%------------------------------------------------------------------------------ % File : Otter---3.3 % Problem : NUM926+6 : TPTP v8.1.0. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : otter-tptp-script %s % Computer : n007.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 13:10:18 EDT 2022 % Result : Unknown 7.84s 7.88s % Output : None % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : NUM926+6 : TPTP v8.1.0. Released v5.3.0. % 0.04/0.13 % Command : otter-tptp-script %s % 0.13/0.34 % Computer : n007.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Jul 27 09:41:01 EDT 2022 % 0.13/0.34 % CPUTime : % 7.78/7.80 ----- Otter 3.3f, August 2004 ----- % 7.78/7.80 The process was started by sandbox2 on n007.cluster.edu, % 7.78/7.80 Wed Jul 27 09:41:01 2022 % 7.78/7.80 The command was "./otter". The process ID is 26166. % 7.78/7.80 % 7.78/7.80 set(prolog_style_variables). % 7.78/7.80 set(auto). % 7.78/7.80 dependent: set(auto1). % 7.78/7.80 dependent: set(process_input). % 7.78/7.80 dependent: clear(print_kept). % 7.78/7.80 dependent: clear(print_new_demod). % 7.78/7.80 dependent: clear(print_back_demod). % 7.78/7.80 dependent: clear(print_back_sub). % 7.78/7.80 dependent: set(control_memory). % 7.78/7.80 dependent: assign(max_mem, 12000). % 7.78/7.80 dependent: assign(pick_given_ratio, 4). % 7.78/7.80 dependent: assign(stats_level, 1). % 7.78/7.80 dependent: assign(max_seconds, 10800). % 7.78/7.80 clear(print_given). % 7.78/7.80 % 7.78/7.80 formula_list(usable). % 7.78/7.80 all A (A=A). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 all X_a (zero_ne_q_one(X_a)->ti(X_a,one_one(X_a))=one_one(X_a)). % 7.78/7.80 all X_a (power(X_a)->ti(X_a,one_one(X_a))=one_one(X_a)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 all X_a (zero_ne_q_one(X_a)->ti(X_a,zero_zero(X_a))=zero_zero(X_a)). % 7.78/7.80 all X_a (no_zero_divisors(X_a)->ti(X_a,zero_zero(X_a))=zero_zero(X_a)). % 7.78/7.80 all X_a (mult_zero(X_a)->ti(X_a,zero_zero(X_a))=zero_zero(X_a)). % 7.78/7.80 all X_a (linord219039673up_add(X_a)->ti(X_a,zero_zero(X_a))=zero_zero(X_a)). % 7.78/7.80 all X_a (ti(X_a,undefined(X_a))=undefined(X_a)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 all B_1_1 (zprime(ti(int,B_1_1))<->zprime(B_1_1)). % 7.78/7.80 all B_1_1 (bit0(ti(int,B_1_1))=bit0(B_1_1)). % 7.78/7.80 all B_1_1 (ti(int,bit0(B_1_1))=bit0(B_1_1)). % 7.78/7.80 all B_1_1 (bit1(ti(int,B_1_1))=bit1(B_1_1)). % 7.78/7.80 all B_1_1 (ti(int,bit1(B_1_1))=bit1(B_1_1)). % 7.78/7.80 ti(int,min)=min. % 7.78/7.80 ti(int,pls)=pls. % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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))). % 7.78/7.80 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))). % 7.78/7.80 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))). % 7.78/7.80 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))). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 all B_1_1 B_2_1 (product_Pair(int,int,ti(int,B_1_1),B_2_1)=product_Pair(int,int,B_1_1,B_2_1)). % 7.78/7.80 all B_1_1 B_2_1 (product_Pair(int,int,B_1_1,ti(int,B_2_1))=product_Pair(int,int,B_1_1,B_2_1)). % 7.78/7.80 all B_1_1 B_2_1 (ti(product_prod(int,int),product_Pair(int,int,B_1_1,B_2_1))=product_Pair(int,int,B_1_1,B_2_1)). % 7.78/7.80 all B_1_1 B_2_1 (legendre(ti(int,B_1_1),B_2_1)=legendre(B_1_1,B_2_1)). % 7.78/7.80 all B_1_1 B_2_1 (legendre(B_1_1,ti(int,B_2_1))=legendre(B_1_1,B_2_1)). % 7.78/7.80 all B_1_1 B_2_1 (ti(int,legendre(B_1_1,B_2_1))=legendre(B_1_1,B_2_1)). % 7.78/7.80 all B_1_1 B_2_1 (quadRes(ti(int,B_1_1),B_2_1)<->quadRes(B_1_1,B_2_1)). % 7.78/7.80 all B_1_1 B_2_1 (quadRes(B_1_1,ti(int,B_2_1))<->quadRes(B_1_1,B_2_1)). % 7.78/7.80 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))). % 7.78/7.80 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))). % 7.78/7.80 all B_1_1 (twoSqu420862341sum2sq(ti(int,B_1_1))<->twoSqu420862341sum2sq(B_1_1)). % 7.78/7.80 all B_1_1 (twoSqu579703163sum2sq(ti(product_prod(int,int),B_1_1))=twoSqu579703163sum2sq(B_1_1)). % 7.78/7.80 all B_1_1 (ti(int,twoSqu579703163sum2sq(B_1_1))=twoSqu579703163sum2sq(B_1_1)). % 7.78/7.80 ti(int,m)=m. % 7.78/7.80 ti(int,s1)=s1. % 7.78/7.80 ti(int,s)=s. % 7.78/7.80 ti(int,t)=t. % 7.78/7.80 ord_less_e_q(int,one_one(int),t). % 7.78/7.80 t=one_one(int)-> (exists X Y (plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,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)))). % 7.78/7.80 ord_less(int,one_one(int),t)-> (exists X Y (plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,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)))). % 7.78/7.80 ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))). % 7.78/7.80 zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))). % 7.78/7.80 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). % 7.78/7.80 twoSqu420862341sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)). % 7.78/7.80 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)))))). % 7.78/7.80 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)))))). % 7.78/7.80 all X_a (number_semiring(X_a)-> (all X_1 Y_1 (power_power(X_a,plus_plus(X_a,X_1,Y_1),number_number_of(nat,bit0(bit1(pls))))=plus_plus(X_a,plus_plus(X_a,power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_1,number_number_of(nat,bit0(bit1(pls))))),times_times(X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),X_1),Y_1))))). % 7.78/7.80 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))))). % 7.78/7.80 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))))). % 7.78/7.80 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)). % 7.78/7.80 all X_a (comm_semiring_1(X_a)-> (all X_1 (times_times(X_a,X_1,X_1)=power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls))))))). % 7.78/7.80 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)))). % 7.78/7.80 all X_a (comm_semiring_1(X_a)-> (all X_1 N (power_power(X_a,X_1,times_times(nat,number_number_of(nat,bit0(bit1(pls))),N))=times_times(X_a,power_power(X_a,X_1,N),power_power(X_a,X_1,N))))). % 7.78/7.80 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))))). % 7.78/7.80 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)))))). % 7.78/7.80 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)))). % 7.78/7.80 -(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))). % 7.78/7.80 all W ord_less_e_q(int,W,W). % 7.78/7.80 all Z W (ord_less_e_q(int,Z,W)|ord_less_e_q(int,W,Z)). % 7.78/7.80 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)). % 7.78/7.80 all X_1 Y_1 (ord_less(int,X_1,Y_1)|ti(int,X_1)=ti(int,Y_1)|ord_less(int,Y_1,X_1)). % 7.78/7.80 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))). % 7.78/7.80 all Z W (ord_less_e_q(int,Z,W)-> (ord_less_e_q(int,W,Z)->ti(int,Z)=ti(int,W))). % 7.78/7.80 all X_a (comm_semiring_1(X_a)-> (all X_1 P Q (power_power(X_a,power_power(X_a,X_1,P),Q)=power_power(X_a,X_1,times_times(nat,P,Q))))). % 7.78/7.80 all X_a (comm_semiring_1(X_a)-> (all X_1 (power_power(X_a,X_1,one_one(nat))=ti(X_a,X_1)))). % 7.78/7.80 all X_1 Y_1 Z (power_power(int,power_power(int,X_1,Y_1),Z)=power_power(int,X_1,times_times(nat,Y_1,Z))). % 7.78/7.80 all X_a (number(X_a)&linorder(X_a)-> (all V_2 W_1 (ord_less_e_q(X_a,number_number_of(X_a,V_2),number_number_of(X_a,W_1))<-> -ord_less(X_a,number_number_of(X_a,W_1),number_number_of(X_a,V_2))))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 all X_a (comm_semiring_1(X_a)-> (all X_1 P Q (times_times(X_a,power_power(X_a,X_1,P),power_power(X_a,X_1,Q))=power_power(X_a,X_1,plus_plus(nat,P,Q))))). % 7.78/7.80 all X_1 Y_1 Z (power_power(int,X_1,plus_plus(nat,Y_1,Z))=times_times(int,power_power(int,X_1,Y_1),power_power(int,X_1,Z))). % 7.78/7.80 all Z (times_times(nat,number_number_of(nat,bit0(bit1(pls))),Z)=plus_plus(nat,Z,Z)). % 7.78/7.80 all Z (times_times(nat,Z,number_number_of(nat,bit0(bit1(pls))))=plus_plus(nat,Z,Z)). % 7.78/7.80 plus_plus(nat,one_one(nat),one_one(nat))=number_number_of(nat,bit0(bit1(pls))). % 7.78/7.80 all K1 K2 (ord_less(int,bit1(K1),bit1(K2))<->ord_less(int,K1,K2)). % 7.78/7.80 all K_1 L_1 (ord_less(int,bit1(K_1),bit1(L_1))<->ord_less(int,K_1,L_1)). % 7.78/7.80 all K1 K2 (ord_less_e_q(int,bit1(K1),bit1(K2))<->ord_less_e_q(int,K1,K2)). % 7.78/7.80 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)). % 7.78/7.80 -ord_less(int,pls,pls). % 7.78/7.80 all K1 K2 (ord_less(int,bit0(K1),bit0(K2))<->ord_less(int,K1,K2)). % 7.78/7.80 all K_1 L_1 (ord_less(int,bit0(K_1),bit0(L_1))<->ord_less(int,K_1,L_1)). % 7.78/7.80 ord_less_e_q(int,pls,pls). % 7.78/7.80 all K1 K2 (ord_less_e_q(int,bit0(K1),bit0(K2))<->ord_less_e_q(int,K1,K2)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 all K I J (ord_less(int,I,J)->ord_less(int,plus_plus(int,I,K),plus_plus(int,J,K))). % 7.78/7.80 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))). % 7.78/7.80 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))))). % 7.78/7.80 number_number_of(nat,bit1(pls))=one_one(nat). % 7.78/7.80 one_one(nat)=number_number_of(nat,bit1(pls)). % 7.78/7.80 all K_1 (ord_less_e_q(int,bit1(K_1),pls)<->ord_less(int,K_1,pls)). % 7.78/7.80 all K_1 (ord_less(int,pls,bit1(K_1))<->ord_less_e_q(int,pls,K_1)). % 7.78/7.80 all K1 K2 (ord_less_e_q(int,bit1(K1),bit0(K2))<->ord_less(int,K1,K2)). % 7.78/7.80 all K_1 L_1 (ord_less_e_q(int,bit1(K_1),bit0(L_1))<->ord_less(int,K_1,L_1)). % 7.78/7.80 all K1 K2 (ord_less(int,bit0(K1),bit1(K2))<->ord_less_e_q(int,K1,K2)). % 7.78/7.80 all K_1 L_1 (ord_less(int,bit0(K_1),bit1(L_1))<->ord_less_e_q(int,K_1,L_1)). % 7.78/7.80 all W Z (ord_less(int,W,Z)->ord_less_e_q(int,plus_plus(int,W,one_one(int)),Z)). % 7.78/7.80 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)). % 7.78/7.80 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)). % 7.78/7.80 zprime(number_number_of(int,bit0(bit1(pls)))). % 7.78/7.80 all Y_1 X_1 (twoSqu420862341sum2sq(X_1)-> (twoSqu420862341sum2sq(Y_1)->twoSqu420862341sum2sq(times_times(int,X_1,Y_1)))). % 7.78/7.80 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))))). % 7.78/7.80 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))))). % 7.78/7.80 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)))))). % 7.78/7.80 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)))). % 7.78/7.80 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))))). % 7.78/7.80 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)))). % 7.78/7.80 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))))). % 7.78/7.80 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)))). % 7.78/7.80 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))))). % 7.78/7.80 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)))). % 7.78/7.80 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))))). % 7.78/7.80 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)))). % 7.78/7.80 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))))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 all K_1 L_1 (bit1(K_1)=bit1(L_1)<->ti(int,K_1)=ti(int,L_1)). % 7.78/7.80 all K_1 L_1 (bit0(K_1)=bit0(L_1)<->ti(int,K_1)=ti(int,L_1)). % 7.78/7.80 all Z1 Z2 Z3 (times_times(int,times_times(int,Z1,Z2),Z3)=times_times(int,Z1,times_times(int,Z2,Z3))). % 7.78/7.80 all Z W (times_times(int,Z,W)=times_times(int,W,Z)). % 7.78/7.80 all K (number_number_of(int,K)=ti(int,K)). % 7.78/7.80 all Z1 Z2 Z3 (plus_plus(int,plus_plus(int,Z1,Z2),Z3)=plus_plus(int,Z1,plus_plus(int,Z2,Z3))). % 7.78/7.80 all X_1 Y_1 Z (plus_plus(int,X_1,plus_plus(int,Y_1,Z))=plus_plus(int,Y_1,plus_plus(int,X_1,Z))). % 7.78/7.80 all Z W (plus_plus(int,Z,W)=plus_plus(int,W,Z)). % 7.78/7.80 all K_1 (ord_less(int,bit1(K_1),pls)<->ord_less(int,K_1,pls)). % 7.78/7.80 all K1 K2 (ord_less(int,bit1(K1),bit0(K2))<->ord_less(int,K1,K2)). % 7.78/7.80 all K_1 L_1 (ord_less(int,bit1(K_1),bit0(L_1))<->ord_less(int,K_1,L_1)). % 7.78/7.80 all K_1 (ord_less(int,bit0(K_1),pls)<->ord_less(int,K_1,pls)). % 7.78/7.80 all K_1 (ord_less(int,pls,bit0(K_1))<->ord_less(int,pls,K_1)). % 7.78/7.80 all K_1 (ord_less_e_q(int,pls,bit1(K_1))<->ord_less_e_q(int,pls,K_1)). % 7.78/7.80 all K1 K2 (ord_less_e_q(int,bit0(K1),bit1(K2))<->ord_less_e_q(int,K1,K2)). % 7.78/7.80 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)). % 7.78/7.80 all K_1 (ord_less_e_q(int,bit0(K_1),pls)<->ord_less_e_q(int,K_1,pls)). % 7.78/7.80 all K_1 (ord_less_e_q(int,pls,bit0(K_1))<->ord_less_e_q(int,pls,K_1)). % 7.78/7.80 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)). % 7.78/7.80 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))))))). % 7.78/7.80 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))))). % 7.78/7.80 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)))). % 7.78/7.80 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))))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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))))). % 7.78/7.80 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))))). % 7.78/7.80 all X_a (comm_semiring_1(X_a)-> (all X_1 Y_1 Z (times_times(X_a,X_1,plus_plus(X_a,Y_1,Z))=plus_plus(X_a,times_times(X_a,X_1,Y_1),times_times(X_a,X_1,Z))))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 all X_a (comm_semiring_1(X_a)-> (all X_1 Y_1 Q (power_power(X_a,times_times(X_a,X_1,Y_1),Q)=times_times(X_a,power_power(X_a,X_1,Q),power_power(X_a,Y_1,Q))))). % 7.78/7.80 all K (bit1(K)!=pls). % 7.78/7.80 all L (pls!=bit1(L)). % 7.78/7.80 all K L (bit1(K)!=bit0(L)). % 7.78/7.80 all K L (bit0(K)!=bit1(L)). % 7.78/7.80 all K_1 (bit0(K_1)=pls<->ti(int,K_1)=pls). % 7.78/7.80 all L_1 (pls=bit0(L_1)<->pls=ti(int,L_1)). % 7.78/7.80 bit0(pls)=pls. % 7.78/7.80 all W (times_times(int,pls,W)=pls). % 7.78/7.80 all K L (times_times(int,bit0(K),L)=bit0(times_times(int,K,L))). % 7.78/7.80 all K (plus_plus(int,K,pls)=ti(int,K)). % 7.78/7.80 all K (plus_plus(int,pls,K)=ti(int,K)). % 7.78/7.80 all K L (plus_plus(int,bit0(K),bit0(L))=bit0(plus_plus(int,K,L))). % 7.78/7.80 all K (bit0(K)=plus_plus(int,K,K)). % 7.78/7.80 all Z (times_times(int,Z,one_one(int))=ti(int,Z)). % 7.78/7.80 all Z (times_times(int,one_one(int),Z)=ti(int,Z)). % 7.78/7.80 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))). % 7.78/7.80 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))). % 7.78/7.80 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))). % 7.78/7.80 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))). % 7.78/7.80 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)))))). % 7.78/7.80 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)))))). % 7.78/7.80 all X_1 ord_less_e_q(int,X_1,power_power(int,X_1,number_number_of(nat,bit0(bit1(pls))))). % 7.78/7.80 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)))))). % 7.78/7.80 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))))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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))))). % 7.78/7.80 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))))). % 7.78/7.80 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)))). % 7.78/7.80 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))))). % 7.78/7.80 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))))). % 7.78/7.80 all K L (plus_plus(int,bit1(K),bit0(L))=bit1(plus_plus(int,K,L))). % 7.78/7.80 all K L (plus_plus(int,bit0(K),bit1(L))=bit1(plus_plus(int,K,L))). % 7.78/7.80 all K (bit1(K)=plus_plus(int,plus_plus(int,one_one(int),K),K)). % 7.78/7.80 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))))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 all X_a (number_semiring(X_a)->number_number_of(X_a,bit1(pls))=one_one(X_a)). % 7.78/7.80 all X_a (number_ring(X_a)->number_number_of(X_a,bit1(pls))=one_one(X_a)). % 7.78/7.80 all X_a (number_ring(X_a)->one_one(X_a)=number_number_of(X_a,bit1(pls))). % 7.78/7.80 one_one(int)=number_number_of(int,bit1(pls)). % 7.78/7.80 all K L (times_times(int,bit1(K),L)=plus_plus(int,bit0(times_times(int,K,L)),L)). % 7.78/7.80 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))))). % 7.78/7.80 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)))). % 7.78/7.80 all X_1 (power_power(int,power_power(int,X_1,number_number_of(nat,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls))))=power_power(int,X_1,number_number_of(nat,bit0(bit0(bit1(pls)))))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))). % 7.78/7.80 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))). % 7.78/7.80 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)))). % 7.78/7.80 twoSqu579703163sum2sq(product_Pair(int,int,s,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). % 7.78/7.80 all X_1 Y_1 (power_power(real,plus_plus(real,X_1,Y_1),number_number_of(nat,bit0(bit1(pls))))=plus_plus(real,plus_plus(real,power_power(real,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(real,Y_1,number_number_of(nat,bit0(bit1(pls))))),times_times(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X_1),Y_1))). % 7.78/7.80 all X_1 (times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,X_1,number_number_of(nat,bit0(bit1(pls)))))=power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X_1),number_number_of(nat,bit0(bit1(pls))))). % 7.78/7.80 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)))))). % 7.78/7.80 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)))))). % 7.78/7.80 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))))). % 7.78/7.80 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))))). % 7.78/7.80 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))). % 7.78/7.80 ord_less_e_q(int,zero_zero(int),s). % 7.78/7.80 ord_less(int,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))). % 7.78/7.80 zcong(s1,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))). % 7.78/7.80 exists X (ord_less_e_q(int,zero_zero(int),X)&ord_less(int,X,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))&zcong(s1,X,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))& (all Y (ord_less_e_q(int,zero_zero(int),Y)&ord_less(int,Y,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))&zcong(s1,Y,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))->ti(int,Y)=ti(int,X)))). % 7.78/7.80 -(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)))))). % 7.78/7.80 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))). % 7.78/7.80 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)))). % 7.78/7.80 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))))). % 7.78/7.80 all X_a (comm_semiring_1(X_a)-> (all N M X_1 Y_1 (dvd_dvd(X_a,X_1,Y_1)-> (ord_less_e_q(nat,N,M)->dvd_dvd(X_a,power_power(X_a,X_1,N),power_power(X_a,Y_1,M)))))). % 7.78/7.80 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))))). % 7.78/7.80 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))))))). % 7.78/7.80 all N M (ord_less(int,zero_zero(int),M)-> (ord_less(int,M,N)-> -dvd_dvd(int,N,M))). % 7.78/7.80 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))))). % 7.78/7.80 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))). % 7.78/7.80 all X_a (comm_semiring_1(X_a)-> (all N X_1 Y_1 (dvd_dvd(X_a,X_1,Y_1)->dvd_dvd(X_a,power_power(X_a,X_1,N),power_power(X_a,Y_1,N))))). % 7.78/7.80 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)))). % 7.78/7.80 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))))). % 7.78/7.80 all Z N (dvd_dvd(int,Z,N)-> (ord_less(int,zero_zero(int),N)->ord_less_e_q(int,Z,N))). % 7.78/7.80 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))))))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 pls=zero_zero(int). % 7.78/7.80 zero_zero(int)!=one_one(int). % 7.78/7.80 all Z (plus_plus(int,zero_zero(int),Z)=ti(int,Z)). % 7.78/7.80 all Z (plus_plus(int,Z,zero_zero(int))=ti(int,Z)). % 7.78/7.80 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))))). % 7.78/7.80 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)))))). % 7.78/7.80 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))))). % 7.78/7.80 all Z X_1 Y_1 P (zcong(power_power(int,X_1,Y_1),one_one(int),P)->zcong(power_power(int,X_1,times_times(nat,Y_1,Z)),one_one(int),P)). % 7.78/7.80 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)). % 7.78/7.80 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)))). % 7.78/7.80 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))))). % 7.78/7.80 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))))))). % 7.78/7.80 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))))))). % 7.78/7.80 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))))). % 7.78/7.80 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)))). % 7.78/7.80 all X_a (semiri456707255roduct(X_a)-> (all C D A_1 B R_1 (ti(X_a,R_1)!=zero_zero(X_a)-> (ti(X_a,A_1)=ti(X_a,B)&ti(X_a,C)!=ti(X_a,D)->plus_plus(X_a,A_1,times_times(X_a,R_1,C))!=plus_plus(X_a,B,times_times(X_a,R_1,D)))))). % 7.78/7.80 all A_1 N P (zprime(P)-> (dvd_dvd(int,P,power_power(int,A_1,N))->dvd_dvd(int,P,A_1))). % 7.78/7.80 all X_a (number_ring(X_a)->zero_zero(X_a)=number_number_of(X_a,pls)). % 7.78/7.80 all X_a (number_ring(X_a)->number_number_of(X_a,pls)=zero_zero(X_a)). % 7.78/7.80 all X_a (number_semiring(X_a)->number_number_of(X_a,pls)=zero_zero(X_a)). % 7.78/7.80 all W_1 (ord_less(int,bit1(W_1),zero_zero(int))<->ord_less(int,W_1,zero_zero(int))). % 7.78/7.80 -ord_less(int,pls,zero_zero(int)). % 7.78/7.80 all W_1 (ord_less(int,bit0(W_1),zero_zero(int))<->ord_less(int,W_1,zero_zero(int))). % 7.78/7.80 zero_zero(int)=number_number_of(int,pls). % 7.78/7.80 ord_less(int,zero_zero(int),one_one(int)). % 7.78/7.80 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))). % 7.78/7.80 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)))). % 7.78/7.80 all Z (plus_plus(int,plus_plus(int,one_one(int),Z),Z)!=zero_zero(int)). % 7.78/7.80 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)))))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 all X_a (linordered_ring(X_a)-> (all X_1 Y_1 ord_less_e_q(X_a,zero_zero(X_a),plus_plus(X_a,times_times(X_a,X_1,X_1),times_times(X_a,Y_1,Y_1))))). % 7.78/7.80 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)))). % 7.78/7.80 all V_2 V_3 (ord_less(nat,number_number_of(nat,V_2),number_number_of(nat,V_3))<-> (ord_less(int,V_2,V_3)->ord_less(int,pls,V_3))&ord_less(int,V_2,V_3)). % 7.78/7.80 all X_a (linordered_ring(X_a)-> (all X_1 Y_1 (-ord_less(X_a,plus_plus(X_a,times_times(X_a,X_1,X_1),times_times(X_a,Y_1,Y_1)),zero_zero(X_a))))). % 7.78/7.80 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)))). % 7.78/7.80 all V_2 V_3 (ord_less_e_q(nat,number_number_of(nat,V_2),number_number_of(nat,V_3))<-> (-ord_less_e_q(int,V_2,V_3)->ord_less_e_q(int,V_2,pls))). % 7.78/7.80 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))))). % 7.78/7.80 all X_a (monoid_mult(X_a)-> (all A_1 (power_power(X_a,A_1,one_one(nat))=ti(X_a,A_1)))). % 7.78/7.80 all Z_1 (ord_less_e_q(int,one_one(int),Z_1)<->ord_less(int,zero_zero(int),Z_1)). % 7.78/7.80 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))). % 7.78/7.80 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))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 all Z (ord_less_e_q(int,zero_zero(int),Z)->ord_less(int,zero_zero(int),plus_plus(int,one_one(int),Z))). % 7.78/7.80 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)). % 7.78/7.80 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)))). % 7.78/7.80 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))))))). % 7.78/7.80 all X_a (linordered_semidom(X_a)-> (all X_1 Y_1 (ord_less_e_q(X_a,power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_1,number_number_of(nat,bit0(bit1(pls)))))-> (ord_less_e_q(X_a,zero_zero(X_a),Y_1)->ord_less_e_q(X_a,X_1,Y_1))))). % 7.78/7.80 all X_a (linordered_semidom(X_a)-> (all X_1 Y_1 (power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls))))=power_power(X_a,Y_1,number_number_of(nat,bit0(bit1(pls))))-> (ord_less_e_q(X_a,zero_zero(X_a),X_1)-> (ord_less_e_q(X_a,zero_zero(X_a),Y_1)->ti(X_a,X_1)=ti(X_a,Y_1)))))). % 7.78/7.80 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))))). % 7.78/7.80 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)))). % 7.78/7.80 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)))). % 7.78/7.80 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))))). % 7.78/7.80 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))))). % 7.78/7.80 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))))). % 7.78/7.80 all X_a (monoid_mult(X_a)-> (all N (power_power(X_a,one_one(X_a),N)=one_one(X_a)))). % 7.78/7.80 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)))). % 7.78/7.80 all X_a (linordered_semidom(X_a)-> (all X_1 Y_1 (ord_less(X_a,power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_1,number_number_of(nat,bit0(bit1(pls)))))-> (ord_less_e_q(X_a,zero_zero(X_a),Y_1)->ord_less(X_a,X_1,Y_1))))). % 7.78/7.80 all X_a (linordered_idom(X_a)-> (all X_1 Y_1 ord_less_e_q(X_a,zero_zero(X_a),plus_plus(X_a,power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_1,number_number_of(nat,bit0(bit1(pls)))))))). % 7.78/7.80 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)))). % 7.78/7.80 all X_a (linordered_idom(X_a)-> (all X_1 Y_1 (-ord_less(X_a,plus_plus(X_a,power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_1,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X_a))))). % 7.78/7.80 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)))). % 7.78/7.80 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))))). % 7.78/7.81 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))))). % 7.78/7.81 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)))))). % 7.78/7.81 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)))). % 7.78/7.81 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))))). % 7.78/7.81 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))))). % 7.78/7.81 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)))))). % 7.78/7.81 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))). % 7.78/7.81 all Y_1 X_1 P (-zcong(X_1,zero_zero(int),P)-> (zcong(power_power(int,Y_1,number_number_of(nat,bit0(bit1(pls)))),X_1,P)-> -dvd_dvd(int,P,Y_1))). % 7.78/7.81 all X_1 (ord_less_e_q(int,zero_zero(int),X_1)-> (ord_less(int,X_1,number_number_of(int,bit0(bit1(pls))))->ti(int,X_1)=zero_zero(int)|ti(int,X_1)=one_one(int))). % 7.78/7.81 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)))). % 7.78/7.81 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)))). % 7.78/7.81 -(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))))). % 7.78/7.81 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). % 7.78/7.81 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)). % 7.78/7.81 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)). % 7.78/7.81 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)). % 7.78/7.81 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))). % 7.78/7.81 all K_1 (bit1(K_1)=min<->ti(int,K_1)=min). % 7.78/7.81 all L_1 (min=bit1(L_1)<->min=ti(int,L_1)). % 7.78/7.81 bit1(min)=min. % 7.78/7.81 pls!