_less_e_q(X_a,B,zero_zero(X_a))|ord_less_e_q(X_a,zero_zero(X_a),times_times(X_a,A_1,B)).
% 8.09/8.09 0 [] semiri456707255roduct(int).
% 8.09/8.09 0 [] linord626643107strict(int).
% 8.09/8.09 0 [] linord219039673up_add(int).
% 8.09/8.09 0 [] ring_11004092258visors(int).
% 8.09/8.09 0 [] ordere453448008miring(int).
% 8.09/8.09 0 [] linord581940658strict(int).
% 8.09/8.09 0 [] ring_n68954251visors(int).
% 8.09/8.09 0 [] linordered_semidom(int).
% 8.09/8.09 0 [] comm_monoid_mult(int).
% 8.09/8.09 0 [] no_zero_divisors(int).
% 8.09/8.09 0 [] linordered_ring(int).
% 8.09/8.09 0 [] linordered_idom(int).
% 8.09/8.09 0 [] comm_semiring_1(int).
% 8.09/8.09 0 [] comm_semiring(int).
% 8.09/8.09 0 [] number_semiring(int).
% 8.09/8.09 0 [] ab_group_add(int).
% 8.09/8.09 0 [] zero_ne_q_one(int).
% 8.09/8.09 0 [] ordered_ring(int).
% 8.09/8.09 0 [] linorder(int).
% 8.09/8.09 0 [] monoid_mult(int).
% 8.09/8.09 0 [] comm_ring_1(int).
% 8.09/8.09 0 [] semiring_1(int).
% 8.09/8.09 0 [] semiring_0(int).
% 8.09/8.09 0 [] mult_zero(int).
% 8.09/8.09 0 [] order(int).
% 8.09/8.09 0 [] ring_char_0(int).
% 8.09/8.09 0 [] number_ring(int).
% 8.09/8.09 0 [] semiring(int).
% 8.09/8.09 0 [] ring_1(int).
% 8.09/8.09 0 [] power(int).
% 8.09/8.09 0 [] ring(int).
% 8.09/8.09 0 [] number(int).
% 8.09/8.09 0 [] dvd(int).
% 8.09/8.09 0 [] semiri456707255roduct(nat).
% 8.09/8.09 0 [] ordere453448008miring(nat).
% 8.09/8.09 0 [] linordered_semidom(nat).
% 8.09/8.09 0 [] comm_monoid_mult(nat).
% 8.09/8.09 0 [] no_zero_divisors(nat).
% 8.09/8.09 0 [] comm_semiring_1(nat).
% 8.09/8.10 0 [] comm_semiring(nat).
% 8.09/8.10 0 [] number_semiring(nat).
% 8.09/8.10 0 [] zero_ne_q_one(nat).
% 8.09/8.10 0 [] linorder(nat).
% 8.09/8.10 0 [] monoid_mult(nat).
% 8.09/8.10 0 [] semiring_1(nat).
% 8.09/8.10 0 [] semiring_0(nat).
% 8.09/8.10 0 [] mult_zero(nat).
% 8.09/8.10 0 [] order(nat).
% 8.09/8.10 0 [] semiring(nat).
% 8.09/8.10 0 [] power(nat).
% 8.09/8.10 0 [] number(nat).
% 8.09/8.10 0 [] dvd(nat).
% 8.09/8.10 0 [] order(bool).
% 8.09/8.10 0 [] semiri456707255roduct(real).
% 8.09/8.10 0 [] linord626643107strict(real).
% 8.09/8.10 0 [] linord219039673up_add(real).
% 8.09/8.10 0 [] ring_11004092258visors(real).
% 8.09/8.10 0 [] ordere453448008miring(real).
% 8.09/8.10 0 [] linord581940658strict(real).
% 8.09/8.10 0 [] ring_n68954251visors(real).
% 8.09/8.10 0 [] linordered_semidom(real).
% 8.09/8.10 0 [] comm_monoid_mult(real).
% 8.09/8.10 0 [] no_zero_divisors(real).
% 8.09/8.10 0 [] linordered_ring(real).
% 8.09/8.10 0 [] linordered_idom(real).
% 8.09/8.10 0 [] comm_semiring_1(real).
% 8.09/8.10 0 [] comm_semiring(real).
% 8.09/8.10 0 [] number_semiring(real).
% 8.09/8.10 0 [] ab_group_add(real).
% 8.09/8.10 0 [] zero_ne_q_one(real).
% 8.09/8.10 0 [] ordered_ring(real).
% 8.09/8.10 0 [] linorder(real).
% 8.09/8.10 0 [] monoid_mult(real).
% 8.09/8.10 0 [] comm_ring_1(real).
% 8.09/8.10 0 [] semiring_1(real).
% 8.09/8.10 0 [] semiring_0(real).
% 8.09/8.10 0 [] mult_zero(real).
% 8.09/8.10 0 [] order(real).
% 8.09/8.10 0 [] ring_char_0(real).
% 8.09/8.10 0 [] number_ring(real).
% 8.09/8.10 0 [] semiring(real).
% 8.09/8.10 0 [] ring_1(real).
% 8.09/8.10 0 [] power(real).
% 8.09/8.10 0 [] ring(real).
% 8.09/8.10 0 [] number(real).
% 8.09/8.10 0 [] dvd(real).
% 8.09/8.10 0 [] ti(T,ti(T,A))=ti(T,A).
% 8.09/8.10 0 [] -ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)).
% 8.09/8.10 end_of_list.
% 8.09/8.10
% 8.09/8.10 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 8.09/8.10
% 8.09/8.10 This ia a non-Horn set with equality. The strategy will be
% 8.09/8.10 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 8.09/8.10 deletion, with positive clauses in sos and nonpositive
% 8.09/8.10 clauses in usable.
% 8.09/8.10
% 8.09/8.10 dependent: set(knuth_bendix).
% 8.09/8.10 dependent: set(anl_eq).
% 8.09/8.10 dependent: set(para_from).
% 8.09/8.10 dependent: set(para_into).
% 8.09/8.10 dependent: clear(para_from_right).
% 8.09/8.10 dependent: clear(para_into_right).
% 8.09/8.10 dependent: set(para_from_vars).
% 8.09/8.10 dependent: set(eq_units_both_ways).
% 8.09/8.10 dependent: set(dynamic_demod_all).
% 8.09/8.10 dependent: set(dynamic_demod).
% 8.09/8.10 dependent: set(order_eq).
% 8.09/8.10 dependent: set(back_demod).
% 8.09/8.10 dependent: set(lrpo).
% 8.09/8.10 dependent: set(hyper_res).
% 8.09/8.10 dependent: set(unit_deletion).
% 8.09/8.10 dependent: set(factor).
% 8.09/8.10
% 8.09/8.10 ------------> process usable:
% 8.09/8.10 ** KEPT (pick-wt=13): 1 [] -ab_group_add(A)|minus_minus(A,ti(A,B),C)=minus_minus(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 2 [] -ab_group_add(A)|minus_minus(A,B,ti(A,C))=minus_minus(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 3 [] -ab_group_add(A)|ti(A,minus_minus(A,B,C))=minus_minus(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=9): 4 [] -zero_ne_q_one(A)|ti(A,one_one(A))=one_one(A).
% 8.09/8.10 ** KEPT (pick-wt=9): 5 [] -power(A)|ti(A,one_one(A))=one_one(A).
% 8.09/8.10 ** KEPT (pick-wt=13): 6 [] -semiring(A)|plus_plus(A,ti(A,B),C)=plus_plus(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 7 [] -semiring(A)|plus_plus(A,B,ti(A,C))=plus_plus(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 8 [] -semiring(A)|ti(A,plus_plus(A,B,C))=plus_plus(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 9 [] -ab_group_add(A)|plus_plus(A,ti(A,B),C)=plus_plus(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 10 [] -ab_group_add(A)|plus_plus(A,B,ti(A,C))=plus_plus(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 11 [] -ab_group_add(A)|ti(A,plus_plus(A,B,C))=plus_plus(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 12 [] -dvd(A)|times_times(A,ti(A,B),C)=times_times(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 13 [] -dvd(A)|times_times(A,B,ti(A,C))=times_times(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 14 [] -dvd(A)|ti(A,times_times(A,B,C))=times_times(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 15 [] -semiring(A)|times_times(A,ti(A,B),C)=times_times(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 16 [] -semiring(A)|times_times(A,B,ti(A,C))=times_times(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 17 [] -semiring(A)|ti(A,times_times(A,B,C))=times_times(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 18 [] -no_zero_divisors(A)|times_times(A,ti(A,B),C)=times_times(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 19 [] -no_zero_divisors(A)|times_times(A,B,ti(A,C))=times_times(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 20 [] -no_zero_divisors(A)|ti(A,times_times(A,B,C))=times_times(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 21 [] -mult_zero(A)|times_times(A,ti(A,B),C)=times_times(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 22 [] -mult_zero(A)|times_times(A,B,ti(A,C))=times_times(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 23 [] -mult_zero(A)|ti(A,times_times(A,B,C))=times_times(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 24 [] -power(A)|times_times(A,ti(A,B),C)=times_times(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 25 [] -power(A)|times_times(A,B,ti(A,C))=times_times(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 26 [] -power(A)|ti(A,times_times(A,B,C))=times_times(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=9): 27 [] -zero_ne_q_one(A)|ti(A,zero_zero(A))=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=9): 28 [] -no_zero_divisors(A)|ti(A,zero_zero(A))=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=9): 29 [] -mult_zero(A)|ti(A,zero_zero(A))=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=9): 30 [] -linord219039673up_add(A)|ti(A,zero_zero(A))=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=10): 31 [] -zcong(ti(int,A),B,C)|zcong(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=10): 32 [] zcong(ti(int,A),B,C)| -zcong(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=10): 33 [] -zcong(A,ti(int,B),C)|zcong(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=10): 34 [] zcong(A,ti(int,B),C)| -zcong(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=10): 35 [] -zcong(A,B,ti(int,C))|zcong(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=10): 36 [] zcong(A,B,ti(int,C))| -zcong(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=6): 37 [] -zprime(ti(int,A))|zprime(A).
% 8.09/8.10 ** KEPT (pick-wt=6): 38 [] zprime(ti(int,A))| -zprime(A).
% 8.09/8.10 ** KEPT (pick-wt=11): 39 [] -number(A)|number_number_of(A,ti(int,B))=number_number_of(A,B).
% 8.09/8.10 ** KEPT (pick-wt=11): 40 [] -number(A)|ti(A,number_number_of(A,B))=number_number_of(A,B).
% 8.09/8.10 ** KEPT (pick-wt=12): 41 [] -order(A)| -ord_less(A,ti(A,B),C)|ord_less(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=12): 42 [] -order(A)|ord_less(A,ti(A,B),C)| -ord_less(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=12): 43 [] -order(A)| -ord_less(A,B,ti(A,C))|ord_less(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=12): 44 [] -order(A)|ord_less(A,B,ti(A,C))| -ord_less(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=12): 45 [] -order(A)| -ord_less_e_q(A,ti(A,B),C)|ord_less_e_q(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=12): 46 [] -order(A)|ord_less_e_q(A,ti(A,B),C)| -ord_less_e_q(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=12): 47 [] -order(A)| -ord_less_e_q(A,B,ti(A,C))|ord_less_e_q(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=12): 48 [] -order(A)|ord_less_e_q(A,B,ti(A,C))| -ord_less_e_q(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 49 [] -power(A)|power_power(A,ti(A,B),C)=power_power(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 50 [] -power(A)|power_power(A,B,ti(nat,C))=power_power(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=13): 51 [] -power(A)|ti(A,power_power(A,B,C))=power_power(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=8): 52 [] -quadRes(ti(int,A),B)|quadRes(A,B).
% 8.09/8.10 ** KEPT (pick-wt=8): 53 [] quadRes(ti(int,A),B)| -quadRes(A,B).
% 8.09/8.10 ** KEPT (pick-wt=8): 54 [] -quadRes(A,ti(int,B))|quadRes(A,B).
% 8.09/8.10 ** KEPT (pick-wt=8): 55 [] quadRes(A,ti(int,B))| -quadRes(A,B).
% 8.09/8.10 ** KEPT (pick-wt=12): 56 [] -dvd(A)| -dvd_dvd(A,ti(A,B),C)|dvd_dvd(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=12): 57 [] -dvd(A)|dvd_dvd(A,ti(A,B),C)| -dvd_dvd(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=12): 58 [] -dvd(A)| -dvd_dvd(A,B,ti(A,C))|dvd_dvd(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=12): 59 [] -dvd(A)|dvd_dvd(A,B,ti(A,C))| -dvd_dvd(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=6): 60 [] -twoSqu420862341sum2sq(ti(int,A))|twoSqu420862341sum2sq(A).
% 8.09/8.10 ** KEPT (pick-wt=6): 61 [] twoSqu420862341sum2sq(ti(int,A))| -twoSqu420862341sum2sq(A).
% 8.09/8.10 ** KEPT (pick-wt=19): 63 [copy,62,flip.1,flip.2] zero_zero(int)!=t|zero_zero(int)=plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)).
% 8.09/8.10 ** KEPT (pick-wt=5): 64 [] -ord_less_e_q(int,one_one(int),t).
% 8.09/8.10 ** KEPT (pick-wt=24): 65 [] -linordered_idom(A)| -ord_less(A,plus_plus(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),power_power(A,C,number_number_of(nat,bit0(bit1(pls))))),zero_zero(A)).
% 8.09/8.10 ** KEPT (pick-wt=36): 66 [] -linordered_idom(A)| -ord_less(A,zero_zero(A),plus_plus(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),power_power(A,C,number_number_of(nat,bit0(bit1(pls))))))|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=30): 67 [] -linordered_idom(A)|ord_less(A,zero_zero(A),plus_plus(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),power_power(A,C,number_number_of(nat,bit0(bit1(pls))))))|ti(A,B)=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=30): 68 [] -linordered_idom(A)|ord_less(A,zero_zero(A),plus_plus(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),power_power(A,C,number_number_of(nat,bit0(bit1(pls))))))|ti(A,C)=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=29): 69 [] -linordered_idom(A)|plus_plus(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),power_power(A,C,number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(A)|ti(A,B)=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=29): 70 [] -linordered_idom(A)|plus_plus(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),power_power(A,C,number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(A)|ti(A,C)=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=35): 71 [] -linordered_idom(A)|plus_plus(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),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).
% 8.09/8.10 ** KEPT (pick-wt=14): 72 [] -linordered_idom(A)| -ord_less(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),zero_zero(A)).
% 8.09/8.10 ** KEPT (pick-wt=20): 73 [] -linordered_idom(A)| -ord_less(A,zero_zero(A),power_power(A,B,number_number_of(nat,bit0(bit1(pls)))))|ti(A,B)!=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=20): 74 [] -linordered_idom(A)|ord_less(A,zero_zero(A),power_power(A,B,number_number_of(nat,bit0(bit1(pls)))))|ti(A,B)=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=14): 75 [] -semiring_1(A)|power_power(A,one_one(A),number_number_of(nat,bit0(bit1(pls))))=one_one(A).
% 8.09/8.10 ** KEPT (pick-wt=14): 76 [] -semiring_1(A)|power_power(A,zero_zero(A),number_number_of(nat,bit0(bit1(pls))))=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=19): 77 [] -ring_11004092258visors(A)|power_power(A,B,number_number_of(nat,bit0(bit1(pls))))!=zero_zero(A)|ti(A,B)=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=19): 78 [] -ring_11004092258visors(A)|power_power(A,B,number_number_of(nat,bit0(bit1(pls))))=zero_zero(A)|ti(A,B)!=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=17): 79 [] -number_ring(A)|plus_plus(A,one_one(A),number_number_of(A,B))=number_number_of(A,plus_plus(int,bit1(pls),B)).
% 8.09/8.10 ** KEPT (pick-wt=17): 80 [] -number_ring(A)|plus_plus(A,number_number_of(A,B),one_one(A))=number_number_of(A,plus_plus(int,B,bit1(pls))).
% 8.09/8.10 ** KEPT (pick-wt=12): 81 [] -ord_less_e_q(int,number_number_of(int,A),number_number_of(int,B))|ord_less_e_q(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=12): 82 [] ord_less_e_q(int,number_number_of(int,A),number_number_of(int,B))| -ord_less_e_q(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=16): 83 [] -number_ring(A)| -linordered_idom(A)| -ord_less_e_q(A,number_number_of(A,B),number_number_of(A,C))|ord_less_e_q(int,B,C).
% 8.09/8.10 ** KEPT (pick-wt=16): 84 [] -number_ring(A)| -linordered_idom(A)|ord_less_e_q(A,number_number_of(A,B),number_number_of(A,C))| -ord_less_e_q(int,B,C).
% 8.09/8.10 ** KEPT (pick-wt=12): 85 [] -ord_less_e_q(int,A,B)| -ord_less_e_q(int,B,C)|ord_less_e_q(int,A,C).
% 8.09/8.10 ** KEPT (pick-wt=15): 86 [] -ord_less_e_q(int,A,B)| -ord_less_e_q(int,B,A)|ti(int,A)=ti(int,B).
% 8.09/8.10 ** KEPT (pick-wt=10): 87 [] -ord_less_e_q(int,bit1(A),bit1(B))|ord_less_e_q(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=10): 88 [] ord_less_e_q(int,bit1(A),bit1(B))| -ord_less_e_q(int,A,B).
% 8.09/8.10 Following clause subsumed by 87 during input processing: 0 [] -ord_less_e_q(int,bit1(A),bit1(B))|ord_less_e_q(int,A,B).
% 8.09/8.10 Following clause subsumed by 88 during input processing: 0 [] ord_less_e_q(int,bit1(A),bit1(B))| -ord_less_e_q(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=10): 89 [] -ord_less_e_q(int,bit0(A),bit0(B))|ord_less_e_q(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=10): 90 [] ord_less_e_q(int,bit0(A),bit0(B))| -ord_less_e_q(int,A,B).
% 8.09/8.10 Following clause subsumed by 89 during input processing: 0 [] -ord_less_e_q(int,bit0(A),bit0(B))|ord_less_e_q(int,A,B).
% 8.09/8.10 Following clause subsumed by 90 during input processing: 0 [] ord_less_e_q(int,bit0(A),bit0(B))| -ord_less_e_q(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=8): 91 [] -ord_less(int,A,B)|ord_less_e_q(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=11): 92 [] -ord_less(int,A,B)|ti(int,A)!=ti(int,B).
% 8.09/8.10 ** KEPT (pick-wt=15): 93 [] ord_less(int,A,B)| -ord_less_e_q(int,A,B)|ti(int,A)=ti(int,B).
% 8.09/8.10 ** KEPT (pick-wt=14): 94 [] -ord_less_e_q(int,A,B)|ord_less_e_q(int,plus_plus(int,C,A),plus_plus(int,C,B)).
% 8.09/8.10 ** KEPT (pick-wt=10): 95 [] number_number_of(nat,A)!=zero_zero(nat)|ord_less_e_q(int,A,pls).
% 8.09/8.10 ** KEPT (pick-wt=10): 96 [] number_number_of(nat,A)=zero_zero(nat)| -ord_less_e_q(int,A,pls).
% 8.09/8.10 ** KEPT (pick-wt=10): 97 [] zero_zero(nat)!=number_number_of(nat,A)|ord_less_e_q(int,A,pls).
% 8.09/8.10 ** KEPT (pick-wt=10): 98 [] zero_zero(nat)=number_number_of(nat,A)| -ord_less_e_q(int,A,pls).
% 8.09/8.10 ** KEPT (pick-wt=25): 100 [copy,99,flip.4] -number_semiring(A)| -ord_less_e_q(int,pls,B)| -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)).