=min. % 7.78/7.81 min!=pls. % 7.78/7.81 all K (bit0(K)!=min). % 7.78/7.81 all L (min!=bit0(L)). % 7.78/7.81 -ord_less(int,min,min). % 7.78/7.81 ord_less_e_q(int,min,min). % 7.78/7.81 all X_2 (-ord_less(real,zero_zero(real),times_times(real,X_2,X_2))<->X_2=zero_zero(real)). % 7.78/7.81 all K_1 (ord_less(int,bit1(K_1),min)<->ord_less(int,K_1,min)). % 7.78/7.81 all K_1 (ord_less(int,min,bit1(K_1))<->ord_less(int,min,K_1)). % 7.78/7.81 -ord_less(int,pls,min). % 7.78/7.81 ord_less(int,min,pls). % 7.78/7.81 all K_1 (ord_less(int,min,bit0(K_1))<->ord_less(int,min,K_1)). % 7.78/7.81 ord_less(int,min,zero_zero(int)). % 7.78/7.81 all K_1 (ord_less_e_q(int,bit1(K_1),min)<->ord_less_e_q(int,K_1,min)). % 7.78/7.81 all K_1 (ord_less_e_q(int,min,bit1(K_1))<->ord_less_e_q(int,min,K_1)). % 7.78/7.81 -ord_less_e_q(int,pls,min). % 7.78/7.81 ord_less_e_q(int,min,pls). % 7.78/7.81 all K_1 (ord_less_e_q(int,bit0(K_1),min)<->ord_less_e_q(int,K_1,min)). % 7.78/7.81 number_number_of(int,pls)!=number_number_of(int,min). % 7.78/7.81 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))). % 7.78/7.81 all X_a (comm_semiring_1(X_a)-> (all X_1 (power_power(X_a,X_1,zero_zero(nat))=one_one(X_a)))). % 7.78/7.81 all X_a (power(X_a)-> (all A_1 (power_power(X_a,A_1,zero_zero(nat))=one_one(X_a)))). % 7.78/7.81 number_number_of(nat,pls)=zero_zero(nat). % 7.78/7.81 zero_zero(nat)=number_number_of(nat,pls). % 7.78/7.81 all K_1 (ord_less_e_q(int,min,bit0(K_1))<->ord_less(int,min,K_1)). % 7.78/7.81 all K_1 (ord_less(int,bit0(K_1),min)<->ord_less_e_q(int,K_1,min)). % 7.78/7.81 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)). % 7.78/7.81 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)). % 7.78/7.81 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)))))). % 7.78/7.81 all X_a (comm_semiring_1(X_a)-> (all X_1 N (ord_less(nat,zero_zero(nat),N)|ti(X_a,X_1)=one_one(X_a)->dvd_dvd(X_a,X_1,power_power(X_a,X_1,N))))). % 7.78/7.81 all V_2 (ord_less(nat,zero_zero(nat),number_number_of(nat,V_2))<->ord_less(int,pls,V_2)). % 7.78/7.81 all V_2 (number_number_of(nat,V_2)=zero_zero(nat)<->ord_less_e_q(int,V_2,pls)). % 7.78/7.81 all V_2 (zero_zero(nat)=number_number_of(nat,V_2)<->ord_less_e_q(int,V_2,pls)). % 7.78/7.81 all A_2 B_1 Ma (zcong(A_2,B_1,Ma)<->zcong(B_1,A_2,Ma)). % 7.78/7.81 all K M zcong(K,K,M). % 7.78/7.81 all C A_1 B M (zcong(A_1,B,M)-> (zcong(B,C,M)->zcong(A_1,C,M))). % 7.78/7.81 ord_less(nat,zero_zero(nat),number_number_of(nat,bit0(bit1(pls)))). % 7.78/7.81 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))). % 7.78/7.81 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)))). % 7.78/7.81 all X_a (order(X_a)-> (all X_1 Y_1 (ord_less_e_q(X_a,X_1,Y_1)-> (ti(X_a,X_1)!=ti(X_a,Y_1)->ord_less(X_a,X_1,Y_1))))). % 7.78/7.81 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))). % 7.78/7.81 all A_2 B_1 (zcong(A_2,B_1,zero_zero(int))<->ti(int,A_2)=ti(int,B_1)). % 7.78/7.81 all A_1 B zcong(A_1,B,one_one(int)). % 7.78/7.81 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))). % 7.78/7.81 all K A_1 B M (zcong(A_1,B,M)->zcong(times_times(int,K,A_1),times_times(int,K,B),M)). % 7.78/7.81 all K A_1 B M (zcong(A_1,B,M)->zcong(times_times(int,A_1,K),times_times(int,B,K),M)). % 7.78/7.81 all A_1 M B zcong(times_times(int,A_1,M),times_times(int,B,M),M). % 7.78/7.81 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))). % 7.78/7.81 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)))). % 7.78/7.81 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)))). % 7.78/7.81 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))))). % 7.78/7.81 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))))). % 7.78/7.81 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))))). % 7.78/7.81 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)))))). % 7.78/7.81 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)))). % 7.78/7.81 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)))). % 7.78/7.81 quadRes(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),number_number_of(int,min)). % 7.78/7.81 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))). % 7.78/7.81 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))). % 7.78/7.81 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)). % 7.78/7.81 -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). % 7.78/7.81 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))). % 7.78/7.81 all K (minus_minus(int,K,pls)=ti(int,K)). % 7.78/7.81 all K L (minus_minus(int,bit0(K),bit0(L))=bit0(minus_minus(int,K,L))). % 7.78/7.81 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))). % 7.78/7.81 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))). % 7.78/7.81 all K M N (dvd_dvd(int,K,minus_minus(int,M,N))-> (dvd_dvd(int,K,N)->dvd_dvd(int,K,M))). % 7.78/7.81 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))))). % 7.78/7.81 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))))). % 7.78/7.81 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)))))). % 7.78/7.81 all K L (minus_minus(int,bit1(K),bit0(L))=bit1(minus_minus(int,K,L))). % 7.78/7.81 all K L (minus_minus(int,bit1(K),bit1(L))=bit0(minus_minus(int,K,L))). % 7.78/7.81 all L (minus_minus(int,pls,bit0(L))=bit0(minus_minus(int,pls,L))). % 7.78/7.81 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))). % 7.78/7.81 all A_1 R_1 B M C D N (plus_plus(int,times_times(int,minus_minus(int,A_1,times_times(int,R_1,B)),M),times_times(int,minus_minus(int,C,times_times(int,R_1,D)),N))=minus_minus(int,plus_plus(int,times_times(int,A_1,M),times_times(int,C,N)),times_times(int,R_1,plus_plus(int,times_times(int,B,M),times_times(int,D,N))))). % 7.78/7.81 all A_2 B_1 Ma (zcong(A_2,B_1,Ma)<->dvd_dvd(int,Ma,minus_minus(int,A_2,B_1))). % 7.78/7.81 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)))). % 7.78/7.81 all A_1 X_1 (ord_less(int,zero_zero(int),X_1)-> (ord_less(int,X_1,A_1)-> (ti(int,X_1)!=minus_minus(int,A_1,one_one(int))->ord_less(int,X_1,minus_minus(int,A_1,one_one(int)))))). % 7.78/7.81 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)). % 7.78/7.81 all L (minus_minus(int,pls,bit1(L))=bit1(minus_minus(int,min,L))). % 7.78/7.81 all L (minus_minus(int,min,bit1(L))=bit0(minus_minus(int,min,L))). % 7.78/7.81 all L (minus_minus(int,min,bit0(L))=bit1(minus_minus(int,min,L))). % 7.78/7.81 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)). % 7.78/7.81 all A_1 B P Q (times_times(int,twoSqu579703163sum2sq(product_Pair(int,int,A_1,B)),twoSqu579703163sum2sq(product_Pair(int,int,P,Q)))=twoSqu579703163sum2sq(product_Pair(int,int,plus_plus(int,times_times(int,A_1,P),times_times(int,B,Q)),minus_minus(int,times_times(int,A_1,Q),times_times(int,B,P))))). % 7.78/7.81 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)))). % 7.78/7.81 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)))))). % 7.78/7.81 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)))))). % 7.78/7.81 all X_a (number_ring(X_a)-> (all X_1 Y_1 (power_power(X_a,minus_minus(X_a,X_1,Y_1),number_number_of(nat,bit0(bit1(pls))))=minus_minus(X_a,plus_plus(X_a,power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_1,number_number_of(nat,bit0(bit1(pls))))),times_times(X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),X_1),Y_1))))). % 7.78/7.81 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)))))). % 7.78/7.81 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)))))). % 7.78/7.81 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)). % 7.78/7.81 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)). % 7.78/7.81 all M (ord_less(int,number_number_of(int,bit0(bit1(pls))),M)-> -zcong(one_one(int),number_number_of(int,min),M)). % 7.78/7.81 all X_1 P (ord_less(int,number_number_of(int,bit0(bit1(pls))),P)-> (zcong(X_1,number_number_of(int,min),P)-> -zcong(X_1,one_one(int),P))). % 7.78/7.81 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)))). % 7.78/7.81 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)). % 7.78/7.81 all X_2 Y_2 (dvd_dvd(nat,X_2,Y_2)&dvd_dvd(nat,Y_2,X_2)<->X_2=Y_2). % 7.78/7.81 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)))). % 7.78/7.81 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)))). % 7.78/7.81 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)))))). % 7.78/7.81 all X_1 Y_1 (minus_minus(nat,power_power(nat,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(nat,Y_1,number_number_of(nat,bit0(bit1(pls)))))=times_times(nat,plus_plus(nat,X_1,Y_1),minus_minus(nat,X_1,Y_1))). % 7.78/7.81 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))). % 7.78/7.81 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))). % 7.78/7.81 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))). % 7.78/7.81 all M zcong(M,zero_zero(int),M). % 7.78/7.81 all N_1 Ma (times_times(nat,N_1,Ma)=one_one(nat)<->N_1=one_one(nat)&Ma=one_one(nat)). % 7.78/7.81 all A_1 B C (minus_minus(int,A_1,B)=ti(int,C)->ti(int,A_1)=plus_plus(int,C,B)). % 7.78/7.81 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))). % 7.78/7.81 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))). % 7.78/7.81 all C A_1 B M (zcong(A_1,B,M)->zcong(plus_plus(int,A_1,C),plus_plus(int,B,C),M)). % 7.78/7.81 all Ma N_1 (power_power(nat,Ma,N_1)=zero_zero(nat)<->N_1!=zero_zero(nat)&Ma=zero_zero(nat)). % 7.78/7.81 all N X_1 Y_1 (dvd_dvd(nat,X_1,Y_1)->dvd_dvd(nat,power_power(nat,X_1,N),power_power(nat,Y_1,N))). % 7.78/7.81 all Z X_1 Y_1 M (zcong(X_1,Y_1,M)->zcong(power_power(int,X_1,Z),power_power(int,Y_1,Z),M)). % 7.78/7.81 all A_1 B (dvd_dvd(nat,A_1,B)->B=zero_zero(nat)|ord_less_e_q(nat,A_1,B)). % 7.78/7.81 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)). % 7.78/7.81 all M X_1 (ord_less(int,zero_zero(int),X_1)-> (ord_less(int,X_1,M)-> -zcong(X_1,zero_zero(int),M))). % 7.78/7.81 all M Y_1 X_1 (ord_less(int,zero_zero(int),X_1)-> (ord_less(int,zero_zero(int),Y_1)-> (ord_less(int,zero_zero(int),M)-> (zcong(X_1,Y_1,M)-> (ord_less(int,X_1,M)-> (ord_less(int,Y_1,M)->ti(int,X_1)=ti(int,Y_1))))))). % 7.78/7.81 all N M (dvd_dvd(int,N,M)->ord_less_e_q(int,M,zero_zero(int))|ord_less_e_q(int,N,M)). % 7.78/7.81 all X_1 Y_1 N (N!=zero_zero(nat)-> (dvd_dvd(nat,power_power(nat,X_1,N),Y_1)->dvd_dvd(nat,X_1,Y_1))). % 7.78/7.81 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))). % 7.78/7.81 all A_2 Ma (zcong(A_2,zero_zero(int),Ma)<->dvd_dvd(int,Ma,A_2)). % 7.78/7.81 all X_2 P_1 (zcong(X_2,zero_zero(int),P_1)<->dvd_dvd(int,P_1,X_2)). % 7.78/7.81 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)). % 7.78/7.81 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))). % 7.78/7.81 all M X_1 (ord_less_e_q(int,zero_zero(int),X_1)-> (ord_less(int,X_1,M)-> (zcong(X_1,zero_zero(int),M)->ti(int,X_1)=zero_zero(int)))). % 7.78/7.81 all P Y_1 N (ord_less(nat,zero_zero(nat),N)-> (dvd_dvd(int,P,Y_1)->dvd_dvd(int,P,power_power(int,Y_1,N)))). % 7.78/7.81 all Y_1 X_1 P (zprime(P)-> (-zcong(X_1,zero_zero(int),P)-> (-zcong(Y_1,zero_zero(int),P)-> -zcong(times_times(int,X_1,Y_1),zero_zero(int),P)))). % 7.78/7.81 all X_1 Q N R_1 (X_1=plus_plus(nat,times_times(nat,Q,N),R_1)-> (ord_less(nat,zero_zero(nat),R_1)-> (ord_less(nat,R_1,N)-> -dvd_dvd(nat,N,X_1)))). % 7.78/7.81 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)))). % 7.78/7.81 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)))). % 7.78/7.81 all Y_1 N P (zprime(P)-> (dvd_dvd(int,P,power_power(int,Y_1,N))-> (ord_less(nat,zero_zero(nat),N)->dvd_dvd(int,P,Y_1)))). % 7.78/7.81 all Ma X_2 (quadRes(Ma,X_2)<-> (exists Y zcong(power_power(int,Y,number_number_of(nat,bit0(bit1(pls)))),X_2,Ma))). % 7.78/7.81 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)). % 7.78/7.81 all R_1 Q A_1 (ord_less(int,zero_zero(int),A_1)-> (ti(int,A_1)=plus_plus(int,R_1,times_times(int,A_1,Q))-> (ord_less(int,R_1,A_1)->ord_less_e_q(int,one_one(int),Q)))). % 7.78/7.81 zero_zero(real)!=one_one(real). % 7.78/7.81 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))). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 all Z (times_times(real,one_one(real),Z)=Z). % 7.78/7.81 all Z W (times_times(real,Z,W)=times_times(real,W,Z)). % 7.78/7.81 all Z1 Z2 Z3 (times_times(real,times_times(real,Z1,Z2),Z3)=times_times(real,Z1,times_times(real,Z2,Z3))). % 7.78/7.81 all Z X_1 Y_1 (ord_less_e_q(real,X_1,Y_1)->ord_less_e_q(real,plus_plus(real,Z,X_1),plus_plus(real,Z,Y_1))). % 7.78/7.81 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))))). % 7.78/7.81 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)). % 7.78/7.81 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)). % 7.78/7.81 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))). % 7.78/7.81 all X_a (ring(X_a)-> (all X_1 Y_1 A_1 B (minus_minus(X_a,times_times(X_a,X_1,Y_1),times_times(X_a,A_1,B))=plus_plus(X_a,times_times(X_a,X_1,minus_minus(X_a,Y_1,B)),times_times(X_a,minus_minus(X_a,X_1,A_1),B))))). % 7.78/7.81 all X_1 Y_1 Z (ord_less(real,zero_zero(real),Z)-> (ord_less(real,X_1,Y_1)->ord_less(real,times_times(real,Z,X_1),times_times(real,Z,Y_1)))). % 7.78/7.81 all Y_1 X_1 (ord_less(real,zero_zero(real),X_1)-> (ord_less(real,zero_zero(real),Y_1)->ord_less(real,zero_zero(real),times_times(real,X_1,Y_1)))). % 7.78/7.81 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))). % 7.78/7.81 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))). % 7.78/7.81 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))). % 7.78/7.81 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)). % 7.78/7.81 all X_a (ring_1(X_a)-> (all X_1 (minus_minus(X_a,times_times(X_a,X_1,X_1),one_one(X_a))=times_times(X_a,plus_plus(X_a,X_1,one_one(X_a)),minus_minus(X_a,X_1,one_one(X_a)))))). % 7.78/7.81 all X_a (monoid_mult(X_a)-> (all X_1 N (ord_less(nat,zero_zero(nat),N)->times_times(X_a,power_power(X_a,X_1,minus_minus(nat,N,one_one(nat))),X_1)=power_power(X_a,X_1,N)))). % 7.78/7.81 all N ord_less_e_q(real,one_one(real),power_power(real,number_number_of(real,bit0(bit1(pls))),N)). % 7.78/7.81 all B_2 Q_1 R_2 (ord_less_e_q(int,zero_zero(int),plus_plus(int,times_times(int,B_2,Q_1),R_2))-> (ord_less(int,R_2,B_2)-> (ord_less(int,zero_zero(int),B_2)->ord_less_e_q(int,zero_zero(int),Q_1)))). % 7.78/7.81 all B_2 Q_1 R_2 (ord_less(int,plus_plus(int,times_times(int,B_2,Q_1),R_2),zero_zero(int))-> (ord_less_e_q(int,zero_zero(int),R_2)-> (ord_less(int,zero_zero(int),B_2)->ord_less_e_q(int,Q_1,zero_zero(int))))). % 7.78/7.81 all B Q_1 R_2 Q R_1 (ord_less_e_q(int,plus_plus(int,times_times(int,B,Q_1),R_2),plus_plus(int,times_times(int,B,Q),R_1))-> (ord_less_e_q(int,zero_zero(int),R_2)-> (ord_less(int,R_2,B)-> (ord_less(int,R_1,B)->ord_less_e_q(int,Q_1,Q))))). % 7.78/7.81 all B Q R_1 B_2 Q_1 R_2 (plus_plus(int,times_times(int,B,Q),R_1)=plus_plus(int,times_times(int,B_2,Q_1),R_2)-> (ord_less_e_q(int,zero_zero(int),plus_plus(int,times_times(int,B_2,Q_1),R_2))-> (ord_less(int,R_2,B_2)-> (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,Q_1))))))). % 7.78/7.81 all B Q_1 R_2 Q R_1 (ord_less_e_q(int,plus_plus(int,times_times(int,B,Q_1),R_2),plus_plus(int,times_times(int,B,Q),R_1))-> (ord_less_e_q(int,R_1,zero_zero(int))-> (ord_less(int,B,R_1)-> (ord_less(int,B,R_2)->ord_less_e_q(int,Q,Q_1))))). % 7.78/7.81 all B Q R_1 B_2 Q_1 R_2 (plus_plus(int,times_times(int,B,Q),R_1)=plus_plus(int,times_times(int,B_2,Q_1),R_2)-> (ord_less(int,plus_plus(int,times_times(int,B_2,Q_1),R_2),zero_zero(int))-> (ord_less(int,R_1,B)-> (ord_less_e_q(int,zero_zero(int),R_2)-> (ord_less(int,zero_zero(int),B_2)-> (ord_less_e_q(int,B_2,B)->ord_less_e_q(int,Q_1,Q))))))). % 7.78/7.81 all R_1 Q A_1 (ord_less(int,zero_zero(int),A_1)-> (ti(int,A_1)=plus_plus(int,R_1,times_times(int,A_1,Q))-> (ord_less_e_q(int,zero_zero(int),R_1)->ord_less_e_q(int,Q,one_one(int))))). % 7.78/7.81 ord_less_e_q(int,zero_zero(int),number_number_of(int,bit0(bit1(pls)))). % 7.78/7.81 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)))))))). % 7.78/7.81 all Z W (ord_less_e_q(real,Z,W)-> (ord_less_e_q(real,W,Z)->Z=W)). % 7.78/7.81 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))). % 7.78/7.81 all Z W (ord_less_e_q(real,Z,W)|ord_less_e_q(real,W,Z)). % 7.78/7.81 all W ord_less_e_q(real,W,W). % 7.78/7.81 ord_less_e_q(int,zero_zero(int),zero_zero(int)). % 7.78/7.81 ord_less_e_q(int,zero_zero(int),one_one(int)). % 7.78/7.81 all Y_1 X_1 (ord_less_e_q(int,zero_zero(int),X_1)-> (ord_less_e_q(int,zero_zero(int),Y_1)->ord_less_e_q(int,zero_zero(int),times_times(int,X_1,Y_1)))). % 7.78/7.81 all Y_1 X_1 (ord_less_e_q(int,zero_zero(int),X_1)-> (ord_less_e_q(int,zero_zero(int),Y_1)->ord_less_e_q(int,zero_zero(int),plus_plus(int,X_1,Y_1)))). % 7.78/7.81 all N X_1 (ord_less_e_q(int,zero_zero(int),X_1)->ord_less_e_q(int,zero_zero(int),power_power(int,X_1,N))). % 7.78/7.81 ord_less_e_q(int,zero_zero(int),number_number_of(int,bit1(bit1(pls)))). % 7.78/7.81 all X_a (linord626643107strict(X_a)-> (all V U Y_1 X_1 A_1 (ord_less(X_a,X_1,A_1)-> (ord_less(X_a,Y_1,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_1),times_times(X_a,V,Y_1)),A_1)))))))). % 7.78/7.81 all A_1 N (ord_less(nat,zero_zero(nat),N)-> (ord_less(real,zero_zero(real),A_1)-> (exists R (ord_less(real,zero_zero(real),R)&power_power(real,R,N)=A_1)))). % 7.78/7.81 all X_a (comm_semiring_1(X_a)-> (all A_1 dvd_dvd(X_a,A_1,zero_zero(X_a)))). % 7.78/7.81 all X_a (linordered_idom(X_a)-> (all X_1 Y_1 (ti(X_a,X_1)!=ti(X_a,Y_1)-> (-ord_less(X_a,X_1,Y_1)->ord_less(X_a,Y_1,X_1))))). % 7.78/7.81 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))))). % 7.78/7.81 all X_a (comm_semiring_1(X_a)-> (all A_1 dvd_dvd(X_a,A_1,A_1))). % 7.78/7.81 all X_a (mult_zero(X_a)-> (all A_1 (times_times(X_a,zero_zero(X_a),A_1)=zero_zero(X_a)))). % 7.78/7.81 all X_a (mult_zero(X_a)-> (all A_1 (times_times(X_a,A_1,zero_zero(X_a))=zero_zero(X_a)))). % 7.78/7.81 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)))). % 7.78/7.81 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))))). % 7.78/7.81 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)))). % 7.78/7.81 all X_a (zero_ne_q_one(X_a)->one_one(X_a)!=zero_zero(X_a)). % 7.78/7.81 all X_a (zero_ne_q_one(X_a)->zero_zero(X_a)!=one_one(X_a)). % 7.78/7.81 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))))). % 7.78/7.81 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)))). % 7.78/7.81 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)))). % 7.78/7.81 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)))). % 7.78/7.81 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)))). % 7.78/7.81 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))))). % 7.78/7.81 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))))). % 7.78/7.81 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)))))). % 7.78/7.81 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)))). % 7.78/7.81 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)))). % 7.78/7.81 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)))). % 7.78/7.81 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)))))). % 7.78/7.81 all X_a (comm_semiring_1(X_a)-> (all A_1 dvd_dvd(X_a,one_one(X_a),A_1))). % 7.78/7.81 all X_a (comm_ring_1(X_a)-> (all Z X_1 Y_1 (dvd_dvd(X_a,X_1,Y_1)-> (dvd_dvd(X_a,X_1,Z)->dvd_dvd(X_a,X_1,minus_minus(X_a,Y_1,Z)))))). % 7.78/7.81 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)))). % 7.78/7.81 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))))). % 7.78/7.81 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)))). % 7.78/7.81 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)))))). % 7.78/7.81 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)))))). % 7.78/7.81 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)))))). % 7.78/7.81 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)))))). % 7.78/7.81 semiri456707255roduct(int). % 7.78/7.81 linord626643107strict(int). % 7.78/7.81 linord219039673up_add(int). % 7.78/7.81 ring_11004092258visors(int). % 7.78/7.81 ordere453448008miring(int). % 7.78/7.81 linord581940658strict(int). % 7.78/7.81 ring_n68954251visors(int). % 7.78/7.81 linordered_semidom(int). % 7.78/7.81 comm_monoid_mult(int). % 7.78/7.81 no_zero_divisors(int). % 7.78/7.81 linordered_ring(int). % 7.78/7.81 linordered_idom(int). % 7.78/7.81 comm_semiring_1(int). % 7.78/7.81 comm_semiring(int). % 7.78/7.81 number_semiring(int). % 7.78/7.81 ab_group_add(int). % 7.78/7.81 zero_ne_q_one(int). % 7.78/7.81 linorder(int). % 7.78/7.81 monoid_mult(int). % 7.78/7.81 comm_ring_1(int). % 7.78/7.81 semiring_1(int). % 7.78/7.81 semiring_0(int). % 7.78/7.81 mult_zero(int). % 7.78/7.81 order(int). % 7.78/7.81 ring_char_0(int). % 7.78/7.81 number_ring(int). % 7.78/7.81 semiring(int). % 7.78/7.81 ring_1(int). % 7.78/7.81 power(int). % 7.78/7.81 ring(int). % 7.78/7.81 number(int). % 7.78/7.81 dvd(int). % 7.78/7.81 semiri456707255roduct(nat). % 7.78/7.81 ordere453448008miring(nat). % 7.78/7.81 linordered_semidom(nat). % 7.78/7.81 comm_monoid_mult(nat). % 7.78/7.81 no_zero_divisors(nat). % 7.78/7.81 comm_semiring_1(nat). % 7.78/7.81 comm_semiring(nat). % 7.78/7.81 number_semiring(nat). % 7.78/7.81 zero_ne_q_one(nat). % 7.78/7.81 linorder(nat). % 7.78/7.81 monoid_mult(nat). % 7.78/7.81 semiring_1(nat). % 7.78/7.81 semiring_0(nat). % 7.78/7.81 mult_zero(nat). % 7.78/7.81 order(nat). % 7.78/7.81 semiring(nat). % 7.78/7.81 power(nat). % 7.78/7.81 number(nat). % 7.78/7.81 dvd(nat). % 7.78/7.81 order(bool). % 7.78/7.81 semiri456707255roduct(real). % 7.78/7.81 linord626643107strict(real). % 7.78/7.81 linord219039673up_add(real). % 7.78/7.81 ring_11004092258visors(real). % 7.78/7.81 ordere453448008miring(real). % 7.78/7.81 linord581940658strict(real). % 7.78/7.81 ring_n68954251visors(real). % 7.78/7.81 linordered_semidom(real). % 7.78/7.81 comm_monoid_mult(real). % 7.78/7.81 no_zero_divisors(real). % 7.78/7.81 linordered_ring(real). % 7.78/7.81 linordered_idom(real). % 7.78/7.81 comm_semiring_1(real). % 7.78/7.81 comm_semiring(real). % 7.78/7.81 number_semiring(real). % 7.78/7.81 ab_group_add(real). % 7.78/7.81 zero_ne_q_one(real). % 7.78/7.81 linorder(real). % 7.78/7.81 monoid_mult(real). % 7.78/7.81 comm_ring_1(real). % 7.78/7.81 semiring_1(real). % 7.78/7.81 semiring_0(real). % 7.78/7.81 mult_zero(real). % 7.78/7.81 order(real). % 7.78/7.81 ring_char_0(real). % 7.78/7.81 number_ring(real). % 7.78/7.81 semiring(real). % 7.78/7.81 ring_1(real). % 7.78/7.81 power(real). % 7.78/7.81 ring(real). % 7.78/7.81 number(real). % 7.78/7.81 dvd(real). % 7.78/7.81 all T A (ti(T,ti(T,A))=ti(T,A)). % 7.78/7.81 -(exists X Y (plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,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)))). % 7.78/7.81 end_of_list. % 7.78/7.81 % 7.78/7.81 -------> usable clausifies to: % 7.78/7.81 % 7.78/7.81 list(usable). % 7.78/7.81 0 [] A=A. % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 0 [] minus_minus(nat,ti(nat,B_1_1),B_2_1)=minus_minus(nat,B_1_1,B_2_1). % 7.78/7.81 0 [] minus_minus(nat,B_1_1,ti(nat,B_2_1))=minus_minus(nat,B_1_1,B_2_1). % 7.78/7.81 0 [] ti(nat,minus_minus(nat,B_1_1,B_2_1))=minus_minus(nat,B_1_1,B_2_1). % 7.78/7.81 0 [] -zero_ne_q_one(X_a)|ti(X_a,one_one(X_a))=one_one(X_a). % 7.78/7.81 0 [] -power(X_a)|ti(X_a,one_one(X_a))=one_one(X_a). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 0 [] -zero_ne_q_one(X_a)|ti(X_a,zero_zero(X_a))=zero_zero(X_a). % 7.78/7.81 0 [] -no_zero_divisors(X_a)|ti(X_a,zero_zero(X_a))=zero_zero(X_a). % 7.78/7.81 0 [] -mult_zero(X_a)|ti(X_a,zero_zero(X_a))=zero_zero(X_a). % 7.78/7.81 0 [] -linord219039673up_add(X_a)|ti(X_a,zero_zero(X_a))=zero_zero(X_a). % 7.78/7.81 0 [] ti(X_a,undefined(X_a))=undefined(X_a). % 7.78/7.81 0 [] -zcong(ti(int,B_1_1),B_2_1,B_3)|zcong(B_1_1,B_2_1,B_3). % 7.78/7.81 0 [] zcong(ti(int,B_1_1),B_2_1,B_3)| -zcong(B_1_1,B_2_1,B_3). % 7.78/7.81 0 [] -zcong(B_1_1,ti(int,B_2_1),B_3)|zcong(B_1_1,B_2_1,B_3). % 7.78/7.81 0 [] zcong(B_1_1,ti(int,B_2_1),B_3)| -zcong(B_1_1,B_2_1,B_3). % 7.78/7.81 0 [] -zcong(B_1_1,B_2_1,ti(int,B_3))|zcong(B_1_1,B_2_1,B_3). % 7.78/7.81 0 [] zcong(B_1_1,B_2_1,ti(int,B_3))| -zcong(B_1_1,B_2_1,B_3). % 7.78/7.81 0 [] -zprime(ti(int,B_1_1))|zprime(B_1_1). % 7.78/7.81 0 [] zprime(ti(int,B_1_1))| -zprime(B_1_1). % 7.78/7.81 0 [] bit0(ti(int,B_1_1))=bit0(B_1_1). % 7.78/7.81 0 [] ti(int,bit0(B_1_1))=bit0(B_1_1). % 7.78/7.81 0 [] bit1(ti(int,B_1_1))=bit1(B_1_1). % 7.78/7.81 0 [] ti(int,bit1(B_1_1))=bit1(B_1_1). % 7.78/7.81 0 [] ti(int,min)=min. % 7.78/7.81 0 [] ti(int,pls)=pls. % 7.78/7.81 0 [] -number(X_a)|number_number_of(X_a,ti(int,B_1_1))=number_number_of(X_a,B_1_1). % 7.78/7.81 0 [] -number(X_a)|ti(X_a,number_number_of(X_a,B_1_1))=number_number_of(X_a,B_1_1). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 0 [] product_Pair(int,int,ti(int,B_1_1),B_2_1)=product_Pair(int,int,B_1_1,B_2_1). % 7.78/7.81 0 [] product_Pair(int,int,B_1_1,ti(int,B_2_1))=product_Pair(int,int,B_1_1,B_2_1). % 7.78/7.81 0 [] ti(product_prod(int,int),product_Pair(int,int,B_1_1,B_2_1))=product_Pair(int,int,B_1_1,B_2_1). % 7.78/7.81 0 [] legendre(ti(int,B_1_1),B_2_1)=legendre(B_1_1,B_2_1). % 7.78/7.81 0 [] legendre(B_1_1,ti(int,B_2_1))=legendre(B_1_1,B_2_1). % 7.78/7.81 0 [] ti(int,legendre(B_1_1,B_2_1))=legendre(B_1_1,B_2_1). % 7.78/7.81 0 [] -quadRes(ti(int,B_1_1),B_2_1)|quadRes(B_1_1,B_2_1). % 7.78/7.81 0 [] quadRes(ti(int,B_1_1),B_2_1)| -quadRes(B_1_1,B_2_1). % 7.78/7.81 0 [] -quadRes(B_1_1,ti(int,B_2_1))|quadRes(B_1_1,B_2_1). % 7.78/7.81 0 [] quadRes(B_1_1,ti(int,B_2_1))| -quadRes(B_1_1,B_2_1). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 0 [] -twoSqu420862341sum2sq(ti(int,B_1_1))|twoSqu420862341sum2sq(B_1_1). % 7.78/7.81 0 [] twoSqu420862341sum2sq(ti(int,B_1_1))| -twoSqu420862341sum2sq(B_1_1). % 7.78/7.81 0 [] twoSqu579703163sum2sq(ti(product_prod(int,int),B_1_1))=twoSqu579703163sum2sq(B_1_1). % 7.78/7.81 0 [] ti(int,twoSqu579703163sum2sq(B_1_1))=twoSqu579703163sum2sq(B_1_1). % 7.78/7.81 0 [] ti(int,m)=m. % 7.78/7.81 0 [] ti(int,s1)=s1. % 7.78/7.81 0 [] ti(int,s)=s. % 7.78/7.81 0 [] ti(int,t)=t. % 7.78/7.81 0 [] ord_less_e_q(int,one_one(int),t). % 7.78/7.81 0 [] t!=one_one(int)|plus_plus(int,power_power(int,$c2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,$c1,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)). % 7.78/7.81 0 [] -ord_less(int,one_one(int),t)|plus_plus(int,power_power(int,$c4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,$c3,number_number_of(nat,bit0(bit1(pls)))))=plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)). % 7.78/7.81 0 [] ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))). % 7.78/7.81 0 [] zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))). % 7.78/7.81 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). % 7.78/7.81 0 [] twoSqu420862341sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)). % 7.78/7.81 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))))). % 7.78/7.81 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))))). % 7.78/7.81 0 [] -number_semiring(X_a)|power_power(X_a,plus_plus(X_a,X_1,Y_1),number_number_of(nat,bit0(bit1(pls))))=plus_plus(X_a,plus_plus(X_a,power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_1,number_number_of(nat,bit0(bit1(pls))))),times_times(X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),X_1),Y_1)). % 7.78/7.81 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)). % 7.78/7.81 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)))). % 7.78/7.81 0 [] -semiring_1(X_a)|power_power(X_a,one_one(X_a),number_number_of(nat,bit0(bit1(pls))))=one_one(X_a). % 7.78/7.81 0 [] -comm_semiring_1(X_a)|times_times(X_a,X_1,X_1)=power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))). % 7.78/7.81 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). % 7.78/7.81 0 [] -comm_semiring_1(X_a)|power_power(X_a,X_1,times_times(nat,number_number_of(nat,bit0(bit1(pls))),N))=times_times(X_a,power_power(X_a,X_1,N),power_power(X_a,X_1,N)). % 7.78/7.81 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)). % 7.78/7.81 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))). % 7.78/7.81 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))). % 7.78/7.81 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)),$c5). % 7.78/7.81 0 [] ord_less_e_q(int,W,W). % 7.78/7.81 0 [] ord_less_e_q(int,Z,W)|ord_less_e_q(int,W,Z). % 7.78/7.81 0 [] -ord_less(int,Z_1,W_1)|ord_less_e_q(int,Z_1,W_1). % 7.78/7.81 0 [] -ord_less(int,Z_1,W_1)|ti(int,Z_1)!=ti(int,W_1). % 7.78/7.81 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). % 7.78/7.81 0 [] ord_less(int,X_1,Y_1)|ti(int,X_1)=ti(int,Y_1)|ord_less(int,Y_1,X_1). % 7.78/7.81 0 [] -ord_less_e_q(int,I,J)| -ord_less_e_q(int,J,K)|ord_less_e_q(int,I,K). % 7.78/7.81 0 [] -ord_less_e_q(int,Z,W)| -ord_less_e_q(int,W,Z)|ti(int,Z)=ti(int,W). % 7.78/7.81 0 [] -comm_semiring_1(X_a)|power_power(X_a,power_power(X_a,X_1,P),Q)=power_power(X_a,X_1,times_times(nat,P,Q)). % 7.78/7.81 0 [] -comm_semiring_1(X_a)|power_power(X_a,X_1,one_one(nat))=ti(X_a,X_1). % 7.78/7.81 0 [] power_power(int,power_power(int,X_1,Y_1),Z)=power_power(int,X_1,times_times(nat,Y_1,Z)). % 7.78/7.81 0 [] -number(X_a)| -linorder(X_a)| -ord_less_e_q(X_a,number_number_of(X_a,V_2),number_number_of(X_a,W_1))| -ord_less(X_a,number_number_of(X_a,W_1),number_number_of(X_a,V_2)). % 7.78/7.81 0 [] -number(X_a)| -linorder(X_a)|ord_less_e_q(X_a,number_number_of(X_a,V_2),number_number_of(X_a,W_1))|ord_less(X_a,number_number_of(X_a,W_1),number_number_of(X_a,V_2)). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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)). % 7.78/7.81 0 [] -comm_semiring_1(X_a)|times_times(X_a,power_power(X_a,X_1,P),power_power(X_a,X_1,Q))=power_power(X_a,X_1,plus_plus(nat,P,Q)). % 7.78/7.81 0 [] power_power(int,X_1,plus_plus(nat,Y_1,Z))=times_times(int,power_power(int,X_1,Y_1),power_power(int,X_1,Z)). % 7.78/7.81 0 [] times_times(nat,number_number_of(nat,bit0(bit1(pls))),Z)=plus_plus(nat,Z,Z). % 7.78/7.81 0 [] times_times(nat,Z,number_number_of(nat,bit0(bit1(pls))))=plus_plus(nat,Z,Z). % 7.78/7.81 0 [] plus_plus(nat,one_one(nat),one_one(nat))=number_number_of(nat,bit0(bit1(pls))). % 7.78/7.81 0 [] -ord_less(int,bit1(K1),bit1(K2))|ord_less(int,K1,K2). % 7.78/7.81 0 [] ord_less(int,bit1(K1),bit1(K2))| -ord_less(int,K1,K2). % 7.78/7.81 0 [] -ord_less(int,bit1(K_1),bit1(L_1))|ord_less(int,K_1,L_1). % 7.78/7.81 0 [] ord_less(int,bit1(K_1),bit1(L_1))| -ord_less(int,K_1,L_1). % 7.78/7.81 0 [] -ord_less_e_q(int,bit1(K1),bit1(K2))|ord_less_e_q(int,K1,K2). % 7.78/7.81 0 [] ord_less_e_q(int,bit1(K1),bit1(K2))| -ord_less_e_q(int,K1,K2). % 7.78/7.81 0 [] -ord_less_e_q(int,bit1(K_1),bit1(L_1))|ord_less_e_q(int,K_1,L_1). % 7.78/7.81 0 [] ord_less_e_q(int,bit1(K_1),bit1(L_1))| -ord_less_e_q(int,K_1,L_1). % 7.78/7.81 0 [] -ord_less(int,pls,pls). % 7.78/7.81 0 [] -ord_less(int,bit0(K1),bit0(K2))|ord_less(int,K1,K2). % 7.78/7.81 0 [] ord_less(int,bit0(K1),bit0(K2))| -ord_less(int,K1,K2). % 7.78/7.81 0 [] -ord_less(int,bit0(K_1),bit0(L_1))|ord_less(int,K_1,L_1). % 7.78/7.81 0 [] ord_less(int,bit0(K_1),bit0(L_1))| -ord_less(int,K_1,L_1). % 7.78/7.81 0 [] ord_less_e_q(int,pls,pls). % 7.78/7.81 0 [] -ord_less_e_q(int,bit0(K1),bit0(K2))|ord_less_e_q(int,K1,K2). % 7.78/7.81 0 [] ord_less_e_q(int,bit0(K1),bit0(K2))| -ord_less_e_q(int,K1,K2). % 7.78/7.81 0 [] -ord_less_e_q(int,bit0(K_1),bit0(L_1))|ord_less_e_q(int,K_1,L_1). % 7.78/7.81 0 [] ord_less_e_q(int,bit0(K_1),bit0(L_1))| -ord_less_e_q(int,K_1,L_1). % 7.78/7.81 0 [] -ord_less(int,number_number_of(int,K_1),number_number_of(int,L_1))|ord_less(int,K_1,L_1). % 7.78/7.81 0 [] ord_less(int,number_number_of(int,K_1),number_number_of(int,L_1))| -ord_less(int,K_1,L_1). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 0 [] -ord_less(int,I,J)|ord_less(int,plus_plus(int,I,K),plus_plus(int,J,K)). % 7.78/7.81 0 [] -ord_less_e_q(int,I,J)|ord_less_e_q(int,plus_plus(int,K,I),plus_plus(int,K,J)). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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)). % 7.78/7.81 0 [] number_number_of(nat,bit1(pls))=one_one(nat). % 7.78/7.81 0 [] one_one(nat)=number_number_of(nat,bit1(pls)). % 7.78/7.81 0 [] -ord_less_e_q(int,bit1(K_1),pls)|ord_less(int,K_1,pls). % 7.78/7.81 0 [] ord_less_e_q(int,bit1(K_1),pls)| -ord_less(int,K_1,pls). % 7.78/7.81 0 [] -ord_less(int,pls,bit1(K_1))|ord_less_e_q(int,pls,K_1). % 7.78/7.81 0 [] ord_less(int,pls,bit1(K_1))| -ord_less_e_q(int,pls,K_1). % 7.78/7.81 0 [] -ord_less_e_q(int,bit1(K1),bit0(K2))|ord_less(int,K1,K2). % 7.78/7.81 0 [] ord_less_e_q(int,bit1(K1),bit0(K2))| -ord_less(int,K1,K2). % 7.78/7.81 0 [] -ord_less_e_q(int,bit1(K_1),bit0(L_1))|ord_less(int,K_1,L_1). % 7.78/7.81 0 [] ord_less_e_q(int,bit1(K_1),bit0(L_1))| -ord_less(int,K_1,L_1). % 7.78/7.81 0 [] -ord_less(int,bit0(K1),bit1(K2))|ord_less_e_q(int,K1,K2). % 7.78/7.81 0 [] ord_less(int,bit0(K1),bit1(K2))| -ord_less_e_q(int,K1,K2). % 7.78/7.81 0 [] -ord_less(int,bit0(K_1),bit1(L_1))|ord_less_e_q(int,K_1,L_1). % 7.78/7.81 0 [] ord_less(int,bit0(K_1),bit1(L_1))| -ord_less_e_q(int,K_1,L_1). % 7.78/7.81 0 [] -ord_less(int,W,Z)|ord_less_e_q(int,plus_plus(int,W,one_one(int)),Z). % 7.78/7.81 0 [] -ord_less_e_q(int,plus_plus(int,W_1,one_one(int)),Z_1)|ord_less(int,W_1,Z_1). % 7.78/7.81 0 [] ord_less_e_q(int,plus_plus(int,W_1,one_one(int)),Z_1)| -ord_less(int,W_1,Z_1). % 7.78/7.81 0 [] -ord_less(int,W_1,plus_plus(int,Z_1,one_one(int)))|ord_less_e_q(int,W_1,Z_1). % 7.78/7.81 0 [] ord_less(int,W_1,plus_plus(int,Z_1,one_one(int)))| -ord_less_e_q(int,W_1,Z_1). % 7.78/7.81 0 [] zprime(number_number_of(int,bit0(bit1(pls)))). % 7.78/7.81 0 [] -twoSqu420862341sum2sq(X_1)| -twoSqu420862341sum2sq(Y_1)|twoSqu420862341sum2sq(times_times(int,X_1,Y_1)). % 7.78/7.81 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)). % 7.78/7.81 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)). % 7.78/7.81 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))). % 7.78/7.81 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). % 7.78/7.81 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)). % 7.78/7.81 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). % 7.78/7.81 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)). % 7.78/7.81 0 [] -comm_semiring_1(X_a)|times_times(X_a,A_1,B)=times_times(X_a,B,A_1). % 7.78/7.81 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)). % 7.78/7.81 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). % 7.78/7.81 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)). % 7.78/7.81 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). % 7.78/7.81 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)). % 7.78/7.81 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,A_1,C)=plus_plus(X_a,C,A_1). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 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). % 7.78/7.81 0 [] bit1(K_1)!=bit1(L_1)|ti(int,K_1)=ti(int,L_1). % 7.78/7.81 0 [] bit1(K_1)=bit1(L_1)|ti(int,K_1)!=ti(int,L_1). % 7.78/7.81 0 [] bit0(K_1)!=bit0(L_1)|ti(int,K_1)=ti(int,L_1). % 7.78/7.81 0 [] bit0(K_1)=bit0(L_1)|ti(int,K_1)!=ti(int,L_1). % 7.78/7.81 0 [] times_times(int,times_times(int,Z1,Z2),Z3)=times_times(int,Z1,times_times(int,Z2,Z3)). % 7.78/7.81 0 [] times_times(int,Z,W)=times_times(int,W,Z). % 7.78/7.81 0 [] number_number_of(int,K)=ti(int,K). % 7.78/7.81 0 [] plus_plus(int,plus_plus(int,Z1,Z2),Z3)=plus_plus(int,Z1,plus_plus(int,Z2,Z3)). % 7.78/7.81 0 [] plus_plus(int,X_1,plus_plus(int,Y_1,Z))=plus_plus(int,Y_1,plus_plus(int,X_1,Z)). % 7.78/7.82 0 [] plus_plus(int,Z,W)=plus_plus(int,W,Z). % 7.78/7.82 0 [] -ord_less(int,bit1(K_1),pls)|ord_less(int,K_1,pls). % 7.78/7.82 0 [] ord_less(int,bit1(K_1),pls)| -ord_less(int,K_1,pls). % 7.78/7.82 0 [] -ord_less(int,bit1(K1),bit0(K2))|ord_less(int,K1,K2). % 7.78/7.82 0 [] ord_less(int,bit1(K1),bit0(K2))| -ord_less(int,K1,K2). % 7.78/7.82 0 [] -ord_less(int,bit1(K_1),bit0(L_1))|ord_less(int,K_1,L_1). % 7.78/7.82 0 [] ord_less(int,bit1(K_1),bit0(L_1))| -ord_less(int,K_1,L_1). % 7.78/7.82 0 [] -ord_less(int,bit0(K_1),pls)|ord_less(int,K_1,pls). % 7.78/7.82 0 [] ord_less(int,bit0(K_1),pls)| -ord_less(int,K_1,pls). % 7.78/7.82 0 [] -ord_less(int,pls,bit0(K_1))|ord_less(int,pls,K_1). % 7.78/7.82 0 [] ord_less(int,pls,bit0(K_1))| -ord_less(int,pls,K_1). % 7.78/7.82 0 [] -ord_less_e_q(int,pls,bit1(K_1))|ord_less_e_q(int,pls,K_1). % 7.78/7.82 0 [] ord_less_e_q(int,pls,bit1(K_1))| -ord_less_e_q(int,pls,K_1). % 7.78/7.82 0 [] -ord_less_e_q(int,bit0(K1),bit1(K2))|ord_less_e_q(int,K1,K2). % 7.78/7.82 0 [] ord_less_e_q(int,bit0(K1),bit1(K2))| -ord_less_e_q(int,K1,K2). % 7.78/7.82 0 [] -ord_less_e_q(int,bit0(K_1),bit1(L_1))|ord_less_e_q(int,K_1,L_1). % 7.78/7.82 0 [] ord_less_e_q(int,bit0(K_1),bit1(L_1))| -ord_less_e_q(int,K_1,L_1). % 7.78/7.82 0 [] -ord_less_e_q(int,bit0(K_1),pls)|ord_less_e_q(int,K_1,pls). % 7.78/7.82 0 [] ord_less_e_q(int,bit0(K_1),pls)| -ord_less_e_q(int,K_1,pls). % 7.78/7.82 0 [] -ord_less_e_q(int,pls,bit0(K_1))|ord_less_e_q(int,pls,K_1). % 7.78/7.82 0 [] ord_less_e_q(int,pls,bit0(K_1))| -ord_less_e_q(int,pls,K_1). % 7.78/7.82 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). % 7.78/7.82 0 [] ord_less(int,W_1,plus_plus(int,Z_1,one_one(int)))| -ord_less(int,W_1,Z_1). % 7.78/7.82 0 [] ord_less(int,W_1,plus_plus(int,Z_1,one_one(int)))|ti(int,W_1)!=ti(int,Z_1). % 7.78/7.82 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)))). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 0 [] -comm_semiring_1(X_a)|times_times(X_a,X_1,plus_plus(X_a,Y_1,Z))=plus_plus(X_a,times_times(X_a,X_1,Y_1),times_times(X_a,X_1,Z)). % 7.78/7.82 0 [] -comm_semiring_1(X_a)|times_times(X_a,A_1,one_one(X_a))=ti(X_a,A_1). % 7.78/7.82 0 [] -comm_semiring_1(X_a)|times_times(X_a,one_one(X_a),A_1)=ti(X_a,A_1). % 7.78/7.82 0 [] -comm_semiring_1(X_a)|power_power(X_a,times_times(X_a,X_1,Y_1),Q)=times_times(X_a,power_power(X_a,X_1,Q),power_power(X_a,Y_1,Q)). % 7.78/7.82 0 [] bit1(K)!=pls. % 7.78/7.82 0 [] pls!=bit1(L). % 7.78/7.82 0 [] bit1(K)!=bit0(L). % 7.78/7.82 0 [] bit0(K)!=bit1(L). % 7.78/7.82 0 [] bit0(K_1)!=pls|ti(int,K_1)=pls. % 7.78/7.82 0 [] bit0(K_1)=pls|ti(int,K_1)!=pls. % 7.78/7.82 0 [] pls!=bit0(L_1)|pls=ti(int,L_1). % 7.78/7.82 0 [] pls=bit0(L_1)|pls!=ti(int,L_1). % 7.78/7.82 0 [] bit0(pls)=pls. % 7.78/7.82 0 [] times_times(int,pls,W)=pls. % 7.78/7.82 0 [] times_times(int,bit0(K),L)=bit0(times_times(int,K,L)). % 7.78/7.82 0 [] plus_plus(int,K,pls)=ti(int,K). % 7.78/7.82 0 [] plus_plus(int,pls,K)=ti(int,K). % 7.78/7.82 0 [] plus_plus(int,bit0(K),bit0(L))=bit0(plus_plus(int,K,L)). % 7.78/7.82 0 [] bit0(K)=plus_plus(int,K,K). % 7.78/7.82 0 [] times_times(int,Z,one_one(int))=ti(int,Z). % 7.78/7.82 0 [] times_times(int,one_one(int),Z)=ti(int,Z). % 7.78/7.82 0 [] times_times(int,number_number_of(int,V),number_number_of(int,W))=number_number_of(int,times_times(int,V,W)). % 7.78/7.82 0 [] times_times(int,plus_plus(int,Z1,Z2),W)=plus_plus(int,times_times(int,Z1,W),times_times(int,Z2,W)). % 7.78/7.82 0 [] times_times(int,W,plus_plus(int,Z1,Z2))=plus_plus(int,times_times(int,W,Z1),times_times(int,W,Z2)). % 7.78/7.82 0 [] plus_plus(int,number_number_of(int,V),number_number_of(int,W))=number_number_of(int,plus_plus(int,V,W)). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 0 [] ord_less_e_q(int,X_1,power_power(int,X_1,number_number_of(nat,bit0(bit1(pls))))). % 7.78/7.82 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))). % 7.78/7.82 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)). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -number_ring(X_a)|plus_plus(X_a,number_number_of(X_a,pls),A_1)=ti(X_a,A_1). % 7.78/7.82 0 [] -number_ring(X_a)|plus_plus(X_a,A_1,number_number_of(X_a,pls))=ti(X_a,A_1). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 0 [] plus_plus(int,bit1(K),bit0(L))=bit1(plus_plus(int,K,L)). % 7.78/7.82 0 [] plus_plus(int,bit0(K),bit1(L))=bit1(plus_plus(int,K,L)). % 7.78/7.82 0 [] bit1(K)=plus_plus(int,plus_plus(int,one_one(int),K),K). % 7.78/7.82 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)). % 7.78/7.82 0 [] -number_ring(X_a)|times_times(X_a,number_number_of(X_a,bit1(pls)),A_1)=ti(X_a,A_1). % 7.78/7.82 0 [] -number_ring(X_a)|times_times(X_a,A_1,number_number_of(X_a,bit1(pls)))=ti(X_a,A_1). % 7.78/7.82 0 [] -number_semiring(X_a)|number_number_of(X_a,bit1(pls))=one_one(X_a). % 7.78/7.82 0 [] -number_ring(X_a)|number_number_of(X_a,bit1(pls))=one_one(X_a). % 7.78/7.82 0 [] -number_ring(X_a)|one_one(X_a)=number_number_of(X_a,bit1(pls)). % 7.78/7.82 0 [] one_one(int)=number_number_of(int,bit1(pls)). % 7.78/7.82 0 [] times_times(int,bit1(K),L)=plus_plus(int,bit0(times_times(int,K,L)),L). % 7.78/7.82 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)). % 7.78/7.82 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). % 7.78/7.82 0 [] power_power(int,power_power(int,X_1,number_number_of(nat,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls))))=power_power(int,X_1,number_number_of(nat,bit0(bit0(bit1(pls))))). % 7.78/7.82 0 [] -number_semiring(X_a)|times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),Z)=plus_plus(X_a,Z,Z). % 7.78/7.82 0 [] -number_ring(X_a)|times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),Z)=plus_plus(X_a,Z,Z). % 7.78/7.82 0 [] -number_semiring(X_a)|times_times(X_a,Z,number_number_of(X_a,bit0(bit1(pls))))=plus_plus(X_a,Z,Z). % 7.78/7.82 0 [] -number_ring(X_a)|times_times(X_a,Z,number_number_of(X_a,bit0(bit1(pls))))=plus_plus(X_a,Z,Z). % 7.78/7.82 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))). % 7.78/7.82 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))). % 7.78/7.82 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))). % 7.78/7.82 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). % 7.78/7.82 0 [] twoSqu579703163sum2sq(product_Pair(int,int,s,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). % 7.78/7.82 0 [] power_power(real,plus_plus(real,X_1,Y_1),number_number_of(nat,bit0(bit1(pls))))=plus_plus(real,plus_plus(real,power_power(real,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(real,Y_1,number_number_of(nat,bit0(bit1(pls))))),times_times(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X_1),Y_1)). % 7.78/7.82 0 [] times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,X_1,number_number_of(nat,bit0(bit1(pls)))))=power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X_1),number_number_of(nat,bit0(bit1(pls)))). % 7.78/7.82 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))). % 7.78/7.82 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))). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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))). % 7.78/7.82 0 [] ord_less_e_q(int,zero_zero(int),s). % 7.78/7.82 0 [] ord_less(int,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))). % 7.78/7.82 0 [] zcong(s1,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))). % 7.78/7.82 0 [] ord_less_e_q(int,zero_zero(int),$c6). % 7.78/7.82 0 [] ord_less(int,$c6,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))). % 7.78/7.82 0 [] zcong(s1,$c6,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))). % 7.78/7.82 0 [] -ord_less_e_q(int,zero_zero(int),Y)| -ord_less(int,Y,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))| -zcong(s1,Y,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))|ti(int,Y)=ti(int,$c6). % 7.78/7.82 0 [] ord_less_e_q(int,zero_zero(int),$c7). % 7.78/7.82 0 [] ord_less(int,$c7,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))). % 7.78/7.82 0 [] zcong(s1,$c7,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))). % 7.78/7.82 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))). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 0 [] -comm_semiring_1(X_a)| -dvd_dvd(X_a,X_1,Y_1)| -ord_less_e_q(nat,N,M)|dvd_dvd(X_a,power_power(X_a,X_1,N),power_power(X_a,Y_1,M)). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -ord_less(int,zero_zero(int),M)| -ord_less(int,M,N)| -dvd_dvd(int,N,M). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -comm_semiring_1(X_a)| -dvd_dvd(X_a,X_1,Y_1)|dvd_dvd(X_a,power_power(X_a,X_1,N),power_power(X_a,Y_1,N)). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -dvd_dvd(int,Z,N)| -ord_less(int,zero_zero(int),N)|ord_less_e_q(int,Z,N). % 7.78/7.82 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)). % 7.78/7.82 0 [] -comm_semiring_1(X_a)|times_times(X_a,zero_zero(X_a),A_1)=zero_zero(X_a). % 7.78/7.82 0 [] -comm_semiring_1(X_a)|times_times(X_a,A_1,zero_zero(X_a))=zero_zero(X_a). % 7.78/7.82 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,zero_zero(X_a),A_1)=ti(X_a,A_1). % 7.78/7.82 0 [] -comm_semiring_1(X_a)|plus_plus(X_a,A_1,zero_zero(X_a))=ti(X_a,A_1). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] pls=zero_zero(int). % 7.78/7.82 0 [] zero_zero(int)!=one_one(int). % 7.78/7.82 0 [] plus_plus(int,zero_zero(int),Z)=ti(int,Z). % 7.78/7.82 0 [] plus_plus(int,Z,zero_zero(int))=ti(int,Z). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 0 [] -zcong(power_power(int,X_1,Y_1),one_one(int),P)|zcong(power_power(int,X_1,times_times(nat,Y_1,Z)),one_one(int),P). % 7.78/7.82 0 [] -dvd_dvd(int,K_1,plus_plus(int,N_1,times_times(int,K_1,Ma)))|dvd_dvd(int,K_1,N_1). % 7.78/7.82 0 [] dvd_dvd(int,K_1,plus_plus(int,N_1,times_times(int,K_1,Ma)))| -dvd_dvd(int,K_1,N_1). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -semiri456707255roduct(X_a)|ti(X_a,R_1)=zero_zero(X_a)|ti(X_a,A_1)!=ti(X_a,B)|ti(X_a,C)=ti(X_a,D)|plus_plus(X_a,A_1,times_times(X_a,R_1,C))!=plus_plus(X_a,B,times_times(X_a,R_1,D)). % 7.78/7.82 0 [] -zprime(P)| -dvd_dvd(int,P,power_power(int,A_1,N))|dvd_dvd(int,P,A_1). % 7.78/7.82 0 [] -number_ring(X_a)|zero_zero(X_a)=number_number_of(X_a,pls). % 7.78/7.82 0 [] -number_ring(X_a)|number_number_of(X_a,pls)=zero_zero(X_a). % 7.78/7.82 0 [] -number_semiring(X_a)|number_number_of(X_a,pls)=zero_zero(X_a). % 7.78/7.82 0 [] -ord_less(int,bit1(W_1),zero_zero(int))|ord_less(int,W_1,zero_zero(int)). % 7.78/7.82 0 [] ord_less(int,bit1(W_1),zero_zero(int))| -ord_less(int,W_1,zero_zero(int)). % 7.78/7.82 0 [] -ord_less(int,pls,zero_zero(int)). % 7.78/7.82 0 [] -ord_less(int,bit0(W_1),zero_zero(int))|ord_less(int,W_1,zero_zero(int)). % 7.78/7.82 0 [] ord_less(int,bit0(W_1),zero_zero(int))| -ord_less(int,W_1,zero_zero(int)). % 7.78/7.82 0 [] zero_zero(int)=number_number_of(int,pls). % 7.78/7.82 0 [] ord_less(int,zero_zero(int),one_one(int)). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 0 [] plus_plus(int,plus_plus(int,one_one(int),Z),Z)!=zero_zero(int). % 7.78/7.82 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)). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -linordered_ring(X_a)|ord_less_e_q(X_a,zero_zero(X_a),plus_plus(X_a,times_times(X_a,X_1,X_1),times_times(X_a,Y_1,Y_1))). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -ord_less(nat,number_number_of(nat,V_2),number_number_of(nat,V_3))| -ord_less(int,V_2,V_3)|ord_less(int,pls,V_3). % 7.78/7.82 0 [] -ord_less(nat,number_number_of(nat,V_2),number_number_of(nat,V_3))|ord_less(int,V_2,V_3). % 7.78/7.82 0 [] ord_less(nat,number_number_of(nat,V_2),number_number_of(nat,V_3))| -ord_less(int,pls,V_3)| -ord_less(int,V_2,V_3). % 7.78/7.82 0 [] -linordered_ring(X_a)| -ord_less(X_a,plus_plus(X_a,times_times(X_a,X_1,X_1),times_times(X_a,Y_1,Y_1)),zero_zero(X_a)). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -ord_less_e_q(nat,number_number_of(nat,V_2),number_number_of(nat,V_3))|ord_less_e_q(int,V_2,V_3)|ord_less_e_q(int,V_2,pls). % 7.78/7.82 0 [] ord_less_e_q(nat,number_number_of(nat,V_2),number_number_of(nat,V_3))| -ord_less_e_q(int,V_2,V_3). % 7.78/7.82 0 [] ord_less_e_q(nat,number_number_of(nat,V_2),number_number_of(nat,V_3))| -ord_less_e_q(int,V_2,pls). % 7.78/7.82 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)). % 7.78/7.82 0 [] -monoid_mult(X_a)|power_power(X_a,A_1,one_one(nat))=ti(X_a,A_1). % 7.78/7.82 0 [] -ord_less_e_q(int,one_one(int),Z_1)|ord_less(int,zero_zero(int),Z_1). % 7.78/7.82 0 [] ord_less_e_q(int,one_one(int),Z_1)| -ord_less(int,zero_zero(int),Z_1). % 7.78/7.82 0 [] -ord_less(int,zero_zero(int),Ma)|times_times(int,Ma,N_1)!=one_one(int)|ti(int,Ma)=one_one(int). % 7.78/7.82 0 [] -ord_less(int,zero_zero(int),Ma)|times_times(int,Ma,N_1)!=one_one(int)|ti(int,N_1)=one_one(int). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -ord_less_e_q(int,zero_zero(int),Z)|ord_less(int,zero_zero(int),plus_plus(int,one_one(int),Z)). % 7.78/7.82 0 [] -semiring_1(X_a)|power_power(X_a,zero_zero(X_a),number_number_of(nat,bit0(bit1(pls))))=zero_zero(X_a). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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))))). % 7.78/7.82 0 [] -linordered_semidom(X_a)| -ord_less_e_q(X_a,power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_1,number_number_of(nat,bit0(bit1(pls)))))| -ord_less_e_q(X_a,zero_zero(X_a),Y_1)|ord_less_e_q(X_a,X_1,Y_1). % 7.78/7.82 0 [] -linordered_semidom(X_a)|power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls))))!=power_power(X_a,Y_1,number_number_of(nat,bit0(bit1(pls))))| -ord_less_e_q(X_a,zero_zero(X_a),X_1)| -ord_less_e_q(X_a,zero_zero(X_a),Y_1)|ti(X_a,X_1)=ti(X_a,Y_1). % 7.78/7.82 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)). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 0 [] -monoid_mult(X_a)|power_power(X_a,one_one(X_a),N)=one_one(X_a). % 7.78/7.82 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). % 7.78/7.82 0 [] -linordered_semidom(X_a)| -ord_less(X_a,power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_1,number_number_of(nat,bit0(bit1(pls)))))| -ord_less_e_q(X_a,zero_zero(X_a),Y_1)|ord_less(X_a,X_1,Y_1). % 7.78/7.82 0 [] -linordered_idom(X_a)|ord_less_e_q(X_a,zero_zero(X_a),plus_plus(X_a,power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_1,number_number_of(nat,bit0(bit1(pls)))))). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -linordered_idom(X_a)| -ord_less(X_a,plus_plus(X_a,power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_1,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X_a)). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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))). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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. % 7.78/7.82 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. % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 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))). % 7.78/7.82 0 [] zcong(X_1,zero_zero(int),P)| -zcong(power_power(int,Y_1,number_number_of(nat,bit0(bit1(pls)))),X_1,P)| -dvd_dvd(int,P,Y_1). % 7.78/7.82 0 [] -ord_less_e_q(int,zero_zero(int),X_1)| -ord_less(int,X_1,number_number_of(int,bit0(bit1(pls))))|ti(int,X_1)=zero_zero(int)|ti(int,X_1)=one_one(int). % 7.78/7.82 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). % 7.78/7.82 0 [] -zprime(P_1)|ord_less(int,one_one(int),P_1). % 7.78/7.82 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). % 7.78/7.82 0 [] zprime(P_1)| -ord_less(int,one_one(int),P_1)|ord_less_e_q(int,zero_zero(int),$f1(P_1)). % 7.78/7.82 0 [] zprime(P_1)| -ord_less(int,one_one(int),P_1)|dvd_dvd(int,$f1(P_1),P_1). % 7.78/7.82 0 [] zprime(P_1)| -ord_less(int,one_one(int),P_1)|ti(int,$f1(P_1))!=one_one(int). % 7.78/7.82 0 [] zprime(P_1)| -ord_less(int,one_one(int),P_1)|ti(int,$f1(P_1))!=ti(int,P_1). % 7.78/7.82 0 [] zcong(power_power(int,$c8,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))). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] ord_less(nat,zero_zero(nat),power_power(nat,X_2,N_1))| -ord_less(nat,zero_zero(nat),X_2). % 7.78/7.82 0 [] ord_less(nat,zero_zero(nat),power_power(nat,X_2,N_1))|N_1!=zero_zero(nat). % 7.78/7.82 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). % 7.78/7.82 0 [] ord_less(nat,zero_zero(nat),power_power(nat,X_2,N_1))|N_1!=zero_zero(nat). % 7.78/7.82 0 [] ord_less(nat,zero_zero(nat),power_power(nat,X_2,N_1))| -ord_less(nat,zero_zero(nat),X_2). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] bit1(K_1)!=min|ti(int,K_1)=min. % 7.78/7.82 0 [] bit1(K_1)=min|ti(int,K_1)!=min. % 7.78/7.82 0 [] min!=bit1(L_1)|min=ti(int,L_1). % 7.78/7.82 0 [] min=bit1(L_1)|min!=ti(int,L_1). % 7.78/7.82 0 [] bit1(min)=min. % 7.78/7.82 0 [] pls!=min. % 7.78/7.82 0 [] min!=pls. % 7.78/7.82 0 [] bit0(K)!=min. % 7.78/7.82 0 [] min!=bit0(L). % 7.78/7.82 0 [] -ord_less(int,min,min). % 7.78/7.82 0 [] ord_less_e_q(int,min,min). % 7.78/7.82 0 [] ord_less(real,zero_zero(real),times_times(real,X_2,X_2))|X_2=zero_zero(real). % 7.78/7.82 0 [] -ord_less(real,zero_zero(real),times_times(real,X_2,X_2))|X_2!=zero_zero(real). % 7.78/7.82 0 [] -ord_less(int,bit1(K_1),min)|ord_less(int,K_1,min). % 7.78/7.82 0 [] ord_less(int,bit1(K_1),min)| -ord_less(int,K_1,min). % 7.78/7.82 0 [] -ord_less(int,min,bit1(K_1))|ord_less(int,min,K_1). % 7.78/7.82 0 [] ord_less(int,min,bit1(K_1))| -ord_less(int,min,K_1). % 7.78/7.82 0 [] -ord_less(int,pls,min). % 7.78/7.82 0 [] ord_less(int,min,pls). % 7.78/7.82 0 [] -ord_less(int,min,bit0(K_1))|ord_less(int,min,K_1). % 7.78/7.82 0 [] ord_less(int,min,bit0(K_1))| -ord_less(int,min,K_1). % 7.78/7.82 0 [] ord_less(int,min,zero_zero(int)). % 7.78/7.82 0 [] -ord_less_e_q(int,bit1(K_1),min)|ord_less_e_q(int,K_1,min). % 7.78/7.82 0 [] ord_less_e_q(int,bit1(K_1),min)| -ord_less_e_q(int,K_1,min). % 7.78/7.82 0 [] -ord_less_e_q(int,min,bit1(K_1))|ord_less_e_q(int,min,K_1). % 7.78/7.82 0 [] ord_less_e_q(int,min,bit1(K_1))| -ord_less_e_q(int,min,K_1). % 7.78/7.82 0 [] -ord_less_e_q(int,pls,min). % 7.78/7.82 0 [] ord_less_e_q(int,min,pls). % 7.78/7.82 0 [] -ord_less_e_q(int,bit0(K_1),min)|ord_less_e_q(int,K_1,min). % 7.78/7.82 0 [] ord_less_e_q(int,bit0(K_1),min)| -ord_less_e_q(int,K_1,min). % 7.78/7.82 0 [] number_number_of(int,pls)!=number_number_of(int,min). % 7.78/7.82 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). % 7.78/7.82 0 [] -comm_semiring_1(X_a)|power_power(X_a,X_1,zero_zero(nat))=one_one(X_a). % 7.78/7.82 0 [] -power(X_a)|power_power(X_a,A_1,zero_zero(nat))=one_one(X_a). % 7.78/7.82 0 [] number_number_of(nat,pls)=zero_zero(nat). % 7.78/7.82 0 [] zero_zero(nat)=number_number_of(nat,pls). % 7.78/7.82 0 [] -ord_less_e_q(int,min,bit0(K_1))|ord_less(int,min,K_1). % 7.78/7.82 0 [] ord_less_e_q(int,min,bit0(K_1))| -ord_less(int,min,K_1). % 7.78/7.82 0 [] -ord_less(int,bit0(K_1),min)|ord_less_e_q(int,K_1,min). % 7.78/7.82 0 [] ord_less(int,bit0(K_1),min)| -ord_less_e_q(int,K_1,min). % 7.78/7.82 0 [] times_times(int,M,N)!=one_one(int)|ti(int,M)=one_one(int)|ti(int,M)=number_number_of(int,min). % 7.78/7.82 0 [] times_times(int,Ma,N_1)!=one_one(int)|ti(int,Ma)=one_one(int)|ti(int,Ma)=number_number_of(int,min). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] times_times(int,Ma,N_1)=one_one(int)|ti(int,Ma)!=one_one(int)|ti(int,N_1)!=one_one(int). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 0 [] -comm_semiring_1(X_a)| -ord_less(nat,zero_zero(nat),N)|dvd_dvd(X_a,X_1,power_power(X_a,X_1,N)). % 7.78/7.82 0 [] -comm_semiring_1(X_a)|ti(X_a,X_1)!=one_one(X_a)|dvd_dvd(X_a,X_1,power_power(X_a,X_1,N)). % 7.78/7.82 0 [] -ord_less(nat,zero_zero(nat),number_number_of(nat,V_2))|ord_less(int,pls,V_2). % 7.78/7.82 0 [] ord_less(nat,zero_zero(nat),number_number_of(nat,V_2))| -ord_less(int,pls,V_2). % 7.78/7.82 0 [] number_number_of(nat,V_2)!=zero_zero(nat)|ord_less_e_q(int,V_2,pls). % 7.78/7.82 0 [] number_number_of(nat,V_2)=zero_zero(nat)| -ord_less_e_q(int,V_2,pls). % 7.78/7.82 0 [] zero_zero(nat)!=number_number_of(nat,V_2)|ord_less_e_q(int,V_2,pls). % 7.78/7.82 0 [] zero_zero(nat)=number_number_of(nat,V_2)| -ord_less_e_q(int,V_2,pls). % 7.78/7.82 0 [] -zcong(A_2,B_1,Ma)|zcong(B_1,A_2,Ma). % 7.78/7.82 0 [] zcong(A_2,B_1,Ma)| -zcong(B_1,A_2,Ma). % 7.78/7.82 0 [] zcong(K,K,M). % 7.78/7.82 0 [] -zcong(A_1,B,M)| -zcong(B,C,M)|zcong(A_1,C,M). % 7.78/7.82 0 [] ord_less(nat,zero_zero(nat),number_number_of(nat,bit0(bit1(pls)))). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -ord_less(int,V,pls)|times_times(nat,number_number_of(nat,V),number_number_of(nat,V_1))=zero_zero(nat). % 7.78/7.82 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)). % 7.78/7.82 0 [] -order(X_a)| -ord_less_e_q(X_a,X_1,Y_1)|ti(X_a,X_1)=ti(X_a,Y_1)|ord_less(X_a,X_1,Y_1). % 7.78/7.82 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). % 7.78/7.82 0 [] -zcong(A_2,B_1,zero_zero(int))|ti(int,A_2)=ti(int,B_1). % 7.78/7.82 0 [] zcong(A_2,B_1,zero_zero(int))|ti(int,A_2)!=ti(int,B_1). % 7.78/7.82 0 [] zcong(A_1,B,one_one(int)). % 7.78/7.82 0 [] -zcong(A_1,B,M)| -zcong(C,D,M)|zcong(times_times(int,A_1,C),times_times(int,B,D),M). % 7.78/7.82 0 [] -zcong(A_1,B,M)|zcong(times_times(int,K,A_1),times_times(int,K,B),M). % 7.78/7.82 0 [] -zcong(A_1,B,M)|zcong(times_times(int,A_1,K),times_times(int,B,K),M). % 7.78/7.82 0 [] zcong(times_times(int,A_1,M),times_times(int,B,M),M). % 7.78/7.82 0 [] -zcong(A_1,B,M)| -zcong(C,D,M)|zcong(plus_plus(int,A_1,C),plus_plus(int,B,D),M). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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))). % 7.78/7.82 0 [] zcong(A_2,B_1,Ma)|ti(int,B_1)!=plus_plus(int,A_2,times_times(int,Ma,K_2)). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 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))). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 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). % 7.78/7.82 0 [] -zcong(A_1,B,M)| -zcong(C,D,M)|zcong(minus_minus(int,A_1,C),minus_minus(int,B,D),M). % 7.78/7.82 0 [] minus_minus(int,K,pls)=ti(int,K). % 7.78/7.82 0 [] minus_minus(int,bit0(K),bit0(L))=bit0(minus_minus(int,K,L)). % 7.78/7.82 0 [] times_times(int,minus_minus(int,Z1,Z2),W)=minus_minus(int,times_times(int,Z1,W),times_times(int,Z2,W)). % 7.78/7.82 0 [] times_times(int,W,minus_minus(int,Z1,Z2))=minus_minus(int,times_times(int,W,Z1),times_times(int,W,Z2)). % 7.78/7.82 0 [] -dvd_dvd(int,K,minus_minus(int,M,N))| -dvd_dvd(int,K,N)|dvd_dvd(int,K,M). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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))). % 7.78/7.82 0 [] minus_minus(int,bit1(K),bit0(L))=bit1(minus_minus(int,K,L)). % 7.78/7.82 0 [] minus_minus(int,bit1(K),bit1(L))=bit0(minus_minus(int,K,L)). % 7.78/7.82 0 [] minus_minus(int,pls,bit0(L))=bit0(minus_minus(int,pls,L)). % 7.78/7.82 0 [] -ord_less(int,K_1,L_1)|ord_less(int,minus_minus(int,K_1,L_1),zero_zero(int)). % 7.78/7.82 0 [] ord_less(int,K_1,L_1)| -ord_less(int,minus_minus(int,K_1,L_1),zero_zero(int)). % 7.78/7.82 0 [] plus_plus(int,times_times(int,minus_minus(int,A_1,times_times(int,R_1,B)),M),times_times(int,minus_minus(int,C,times_times(int,R_1,D)),N))=minus_minus(int,plus_plus(int,times_times(int,A_1,M),times_times(int,C,N)),times_times(int,R_1,plus_plus(int,times_times(int,B,M),times_times(int,D,N)))). % 7.78/7.82 0 [] -zcong(A_2,B_1,Ma)|dvd_dvd(int,Ma,minus_minus(int,A_2,B_1)). % 7.78/7.82 0 [] zcong(A_2,B_1,Ma)| -dvd_dvd(int,Ma,minus_minus(int,A_2,B_1)). % 7.78/7.82 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). % 7.78/7.82 0 [] -ord_less(int,zero_zero(int),X_1)| -ord_less(int,X_1,A_1)|ti(int,X_1)=minus_minus(int,A_1,one_one(int))|ord_less(int,X_1,minus_minus(int,A_1,one_one(int))). % 7.78/7.82 0 [] -ord_less_e_q(int,W_1,minus_minus(int,Z_1,one_one(int)))|ord_less(int,W_1,Z_1). % 7.78/7.82 0 [] ord_less_e_q(int,W_1,minus_minus(int,Z_1,one_one(int)))| -ord_less(int,W_1,Z_1). % 7.78/7.82 0 [] minus_minus(int,pls,bit1(L))=bit1(minus_minus(int,min,L)). % 7.78/7.82 0 [] minus_minus(int,min,bit1(L))=bit0(minus_minus(int,min,L)). % 7.78/7.82 0 [] minus_minus(int,min,bit0(L))=bit1(minus_minus(int,min,L)). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] times_times(int,twoSqu579703163sum2sq(product_Pair(int,int,A_1,B)),twoSqu579703163sum2sq(product_Pair(int,int,P,Q)))=twoSqu579703163sum2sq(product_Pair(int,int,plus_plus(int,times_times(int,A_1,P),times_times(int,B,Q)),minus_minus(int,times_times(int,A_1,Q),times_times(int,B,P)))). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 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))))). % 7.78/7.82 0 [] -number_ring(X_a)|power_power(X_a,minus_minus(X_a,X_1,Y_1),number_number_of(nat,bit0(bit1(pls))))=minus_minus(X_a,plus_plus(X_a,power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_1,number_number_of(nat,bit0(bit1(pls))))),times_times(X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),X_1),Y_1)). % 7.78/7.82 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))))). % 7.78/7.82 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))))). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -ord_less(int,number_number_of(int,bit0(bit1(pls))),M)| -zcong(one_one(int),number_number_of(int,min),M). % 7.78/7.82 0 [] -ord_less(int,number_number_of(int,bit0(bit1(pls))),P)| -zcong(X_1,number_number_of(int,min),P)| -zcong(X_1,one_one(int),P). % 7.78/7.82 0 [] -zcong(A_1,zero_zero(int),P)|legendre(A_1,P)=zero_zero(int). % 7.78/7.82 0 [] zcong(A_1,zero_zero(int),P)| -quadRes(P,A_1)|legendre(A_1,P)=one_one(int). % 7.78/7.82 0 [] zcong(A_1,zero_zero(int),P)|quadRes(P,A_1)|legendre(A_1,P)=number_number_of(int,min). % 7.78/7.82 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). % 7.78/7.82 0 [] -dvd_dvd(nat,X_2,Y_2)| -dvd_dvd(nat,Y_2,X_2)|X_2=Y_2. % 7.78/7.82 0 [] dvd_dvd(nat,X_2,Y_2)|X_2!=Y_2. % 7.78/7.82 0 [] dvd_dvd(nat,Y_2,X_2)|X_2!=Y_2. % 7.78/7.82 0 [] -zcong(A_1,B,M)|ti(int,B)!=ti(int,C)| -zcong(C,D,M)|zcong(A_1,D,M). % 7.78/7.82 0 [] M!=zero_zero(nat)|times_times(nat,M,N)=zero_zero(nat). % 7.78/7.82 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)). % 7.78/7.82 0 [] M!=zero_zero(nat)|power_power(nat,P,M)=one_one(nat). % 7.78/7.82 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)))). % 7.78/7.82 0 [] minus_minus(nat,power_power(nat,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(nat,Y_1,number_number_of(nat,bit0(bit1(pls)))))=times_times(nat,plus_plus(nat,X_1,Y_1),minus_minus(nat,X_1,Y_1)). % 7.78/7.82 0 [] -dvd_dvd(nat,D,A_1)| -dvd_dvd(nat,D,plus_plus(nat,A_1,B))|dvd_dvd(nat,D,B). % 7.78/7.82 0 [] -dvd_dvd(nat,A_1,B)|dvd_dvd(nat,times_times(nat,C,A_1),times_times(nat,C,B)). % 7.78/7.82 0 [] -dvd_dvd(nat,A_1,B)|dvd_dvd(nat,times_times(nat,A_1,C),times_times(nat,B,C)). % 7.78/7.82 0 [] zcong(M,zero_zero(int),M). % 7.78/7.82 0 [] times_times(nat,N_1,Ma)!=one_one(nat)|N_1=one_one(nat). % 7.78/7.82 0 [] times_times(nat,N_1,Ma)!=one_one(nat)|Ma=one_one(nat). % 7.78/7.82 0 [] times_times(nat,N_1,Ma)=one_one(nat)|N_1!=one_one(nat)|Ma!=one_one(nat). % 7.78/7.82 0 [] minus_minus(int,A_1,B)!=ti(int,C)|ti(int,A_1)=plus_plus(int,C,B). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -zcong(A_1,B,M)|zcong(plus_plus(int,A_1,C),plus_plus(int,B,C),M). % 7.78/7.82 0 [] power_power(nat,Ma,N_1)!=zero_zero(nat)|N_1!=zero_zero(nat). % 7.78/7.82 0 [] power_power(nat,Ma,N_1)!=zero_zero(nat)|Ma=zero_zero(nat). % 7.78/7.82 0 [] power_power(nat,Ma,N_1)=zero_zero(nat)|N_1=zero_zero(nat)|Ma!=zero_zero(nat). % 7.78/7.82 0 [] -dvd_dvd(nat,X_1,Y_1)|dvd_dvd(nat,power_power(nat,X_1,N),power_power(nat,Y_1,N)). % 7.78/7.82 0 [] -zcong(X_1,Y_1,M)|zcong(power_power(int,X_1,Z),power_power(int,Y_1,Z),M). % 7.78/7.82 0 [] -dvd_dvd(nat,A_1,B)|B=zero_zero(nat)|ord_less_e_q(nat,A_1,B). % 7.78/7.82 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). % 7.78/7.82 0 [] dvd_dvd(nat,times_times(nat,Ma,K_1),times_times(nat,N_1,K_1))|K_1!=zero_zero(nat). % 7.78/7.82 0 [] dvd_dvd(nat,times_times(nat,Ma,K_1),times_times(nat,N_1,K_1))| -dvd_dvd(nat,Ma,N_1). % 7.78/7.82 0 [] -ord_less(int,zero_zero(int),X_1)| -ord_less(int,X_1,M)| -zcong(X_1,zero_zero(int),M). % 7.78/7.82 0 [] -ord_less(int,zero_zero(int),X_1)| -ord_less(int,zero_zero(int),Y_1)| -ord_less(int,zero_zero(int),M)| -zcong(X_1,Y_1,M)| -ord_less(int,X_1,M)| -ord_less(int,Y_1,M)|ti(int,X_1)=ti(int,Y_1). % 7.78/7.82 0 [] -dvd_dvd(int,N,M)|ord_less_e_q(int,M,zero_zero(int))|ord_less_e_q(int,N,M). % 7.78/7.82 0 [] N=zero_zero(nat)| -dvd_dvd(nat,power_power(nat,X_1,N),Y_1)|dvd_dvd(nat,X_1,Y_1). % 7.78/7.82 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). % 7.78/7.82 0 [] -zcong(A_2,zero_zero(int),Ma)|dvd_dvd(int,Ma,A_2). % 7.78/7.82 0 [] zcong(A_2,zero_zero(int),Ma)| -dvd_dvd(int,Ma,A_2). % 7.78/7.82 0 [] -zcong(X_2,zero_zero(int),P_1)|dvd_dvd(int,P_1,X_2). % 7.78/7.82 0 [] zcong(X_2,zero_zero(int),P_1)| -dvd_dvd(int,P_1,X_2). % 7.78/7.82 0 [] power_power(nat,X_2,N_1)!=one_one(nat)|X_2=one_one(nat)|N_1=zero_zero(nat). % 7.78/7.82 0 [] power_power(nat,X_2,N_1)=one_one(nat)|X_2!=one_one(nat). % 7.78/7.82 0 [] power_power(nat,X_2,N_1)=one_one(nat)|N_1!=zero_zero(nat). % 7.78/7.82 0 [] -zprime(P)| -dvd_dvd(int,P,times_times(int,M,N))|dvd_dvd(int,P,M)|dvd_dvd(int,P,N). % 7.78/7.82 0 [] -ord_less_e_q(int,zero_zero(int),X_1)| -ord_less(int,X_1,M)| -zcong(X_1,zero_zero(int),M)|ti(int,X_1)=zero_zero(int). % 7.78/7.82 0 [] -ord_less(nat,zero_zero(nat),N)| -dvd_dvd(int,P,Y_1)|dvd_dvd(int,P,power_power(int,Y_1,N)). % 7.78/7.82 0 [] -zprime(P)|zcong(X_1,zero_zero(int),P)|zcong(Y_1,zero_zero(int),P)| -zcong(times_times(int,X_1,Y_1),zero_zero(int),P). % 7.78/7.82 0 [] X_1!=plus_plus(nat,times_times(nat,Q,N),R_1)| -ord_less(nat,zero_zero(nat),R_1)| -ord_less(nat,R_1,N)| -dvd_dvd(nat,N,X_1). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -zprime(P)| -dvd_dvd(int,P,power_power(int,Y_1,N))| -ord_less(nat,zero_zero(nat),N)|dvd_dvd(int,P,Y_1). % 7.78/7.82 0 [] -quadRes(Ma,X_2)|zcong(power_power(int,$f3(Ma,X_2),number_number_of(nat,bit0(bit1(pls)))),X_2,Ma). % 7.78/7.82 0 [] quadRes(Ma,X_2)| -zcong(power_power(int,Y,number_number_of(nat,bit0(bit1(pls)))),X_2,Ma). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -ord_less(int,zero_zero(int),A_1)|ti(int,A_1)!=plus_plus(int,R_1,times_times(int,A_1,Q))| -ord_less(int,R_1,A_1)|ord_less_e_q(int,one_one(int),Q). % 7.78/7.82 0 [] zero_zero(real)!=one_one(real). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 0 [] -ord_less(real,X_2,Y_2)|ord_less_e_q(real,X_2,Y_2). % 7.78/7.82 0 [] -ord_less(real,X_2,Y_2)|X_2!=Y_2. % 7.78/7.82 0 [] ord_less(real,X_2,Y_2)| -ord_less_e_q(real,X_2,Y_2)|X_2=Y_2. % 7.78/7.82 0 [] -ord_less_e_q(real,X_2,Y_2)|ord_less(real,X_2,Y_2)|X_2=Y_2. % 7.78/7.82 0 [] ord_less_e_q(real,X_2,Y_2)| -ord_less(real,X_2,Y_2). % 7.78/7.82 0 [] ord_less_e_q(real,X_2,Y_2)|X_2!=Y_2. % 7.78/7.82 0 [] times_times(real,one_one(real),Z)=Z. % 7.78/7.82 0 [] times_times(real,Z,W)=times_times(real,W,Z). % 7.78/7.82 0 [] times_times(real,times_times(real,Z1,Z2),Z3)=times_times(real,Z1,times_times(real,Z2,Z3)). % 7.78/7.82 0 [] -ord_less_e_q(real,X_1,Y_1)|ord_less_e_q(real,plus_plus(real,Z,X_1),plus_plus(real,Z,Y_1)). % 7.78/7.82 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)). % 7.78/7.82 0 [] C_1=zero_zero(real)|times_times(real,C_1,A_2)!=times_times(real,C_1,B_1)|A_2=B_1. % 7.78/7.82 0 [] C_1=zero_zero(real)|times_times(real,C_1,A_2)=times_times(real,C_1,B_1)|A_2!=B_1. % 7.78/7.82 0 [] C_1=zero_zero(real)|times_times(real,A_2,C_1)!=times_times(real,B_1,C_1)|A_2=B_1. % 7.78/7.82 0 [] C_1=zero_zero(real)|times_times(real,A_2,C_1)=times_times(real,B_1,C_1)|A_2!=B_1. % 7.78/7.82 0 [] times_times(real,plus_plus(real,Z1,Z2),W)=plus_plus(real,times_times(real,Z1,W),times_times(real,Z2,W)). % 7.78/7.82 0 [] -ring(X_a)|minus_minus(X_a,times_times(X_a,X_1,Y_1),times_times(X_a,A_1,B))=plus_plus(X_a,times_times(X_a,X_1,minus_minus(X_a,Y_1,B)),times_times(X_a,minus_minus(X_a,X_1,A_1),B)). % 7.78/7.82 0 [] -ord_less(real,zero_zero(real),Z)| -ord_less(real,X_1,Y_1)|ord_less(real,times_times(real,Z,X_1),times_times(real,Z,Y_1)). % 7.78/7.82 0 [] -ord_less(real,zero_zero(real),X_1)| -ord_less(real,zero_zero(real),Y_1)|ord_less(real,zero_zero(real),times_times(real,X_1,Y_1)). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -ring_1(X_a)|minus_minus(X_a,times_times(X_a,X_1,X_1),one_one(X_a))=times_times(X_a,plus_plus(X_a,X_1,one_one(X_a)),minus_minus(X_a,X_1,one_one(X_a))). % 7.78/7.82 0 [] -monoid_mult(X_a)| -ord_less(nat,zero_zero(nat),N)|times_times(X_a,power_power(X_a,X_1,minus_minus(nat,N,one_one(nat))),X_1)=power_power(X_a,X_1,N). % 7.78/7.82 0 [] ord_less_e_q(real,one_one(real),power_power(real,number_number_of(real,bit0(bit1(pls))),N)). % 7.78/7.82 0 [] -ord_less_e_q(int,zero_zero(int),plus_plus(int,times_times(int,B_2,Q_1),R_2))| -ord_less(int,R_2,B_2)| -ord_less(int,zero_zero(int),B_2)|ord_less_e_q(int,zero_zero(int),Q_1). % 7.78/7.82 0 [] -ord_less(int,plus_plus(int,times_times(int,B_2,Q_1),R_2),zero_zero(int))| -ord_less_e_q(int,zero_zero(int),R_2)| -ord_less(int,zero_zero(int),B_2)|ord_less_e_q(int,Q_1,zero_zero(int)). % 7.78/7.82 0 [] -ord_less_e_q(int,plus_plus(int,times_times(int,B,Q_1),R_2),plus_plus(int,times_times(int,B,Q),R_1))| -ord_less_e_q(int,zero_zero(int),R_2)| -ord_less(int,R_2,B)| -ord_less(int,R_1,B)|ord_less_e_q(int,Q_1,Q). % 7.78/7.82 0 [] plus_plus(int,times_times(int,B,Q),R_1)!=plus_plus(int,times_times(int,B_2,Q_1),R_2)| -ord_less_e_q(int,zero_zero(int),plus_plus(int,times_times(int,B_2,Q_1),R_2))| -ord_less(int,R_2,B_2)| -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,Q_1). % 7.78/7.82 0 [] -ord_less_e_q(int,plus_plus(int,times_times(int,B,Q_1),R_2),plus_plus(int,times_times(int,B,Q),R_1))| -ord_less_e_q(int,R_1,zero_zero(int))| -ord_less(int,B,R_1)| -ord_less(int,B,R_2)|ord_less_e_q(int,Q,Q_1). % 7.78/7.82 0 [] plus_plus(int,times_times(int,B,Q),R_1)!=plus_plus(int,times_times(int,B_2,Q_1),R_2)| -ord_less(int,plus_plus(int,times_times(int,B_2,Q_1),R_2),zero_zero(int))| -ord_less(int,R_1,B)| -ord_less_e_q(int,zero_zero(int),R_2)| -ord_less(int,zero_zero(int),B_2)| -ord_less_e_q(int,B_2,B)|ord_less_e_q(int,Q_1,Q). % 7.78/7.82 0 [] -ord_less(int,zero_zero(int),A_1)|ti(int,A_1)!=plus_plus(int,R_1,times_times(int,A_1,Q))| -ord_less_e_q(int,zero_zero(int),R_1)|ord_less_e_q(int,Q,one_one(int)). % 7.78/7.82 0 [] ord_less_e_q(int,zero_zero(int),number_number_of(int,bit0(bit1(pls)))). % 7.78/7.82 0 [] -power(X_a)|N!=zero_zero(nat)|power_power(X_a,M,N)=one_one(X_a). % 7.78/7.82 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)))). % 7.78/7.82 0 [] -ord_less_e_q(real,Z,W)| -ord_less_e_q(real,W,Z)|Z=W. % 7.78/7.82 0 [] -ord_less_e_q(real,I,J)| -ord_less_e_q(real,J,K)|ord_less_e_q(real,I,K). % 7.78/7.82 0 [] ord_less_e_q(real,Z,W)|ord_less_e_q(real,W,Z). % 7.78/7.82 0 [] ord_less_e_q(real,W,W). % 7.78/7.82 0 [] ord_less_e_q(int,zero_zero(int),zero_zero(int)). % 7.78/7.82 0 [] ord_less_e_q(int,zero_zero(int),one_one(int)). % 7.78/7.82 0 [] -ord_less_e_q(int,zero_zero(int),X_1)| -ord_less_e_q(int,zero_zero(int),Y_1)|ord_less_e_q(int,zero_zero(int),times_times(int,X_1,Y_1)). % 7.78/7.82 0 [] -ord_less_e_q(int,zero_zero(int),X_1)| -ord_less_e_q(int,zero_zero(int),Y_1)|ord_less_e_q(int,zero_zero(int),plus_plus(int,X_1,Y_1)). % 7.78/7.82 0 [] -ord_less_e_q(int,zero_zero(int),X_1)|ord_less_e_q(int,zero_zero(int),power_power(int,X_1,N)). % 7.78/7.82 0 [] ord_less_e_q(int,zero_zero(int),number_number_of(int,bit1(bit1(pls)))). % 7.78/7.82 0 [] -linord626643107strict(X_a)| -ord_less(X_a,X_1,A_1)| -ord_less(X_a,Y_1,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_1),times_times(X_a,V,Y_1)),A_1). % 7.78/7.82 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)). % 7.78/7.82 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. % 7.78/7.82 0 [] -comm_semiring_1(X_a)|dvd_dvd(X_a,A_1,zero_zero(X_a)). % 7.78/7.82 0 [] -linordered_idom(X_a)|ti(X_a,X_1)=ti(X_a,Y_1)|ord_less(X_a,X_1,Y_1)|ord_less(X_a,Y_1,X_1). % 7.78/7.82 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). % 7.78/7.82 0 [] -comm_semiring_1(X_a)|dvd_dvd(X_a,A_1,A_1). % 7.78/7.82 0 [] -mult_zero(X_a)|times_times(X_a,zero_zero(X_a),A_1)=zero_zero(X_a). % 7.78/7.82 0 [] -mult_zero(X_a)|times_times(X_a,A_1,zero_zero(X_a))=zero_zero(X_a). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -zero_ne_q_one(X_a)|one_one(X_a)!=zero_zero(X_a). % 7.78/7.82 0 [] -zero_ne_q_one(X_a)|zero_zero(X_a)!=one_one(X_a). % 7.78/7.82 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)). % 7.78/7.82 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). % 7.78/7.82 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). % 7.78/7.82 0 [] -comm_semiring_1(X_a)|dvd_dvd(X_a,A_1,times_times(X_a,A_1,B)). % 7.78/7.82 0 [] -comm_semiring_1(X_a)|dvd_dvd(X_a,A_1,times_times(X_a,B,A_1)). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 0 [] -dvd(X_a)|A_1!=times_times(X_a,B,K)|dvd_dvd(X_a,B,A_1). % 7.78/7.82 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). % 7.78/7.82 0 [] -comm_semiring_1(X_a)| -dvd_dvd(X_a,times_times(X_a,A_1,B),C)|dvd_dvd(X_a,B,C). % 7.78/7.82 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)). % 7.78/7.82 0 [] -comm_semiring_1(X_a)|dvd_dvd(X_a,one_one(X_a),A_1). % 7.78/7.82 0 [] -comm_ring_1(X_a)| -dvd_dvd(X_a,X_1,Y_1)| -dvd_dvd(X_a,X_1,Z)|dvd_dvd(X_a,X_1,minus_minus(X_a,Y_1,Z)). % 7.78/7.82 0 [] -linordered_ring(X_a)|ord_less_e_q(X_a,zero_zero(X_a),times_times(X_a,A_1,A_1)). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 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). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 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)). % 7.78/7.82 0 [] semiri456707255roduct(int). % 7.78/7.82 0 [] linord626643107strict(int). % 7.78/7.82 0 [] linord219039673up_add(int). % 7.78/7.82 0 [] ring_11004092258visors(int). % 7.78/7.82 0 [] ordere453448008miring(int). % 7.78/7.82 0 [] linord581940658strict(int). % 7.78/7.82 0 [] ring_n68954251visors(int). % 7.78/7.82 0 [] linordered_semidom(int). % 7.78/7.82 0 [] comm_monoid_mult(int). % 7.78/7.82 0 [] no_zero_divisors(int). % 7.78/7.82 0 [] linordered_ring(int). % 7.78/7.82 0 [] linordered_idom(int). % 7.78/7.82 0 [] comm_semiring_1(int). % 7.78/7.82 0 [] comm_semiring(int). % 7.78/7.82 0 [] number_semiring(int). % 7.78/7.82 0 [] ab_group_add(int). % 7.78/7.82 0 [] zero_ne_q_one(int). % 7.78/7.82 0 [] linorder(int). % 7.78/7.82 0 [] monoid_mult(int). % 7.78/7.82 0 [] comm_ring_1(int). % 7.78/7.82 0 [] semiring_1(int). % 7.78/7.82 0 [] semiring_0(int). % 7.78/7.82 0 [] mult_zero(int). % 7.78/7.82 0 [] order(int). % 7.78/7.82 0 [] ring_char_0(int). % 7.78/7.82 0 [] number_ring(int). % 7.78/7.82 0 [] semiring(int). % 7.78/7.82 0 [] ring_1(int). % 7.78/7.82 0 [] power(int). % 7.78/7.82 0 [] ring(int). % 7.78/7.82 0 [] number(int). % 7.78/7.82 0 [] dvd(int). % 7.78/7.82 0 [] semiri456707255roduct(nat). % 7.78/7.82 0 [] ordere453448008miring(nat). % 7.78/7.82 0 [] linordered_semidom(nat). % 7.78/7.82 0 [] comm_monoid_mult(nat). % 7.78/7.82 0 [] no_zero_divisors(nat). % 7.78/7.82 0 [] comm_semiring_1(nat). % 7.78/7.82 0 [] comm_semiring(nat). % 7.78/7.82 0 [] number_semiring(nat). % 7.78/7.82 0 [] zero_ne_q_one(nat). % 7.78/7.82 0 [] linorder(nat). % 7.78/7.82 0 [] monoid_mult(nat). % 7.78/7.82 0 [] semiring_1(nat). % 7.78/7.82 0 [] semiring_0(nat). % 7.78/7.82 0 [] mult_zero(nat). % 7.78/7.82 0 [] order(nat). % 7.78/7.82 0 [] semiring(nat). % 7.78/7.82 0 [] power(nat). % 7.78/7.82 0 [] number(nat). % 7.78/7.82 0 [] dvd(nat). % 7.78/7.82 0 [] order(bool). % 7.78/7.82 0 [] semiri456707255roduct(real). % 7.78/7.82 0 [] linord626643107strict(real). % 7.78/7.82 0 [] linord219039673up_add(real). % 7.78/7.82 0 [] ring_11004092258visors(real). % 7.78/7.82 0 [] ordere453448008miring(real). % 7.78/7.82 0 [] linord581940658strict(real). % 7.78/7.82 0 [] ring_n68954251visors(real). % 7.78/7.82 0 [] linordered_semidom(real). % 7.78/7.82 0 [] comm_monoid_mult(real). % 7.78/7.82 0 [] no_zero_divisors(real). % 7.78/7.82 0 [] linordered_ring(real). % 7.78/7.82 0 [] linordered_idom(real). % 7.78/7.82 0 [] comm_semiring_1(real). % 7.78/7.82 0 [] comm_semiring(real). % 7.78/7.82 0 [] number_semiring(real). % 7.78/7.82 0 [] ab_group_add(real). % 7.78/7.82 0 [] zero_ne_q_one(real). % 7.78/7.82 0 [] linorder(real). % 7.78/7.82 0 [] monoid_mult(real). % 7.78/7.82 0 [] comm_ring_1(real). % 7.78/7.82 0 [] semiring_1(real). % 7.78/7.82 0 [] semiring_0(real). % 7.78/7.82 0 [] mult_zero(real). % 7.78/7.82 0 [] order(real). % 7.78/7.82 0 [] ring_char_0(real). % 7.78/7.82 0 [] number_ring(real). % 7.78/7.82 0 [] semiring(real). % 7.78/7.82 0 [] ring_1(real). % 7.78/7.82 0 [] power(real). % 7.78/7.82 0 [] ring(real). % 7.78/7.82 0 [] number(real). % 7.78/7.82 0 [] dvd(real). % 7.78/7.82 0 [] ti(T,ti(T,A))=ti(T,A). % 7.78/7.82 0 [] plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,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)). % 7.82/7.83 end_of_list. % 7.82/7.83 % 7.82/7.83 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7. % 7.82/7.83 % 7.82/7.83 This ia a non-Horn set with equality. The strategy will be % 7.82/7.83 Knuth-Bendix, ordered hyper_res, factoring, and unit % 7.82/7.83 deletion, with positive clauses in sos and nonpositive % 7.82/7.83 clauses in usable. % 7.82/7.83 % 7.82/7.83 dependent: set(knuth_bendix). % 7.82/7.83 dependent: set(anl_eq). % 7.82/7.83 dependent: set(para_from). % 7.82/7.83 dependent: set(para_into). % 7.82/7.83 dependent: clear(para_from_right). % 7.82/7.83 dependent: clear(para_into_right). % 7.82/7.83 dependent: set(para_from_vars). % 7.82/7.83 dependent: set(eq_units_both_ways). % 7.82/7.83 dependent: set(dynamic_demod_all). % 7.82/7.83 dependent: set(dynamic_demod). % 7.82/7.83 dependent: set(order_eq). % 7.82/7.83 dependent: set(back_demod). % 7.82/7.83 dependent: set(lrpo). % 7.82/7.83 dependent: set(hyper_res). % 7.82/7.83 dependent: set(unit_deletion). % 7.82/7.83 dependent: set(factor). % 7.82/7.83 % 7.82/7.83 ------------> process usable: % 7.82/7.83 ** KEPT (pick-wt=13): 1 [] -ab_group_add(A)|minus_minus(A,ti(A,B),C)=minus_minus(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 2 [] -ab_group_add(A)|minus_minus(A,B,ti(A,C))=minus_minus(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 3 [] -ab_group_add(A)|ti(A,minus_minus(A,B,C))=minus_minus(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=9): 4 [] -zero_ne_q_one(A)|ti(A,one_one(A))=one_one(A). % 7.82/7.83 ** KEPT (pick-wt=9): 5 [] -power(A)|ti(A,one_one(A))=one_one(A). % 7.82/7.83 ** KEPT (pick-wt=13): 6 [] -semiring(A)|plus_plus(A,ti(A,B),C)=plus_plus(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 7 [] -semiring(A)|plus_plus(A,B,ti(A,C))=plus_plus(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 8 [] -semiring(A)|ti(A,plus_plus(A,B,C))=plus_plus(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 9 [] -ab_group_add(A)|plus_plus(A,ti(A,B),C)=plus_plus(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 10 [] -ab_group_add(A)|plus_plus(A,B,ti(A,C))=plus_plus(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 11 [] -ab_group_add(A)|ti(A,plus_plus(A,B,C))=plus_plus(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 12 [] -dvd(A)|times_times(A,ti(A,B),C)=times_times(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 13 [] -dvd(A)|times_times(A,B,ti(A,C))=times_times(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 14 [] -dvd(A)|ti(A,times_times(A,B,C))=times_times(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 15 [] -semiring(A)|times_times(A,ti(A,B),C)=times_times(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 16 [] -semiring(A)|times_times(A,B,ti(A,C))=times_times(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 17 [] -semiring(A)|ti(A,times_times(A,B,C))=times_times(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 18 [] -no_zero_divisors(A)|times_times(A,ti(A,B),C)=times_times(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 19 [] -no_zero_divisors(A)|times_times(A,B,ti(A,C))=times_times(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 20 [] -no_zero_divisors(A)|ti(A,times_times(A,B,C))=times_times(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 21 [] -mult_zero(A)|times_times(A,ti(A,B),C)=times_times(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 22 [] -mult_zero(A)|times_times(A,B,ti(A,C))=times_times(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 23 [] -mult_zero(A)|ti(A,times_times(A,B,C))=times_times(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 24 [] -power(A)|times_times(A,ti(A,B),C)=times_times(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 25 [] -power(A)|times_times(A,B,ti(A,C))=times_times(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 26 [] -power(A)|ti(A,times_times(A,B,C))=times_times(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=9): 27 [] -zero_ne_q_one(A)|ti(A,zero_zero(A))=zero_zero(A). % 7.82/7.83 ** KEPT (pick-wt=9): 28 [] -no_zero_divisors(A)|ti(A,zero_zero(A))=zero_zero(A). % 7.82/7.83 ** KEPT (pick-wt=9): 29 [] -mult_zero(A)|ti(A,zero_zero(A))=zero_zero(A). % 7.82/7.83 ** KEPT (pick-wt=9): 30 [] -linord219039673up_add(A)|ti(A,zero_zero(A))=zero_zero(A). % 7.82/7.83 ** KEPT (pick-wt=10): 31 [] -zcong(ti(int,A),B,C)|zcong(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=10): 32 [] zcong(ti(int,A),B,C)| -zcong(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=10): 33 [] -zcong(A,ti(int,B),C)|zcong(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=10): 34 [] zcong(A,ti(int,B),C)| -zcong(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=10): 35 [] -zcong(A,B,ti(int,C))|zcong(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=10): 36 [] zcong(A,B,ti(int,C))| -zcong(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=6): 37 [] -zprime(ti(int,A))|zprime(A). % 7.82/7.83 ** KEPT (pick-wt=6): 38 [] zprime(ti(int,A))| -zprime(A). % 7.82/7.83 ** KEPT (pick-wt=11): 39 [] -number(A)|number_number_of(A,ti(int,B))=number_number_of(A,B). % 7.82/7.83 ** KEPT (pick-wt=11): 40 [] -number(A)|ti(A,number_number_of(A,B))=number_number_of(A,B). % 7.82/7.83 ** KEPT (pick-wt=12): 41 [] -order(A)| -ord_less(A,ti(A,B),C)|ord_less(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=12): 42 [] -order(A)|ord_less(A,ti(A,B),C)| -ord_less(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=12): 43 [] -order(A)| -ord_less(A,B,ti(A,C))|ord_less(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=12): 44 [] -order(A)|ord_less(A,B,ti(A,C))| -ord_less(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=12): 45 [] -order(A)| -ord_less_e_q(A,ti(A,B),C)|ord_less_e_q(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=12): 46 [] -order(A)|ord_less_e_q(A,ti(A,B),C)| -ord_less_e_q(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=12): 47 [] -order(A)| -ord_less_e_q(A,B,ti(A,C))|ord_less_e_q(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=12): 48 [] -order(A)|ord_less_e_q(A,B,ti(A,C))| -ord_less_e_q(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 49 [] -power(A)|power_power(A,ti(A,B),C)=power_power(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 50 [] -power(A)|power_power(A,B,ti(nat,C))=power_power(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=13): 51 [] -power(A)|ti(A,power_power(A,B,C))=power_power(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=8): 52 [] -quadRes(ti(int,A),B)|quadRes(A,B). % 7.82/7.83 ** KEPT (pick-wt=8): 53 [] quadRes(ti(int,A),B)| -quadRes(A,B). % 7.82/7.83 ** KEPT (pick-wt=8): 54 [] -quadRes(A,ti(int,B))|quadRes(A,B). % 7.82/7.83 ** KEPT (pick-wt=8): 55 [] quadRes(A,ti(int,B))| -quadRes(A,B). % 7.82/7.83 ** KEPT (pick-wt=12): 56 [] -dvd(A)| -dvd_dvd(A,ti(A,B),C)|dvd_dvd(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=12): 57 [] -dvd(A)|dvd_dvd(A,ti(A,B),C)| -dvd_dvd(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=12): 58 [] -dvd(A)| -dvd_dvd(A,B,ti(A,C))|dvd_dvd(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=12): 59 [] -dvd(A)|dvd_dvd(A,B,ti(A,C))| -dvd_dvd(A,B,C). % 7.82/7.83 ** KEPT (pick-wt=6): 60 [] -twoSqu420862341sum2sq(ti(int,A))|twoSqu420862341sum2sq(A). % 7.82/7.83 ** KEPT (pick-wt=6): 61 [] twoSqu420862341sum2sq(ti(int,A))| -twoSqu420862341sum2sq(A). % 7.82/7.83 ** KEPT (pick-wt=36): 63 [copy,62,flip.1,flip.2] one_one(int)!=t|plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))=plus_plus(int,power_power(int,$c2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,$c1,number_number_of(nat,bit0(bit1(pls))))). % 7.82/7.83 ** KEPT (pick-wt=37): 65 [copy,64,flip.2] -ord_less(int,one_one(int),t)|plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))=plus_plus(int,power_power(int,$c4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,$c3,number_number_of(nat,bit0(bit1(pls))))). % 7.82/7.83 ** KEPT (pick-wt=45): 66 [] -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)). % 7.82/7.83 ** KEPT (pick-wt=23): 67 [] -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)). % 7.82/7.83 ** KEPT (pick-wt=14): 68 [] -semiring_1(A)|power_power(A,one_one(A),number_number_of(nat,bit0(bit1(pls))))=one_one(A). % 7.82/7.83 ** KEPT (pick-wt=15): 69 [] -comm_semiring_1(A)|times_times(A,B,B)=power_power(A,B,number_number_of(nat,bit0(bit1(pls)))). % 7.82/7.83 ** KEPT (pick-wt=15): 70 [] -monoid_mult(A)|power_power(A,B,number_number_of(nat,bit0(bit1(pls))))=times_times(A,B,B). % 7.82/7.83 ** KEPT (pick-wt=24): 71 [] -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)). % 7.82/7.83 ** KEPT (pick-wt=17): 72 [] -number_ring(A)|plus_plus(A,one_one(A),number_number_of(A,B))=number_number_of(A,plus_plus(int,bit1(pls),B)). % 7.82/7.83 ** KEPT (pick-wt=17): 73 [] -number_ring(A)|plus_plus(A,number_number_of(A,B),one_one(A))=number_number_of(A,plus_plus(int,B,bit1(pls))). % 7.82/7.83 ** KEPT (pick-wt=14): 74 [] -number_ring(A)|plus_plus(A,one_one(A),one_one(A))=number_number_of(A,bit0(bit1(pls))). % 7.82/7.83 ** KEPT (pick-wt=8): 75 [] -ord_less(int,A,B)|ord_less_e_q(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=11): 76 [] -ord_less(int,A,B)|ti(int,A)!=ti(int,B). % 7.82/7.83 ** KEPT (pick-wt=15): 77 [] ord_less(int,A,B)| -ord_less_e_q(int,A,B)|ti(int,A)=ti(int,B). % 7.82/7.83 ** KEPT (pick-wt=12): 78 [] -ord_less_e_q(int,A,B)| -ord_less_e_q(int,B,C)|ord_less_e_q(int,A,C). % 7.82/7.83 ** KEPT (pick-wt=15): 79 [] -ord_less_e_q(int,A,B)| -ord_less_e_q(int,B,A)|ti(int,A)=ti(int,B). % 7.82/7.83 ** KEPT (pick-wt=17): 80 [] -comm_semiring_1(A)|power_power(A,power_power(A,B,C),D)=power_power(A,B,times_times(nat,C,D)). % 7.82/7.83 ** KEPT (pick-wt=11): 81 [] -comm_semiring_1(A)|power_power(A,B,one_one(nat))=ti(A,B). % 7.82/7.83 ** KEPT (pick-wt=20): 82 [] -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)). % 7.82/7.83 ** KEPT (pick-wt=20): 83 [] -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)). % 7.82/7.83 ** KEPT (pick-wt=16): 84 [] -number_ring(A)| -linordered_idom(A)| -ord_less(A,number_number_of(A,B),number_number_of(A,C))|ord_less(int,B,C). % 7.82/7.83 ** KEPT (pick-wt=16): 85 [] -number_ring(A)| -linordered_idom(A)|ord_less(A,number_number_of(A,B),number_number_of(A,C))| -ord_less(int,B,C). % 7.82/7.83 ** KEPT (pick-wt=16): 86 [] -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). % 7.82/7.83 ** KEPT (pick-wt=16): 87 [] -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). % 7.82/7.83 ** KEPT (pick-wt=18): 88 [] -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)). % 7.82/7.83 ** KEPT (pick-wt=20): 89 [] -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)). % 7.82/7.83 ** KEPT (pick-wt=10): 90 [] -ord_less(int,bit1(A),bit1(B))|ord_less(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=10): 91 [] ord_less(int,bit1(A),bit1(B))| -ord_less(int,A,B). % 7.82/7.83 Following clause subsumed by 90 during input processing: 0 [] -ord_less(int,bit1(A),bit1(B))|ord_less(int,A,B). % 7.82/7.83 Following clause subsumed by 91 during input processing: 0 [] ord_less(int,bit1(A),bit1(B))| -ord_less(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=10): 92 [] -ord_less_e_q(int,bit1(A),bit1(B))|ord_less_e_q(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=10): 93 [] ord_less_e_q(int,bit1(A),bit1(B))| -ord_less_e_q(int,A,B). % 7.82/7.83 Following clause subsumed by 92 during input processing: 0 [] -ord_less_e_q(int,bit1(A),bit1(B))|ord_less_e_q(int,A,B). % 7.82/7.83 Following clause subsumed by 93 during input processing: 0 [] ord_less_e_q(int,bit1(A),bit1(B))| -ord_less_e_q(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=4): 94 [] -ord_less(int,pls,pls). % 7.82/7.83 ** KEPT (pick-wt=10): 95 [] -ord_less(int,bit0(A),bit0(B))|ord_less(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=10): 96 [] ord_less(int,bit0(A),bit0(B))| -ord_less(int,A,B). % 7.82/7.83 Following clause subsumed by 95 during input processing: 0 [] -ord_less(int,bit0(A),bit0(B))|ord_less(int,A,B). % 7.82/7.83 Following clause subsumed by 96 during input processing: 0 [] ord_less(int,bit0(A),bit0(B))| -ord_less(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=10): 97 [] -ord_less_e_q(int,bit0(A),bit0(B))|ord_less_e_q(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=10): 98 [] ord_less_e_q(int,bit0(A),bit0(B))| -ord_less_e_q(int,A,B). % 7.82/7.83 Following clause subsumed by 97 during input processing: 0 [] -ord_less_e_q(int,bit0(A),bit0(B))|ord_less_e_q(int,A,B). % 7.82/7.83 Following clause subsumed by 98 during input processing: 0 [] ord_less_e_q(int,bit0(A),bit0(B))| -ord_less_e_q(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=12): 99 [] -ord_less(int,number_number_of(int,A),number_number_of(int,B))|ord_less(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=12): 100 [] ord_less(int,number_number_of(int,A),number_number_of(int,B))| -ord_less(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=12): 101 [] -ord_less_e_q(int,number_number_of(int,A),number_number_of(int,B))|ord_less_e_q(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=12): 102 [] ord_less_e_q(int,number_number_of(int,A),number_number_of(int,B))| -ord_less_e_q(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=14): 103 [] -ord_less(int,A,B)|ord_less(int,plus_plus(int,A,C),plus_plus(int,B,C)). % 7.82/7.83 ** KEPT (pick-wt=14): 104 [] -ord_less_e_q(int,A,B)|ord_less_e_q(int,plus_plus(int,C,A),plus_plus(int,C,B)). % 7.82/7.83 ** KEPT (pick-wt=16): 105 [] -ord_less(int,A,pls)|plus_plus(nat,number_number_of(nat,A),number_number_of(nat,B))=number_number_of(nat,B). % 7.82/7.83 ** KEPT (pick-wt=20): 106 [] 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). % 7.82/7.83 ** KEPT (pick-wt=9): 107 [] -ord_less_e_q(int,bit1(A),pls)|ord_less(int,A,pls). % 7.82/7.83 ** KEPT (pick-wt=9): 108 [] ord_less_e_q(int,bit1(A),pls)| -ord_less(int,A,pls). % 7.82/7.83 ** KEPT (pick-wt=9): 109 [] -ord_less(int,pls,bit1(A))|ord_less_e_q(int,pls,A). % 7.82/7.83 ** KEPT (pick-wt=9): 110 [] ord_less(int,pls,bit1(A))| -ord_less_e_q(int,pls,A). % 7.82/7.83 ** KEPT (pick-wt=10): 111 [] -ord_less_e_q(int,bit1(A),bit0(B))|ord_less(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=10): 112 [] ord_less_e_q(int,bit1(A),bit0(B))| -ord_less(int,A,B). % 7.82/7.83 Following clause subsumed by 111 during input processing: 0 [] -ord_less_e_q(int,bit1(A),bit0(B))|ord_less(int,A,B). % 7.82/7.83 Following clause subsumed by 112 during input processing: 0 [] ord_less_e_q(int,bit1(A),bit0(B))| -ord_less(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=10): 113 [] -ord_less(int,bit0(A),bit1(B))|ord_less_e_q(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=10): 114 [] ord_less(int,bit0(A),bit1(B))| -ord_less_e_q(int,A,B). % 7.82/7.83 Following clause subsumed by 113 during input processing: 0 [] -ord_less(int,bit0(A),bit1(B))|ord_less_e_q(int,A,B). % 7.82/7.83 Following clause subsumed by 114 during input processing: 0 [] ord_less(int,bit0(A),bit1(B))| -ord_less_e_q(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=12): 115 [] -ord_less(int,A,B)|ord_less_e_q(int,plus_plus(int,A,one_one(int)),B). % 7.82/7.83 ** KEPT (pick-wt=12): 116 [] -ord_less_e_q(int,plus_plus(int,A,one_one(int)),B)|ord_less(int,A,B). % 7.82/7.83 Following clause subsumed by 115 during input processing: 0 [] ord_less_e_q(int,plus_plus(int,A,one_one(int)),B)| -ord_less(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=12): 117 [] -ord_less(int,A,plus_plus(int,B,one_one(int)))|ord_less_e_q(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=12): 118 [] ord_less(int,A,plus_plus(int,B,one_one(int)))| -ord_less_e_q(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=9): 119 [] -twoSqu420862341sum2sq(A)| -twoSqu420862341sum2sq(B)|twoSqu420862341sum2sq(times_times(int,A,B)). % 7.82/7.83 ** KEPT (pick-wt=23): 120 [] -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)). % 7.82/7.83 ** KEPT (pick-wt=23): 121 [] -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)). % 7.82/7.83 ** KEPT (pick-wt=23): 122 [] -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))). % 7.82/7.83 ** KEPT (pick-wt=17): 123 [] -comm_semiring_1(A)|times_times(A,times_times(A,B,C),D)=times_times(A,times_times(A,B,D),C). % 7.82/7.83 ** KEPT (pick-wt=17): 124 [] -comm_semiring_1(A)|times_times(A,times_times(A,B,C),D)=times_times(A,B,times_times(A,C,D)). % 7.82/7.83 Following clause subsumed by 124 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)). % 7.82/7.83 ** KEPT (pick-wt=17): 125 [] -comm_semiring_1(A)|times_times(A,B,times_times(A,C,D))=times_times(A,C,times_times(A,B,D)). % 7.82/7.83 ** KEPT (pick-wt=11): 126 [] -comm_semiring_1(A)|times_times(A,B,C)=times_times(A,C,B). % 7.82/7.83 ** KEPT (pick-wt=23): 127 [] -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)). % 7.82/7.83 ** KEPT (pick-wt=17): 128 [] -comm_semiring_1(A)|plus_plus(A,plus_plus(A,B,C),D)=plus_plus(A,plus_plus(A,B,D),C). % 7.82/7.83 ** KEPT (pick-wt=17): 129 [] -comm_semiring_1(A)|plus_plus(A,plus_plus(A,B,C),D)=plus_plus(A,B,plus_plus(A,C,D)). % 7.82/7.83 Following clause subsumed by 129 during input processing: 0 [flip.2] -comm_semiring_1(A)|plus_plus(A,plus_plus(A,B,C),D)=plus_plus(A,B,plus_plus(A,C,D)). % 7.82/7.83 ** KEPT (pick-wt=17): 130 [] -comm_semiring_1(A)|plus_plus(A,B,plus_plus(A,C,D))=plus_plus(A,C,plus_plus(A,B,D)). % 7.82/7.83 ** KEPT (pick-wt=11): 131 [] -comm_semiring_1(A)|plus_plus(A,B,C)=plus_plus(A,C,B). % 7.82/7.83 ** KEPT (pick-wt=18): 132 [] -number_ring(A)| -ring_char_0(A)|number_number_of(A,B)!=number_number_of(A,C)|ti(int,B)=ti(int,C). % 7.82/7.83 ** KEPT (pick-wt=18): 133 [] -number_ring(A)| -ring_char_0(A)|number_number_of(A,B)=number_number_of(A,C)|ti(int,B)!=ti(int,C). % 7.82/7.83 ** KEPT (pick-wt=16): 134 [] -number(A)|number_number_of(A,B)!=ti(A,C)|ti(A,C)=number_number_of(A,B). % 7.82/7.83 ** KEPT (pick-wt=16): 135 [] -number(A)|number_number_of(A,B)=ti(A,C)|ti(A,C)!=number_number_of(A,B). % 7.82/7.83 ** KEPT (pick-wt=12): 136 [] bit1(A)!=bit1(B)|ti(int,A)=ti(int,B). % 7.82/7.83 ** KEPT (pick-wt=12): 137 [] bit1(A)=bit1(B)|ti(int,A)!=ti(int,B). % 7.82/7.83 ** KEPT (pick-wt=12): 138 [] bit0(A)!=bit0(B)|ti(int,A)=ti(int,B). % 7.82/7.83 ** KEPT (pick-wt=12): 139 [] bit0(A)=bit0(B)|ti(int,A)!=ti(int,B). % 7.82/7.83 ** KEPT (pick-wt=9): 140 [] -ord_less(int,bit1(A),pls)|ord_less(int,A,pls). % 7.82/7.83 ** KEPT (pick-wt=9): 141 [] ord_less(int,bit1(A),pls)| -ord_less(int,A,pls). % 7.82/7.83 ** KEPT (pick-wt=10): 142 [] -ord_less(int,bit1(A),bit0(B))|ord_less(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=10): 143 [] ord_less(int,bit1(A),bit0(B))| -ord_less(int,A,B). % 7.82/7.83 Following clause subsumed by 142 during input processing: 0 [] -ord_less(int,bit1(A),bit0(B))|ord_less(int,A,B). % 7.82/7.83 Following clause subsumed by 143 during input processing: 0 [] ord_less(int,bit1(A),bit0(B))| -ord_less(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=9): 144 [] -ord_less(int,bit0(A),pls)|ord_less(int,A,pls). % 7.82/7.83 ** KEPT (pick-wt=9): 145 [] ord_less(int,bit0(A),pls)| -ord_less(int,A,pls). % 7.82/7.83 ** KEPT (pick-wt=9): 146 [] -ord_less(int,pls,bit0(A))|ord_less(int,pls,A). % 7.82/7.83 ** KEPT (pick-wt=9): 147 [] ord_less(int,pls,bit0(A))| -ord_less(int,pls,A). % 7.82/7.83 ** KEPT (pick-wt=9): 148 [] -ord_less_e_q(int,pls,bit1(A))|ord_less_e_q(int,pls,A). % 7.82/7.83 ** KEPT (pick-wt=9): 149 [] ord_less_e_q(int,pls,bit1(A))| -ord_less_e_q(int,pls,A). % 7.82/7.83 ** KEPT (pick-wt=10): 150 [] -ord_less_e_q(int,bit0(A),bit1(B))|ord_less_e_q(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=10): 151 [] ord_less_e_q(int,bit0(A),bit1(B))| -ord_less_e_q(int,A,B). % 7.82/7.83 Following clause subsumed by 150 during input processing: 0 [] -ord_less_e_q(int,bit0(A),bit1(B))|ord_less_e_q(int,A,B). % 7.82/7.83 Following clause subsumed by 151 during input processing: 0 [] ord_less_e_q(int,bit0(A),bit1(B))| -ord_less_e_q(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=9): 152 [] -ord_less_e_q(int,bit0(A),pls)|ord_less_e_q(int,A,pls). % 7.82/7.83 ** KEPT (pick-wt=9): 153 [] ord_less_e_q(int,bit0(A),pls)| -ord_less_e_q(int,A,pls). % 7.82/7.83 ** KEPT (pick-wt=9): 154 [] -ord_less_e_q(int,pls,bit0(A))|ord_less_e_q(int,pls,A). % 7.82/7.83 ** KEPT (pick-wt=9): 155 [] ord_less_e_q(int,pls,bit0(A))| -ord_less_e_q(int,pls,A). % 7.82/7.83 ** KEPT (pick-wt=19): 156 [] -ord_less(int,A,plus_plus(int,B,one_one(int)))|ord_less(int,A,B)|ti(int,A)=ti(int,B). % 7.82/7.83 ** KEPT (pick-wt=12): 157 [] ord_less(int,A,plus_plus(int,B,one_one(int)))| -ord_less(int,A,B). % 7.82/7.83 ** KEPT (pick-wt=15): 158 [] ord_less(int,A,plus_plus(int,B,one_one(int)))|ti(int,A)!=ti(int,B). % 7.82/7.83 ** KEPT (pick-wt=25): 159 [] -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)))). % 7.82/7.83 ** KEPT (pick-wt=16): 160 [] -number_ring(A)| -linordered_idom(A)| -ord_less(A,number_number_of(A,B),one_one(A))|ord_less(int,B,bit1(pls)). % 7.82/7.83 ** KEPT (pick-wt=16): 161 [] -number_ring(A)| -linordered_idom(A)|ord_less(A,number_number_of(A,B),one_one(A))| -ord_less(int,B,bit1(pls)). % 7.82/7.83 ** KEPT (pick-wt=16): 162 [] -number_ring(A)| -linordered_idom(A)| -ord_less(A,one_one(A),number_number_of(A,B))|ord_less(int,bit1(pls),B). % 7.82/7.83 ** KEPT (pick-wt=16): 163 [] -number_ring(A)| -linordered_idom(A)|ord_less(A,one_one(A),number_number_of(A,B))| -ord_less(int,bit1(pls),B). % 7.82/7.83 ** KEPT (pick-wt=16): 164 [] -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)). % 7.82/7.83 ** KEPT (pick-wt=16): 165 [] -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)). % 7.82/7.83 ** KEPT (pick-wt=16): 166 [] -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). % 7.82/7.83 ** KEPT (pick-wt=16): 167 [] -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). % 7.82/7.83 ** KEPT (pick-wt=37): 168 [] -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). % 7.82/7.83 ** KEPT (pick-wt=30): 169 [] -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). % 7.82/7.83 ** KEPT (pick-wt=30): 170 [] -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). % 7.82/7.83 ** KEPT (pick-wt=20): 172 [copy,171,flip.2] -comm_semiring_1(A)|times_times(A,plus_plus(A,B,C),D)=plus_plus(A,times_times(A,B,D),times_times(A,C,D)). % 7.82/7.83 Following clause subsumed by 172 during input processing: 0 [] -comm_semiring_1(A)|times_times(A,plus_plus(A,B,C),D)=plus_plus(A,times_times(A,B,D),times_times(A,C,D)). % 7.82/7.83 Following clause subsumed by 168 during input processing: 0 [] -semiri456707255roduct(A)|ti(A,B)=ti(A,C)|ti(A,D)=ti(A,E)|plus_plus(A,times_times(A,B,D),times_times(A,C,E))!