% 8.09/8.10 ** KEPT (pick-wt=23): 102 [copy,101,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)).
% 8.09/8.10 ** KEPT (pick-wt=17): 104 [copy,103,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)).
% 8.09/8.10 Following clause subsumed by 104 during input processing: 0 [] -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)).
% 8.09/8.10 ** KEPT (pick-wt=22): 105 [] -linord581940658strict(A)| -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).
% 8.09/8.10 ** KEPT (pick-wt=22): 106 [] -linord581940658strict(A)| -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).
% 8.09/8.10 ** KEPT (pick-wt=28): 107 [] -linord581940658strict(A)|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).
% 8.09/8.10 ** KEPT (pick-wt=16): 108 [] -linordered_ring(A)|ord_less_e_q(A,zero_zero(A),plus_plus(A,times_times(A,B,B),times_times(A,C,C))).
% 8.09/8.10 ** KEPT (pick-wt=15): 109 [] -number_ring(A)| -linordered_idom(A)| -ord_less_e_q(A,number_number_of(A,B),zero_zero(A))|ord_less_e_q(int,B,pls).
% 8.09/8.10 ** KEPT (pick-wt=15): 110 [] -number_ring(A)| -linordered_idom(A)|ord_less_e_q(A,number_number_of(A,B),zero_zero(A))| -ord_less_e_q(int,B,pls).
% 8.09/8.10 ** KEPT (pick-wt=15): 111 [] -number_ring(A)| -linordered_idom(A)| -ord_less_e_q(A,zero_zero(A),number_number_of(A,B))|ord_less_e_q(int,pls,B).
% 8.09/8.10 ** KEPT (pick-wt=15): 112 [] -number_ring(A)| -linordered_idom(A)|ord_less_e_q(A,zero_zero(A),number_number_of(A,B))| -ord_less_e_q(int,pls,B).
% 8.09/8.10 ** KEPT (pick-wt=11): 113 [] -ord_less(nat,zero_zero(nat),number_number_of(nat,A))|ord_less(int,pls,A).
% 8.09/8.10 ** KEPT (pick-wt=11): 114 [] ord_less(nat,zero_zero(nat),number_number_of(nat,A))| -ord_less(int,pls,A).
% 8.09/8.10 ** KEPT (pick-wt=20): 115 [] -number(A)| -linorder(A)| -ord_less_e_q(A,number_number_of(A,B),number_number_of(A,C))| -ord_less(A,number_number_of(A,C),number_number_of(A,B)).
% 8.09/8.10 ** KEPT (pick-wt=20): 116 [] -number(A)| -linorder(A)|ord_less_e_q(A,number_number_of(A,B),number_number_of(A,C))|ord_less(A,number_number_of(A,C),number_number_of(A,B)).
% 8.09/8.10 ** KEPT (pick-wt=9): 117 [] -ord_less_e_q(int,pls,bit1(A))|ord_less_e_q(int,pls,A).
% 8.09/8.10 ** KEPT (pick-wt=9): 118 [] ord_less_e_q(int,pls,bit1(A))| -ord_less_e_q(int,pls,A).
% 8.09/8.10 ** KEPT (pick-wt=10): 119 [] -ord_less_e_q(int,bit0(A),bit1(B))|ord_less_e_q(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=10): 120 [] ord_less_e_q(int,bit0(A),bit1(B))| -ord_less_e_q(int,A,B).
% 8.09/8.10 Following clause subsumed by 119 during input processing: 0 [] -ord_less_e_q(int,bit0(A),bit1(B))|ord_less_e_q(int,A,B).
% 8.09/8.10 Following clause subsumed by 120 during input processing: 0 [] ord_less_e_q(int,bit0(A),bit1(B))| -ord_less_e_q(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=9): 121 [] -ord_less_e_q(int,bit0(A),pls)|ord_less_e_q(int,A,pls).
% 8.09/8.10 ** KEPT (pick-wt=9): 122 [] ord_less_e_q(int,bit0(A),pls)| -ord_less_e_q(int,A,pls).
% 8.09/8.10 ** KEPT (pick-wt=9): 123 [] -ord_less_e_q(int,pls,bit0(A))|ord_less_e_q(int,pls,A).
% 8.09/8.10 ** KEPT (pick-wt=9): 124 [] ord_less_e_q(int,pls,bit0(A))| -ord_less_e_q(int,pls,A).
% 8.09/8.10 ** KEPT (pick-wt=18): 125 [] -ord_less(int,A,B)| -ord_less_e_q(int,C,D)|ord_less(int,plus_plus(int,A,C),plus_plus(int,B,D)).
% 8.09/8.10 ** KEPT (pick-wt=16): 126 [] -number_ring(A)| -linordered_idom(A)| -ord_less_e_q(A,number_number_of(A,B),one_one(A))|ord_less_e_q(int,B,bit1(pls)).
% 8.09/8.10 ** KEPT (pick-wt=16): 127 [] -number_ring(A)| -linordered_idom(A)|ord_less_e_q(A,number_number_of(A,B),one_one(A))| -ord_less_e_q(int,B,bit1(pls)).
% 8.09/8.10 ** KEPT (pick-wt=16): 128 [] -number_ring(A)| -linordered_idom(A)| -ord_less_e_q(A,one_one(A),number_number_of(A,B))|ord_less_e_q(int,bit1(pls),B).
% 8.09/8.10 ** KEPT (pick-wt=16): 129 [] -number_ring(A)| -linordered_idom(A)|ord_less_e_q(A,one_one(A),number_number_of(A,B))| -ord_less_e_q(int,bit1(pls),B).
% 8.09/8.10 ** KEPT (pick-wt=12): 130 [] -ord_less(int,number_number_of(int,A),number_number_of(int,B))|ord_less(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=12): 131 [] ord_less(int,number_number_of(int,A),number_number_of(int,B))| -ord_less(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=9): 132 [] -ord_less_e_q(int,bit1(A),pls)|ord_less(int,A,pls).
% 8.09/8.10 ** KEPT (pick-wt=9): 133 [] ord_less_e_q(int,bit1(A),pls)| -ord_less(int,A,pls).
% 8.09/8.10 ** KEPT (pick-wt=9): 134 [] -ord_less(int,pls,bit1(A))|ord_less_e_q(int,pls,A).
% 8.09/8.10 ** KEPT (pick-wt=9): 135 [] ord_less(int,pls,bit1(A))| -ord_less_e_q(int,pls,A).
% 8.09/8.10 ** KEPT (pick-wt=10): 136 [] -ord_less_e_q(int,bit1(A),bit0(B))|ord_less(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=10): 137 [] ord_less_e_q(int,bit1(A),bit0(B))| -ord_less(int,A,B).
% 8.09/8.10 Following clause subsumed by 136 during input processing: 0 [] -ord_less_e_q(int,bit1(A),bit0(B))|ord_less(int,A,B).
% 8.09/8.10 Following clause subsumed by 137 during input processing: 0 [] ord_less_e_q(int,bit1(A),bit0(B))| -ord_less(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=10): 138 [] -ord_less(int,bit0(A),bit1(B))|ord_less_e_q(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=10): 139 [] ord_less(int,bit0(A),bit1(B))| -ord_less_e_q(int,A,B).
% 8.09/8.10 Following clause subsumed by 138 during input processing: 0 [] -ord_less(int,bit0(A),bit1(B))|ord_less_e_q(int,A,B).
% 8.09/8.10 Following clause subsumed by 139 during input processing: 0 [] ord_less(int,bit0(A),bit1(B))| -ord_less_e_q(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=16): 140 [] -ord_less(nat,number_number_of(nat,A),number_number_of(nat,B))| -ord_less(int,A,B)|ord_less(int,pls,B).
% 8.09/8.10 ** KEPT (pick-wt=12): 141 [] -ord_less(nat,number_number_of(nat,A),number_number_of(nat,B))|ord_less(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=16): 142 [] ord_less(nat,number_number_of(nat,A),number_number_of(nat,B))| -ord_less(int,pls,B)| -ord_less(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=10): 143 [] -ord_less_e_q(int,one_one(int),A)|ord_less(int,zero_zero(int),A).
% 8.09/8.10 ** KEPT (pick-wt=10): 144 [] ord_less_e_q(int,one_one(int),A)| -ord_less(int,zero_zero(int),A).
% 8.09/8.10 ** KEPT (pick-wt=12): 145 [] -ord_less(int,A,B)|ord_less_e_q(int,plus_plus(int,A,one_one(int)),B).
% 8.09/8.10 ** KEPT (pick-wt=12): 146 [] -ord_less_e_q(int,plus_plus(int,A,one_one(int)),B)|ord_less(int,A,B).
% 8.09/8.10 Following clause subsumed by 145 during input processing: 0 [] ord_less_e_q(int,plus_plus(int,A,one_one(int)),B)| -ord_less(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=12): 147 [] -ord_less(int,A,plus_plus(int,B,one_one(int)))|ord_less_e_q(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=12): 148 [] ord_less(int,A,plus_plus(int,B,one_one(int)))| -ord_less_e_q(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=25): 150 [copy,149,flip.4] -number_semiring(A)| -ord_less_e_q(int,pls,B)| -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)).
% 8.09/8.10 ** KEPT (pick-wt=16): 151 [] -ord_less(int,A,pls)|plus_plus(nat,number_number_of(nat,A),number_number_of(nat,B))=number_number_of(nat,B).
% 8.09/8.10 ** KEPT (pick-wt=20): 152 [] ord_less(int,A,pls)| -ord_less(int,B,pls)|plus_plus(nat,number_number_of(nat,A),number_number_of(nat,B))=number_number_of(nat,A).
% 8.09/8.10 ** KEPT (pick-wt=14): 153 [] -ord_less_e_q(int,zero_zero(int),A)|ord_less(int,zero_zero(int),plus_plus(int,one_one(int),A)).
% 8.09/8.10 ** KEPT (pick-wt=18): 154 [] -number_ring(A)| -ring_char_0(A)|number_number_of(A,B)!=number_number_of(A,C)|ti(int,B)=ti(int,C).
% 8.09/8.10 ** KEPT (pick-wt=18): 155 [] -number_ring(A)| -ring_char_0(A)|number_number_of(A,B)=number_number_of(A,C)|ti(int,B)!=ti(int,C).
% 8.09/8.10 ** KEPT (pick-wt=16): 156 [] -number(A)|number_number_of(A,B)!=ti(A,C)|ti(A,C)=number_number_of(A,B).
% 8.09/8.10 ** KEPT (pick-wt=16): 157 [] -number(A)|number_number_of(A,B)=ti(A,C)|ti(A,C)!=number_number_of(A,B).
% 8.09/8.10 ** KEPT (pick-wt=12): 158 [] bit1(A)!=bit1(B)|ti(int,A)=ti(int,B).
% 8.09/8.10 ** KEPT (pick-wt=12): 159 [] bit1(A)=bit1(B)|ti(int,A)!=ti(int,B).
% 8.09/8.10 ** KEPT (pick-wt=12): 160 [] bit0(A)!=bit0(B)|ti(int,A)=ti(int,B).
% 8.09/8.10 ** KEPT (pick-wt=12): 161 [] bit0(A)=bit0(B)|ti(int,A)!=ti(int,B).
% 8.09/8.10 ** KEPT (pick-wt=21): 162 [] -linord581940658strict(A)|plus_plus(A,times_times(A,B,B),times_times(A,C,C))!=zero_zero(A)|ti(A,B)=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=21): 163 [] -linord581940658strict(A)|plus_plus(A,times_times(A,B,B),times_times(A,C,C))!=zero_zero(A)|ti(A,C)=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=27): 164 [] -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).
% 8.09/8.10 ** KEPT (pick-wt=28): 165 [] -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))).
% 8.09/8.10 ** KEPT (pick-wt=28): 166 [] -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)).
% 8.09/8.10 ** KEPT (pick-wt=19): 167 [] -ord_less(int,A,B)| -ord_less(int,zero_zero(int),C)|ord_less(int,times_times(int,C,A),times_times(int,C,B)).
% 8.09/8.10 ** KEPT (pick-wt=36): 168 [] -linordered_semidom(A)|power_power(A,B,number_number_of(nat,bit0(bit1(pls))))!=power_power(A,C,number_number_of(nat,bit0(bit1(pls))))| -ord_less_e_q(A,zero_zero(A),B)| -ord_less_e_q(A,zero_zero(A),C)|ti(A,B)=ti(A,C).
% 8.09/8.10 ** KEPT (pick-wt=29): 169 [] -linordered_semidom(A)| -ord_less_e_q(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),power_power(A,C,number_number_of(nat,bit0(bit1(pls)))))| -ord_less_e_q(A,zero_zero(A),C)|ord_less_e_q(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=14): 170 [] -linordered_idom(A)|ord_less_e_q(A,zero_zero(A),power_power(A,B,number_number_of(nat,bit0(bit1(pls))))).
% 8.09/8.10 ** KEPT (pick-wt=29): 171 [] -linordered_semidom(A)| -ord_less(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),power_power(A,C,number_number_of(nat,bit0(bit1(pls)))))| -ord_less_e_q(A,zero_zero(A),C)|ord_less(A,B,C).
% 8.09/8.10 ** KEPT (pick-wt=30): 172 [] -linordered_idom(A)| -ord_less_e_q(A,plus_plus(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),power_power(A,C,number_number_of(nat,bit0(bit1(pls))))),zero_zero(A))|ti(A,B)=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=30): 173 [] -linordered_idom(A)| -ord_less_e_q(A,plus_plus(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),power_power(A,C,number_number_of(nat,bit0(bit1(pls))))),zero_zero(A))|ti(A,C)=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=36): 174 [] -linordered_idom(A)|ord_less_e_q(A,plus_plus(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),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).
% 8.09/8.10 ** KEPT (pick-wt=24): 175 [] -linordered_idom(A)|ord_less_e_q(A,zero_zero(A),plus_plus(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),power_power(A,C,number_number_of(nat,bit0(bit1(pls)))))).
% 8.09/8.10 ** KEPT (pick-wt=28): 176 [] -linord581940658strict(A)| -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).
% 8.09/8.10 ** KEPT (pick-wt=22): 177 [] -linord581940658strict(A)|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).
% 8.09/8.10 ** KEPT (pick-wt=22): 178 [] -linord581940658strict(A)|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).
% 8.09/8.10 ** KEPT (pick-wt=16): 179 [] -linordered_ring(A)| -ord_less(A,plus_plus(A,times_times(A,B,B),times_times(A,C,C)),zero_zero(A)).
% 8.09/8.10 ** KEPT (pick-wt=13): 180 [] -number_ring(A)|times_times(A,number_number_of(A,bit1(pls)),B)=ti(A,B).
% 8.09/8.10 ** KEPT (pick-wt=13): 181 [] -number_ring(A)|times_times(A,B,number_number_of(A,bit1(pls)))=ti(A,B).
% 8.09/8.10 ** KEPT (pick-wt=18): 182 [] -ord_less(int,zero_zero(int),A)|times_times(int,A,B)!=one_one(int)|ti(int,A)=one_one(int).
% 8.09/8.10 ** KEPT (pick-wt=18): 183 [] -ord_less(int,zero_zero(int),A)|times_times(int,A,B)!=one_one(int)|ti(int,B)=one_one(int).
% 8.09/8.10 ** KEPT (pick-wt=24): 184 [] -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).
% 8.09/8.10 ** KEPT (pick-wt=15): 185 [] -linord219039673up_add(A)|plus_plus(A,B,B)!=zero_zero(A)|ti(A,B)=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=15): 186 [] -linord219039673up_add(A)|plus_plus(A,B,B)=zero_zero(A)|ti(A,B)!=zero_zero(A).
% 8.09/8.10 ** KEPT (pick-wt=4): 187 [] bit1(A)!=pls.
% 8.09/8.10 Following clause subsumed by 187 during input processing: 0 [flip.1] bit1(A)!=pls.
% 8.09/8.10 ** KEPT (pick-wt=5): 188 [] bit1(A)!=bit0(B).
% 8.09/8.10 ** KEPT (pick-wt=5): 189 [] bit0(A)!=bit1(B).
% 8.09/8.10 ** KEPT (pick-wt=9): 190 [] bit0(A)!=pls|ti(int,A)=pls.
% 8.09/8.10 ** KEPT (pick-wt=9): 191 [] bit0(A)=pls|ti(int,A)!=pls.
% 8.09/8.10 Following clause subsumed by 190 during input processing: 0 [flip.1,flip.2] bit0(A)!=pls|ti(int,A)=pls.
% 8.09/8.10 Following clause subsumed by 191 during input processing: 0 [flip.1,flip.2] bit0(A)=pls|ti(int,A)!=pls.
% 8.09/8.10 ** KEPT (pick-wt=10): 192 [] -ord_less(int,bit1(A),bit1(B))|ord_less(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=10): 193 [] ord_less(int,bit1(A),bit1(B))| -ord_less(int,A,B).
% 8.09/8.10 Following clause subsumed by 192 during input processing: 0 [] -ord_less(int,bit1(A),bit1(B))|ord_less(int,A,B).
% 8.09/8.10 Following clause subsumed by 193 during input processing: 0 [] ord_less(int,bit1(A),bit1(B))| -ord_less(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=4): 194 [] -ord_less(int,pls,pls).
% 8.09/8.10 ** KEPT (pick-wt=10): 195 [] -ord_less(int,bit0(A),bit0(B))|ord_less(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=10): 196 [] ord_less(int,bit0(A),bit0(B))| -ord_less(int,A,B).
% 8.09/8.10 Following clause subsumed by 195 during input processing: 0 [] -ord_less(int,bit0(A),bit0(B))|ord_less(int,A,B).
% 8.09/8.10 Following clause subsumed by 196 during input processing: 0 [] ord_less(int,bit0(A),bit0(B))| -ord_less(int,A,B).
% 8.09/8.10 ** KEPT (pick-wt=5): 197 [] zero_zero(int)!=one_one(int).
% 8.09/8.10 ** KEPT (pick-wt=14): 198 [] -ord_less(int,A,B)|ord_less(int,plus_plus(int,A,C),plus_plus(int,B,C)).
% 8.09/8.10 ** KEPT (pick-wt=18): 199 [] -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)).
% 8.09/8.10 ** KEPT (pick-wt=18): 200 [] -monoid_mult(A)|power_power(A,B,number_number_of(nat,bit1(bit1(pls))))=times_times(A,times_times(A,B,B),B).
% 8.09/8.10 ** KEPT (pick-wt=15): 201 [] -number_semiring(A)|times_times(A,number_number_of(A,bit0(bit1(pls))),B)=plus_plus(A,B,B).
% 8.09/8.10 ** KEPT (pick-wt=15): 202 [] -number_ring(A)|times_times(A,number_number_of(A,bit0(bit1(pls))),B)=plus_plus(A,B,B).
% 8.09/8.10 ** KEPT (pick-wt=15): 203 [] -number_semiring(A)|times_times(A,B,number_number_of(A,bit0(bit1(pls))))=plus_plus(A,B,B).
% 8.09/8.10 ** KEPT (pick-wt=15): 204 [] -number_ring(A)|times_times(A,B,number_number_of(A,bit0(bit1(pls))))=plus_plus(A,B,B).
% 8.09/8.11 ** KEPT (pick-wt=15): 205 [] -monoid_mult(A)|power_power(A,B,number_number_of(nat,bit0(bit1(pls))))=times_times(A,B,B).
% 8.09/8.11 ** KEPT (pick-wt=15): 206 [] -linordered_idom(A)| -ord_less(A,plus_plus(A,B,B),zero_zero(A))|ord_less(A,B,zero_zero(A)).
% 8.09/8.11 ** KEPT (pick-wt=15): 207 [] -linordered_idom(A)|ord_less(A,plus_plus(A,B,B),zero_zero(A))| -ord_less(A,B,zero_zero(A)).
% 8.09/8.11 ** KEPT (pick-wt=8): 209 [copy,208,flip.2] -number_semiring(A)|zero_zero(A)=number_number_of(A,pls).
% 8.09/8.11 ** KEPT (pick-wt=8): 211 [copy,210,flip.2] -number_ring(A)|zero_zero(A)=number_number_of(A,pls).
% 8.09/8.11 Following clause subsumed by 211 during input processing: 0 [] -number_ring(A)|zero_zero(A)=number_number_of(A,pls).
% 8.09/8.11 ** KEPT (pick-wt=12): 213 [copy,212,flip.2] -number_ring(A)|ti(A,B)=plus_plus(A,number_number_of(A,pls),B).
% 8.09/8.11 ** KEPT (pick-wt=12): 215 [copy,214,flip.2] -number_ring(A)|ti(A,B)=plus_plus(A,B,number_number_of(A,pls)).
% 8.09/8.11 ** KEPT (pick-wt=16): 216 [] -number_ring(A)| -linordered_idom(A)| -ord_less(A,number_number_of(A,B),number_number_of(A,C))|ord_less(int,B,C).
% 8.09/8.11 ** KEPT (pick-wt=16): 217 [] -number_ring(A)| -linordered_idom(A)|ord_less(A,number_number_of(A,B),number_number_of(A,C))| -ord_less(int,B,C).
% 8.09/8.11 ** KEPT (pick-wt=23): 219 [copy,218,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)).
% 8.09/8.11 ** KEPT (pick-wt=17): 221 [copy,220,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)).
% 8.09/8.11 Following clause subsumed by 221 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)).
% 8.09/8.11 ** KEPT (pick-wt=9): 222 [] -ord_less(int,bit1(A),pls)|ord_less(int,A,pls).
% 8.09/8.11 ** KEPT (pick-wt=9): 223 [] ord_less(int,bit1(A),pls)| -ord_less(int,A,pls).
% 8.09/8.11 ** KEPT (pick-wt=10): 224 [] -ord_less(int,bit1(A),bit0(B))|ord_less(int,A,B).
% 8.09/8.11 ** KEPT (pick-wt=10): 225 [] ord_less(int,bit1(A),bit0(B))| -ord_less(int,A,B).
% 8.09/8.11 Following clause subsumed by 224 during input processing: 0 [] -ord_less(int,bit1(A),bit0(B))|ord_less(int,A,B).
% 8.09/8.11 Following clause subsumed by 225 during input processing: 0 [] ord_less(int,bit1(A),bit0(B))| -ord_less(int,A,B).
% 8.09/8.11 ** KEPT (pick-wt=11): 226 [] -ord_less(int,bit1(A),zero_zero(int))|ord_less(int,A,zero_zero(int)).
% 8.09/8.11 ** KEPT (pick-wt=11): 227 [] ord_less(int,bit1(A),zero_zero(int))| -ord_less(int,A,zero_zero(int)).
% 8.09/8.11 ** KEPT (pick-wt=9): 228 [] -ord_less(int,bit0(A),pls)|ord_less(int,A,pls).
% 8.09/8.11 ** KEPT (pick-wt=9): 229 [] ord_less(int,bit0(A),pls)| -ord_less(int,A,pls).
% 8.09/8.11 ** KEPT (pick-wt=9): 230 [] -ord_less(int,pls,bit0(A))|ord_less(int,pls,A).
% 8.09/8.11 ** KEPT (pick-wt=9): 231 [] ord_less(int,pls,bit0(A))| -ord_less(int,pls,A).
% 8.09/8.11 ** KEPT (pick-wt=5): 232 [] -ord_less(int,pls,zero_zero(int)).
% 8.09/8.11 ** KEPT (pick-wt=11): 233 [] -ord_less(int,bit0(A),zero_zero(int))|ord_less(int,A,zero_zero(int)).
% 8.09/8.11 ** KEPT (pick-wt=11): 234 [] ord_less(int,bit0(A),zero_zero(int))| -ord_less(int,A,zero_zero(int)).
% 8.09/8.11 ** KEPT (pick-wt=11): 235 [] plus_plus(int,plus_plus(int,one_one(int),A),A)!=zero_zero(int).
% 8.09/8.11 ** KEPT (pick-wt=19): 236 [] -ord_less(int,A,plus_plus(int,B,one_one(int)))|ord_less(int,A,B)|ti(int,A)=ti(int,B).
% 8.09/8.11 ** KEPT (pick-wt=12): 237 [] ord_less(int,A,plus_plus(int,B,one_one(int)))| -ord_less(int,A,B).
% 8.09/8.11 ** KEPT (pick-wt=15): 238 [] ord_less(int,A,plus_plus(int,B,one_one(int)))|ti(int,A)!=ti(int,B).
% 8.09/8.11 Following clause subsumed by 205 during input processing: 0 [] -monoid_mult(A)| -number(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)).
% 8.09/8.11 ** KEPT (pick-wt=45): 239 [] -number_semiring(A)|power_power(A,plus_plus(A,B,C),number_number_of(nat,bit0(bit1(pls))))=plus_plus(A,plus_plus(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),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)).
% 8.09/8.11 ** KEPT (pick-wt=19): 240 [] -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)).
% 8.09/8.11 ** KEPT (pick-wt=19): 241 [] -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)).
% 8.09/8.11 ** KEPT (pick-wt=9): 243 [copy,242,flip.2] -number_semiring(A)|one_one(A)=number_number_of(A,bit1(pls)).
% 8.09/8.11 ** KEPT (pick-wt=9): 245 [copy,244,flip.2] -number_ring(A)|one_one(A)=number_number_of(A,bit1(pls)).
% 8.09/8.11 Following clause subsumed by 245 during input processing: 0 [] -number_ring(A)|one_one(A)=number_number_of(A,bit1(pls)).
% 8.09/8.11 ** KEPT (pick-wt=17): 246 [] -ord_less(int,plus_plus(int,plus_plus(int,one_one(int),A),A),zero_zero(int))|ord_less(int,A,zero_zero(int)).
% 8.09/8.11 ** KEPT (pick-wt=17): 247 [] ord_less(int,plus_plus(int,plus_plus(int,one_one(int),A),A),zero_zero(int))| -ord_less(int,A,zero_zero(int)).
% 8.09/8.11 ** KEPT (pick-wt=15): 248 [] -number_ring(A)| -linordered_idom(A)| -ord_less(A,number_number_of(A,B),zero_zero(A))|ord_less(int,B,pls).
% 8.09/8.11 ** KEPT (pick-wt=15): 249 [] -number_ring(A)| -linordered_idom(A)|ord_less(A,number_number_of(A,B),zero_zero(A))| -ord_less(int,B,pls).
% 8.09/8.11 ** KEPT (pick-wt=15): 250 [] -number_ring(A)| -linordered_idom(A)| -ord_less(A,zero_zero(A),number_number_of(A,B))|ord_less(int,pls,B).
% 8.09/8.11 ** KEPT (pick-wt=15): 251 [] -number_ring(A)| -linordered_idom(A)|ord_less(A,zero_zero(A),number_number_of(A,B))| -ord_less(int,pls,B).
% 8.09/8.11 ** KEPT (pick-wt=14): 252 [] -number_semiring(A)|plus_plus(A,one_one(A),one_one(A))=number_number_of(A,bit0(bit1(pls))).
% 8.09/8.11 ** KEPT (pick-wt=14): 253 [] -number_ring(A)|plus_plus(A,one_one(A),one_one(A))=number_number_of(A,bit0(bit1(pls))).
% 8.09/8.11 ** KEPT (pick-wt=16): 254 [] -number_ring(A)| -linordered_idom(A)| -ord_less(A,number_number_of(A,B),one_one(A))|ord_less(int,B,bit1(pls)).
% 8.09/8.11 ** KEPT (pick-wt=16): 255 [] -number_ring(A)| -linordered_idom(A)|ord_less(A,number_number_of(A,B),one_one(A))| -ord_less(int,B,bit1(pls)).
% 8.09/8.11 ** KEPT (pick-wt=16): 256 [] -number_ring(A)| -linordered_idom(A)| -ord_less(A,one_one(A),number_number_of(A,B))|ord_less(int,bit1(pls),B).
% 8.09/8.11 ** KEPT (pick-wt=16): 257 [] -number_ring(A)| -linordered_idom(A)|ord_less(A,one_one(A),number_number_of(A,B))| -ord_less(int,bit1(pls),B).
% 8.09/8.11 ** KEPT (pick-wt=25): 258 [] -ord_less_e_q(int,zero_zero(int),A)| -ord_less(int,A,number_number_of(int,bit0(bit1(pls))))|ti(int,A)=zero_zero(int)|ti(int,A)=one_one(int).
% 8.09/8.11 ** KEPT (pick-wt=25): 259 [] -ord_less(int,zero_zero(int),A)|ti(int,A)!=plus_plus(int,B,times_times(int,A,C))| -ord_less(int,B,A)|ord_less_e_q(int,one_one(int),C).
% 8.09/8.11 ** KEPT (pick-wt=26): 260 [] -ord_less(int,zero_zero(int),A)|ti(int,A)!=plus_plus(int,B,times_times(int,A,C))| -ord_less_e_q(int,zero_zero(int),B)|ord_less_e_q(int,C,one_one(int)).
% 8.09/8.11 ** KEPT (pick-wt=24): 261 [] -comm_semiring_1(A)|power_power(A,B,times_times(nat,number_number_of(nat,bit0(bit1(pls))),C))=times_times(A,power_power(A,B,C),power_power(A,B,C)).
% 8.09/8.11 ** KEPT (pick-wt=44): 262 [] -ord_less_e_q(int,zero_zero(int),A)| -ord_less(int,A,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))| -zcong(s1,A,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))|ti(int,A)=ti(int,$c2).
% 8.09/8.11 ** KEPT (pick-wt=17): 263 [] -ord_less(nat,zero_zero(nat),power_power(nat,A,B))|B=zero_zero(nat)|ord_less(nat,zero_zero(nat),A).
% 8.09/8.11 ** KEPT (pick-wt=12): 264 [] ord_less(nat,zero_zero(nat),power_power(nat,A,B))|B!=zero_zero(nat).
% 8.09/8.11 ** KEPT (pick-wt=13): 265 [] ord_less(nat,zero_zero(nat),power_power(nat,A,B))| -ord_less(nat,zero_zero(nat),A).
% 8.09/8.11 ** KEPT (pick-wt=13): 266 [] -zprime(A)| -dvd_dvd(int,A,power_power(int,B,C))|dvd_dvd(int,A,B).
% 8.09/8.11 ** KEPT (pick-wt=17): 267 [] -comm_semiring_1(A)|power_power(A,power_power(A,B,C),D)=power_power(A,B,times_times(nat,C,D)).
% 8.09/8.11 ** KEPT (pick-wt=23): 268 [] -zprime(A)|dvd_dvd(int,A,B)| -dvd_dvd(int,power_power(int,A,C),times_times(int,D,B))|dvd_dvd(int,power_power(int,A,C),D).
% 8.09/8.11 ** KEPT (pick-wt=23): 269 [] -zprime(A)|dvd_dvd(int,A,B)| -dvd_dvd(int,power_power(int,A,C),times_times(int,B,D))|dvd_dvd(int,power_power(int,A,C),D).
% 8.09/8.11 ** KEPT (pick-wt=13): 270 [] -ord_less(int,zero_zero(int),A)| -ord_less(int,A,B)| -dvd_dvd(int,B,A).
% 8.09/8.11 ** KEPT (pick-wt=25): 271 [] -ord_less_e_q(int,zero_zero(int),A)| -ord_less_e_q(int,zero_zero(int),B)| -dvd_dvd(int,A,B)| -dvd_dvd(int,B,A)|ti(int,A)=ti(int,B).
% 8.09/8.11 ** KEPT (pick-wt=20): 272 [] -dvd_dvd(int,times_times(int,A,B),times_times(int,A,C))|ti(int,A)=zero_zero(int)|dvd_dvd(int,B,C).
% 8.09/8.11 ** KEPT (pick-wt=14): 273 [] -dvd_dvd(int,A,plus_plus(int,B,times_times(int,A,C)))|dvd_dvd(int,A,B).
% 8.09/8.11 ** KEPT (pick-wt=14): 274 [] dvd_dvd(int,A,plus_plus(int,B,times_times(int,A,C)))| -dvd_dvd(int,A,B).
% 8.09/8.11 ** KEPT (pick-wt=24): 275 [] -dvd_dvd(int,A,B)| -dvd_dvd(int,A,plus_plus(int,C,D))|dvd_dvd(int,A,plus_plus(int,plus_plus(int,C,times_times(int,E,B)),D)).
% 8.09/8.11 ** KEPT (pick-wt=24): 276 [] -dvd_dvd(int,A,B)|dvd_dvd(int,A,plus_plus(int,C,D))| -dvd_dvd(int,A,plus_plus(int,plus_plus(int,C,times_times(int,E,B)),D)).
% 8.09/8.11 ** KEPT (pick-wt=13): 277 [] -dvd_dvd(int,A,B)| -ord_less(int,zero_zero(int),B)|ord_less_e_q(int,A,B).
% 8.09/8.11 ** KEPT (pick-wt=9): 278 [] -twoSqu420862341sum2sq(A)| -twoSqu420862341sum2sq(B)|twoSqu420862341sum2sq(times_times(int,A,B)).
% 8.09/8.11 ** KEPT (pick-wt=16): 279 [] -ord_less_e_q(nat,number_number_of(nat,A),number_number_of(nat,B))|ord_less_e_q(int,A,B)|ord_less_e_q(int,A,pls).
% 8.09/8.11 ** KEPT (pick-wt=12): 280 [] ord_less_e_q(nat,number_number_of(nat,A),number_number_of(nat,B))| -ord_less_e_q(int,A,B).
% 8.09/8.11 ** KEPT (pick-wt=12): 281 [] ord_less_e_q(nat,number_number_of(nat,A),number_number_of(nat,B))| -ord_less_e_q(int,A,pls).
% 8.09/8.11 ** KEPT (pick-wt=23): 282 [] -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)).
% 8.09/8.11 ** KEPT (pick-wt=23): 283 [] -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)).
% 8.09/8.11 ** KEPT (pick-wt=23): 284 [] -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))).
% 8.09/8.11 ** KEPT (pick-wt=17): 285 [] -comm_semiring_1(A)|times_times(A,times_times(A,B,C),D)=times_times(A,times_times(A,B,D),C).
% 8.09/8.11 ** KEPT (pick-wt=17): 286 [] -comm_semiring_1(A)|times_times(A,times_times(A,B,C),D)=times_times(A,B,times_times(A,C,D)).
% 8.09/8.11 Following clause subsumed by 286 during input processing: 0 [flip.2] -comm_semiring_1(A)|times_times(A,times_times(A,B,C),D)=times_times(A,B,times_times(A,C,D)).
% 8.09/8.11 ** KEPT (pick-wt=17): 287 [] -comm_semiring_1(A)|times_times(A,B,times_times(A,C,D))=times_times(A,C,times_times(A,B,D)).
% 8.09/8.11 ** KEPT (pick-wt=11): 288 [] -comm_semiring_1(A)|times_times(A,B,C)=times_times(A,C,B).
% 8.09/8.11 ** KEPT (pick-wt=11): 289 [] -comm_semiring_1(A)|plus_plus(A,B,C)=plus_plus(A,C,B).
% 8.09/8.11 ** KEPT (pick-wt=17): 290 [] -comm_semiring_1(A)|plus_plus(A,B,plus_plus(A,C,D))=plus_plus(A,C,plus_plus(A,B,D)).
% 8.09/8.11 ** KEPT (pick-wt=17): 292 [copy,291,flip.2] -comm_semiring_1(A)|plus_plus(A,plus_plus(A,B,C),D)=plus_plus(A,B,plus_plus(A,C,D)).
% 8.09/8.11 Following clause subsumed by 292 during input processing: 0 [] -comm_semiring_1(A)|plus_plus(A,plus_plus(A,B,C),D)=plus_plus(A,B,plus_plus(A,C,D)).
% 8.09/8.11 ** KEPT (pick-wt=17): 293 [] -comm_semiring_1(A)|plus_plus(A,plus_plus(A,B,C),D)=plus_plus(A,plus_plus(A,B,D),C).
% 8.09/8.11 ** KEPT (pick-wt=23): 294 [] -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)).
% 8.09/8.11 ** KEPT (pick-wt=11): 295 [] -comm_semiring_1(A)|power_power(A,B,one_one(nat))=ti(A,B).
% 8.09/8.11 Following clause subsumed by 263 during input processing: 0 [] -ord_less(nat,zero_zero(nat),power_power(nat,A,number_number_of(nat,B)))|number_number_of(nat,B)=zero_zero(nat)|ord_less(nat,zero_zero(nat),A).
% 8.09/8.11 Following clause subsumed by 264 during input processing: 0 [] ord_less(nat,zero_zero(nat),power_power(nat,A,number_number_of(nat,B)))|number_number_of(nat,B)!=zero_zero(nat).
% 8.09/8.11 Following clause subsumed by 265 during input processing: 0 [] ord_less(nat,zero_zero(nat),power_power(nat,A,number_number_of(nat,B)))| -ord_less(nat,zero_zero(nat),A).
% 8.09/8.11 ** KEPT (pick-wt=15): 296 [] -ord_less(int,A,pls)|times_times(nat,number_number_of(nat,A),number_number_of(nat,B))=zero_zero(nat).
% 8.09/8.11 ** KEPT (pick-wt=18): 297 [] -ord_less(int,A,pls)|times_times(nat,number_number_of(nat,A),times_times(nat,number_number_of(nat,B),C))=zero_zero(nat).
% 8.09/8.11 ** KEPT (pick-wt=25): 298 [] -monoid_mult(A)|power_power(A,B,times_times(nat,number_number_of(nat,bit0(bit1(pls))),C))=power_power(A,power_power(A,B,C),number_number_of(nat,bit0(bit1(pls)))).
% 8.09/8.11 ** KEPT (pick-wt=23): 299 [] -linordered_idom(A)| -ord_less_e_q(A,power_power(A,B,times_times(nat,number_number_of(nat,bit0(bit1(pls))),C)),zero_zero(A))|ti(A,B)=zero_zero(A).
% 8.09/8.11 ** KEPT (pick-wt=10): 300 [] -comm_semiring_1(A)|times_times(A,zero_zero(A),B)=zero_zero(A).
% 8.09/8.11 ** KEPT (pick-wt=10): 301 [] -comm_semiring_1(A)|times_times(A,B,zero_zero(A))=zero_zero(A).
% 8.09/8.11 ** KEPT (pick-wt=11): 302 [] -comm_semiring_1(A)|plus_plus(A,zero_zero(A),B)=ti(A,B).
% 8.09/8.11 ** KEPT (pick-wt=11): 303 [] -comm_semiring_1(A)|plus_plus(A,B,zero_zero(A))=ti(A,B).
% 8.09/8.11 ** KEPT (pick-wt=16): 304 [] -semiri456707255roduct(A)|ti(A,B)!=plus_plus(A,B,C)|ti(A,C)=zero_zero(A).
% 8.09/8.11 ** KEPT (pick-wt=16): 305 [] -semiri456707255roduct(A)|ti(A,B)=plus_plus(A,B,C)|ti(A,C)!=zero_zero(A).