=plus_plus(A,times_times(A,B,E),times_times(A,C,D)). % 7.82/7.83 Following clause subsumed by 169 during input processing: 0 [] -semiri456707255roduct(A)|ti(A,B)!=ti(A,C)|plus_plus(A,times_times(A,B,D),times_times(A,C,E))=plus_plus(A,times_times(A,B,E),times_times(A,C,D)). % 7.82/7.83 Following clause subsumed by 170 during input processing: 0 [] -semiri456707255roduct(A)|ti(A,B)!=ti(A,C)|plus_plus(A,times_times(A,D,B),times_times(A,E,C))=plus_plus(A,times_times(A,D,C),times_times(A,E,B)). % 7.82/7.83 ** KEPT (pick-wt=20): 173 [] -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)). % 7.82/7.83 ** KEPT (pick-wt=11): 174 [] -comm_semiring_1(A)|times_times(A,B,one_one(A))=ti(A,B). % 7.82/7.83 ** KEPT (pick-wt=11): 175 [] -comm_semiring_1(A)|times_times(A,one_one(A),B)=ti(A,B). % 7.82/7.83 ** KEPT (pick-wt=20): 177 [copy,176,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). % 7.82/7.83 ** KEPT (pick-wt=4): 178 [] bit1(A)!=pls. % 7.82/7.83 Following clause subsumed by 178 during input processing: 0 [flip.1] bit1(A)!=pls. % 7.82/7.83 ** KEPT (pick-wt=5): 179 [] bit1(A)!=bit0(B). % 7.82/7.83 ** KEPT (pick-wt=5): 180 [] bit0(A)!=bit1(B). % 7.82/7.83 ** KEPT (pick-wt=9): 181 [] bit0(A)!=pls|ti(int,A)=pls. % 7.82/7.83 ** KEPT (pick-wt=9): 182 [] bit0(A)=pls|ti(int,A)!=pls. % 7.82/7.83 Following clause subsumed by 181 during input processing: 0 [flip.1,flip.2] bit0(A)!=pls|ti(int,A)=pls. % 7.82/7.83 Following clause subsumed by 182 during input processing: 0 [flip.1,flip.2] bit0(A)=pls|ti(int,A)!=pls. % 7.82/7.83 ** KEPT (pick-wt=25): 184 [copy,183,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)). % 7.82/7.83 ** KEPT (pick-wt=25): 186 [copy,185,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)). % 7.82/7.83 ** KEPT (pick-wt=28): 187 [] -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))). % 7.82/7.83 ** KEPT (pick-wt=28): 188 [] -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)). % 7.82/7.83 ** KEPT (pick-wt=18): 190 [copy,189,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). % 7.82/7.83 ** KEPT (pick-wt=18): 192 [copy,191,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)). % 7.82/7.83 ** KEPT (pick-wt=16): 194 [copy,193,flip.2] -comm_semiring_1(A)|times_times(A,plus_plus(A,one_one(A),one_one(A)),B)=plus_plus(A,B,B). % 7.82/7.83 ** KEPT (pick-wt=12): 196 [copy,195,flip.2] -number_ring(A)|ti(A,B)=plus_plus(A,number_number_of(A,pls),B). % 7.82/7.83 ** KEPT (pick-wt=12): 198 [copy,197,flip.2] -number_ring(A)|ti(A,B)=plus_plus(A,B,number_number_of(A,pls)). % 7.82/7.83 ** KEPT (pick-wt=23): 200 [copy,199,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)). % 7.82/7.83 ** KEPT (pick-wt=17): 202 [copy,201,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)). % 7.82/7.83 Following clause subsumed by 202 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)). % 7.82/7.83 ** KEPT (pick-wt=23): 204 [copy,203,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)). % 7.82/7.83 ** KEPT (pick-wt=17): 206 [copy,205,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)). % 7.82/7.83 Following clause subsumed by 206 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)). % 7.82/7.83 ** KEPT (pick-wt=19): 207 [] -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)). % 7.82/7.83 ** KEPT (pick-wt=13): 208 [] -number_ring(A)|times_times(A,number_number_of(A,bit1(pls)),B)=ti(A,B). % 7.82/7.83 ** KEPT (pick-wt=13): 209 [] -number_ring(A)|times_times(A,B,number_number_of(A,bit1(pls)))=ti(A,B). % 7.82/7.83 ** KEPT (pick-wt=9): 211 [copy,210,flip.2] -number_semiring(A)|one_one(A)=number_number_of(A,bit1(pls)). % 7.82/7.83 ** KEPT (pick-wt=9): 213 [copy,212,flip.2] -number_ring(A)|one_one(A)=number_number_of(A,bit1(pls)). % 7.82/7.83 Following clause subsumed by 213 during input processing: 0 [] -number_ring(A)|one_one(A)=number_number_of(A,bit1(pls)). % 7.82/7.83 ** KEPT (pick-wt=18): 214 [] -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)). % 7.82/7.83 ** KEPT (pick-wt=18): 215 [] -monoid_mult(A)|power_power(A,B,number_number_of(nat,bit1(bit1(pls))))=times_times(A,times_times(A,B,B),B). % 7.82/7.83 ** KEPT (pick-wt=15): 216 [] -number_semiring(A)|times_times(A,number_number_of(A,bit0(bit1(pls))),B)=plus_plus(A,B,B). % 7.82/7.83 ** KEPT (pick-wt=15): 217 [] -number_ring(A)|times_times(A,number_number_of(A,bit0(bit1(pls))),B)=plus_plus(A,B,B). % 7.82/7.83 ** KEPT (pick-wt=15): 218 [] -number_semiring(A)|times_times(A,B,number_number_of(A,bit0(bit1(pls))))=plus_plus(A,B,B). % 7.82/7.83 ** KEPT (pick-wt=15): 219 [] -number_ring(A)|times_times(A,B,number_number_of(A,bit0(bit1(pls))))=plus_plus(A,B,B). % 7.82/7.83 ** KEPT (pick-wt=14): 220 [] -number_semiring(A)|plus_plus(A,one_one(A),one_one(A))=number_number_of(A,bit0(bit1(pls))). % 7.82/7.83 ** KEPT (pick-wt=29): 221 [] -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). % 7.82/7.83 ** KEPT (pick-wt=20): 222 [] -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))). % 7.82/7.83 ** KEPT (pick-wt=18): 223 [] -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))). % 7.82/7.83 ** KEPT (pick-wt=21): 224 [] -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). % 7.82/7.83 Following clause subsumed by 224 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). % 7.82/7.83 ** KEPT (pick-wt=21): 225 [] -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). % 7.82/7.83 ** KEPT (pick-wt=44): 226 [] -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,$c6). % 7.82/7.83 ** KEPT (pick-wt=21): 227 [] -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). % 7.82/7.83 ** KEPT (pick-wt=19): 228 [] -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). % 7.82/7.83 ** KEPT (pick-wt=25): 229 [] -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). % 7.82/7.83 ** KEPT (pick-wt=16): 230 [] -comm_semiring_1(A)| -ord_less_e_q(nat,B,C)|dvd_dvd(A,power_power(A,D,B),power_power(A,D,C)). % 7.82/7.83 ** KEPT (pick-wt=20): 231 [] -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)). % 7.82/7.83 ** KEPT (pick-wt=20): 232 [] -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). % 7.82/7.84 ** KEPT (pick-wt=33): 233 [] -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). % 7.82/7.84 ** KEPT (pick-wt=13): 234 [] -ord_less(int,zero_zero(int),A)| -ord_less(int,A,B)| -dvd_dvd(int,B,A). % 7.82/7.84 ** KEPT (pick-wt=25): 235 [] -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). % 7.82/7.84 ** KEPT (pick-wt=20): 236 [] -dvd_dvd(int,times_times(int,A,B),times_times(int,A,C))|ti(int,A)=zero_zero(int)|dvd_dvd(int,B,C). % 7.82/7.84 ** KEPT (pick-wt=16): 237 [] -comm_semiring_1(A)| -dvd_dvd(A,B,C)|dvd_dvd(A,power_power(A,B,D),power_power(A,C,D)). % 7.82/7.84 ** KEPT (pick-wt=15): 238 [] -ring_11004092258visors(A)|ti(A,B)=zero_zero(A)|power_power(A,B,C)!=zero_zero(A). % 7.82/7.84 ** KEPT (pick-wt=16): 239 [] -power(A)| -semiring_0(A)|B!=zero_zero(nat)|power_power(A,zero_zero(A),B)=one_one(A). % 7.82/7.84 ** KEPT (pick-wt=16): 240 [] -power(A)| -semiring_0(A)|B=zero_zero(nat)|power_power(A,zero_zero(A),B)=zero_zero(A). % 7.82/7.84 ** KEPT (pick-wt=13): 241 [] -dvd_dvd(int,A,B)| -ord_less(int,zero_zero(int),B)|ord_less_e_q(int,A,B). % 7.82/7.84 ** KEPT (pick-wt=26): 242 [] -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)). % 7.82/7.84 ** KEPT (pick-wt=10): 243 [] -comm_semiring_1(A)|times_times(A,zero_zero(A),B)=zero_zero(A). % 7.82/7.84 ** KEPT (pick-wt=10): 244 [] -comm_semiring_1(A)|times_times(A,B,zero_zero(A))=zero_zero(A). % 7.82/7.84 ** KEPT (pick-wt=11): 245 [] -comm_semiring_1(A)|plus_plus(A,zero_zero(A),B)=ti(A,B). % 7.82/7.84 ** KEPT (pick-wt=11): 246 [] -comm_semiring_1(A)|plus_plus(A,B,zero_zero(A))=ti(A,B). % 7.82/7.84 ** KEPT (pick-wt=16): 247 [] -semiri456707255roduct(A)|ti(A,B)!=plus_plus(A,B,C)|ti(A,C)=zero_zero(A). % 7.82/7.84 ** KEPT (pick-wt=16): 248 [] -semiri456707255roduct(A)|ti(A,B)=plus_plus(A,B,C)|ti(A,C)!=zero_zero(A). % 7.82/7.84 ** KEPT (pick-wt=15): 249 [] -linord219039673up_add(A)|plus_plus(A,B,B)!=zero_zero(A)|ti(A,B)=zero_zero(A). % 7.82/7.84 ** KEPT (pick-wt=15): 250 [] -linord219039673up_add(A)|plus_plus(A,B,B)=zero_zero(A)|ti(A,B)!=zero_zero(A). % 7.82/7.84 ** KEPT (pick-wt=5): 251 [] zero_zero(int)!=one_one(int). % 7.82/7.84 ** KEPT (pick-wt=15): 252 [] -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)). % 7.82/7.84 ** KEPT (pick-wt=21): 253 [] -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)). % 7.82/7.84 ** KEPT (pick-wt=15): 254 [] -linordered_semidom(A)| -ord_less(A,zero_zero(A),B)|ord_less(A,zero_zero(A),power_power(A,B,C)). % 7.82/7.84 ** KEPT (pick-wt=19): 255 [] -zcong(power_power(int,A,B),one_one(int),C)|zcong(power_power(int,A,times_times(nat,B,D)),one_one(int),C). % 7.82/7.84 ** KEPT (pick-wt=14): 256 [] -dvd_dvd(int,A,plus_plus(int,B,times_times(int,A,C)))|dvd_dvd(int,A,B). % 7.82/7.84 ** KEPT (pick-wt=14): 257 [] dvd_dvd(int,A,plus_plus(int,B,times_times(int,A,C)))| -dvd_dvd(int,A,B). % 7.82/7.84 ** KEPT (pick-wt=24): 258 [] -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)). % 7.82/7.84 ** KEPT (pick-wt=24): 259 [] -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)). % 7.82/7.84 ** KEPT (pick-wt=21): 260 [] -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). % 7.82/7.84 ** KEPT (pick-wt=26): 261 [] -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)). % 7.82/7.84 ** KEPT (pick-wt=26): 262 [] -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)). % 7.82/7.84 ** KEPT (pick-wt=15): 263 [] -linordered_idom(A)| -ord_less(A,plus_plus(A,B,B),zero_zero(A))|ord_less(A,B,zero_zero(A)). % 7.82/7.84 ** KEPT (pick-wt=15): 264 [] -linordered_idom(A)|ord_less(A,plus_plus(A,B,B),zero_zero(A))| -ord_less(A,B,zero_zero(A)). % 7.82/7.84 ** KEPT (pick-wt=21): 265 [] -linord581940658strict(A)|plus_plus(A,times_times(A,B,B),times_times(A,C,C))!=zero_zero(A)|ti(A,B)=zero_zero(A). % 7.82/7.84 ** KEPT (pick-wt=21): 266 [] -linord581940658strict(A)|plus_plus(A,times_times(A,B,B),times_times(A,C,C))!=zero_zero(A)|ti(A,C)=zero_zero(A). % 7.82/7.84 ** KEPT (pick-wt=27): 267 [] -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). % 7.82/7.84 ** KEPT (pick-wt=37): 268 [] -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)). % 7.82/7.84 ** KEPT (pick-wt=13): 269 [] -zprime(A)| -dvd_dvd(int,A,power_power(int,B,C))|dvd_dvd(int,A,B). % 7.82/7.84 ** KEPT (pick-wt=8): 270 [] -number_ring(A)|zero_zero(A)=number_number_of(A,pls). % 7.82/7.84 Following clause subsumed by 270 during input processing: 0 [flip.2] -number_ring(A)|zero_zero(A)=number_number_of(A,pls). % 7.82/7.84 ** KEPT (pick-wt=8): 272 [copy,271,flip.2] -number_semiring(A)|zero_zero(A)=number_number_of(A,pls). % 7.82/7.84 ** KEPT (pick-wt=11): 273 [] -ord_less(int,bit1(A),zero_zero(int))|ord_less(int,A,zero_zero(int)). % 7.82/7.84 ** KEPT (pick-wt=11): 274 [] ord_less(int,bit1(A),zero_zero(int))| -ord_less(int,A,zero_zero(int)). % 7.82/7.84 ** KEPT (pick-wt=5): 275 [] -ord_less(int,pls,zero_zero(int)). % 7.82/7.84 ** KEPT (pick-wt=11): 276 [] -ord_less(int,bit0(A),zero_zero(int))|ord_less(int,A,zero_zero(int)). % 7.82/7.84 ** KEPT (pick-wt=11): 277 [] ord_less(int,bit0(A),zero_zero(int))| -ord_less(int,A,zero_zero(int)). % 7.82/7.84 ** KEPT (pick-wt=18): 278 [] -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). % 7.82/7.84 ** KEPT (pick-wt=19): 279 [] -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)). % 7.82/7.84 ** KEPT (pick-wt=11): 280 [] plus_plus(int,plus_plus(int,one_one(int),A),A)!=zero_zero(int). % 7.82/7.84 ** KEPT (pick-wt=25): 281 [] -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)). % 7.82/7.84 ** KEPT (pick-wt=23): 282 [] -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). % 7.82/7.84 ** KEPT (pick-wt=23): 283 [] -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). % 7.82/7.84 ** KEPT (pick-wt=16): 284 [] -linordered_ring(A)|ord_less_e_q(A,zero_zero(A),plus_plus(A,times_times(A,B,B),times_times(A,C,C))). % 7.82/7.84 ** KEPT (pick-wt=22): 285 [] -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). % 7.82/7.84 ** KEPT (pick-wt=22): 286 [] -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). % 7.82/7.84 ** KEPT (pick-wt=28): 287 [] -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). % 7.82/7.84 ** KEPT (pick-wt=16): 288 [] -ord_less(nat,number_number_of(nat,A),number_number_of(nat,B))| -ord_less(int,A,B)|ord_less(int,pls,B). % 7.82/7.84 ** KEPT (pick-wt=12): 289 [] -ord_less(nat,number_number_of(nat,A),number_number_of(nat,B))|ord_less(int,A,B). % 7.82/7.84 ** KEPT (pick-wt=16): 290 [] ord_less(nat,number_number_of(nat,A),number_number_of(nat,B))| -ord_less(int,pls,B)| -ord_less(int,A,B). % 7.82/7.84 ** KEPT (pick-wt=16): 291 [] -linordered_ring(A)| -ord_less(A,plus_plus(A,times_times(A,B,B),times_times(A,C,C)),zero_zero(A)). % 7.82/7.84 ** KEPT (pick-wt=28): 292 [] -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). % 7.82/7.84 ** KEPT (pick-wt=22): 293 [] -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). % 7.82/7.84 ** KEPT (pick-wt=22): 294 [] -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). % 7.82/7.84 ** KEPT (pick-wt=16): 295 [] -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). % 7.82/7.84 ** KEPT (pick-wt=12): 296 [] ord_less_e_q(nat,number_number_of(nat,A),number_number_of(nat,B))| -ord_less_e_q(int,A,B). % 7.82/7.84 ** KEPT (pick-wt=12): 297 [] ord_less_e_q(nat,number_number_of(nat,A),number_number_of(nat,B))| -ord_less_e_q(int,A,pls). % 7.82/7.84 ** KEPT (pick-wt=19): 298 [] -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)). % 7.82/7.84 ** KEPT (pick-wt=11): 299 [] -monoid_mult(A)|power_power(A,B,one_one(nat))=ti(A,B). % 7.82/7.84 ** KEPT (pick-wt=10): 300 [] -ord_less_e_q(int,one_one(int),A)|ord_less(int,zero_zero(int),A). % 7.82/7.84 ** KEPT (pick-wt=10): 301 [] ord_less_e_q(int,one_one(int),A)| -ord_less(int,zero_zero(int),A). % 7.82/7.84 ** KEPT (pick-wt=18): 302 [] -ord_less(int,zero_zero(int),A)|times_times(int,A,B)!=one_one(int)|ti(int,A)=one_one(int). % 7.82/7.84 ** KEPT (pick-wt=18): 303 [] -ord_less(int,zero_zero(int),A)|times_times(int,A,B)!=one_one(int)|ti(int,B)=one_one(int). % 7.82/7.84 ** KEPT (pick-wt=24): 304 [] -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). % 7.82/7.84 ** KEPT (pick-wt=17): 305 [] -ord_less(int,plus_plus(int,plus_plus(int,one_one(int),A),A),zero_zero(int))|ord_less(int,A,zero_zero(int)). % 7.82/7.84 ** KEPT (pick-wt=17): 306 [] ord_less(int,plus_plus(int,plus_plus(int,one_one(int),A),A),zero_zero(int))| -ord_less(int,A,zero_zero(int)). % 7.82/7.84 ** KEPT (pick-wt=15): 307 [] -number_ring(A)| -linordered_idom(A)| -ord_less(A,zero_zero(A),number_number_of(A,B))|ord_less(int,pls,B). % 7.82/7.84 ** KEPT (pick-wt=15): 308 [] -number_ring(A)| -linordered_idom(A)|ord_less(A,zero_zero(A),number_number_of(A,B))| -ord_less(int,pls,B). % 7.82/7.84 ** KEPT (pick-wt=15): 309 [] -number_ring(A)| -linordered_idom(A)| -ord_less(A,number_number_of(A,B),zero_zero(A))|ord_less(int,B,pls). % 7.82/7.84 ** KEPT (pick-wt=15): 310 [] -number_ring(A)| -linordered_idom(A)|ord_less(A,number_number_of(A,B),zero_zero(A))| -ord_less(int,B,pls). % 7.82/7.84 ** KEPT (pick-wt=15): 311 [] -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). % 7.82/7.84 ** KEPT (pick-wt=15): 312 [] -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). % 7.82/7.84 ** KEPT (pick-wt=15): 313 [] -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). % 7.82/7.84 ** KEPT (pick-wt=15): 314 [] -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). % 7.82/7.84 ** KEPT (pick-wt=14): 315 [] -ord_less_e_q(int,zero_zero(int),A)|ord_less(int,zero_zero(int),plus_plus(int,one_one(int),A)). % 7.82/7.84 ** KEPT (pick-wt=14): 316 [] -semiring_1(A)|power_power(A,zero_zero(A),number_number_of(nat,bit0(bit1(pls))))=zero_zero(A). % 7.82/7.84 Following clause subsumed by 238 during input processing: 0 [] -ring_11004092258visors(A)|power_power(A,B,number_number_of(nat,bit0(bit1(pls))))!=zero_zero(A)|ti(A,B)=zero_zero(A). % 7.82/7.84 ** KEPT (pick-wt=19): 317 [] -ring_11004092258visors(A)|power_power(A,B,number_number_of(nat,bit0(bit1(pls))))=zero_zero(A)|ti(A,B)!=zero_zero(A). % 7.82/7.84 ** KEPT (pick-wt=14): 318 [] -linordered_idom(A)|ord_less_e_q(A,zero_zero(A),power_power(A,B,number_number_of(nat,bit0(bit1(pls))))). % 7.82/7.84 ** KEPT (pick-wt=29): 319 [] -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). % 7.82/7.84 ** KEPT (pick-wt=36): 320 [] -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). % 7.82/7.84 ** KEPT (pick-wt=14): 321 [] -linordered_idom(A)| -ord_less(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),zero_zero(A)). % 7.82/7.84 ** KEPT (pick-wt=20): 322 [] -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). % 7.82/7.84 ** KEPT (pick-wt=20): 323 [] -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). % 7.82/7.84 ** KEPT (pick-wt=29): 324 [] -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). % 7.82/7.84 ** KEPT (pick-wt=29): 325 [] -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). % 7.82/7.84 ** KEPT (pick-wt=35): 326 [] -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). % 7.82/7.84 ** KEPT (pick-wt=17): 327 [] -monoid_mult(A)|times_times(A,power_power(A,B,C),B)=times_times(A,B,power_power(A,B,C)). % 7.82/7.84 ** KEPT (pick-wt=20): 329 [copy,328,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). % 7.82/7.84 ** KEPT (pick-wt=20): 331 [copy,330,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)). % 7.82/7.84 ** KEPT (pick-wt=10): 332 [] -monoid_mult(A)|power_power(A,one_one(A),B)=one_one(A). % 7.82/7.84 ** KEPT (pick-wt=17): 333 [] -monoid_mult(A)|power_power(A,B,times_times(nat,C,D))=power_power(A,power_power(A,B,C),D). % 7.82/7.84 Following clause subsumed by 260 during input processing: 0 [] -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). % 7.82/7.84 ** KEPT (pick-wt=24): 334 [] -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)))))). % 7.82/7.84 ** KEPT (pick-wt=30): 335 [] -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). % 7.82/7.84 ** KEPT (pick-wt=30): 336 [] -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). % 7.82/7.84 ** KEPT (pick-wt=36): 337 [] -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). % 7.82/7.84 ** KEPT (pick-wt=24): 338 [] -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)). % 7.82/7.84 ** KEPT (pick-wt=36): 339 [] -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). % 7.82/7.84 ** KEPT (pick-wt=30): 340 [] -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). % 7.82/7.84 ** KEPT (pick-wt=30): 341 [] -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). % 7.82/7.84 ** KEPT (pick-wt=17): 342 [] -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))). % 7.82/7.84 ** KEPT (pick-wt=15): 343 [] -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)). % 7.82/7.84 ** KEPT (pick-wt=21): 344 [] -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)). % 7.82/7.84 ** KEPT (pick-wt=19): 345 [] -linordered_semidom(A)| -ord_less(A,one_one(A),B)|power_power(A,B,C)!=power_power(A,B,D)|C=D. % 7.82/7.84 ** KEPT (pick-wt=19): 346 [] -linordered_semidom(A)| -ord_less(A,one_one(A),B)|power_power(A,B,C)=power_power(A,B,D)|C!=D. % 7.82/7.84 ** KEPT (pick-wt=21): 347 [] -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). % 7.82/7.84 ** KEPT (pick-wt=21): 348 [] -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). % 7.82/7.84 Following clause subsumed by 347 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). % 7.82/7.84 Following clause subsumed by 348 during input processing: 0 [] -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)). % 7.82/7.84 ** KEPT (pick-wt=20): 349 [] 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). % 7.82/7.84 ** KEPT (pick-wt=25): 350 [] -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). % 7.82/7.84 ** KEPT (pick-wt=23): 351 [] -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). % 7.82/7.84 ** KEPT (pick-wt=7): 352 [] -zprime(A)|ord_less(int,one_one(int),A). % 7.82/7.84 ** KEPT (pick-wt=24): 353 [] -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). % 7.82/7.84 ** KEPT (pick-wt=13): 354 [] zprime(A)| -ord_less(int,one_one(int),A)|ord_less_e_q(int,zero_zero(int),$f1(A)). % 7.82/7.84 ** KEPT (pick-wt=12): 355 [] zprime(A)| -ord_less(int,one_one(int),A)|dvd_dvd(int,$f1(A),A). % 7.82/7.84 ** KEPT (pick-wt=14): 356 [] zprime(A)| -ord_less(int,one_one(int),A)|ti(int,$f1(A))!=one_one(int). % 7.82/7.84 ** KEPT (pick-wt=15): 357 [] zprime(A)| -ord_less(int,one_one(int),A)|ti(int,$f1(A))!=ti(int,A). % 7.82/7.84 ** KEPT (pick-wt=17): 358 [] -ord_less(nat,zero_zero(nat),power_power(nat,A,B))|ord_less(nat,zero_zero(nat),A)|B=zero_zero(nat). % 7.82/7.84 ** KEPT (pick-wt=13): 359 [] ord_less(nat,zero_zero(nat),power_power(nat,A,B))| -ord_less(nat,zero_zero(nat),A). % 7.82/7.84 ** KEPT (pick-wt=12): 360 [] ord_less(nat,zero_zero(nat),power_power(nat,A,B))|B!=zero_zero(nat). % 7.82/7.84 Following clause subsumed by 358 during input processing: 0 [] -ord_less(nat,zero_zero(nat),power_power(nat,A,B))|B=zero_zero(nat)|ord_less(nat,zero_zero(nat),A). % 7.82/7.84 Following clause subsumed by 360 during input processing: 0 [] ord_less(nat,zero_zero(nat),power_power(nat,A,B))|B!=zero_zero(nat). % 7.82/7.84 Following clause subsumed by 359 during input processing: 0 [] ord_less(nat,zero_zero(nat),power_power(nat,A,B))| -ord_less(nat,zero_zero(nat),A). % 7.82/7.84 Following clause subsumed by 358 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). % 7.82/7.84 Following clause subsumed by 360 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). % 7.82/7.84 Following clause subsumed by 359 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). % 7.82/7.84 ** KEPT (pick-wt=19): 361 [] -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). % 7.82/7.84 ** KEPT (pick-wt=9): 362 [] bit1(A)!=min|ti(int,A)=min. % 7.82/7.84 ** KEPT (pick-wt=9): 363 [] bit1(A)=min|ti(int,A)!=min. % 7.82/7.84 Following clause subsumed by 362 during input processing: 0 [flip.1,flip.2] bit1(A)!=min|ti(int,A)=min. % 7.82/7.84 Following clause subsumed by 363 during input processing: 0 [flip.1,flip.2] bit1(A)=min|ti(int,A)!=min. % 7.82/7.84 ** KEPT (pick-wt=3): 364 [] pls!=min. % 7.82/7.84 Following clause subsumed by 364 during input processing: 0 [flip.1] pls!=min. % 7.82/7.84 ** KEPT (pick-wt=4): 365 [] bit0(A)!=min. % 7.82/7.84 Following clause subsumed by 365 during input processing: 0 [flip.1] bit0(A)!=min. % 7.82/7.84 ** KEPT (pick-wt=4): 366 [] -ord_less(int,min,min). % 7.82/7.84 ** KEPT (pick-wt=12): 367 [] -ord_less(real,zero_zero(real),times_times(real,A,A))|A!=zero_zero(real). % 7.82/7.84 ** KEPT (pick-wt=9): 368 [] -ord_less(int,bit1(A),min)|ord_less(int,A,min). % 7.82/7.84 ** KEPT (pick-wt=9): 369 [] ord_less(int,bit1(A),min)| -ord_less(int,A,min). % 7.82/7.84 ** KEPT (pick-wt=9): 370 [] -ord_less(int,min,bit1(A))|ord_less(int,min,A). % 7.82/7.84 ** KEPT (pick-wt=9): 371 [] ord_less(int,min,bit1(A))| -ord_less(int,min,A). % 7.82/7.84 ** KEPT (pick-wt=4): 372 [] -ord_less(int,pls,min). % 7.82/7.84 ** KEPT (pick-wt=9): 373 [] -ord_less(int,min,bit0(A))|ord_less(int,min,A). % 7.82/7.84 ** KEPT (pick-wt=9): 374 [] ord_less(int,min,bit0(A))| -ord_less(int,min,A). % 7.82/7.84 ** KEPT (pick-wt=9): 375 [] -ord_less_e_q(int,bit1(A),min)|ord_less_e_q(int,A,min). % 7.82/7.84 ** KEPT (pick-wt=9): 376 [] ord_less_e_q(int,bit1(A),min)| -ord_less_e_q(int,A,min). % 7.82/7.84 ** KEPT (pick-wt=9): 377 [] -ord_less_e_q(int,min,bit1(A))|ord_less_e_q(int,min,A). % 7.82/7.84 ** KEPT (pick-wt=9): 378 [] ord_less_e_q(int,min,bit1(A))| -ord_less_e_q(int,min,A). % 7.82/7.84 ** KEPT (pick-wt=4): 379 [] -ord_less_e_q(int,pls,min). % 7.82/7.84 ** KEPT (pick-wt=9): 380 [] -ord_less_e_q(int,bit0(A),min)|ord_less_e_q(int,A,min). % 7.82/7.84 ** KEPT (pick-wt=9): 381 [] ord_less_e_q(int,bit0(A),min)| -ord_less_e_q(int,A,min). % 7.82/7.84 ** KEPT (pick-wt=7): 382 [] number_number_of(int,pls)!=number_number_of(int,min). % 7.82/7.84 ** KEPT (pick-wt=19): 383 [] -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). % 7.82/7.84 ** KEPT (pick-wt=10): 384 [] -comm_semiring_1(A)|power_power(A,B,zero_zero(nat))=one_one(A). % 7.82/7.84 ** KEPT (pick-wt=10): 385 [] -power(A)|power_power(A,B,zero_zero(nat))=one_one(A). % 7.82/7.84 ** KEPT (pick-wt=9): 386 [] -ord_less_e_q(int,min,bit0(A))|ord_less(int,min,A). % 7.82/7.84 ** KEPT (pick-wt=9): 387 [] ord_less_e_q(int,min,bit0(A))| -ord_less(int,min,A). % 7.82/7.84 ** KEPT (pick-wt=9): 388 [] -ord_less(int,bit0(A),min)|ord_less_e_q(int,A,min). % 7.82/7.84 ** KEPT (pick-wt=9): 389 [] ord_less(int,bit0(A),min)| -ord_less_e_q(int,A,min). % 7.82/7.84 ** KEPT (pick-wt=20): 390 [] times_times(int,A,B)!=one_one(int)|ti(int,A)=one_one(int)|ti(int,A)=number_number_of(int,min). % 7.82/7.84 Following clause subsumed by 390 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). % 7.82/7.84 ** KEPT (pick-wt=20): 391 [] times_times(int,A,B)!