% 8.09/8.11 ** KEPT (pick-wt=20): 306 [] -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)).
% 8.09/8.11 ** KEPT (pick-wt=37): 307 [] -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)).
% 8.09/8.11 ** KEPT (pick-wt=30): 308 [] -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)).
% 8.09/8.11 ** KEPT (pick-wt=30): 309 [] -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)).
% 8.09/8.11 ** KEPT (pick-wt=20): 310 [] -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)).
% 8.09/8.11 Following clause subsumed by 310 during input processing: 0 [flip.2] -comm_semiring_1(A)|times_times(A,plus_plus(A,B,D),C)=plus_plus(A,times_times(A,B,C),times_times(A,D,C)).
% 8.09/8.11 Following clause subsumed by 307 during input processing: 0 [] -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).
% 8.09/8.11 Following clause subsumed by 308 during input processing: 0 [] -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).
% 8.09/8.11 Following clause subsumed by 309 during input processing: 0 [] -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).
% 8.09/8.11 ** KEPT (pick-wt=11): 311 [] -comm_semiring_1(A)|times_times(A,one_one(A),B)=ti(A,B).
% 8.09/8.11 ** KEPT (pick-wt=11): 312 [] -comm_semiring_1(A)|times_times(A,B,one_one(A))=ti(A,B).
% 8.09/8.11 ** KEPT (pick-wt=20): 314 [copy,313,flip.2] -comm_semiring_1(A)|times_times(A,power_power(A,B,C),power_power(A,D,C))=power_power(A,times_times(A,B,D),C).
% 8.09/8.11 ** KEPT (pick-wt=20): 315 [] -comm_semiring_1(A)|times_times(A,power_power(A,B,C),power_power(A,B,D))=power_power(A,B,plus_plus(nat,C,D)).
% 8.09/8.11 ** KEPT (pick-wt=10): 316 [] -comm_semiring_1(A)|power_power(A,B,zero_zero(nat))=one_one(A).
% 8.09/8.11 ** KEPT (pick-wt=17): 317 [] -linordered_idom(A)|ord_less_e_q(A,zero_zero(A),power_power(A,B,times_times(nat,number_number_of(nat,bit0(bit1(pls))),C))).
% 8.09/8.11 ** KEPT (pick-wt=37): 318 [] -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)).
% 8.09/8.11 ** KEPT (pick-wt=16): 320 [copy,319,flip.2] -comm_semiring_1(A)|times_times(A,plus_plus(A,one_one(A),one_one(A)),B)=plus_plus(A,B,B).
% 8.09/8.11 ** KEPT (pick-wt=18): 322 [copy,321,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)).
% 8.09/8.11 ** KEPT (pick-wt=18): 324 [copy,323,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).
% 8.09/8.11 ** KEPT (pick-wt=23): 325 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|power_power(A,B,number_number_of(nat,C))!=zero_zero(A)|ti(A,B)=zero_zero(A).
% 8.09/8.11 ** KEPT (pick-wt=23): 326 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|power_power(A,B,number_number_of(nat,C))!=zero_zero(A)|number_number_of(nat,C)!=zero_zero(nat).
% 8.09/8.11 ** KEPT (pick-wt=29): 327 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(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).
% 8.09/8.11 ** KEPT (pick-wt=18): 328 [] -ord_less(int,zero_zero(int),A)| -ord_less(int,zero_zero(int),times_times(int,A,B))|ord_less(int,zero_zero(int),B).
% 8.09/8.11 ** KEPT (pick-wt=18): 329 [] -ord_less_e_q(int,zero_zero(int),A)| -ord_less_e_q(int,zero_zero(int),B)|ord_less_e_q(int,zero_zero(int),times_times(int,A,B)).
% 8.09/8.11 ** KEPT (pick-wt=18): 330 [] -ord_less_e_q(int,zero_zero(int),A)| -ord_less_e_q(int,zero_zero(int),B)|ord_less_e_q(int,zero_zero(int),plus_plus(int,A,B)).
% 8.09/8.11 ** KEPT (pick-wt=13): 331 [] -ord_less_e_q(int,zero_zero(int),A)|ord_less_e_q(int,zero_zero(int),power_power(int,A,B)).
% 8.09/8.11 ** KEPT (pick-wt=20): 332 [] -power(A)| -semiring_0(A)|number_number_of(nat,B)!=zero_zero(nat)|power_power(A,zero_zero(A),number_number_of(nat,B))=one_one(A).
% 8.09/8.11 ** KEPT (pick-wt=20): 333 [] -power(A)| -semiring_0(A)|number_number_of(nat,B)=zero_zero(nat)|power_power(A,zero_zero(A),number_number_of(nat,B))=zero_zero(A).
% 8.09/8.11 ** KEPT (pick-wt=25): 334 [] -ord_less_e_q(int,zero_zero(int),plus_plus(int,times_times(int,A,B),C))| -ord_less(int,C,A)| -ord_less(int,zero_zero(int),A)|ord_less_e_q(int,zero_zero(int),B).
% 8.09/8.11 ** KEPT (pick-wt=26): 335 [] -ord_less(int,plus_plus(int,times_times(int,A,B),C),zero_zero(int))| -ord_less_e_q(int,zero_zero(int),C)| -ord_less(int,zero_zero(int),A)|ord_less_e_q(int,B,zero_zero(int)).
% 8.09/8.11 ** KEPT (pick-wt=33): 336 [] -ord_less_e_q(int,plus_plus(int,times_times(int,A,B),C),plus_plus(int,times_times(int,A,D),E))| -ord_less_e_q(int,zero_zero(int),C)| -ord_less(int,C,A)| -ord_less(int,E,A)|ord_less_e_q(int,B,D).
% 8.09/8.11 ** KEPT (pick-wt=48): 337 [] plus_plus(int,times_times(int,A,B),C)!=plus_plus(int,times_times(int,D,E),F)| -ord_less_e_q(int,zero_zero(int),plus_plus(int,times_times(int,D,E),F))| -ord_less(int,F,D)| -ord_less_e_q(int,zero_zero(int),C)| -ord_less(int,zero_zero(int),D)| -ord_less_e_q(int,D,A)|ord_less_e_q(int,B,E).
% 8.09/8.11 ** KEPT (pick-wt=33): 338 [] -ord_less_e_q(int,plus_plus(int,times_times(int,A,B),C),plus_plus(int,times_times(int,A,D),E))| -ord_less_e_q(int,E,zero_zero(int))| -ord_less(int,A,E)| -ord_less(int,A,C)|ord_less_e_q(int,D,B).
% 8.09/8.11 ** KEPT (pick-wt=48): 339 [] plus_plus(int,times_times(int,A,B),C)!=plus_plus(int,times_times(int,D,E),F)| -ord_less(int,plus_plus(int,times_times(int,D,E),F),zero_zero(int))| -ord_less(int,C,A)| -ord_less_e_q(int,zero_zero(int),F)| -ord_less(int,zero_zero(int),D)| -ord_less_e_q(int,D,A)|ord_less_e_q(int,E,B).
% 8.09/8.11 ** KEPT (pick-wt=15): 340 [] -comm_semiring_1(A)|times_times(A,B,B)=power_power(A,B,number_number_of(nat,bit0(bit1(pls)))).
% 8.09/8.11 ** KEPT (pick-wt=20): 341 [] zcong(A,zero_zero(int),B)| -zcong(power_power(int,C,number_number_of(nat,bit0(bit1(pls)))),A,B)| -dvd_dvd(int,B,C).
% 8.09/8.11 ** KEPT (pick-wt=7): 342 [] -zprime(A)|ord_less(int,one_one(int),A).
% 8.09/8.11 ** KEPT (pick-wt=24): 343 [] -zprime(A)| -ord_less_e_q(int,zero_zero(int),B)| -dvd_dvd(int,B,A)|ti(int,B)=one_one(int)|ti(int,B)=ti(int,A).
% 8.09/8.11 ** KEPT (pick-wt=13): 344 [] zprime(A)| -ord_less(int,one_one(int),A)|ord_less_e_q(int,zero_zero(int),$f1(A)).
% 8.09/8.11 ** KEPT (pick-wt=12): 345 [] zprime(A)| -ord_less(int,one_one(int),A)|dvd_dvd(int,$f1(A),A).
% 8.09/8.11 ** KEPT (pick-wt=14): 346 [] zprime(A)| -ord_less(int,one_one(int),A)|ti(int,$f1(A))!=one_one(int).
% 8.09/8.11 ** KEPT (pick-wt=15): 347 [] zprime(A)| -ord_less(int,one_one(int),A)|ti(int,$f1(A))!=ti(int,A).
% 8.09/8.11 ** KEPT (pick-wt=29): 348 [] -zprime(A)|ti(int,A)=number_number_of(int,bit0(bit1(pls)))|ti(int,A)=number_number_of(int,bit1(bit1(pls)))|ord_less_e_q(int,number_number_of(int,bit1(bit0(bit1(pls)))),A).
% 8.09/8.11 ** KEPT (pick-wt=9): 350 [copy,349,flip.1,flip.2] bit1(A)!=min|ti(int,A)=min.
% 8.09/8.11 ** KEPT (pick-wt=9): 352 [copy,351,flip.1,flip.2] bit1(A)=min|ti(int,A)!=min.
% 8.09/8.11 Following clause subsumed by 350 during input processing: 0 [] bit1(A)!=min|ti(int,A)=min.
% 8.09/8.11 Following clause subsumed by 352 during input processing: 0 [] bit1(A)=min|ti(int,A)!=min.
% 8.09/8.11 ** KEPT (pick-wt=3): 354 [copy,353,flip.1] pls!=min.
% 8.09/8.11 Following clause subsumed by 354 during input processing: 0 [] pls!=min.
% 8.09/8.11 ** KEPT (pick-wt=4): 356 [copy,355,flip.1] bit0(A)!=min.
% 8.09/8.11 Following clause subsumed by 356 during input processing: 0 [] bit0(A)!=min.
% 8.09/8.11 ** KEPT (pick-wt=4): 357 [] -ord_less(int,min,min).
% 8.09/8.11 ** KEPT (pick-wt=9): 358 [] -ord_less(int,bit1(A),min)|ord_less(int,A,min).
% 8.09/8.11 ** KEPT (pick-wt=9): 359 [] ord_less(int,bit1(A),min)| -ord_less(int,A,min).
% 8.09/8.11 ** KEPT (pick-wt=9): 360 [] -ord_less(int,min,bit1(A))|ord_less(int,min,A).
% 8.09/8.11 ** KEPT (pick-wt=9): 361 [] ord_less(int,min,bit1(A))| -ord_less(int,min,A).
% 8.09/8.11 ** KEPT (pick-wt=4): 362 [] -ord_less(int,pls,min).
% 8.09/8.11 ** KEPT (pick-wt=9): 363 [] -ord_less(int,min,bit0(A))|ord_less(int,min,A).
% 8.09/8.11 ** KEPT (pick-wt=9): 364 [] ord_less(int,min,bit0(A))| -ord_less(int,min,A).
% 8.09/8.11 ** KEPT (pick-wt=9): 365 [] -ord_less_e_q(int,min,bit1(A))|ord_less_e_q(int,min,A).
% 8.09/8.11 ** KEPT (pick-wt=9): 366 [] ord_less_e_q(int,min,bit1(A))| -ord_less_e_q(int,min,A).
% 8.09/8.11 ** KEPT (pick-wt=9): 367 [] -ord_less_e_q(int,bit1(A),min)|ord_less_e_q(int,A,min).
% 8.09/8.11 ** KEPT (pick-wt=9): 368 [] ord_less_e_q(int,bit1(A),min)| -ord_less_e_q(int,A,min).
% 8.09/8.11 ** KEPT (pick-wt=4): 369 [] -ord_less_e_q(int,pls,min).
% 8.09/8.11 ** KEPT (pick-wt=9): 370 [] -ord_less_e_q(int,bit0(A),min)|ord_less_e_q(int,A,min).
% 8.09/8.11 ** KEPT (pick-wt=9): 371 [] ord_less_e_q(int,bit0(A),min)| -ord_less_e_q(int,A,min).
% 8.09/8.11 ** KEPT (pick-wt=7): 372 [] number_number_of(int,pls)!=number_number_of(int,min).
% 8.09/8.11 ** KEPT (pick-wt=9): 373 [] -ord_less(int,bit0(A),min)|ord_less_e_q(int,A,min).
% 8.09/8.11 ** KEPT (pick-wt=9): 374 [] ord_less(int,bit0(A),min)| -ord_less_e_q(int,A,min).
% 8.09/8.11 ** KEPT (pick-wt=9): 375 [] -ord_less_e_q(int,min,bit0(A))|ord_less(int,min,A).
% 8.09/8.11 ** KEPT (pick-wt=9): 376 [] ord_less_e_q(int,min,bit0(A))| -ord_less(int,min,A).
% 8.09/8.11 ** KEPT (pick-wt=20): 377 [] times_times(int,A,B)!=one_one(int)|ti(int,A)=one_one(int)|ti(int,A)=number_number_of(int,min).
% 8.09/8.11 ** KEPT (pick-wt=20): 378 [] times_times(int,A,B)!=one_one(int)|ti(int,A)=one_one(int)|ti(int,B)=number_number_of(int,min).
% 8.09/8.12 ** KEPT (pick-wt=20): 379 [] times_times(int,A,B)!=one_one(int)|ti(int,B)=one_one(int)|ti(int,A)=number_number_of(int,min).
% 8.09/8.12 ** KEPT (pick-wt=20): 380 [] times_times(int,A,B)!=one_one(int)|ti(int,B)=one_one(int)|ti(int,B)=number_number_of(int,min).
% 8.09/8.12 ** KEPT (pick-wt=19): 381 [] times_times(int,A,B)=one_one(int)|ti(int,A)!=one_one(int)|ti(int,B)!=one_one(int).
% 8.09/8.12 ** KEPT (pick-wt=21): 382 [] times_times(int,A,B)=one_one(int)|ti(int,A)!=number_number_of(int,min)|ti(int,B)!=number_number_of(int,min).
% 8.09/8.12 Following clause subsumed by 377 during input processing: 0 [] times_times(int,A,B)!=one_one(int)|ti(int,A)=one_one(int)|ti(int,A)=number_number_of(int,min).
% 8.09/8.12 ** KEPT (pick-wt=8): 383 [] -zcong(A,B,C)|zcong(B,A,C).
% 8.09/8.12 Following clause subsumed by 383 during input processing: 0 [] zcong(A,B,C)| -zcong(B,A,C).
% 8.09/8.12 ** KEPT (pick-wt=12): 384 [] -zcong(A,B,C)| -zcong(B,D,C)|zcong(A,D,C).
% 8.09/8.12 ** KEPT (pick-wt=17): 385 [] -order(A)| -ord_less_e_q(A,B,C)|ti(A,B)=ti(A,C)|ord_less(A,B,C).
% 8.09/8.12 ** KEPT (pick-wt=16): 386 [] -ord_less(int,A,B)| -ord_less(int,C,B)|ord_less_e_q(int,A,C)|ord_less_e_q(int,C,A).
% 8.09/8.12 ** KEPT (pick-wt=12): 387 [] -zcong(A,B,zero_zero(int))|ti(int,A)=ti(int,B).
% 8.09/8.12 ** KEPT (pick-wt=12): 388 [] zcong(A,B,zero_zero(int))|ti(int,A)!=ti(int,B).
% 8.09/8.12 ** KEPT (pick-wt=14): 389 [] -zcong(A,B,C)|zcong(times_times(int,A,D),times_times(int,B,D),C).
% 8.09/8.12 ** KEPT (pick-wt=14): 390 [] -zcong(A,B,C)|zcong(times_times(int,D,A),times_times(int,D,B),C).
% 8.09/8.12 ** KEPT (pick-wt=18): 391 [] -zcong(A,B,C)| -zcong(D,E,C)|zcong(times_times(int,A,D),times_times(int,B,E),C).
% 8.09/8.12 ** KEPT (pick-wt=18): 392 [] -zcong(A,B,C)| -zcong(D,E,C)|zcong(plus_plus(int,A,D),plus_plus(int,B,E),C).
% 8.09/8.12 ** KEPT (pick-wt=18): 393 [] -number_ring(A)|power_power(A,number_number_of(A,min),times_times(nat,number_number_of(nat,bit0(bit1(pls))),B))=one_one(A).
% 8.09/8.12 ** KEPT (pick-wt=22): 394 [] -ord_less(int,zero_zero(int),A)| -ord_less(int,A,B)| -ord_less(int,zero_zero(int),C)| -ord_less(int,C,A)| -zcong(A,C,B).
% 8.09/8.12 ** KEPT (pick-wt=18): 395 [] -zcong(A,B,C)|ti(int,B)=plus_plus(int,A,times_times(int,C,$f2(A,B,C))).
% 8.09/8.12 ** KEPT (pick-wt=15): 396 [] zcong(A,B,C)|ti(int,B)!=plus_plus(int,A,times_times(int,C,D)).
% 8.09/8.12 ** KEPT (pick-wt=20): 397 [] -ord_less_e_q(int,zero_zero(int),A)| -ord_less(int,A,B)| -zcong(A,zero_zero(int),B)|ti(int,A)=zero_zero(int).
% 8.09/8.12 ** KEPT (pick-wt=29): 398 [] -ord_less_e_q(int,zero_zero(int),A)| -ord_less(int,A,B)| -ord_less_e_q(int,zero_zero(int),C)| -ord_less(int,C,B)| -zcong(A,C,B)|ti(int,A)=ti(int,C).
% 8.09/8.12 ** KEPT (pick-wt=19): 399 [] -zcong(power_power(int,A,B),one_one(int),C)|zcong(power_power(int,A,times_times(nat,B,D)),one_one(int),C).
% 8.09/8.12 ** KEPT (pick-wt=22): 400 [] -ord_less_e_q(int,zero_zero(int),A)| -zprime(B)| -dvd_dvd(int,B,times_times(int,A,C))|dvd_dvd(int,B,A)|dvd_dvd(int,B,C).
% 8.09/8.12 ** KEPT (pick-wt=35): 401 [] -ord_less(int,number_number_of(int,bit0(bit1(pls))),A)| -zcong(power_power(int,number_number_of(int,min),B),power_power(int,number_number_of(int,min),C),A)|power_power(int,number_number_of(int,min),B)=power_power(int,number_number_of(int,min),C).
% 8.09/8.12 ** KEPT (pick-wt=19): 402 [] -ord_less(int,number_number_of(int,bit0(bit1(pls))),A)| -zcong(B,number_number_of(int,min),A)| -zcong(B,one_one(int),A).
% 8.09/8.12 ** KEPT (pick-wt=37): 403 [] 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).
% 8.09/8.12 ** KEPT (pick-wt=12): 404 [] -ord_less(real,zero_zero(real),times_times(real,A,A))|A!=zero_zero(real).
% 8.09/8.12 ** KEPT (pick-wt=18): 405 [] -zcong(A,B,C)| -zcong(D,E,C)|zcong(minus_minus(int,A,D),minus_minus(int,B,E),C).
% 8.09/8.12 ** KEPT (pick-wt=15): 406 [] -dvd_dvd(int,A,minus_minus(int,B,C))| -dvd_dvd(int,A,C)|dvd_dvd(int,A,B).
% 8.09/8.12 ** KEPT (pick-wt=16): 407 [] minus_minus(int,A,B)!=ti(int,C)|ti(int,A)=plus_plus(int,C,B).
% 8.09/8.12 ** KEPT (pick-wt=17): 408 [] -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)).
% 8.09/8.12 ** KEPT (pick-wt=28): 409 [] -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)).
% 8.09/8.12 ** KEPT (pick-wt=28): 410 [] -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))).
% 8.09/8.12 ** KEPT (pick-wt=12): 411 [] -ord_less(int,A,B)|ord_less(int,minus_minus(int,A,B),zero_zero(int)).
% 8.09/8.12 ** KEPT (pick-wt=12): 412 [] ord_less(int,A,B)| -ord_less(int,minus_minus(int,A,B),zero_zero(int)).
% 8.09/8.12 ** KEPT (pick-wt=11): 413 [] -zcong(A,B,C)|dvd_dvd(int,C,minus_minus(int,A,B)).
% 8.09/8.12 ** KEPT (pick-wt=11): 414 [] zcong(A,B,C)| -dvd_dvd(int,C,minus_minus(int,A,B)).
% 8.09/8.12 ** KEPT (pick-wt=23): 415 [] -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).
% 8.09/8.12 ** KEPT (pick-wt=26): 416 [] -ord_less(int,zero_zero(int),A)| -ord_less(int,A,B)|ti(int,A)=minus_minus(int,B,one_one(int))|ord_less(int,A,minus_minus(int,B,one_one(int))).
% 8.09/8.12 ** KEPT (pick-wt=12): 417 [] -ord_less_e_q(int,A,minus_minus(int,B,one_one(int)))|ord_less(int,A,B).
% 8.09/8.12 ** KEPT (pick-wt=12): 418 [] ord_less_e_q(int,A,minus_minus(int,B,one_one(int)))| -ord_less(int,A,B).
% 8.09/8.12 ** KEPT (pick-wt=20): 419 [] -zcong(times_times(int,A,minus_minus(int,B,one_one(int))),one_one(int),B)|zcong(A,minus_minus(int,B,one_one(int)),B).
% 8.09/8.12 ** KEPT (pick-wt=20): 420 [] zcong(times_times(int,A,minus_minus(int,B,one_one(int))),one_one(int),B)| -zcong(A,minus_minus(int,B,one_one(int)),B).
% 8.09/8.12 ** KEPT (pick-wt=19): 421 [] -zcong(A,B,C)|ti(int,B)!=ti(int,D)| -zcong(D,E,C)|zcong(A,E,C).
% 8.09/8.12 ** KEPT (pick-wt=34): 422 [] -zprime(A)| -ord_less(int,zero_zero(int),B)| -ord_less(int,B,A)| -zcong(times_times(int,B,B),one_one(int),A)|ti(int,B)=one_one(int)|ti(int,B)=minus_minus(int,A,one_one(int)).
% 8.09/8.12 ** KEPT (pick-wt=28): 423 [] -zprime(A)| -ord_less(int,zero_zero(int),B)| -zcong(times_times(int,B,B),one_one(int),A)|zcong(B,one_one(int),A)|zcong(B,minus_minus(int,A,one_one(int)),A).
% 8.09/8.12 ** KEPT (pick-wt=18): 424 [] -zcong(A,B,C)| -zcong(D,times_times(int,E,A),C)|zcong(D,times_times(int,E,B),C).
% 8.09/8.12 ** KEPT (pick-wt=18): 425 [] -zcong(A,B,C)|zcong(D,times_times(int,E,A),C)| -zcong(D,times_times(int,E,B),C).
% 8.09/8.12 ** KEPT (pick-wt=18): 426 [] -zcong(A,B,C)| -zcong(D,times_times(int,A,E),C)|zcong(D,times_times(int,B,E),C).
% 8.09/8.12 ** KEPT (pick-wt=18): 427 [] -zcong(A,B,C)|zcong(D,times_times(int,A,E),C)| -zcong(D,times_times(int,B,E),C).
% 8.09/8.12 ** KEPT (pick-wt=14): 428 [] -zcong(A,B,C)|zcong(plus_plus(int,A,D),plus_plus(int,B,D),C).
% 8.09/8.12 ** KEPT (pick-wt=14): 429 [] -zcong(A,B,C)|zcong(power_power(int,A,D),power_power(int,B,D),C).
% 8.09/8.12 ** KEPT (pick-wt=45): 430 [] -number_ring(A)|power_power(A,minus_minus(A,B,C),number_number_of(nat,bit0(bit1(pls))))=minus_minus(A,plus_plus(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),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)).
% 8.09/8.12 ** KEPT (pick-wt=34): 431 [] -ord_less(int,zero_zero(int),A)| -ord_less(int,zero_zero(int),B)| -ord_less(int,zero_zero(int),C)| -zcong(A,B,C)| -ord_less(int,A,C)| -ord_less(int,B,C)|ti(int,A)=ti(int,B).
% 8.09/8.12 ** KEPT (pick-wt=14): 432 [] -ord_less(int,zero_zero(int),A)| -ord_less(int,A,B)| -zcong(A,zero_zero(int),B).
% 8.09/8.12 ** KEPT (pick-wt=13): 433 [] -dvd_dvd(int,A,B)|ord_less_e_q(int,B,zero_zero(int))|ord_less_e_q(int,A,B).
% 8.09/8.12 ** KEPT (pick-wt=9): 434 [] -zcong(A,zero_zero(int),B)|dvd_dvd(int,B,A).
% 8.09/8.12 ** KEPT (pick-wt=9): 435 [] zcong(A,zero_zero(int),B)| -dvd_dvd(int,B,A).
% 8.09/8.12 Following clause subsumed by 434 during input processing: 0 [] -zcong(A,zero_zero(int),B)|dvd_dvd(int,B,A).
% 8.09/8.12 Following clause subsumed by 435 during input processing: 0 [] zcong(A,zero_zero(int),B)| -dvd_dvd(int,B,A).
% 8.09/8.12 ** KEPT (pick-wt=17): 436 [] -zprime(A)| -dvd_dvd(int,A,times_times(int,B,C))|dvd_dvd(int,A,B)|dvd_dvd(int,A,C).
% 8.09/8.12 Following clause subsumed by 397 during input processing: 0 [] -ord_less_e_q(int,zero_zero(int),A)| -ord_less(int,A,B)| -zcong(A,zero_zero(int),B)|ti(int,A)=zero_zero(int).
% 8.09/8.12 ** KEPT (pick-wt=16): 437 [] -ord_less(nat,zero_zero(nat),A)| -dvd_dvd(int,B,C)|dvd_dvd(int,B,power_power(int,C,A)).
% 8.09/8.12 ** KEPT (pick-wt=20): 438 [] -zprime(A)|zcong(B,zero_zero(int),A)|zcong(C,zero_zero(int),A)| -zcong(times_times(int,B,C),zero_zero(int),A).
% 8.09/8.12 Following clause subsumed by 438 during input processing: 0 [] -zprime(A)| -ord_less(int,zero_zero(int),B)|zcong(B,zero_zero(int),A)|zcong(C,zero_zero(int),A)| -zcong(times_times(int,B,C),zero_zero(int),A).
% 8.09/8.12 Following clause subsumed by 438 during input processing: 0 [] -zprime(A)| -ord_less(int,zero_zero(int),B)| -zcong(times_times(int,B,C),zero_zero(int),A)|zcong(B,zero_zero(int),A)|zcong(C,zero_zero(int),A).
% 8.09/8.12 Following clause subsumed by 266 during input processing: 0 [] -zprime(A)| -dvd_dvd(int,A,power_power(int,B,C))| -ord_less(nat,zero_zero(nat),C)|dvd_dvd(int,A,B).
% 8.09/8.12 ** KEPT (pick-wt=34): 439 [] -zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),A),one_one(int)))|legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),A),one_one(int)))=one_one(int).
% 8.09/8.12 ** KEPT (pick-wt=15): 440 [] -ord_less(int,number_number_of(int,bit0(bit1(pls))),A)| -zcong(one_one(int),number_number_of(int,min),A).
% 8.09/8.12 ** KEPT (pick-wt=11): 441 [] -zcong(A,zero_zero(int),B)|legendre(A,B)=zero_zero(int).
% 8.09/8.12 ** KEPT (pick-wt=14): 442 [] zcong(A,zero_zero(int),B)| -quadRes(B,A)|legendre(A,B)=one_one(int).
% 8.09/8.12 ** KEPT (pick-wt=16): 443 [] -quadRes(A,B)|zcong(power_power(int,$f3(A,B),number_number_of(nat,bit0(bit1(pls)))),B,A).
% 8.09/8.12 ** KEPT (pick-wt=14): 444 [] quadRes(A,B)| -zcong(power_power(int,C,number_number_of(nat,bit0(bit1(pls)))),B,A).
% 8.09/8.12 ** KEPT (pick-wt=11): 445 [] A!=zero_zero(nat)|times_times(nat,A,B)=zero_zero(nat).
% 8.09/8.12 ** KEPT (pick-wt=11): 446 [] A!=zero_zero(nat)|power_power(nat,B,A)=one_one(nat).
% 8.09/8.12 ** KEPT (pick-wt=25): 447 [] plus_plus(real,power_power(real,A,number_number_of(nat,bit0(bit1(pls)))),power_power(real,B,number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(real)|A=zero_zero(real).
% 8.09/8.12 ** KEPT (pick-wt=25): 448 [] plus_plus(real,power_power(real,A,number_number_of(nat,bit0(bit1(pls)))),power_power(real,B,number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(real)|B=zero_zero(real).
% 8.09/8.12 ** KEPT (pick-wt=29): 449 [] plus_plus(real,power_power(real,A,number_number_of(nat,bit0(bit1(pls)))),power_power(real,B,number_number_of(nat,bit0(bit1(pls)))))=zero_zero(real)|A!=zero_zero(real)|B!=zero_zero(real).
% 8.09/8.12 ** KEPT (pick-wt=5): 450 [] zero_zero(real)!=one_one(real).
% 8.09/8.12 ** KEPT (pick-wt=12): 451 [] -ord_less_e_q(real,A,B)|ord_less_e_q(real,minus_minus(real,A,B),zero_zero(real)).
% 8.09/8.12 ** KEPT (pick-wt=12): 452 [] ord_less_e_q(real,A,B)| -ord_less_e_q(real,minus_minus(real,A,B),zero_zero(real)).
% 8.09/8.12 ** KEPT (pick-wt=8): 453 [] -ord_less(real,A,B)|ord_less_e_q(real,A,B).
% 8.09/8.12 ** KEPT (pick-wt=7): 454 [] -ord_less(real,A,B)|A!=B.
% 8.09/8.12 ** KEPT (pick-wt=11): 455 [] ord_less(real,A,B)| -ord_less_e_q(real,A,B)|A=B.
% 8.09/8.12 Following clause subsumed by 455 during input processing: 0 [] -ord_less_e_q(real,A,B)|ord_less(real,A,B)|A=B.
% 8.09/8.12 Following clause subsumed by 453 during input processing: 0 [] ord_less_e_q(real,A,B)| -ord_less(real,A,B).
% 8.09/8.12 ** KEPT (pick-wt=7): 456 [] ord_less_e_q(real,A,B)|A!=B.
% 8.09/8.12 ** KEPT (pick-wt=14): 457 [] -ord_less_e_q(real,A,B)|ord_less_e_q(real,plus_plus(real,C,A),plus_plus(real,C,B)).
% 8.09/8.12 ** KEPT (pick-wt=23): 459 [copy,458,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)).
% 8.09/8.12 ** KEPT (pick-wt=16): 460 [] A=zero_zero(real)|times_times(real,A,B)!=times_times(real,A,C)|B=C.
% 8.09/8.12 ** KEPT (pick-wt=16): 461 [] A=zero_zero(real)|times_times(real,A,B)=times_times(real,A,C)|B!=C.
% 8.09/8.12 ** KEPT (pick-wt=16): 462 [] A=zero_zero(real)|times_times(real,B,A)!=times_times(real,C,A)|B=C.
% 8.09/8.12 ** KEPT (pick-wt=16): 463 [] A=zero_zero(real)|times_times(real,B,A)=times_times(real,C,A)|B!=C.
% 8.09/8.12 ** KEPT (pick-wt=11): 464 [] times_times(nat,A,B)!=one_one(nat)|A=one_one(nat).
% 8.09/8.12 ** KEPT (pick-wt=11): 465 [] times_times(nat,A,B)!=one_one(nat)|B=one_one(nat).
% 8.09/8.12 ** KEPT (pick-wt=15): 466 [] times_times(nat,A,B)=one_one(nat)|A!=one_one(nat)|B!=one_one(nat).
% 8.09/8.12 ** KEPT (pick-wt=11): 467 [] power_power(nat,A,B)!=zero_zero(nat)|B!=zero_zero(nat).
% 8.09/8.12 ** KEPT (pick-wt=11): 468 [] power_power(nat,A,B)!=zero_zero(nat)|A=zero_zero(nat).
% 8.09/8.12 ** KEPT (pick-wt=15): 469 [] power_power(nat,A,B)=zero_zero(nat)|B=zero_zero(nat)|A!=zero_zero(nat).
% 8.09/8.12 ** KEPT (pick-wt=29): 471 [copy,470,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)).
% 8.09/8.12 ** KEPT (pick-wt=19): 472 [] -ord_less(real,zero_zero(real),A)| -ord_less_e_q(real,times_times(real,B,A),times_times(real,C,A))|ord_less_e_q(real,B,C).
% 8.09/8.12 ** KEPT (pick-wt=19): 473 [] -ord_less(real,zero_zero(real),A)|ord_less_e_q(real,times_times(real,B,A),times_times(real,C,A))| -ord_less_e_q(real,B,C).
% 8.09/8.12 ** KEPT (pick-wt=19): 474 [] -ord_less(real,zero_zero(real),A)| -ord_less_e_q(real,times_times(real,A,B),times_times(real,A,C))|ord_less_e_q(real,B,C).
% 8.09/8.12 ** KEPT (pick-wt=19): 475 [] -ord_less(real,zero_zero(real),A)|ord_less_e_q(real,times_times(real,A,B),times_times(real,A,C))| -ord_less_e_q(real,B,C).
% 8.09/8.12 ** KEPT (pick-wt=19): 476 [] -ord_less(real,zero_zero(real),A)| -ord_less(real,B,C)|ord_less(real,times_times(real,A,B),times_times(real,A,C)).
% 8.09/8.12 ** KEPT (pick-wt=18): 477 [] -ord_less(real,zero_zero(real),A)| -ord_less(real,zero_zero(real),B)|ord_less(real,zero_zero(real),times_times(real,A,B)).
% 8.09/8.12 ** KEPT (pick-wt=19): 478 [] -ord_less(real,zero_zero(real),A)| -ord_less(real,times_times(real,B,A),times_times(real,C,A))|ord_less(real,B,C).
% 8.09/8.12 ** KEPT (pick-wt=19): 479 [] -ord_less(real,zero_zero(real),A)|ord_less(real,times_times(real,B,A),times_times(real,C,A))| -ord_less(real,B,C).
% 8.09/8.12 ** KEPT (pick-wt=17): 480 [] plus_plus(real,times_times(real,A,A),times_times(real,B,B))!=zero_zero(real)|A=zero_zero(real).
% 8.09/8.12 ** KEPT (pick-wt=17): 481 [] plus_plus(real,times_times(real,A,A),times_times(real,B,B))!=zero_zero(real)|B=zero_zero(real).
% 8.09/8.12 ** KEPT (pick-wt=21): 482 [] plus_plus(real,times_times(real,A,A),times_times(real,B,B))=zero_zero(real)|A!=zero_zero(real)|B!=zero_zero(real).
% 8.09/8.12 ** KEPT (pick-wt=15): 483 [] power_power(nat,A,B)!=one_one(nat)|A=one_one(nat)|B=zero_zero(nat).
% 8.09/8.12 ** KEPT (pick-wt=11): 484 [] power_power(nat,A,B)=one_one(nat)|A!=one_one(nat).
% 8.09/8.12 Following clause subsumed by 446 during input processing: 0 [] power_power(nat,A,B)=one_one(nat)|B!=zero_zero(nat).
% 8.09/8.12 ** KEPT (pick-wt=23): 486 [copy,485,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)).
% 8.09/8.12 ** KEPT (pick-wt=23): 487 [] -monoid_mult(A)| -ord_less(nat,zero_zero(nat),B)|times_times(A,power_power(A,C,minus_minus(nat,B,one_one(nat))),C)=power_power(A,C,B).
% 8.09/8.12 ** KEPT (pick-wt=13): 488 [] -power(A)|B!=zero_zero(nat)|power_power(A,C,B)=one_one(A).
% 8.09/8.12 ** KEPT (pick-wt=22): 490 [copy,489,flip.3] -power(A)|B=zero_zero(nat)|times_times(A,C,power_power(A,C,minus_minus(nat,B,one_one(nat))))=power_power(A,C,B).
% 8.09/8.12 ** KEPT (pick-wt=26): 491 [] -linordered_semidom(A)| -ord_less(A,B,C)| -ord_less_e_q(A,zero_zero(A),B)| -ord_less(nat,zero_zero(nat),D)|ord_less(A,power_power(A,B,D),power_power(A,C,D)).
% 8.09/8.12 ** KEPT (pick-wt=12): 492 [] -ord_less_e_q(real,A,B)| -ord_less_e_q(real,B,C)|ord_less_e_q(real,A,C).
% 8.09/8.12 ** KEPT (pick-wt=11): 493 [] -ord_less_e_q(real,A,B)| -ord_less_e_q(real,B,A)|A=B.
% 8.09/8.12 ** KEPT (pick-wt=15): 494 [] -ring_11004092258visors(A)|ti(A,B)=zero_zero(A)|power_power(A,B,C)!=zero_zero(A).
% 8.09/8.12 ** KEPT (pick-wt=20): 496 [copy,495,flip.2] -comm_monoid_mult(A)|times_times(A,power_power(A,B,C),power_power(A,D,C))=power_power(A,times_times(A,B,D),C).
% 8.09/8.12 ** KEPT (pick-wt=17): 497 [] -monoid_mult(A)|times_times(A,power_power(A,B,C),B)=times_times(A,B,power_power(A,B,C)).
% 8.09/8.12 ** KEPT (pick-wt=10): 498 [] -monoid_mult(A)|power_power(A,one_one(A),B)=one_one(A).
% 8.09/8.12 ** KEPT (pick-wt=16): 499 [] -comm_semiring_1(A)| -dvd_dvd(A,B,C)|dvd_dvd(A,power_power(A,B,D),power_power(A,C,D)).
% 8.09/8.12 ** KEPT (pick-wt=17): 500 [] -monoid_mult(A)|power_power(A,B,times_times(nat,C,D))=power_power(A,power_power(A,B,C),D).
% 8.09/8.12 ** KEPT (pick-wt=11): 501 [] -monoid_mult(A)|power_power(A,B,one_one(nat))=ti(A,B).
% 8.09/8.12 ** KEPT (pick-wt=21): 502 [] -linordered_semidom(A)| -ord_less_e_q(A,B,C)| -ord_less_e_q(A,zero_zero(A),B)|ord_less_e_q(A,power_power(A,B,D),power_power(A,C,D)).
% 8.09/8.12 ** KEPT (pick-wt=15): 503 [] -linordered_semidom(A)| -ord_less_e_q(A,zero_zero(A),B)|ord_less_e_q(A,zero_zero(A),power_power(A,B,C)).
% 8.09/8.12 ** KEPT (pick-wt=15): 504 [] -linordered_semidom(A)| -ord_less(A,zero_zero(A),B)|ord_less(A,zero_zero(A),power_power(A,B,C)).
% 8.09/8.12 ** KEPT (pick-wt=15): 505 [] -linordered_semidom(A)| -ord_less_e_q(A,one_one(A),B)|ord_less_e_q(A,one_one(A),power_power(A,B,C)).