=one_one(int)|ti(int,A)=one_one(int)|ti(int,B)=number_number_of(int,min). % 7.82/7.84 ** KEPT (pick-wt=20): 392 [] times_times(int,A,B)!=one_one(int)|ti(int,B)=one_one(int)|ti(int,A)=number_number_of(int,min). % 7.82/7.84 ** KEPT (pick-wt=20): 393 [] times_times(int,A,B)!=one_one(int)|ti(int,B)=one_one(int)|ti(int,B)=number_number_of(int,min). % 7.82/7.84 ** KEPT (pick-wt=19): 394 [] times_times(int,A,B)=one_one(int)|ti(int,A)!=one_one(int)|ti(int,B)!=one_one(int). % 7.82/7.84 ** KEPT (pick-wt=21): 395 [] times_times(int,A,B)=one_one(int)|ti(int,A)!=number_number_of(int,min)|ti(int,B)!=number_number_of(int,min). % 7.82/7.84 ** KEPT (pick-wt=20): 396 [] -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)). % 7.82/7.84 ** KEPT (pick-wt=14): 397 [] -comm_semiring_1(A)| -ord_less(nat,zero_zero(nat),B)|dvd_dvd(A,C,power_power(A,C,B)). % 7.82/7.84 ** KEPT (pick-wt=15): 398 [] -comm_semiring_1(A)|ti(A,B)!=one_one(A)|dvd_dvd(A,B,power_power(A,B,C)). % 7.82/7.84 ** KEPT (pick-wt=11): 399 [] -ord_less(nat,zero_zero(nat),number_number_of(nat,A))|ord_less(int,pls,A). % 7.82/7.84 ** KEPT (pick-wt=11): 400 [] ord_less(nat,zero_zero(nat),number_number_of(nat,A))| -ord_less(int,pls,A). % 7.82/7.84 ** KEPT (pick-wt=10): 401 [] number_number_of(nat,A)!=zero_zero(nat)|ord_less_e_q(int,A,pls). % 7.82/7.84 ** KEPT (pick-wt=10): 402 [] number_number_of(nat,A)=zero_zero(nat)| -ord_less_e_q(int,A,pls). % 7.82/7.84 ** KEPT (pick-wt=10): 403 [] zero_zero(nat)!=number_number_of(nat,A)|ord_less_e_q(int,A,pls). % 7.82/7.84 ** KEPT (pick-wt=10): 404 [] zero_zero(nat)=number_number_of(nat,A)| -ord_less_e_q(int,A,pls). % 7.82/7.84 ** KEPT (pick-wt=8): 405 [] -zcong(A,B,C)|zcong(B,A,C). % 7.82/7.84 Following clause subsumed by 405 during input processing: 0 [] zcong(A,B,C)| -zcong(B,A,C). % 7.82/7.84 ** KEPT (pick-wt=12): 406 [] -zcong(A,B,C)| -zcong(B,D,C)|zcong(A,D,C). % 7.82/7.84 ** KEPT (pick-wt=18): 407 [] -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). % 7.82/7.84 ** KEPT (pick-wt=15): 408 [] -ord_less(int,A,pls)|times_times(nat,number_number_of(nat,A),number_number_of(nat,B))=zero_zero(nat). % 7.82/7.84 ** KEPT (pick-wt=17): 409 [] -order(A)| -ord_less_e_q(A,B,C)|ti(A,B)=ti(A,C)|ord_less(A,B,C). % 7.82/7.84 ** KEPT (pick-wt=16): 410 [] -ord_less(int,A,B)| -ord_less(int,C,B)|ord_less_e_q(int,A,C)|ord_less_e_q(int,C,A). % 7.84/7.85 ** KEPT (pick-wt=12): 411 [] -zcong(A,B,zero_zero(int))|ti(int,A)=ti(int,B). % 7.84/7.85 ** KEPT (pick-wt=12): 412 [] zcong(A,B,zero_zero(int))|ti(int,A)!=ti(int,B). % 7.84/7.85 ** KEPT (pick-wt=18): 413 [] -zcong(A,B,C)| -zcong(D,E,C)|zcong(times_times(int,A,D),times_times(int,B,E),C). % 7.84/7.85 ** KEPT (pick-wt=14): 414 [] -zcong(A,B,C)|zcong(times_times(int,D,A),times_times(int,D,B),C). % 7.84/7.85 ** KEPT (pick-wt=14): 415 [] -zcong(A,B,C)|zcong(times_times(int,A,D),times_times(int,B,D),C). % 7.84/7.85 ** KEPT (pick-wt=18): 416 [] -zcong(A,B,C)| -zcong(D,E,C)|zcong(plus_plus(int,A,D),plus_plus(int,B,E),C). % 7.84/7.85 ** KEPT (pick-wt=18): 417 [] -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). % 7.84/7.85 Following clause subsumed by 227 during input processing: 0 [] -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). % 7.84/7.85 Following clause subsumed by 228 during input processing: 0 [] -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). % 7.84/7.85 Following clause subsumed by 229 during input processing: 0 [] -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). % 7.84/7.85 ** KEPT (pick-wt=22): 418 [] -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). % 7.84/7.85 ** KEPT (pick-wt=18): 419 [] -zcong(A,B,C)|ti(int,B)=plus_plus(int,A,times_times(int,C,$f2(A,B,C))). % 7.84/7.85 ** KEPT (pick-wt=15): 420 [] zcong(A,B,C)|ti(int,B)!=plus_plus(int,A,times_times(int,C,D)). % 7.84/7.85 Following clause subsumed by 239 during input processing: 0 [] -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). % 7.84/7.85 Following clause subsumed by 240 during input processing: 0 [] -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). % 7.84/7.85 ** KEPT (pick-wt=29): 421 [] -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). % 7.84/7.85 ** KEPT (pick-wt=20): 422 [] -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). % 7.84/7.85 ** KEPT (pick-wt=22): 423 [] -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). % 7.84/7.85 ** KEPT (pick-wt=35): 424 [] -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). % 7.84/7.85 ** KEPT (pick-wt=37): 425 [] 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). % 7.84/7.85 ** KEPT (pick-wt=18): 426 [] -zcong(A,B,C)| -zcong(D,E,C)|zcong(minus_minus(int,A,D),minus_minus(int,B,E),C). % 7.84/7.85 ** KEPT (pick-wt=15): 427 [] -dvd_dvd(int,A,minus_minus(int,B,C))| -dvd_dvd(int,A,C)|dvd_dvd(int,A,B). % 7.84/7.85 ** KEPT (pick-wt=17): 428 [] -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)). % 7.84/7.85 ** KEPT (pick-wt=28): 429 [] -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)). % 7.84/7.85 ** KEPT (pick-wt=28): 430 [] -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))). % 7.84/7.85 ** KEPT (pick-wt=12): 431 [] -ord_less(int,A,B)|ord_less(int,minus_minus(int,A,B),zero_zero(int)). % 7.84/7.85 ** KEPT (pick-wt=12): 432 [] ord_less(int,A,B)| -ord_less(int,minus_minus(int,A,B),zero_zero(int)). % 7.84/7.85 ** KEPT (pick-wt=11): 433 [] -zcong(A,B,C)|dvd_dvd(int,C,minus_minus(int,A,B)). % 7.84/7.85 ** KEPT (pick-wt=11): 434 [] zcong(A,B,C)| -dvd_dvd(int,C,minus_minus(int,A,B)). % 7.84/7.85 ** KEPT (pick-wt=23): 435 [] -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). % 7.84/7.85 ** KEPT (pick-wt=26): 436 [] -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))). % 7.84/7.85 ** KEPT (pick-wt=12): 437 [] -ord_less_e_q(int,A,minus_minus(int,B,one_one(int)))|ord_less(int,A,B). % 7.84/7.85 ** KEPT (pick-wt=12): 438 [] ord_less_e_q(int,A,minus_minus(int,B,one_one(int)))| -ord_less(int,A,B). % 7.84/7.85 ** KEPT (pick-wt=20): 439 [] -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). % 7.84/7.85 ** KEPT (pick-wt=20): 440 [] 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). % 7.84/7.85 ** KEPT (pick-wt=28): 441 [] -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). % 7.84/7.85 ** KEPT (pick-wt=34): 442 [] -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)). % 7.84/7.85 ** KEPT (pick-wt=45): 443 [] -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)). % 7.84/7.85 ** KEPT (pick-wt=34): 444 [] -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). % 7.84/7.85 ** KEPT (pick-wt=15): 445 [] -ord_less(int,number_number_of(int,bit0(bit1(pls))),A)| -zcong(one_one(int),number_number_of(int,min),A). % 7.84/7.85 ** KEPT (pick-wt=19): 446 [] -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). % 7.84/7.85 ** KEPT (pick-wt=11): 447 [] -zcong(A,zero_zero(int),B)|legendre(A,B)=zero_zero(int). % 7.84/7.85 ** KEPT (pick-wt=14): 448 [] zcong(A,zero_zero(int),B)| -quadRes(B,A)|legendre(A,B)=one_one(int). % 7.84/7.85 ** KEPT (pick-wt=22): 449 [] -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). % 7.84/7.85 ** KEPT (pick-wt=11): 450 [] -dvd_dvd(nat,A,B)| -dvd_dvd(nat,B,A)|A=B. % 7.84/7.85 ** KEPT (pick-wt=7): 451 [] dvd_dvd(nat,A,B)|A!=B. % 7.84/7.85 ** KEPT (pick-wt=7): 452 [] dvd_dvd(nat,A,B)|B!=A. % 7.84/7.85 ** KEPT (pick-wt=19): 453 [] -zcong(A,B,C)|ti(int,B)!=ti(int,D)| -zcong(D,E,C)|zcong(A,E,C). % 7.84/7.85 ** KEPT (pick-wt=11): 454 [] A!=zero_zero(nat)|times_times(nat,A,B)=zero_zero(nat). % 7.84/7.85 ** KEPT (pick-wt=11): 455 [] A!=zero_zero(nat)|power_power(nat,B,A)=one_one(nat). % 7.84/7.85 ** KEPT (pick-wt=15): 456 [] -dvd_dvd(nat,A,B)| -dvd_dvd(nat,A,plus_plus(nat,B,C))|dvd_dvd(nat,A,C). % 7.84/7.85 ** KEPT (pick-wt=14): 457 [] -dvd_dvd(nat,A,B)|dvd_dvd(nat,times_times(nat,C,A),times_times(nat,C,B)). % 7.84/7.85 ** KEPT (pick-wt=14): 458 [] -dvd_dvd(nat,A,B)|dvd_dvd(nat,times_times(nat,A,C),times_times(nat,B,C)). % 7.84/7.85 ** KEPT (pick-wt=11): 459 [] times_times(nat,A,B)!=one_one(nat)|A=one_one(nat). % 7.84/7.85 ** KEPT (pick-wt=11): 460 [] times_times(nat,A,B)!=one_one(nat)|B=one_one(nat). % 7.84/7.85 ** KEPT (pick-wt=15): 461 [] times_times(nat,A,B)=one_one(nat)|A!=one_one(nat)|B!=one_one(nat). % 7.84/7.85 ** KEPT (pick-wt=16): 462 [] minus_minus(int,A,B)!=ti(int,C)|ti(int,A)=plus_plus(int,C,B). % 7.84/7.85 ** KEPT (pick-wt=18): 463 [] -zcong(A,B,C)| -zcong(D,times_times(int,E,A),C)|zcong(D,times_times(int,E,B),C). % 7.84/7.85 ** KEPT (pick-wt=18): 464 [] -zcong(A,B,C)|zcong(D,times_times(int,E,A),C)| -zcong(D,times_times(int,E,B),C). % 7.84/7.85 ** KEPT (pick-wt=18): 465 [] -zcong(A,B,C)| -zcong(D,times_times(int,A,E),C)|zcong(D,times_times(int,B,E),C). % 7.84/7.85 ** KEPT (pick-wt=18): 466 [] -zcong(A,B,C)|zcong(D,times_times(int,A,E),C)| -zcong(D,times_times(int,B,E),C). % 7.84/7.85 ** KEPT (pick-wt=14): 467 [] -zcong(A,B,C)|zcong(plus_plus(int,A,D),plus_plus(int,B,D),C). % 7.84/7.85 ** KEPT (pick-wt=11): 468 [] power_power(nat,A,B)!=zero_zero(nat)|B!=zero_zero(nat). % 7.84/7.85 ** KEPT (pick-wt=11): 469 [] power_power(nat,A,B)!=zero_zero(nat)|A=zero_zero(nat). % 7.84/7.85 ** KEPT (pick-wt=15): 470 [] power_power(nat,A,B)=zero_zero(nat)|B=zero_zero(nat)|A!=zero_zero(nat). % 7.84/7.85 ** KEPT (pick-wt=14): 471 [] -dvd_dvd(nat,A,B)|dvd_dvd(nat,power_power(nat,A,C),power_power(nat,B,C)). % 7.84/7.85 ** KEPT (pick-wt=14): 472 [] -zcong(A,B,C)|zcong(power_power(int,A,D),power_power(int,B,D),C). % 7.84/7.85 ** KEPT (pick-wt=12): 473 [] -dvd_dvd(nat,A,B)|B=zero_zero(nat)|ord_less_e_q(nat,A,B). % 7.84/7.85 ** KEPT (pick-wt=18): 474 [] -dvd_dvd(nat,times_times(nat,A,B),times_times(nat,C,B))|B=zero_zero(nat)|dvd_dvd(nat,A,C). % 7.84/7.85 ** KEPT (pick-wt=14): 475 [] dvd_dvd(nat,times_times(nat,A,B),times_times(nat,C,B))|B!=zero_zero(nat). % 7.84/7.85 Following clause subsumed by 458 during input processing: 0 [] dvd_dvd(nat,times_times(nat,A,B),times_times(nat,C,B))| -dvd_dvd(nat,A,C). % 7.84/7.85 ** KEPT (pick-wt=14): 476 [] -ord_less(int,zero_zero(int),A)| -ord_less(int,A,B)| -zcong(A,zero_zero(int),B). % 7.84/7.85 ** KEPT (pick-wt=34): 477 [] -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). % 7.84/7.85 ** KEPT (pick-wt=13): 478 [] -dvd_dvd(int,A,B)|ord_less_e_q(int,B,zero_zero(int))|ord_less_e_q(int,A,B). % 7.84/7.85 ** KEPT (pick-wt=15): 479 [] A=zero_zero(nat)| -dvd_dvd(nat,power_power(nat,B,A),C)|dvd_dvd(nat,B,C). % 7.84/7.85 ** KEPT (pick-wt=18): 480 [] -dvd_dvd(nat,power_power(nat,A,B),power_power(nat,C,B))|B=zero_zero(nat)|dvd_dvd(nat,A,C). % 7.84/7.85 ** KEPT (pick-wt=9): 481 [] -zcong(A,zero_zero(int),B)|dvd_dvd(int,B,A). % 7.84/7.85 ** KEPT (pick-wt=9): 482 [] zcong(A,zero_zero(int),B)| -dvd_dvd(int,B,A). % 7.84/7.85 Following clause subsumed by 481 during input processing: 0 [] -zcong(A,zero_zero(int),B)|dvd_dvd(int,B,A). % 7.84/7.85 Following clause subsumed by 482 during input processing: 0 [] zcong(A,zero_zero(int),B)| -dvd_dvd(int,B,A). % 7.84/7.85 ** KEPT (pick-wt=15): 483 [] power_power(nat,A,B)!=one_one(nat)|A=one_one(nat)|B=zero_zero(nat). % 7.84/7.85 ** KEPT (pick-wt=11): 484 [] power_power(nat,A,B)=one_one(nat)|A!=one_one(nat). % 7.84/7.85 Following clause subsumed by 455 during input processing: 0 [] power_power(nat,A,B)=one_one(nat)|B!=zero_zero(nat). % 7.84/7.85 ** KEPT (pick-wt=17): 485 [] -zprime(A)| -dvd_dvd(int,A,times_times(int,B,C))|dvd_dvd(int,A,B)|dvd_dvd(int,A,C). % 7.84/7.85 Following clause subsumed by 422 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). % 7.84/7.85 ** KEPT (pick-wt=16): 486 [] -ord_less(nat,zero_zero(nat),A)| -dvd_dvd(int,B,C)|dvd_dvd(int,B,power_power(int,C,A)). % 7.84/7.85 ** KEPT (pick-wt=20): 487 [] -zprime(A)|zcong(B,zero_zero(int),A)|zcong(C,zero_zero(int),A)| -zcong(times_times(int,B,C),zero_zero(int),A). % 7.84/7.85 ** KEPT (pick-wt=22): 488 [] 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). % 7.84/7.85 Following clause subsumed by 487 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). % 7.84/7.85 Following clause subsumed by 487 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). % 7.84/7.85 Following clause subsumed by 269 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). % 7.84/7.85 ** KEPT (pick-wt=16): 489 [] -quadRes(A,B)|zcong(power_power(int,$f3(A,B),number_number_of(nat,bit0(bit1(pls)))),B,A). % 7.84/7.85 ** KEPT (pick-wt=14): 490 [] quadRes(A,B)| -zcong(power_power(int,C,number_number_of(nat,bit0(bit1(pls)))),B,A). % 7.84/7.85 ** KEPT (pick-wt=25): 491 [] 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). % 7.84/7.85 ** KEPT (pick-wt=25): 492 [] 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). % 7.84/7.85 ** KEPT (pick-wt=29): 493 [] 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). % 7.84/7.85 ** KEPT (pick-wt=25): 494 [] -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). % 7.84/7.85 ** KEPT (pick-wt=5): 495 [] zero_zero(real)!=one_one(real). % 7.84/7.85 ** KEPT (pick-wt=12): 496 [] -ord_less_e_q(real,A,B)|ord_less_e_q(real,minus_minus(real,A,B),zero_zero(real)). % 7.84/7.85 ** KEPT (pick-wt=12): 497 [] ord_less_e_q(real,A,B)| -ord_less_e_q(real,minus_minus(real,A,B),zero_zero(real)). % 7.84/7.85 ** KEPT (pick-wt=8): 498 [] -ord_less(real,A,B)|ord_less_e_q(real,A,B). % 7.84/7.85 ** KEPT (pick-wt=7): 499 [] -ord_less(real,A,B)|A!=B. % 7.84/7.85 ** KEPT (pick-wt=11): 500 [] ord_less(real,A,B)| -ord_less_e_q(real,A,B)|A=B. % 7.84/7.85 Following clause subsumed by 500 during input processing: 0 [] -ord_less_e_q(real,A,B)|ord_less(real,A,B)|A=B. % 7.84/7.85 Following clause subsumed by 498 during input processing: 0 [] ord_less_e_q(real,A,B)| -ord_less(real,A,B). % 7.84/7.85 ** KEPT (pick-wt=7): 501 [] ord_less_e_q(real,A,B)|A!=B. % 7.84/7.85 ** KEPT (pick-wt=14): 502 [] -ord_less_e_q(real,A,B)|ord_less_e_q(real,plus_plus(real,C,A),plus_plus(real,C,B)). % 7.84/7.85 ** KEPT (pick-wt=23): 504 [copy,503,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)). % 7.84/7.85 ** KEPT (pick-wt=16): 505 [] A=zero_zero(real)|times_times(real,A,B)!=times_times(real,A,C)|B=C. % 7.84/7.85 ** KEPT (pick-wt=16): 506 [] A=zero_zero(real)|times_times(real,A,B)=times_times(real,A,C)|B!=C. % 7.84/7.85 ** KEPT (pick-wt=16): 507 [] A=zero_zero(real)|times_times(real,B,A)!=times_times(real,C,A)|B=C. % 7.84/7.85 ** KEPT (pick-wt=16): 508 [] A=zero_zero(real)|times_times(real,B,A)=times_times(real,C,A)|B!=C. % 7.84/7.85 ** KEPT (pick-wt=29): 510 [copy,509,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)). % 7.84/7.85 ** KEPT (pick-wt=19): 511 [] -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)). % 7.84/7.85 ** KEPT (pick-wt=18): 512 [] -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)). % 7.84/7.85 ** KEPT (pick-wt=19): 513 [] -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). % 7.84/7.85 ** KEPT (pick-wt=19): 514 [] -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). % 7.84/7.85 ** KEPT (pick-wt=19): 515 [] -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). % 7.84/7.85 ** KEPT (pick-wt=19): 516 [] -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). % 7.84/7.85 ** KEPT (pick-wt=19): 517 [] -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). % 7.84/7.85 ** KEPT (pick-wt=19): 518 [] -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). % 7.84/7.85 ** KEPT (pick-wt=17): 519 [] plus_plus(real,times_times(real,A,A),times_times(real,B,B))!=zero_zero(real)|A=zero_zero(real). % 7.84/7.85 ** KEPT (pick-wt=17): 520 [] plus_plus(real,times_times(real,A,A),times_times(real,B,B))!=zero_zero(real)|B=zero_zero(real). % 7.84/7.85 ** KEPT (pick-wt=21): 521 [] plus_plus(real,times_times(real,A,A),times_times(real,B,B))=zero_zero(real)|A!=zero_zero(real)|B!=zero_zero(real). % 7.84/7.85 ** KEPT (pick-wt=23): 523 [copy,522,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)). % 7.84/7.85 ** KEPT (pick-wt=23): 524 [] -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). % 7.84/7.85 ** KEPT (pick-wt=25): 525 [] -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). % 7.84/7.85 ** KEPT (pick-wt=26): 526 [] -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)). % 7.84/7.85 ** KEPT (pick-wt=33): 527 [] -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). % 7.84/7.85 ** KEPT (pick-wt=48): 528 [] 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). % 7.84/7.85 ** KEPT (pick-wt=33): 529 [] -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). % 7.84/7.85 ** KEPT (pick-wt=48): 530 [] 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). % 7.84/7.85 ** KEPT (pick-wt=26): 531 [] -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)). % 7.84/7.85 ** KEPT (pick-wt=13): 532 [] -power(A)|B!=zero_zero(nat)|power_power(A,C,B)=one_one(A). % 7.84/7.85 ** KEPT (pick-wt=22): 534 [copy,533,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). % 7.84/7.85 ** KEPT (pick-wt=11): 535 [] -ord_less_e_q(real,A,B)| -ord_less_e_q(real,B,A)|A=B. % 7.84/7.85 ** KEPT (pick-wt=12): 536 [] -ord_less_e_q(real,A,B)| -ord_less_e_q(real,B,C)|ord_less_e_q(real,A,C). % 7.84/7.85 ** KEPT (pick-wt=18): 537 [] -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)). % 7.84/7.85 ** KEPT (pick-wt=18): 538 [] -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)). % 7.84/7.85 ** KEPT (pick-wt=13): 539 [] -ord_less_e_q(int,zero_zero(int),A)|ord_less_e_q(int,zero_zero(int),power_power(int,A,B)). % 7.84/7.85 ** KEPT (pick-wt=40): 540 [] -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). % 7.84/7.85 ** KEPT (pick-wt=17): 541 [] -ord_less(nat,zero_zero(nat),A)| -ord_less(real,zero_zero(real),B)|ord_less(real,zero_zero(real),$f4(B,A)). % 7.84/7.85 ** KEPT (pick-wt=18): 542 [] -ord_less(nat,zero_zero(nat),A)| -ord_less(real,zero_zero(real),B)|power_power(real,$f4(B,A),A)=B. % 7.84/7.85 ** KEPT (pick-wt=7): 543 [] -comm_semiring_1(A)|dvd_dvd(A,B,zero_zero(A)). % 7.84/7.85 ** KEPT (pick-wt=17): 544 [] -linordered_idom(A)|ti(A,B)=ti(A,C)|ord_less(A,B,C)|ord_less(A,C,B). % 7.84/7.85 ** KEPT (pick-wt=14): 545 [] -comm_semiring_1(A)| -dvd_dvd(A,B,C)| -dvd_dvd(A,C,D)|dvd_dvd(A,B,D). % 7.84/7.85 ** KEPT (pick-wt=6): 546 [] -comm_semiring_1(A)|dvd_dvd(A,B,B). % 7.84/7.85 ** KEPT (pick-wt=10): 547 [] -mult_zero(A)|times_times(A,zero_zero(A),B)=zero_zero(A). % 7.84/7.85 ** KEPT (pick-wt=10): 548 [] -mult_zero(A)|times_times(A,B,zero_zero(A))=zero_zero(A). % 7.84/7.85 ** KEPT (pick-wt=21): 549 [] -ring_n68954251visors(A)|times_times(A,B,C)!=zero_zero(A)|ti(A,B)=zero_zero(A)|ti(A,C)=zero_zero(A). % 7.84/7.85 ** KEPT (pick-wt=15): 550 [] -ring_n68954251visors(A)|times_times(A,B,C)=zero_zero(A)|ti(A,B)!=zero_zero(A). % 7.84/7.85 ** KEPT (pick-wt=15): 551 [] -ring_n68954251visors(A)|times_times(A,B,C)=zero_zero(A)|ti(A,C)!=zero_zero(A). % 7.84/7.85 ** KEPT (pick-wt=21): 552 [] -no_zero_divisors(A)|ti(A,B)=zero_zero(A)|ti(A,C)=zero_zero(A)|times_times(A,B,C)!=zero_zero(A). % 7.84/7.87 Following clause subsumed by 552 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). % 7.84/7.87 ** KEPT (pick-wt=7): 554 [copy,553,flip.2] -zero_ne_q_one(A)|zero_zero(A)!=one_one(A). % 7.84/7.87 Following clause subsumed by 554 during input processing: 0 [] -zero_ne_q_one(A)|zero_zero(A)!=one_one(A). % 7.84/7.87 ** KEPT (pick-wt=20): 555 [] -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)). % 7.84/7.87 ** KEPT (pick-wt=26): 557 [copy,556,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)). % 7.84/7.87 ** KEPT (pick-wt=13): 558 [] -comm_semiring_1(A)| -dvd_dvd(A,zero_zero(A),B)|ti(A,B)=zero_zero(A). % 7.84/7.87 ** KEPT (pick-wt=9): 559 [] -comm_semiring_1(A)|dvd_dvd(A,B,times_times(A,B,C)). % 7.84/7.87 ** KEPT (pick-wt=9): 560 [] -comm_semiring_1(A)|dvd_dvd(A,B,times_times(A,C,B)). % 7.84/7.87 ** KEPT (pick-wt=13): 561 [] -comm_semiring_1(A)| -dvd_dvd(A,B,C)|dvd_dvd(A,B,times_times(A,C,D)). % 7.84/7.87 ** KEPT (pick-wt=13): 562 [] -comm_semiring_1(A)| -dvd_dvd(A,B,C)|dvd_dvd(A,B,times_times(A,D,C)). % 7.84/7.87 ** KEPT (pick-wt=20): 563 [] -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)). % 7.84/7.87 ** KEPT (pick-wt=12): 564 [] -dvd(A)|B!=times_times(A,C,D)|dvd_dvd(A,C,B). % 7.84/7.87 ** KEPT (pick-wt=13): 565 [] -comm_semiring_1(A)| -dvd_dvd(A,times_times(A,B,C),D)|dvd_dvd(A,B,D). % 7.84/7.87 ** KEPT (pick-wt=13): 566 [] -comm_semiring_1(A)| -dvd_dvd(A,times_times(A,B,C),D)|dvd_dvd(A,C,D). % 7.84/7.87 ** KEPT (pick-wt=17): 567 [] -comm_semiring_1(A)| -dvd_dvd(A,B,C)| -dvd_dvd(A,B,D)|dvd_dvd(A,B,plus_plus(A,C,D)). % 7.84/7.87 ** KEPT (pick-wt=7): 568 [] -comm_semiring_1(A)|dvd_dvd(A,one_one(A),B). % 7.84/7.87 ** KEPT (pick-wt=17): 569 [] -comm_ring_1(A)| -dvd_dvd(A,B,C)| -dvd_dvd(A,B,D)|dvd_dvd(A,B,minus_minus(A,C,D)). % 7.84/7.87 ** KEPT (pick-wt=10): 570 [] -linordered_ring(A)|ord_less_e_q(A,zero_zero(A),times_times(A,B,B)). % 7.84/7.87 ** KEPT (pick-wt=20): 571 [] -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)). % 7.84/7.87 ** KEPT (pick-wt=20): 572 [] -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)). % 7.84/7.87 ** KEPT (pick-wt=20): 573 [] -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)). % 7.84/7.87 ** KEPT (pick-wt=20): 574 [] -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)). % 7.84/7.87 ** KEPT (pick-wt=20): 575 [] -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). % 7.84/7.87 ** KEPT (pick-wt=20): 576 [] -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)). % 7.84/7.87 ** KEPT (pick-wt=20): 577 [] -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)). % 7.84/7.87 ** KEPT (pick-wt=20): 578 [] -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). % 7.84/7.87 ** KEPT (pick-wt=20): 579 [] -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)). % 7.84/7.87 ** KEPT (pick-wt=20): 580 [] -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). % 7.84/7.87 ** KEPT (pick-wt=20): 581 [] -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)). % 7.84/7.87 ** KEPT (pick-wt=20): 582 [] -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). % 7.84/7.87 ** KEPT (pick-wt=20): 583 [] -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)). % 7.84/7.87 ** KEPT (pick-wt=20): 584 [] -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)). % 7.84/7.87 ** KEPT (pick-wt=20): 585 [] -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)). % 7.84/7.87 Following clause subsumed by 585 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)). % 7.84/7.87 ** KEPT (pick-wt=32): 586 [] plus_plus(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),power_power(int,B,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)). % 7.84/7.87 70 back subsumes 67. % 7.84/7.87 124 back subsumes 122. % 7.84/7.87 125 back subsumes 121. % 7.84/7.87 Following clause subsumed by 180 during input processing: 0 [copy,179,flip.1] bit0(A)!=bit1(B). % 7.84/7.87 Following clause subsumed by 179 during input processing: 0 [copy,180,flip.1] bit1(A)!=bit0(B). % 7.84/7.87 ** KEPT (pick-wt=11): 604 [copy,280,flip.1] zero_zero(int)!=plus_plus(int,plus_plus(int,one_one(int),A),A). % 7.84/7.87 394 back subsumes 304. % 7.84/7.87 485 back subsumes 423. % 7.84/7.87 532 back subsumes 239. % 7.84/7.87 ** KEPT (pick-wt=32): 682 [copy,586,flip.1] plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))!=plus_plus(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),power_power(int,B,number_number_of(nat,bit0(bit1(pls))))). % 7.84/7.87 Following clause subsumed by 280 during input processing: 0 [copy,604,flip.1] plus_plus(int,plus_plus(int,one_one(int),A),A)!