% 8.09/8.12 ** KEPT (pick-wt=19): 506 [] -linordered_semidom(A)| -ord_less(A,one_one(A),B)|power_power(A,B,C)!=power_power(A,B,D)|C=D.
% 8.09/8.12 ** KEPT (pick-wt=19): 507 [] -linordered_semidom(A)| -ord_less(A,one_one(A),B)|power_power(A,B,C)=power_power(A,B,D)|C!=D.
% 8.09/8.12 ** KEPT (pick-wt=21): 508 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|power_power(A,B,C)!=zero_zero(A)|ti(A,B)=zero_zero(A).
% 8.09/8.12 ** KEPT (pick-wt=19): 509 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|power_power(A,B,C)!=zero_zero(A)|C!=zero_zero(nat).
% 8.09/8.12 ** KEPT (pick-wt=25): 510 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|power_power(A,B,C)=zero_zero(A)|ti(A,B)!=zero_zero(A)|C=zero_zero(nat).
% 8.09/8.12 ** KEPT (pick-wt=10): 511 [] -power(A)|power_power(A,B,zero_zero(nat))=one_one(A).
% 8.09/8.12 ** KEPT (pick-wt=20): 513 [copy,512,flip.2] -monoid_mult(A)|times_times(A,power_power(A,B,C),power_power(A,B,D))=power_power(A,B,plus_plus(nat,C,D)).
% 8.09/8.12 ** KEPT (pick-wt=20): 514 [] -comm_semiring_1(A)| -dvd_dvd(A,power_power(A,B,C),D)| -ord_less_e_q(nat,E,C)|dvd_dvd(A,power_power(A,B,E),D).
% 8.09/8.12 ** KEPT (pick-wt=20): 515 [] -comm_semiring_1(A)| -dvd_dvd(A,B,C)| -ord_less_e_q(nat,D,E)|dvd_dvd(A,power_power(A,B,D),power_power(A,C,E)).
% 8.09/8.12 ** KEPT (pick-wt=16): 516 [] -comm_semiring_1(A)| -ord_less_e_q(nat,B,C)|dvd_dvd(A,power_power(A,D,B),power_power(A,D,C)).
% 8.09/8.12 ** KEPT (pick-wt=19): 517 [] -ord_less(nat,zero_zero(nat),A)| -ord_less(nat,power_power(nat,A,B),power_power(nat,A,C))|ord_less(nat,B,C).
% 8.09/8.12 Following clause subsumed by 263 during input processing: 0 [] -ord_less(nat,zero_zero(nat),power_power(nat,A,B))|ord_less(nat,zero_zero(nat),A)|B=zero_zero(nat).
% 8.09/8.12 Following clause subsumed by 265 during input processing: 0 [] ord_less(nat,zero_zero(nat),power_power(nat,A,B))| -ord_less(nat,zero_zero(nat),A).
% 8.09/8.12 Following clause subsumed by 264 during input processing: 0 [] ord_less(nat,zero_zero(nat),power_power(nat,A,B))|B!=zero_zero(nat).
% 8.09/8.12 ** KEPT (pick-wt=21): 518 [] -linordered_semidom(A)| -ord_less(A,power_power(A,B,C),power_power(A,D,C))| -ord_less_e_q(A,zero_zero(A),D)|ord_less(A,B,D).
% 8.09/8.12 ** KEPT (pick-wt=20): 519 [] -linordered_semidom(A)| -ord_less(A,one_one(A),B)|ord_less(A,power_power(A,B,C),times_times(A,B,power_power(A,B,C))).
% 8.09/8.12 ** KEPT (pick-wt=18): 520 [] -linordered_semidom(A)| -ord_less(A,one_one(A),B)|ord_less(A,one_one(A),times_times(A,B,power_power(A,B,C))).
% 8.09/8.12 Following clause subsumed by 488 during input processing: 0 [] -power(A)| -semiring_0(A)|B!=zero_zero(nat)|power_power(A,zero_zero(A),B)=one_one(A).
% 8.09/8.12 ** KEPT (pick-wt=16): 521 [] -power(A)| -semiring_0(A)|B=zero_zero(nat)|power_power(A,zero_zero(A),B)=zero_zero(A).
% 8.09/8.12 ** KEPT (pick-wt=21): 522 [] -linordered_semidom(A)| -ord_less(nat,B,C)| -ord_less(A,one_one(A),D)|ord_less(A,power_power(A,D,B),power_power(A,D,C)).
% 8.09/8.12 ** KEPT (pick-wt=21): 523 [] -linordered_semidom(A)| -ord_less(A,one_one(A),B)| -ord_less(A,power_power(A,B,C),power_power(A,B,D))|ord_less(nat,C,D).
% 8.09/8.12 Following clause subsumed by 523 during input processing: 0 [] -linordered_semidom(A)| -ord_less(A,one_one(A),B)| -ord_less(A,power_power(A,B,C),power_power(A,B,D))|ord_less(nat,C,D).
% 8.09/8.12 Following clause subsumed by 522 during input processing: 0 [] -linordered_semidom(A)| -ord_less(A,one_one(A),B)|ord_less(A,power_power(A,B,C),power_power(A,B,D))| -ord_less(nat,C,D).
% 8.09/8.12 ** KEPT (pick-wt=21): 524 [] -linordered_semidom(A)| -ord_less_e_q(nat,B,C)| -ord_less_e_q(A,one_one(A),D)|ord_less_e_q(A,power_power(A,D,B),power_power(A,D,C)).
% 8.09/8.12 ** KEPT (pick-wt=25): 525 [] -linordered_semidom(A)| -ord_less(A,zero_zero(A),B)| -ord_less(A,B,one_one(A))|ord_less(A,times_times(A,B,power_power(A,B,C)),power_power(A,B,C)).
% 8.09/8.12 ** KEPT (pick-wt=26): 526 [] -linordered_semidom(A)| -ord_less(nat,B,C)| -ord_less(A,zero_zero(A),D)| -ord_less(A,D,one_one(A))|ord_less(A,power_power(A,D,C),power_power(A,D,B)).
% 8.09/8.12 ** KEPT (pick-wt=33): 527 [] -linordered_semidom(A)|power_power(A,B,C)!=power_power(A,D,C)| -ord_less_e_q(A,zero_zero(A),B)| -ord_less_e_q(A,zero_zero(A),D)| -ord_less(nat,zero_zero(nat),C)|ti(A,B)=ti(A,D).
% 8.09/8.12 ** KEPT (pick-wt=26): 528 [] -linordered_semidom(A)| -ord_less_e_q(nat,B,C)| -ord_less_e_q(A,zero_zero(A),D)| -ord_less_e_q(A,D,one_one(A))|ord_less_e_q(A,power_power(A,D,C),power_power(A,D,B)).
% 8.09/8.12 ** KEPT (pick-wt=21): 529 [] -linordered_semidom(A)| -ord_less(A,one_one(A),B)| -ord_less_e_q(A,power_power(A,B,C),power_power(A,B,D))|ord_less_e_q(nat,C,D).
% 8.09/8.12 Following clause subsumed by 529 during input processing: 0 [] -linordered_semidom(A)| -ord_less(A,one_one(A),B)| -ord_less_e_q(A,power_power(A,B,C),power_power(A,B,D))|ord_less_e_q(nat,C,D).
% 8.09/8.12 ** KEPT (pick-wt=21): 530 [] -linordered_semidom(A)| -ord_less(A,one_one(A),B)|ord_less_e_q(A,power_power(A,B,C),power_power(A,B,D))| -ord_less_e_q(nat,C,D).
% 8.09/8.12 ** KEPT (pick-wt=20): 531 [] -linordered_semidom(A)| -ord_less(A,one_one(A),B)| -ord_less(nat,zero_zero(nat),C)|ord_less(A,one_one(A),power_power(A,B,C)).
% 8.09/8.12 ** KEPT (pick-wt=14): 532 [] -comm_semiring_1(A)| -ord_less(nat,zero_zero(nat),B)|dvd_dvd(A,C,power_power(A,C,B)).
% 8.09/8.12 ** KEPT (pick-wt=15): 533 [] -comm_semiring_1(A)|ti(A,B)!=one_one(A)|dvd_dvd(A,B,power_power(A,B,C)).
% 8.09/8.12 ** KEPT (pick-wt=40): 534 [] -linord626643107strict(A)| -ord_less(A,B,C)| -ord_less(A,D,C)| -ord_less_e_q(A,zero_zero(A),E)| -ord_less_e_q(A,zero_zero(A),F)|plus_plus(A,E,F)!=one_one(A)|ord_less(A,plus_plus(A,times_times(A,E,B),times_times(A,F,D)),C).
% 8.09/8.12 ** KEPT (pick-wt=17): 535 [] -ord_less(nat,zero_zero(nat),A)| -ord_less(real,zero_zero(real),B)|ord_less(real,zero_zero(real),$f4(B,A)).
% 8.09/8.12 ** KEPT (pick-wt=18): 536 [] -ord_less(nat,zero_zero(nat),A)| -ord_less(real,zero_zero(real),B)|power_power(real,$f4(B,A),A)=B.
% 8.09/8.12 ** KEPT (pick-wt=26): 537 [] -ord_less(nat,zero_zero(nat),A)| -ord_less(real,zero_zero(real),B)| -ord_less(real,zero_zero(real),C)|power_power(real,C,A)!=B|C=$f4(B,A).
% 8.09/8.12 ** KEPT (pick-wt=7): 538 [] -comm_semiring_1(A)|dvd_dvd(A,B,zero_zero(A)).
% 8.09/8.12 ** KEPT (pick-wt=12): 539 [] -dvd_dvd(nat,A,B)|B=zero_zero(nat)|ord_less_e_q(nat,A,B).
% 8.09/8.12 ** KEPT (pick-wt=14): 540 [] -dvd_dvd(nat,A,B)|dvd_dvd(nat,power_power(nat,A,C),power_power(nat,B,C)).
% 8.09/8.12 ** KEPT (pick-wt=14): 541 [] -dvd_dvd(nat,A,B)|dvd_dvd(nat,times_times(nat,C,A),times_times(nat,C,B)).
% 8.09/8.12 ** KEPT (pick-wt=14): 542 [] -dvd_dvd(nat,A,B)|dvd_dvd(nat,times_times(nat,A,C),times_times(nat,B,C)).
% 8.09/8.12 ** KEPT (pick-wt=15): 543 [] -dvd_dvd(nat,A,B)| -dvd_dvd(nat,A,plus_plus(nat,B,C))|dvd_dvd(nat,A,C).
% 8.09/8.12 ** KEPT (pick-wt=18): 544 [] -dvd_dvd(nat,times_times(nat,A,B),times_times(nat,C,B))|B=zero_zero(nat)|dvd_dvd(nat,A,C).
% 8.09/8.12 ** KEPT (pick-wt=14): 545 [] dvd_dvd(nat,times_times(nat,A,B),times_times(nat,C,B))|B!=zero_zero(nat).
% 8.09/8.12 Following clause subsumed by 542 during input processing: 0 [] dvd_dvd(nat,times_times(nat,A,B),times_times(nat,C,B))| -dvd_dvd(nat,A,C).
% 8.09/8.12 ** KEPT (pick-wt=18): 546 [] -dvd_dvd(nat,power_power(nat,A,B),power_power(nat,C,B))|B=zero_zero(nat)|dvd_dvd(nat,A,C).
% 8.09/8.12 ** KEPT (pick-wt=15): 547 [] A=zero_zero(nat)| -dvd_dvd(nat,power_power(nat,B,A),C)|dvd_dvd(nat,B,C).
% 8.09/8.12 ** KEPT (pick-wt=17): 548 [] -linordered_idom(A)|ti(A,B)=ti(A,C)|ord_less(A,B,C)|ord_less(A,C,B).
% 8.09/8.12 ** KEPT (pick-wt=14): 549 [] -comm_semiring_1(A)| -dvd_dvd(A,B,C)| -dvd_dvd(A,C,D)|dvd_dvd(A,B,D).
% 8.09/8.12 ** KEPT (pick-wt=6): 550 [] -comm_semiring_1(A)|dvd_dvd(A,B,B).
% 8.09/8.12 ** KEPT (pick-wt=22): 551 [] A!=plus_plus(nat,times_times(nat,B,C),D)| -ord_less(nat,zero_zero(nat),D)| -ord_less(nat,D,C)| -dvd_dvd(nat,C,A).
% 8.09/8.12 ** KEPT (pick-wt=19): 552 [] -dvd_dvd(nat,power_power(nat,A,B),power_power(nat,A,C))| -ord_less(nat,one_one(nat),A)|ord_less_e_q(nat,B,C).
% 8.09/8.12 ** KEPT (pick-wt=10): 553 [] -mult_zero(A)|times_times(A,zero_zero(A),B)=zero_zero(A).
% 8.12/8.14 ** KEPT (pick-wt=10): 554 [] -mult_zero(A)|times_times(A,B,zero_zero(A))=zero_zero(A).
% 8.12/8.14 ** KEPT (pick-wt=21): 555 [] -ring_n68954251visors(A)|times_times(A,B,C)!=zero_zero(A)|ti(A,B)=zero_zero(A)|ti(A,C)=zero_zero(A).
% 8.12/8.14 ** KEPT (pick-wt=15): 556 [] -ring_n68954251visors(A)|times_times(A,B,C)=zero_zero(A)|ti(A,B)!=zero_zero(A).
% 8.12/8.14 ** KEPT (pick-wt=15): 557 [] -ring_n68954251visors(A)|times_times(A,B,C)=zero_zero(A)|ti(A,C)!=zero_zero(A).
% 8.12/8.14 ** KEPT (pick-wt=21): 558 [] -no_zero_divisors(A)|ti(A,B)=zero_zero(A)|ti(A,C)=zero_zero(A)|times_times(A,B,C)!=zero_zero(A).
% 8.12/8.14 Following clause subsumed by 558 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).
% 8.12/8.14 ** KEPT (pick-wt=7): 560 [copy,559,flip.2] -zero_ne_q_one(A)|zero_zero(A)!=one_one(A).
% 8.12/8.14 Following clause subsumed by 560 during input processing: 0 [] -zero_ne_q_one(A)|zero_zero(A)!=one_one(A).
% 8.12/8.14 ** KEPT (pick-wt=20): 561 [] -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)).
% 8.12/8.14 ** KEPT (pick-wt=26): 563 [copy,562,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)).
% 8.12/8.14 ** KEPT (pick-wt=13): 564 [] -comm_semiring_1(A)| -dvd_dvd(A,zero_zero(A),B)|ti(A,B)=zero_zero(A).
% 8.12/8.14 ** KEPT (pick-wt=13): 565 [] -comm_semiring_1(A)| -dvd_dvd(A,times_times(A,B,C),D)|dvd_dvd(A,C,D).
% 8.12/8.14 ** KEPT (pick-wt=13): 566 [] -comm_semiring_1(A)| -dvd_dvd(A,times_times(A,B,C),D)|dvd_dvd(A,B,D).
% 8.12/8.14 ** KEPT (pick-wt=12): 567 [] -dvd(A)|B!=times_times(A,C,D)|dvd_dvd(A,C,B).
% 8.12/8.14 ** KEPT (pick-wt=20): 568 [] -comm_semiring_1(A)| -dvd_dvd(A,B,C)| -dvd_dvd(A,D,E)|dvd_dvd(A,times_times(A,B,D),times_times(A,C,E)).
% 8.12/8.14 ** KEPT (pick-wt=13): 569 [] -comm_semiring_1(A)| -dvd_dvd(A,B,C)|dvd_dvd(A,B,times_times(A,D,C)).
% 8.12/8.14 ** KEPT (pick-wt=13): 570 [] -comm_semiring_1(A)| -dvd_dvd(A,B,C)|dvd_dvd(A,B,times_times(A,C,D)).
% 8.12/8.14 ** KEPT (pick-wt=9): 571 [] -comm_semiring_1(A)|dvd_dvd(A,B,times_times(A,C,B)).
% 8.12/8.14 ** KEPT (pick-wt=9): 572 [] -comm_semiring_1(A)|dvd_dvd(A,B,times_times(A,B,C)).
% 8.12/8.14 ** KEPT (pick-wt=17): 573 [] -comm_semiring_1(A)| -dvd_dvd(A,B,C)| -dvd_dvd(A,B,D)|dvd_dvd(A,B,plus_plus(A,C,D)).
% 8.12/8.14 ** KEPT (pick-wt=7): 574 [] -comm_semiring_1(A)|dvd_dvd(A,one_one(A),B).
% 8.12/8.14 ** KEPT (pick-wt=17): 575 [] -comm_ring_1(A)| -dvd_dvd(A,B,C)| -dvd_dvd(A,B,D)|dvd_dvd(A,B,minus_minus(A,C,D)).
% 8.12/8.14 ** KEPT (pick-wt=22): 576 [] -dvd_dvd(nat,A,B)|B=zero_zero(nat)|B=A|ord_less_e_q(nat,times_times(nat,number_number_of(nat,bit0(bit1(pls))),A),B).
% 8.12/8.14 ** KEPT (pick-wt=10): 577 [] -linordered_ring(A)|ord_less_e_q(A,zero_zero(A),times_times(A,B,B)).
% 8.12/8.14 ** KEPT (pick-wt=20): 578 [] -linord581940658strict(A)| -ord_less_e_q(A,zero_zero(A),times_times(A,B,C))|ord_less_e_q(A,zero_zero(A),B)|ord_less_e_q(A,B,zero_zero(A)).
% 8.12/8.14 ** KEPT (pick-wt=20): 579 [] -linord581940658strict(A)| -ord_less_e_q(A,zero_zero(A),times_times(A,B,C))|ord_less_e_q(A,zero_zero(A),B)|ord_less_e_q(A,C,zero_zero(A)).
% 8.12/8.14 ** KEPT (pick-wt=20): 580 [] -linord581940658strict(A)| -ord_less_e_q(A,zero_zero(A),times_times(A,B,C))|ord_less_e_q(A,zero_zero(A),C)|ord_less_e_q(A,B,zero_zero(A)).
% 8.12/8.14 ** KEPT (pick-wt=20): 581 [] -linord581940658strict(A)| -ord_less_e_q(A,zero_zero(A),times_times(A,B,C))|ord_less_e_q(A,zero_zero(A),C)|ord_less_e_q(A,C,zero_zero(A)).
% 8.12/8.14 ** KEPT (pick-wt=20): 582 [] -linord581940658strict(A)|ord_less_e_q(A,zero_zero(A),times_times(A,B,C))| -ord_less_e_q(A,zero_zero(A),B)| -ord_less_e_q(A,zero_zero(A),C).
% 8.12/8.14 ** KEPT (pick-wt=20): 583 [] -linord581940658strict(A)|ord_less_e_q(A,zero_zero(A),times_times(A,B,C))| -ord_less_e_q(A,B,zero_zero(A))| -ord_less_e_q(A,C,zero_zero(A)).
% 8.12/8.14 ** KEPT (pick-wt=20): 584 [] -linord581940658strict(A)| -ord_less_e_q(A,times_times(A,B,C),zero_zero(A))|ord_less_e_q(A,zero_zero(A),B)|ord_less_e_q(A,B,zero_zero(A)).
% 8.12/8.14 ** KEPT (pick-wt=20): 585 [] -linord581940658strict(A)| -ord_less_e_q(A,times_times(A,B,C),zero_zero(A))|ord_less_e_q(A,zero_zero(A),B)|ord_less_e_q(A,zero_zero(A),C).
% 8.12/8.14 ** KEPT (pick-wt=20): 586 [] -linord581940658strict(A)| -ord_less_e_q(A,times_times(A,B,C),zero_zero(A))|ord_less_e_q(A,C,zero_zero(A))|ord_less_e_q(A,B,zero_zero(A)).
% 8.12/8.14 ** KEPT (pick-wt=20): 587 [] -linord581940658strict(A)| -ord_less_e_q(A,times_times(A,B,C),zero_zero(A))|ord_less_e_q(A,C,zero_zero(A))|ord_less_e_q(A,zero_zero(A),C).
% 8.12/8.14 ** KEPT (pick-wt=20): 588 [] -linord581940658strict(A)|ord_less_e_q(A,times_times(A,B,C),zero_zero(A))| -ord_less_e_q(A,zero_zero(A),B)| -ord_less_e_q(A,C,zero_zero(A)).
% 8.12/8.14 ** KEPT (pick-wt=20): 589 [] -linord581940658strict(A)|ord_less_e_q(A,times_times(A,B,C),zero_zero(A))| -ord_less_e_q(A,B,zero_zero(A))| -ord_less_e_q(A,zero_zero(A),C).
% 8.12/8.14 ** KEPT (pick-wt=20): 590 [] -ordere453448008miring(A)| -ord_less_e_q(A,zero_zero(A),B)| -ord_less_e_q(A,zero_zero(A),C)|ord_less_e_q(A,zero_zero(A),times_times(A,B,C)).
% 8.12/8.14 ** KEPT (pick-wt=20): 591 [] -ordere453448008miring(A)| -ord_less_e_q(A,zero_zero(A),B)| -ord_less_e_q(A,C,zero_zero(A))|ord_less_e_q(A,times_times(A,B,C),zero_zero(A)).
% 8.12/8.14 ** KEPT (pick-wt=20): 592 [] -ordere453448008miring(A)| -ord_less_e_q(A,zero_zero(A),B)| -ord_less_e_q(A,C,zero_zero(A))|ord_less_e_q(A,times_times(A,C,B),zero_zero(A)).
% 8.12/8.14 Following clause subsumed by 592 during input processing: 0 [] -ordere453448008miring(A)| -ord_less_e_q(A,B,zero_zero(A))| -ord_less_e_q(A,zero_zero(A),C)|ord_less_e_q(A,times_times(A,B,C),zero_zero(A)).
% 8.12/8.14 ** KEPT (pick-wt=20): 593 [] -ordered_ring(A)| -ord_less_e_q(A,B,zero_zero(A))| -ord_less_e_q(A,C,zero_zero(A))|ord_less_e_q(A,zero_zero(A),times_times(A,B,C)).
% 8.12/8.14 ** KEPT (pick-wt=16): 594 [] -ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)).
% 8.12/8.14 Following clause subsumed by 189 during input processing: 0 [copy,188,flip.1] bit0(A)!=bit1(B).
% 8.12/8.14 Following clause subsumed by 188 during input processing: 0 [copy,189,flip.1] bit1(A)!=bit0(B).
% 8.12/8.14 ** KEPT (pick-wt=11): 607 [copy,235,flip.1] zero_zero(int)!=plus_plus(int,plus_plus(int,one_one(int),A),A).
% 8.12/8.14 286 back subsumes 284.
% 8.12/8.14 287 back subsumes 283.
% 8.12/8.14 381 back subsumes 184.
% 8.12/8.14 436 back subsumes 400.
% 8.12/8.14 488 back subsumes 332.
% 8.12/8.14 494 back subsumes 77.
% 8.12/8.14 508 back subsumes 325.
% 8.12/8.14 509 back subsumes 326.
% 8.12/8.14 510 back subsumes 327.
% 8.12/8.14 518 back subsumes 171.
% 8.12/8.14 521 back subsumes 333.
% 8.12/8.14 Following clause subsumed by 235 during input processing: 0 [copy,607,flip.1] plus_plus(int,plus_plus(int,one_one(int),A),A)!=zero_zero(int).
% 8.12/8.14
% 8.12/8.14 ------------> process sos:
% 8.12/8.14 ** KEPT (pick-wt=3): 699 [] A=A.
% 8.12/8.14 ** KEPT (pick-wt=11): 700 [] minus_minus(nat,ti(nat,A),B)=minus_minus(nat,A,B).
% 8.12/8.14 ---> New Demodulator: 701 [new_demod,700] minus_minus(nat,ti(nat,A),B)=minus_minus(nat,A,B).
% 8.12/8.14 ** KEPT (pick-wt=11): 702 [] minus_minus(nat,A,ti(nat,B))=minus_minus(nat,A,B).
% 8.12/8.14 ---> New Demodulator: 703 [new_demod,702] minus_minus(nat,A,ti(nat,B))=minus_minus(nat,A,B).
% 8.12/8.14 ** KEPT (pick-wt=11): 704 [] ti(nat,minus_minus(nat,A,B))=minus_minus(nat,A,B).
% 8.12/8.14 ---> New Demodulator: 705 [new_demod,704] ti(nat,minus_minus(nat,A,B))=minus_minus(nat,A,B).
% 8.12/8.14 ** KEPT (pick-wt=7): 706 [] ti(A,undefined(A))=undefined(A).
% 8.12/8.14 ---> New Demodulator: 707 [new_demod,706] ti(A,undefined(A))=undefined(A).
% 8.12/8.14 ** KEPT (pick-wt=7): 708 [] bit0(ti(int,A))=bit0(A).
% 8.12/8.14 ---> New Demodulator: 709 [new_demod,708] bit0(ti(int,A))=bit0(A).
% 8.12/8.14 ** KEPT (pick-wt=7): 710 [] ti(int,bit0(A))=bit0(A).
% 8.12/8.14 ---> New Demodulator: 711 [new_demod,710] ti(int,bit0(A))=bit0(A).
% 8.12/8.14 ** KEPT (pick-wt=7): 712 [] bit1(ti(int,A))=bit1(A).
% 8.12/8.14 ---> New Demodulator: 713 [new_demod,712] bit1(ti(int,A))=bit1(A).
% 8.12/8.14 ** KEPT (pick-wt=7): 714 [] ti(int,bit1(A))=bit1(A).
% 8.12/8.14 ---> New Demodulator: 715 [new_demod,714] ti(int,bit1(A))=bit1(A).
% 8.12/8.14 ** KEPT (pick-wt=5): 716 [] ti(int,min)=min.
% 8.12/8.14 ---> New Demodulator: 717 [new_demod,716] ti(int,min)=min.
% 8.12/8.14 ** KEPT (pick-wt=5): 718 [] ti(int,pls)=pls.
% 8.12/8.14 ---> New Demodulator: 719 [new_demod,718] ti(int,pls)=pls.
% 8.12/8.14 ** KEPT (pick-wt=9): 720 [] legendre(ti(int,A),B)=legendre(A,B).
% 8.12/8.14 ---> New Demodulator: 721 [new_demod,720] legendre(ti(int,A),B)=legendre(A,B).
% 8.12/8.14 ** KEPT (pick-wt=9): 722 [] legendre(A,ti(int,B))=legendre(A,B).
% 8.12/8.14 ---> New Demodulator: 723 [new_demod,722] legendre(A,ti(int,B))=legendre(A,B).
% 8.12/8.14 ** KEPT (pick-wt=9): 724 [] ti(int,legendre(A,B))=legendre(A,B).
% 8.12/8.14 ---> New Demodulator: 725 [new_demod,724] ti(int,legendre(A,B))=legendre(A,B).
% 8.12/8.14 ** KEPT (pick-wt=5): 726 [] ti(int,m)=m.
% 8.12/8.14 ---> New Demodulator: 727 [new_demod,726] ti(int,m)=m.
% 8.12/8.14 ** KEPT (pick-wt=5): 728 [] ti(int,s1)=s1.
% 8.12/8.14 ---> New Demodulator: 729 [new_demod,728] ti(int,s1)=s1.
% 8.12/8.14 ** KEPT (pick-wt=5): 730 [] ti(int,s)=s.
% 8.12/8.14 ---> New Demodulator: 731 [new_demod,730] ti(int,s)=s.
% 8.12/8.14 ** KEPT (pick-wt=5): 732 [] ti(int,t)=t.
% 8.12/8.14 ---> New Demodulator: 733 [new_demod,732] ti(int,t)=t.
% 8.12/8.14 ** KEPT (pick-wt=5): 734 [] ord_less(int,t,zero_zero(int)).
% 8.12/8.14 ** KEPT (pick-wt=5): 735 [] ord_less(int,t,one_one(int)).
% 8.12/8.14 ** KEPT (pick-wt=35): 736 [] ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))).
% 8.12/8.14 ** KEPT (pick-wt=29): 738 [copy,737,flip.1] times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)=plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)).
% 8.12/8.14 ---> New Demodulator: 739 [new_demod,738] times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)=plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)).
% 8.12/8.14 ** KEPT (pick-wt=17): 740 [] ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 8.12/8.14 ** KEPT (pick-wt=16): 741 [] ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 8.12/8.14 ** KEPT (pick-wt=29): 743 [copy,742,flip.1] times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),$c1)=plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)).
% 8.12/8.14 ---> New Demodulator: 744 [new_demod,743] times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),$c1)=plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)).
% 8.12/8.14 ** KEPT (pick-wt=14): 745 [] zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))).
% 8.12/8.14 ** KEPT (pick-wt=13): 747 [copy,746,demod,739] twoSqu420862341sum2sq(plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))).
% 8.12/8.14 ** KEPT (pick-wt=4): 748 [] ord_less_e_q(int,A,A).
% 8.12/8.14 ** KEPT (pick-wt=7): 750 [copy,749,flip.1] ti(int,A)=number_number_of(int,A).
% 8.12/8.14 ---> New Demodulator: 751 [new_demod,750] ti(int,A)=number_number_of(int,A).
% 8.12/8.14 ** KEPT (pick-wt=9): 752 [] times_times(int,A,B)=times_times(int,B,A).
% 8.12/8.14 ** KEPT (pick-wt=8): 753 [] ord_less_e_q(int,A,B)|ord_less_e_q(int,B,A).
% 8.12/8.14 ** KEPT (pick-wt=15): 755 [copy,754,flip.1] number_number_of(int,times_times(int,A,B))=times_times(int,number_number_of(int,A),number_number_of(int,B)).
% 8.12/8.14 ---> New Demodulator: 756 [new_demod,755] number_number_of(int,times_times(int,A,B))=times_times(int,number_number_of(int,A),number_number_of(int,B)).
% 8.12/8.14 ** KEPT (pick-wt=15): 757 [] times_times(int,times_times(int,A,B),C)=times_times(int,A,times_times(int,B,C)).
% 8.12/8.14 ---> New Demodulator: 758 [new_demod,757] times_times(int,times_times(int,A,B),C)=times_times(int,A,times_times(int,B,C)).
% 8.12/8.14 ** KEPT (pick-wt=18): 760 [copy,759,flip.1] times_times(int,power_power(int,A,B),power_power(int,A,C))=power_power(int,A,plus_plus(nat,B,C)).
% 8.12/8.14 ---> New Demodulator: 761 [new_demod,760] times_times(int,power_power(int,A,B),power_power(int,A,C))=power_power(int,A,plus_plus(nat,B,C)).
% 8.12/8.14 Following clause subsumed by 748 during input processing: 0 [] ord_less_e_q(int,pls,pls).
% 8.12/8.14 ** KEPT (pick-wt=6): 763 [copy,762,flip.1] zero_zero(nat)=number_number_of(nat,pls).
% 8.12/8.14 ---> New Demodulator: 764 [new_demod,763] zero_zero(nat)=number_number_of(nat,pls).
% 8.12/8.14 Following clause subsumed by 699 during input processing: 0 [demod,764] number_number_of(nat,pls)=number_number_of(nat,pls).
% 8.12/8.14 ** KEPT (pick-wt=12): 765 [] plus_plus(nat,one_one(nat),one_one(nat))=number_number_of(nat,bit0(bit1(pls))).
% 8.12/8.14 ---> New Demodulator: 766 [new_demod,765] plus_plus(nat,one_one(nat),one_one(nat))=number_number_of(nat,bit0(bit1(pls))).
% 8.12/8.14 ** KEPT (pick-wt=6): 767 [] times_times(int,pls,A)=pls.
% 8.12/8.14 ---> New Demodulator: 768 [new_demod,767] times_times(int,pls,A)=pls.
% 8.12/8.14 ** KEPT (pick-wt=11): 770 [copy,769,flip.1] bit0(times_times(int,A,B))=times_times(int,bit0(A),B).
% 8.12/8.14 ---> New Demodulator: 771 [new_demod,770] bit0(times_times(int,A,B))=times_times(int,bit0(A),B).
% 8.12/8.14 ** KEPT (pick-wt=9): 773 [copy,772,demod,751] times_times(int,A,one_one(int))=number_number_of(int,A).
% 8.12/8.14 ** KEPT (pick-wt=9): 775 [copy,774,demod,751] times_times(int,one_one(int),A)=number_number_of(int,A).
% 8.12/8.14 ** KEPT (pick-wt=15): 777 [copy,776,flip.1] number_number_of(int,plus_plus(int,A,B))=plus_plus(int,number_number_of(int,A),number_number_of(int,B)).
% 8.12/8.14 ---> New Demodulator: 778 [new_demod,777] number_number_of(int,plus_plus(int,A,B))=plus_plus(int,number_number_of(int,A),number_number_of(int,B)).
% 8.12/8.14 ** KEPT (pick-wt=18): 779 [] times_times(int,plus_plus(int,A,B),C)=plus_plus(int,times_times(int,A,C),times_times(int,B,C)).
% 8.12/8.14 ---> New Demodulator: 780 [new_demod,779] times_times(int,plus_plus(int,A,B),C)=plus_plus(int,times_times(int,A,C),times_times(int,B,C)).
% 8.12/8.14 ** KEPT (pick-wt=18): 781 [] times_times(int,A,plus_plus(int,B,C))=plus_plus(int,times_times(int,A,B),times_times(int,A,C)).
% 8.12/8.14 ---> New Demodulator: 782 [new_demod,781] times_times(int,A,plus_plus(int,B,C))=plus_plus(int,times_times(int,A,B),times_times(int,A,C)).
% 8.12/8.14 ** KEPT (pick-wt=7): 784 [copy,783,flip.1] one_one(nat)=number_number_of(nat,bit1(pls)).
% 8.12/8.14 ---> New Demodulator: 785 [new_demod,784] one_one(nat)=number_number_of(nat,bit1(pls)).
% 8.12/8.14 Following clause subsumed by 699 during input processing: 0 [demod,785] number_number_of(nat,bit1(pls))=number_number_of(nat,bit1(pls)).
% 8.12/8.14 ** KEPT (pick-wt=23): 787 [copy,786,flip.3] ord_less(int,A,pls)|ord_less(int,B,pls)|number_number_of(nat,plus_plus(int,A,B))=plus_plus(nat,number_number_of(nat,A),number_number_of(nat,B)).
% 8.12/8.14 ** KEPT (pick-wt=15): 789 [copy,788,demod,751,751] ord_less(int,A,B)|number_number_of(int,A)=number_number_of(int,B)|ord_less(int,B,A).
% 8.12/8.14 ** KEPT (pick-wt=15): 790 [] plus_plus(int,plus_plus(int,A,B),C)=plus_plus(int,A,plus_plus(int,B,C)).
% 8.12/8.14 ---> New Demodulator: 791 [new_demod,790] plus_plus(int,plus_plus(int,A,B),C)=plus_plus(int,A,plus_plus(int,B,C)).
% 8.12/8.14 ** KEPT (pick-wt=15): 792 [] plus_plus(int,A,plus_plus(int,B,C))=plus_plus(int,B,plus_plus(int,A,C)).
% 8.12/8.14 ** KEPT (pick-wt=9): 793 [] plus_plus(int,A,B)=plus_plus(int,B,A).
% 8.12/8.14 ** KEPT (pick-wt=6): 794 [] zero_zero(int)=number_number_of(int,pls).
% 8.12/8.14 ---> New Demodulator: 795 [new_demod,794] zero_zero(int)=number_number_of(int,pls).
% 8.12/8.14 ** KEPT (pick-wt=7): 796 [] one_one(int)=number_number_of(int,bit1(pls)).
% 8.12/8.14 ---> New Demodulator: 797 [new_demod,796] one_one(int)=number_number_of(int,bit1(pls)).
% 8.12/8.14 ** KEPT (pick-wt=14): 799 [copy,798,demod,771] times_times(int,bit1(A),B)=plus_plus(int,times_times(int,bit0(A),B),B).
% 8.12/8.14 ---> New Demodulator: 800 [new_demod,799] times_times(int,bit1(A),B)=plus_plus(int,times_times(int,bit0(A),B),B).
% 8.12/8.14 ** KEPT (pick-wt=4): 801 [] bit0(pls)=pls.
% 8.12/8.14 ---> New Demodulator: 802 [new_demod,801] bit0(pls)=pls.
% 8.12/8.14 ** KEPT (pick-wt=5): 804 [copy,803,demod,795,flip.1] number_number_of(int,pls)=pls.
% 8.12/8.14 ---> New Demodulator: 805 [new_demod,804] number_number_of(int,pls)=pls.
% 8.12/8.14 ** KEPT (pick-wt=8): 807 [copy,806,demod,751,flip.1] number_number_of(int,A)=plus_plus(int,A,pls).
% 8.12/8.14 ---> New Demodulator: 808 [new_demod,807] number_number_of(int,A)=plus_plus(int,A,pls).
% 8.12/8.14 Following clause subsumed by 793 during input processing: 0 [demod,751,808] plus_plus(int,pls,A)=plus_plus(int,A,pls).
% 8.12/8.14 ** KEPT (pick-wt=12): 810 [copy,809,flip.1] bit0(plus_plus(int,A,B))=plus_plus(int,bit0(A),bit0(B)).
% 8.12/8.14 ---> New Demodulator: 811 [new_demod,810] bit0(plus_plus(int,A,B))=plus_plus(int,bit0(A),bit0(B)).
% 8.12/8.14 ** KEPT (pick-wt=7): 812 [] bit0(A)=plus_plus(int,A,A).
% 8.12/8.14 ---> New Demodulator: 813 [new_demod,812] bit0(A)=plus_plus(int,A,A).
% 8.12/8.14 ** KEPT (pick-wt=12): 815 [copy,814,demod,795,808,751,808] plus_plus(int,A,plus_plus(int,pls,pls))=plus_plus(int,A,pls).
% 8.12/8.14 ---> New Demodulator: 816 [new_demod,815] plus_plus(int,A,plus_plus(int,pls,pls))=plus_plus(int,A,pls).
% 8.12/8.14 ** KEPT (pick-wt=12): 818 [copy,817,demod,795,808,791,751,808] plus_plus(int,pls,plus_plus(int,pls,A))=plus_plus(int,A,pls).
% 8.12/8.14 ** KEPT (pick-wt=14): 820 [copy,819,demod,813,flip.1] bit1(plus_plus(int,A,B))=plus_plus(int,bit1(A),plus_plus(int,B,B)).
% 8.12/8.14 ---> New Demodulator: 821 [new_demod,820] bit1(plus_plus(int,A,B))=plus_plus(int,bit1(A),plus_plus(int,B,B)).
% 8.12/8.14 ** KEPT (pick-wt=17): 823 [copy,822,demod,813,791,821] plus_plus(int,A,plus_plus(int,A,bit1(B)))=plus_plus(int,bit1(A),plus_plus(int,B,B)).
% 8.12/8.14 ** KEPT (pick-wt=11): 825 [copy,824,demod,795,808,797,808] ord_less(int,plus_plus(int,pls,pls),plus_plus(int,bit1(pls),pls)).