=zero_zero(int). % 7.84/7.87 Following clause subsumed by 586 during input processing: 0 [copy,682,flip.1] plus_plus(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),power_power(int,B,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)). % 7.84/7.87 % 7.84/7.87 ------------> process sos: % 7.84/7.87 ** KEPT (pick-wt=3): 691 [] A=A. % 7.84/7.87 ** KEPT (pick-wt=11): 692 [] minus_minus(nat,ti(nat,A),B)=minus_minus(nat,A,B). % 7.84/7.87 ---> New Demodulator: 693 [new_demod,692] minus_minus(nat,ti(nat,A),B)=minus_minus(nat,A,B). % 7.84/7.87 ** KEPT (pick-wt=11): 694 [] minus_minus(nat,A,ti(nat,B))=minus_minus(nat,A,B). % 7.84/7.87 ---> New Demodulator: 695 [new_demod,694] minus_minus(nat,A,ti(nat,B))=minus_minus(nat,A,B). % 7.84/7.87 ** KEPT (pick-wt=11): 696 [] ti(nat,minus_minus(nat,A,B))=minus_minus(nat,A,B). % 7.84/7.87 ---> New Demodulator: 697 [new_demod,696] ti(nat,minus_minus(nat,A,B))=minus_minus(nat,A,B). % 7.84/7.87 ** KEPT (pick-wt=7): 698 [] ti(A,undefined(A))=undefined(A). % 7.84/7.87 ---> New Demodulator: 699 [new_demod,698] ti(A,undefined(A))=undefined(A). % 7.84/7.87 ** KEPT (pick-wt=7): 700 [] bit0(ti(int,A))=bit0(A). % 7.84/7.87 ---> New Demodulator: 701 [new_demod,700] bit0(ti(int,A))=bit0(A). % 7.84/7.87 ** KEPT (pick-wt=7): 702 [] ti(int,bit0(A))=bit0(A). % 7.84/7.87 ---> New Demodulator: 703 [new_demod,702] ti(int,bit0(A))=bit0(A). % 7.84/7.87 ** KEPT (pick-wt=7): 704 [] bit1(ti(int,A))=bit1(A). % 7.84/7.87 ---> New Demodulator: 705 [new_demod,704] bit1(ti(int,A))=bit1(A). % 7.84/7.87 ** KEPT (pick-wt=7): 706 [] ti(int,bit1(A))=bit1(A). % 7.84/7.87 ---> New Demodulator: 707 [new_demod,706] ti(int,bit1(A))=bit1(A). % 7.84/7.87 ** KEPT (pick-wt=5): 708 [] ti(int,min)=min. % 7.84/7.87 ---> New Demodulator: 709 [new_demod,708] ti(int,min)=min. % 7.84/7.87 ** KEPT (pick-wt=5): 710 [] ti(int,pls)=pls. % 7.84/7.87 ---> New Demodulator: 711 [new_demod,710] ti(int,pls)=pls. % 7.84/7.87 ** KEPT (pick-wt=13): 712 [] product_Pair(int,int,ti(int,A),B)=product_Pair(int,int,A,B). % 7.84/7.87 ---> New Demodulator: 713 [new_demod,712] product_Pair(int,int,ti(int,A),B)=product_Pair(int,int,A,B). % 7.84/7.87 ** KEPT (pick-wt=13): 714 [] product_Pair(int,int,A,ti(int,B))=product_Pair(int,int,A,B). % 7.84/7.87 ---> New Demodulator: 715 [new_demod,714] product_Pair(int,int,A,ti(int,B))=product_Pair(int,int,A,B). % 7.84/7.87 ** KEPT (pick-wt=15): 716 [] ti(product_prod(int,int),product_Pair(int,int,A,B))=product_Pair(int,int,A,B). % 7.84/7.87 ---> New Demodulator: 717 [new_demod,716] ti(product_prod(int,int),product_Pair(int,int,A,B))=product_Pair(int,int,A,B). % 7.84/7.87 ** KEPT (pick-wt=9): 718 [] legendre(ti(int,A),B)=legendre(A,B). % 7.84/7.87 ---> New Demodulator: 719 [new_demod,718] legendre(ti(int,A),B)=legendre(A,B). % 7.84/7.87 ** KEPT (pick-wt=9): 720 [] legendre(A,ti(int,B))=legendre(A,B). % 7.84/7.87 ---> New Demodulator: 721 [new_demod,720] legendre(A,ti(int,B))=legendre(A,B). % 7.84/7.87 ** KEPT (pick-wt=9): 722 [] ti(int,legendre(A,B))=legendre(A,B). % 7.84/7.87 ---> New Demodulator: 723 [new_demod,722] ti(int,legendre(A,B))=legendre(A,B). % 7.84/7.87 ** KEPT (pick-wt=9): 724 [] twoSqu579703163sum2sq(ti(product_prod(int,int),A))=twoSqu579703163sum2sq(A). % 7.84/7.87 ---> New Demodulator: 725 [new_demod,724] twoSqu579703163sum2sq(ti(product_prod(int,int),A))=twoSqu579703163sum2sq(A). % 7.84/7.87 ** KEPT (pick-wt=7): 726 [] ti(int,twoSqu579703163sum2sq(A))=twoSqu579703163sum2sq(A). % 7.84/7.87 ---> New Demodulator: 727 [new_demod,726] ti(int,twoSqu579703163sum2sq(A))=twoSqu579703163sum2sq(A). % 7.84/7.87 ** KEPT (pick-wt=5): 728 [] ti(int,m)=m. % 7.84/7.87 ---> New Demodulator: 729 [new_demod,728] ti(int,m)=m. % 7.84/7.87 ** KEPT (pick-wt=5): 730 [] ti(int,s1)=s1. % 7.84/7.87 ---> New Demodulator: 731 [new_demod,730] ti(int,s1)=s1. % 7.84/7.87 ** KEPT (pick-wt=5): 732 [] ti(int,s)=s. % 7.84/7.87 ---> New Demodulator: 733 [new_demod,732] ti(int,s)=s. % 7.84/7.87 ** KEPT (pick-wt=5): 734 [] ti(int,t)=t. % 7.84/7.87 ---> New Demodulator: 735 [new_demod,734] ti(int,t)=t. % 7.84/7.87 ** KEPT (pick-wt=5): 736 [] ord_less_e_q(int,one_one(int),t). % 7.84/7.87 ** KEPT (pick-wt=16): 737 [] ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))). % 7.84/7.87 ** KEPT (pick-wt=14): 738 [] zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))). % 7.84/7.87 ** KEPT (pick-wt=29): 740 [copy,739,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)). % 7.84/7.87 ---> New Demodulator: 741 [new_demod,740] 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)). % 7.84/7.87 ** KEPT (pick-wt=13): 743 [copy,742,demod,741] twoSqu420862341sum2sq(plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))). % 7.84/7.87 ** KEPT (pick-wt=43): 744 [] power_power(int,plus_plus(int,A,B),number_number_of(nat,bit0(bit1(pls))))=plus_plus(int,plus_plus(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),A),B)),power_power(int,B,number_number_of(nat,bit0(bit1(pls))))). % 7.84/7.87 ** KEPT (pick-wt=70): 745 [] power_power(int,plus_plus(int,A,B),number_number_of(nat,bit1(bit1(pls))))=plus_plus(int,plus_plus(int,plus_plus(int,power_power(int,A,number_number_of(nat,bit1(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),power_power(int,A,number_number_of(nat,bit0(bit1(pls))))),B)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),A),power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,B,number_number_of(nat,bit1(bit1(pls))))). % 7.84/7.87 ** KEPT (pick-wt=20): 746 [] times_times(int,A,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))))=power_power(int,A,number_number_of(nat,bit1(bit1(pls)))). % 7.84/7.87 ** KEPT (pick-wt=29): 748 [copy,747,flip.1] times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),$c5)=plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)). % 7.84/7.87 ---> New Demodulator: 749 [new_demod,748] times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),$c5)=plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)). % 7.84/7.87 ** KEPT (pick-wt=4): 750 [] ord_less_e_q(int,A,A). % 7.84/7.87 ** KEPT (pick-wt=8): 751 [] ord_less_e_q(int,A,B)|ord_less_e_q(int,B,A). % 7.84/7.87 ** KEPT (pick-wt=15): 752 [] ord_less(int,A,B)|ti(int,A)=ti(int,B)|ord_less(int,B,A). % 7.84/7.87 ** KEPT (pick-wt=15): 753 [] power_power(int,power_power(int,A,B),C)=power_power(int,A,times_times(nat,B,C)). % 7.84/7.87 ** KEPT (pick-wt=18): 755 [copy,754,flip.1] times_times(int,power_power(int,A,B),power_power(int,A,C))=power_power(int,A,plus_plus(nat,B,C)). % 7.84/7.87 ---> New Demodulator: 756 [new_demod,755] times_times(int,power_power(int,A,B),power_power(int,A,C))=power_power(int,A,plus_plus(nat,B,C)). % 7.84/7.87 ** KEPT (pick-wt=13): 757 [] times_times(nat,number_number_of(nat,bit0(bit1(pls))),A)=plus_plus(nat,A,A). % 7.84/7.87 ---> New Demodulator: 758 [new_demod,757] times_times(nat,number_number_of(nat,bit0(bit1(pls))),A)=plus_plus(nat,A,A). % 7.84/7.87 ** KEPT (pick-wt=13): 759 [] times_times(nat,A,number_number_of(nat,bit0(bit1(pls))))=plus_plus(nat,A,A). % 7.84/7.87 ---> New Demodulator: 760 [new_demod,759] times_times(nat,A,number_number_of(nat,bit0(bit1(pls))))=plus_plus(nat,A,A). % 7.84/7.87 ** KEPT (pick-wt=12): 761 [] plus_plus(nat,one_one(nat),one_one(nat))=number_number_of(nat,bit0(bit1(pls))). % 7.84/7.87 ---> New Demodulator: 762 [new_demod,761] plus_plus(nat,one_one(nat),one_one(nat))=number_number_of(nat,bit0(bit1(pls))). % 7.84/7.87 Following clause subsumed by 750 during input processing: 0 [] ord_less_e_q(int,pls,pls). % 7.84/7.87 ** KEPT (pick-wt=23): 764 [copy,763,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)). % 7.84/7.87 ** KEPT (pick-wt=7): 766 [copy,765,flip.1] one_one(nat)=number_number_of(nat,bit1(pls)). % 7.84/7.87 ---> New Demodulator: 767 [new_demod,766] one_one(nat)=number_number_of(nat,bit1(pls)). % 7.84/7.87 Following clause subsumed by 691 during input processing: 0 [demod,767] number_number_of(nat,bit1(pls))=number_number_of(nat,bit1(pls)). % 7.84/7.87 ** KEPT (pick-wt=6): 768 [] zprime(number_number_of(int,bit0(bit1(pls)))). % 7.84/7.87 ** KEPT (pick-wt=15): 769 [] times_times(int,times_times(int,A,B),C)=times_times(int,A,times_times(int,B,C)). % 7.84/7.87 ---> New Demodulator: 770 [new_demod,769] times_times(int,times_times(int,A,B),C)=times_times(int,A,times_times(int,B,C)). % 7.84/7.87 ** KEPT (pick-wt=9): 771 [] times_times(int,A,B)=times_times(int,B,A). % 7.84/7.87 ** KEPT (pick-wt=7): 773 [copy,772,flip.1] ti(int,A)=number_number_of(int,A). % 7.84/7.87 ---> New Demodulator: 774 [new_demod,773] ti(int,A)=number_number_of(int,A). % 7.84/7.87 ** KEPT (pick-wt=15): 775 [] plus_plus(int,plus_plus(int,A,B),C)=plus_plus(int,A,plus_plus(int,B,C)). % 7.84/7.87 ---> New Demodulator: 776 [new_demod,775] plus_plus(int,plus_plus(int,A,B),C)=plus_plus(int,A,plus_plus(int,B,C)). % 7.84/7.87 ** KEPT (pick-wt=15): 777 [] plus_plus(int,A,plus_plus(int,B,C))=plus_plus(int,B,plus_plus(int,A,C)). % 7.84/7.87 ** KEPT (pick-wt=9): 778 [] plus_plus(int,A,B)=plus_plus(int,B,A). % 7.84/7.87 ** KEPT (pick-wt=4): 779 [] bit0(pls)=pls. % 7.84/7.87 ---> New Demodulator: 780 [new_demod,779] bit0(pls)=pls. % 7.84/7.87 ** KEPT (pick-wt=6): 781 [] times_times(int,pls,A)=pls. % 7.84/7.87 ---> New Demodulator: 782 [new_demod,781] times_times(int,pls,A)=pls. % 7.84/7.87 ** KEPT (pick-wt=11): 784 [copy,783,flip.1] bit0(times_times(int,A,B))=times_times(int,bit0(A),B). % 7.84/7.87 ---> New Demodulator: 785 [new_demod,784] bit0(times_times(int,A,B))=times_times(int,bit0(A),B). % 7.84/7.87 ** KEPT (pick-wt=8): 787 [copy,786,demod,774,flip.1] number_number_of(int,A)=plus_plus(int,A,pls). % 7.84/7.87 ---> New Demodulator: 788 [new_demod,787] number_number_of(int,A)=plus_plus(int,A,pls). % 7.84/7.87 Following clause subsumed by 778 during input processing: 0 [demod,774,788] plus_plus(int,pls,A)=plus_plus(int,A,pls). % 7.84/7.87 ** KEPT (pick-wt=12): 790 [copy,789,flip.1] bit0(plus_plus(int,A,B))=plus_plus(int,bit0(A),bit0(B)). % 7.84/7.87 ---> New Demodulator: 791 [new_demod,790] bit0(plus_plus(int,A,B))=plus_plus(int,bit0(A),bit0(B)). % 7.84/7.87 ** KEPT (pick-wt=7): 792 [] bit0(A)=plus_plus(int,A,A). % 7.84/7.87 ---> New Demodulator: 793 [new_demod,792] bit0(A)=plus_plus(int,A,A). % 7.84/7.87 ** KEPT (pick-wt=10): 795 [copy,794,demod,774,788] times_times(int,A,one_one(int))=plus_plus(int,A,pls). % 7.84/7.87 ---> New Demodulator: 796 [new_demod,795] times_times(int,A,one_one(int))=plus_plus(int,A,pls). % 7.84/7.87 ** KEPT (pick-wt=10): 798 [copy,797,demod,774,788] times_times(int,one_one(int),A)=plus_plus(int,A,pls). % 7.84/7.87 ---> New Demodulator: 799 [new_demod,798] times_times(int,one_one(int),A)=plus_plus(int,A,pls). % 7.84/7.87 ** KEPT (pick-wt=18): 801 [copy,800,demod,788,788,788] times_times(int,plus_plus(int,A,pls),plus_plus(int,B,pls))=plus_plus(int,times_times(int,A,B),pls). % 7.84/7.87 ---> New Demodulator: 802 [new_demod,801] times_times(int,plus_plus(int,A,pls),plus_plus(int,B,pls))=plus_plus(int,times_times(int,A,B),pls). % 7.84/7.87 ** KEPT (pick-wt=18): 803 [] times_times(int,plus_plus(int,A,B),C)=plus_plus(int,times_times(int,A,C),times_times(int,B,C)). % 7.84/7.87 ---> New Demodulator: 804 [new_demod,803] times_times(int,plus_plus(int,A,B),C)=plus_plus(int,times_times(int,A,C),times_times(int,B,C)). % 7.84/7.87 ** KEPT (pick-wt=18): 805 [] times_times(int,A,plus_plus(int,B,C))=plus_plus(int,times_times(int,A,B),times_times(int,A,C)). % 7.84/7.87 ---> New Demodulator: 806 [new_demod,805] times_times(int,A,plus_plus(int,B,C))=plus_plus(int,times_times(int,A,B),times_times(int,A,C)). % 7.84/7.87 ** KEPT (pick-wt=18): 808 [copy,807,demod,788,788,776,788,776] plus_plus(int,A,plus_plus(int,pls,plus_plus(int,B,pls)))=plus_plus(int,A,plus_plus(int,B,pls)). % 7.84/7.87 ---> New Demodulator: 809 [new_demod,808] plus_plus(int,A,plus_plus(int,pls,plus_plus(int,B,pls)))=plus_plus(int,A,plus_plus(int,B,pls)). % 7.84/7.87 ** KEPT (pick-wt=14): 811 [copy,810,demod,793] ord_less_e_q(int,A,power_power(int,A,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))). % 7.84/7.87 ** KEPT (pick-wt=14): 813 [copy,812,demod,793,flip.1] bit1(plus_plus(int,A,B))=plus_plus(int,bit1(A),plus_plus(int,B,B)). % 7.84/7.87 ---> New Demodulator: 814 [new_demod,813] bit1(plus_plus(int,A,B))=plus_plus(int,bit1(A),plus_plus(int,B,B)). % 7.84/7.87 ** KEPT (pick-wt=17): 816 [copy,815,demod,793,776,814] plus_plus(int,A,plus_plus(int,A,bit1(B)))=plus_plus(int,bit1(A),plus_plus(int,B,B)). % 7.84/7.87 ** KEPT (pick-wt=11): 818 [copy,817,demod,776] bit1(A)=plus_plus(int,one_one(int),plus_plus(int,A,A)). % 7.84/7.87 ** KEPT (pick-wt=8): 820 [copy,819,demod,788] one_one(int)=plus_plus(int,bit1(pls),pls). % 7.84/7.87 ---> New Demodulator: 821 [new_demod,820] one_one(int)=plus_plus(int,bit1(pls),pls). % 7.84/7.87 ** KEPT (pick-wt=19): 823 [copy,822,demod,793,776] times_times(int,bit1(A),B)=plus_plus(int,times_times(int,A,B),plus_plus(int,times_times(int,A,B),B)). % 7.84/7.87 ---> New Demodulator: 824 [new_demod,823] times_times(int,bit1(A),B)=plus_plus(int,times_times(int,A,B),plus_plus(int,times_times(int,A,B),B)). % 7.84/7.87 ** KEPT (pick-wt=41): 826 [copy,825,demod,793,793,793,793,776] 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)))))). % 7.84/7.87 ** KEPT (pick-wt=39): 828 [copy,827,demod,793,793,776,788,776,776,776,804,824,782,782,804,824,782,782,804,824,782,782,804,824,782,782,782,776,776,809,809,776,776,776,776,776,776,821,776,776,776,776,776,776,776,776,776,776,809] ord_less(int,zero_zero(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,m,plus_plus(int,bit1(pls),pls)))))))))))). % 7.84/7.87 ** KEPT (pick-wt=55): 830 [copy,829,demod,793,793,776,788,776,776,776,804,824,782,782,804,824,782,782,804,824,782,782,804,824,782,782,782,776,776,809,809,776,776,776,776,776,776,821,776,776,776,776,776,776,776,776,776,776,809,793,821] 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,m,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))). % 7.84/7.87 ** KEPT (pick-wt=57): 832 [copy,831,demod,821,793,793,776,788,776,776,776,804,824,782,782,804,824,782,782,804,824,782,782,804,824,782,782,782,776,776,809,809,776,776,776,776,776,776,821,776,776,776,776,776,776,776,776,776,776,809,804,782,804,782,804,804,782,804,782,804,804,782,804,782,804,804,804,824,782,782,782,776,776,809,809] twoSqu579703163sum2sq(product_Pair(int,int,s,plus_plus(int,bit1(pls),pls)))=plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,times_times(int,m,t),plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,times_times(int,m,t),plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,times_times(int,m,t),plus_plus(int,times_times(int,m,t),plus_plus(int,t,pls))))))))))). % 7.84/7.87 ---> New Demodulator: 833 [new_demod,832] twoSqu579703163sum2sq(product_Pair(int,int,s,plus_plus(int,bit1(pls),pls)))=plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,times_times(int,m,t),plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,times_times(int,m,t),plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,times_times(int,m,t),plus_plus(int,times_times(int,m,t),plus_plus(int,t,pls))))))))))). % 7.84/7.87 ** KEPT (pick-wt=55): 835 [copy,834,demod,793,793,793,793,flip.1] plus_plus(real,plus_plus(real,power_power(real,A,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(real,B,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),times_times(real,times_times(real,number_number_of(real,plus_plus(int,bit1(pls),bit1(pls))),A),B))=power_power(real,plus_plus(real,A,B),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))). % 7.84/7.87 ---> New Demodulator: 836 [new_demod,835] plus_plus(real,plus_plus(real,power_power(real,A,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(real,B,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),times_times(real,times_times(real,number_number_of(real,plus_plus(int,bit1(pls),bit1(pls))),A),B))=power_power(real,plus_plus(real,A,B),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))). % 7.84/7.87 ** KEPT (pick-wt=51): 838 [copy,837,demod,793,793,776,793,793,793] 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)))). % 7.84/7.87 ---> New Demodulator: 839 [new_demod,838] 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)))). % 7.84/7.87 ** KEPT (pick-wt=58): 841 [copy,840,demod,793,793,793,793,776,788,776,776,776,804,824,782,782,804,824,782,782,804,824,782,782,804,824,782,782,782,776,776,809,809,776,776,776,776,776,776,821,776,776,776,776,776,776,776,776,776,776,809] 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,m,plus_plus(int,bit1(pls),pls)))))))))))). % 7.84/7.87 ** KEPT (pick-wt=5): 842 [] ord_less_e_q(int,zero_zero(int),s). % 7.84/7.87 ** KEPT (pick-wt=38): 844 [copy,843,demod,793,793,776,788,776,776,776,804,824,782,782,804,824,782,782,804,824,782,782,804,824,782,782,782,776,776,809,809,776,776,776,776,776,776,821,776,776,776,776,776,776,776,776,776,776,809] 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,m,plus_plus(int,bit1(pls),pls)))))))))))). % 7.84/7.87 ** KEPT (pick-wt=38): 846 [copy,845,demod,793,793,776,788,776,776,776,804,824,782,782,804,824,782,782,804,824,782,782,804,824,782,782,782,776,776,809,809,776,776,776,776,776,776,821,776,776,776,776,776,776,776,776,776,776,809] 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,m,plus_plus(int,bit1(pls),pls)))))))))))). % 7.84/7.87 ** KEPT (pick-wt=5): 847 [] ord_less_e_q(int,zero_zero(int),$c6). % 7.84/7.87 ** KEPT (pick-wt=38): 849 [copy,848,demod,793,793,776,788,776,776,776,804,824,782,782,804,824,782,782,804,824,782,782,804,824,782,782,782,776,776,809,809,776,776,776,776,776,776,821,776,776,776,776,776,776,776,776,776,776,809] ord_less(int,$c6,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,m,plus_plus(int,bit1(pls),pls)))))))))))). % 7.84/7.87 ** KEPT (pick-wt=38): 851 [copy,850,demod,793,793,776,788,776,776,776,804,824,782,782,804,824,782,782,804,824,782,782,804,824,782,782,782,776,776,809,809,776,776,776,776,776,776,821,776,776,776,776,776,776,776,776,776,776,809] zcong(s1,$c6,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,m,plus_plus(int,bit1(pls),pls)))))))))))). % 7.84/7.88 ** KEPT (pick-wt=5): 852 [] ord_less_e_q(int,zero_zero(int),$c7). % 7.84/7.88 ** KEPT (pick-wt=38): 854 [copy,853,demod,793,793,776,788,776,776,776,804,824,782,782,804,824,782,782,804,824,782,782,804,824,782,782,782,776,776,809,809,776,776,776,776,776,776,821,776,776,776,776,776,776,776,776,776,776,809] ord_less(int,$c7,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,m,plus_plus(int,m,plus_plus(int,bit1(pls),pls)))))))))))). % 7.84/7.88 ** KEPT (pick-wt=38): 856 [copy,855,demod,793,793,776,788,776,776,776,804,824,782,782,804,824,782,782,804,824,782,782,804,824,782,782,782,776,776,809,809,776,776,776,776,776,776,821,776,776,776,776,776,776,776,776,776,776,809] zcong(s1,$c7,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,m,plus_plus(int,bit1(pls),pls)))))))))))). % 7.84/7.88 ** KEPT (pick-wt=51): 858 [copy,857,demod,793,788,793,793,776,788,776,776,776,804,824,782,782,804,824,782,782,804,824,782,782,804,824,782,782,782,776,776,809,809,776,776,776,776,776,776,821,776,776,776,776,776,776,776,776,776,776,809] 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,m,plus_plus(int,bit1(pls),pls)))))))))))). % 7.84/7.88 ** KEPT (pick-wt=4): 860 [copy,859,flip.1] zero_zero(int)=pls. % 7.84/7.88 ---> New Demodulator: 861 [new_demod,860] zero_zero(int)=pls. % 7.84/7.88 Following clause subsumed by 778 during input processing: 0 [demod,861,774,788] plus_plus(int,pls,A)=plus_plus(int,A,pls). % 7.84/7.88 Following clause subsumed by 691 during input processing: 0 [demod,861,774,788] plus_plus(int,A,pls)=plus_plus(int,A,pls). % 7.84/7.88 ** KEPT (pick-wt=6): 863 [copy,862,demod,861,788,flip.1] plus_plus(int,pls,pls)=pls. % 7.84/7.88 ---> New Demodulator: 864 [new_demod,863] plus_plus(int,pls,pls)=pls. % 7.84/7.88 ** KEPT (pick-wt=8): 866 [copy,865,demod,861,821] ord_less(int,pls,plus_plus(int,bit1(pls),pls)). % 7.84/7.88 ** KEPT (pick-wt=51): 868 [copy,867,demod,793,788,793,793,776,788,776,776,776,804,824,782,782,804,824,782,782,804,824,782,782,804,824,782,782,782,776,776,809,809,776,776,776,776,776,776,821,776,776,776,776,776,776,776,776,776,776,809] 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,m,plus_plus(int,bit1(pls),pls)))))))))))). % 7.84/7.88 ** KEPT (pick-wt=51): 870 [copy,869,demod,793,788,793,793,776,788,776,776,776,804,824,782,782,804,824,782,782,804,824,782,782,804,824,782,782,782,776,776,809,809,776,776,776,776,776,776,821,776,776,776,776,776,776,776,776,776,776,809] zcong(power_power(int,$c8,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,m,plus_plus(int,bit1(pls),pls)))))))))))). % 7.84/7.88 ** KEPT (pick-wt=46): 872 [copy,871,demod,788,793,793,776,788,776,776,776,804,824,782,782,804,824,782,782,804,824,782,782,804,824,782,782,782,776,776,809,809,776,776,776,776,776,776,821,776,776,776,776,776,776,776,776,776,776,809,821] 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,m,plus_plus(int,bit1(pls),pls))))))))))))=plus_plus(int,bit1(pls),pls). % 7.84/7.88 ---> New Demodulator: 873 [new_demod,872] 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,m,plus_plus(int,bit1(pls),pls))))))))))))=plus_plus(int,bit1(pls),pls). % 7.84/7.88 ** KEPT (pick-wt=4): 874 [] bit1(min)=min. % 7.84/7.88 ---> New Demodulator: 875 [new_demod,874] bit1(min)=min. % 7.84/7.88 Following clause subsumed by 750 during input processing: 0 [] ord_less_e_q(int,min,min). % 7.84/7.88 ** KEPT (pick-wt=12): 876 [] ord_less(real,zero_zero(real),times_times(real,A,A))|A=zero_zero(real). % 7.84/7.88 ** KEPT (pick-wt=4): 877 [] ord_less(int,min,pls). % 7.84/7.88 Following clause subsumed by 877 during input processing: 0 [demod,861] ord_less(int,min,pls). % 7.84/7.88 ** KEPT (pick-wt=4): 878 [] ord_less_e_q(int,min,pls). % 7.84/7.88 ** KEPT (pick-wt=6): 880 [copy,879,flip.1] zero_zero(nat)=number_number_of(nat,pls). % 7.84/7.88 ---> New Demodulator: 881 [new_demod,880] zero_zero(nat)=number_number_of(nat,pls). % 7.84/7.88 Following clause subsumed by 691 during input processing: 0 [demod,881] number_number_of(nat,pls)=number_number_of(nat,pls). % 7.84/7.88 ** KEPT (pick-wt=4): 882 [] zcong(A,A,B). % 7.84/7.88 ** KEPT (pick-wt=13): 884 [copy,883,demod,881,793] ord_less(nat,number_number_of(nat,pls),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))). % 7.84/7.88 ** KEPT (pick-wt=25): 886 [copy,885,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)). % 7.84/7.88 ** KEPT (pick-wt=19): 888 [copy,887,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)). % 7.84/7.88 ** KEPT (pick-wt=8): 890 [copy,889,demod,821] zcong(A,B,plus_plus(int,bit1(pls),pls)). % 7.84/7.88 ** KEPT (pick-wt=10): 891 [] zcong(times_times(int,A,B),times_times(int,C,B),B). % 7.84/7.88 ** KEPT (pick-wt=40): 893 [copy,892,demod,793,793,776,788,776,776,776,804,824,782,782,804,824,782,782,804,824,782,782,804,824,782,782,782,776,776,809,809,776,776,776,776,776,776,821,776,776,776,776,776,776,776,776,776,776,809,788] 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,m,plus_plus(int,bit1(pls),pls))))))))))),plus_plus(int,min,pls)). % 7.84/7.88 ** KEPT (pick-wt=54): 895 [copy,894,demod,793,793,776,788,776,776,776,804,824,782,782,804,824,782,782,804,824,782,782,804,824,782,782,782,776,776,809,809,776,776,776,776,776,776,821,776,776,776,776,776,776,776,776,776,776,809,793,788] 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,m,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))). % 7.84/7.88 ** KEPT (pick-wt=36): 897 [copy,896,demod,793,788,793,821,flip.1] 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)). % 7.84/7.88 ---> New Demodulator: 898 [new_demod,897] 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)). % 7.84/7.88 ** KEPT (pick-wt=9): 900 [copy,899,demod,774,788,flip.1] plus_plus(int,A,pls)=minus_minus(int,A,pls). % 7.84/7.88 ---> New Demodulator: 901 [new_demod,900] plus_plus(int,A,pls)=minus_minus(int,A,pls). % 7.84/7.88 ** KEPT (pick-wt=21): 903 [copy,902,demod,793,793,793,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)). % 7.84/7.88 ---> New Demodulator: 904 [new_demod,903] plus_plus(int,minus_minus(int,A,B),minus_minus(int,A,B))=minus_minus(int,plus_plus(int,A,A),plus_plus(int, % 7.84/7.88 Search stopped in tp_alloc by max_mem option. % 7.84/7.88 B,B)). % 7.84/7.88 ** KEPT (pick-wt=18): 905 [] times_times(int,minus_minus(int,A,B),C)=minus_minus(int,times_times(int,A,C),times_times(int,B,C)). % 7.84/7.88 ---> New Demodulator: 906 [new_demod,905] times_times(int,minus_minus(int,A,B),C)=minus_minus(int,times_times(int,A,C),times_times(int,B,C)). % 7.84/7.88 ** KEPT (pick-wt=18): 907 [] times_times(int,A,minus_minus(int,B,C))=minus_minus(int,times_times(int,A,B),times_times(int,A,C)). % 7.84/7.88 ---> New Demodulator: 908 [new_demod,907] times_times(int,A,minus_minus(int,B,C))=minus_minus(int,times_times(int,A,B),times_times(int,A,C)). % 7.84/7.88 ** KEPT (pick-wt=14): 910 [copy,909,demod,793,flip.1] bit1(minus_minus(int,A,B))=minus_minus(int,bit1(A),plus_plus(int,B,B)). % 7.84/7.88 ---> New Demodulator: 911 [new_demod,910] bit1(minus_minus(int,A,B))=minus_minus(int,bit1(A),plus_plus(int,B,B)). % 7.84/7.88 ** KEPT (pick-wt=17): 913 [copy,912,demod,793,904] minus_minus(int,bit1(A),bit1(B))=minus_minus(int,plus_plus(int,A,A),plus_plus(int,B,B)). % 7.84/7.88 ---> New Demodulator: 914 [new_demod,913] minus_minus(int,bit1(A),bit1(B))=minus_minus(int,plus_plus(int,A,A),plus_plus(int,B,B)). % 7.84/7.88 ** KEPT (pick-wt=18): 916 [copy,915,demod,793,793,904,901,flip.1] minus_minus(int,minus_minus(int,pls,pls),plus_plus(int,A,A))=minus_minus(int,pls,plus_plus(int,A,A)). % 7.84/7.88 ---> New Demodulator: 917 [new_demod,916] minus_minus(int,minus_minus(int,pls,pls),plus_plus(int,A,A))=minus_minus(int,pls,plus_plus(int,A,A)). % 7.84/7.88 % 7.84/7.88 Search stopped in tp_alloc by max_mem option. % 7.84/7.88 % 7.84/7.88 ============ end of search ============ % 7.84/7.88 % 7.84/7.88 -------------- statistics ------------- % 7.84/7.88 clauses given 0 % 7.84/7.88 clauses generated 163 % 7.84/7.88 clauses kept 775 % 7.84/7.88 clauses forward subsumed 133 % 7.84/7.88 clauses back subsumed 6 % 7.84/7.88 Kbytes malloced 11718 % 7.84/7.88 % 7.84/7.88 ----------- times (seconds) ----------- % 7.84/7.88 user CPU time 0.11 (0 hr, 0 min, 0 sec) % 7.84/7.88 system CPU time 0.01 (0 hr, 0 min, 0 sec) % 7.84/7.88 wall-clock time 7 (0 hr, 0 min, 7 sec) % 7.84/7.88 % 7.84/7.88 Process 26166 finished Wed Jul 27 09:41:08 2022 % 7.84/7.88 Otter interrupted % 7.84/7.88 PROOF NOT FOUND %------------------------------------------------------------------------------