% 8.12/8.14 ** KEPT (pick-wt=14): 827 [copy,826,demod,797,808,791,791,791] bit1(A)=plus_plus(int,bit1(pls),plus_plus(int,pls,plus_plus(int,A,A))).
% 8.12/8.14 ** KEPT (pick-wt=64): 829 [copy,828,demod,813,813,791,808,791,791,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,768,791,791,791,791,791,791,791,791,797,808,791,791,791,791,791,791,791,791,791,791,791,791,813,797,808] dvd_dvd(int,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,bit1(pls),pls)))))))))))))),plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),plus_plus(int,bit1(pls),pls))).
% 8.12/8.14 ** KEPT (pick-wt=156): 831 [copy,830,demod,808,813,780,800,813,780,800,813,780,768,768,791,800,813,780,768,768,791,791,791,791,791,791,791,791,768,791,791,791,791,791,791,780,768,780,768,780,780,768,780,768,780,780,768,808,780,800,813,780,800,813,780,768,768,791,800,813,780,768,768,791,791,791,791,791,791,791,791,768,791,791,791,791,791,791,813,780,768,780,768,780,780,768,780,768,780,780,768,791,791,791,791,791,791,791,791,791,791,791,791,791,791,791,791,791,791,791,791,791,791,791,791] power_power(int,plus_plus(int,A,B),number_number_of(nat,bit1(bit1(pls))))=plus_plus(int,power_power(int,A,number_number_of(nat,bit1(bit1(pls)))),plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,times_times(int,power_power(int,A,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),B),plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,times_times(int,power_power(int,A,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),B),plus_plus(int,times_times(int,power_power(int,A,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),B),plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,times_times(int,A,power_power(int,B,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,times_times(int,A,power_power(int,B,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),plus_plus(int,times_times(int,A,power_power(int,B,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),plus_plus(int,pls,power_power(int,B,number_number_of(nat,bit1(bit1(pls))))))))))))))))))))).
% 8.12/8.14 ** KEPT (pick-wt=66): 833 [copy,832,demod,813,813,813,808,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,768,791,791,791,791,780,768,780,768,780,780,768,780,768,780,768,813,791,791,791,791,791,791,791] power_power(int,plus_plus(int,A,B),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))=plus_plus(int,power_power(int,A,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,times_times(int,A,B),plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,times_times(int,A,B),plus_plus(int,pls,power_power(int,B,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))))))))).
% 8.12/8.14 ** KEPT (pick-wt=7): 835 [copy,834,demod,795,808] ord_less_e_q(int,plus_plus(int,pls,pls),s).
% 8.12/8.14 ** KEPT (pick-wt=47): 837 [copy,836,demod,813,813,791,808,791,791,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,768,791,791,791,791,791,791,791,791,797,808,791,791,791,791,791,791,791,791,791,791,791,791] ord_less(int,s,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,bit1(pls),pls))))))))))))))).
% 8.12/8.14 ** KEPT (pick-wt=47): 839 [copy,838,demod,813,813,791,808,791,791,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,768,791,791,791,791,791,791,791,791,797,808,791,791,791,791,791,791,791,791,791,791,791,791] zcong(s1,s,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,bit1(pls),pls))))))))))))))).
% 8.12/8.14 ** KEPT (pick-wt=23): 841 [copy,840,demod,813] times_times(int,A,power_power(int,A,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))=power_power(int,A,number_number_of(nat,bit1(bit1(pls)))).
% 8.12/8.14 ** KEPT (pick-wt=14): 843 [copy,842,demod,813] ord_less_e_q(int,A,power_power(int,A,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))).
% 8.12/8.14 ** KEPT (pick-wt=15): 845 [copy,844,demod,795,808,813,808,791] ord_less_e_q(int,plus_plus(int,pls,pls),plus_plus(int,bit1(pls),plus_plus(int,bit1(pls),pls))).
% 8.12/8.14 ** KEPT (pick-wt=67): 847 [copy,846,demod,813,813,813,813,791,808,791,791,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,768,791,791,791,791,791,791,791,791,797,808,791,791,791,791,791,791,791,791,791,791,791,791] zcong(power_power(int,s,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,s1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,bit1(pls),pls))))))))))))))).
% 8.12/8.14 ** KEPT (pick-wt=7): 849 [copy,848,demod,795,808] ord_less_e_q(int,plus_plus(int,pls,pls),$c2).
% 8.12/8.14 ** KEPT (pick-wt=47): 851 [copy,850,demod,813,813,791,808,791,791,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,768,791,791,791,791,791,791,791,791,797,808,791,791,791,791,791,791,791,791,791,791,791,791] ord_less(int,$c2,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,bit1(pls),pls))))))))))))))).
% 8.12/8.14 ** KEPT (pick-wt=47): 853 [copy,852,demod,813,813,791,808,791,791,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,768,791,791,791,791,791,791,791,791,797,808,791,791,791,791,791,791,791,791,791,791,791,791] zcong(s1,$c2,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,bit1(pls),pls))))))))))))))).
% 8.12/8.14 ** KEPT (pick-wt=7): 855 [copy,854,demod,795,808] ord_less_e_q(int,plus_plus(int,pls,pls),$c3).
% 8.12/8.14 ** KEPT (pick-wt=47): 857 [copy,856,demod,813,813,791,808,791,791,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,768,791,791,791,791,791,791,791,791,797,808,791,791,791,791,791,791,791,791,791,791,791,791] ord_less(int,$c3,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,bit1(pls),pls))))))))))))))).
% 8.12/8.14 ** KEPT (pick-wt=47): 859 [copy,858,demod,813,813,791,808,791,791,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,768,791,791,791,791,791,791,791,791,797,808,791,791,791,791,791,791,791,791,791,791,791,791] zcong(s1,$c3,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,bit1(pls),pls))))))))))))))).
% 8.12/8.14 ** KEPT (pick-wt=60): 861 [copy,860,demod,813,808,813,813,791,808,791,791,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,768,791,791,791,791,791,791,791,791,797,808,791,791,791,791,791,791,791,791,791,791,791,791] zcong(power_power(int,s1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),plus_plus(int,min,pls),plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,bit1(pls),pls))))))))))))))).
% 8.12/8.14 ** KEPT (pick-wt=15): 862 [] power_power(int,power_power(int,A,B),C)=power_power(int,A,times_times(nat,B,C)).
% 8.12/8.14 ** KEPT (pick-wt=10): 864 [copy,863,demod,813,808,791] zprime(plus_plus(int,bit1(pls),plus_plus(int,bit1(pls),pls))).
% 8.12/8.14 ** KEPT (pick-wt=16): 866 [copy,865,demod,813] times_times(nat,A,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))=plus_plus(nat,A,A).
% 8.12/8.14 ---> New Demodulator: 867 [new_demod,866] times_times(nat,A,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))=plus_plus(nat,A,A).
% 8.12/8.14 ** KEPT (pick-wt=16): 869 [copy,868,demod,813] times_times(nat,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))),A)=plus_plus(nat,A,A).
% 8.12/8.14 ---> New Demodulator: 870 [new_demod,869] times_times(nat,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))),A)=plus_plus(nat,A,A).
% 8.12/8.14 ** KEPT (pick-wt=19): 872 [copy,871,flip.2] ord_less(int,A,pls)|number_number_of(nat,times_times(int,A,B))=times_times(nat,number_number_of(nat,A),number_number_of(nat,B)).
% 8.12/8.14 ** KEPT (pick-wt=25): 874 [copy,873,flip.2] ord_less(int,A,pls)|times_times(nat,number_number_of(nat,times_times(int,A,B)),C)=times_times(nat,number_number_of(nat,A),times_times(nat,number_number_of(nat,B),C)).
% 8.12/8.14 Following clause subsumed by 748 during input processing: 0 [demod,795,808,795,808] ord_less_e_q(int,plus_plus(int,pls,pls),plus_plus(int,pls,pls)).
% 8.12/8.14 ** KEPT (pick-wt=11): 876 [copy,875,demod,795,808,797,808] ord_less_e_q(int,plus_plus(int,pls,pls),plus_plus(int,bit1(pls),pls)).
% 8.12/8.14 ** KEPT (pick-wt=12): 878 [copy,877,demod,795,808,808] ord_less_e_q(int,plus_plus(int,pls,pls),plus_plus(int,bit1(bit1(pls)),pls)).
% 8.12/8.14 ** KEPT (pick-wt=41): 880 [copy,879,demod,813,813,813,813,791] power_power(int,power_power(int,A,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))=power_power(int,A,number_number_of(nat,plus_plus(int,bit1(pls),plus_plus(int,bit1(pls),plus_plus(int,bit1(pls),bit1(pls)))))).
% 8.12/8.14 ** KEPT (pick-wt=60): 882 [copy,881,demod,813,808,813,813,791,808,791,791,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,768,791,791,791,791,791,791,791,791,797,808,791,791,791,791,791,791,791,791,791,791,791,791] zcong(power_power(int,s,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),plus_plus(int,min,pls),plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,bit1(pls),pls))))))))))))))).
% 8.12/8.14 ** KEPT (pick-wt=13): 884 [copy,883,demod,764,813] ord_less(nat,number_number_of(nat,pls),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))).
% 8.12/8.14 ** KEPT (pick-wt=60): 886 [copy,885,demod,813,808,813,813,791,808,791,791,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,768,791,791,791,791,791,791,791,791,797,808,791,791,791,791,791,791,791,791,791,791,791,791] zcong(power_power(int,$c4,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),plus_plus(int,min,pls),plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,bit1(pls),pls))))))))))))))).
% 8.12/8.15 ** KEPT (pick-wt=55): 888 [copy,887,demod,808,813,813,791,808,791,791,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,768,791,791,791,791,791,791,791,791,797,808,791,791,791,791,791,791,791,791,791,791,791,791,797,808] legendre(plus_plus(int,min,pls),plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,bit1(pls),pls)))))))))))))))=plus_plus(int,bit1(pls),pls).
% 8.12/8.15 ---> New Demodulator: 889 [new_demod,888] legendre(plus_plus(int,min,pls),plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,bit1(pls),pls)))))))))))))))=plus_plus(int,bit1(pls),pls).
% 8.12/8.15 ** KEPT (pick-wt=4): 890 [] bit1(min)=min.
% 8.12/8.15 ---> New Demodulator: 891 [new_demod,890] bit1(min)=min.
% 8.12/8.15 Following clause subsumed by 748 during input processing: 0 [] ord_less_e_q(int,min,min).
% 8.12/8.15 ** KEPT (pick-wt=4): 892 [] ord_less(int,min,pls).
% 8.12/8.15 ** KEPT (pick-wt=7): 894 [copy,893,demod,795,808] ord_less(int,min,plus_plus(int,pls,pls)).
% 8.12/8.15 ** KEPT (pick-wt=4): 895 [] ord_less_e_q(int,min,pls).
% 8.12/8.15 ** KEPT (pick-wt=4): 896 [] zcong(A,A,B).
% 8.12/8.15 ** KEPT (pick-wt=8): 898 [copy,897,demod,797,808] zcong(A,B,plus_plus(int,bit1(pls),pls)).
% 8.12/8.15 ** KEPT (pick-wt=10): 899 [] zcong(times_times(int,A,B),times_times(int,C,B),B).
% 8.12/8.15 ** KEPT (pick-wt=51): 901 [copy,900,demod,813,813,791,813,813,813] times_times(real,number_number_of(real,plus_plus(int,bit1(pls),plus_plus(int,bit1(pls),plus_plus(int,bit1(pls),bit1(pls))))),power_power(real,A,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))=power_power(real,times_times(real,number_number_of(real,plus_plus(int,bit1(pls),bit1(pls))),A),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))).
% 8.12/8.15 ---> New Demodulator: 902 [new_demod,901] times_times(real,number_number_of(real,plus_plus(int,bit1(pls),plus_plus(int,bit1(pls),plus_plus(int,bit1(pls),bit1(pls))))),power_power(real,A,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))=power_power(real,times_times(real,number_number_of(real,plus_plus(int,bit1(pls),bit1(pls))),A),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))).
% 8.12/8.15 ** KEPT (pick-wt=49): 904 [copy,903,demod,813,813,791,808,791,791,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,768,791,791,791,791,791,791,791,791,797,808,791,791,791,791,791,791,791,791,791,791,791,791,808] quadRes(plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,bit1(pls),pls)))))))))))))),plus_plus(int,min,pls)).
% 8.12/8.15 ** KEPT (pick-wt=63): 906 [copy,905,demod,813,813,791,808,791,791,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,780,800,813,780,768,768,791,768,791,791,791,791,791,791,791,791,797,808,791,791,791,791,791,791,791,791,791,791,791,791,813,808] dvd_dvd(int,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,bit1(pls),pls)))))))))))))),minus_minus(int,power_power(int,s,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),plus_plus(int,min,pls))).
% 8.12/8.15 ** KEPT (pick-wt=36): 908 [copy,907,demod,813,808,813,797,808,flip.1] plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),
% 8.12/8.15 Search stopped in tp_alloc by max_mem option.
% 8.12/8.15 plus_plus(int,bit1(pls),pls))=minus_minus(int,power_power(int,s,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),plus_plus(int,min,pls)).
% 8.12/8.15 ---> New Demodulator: 909 [new_demod,908] plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),plus_plus(int,bit1(pls),pls))=minus_minus(int,power_power(int,s,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),plus_plus(int,min,pls)).
% 8.12/8.15 ** KEPT (pick-wt=12): 910 [] ord_less(real,zero_zero(real),times_times(real,A,A))|A=zero_zero(real).
% 8.12/8.15 ** KEPT (pick-wt=18): 911 [] times_times(int,A,minus_minus(int,B,C))=minus_minus(int,times_times(int,A,B),times_times(int,A,C)).
% 8.12/8.15 ---> New Demodulator: 912 [new_demod,911] times_times(int,A,minus_minus(int,B,C))=minus_minus(int,times_times(int,A,B),times_times(int,A,C)).
% 8.12/8.15 ** KEPT (pick-wt=18): 913 [] times_times(int,minus_minus(int,A,B),C)=minus_minus(int,times_times(int,A,C),times_times(int,B,C)).
% 8.12/8.15 ---> New Demodulator: 914 [new_demod,913] times_times(int,minus_minus(int,A,B),C)=minus_minus(int,times_times(int,A,C),times_times(int,B,C)).
% 8.12/8.15 ** KEPT (pick-wt=21): 916 [copy,915,demod,813,813,813,flip.1] plus_plus(int,minus_minus(int,A,B),minus_minus(int,A,B))=minus_minus(int,plus_plus(int,A,A),plus_plus(int,B,B)).
% 8.12/8.15 ---> New Demodulator: 917 [new_demod,916] plus_plus(int,minus_minus(int,A,B),minus_minus(int,A,B))=minus_minus(int,plus_plus(int,A,A),plus_plus(int,B,B)).
% 8.12/8.15 ** KEPT (pick-wt=9): 919 [copy,918,demod,751,808,flip.1] plus_plus(int,A,pls)=minus_minus(int,A,pls).
% 8.12/8.15 ---> New Demodulator: 920 [new_demod,919] plus_plus(int,A,pls)=minus_minus(int,A,pls).
% 8.12/8.15 ** KEPT (pick-wt=14): 922 [copy,921,demod,813,flip.1] bit1(minus_minus(int,A,B))=minus_minus(int,bit1(A),plus_plus(int,B,B)).
% 8.12/8.15 ---> New Demodulator: 923 [new_demod,922] bit1(minus_minus(int,A,B))=minus_minus(int,bit1(A),plus_plus(int,B,B)).
% 8.12/8.15 ** KEPT (pick-wt=17): 925 [copy,924,demod,813,917] minus_minus(int,bit1(A),bit1(B))=minus_minus(int,plus_plus(int,A,A),plus_plus(int,B,B)).
% 8.12/8.15 ---> New Demodulator: 926 [new_demod,925] minus_minus(int,bit1(A),bit1(B))=minus_minus(int,plus_plus(int,A,A),plus_plus(int,B,B)).
% 8.12/8.15 ** KEPT (pick-wt=18): 928 [copy,927,demod,813,813,917,920,flip.1] minus_minus(int,minus_minus(int,pls,pls),plus_plus(int,A,A))=minus_minus(int,pls,plus_plus(int,A,A)).
% 8.12/8.15 ---> New Demodulator: 929 [new_demod,928] minus_minus(int,minus_minus(int,pls,pls),plus_plus(int,A,A))=minus_minus(int,pls,plus_plus(int,A,A)).
% 8.12/8.15 ** KEPT (pick-wt=57): 931 [copy,930,demod,914,758,914,758,782] plus_plus(int,minus_minus(int,times_times(int,A,B),times_times(int,C,times_times(int,D,B))),minus_minus(int,times_times(int,E,F),times_times(int,C,times_times(int,G,F))))=minus_minus(int,plus_plus(int,times_times(int,A,B),times_times(int,E,F)),plus_plus(int,times_times(int,C,times_times(int,D,B)),times_times(int,C,times_times(int,G,F)))).
% 8.12/8.15 ---> New Demodulator: 932 [new_demod,931] plus_plus(int,minus_minus(int,times_times(int,A,B),times_times(int,C,times_times(int,D,B))),minus_minus(int,times_times(int,E,F),times_times(int,C,times_times(int,G,F))))=minus_minus(int,plus_plus(int,times_times(int,A,B),times_times(int,E,F)),plus_plus(int,times_times(int,C,times_times(int,D,B)),times_times(int,C,times_times(int,G,F)))).
% 8.12/8.15 ** KEPT (pick-wt=13): 934 [copy,933,demod,923,891] minus_minus(int,pls,bit1(A))=minus_minus(int,min,plus_plus(int,A,A)).
% 8.12/8.15 ---> New Demodulator: 935 [new_demod,934] minus_minus(int,pls,bit1(A))=minus_minus(int,min,plus_plus(int,A,A)).
% 8.12/8.15 ** KEPT (pick-wt=16): 937 [copy,936,demod,813,917] minus_minus(int,min,bit1(A))=minus_minus(int,plus_plus(int,min,min),plus_plus(int,A,A)).
% 8.12/8.15 ---> New Demodulator: 938 [new_demod,937] minus_minus(int,min,bit1(A))=minus_minus(int,plus_plus(int,min,min),plus_plus(int,A,A)).
% 8.12/8.15 Following clause subsumed by 699 during input processing: 0 [demod,813,923,891] minus_minus(int,min,plus_plus(int,A,A))=minus_minus(int,min,plus_plus(int,A,A)).
% 8.12/8.15
% 8.12/8.15 Search stopped in tp_alloc by max_mem option.
% 8.12/8.15
% 8.12/8.15 ============ end of search ============
% 8.12/8.15
% 8.12/8.15 -------------- statistics -------------
% 8.12/8.15 clauses given 0
% 8.12/8.15 clauses generated 164
% 8.12/8.15 clauses kept 783
% 8.12/8.15 clauses forward subsumed 126
% 8.12/8.15 clauses back subsumed 11
% 8.12/8.15 Kbytes malloced 11718
% 8.12/8.15
% 8.12/8.15 ----------- times (seconds) -----------
% 8.12/8.15 user CPU time 0.12 (0 hr, 0 min, 0 sec)
% 8.12/8.15 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 8.12/8.15 wall-clock time 8 (0 hr, 0 min, 8 sec)
% 8.12/8.15
% 8.12/8.15 Process 1906 finished Wed Jul 27 10:01:26 2022
% 8.12/8.15 Otter interrupted
% 8.12/8.15 PROOF NOT FOUND
%------------------------------------------------------------------------------