%------------------------------------------------------------------------------ % File : Otter---3.3 % Problem : NUM926+7 : TPTP v8.1.0. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : otter-tptp-script %s % Computer : n006.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jul 27 13:10:18 EDT 2022 % Result : Unknown 32.69s 32.51s % Output : None % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : NUM926+7 : TPTP v8.1.0. Released v5.3.0. % 0.04/0.13 % Command : otter-tptp-script %s % 0.13/0.34 % Computer : n006.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Jul 27 09:43:46 EDT 2022 % 0.13/0.34 % CPUTime : % 32.58/32.44 ----- Otter 3.3f, August 2004 ----- % 32.58/32.44 The process was started by sandbox on n006.cluster.edu, % 32.58/32.44 Wed Jul 27 09:43:47 2022 % 32.58/32.44 The command was "./otter". The process ID is 20062. % 32.58/32.44 % 32.58/32.44 set(prolog_style_variables). % 32.58/32.44 set(auto). % 32.58/32.44 dependent: set(auto1). % 32.58/32.44 dependent: set(process_input). % 32.58/32.44 dependent: clear(print_kept). % 32.58/32.44 dependent: clear(print_new_demod). % 32.58/32.44 dependent: clear(print_back_demod). % 32.58/32.44 dependent: clear(print_back_sub). % 32.58/32.44 dependent: set(control_memory). % 32.58/32.44 dependent: assign(max_mem, 12000). % 32.58/32.44 dependent: assign(pick_given_ratio, 4). % 32.58/32.44 dependent: assign(stats_level, 1). % 32.58/32.44 dependent: assign(max_seconds, 10800). % 32.58/32.44 clear(print_given). % 32.58/32.44 % 32.58/32.44 formula_list(usable). % 32.58/32.44 all A (A=A). % 32.58/32.44 all X_b X_c X_a B_1_1 B_2_1 (combb(X_b,X_c,X_a,ti(fun(X_b,X_c),B_1_1),B_2_1)=combb(X_b,X_c,X_a,B_1_1,B_2_1)). % 32.58/32.44 all X_b X_c X_a B_1_1 B_2_1 (combb(X_b,X_c,X_a,B_1_1,ti(fun(X_a,X_b),B_2_1))=combb(X_b,X_c,X_a,B_1_1,B_2_1)). % 32.58/32.44 all X_a X_c X_b B_1_1 B_2_1 (ti(fun(X_a,X_c),combb(X_b,X_c,X_a,B_1_1,B_2_1))=combb(X_b,X_c,X_a,B_1_1,B_2_1)). % 32.58/32.44 all X_a X_b X_c B_1_1 B_2_1 (combc(X_a,X_b,X_c,ti(fun(X_a,fun(X_b,X_c)),B_1_1),B_2_1)=combc(X_a,X_b,X_c,B_1_1,B_2_1)). % 32.58/32.44 all X_a X_b X_c B_1_1 B_2_1 (combc(X_a,X_b,X_c,B_1_1,ti(X_b,B_2_1))=combc(X_a,X_b,X_c,B_1_1,B_2_1)). % 32.58/32.44 all X_a X_c X_b B_1_1 B_2_1 (ti(fun(X_a,X_c),combc(X_a,X_b,X_c,B_1_1,B_2_1))=combc(X_a,X_b,X_c,B_1_1,B_2_1)). % 32.58/32.44 all X_a X_b X_c B_1_1 B_2_1 (combs(X_a,X_b,X_c,ti(fun(X_a,fun(X_b,X_c)),B_1_1),B_2_1)=combs(X_a,X_b,X_c,B_1_1,B_2_1)). % 32.58/32.44 all X_a X_b X_c B_1_1 B_2_1 (combs(X_a,X_b,X_c,B_1_1,ti(fun(X_a,X_b),B_2_1))=combs(X_a,X_b,X_c,B_1_1,B_2_1)). % 32.58/32.44 all X_a X_c X_b B_1_1 B_2_1 (ti(fun(X_a,X_c),combs(X_a,X_b,X_c,B_1_1,B_2_1))=combs(X_a,X_b,X_c,B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 X_a (semiring_div(X_a)->div_mod(X_a,ti(X_a,B_1_1))=div_mod(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (semiring_div(X_a)->ti(fun(X_a,X_a),div_mod(X_a,B_1_1))=div_mod(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (group_add(X_a)->minus_minus(X_a,ti(X_a,B_1_1))=minus_minus(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (group_add(X_a)->ti(fun(X_a,X_a),minus_minus(X_a,B_1_1))=minus_minus(X_a,B_1_1)). % 32.58/32.44 all B_1_1 (minus_minus(nat,ti(nat,B_1_1))=minus_minus(nat,B_1_1)). % 32.58/32.44 all B_1_1 (ti(fun(nat,nat),minus_minus(nat,B_1_1))=minus_minus(nat,B_1_1)). % 32.58/32.44 all X_a (one(X_a)->ti(X_a,one_one(X_a))=one_one(X_a)). % 32.58/32.44 all B_1_1 X_a (plus(X_a)&linorder(X_a)&dvd(X_a)->plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (plus(X_a)&linorder(X_a)&dvd(X_a)->ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (monoid_add(X_a)->plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (monoid_add(X_a)->ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (cancel_semigroup_add(X_a)->plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (cancel_semigroup_add(X_a)->ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (ab_semigroup_add(X_a)->plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (ab_semigroup_add(X_a)->ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (ab_semigroup_mult(X_a)->times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (ab_semigroup_mult(X_a)->ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (power(X_a)->times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (power(X_a)->ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (dvd(X_a)->times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (dvd(X_a)->ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (semiring(X_a)->times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (semiring(X_a)->ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (mult_zero(X_a)->times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (mult_zero(X_a)->ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (no_zero_divisors(X_a)->times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (no_zero_divisors(X_a)->ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1)). % 32.58/32.44 all X_a (zero(X_a)->ti(X_a,zero_zero(X_a))=zero_zero(X_a)). % 32.58/32.44 all X_a (ti(X_a,undefined(X_a))=undefined(X_a)). % 32.58/32.44 all B_1_1 B_2_1 (multInv(ti(int,B_1_1),B_2_1)=multInv(B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 B_2_1 (multInv(B_1_1,ti(int,B_2_1))=multInv(B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 B_2_1 (ti(int,multInv(B_1_1,B_2_1))=multInv(B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 (d22set(ti(int,B_1_1))=d22set(B_1_1)). % 32.58/32.44 all B_1_1 (ti(fun(int,bool),d22set(B_1_1))=d22set(B_1_1)). % 32.58/32.44 all B_1_1 (zfact(ti(int,B_1_1))=zfact(B_1_1)). % 32.58/32.44 all B_1_1 (ti(int,zfact(B_1_1))=zfact(B_1_1)). % 32.58/32.44 all B_1_1 B_2_1 (zcong(ti(int,B_1_1),B_2_1)=zcong(B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 B_2_1 (zcong(B_1_1,ti(int,B_2_1))=zcong(B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 B_2_1 (ti(fun(int,bool),zcong(B_1_1,B_2_1))=zcong(B_1_1,B_2_1)). % 32.58/32.44 ti(fun(int,bool),zprime)=zprime. % 32.58/32.44 all B_1_1 (bit0(ti(int,B_1_1))=bit0(B_1_1)). % 32.58/32.44 all B_1_1 (ti(int,bit0(B_1_1))=bit0(B_1_1)). % 32.58/32.44 all B_1_1 (bit1(ti(int,B_1_1))=bit1(B_1_1)). % 32.58/32.44 all B_1_1 (ti(int,bit1(B_1_1))=bit1(B_1_1)). % 32.58/32.44 ti(int,min)=min. % 32.58/32.44 ti(int,pls)=pls. % 32.58/32.44 all B_1_1 X_a (number(X_a)->number_number_of(X_a,ti(int,B_1_1))=number_number_of(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (number(X_a)->ti(X_a,number_number_of(X_a,B_1_1))=number_number_of(X_a,B_1_1)). % 32.58/32.44 all X_a (order(X_a)->ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a)). % 32.58/32.44 all X_a (order(X_a)->ti(fun(X_a,fun(X_a,bool)),ord_less_e_q(X_a))=ord_less_e_q(X_a)). % 32.58/32.44 all B_1_1 X_a (power(X_a)->power_power(X_a,ti(X_a,B_1_1))=power_power(X_a,B_1_1)). % 32.58/32.44 all B_1_1 X_a (power(X_a)->ti(fun(nat,X_a),power_power(X_a,B_1_1))=power_power(X_a,B_1_1)). % 32.58/32.44 all B_1_1 B_2_1 (product_Pair(int,int,ti(int,B_1_1),B_2_1)=product_Pair(int,int,B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 B_2_1 (product_Pair(int,int,B_1_1,ti(int,B_2_1))=product_Pair(int,int,B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 B_2_1 (ti(product_prod(int,int),product_Pair(int,int,B_1_1,B_2_1))=product_Pair(int,int,B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 B_2_1 (legendre(ti(int,B_1_1),B_2_1)=legendre(B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 B_2_1 (legendre(B_1_1,ti(int,B_2_1))=legendre(B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 B_2_1 (ti(int,legendre(B_1_1,B_2_1))=legendre(B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 (quadRes(ti(int,B_1_1))=quadRes(B_1_1)). % 32.58/32.44 all B_1_1 (ti(fun(int,bool),quadRes(B_1_1))=quadRes(B_1_1)). % 32.58/32.44 all B_1_1 (sr(ti(int,B_1_1))=sr(B_1_1)). % 32.58/32.44 all B_1_1 (ti(fun(int,bool),sr(B_1_1))=sr(B_1_1)). % 32.58/32.44 all B_1_1 B_2_1 (standardRes(ti(int,B_1_1),B_2_1)=standardRes(B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 B_2_1 (standardRes(B_1_1,ti(int,B_2_1))=standardRes(B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 B_2_1 (ti(int,standardRes(B_1_1,B_2_1))=standardRes(B_1_1,B_2_1)). % 32.58/32.44 all X_a (dvd(X_a)->ti(fun(X_a,fun(X_a,bool)),dvd_dvd(X_a))=dvd_dvd(X_a)). % 32.58/32.44 all X_a B_1_1 (collect(X_a,ti(fun(X_a,bool),B_1_1))=collect(X_a,B_1_1)). % 32.58/32.44 all X_a B_1_1 (ti(fun(X_a,bool),collect(X_a,B_1_1))=collect(X_a,B_1_1)). % 32.58/32.44 ti(fun(int,bool),twoSqu658283162sum2sq)=twoSqu658283162sum2sq. % 32.58/32.44 all B_1_1 (twoSqu1929807760sum2sq(ti(product_prod(int,int),B_1_1))=twoSqu1929807760sum2sq(B_1_1)). % 32.58/32.44 all B_1_1 (ti(int,twoSqu1929807760sum2sq(B_1_1))=twoSqu1929807760sum2sq(B_1_1)). % 32.58/32.44 all B_1_1 B_2_1 (inv(ti(int,B_1_1),B_2_1)=inv(B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 B_2_1 (inv(B_1_1,ti(int,B_2_1))=inv(B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 B_2_1 (ti(int,inv(B_1_1,B_2_1))=inv(B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 B_2_1 (wset(ti(int,B_1_1),B_2_1)=wset(B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 B_2_1 (wset(B_1_1,ti(int,B_2_1))=wset(B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 B_2_1 (ti(fun(int,bool),wset(B_1_1,B_2_1))=wset(B_1_1,B_2_1)). % 32.58/32.44 ti(fun(bool,fun(bool,bool)),fconj)=fconj. % 32.58/32.44 all X_a X_c B_1_1 B_2_1 (hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1)=hAPP(X_a,X_c,B_1_1,B_2_1)). % 32.58/32.44 all X_a X_c B_1_1 B_2_1 (hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1))=hAPP(X_a,X_c,B_1_1,B_2_1)). % 32.58/32.44 all X_c X_a B_1_1 B_2_1 (ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1))=hAPP(X_a,X_c,B_1_1,B_2_1)). % 32.58/32.44 all B_1_1 (hBOOL(ti(bool,B_1_1))<->hBOOL(B_1_1)). % 32.58/32.44 all X_a B_1_1 (member(X_a,ti(X_a,B_1_1))=member(X_a,B_1_1)). % 32.58/32.44 all X_a B_1_1 (ti(fun(fun(X_a,bool),bool),member(X_a,B_1_1))=member(X_a,B_1_1)). % 32.58/32.44 ti(int,m)=m. % 32.58/32.44 ti(int,s1)=s1. % 32.58/32.44 ti(int,s)=s. % 32.58/32.44 ti(int,t)=t. % 32.58/32.44 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),t)). % 32.58/32.44 t=one_one(int)-> (exists X Y (hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,Y),number_number_of(nat,bit0(bit1(pls)))))=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.44 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t))-> (exists X Y (hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,Y),number_number_of(nat,bit0(bit1(pls)))))=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.44 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.44 hBOOL(hAPP(int,bool,zprime,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.44 hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))=hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t). % 32.58/32.44 hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))). % 32.58/32.44 all A_1 B (hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,A_1),B)),number_number_of(nat,bit0(bit1(pls))))=hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),A_1)),B))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls)))))). % 32.58/32.44 all A_1 B (hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,A_1),B)),number_number_of(nat,bit1(bit1(pls))))=hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit1(bit1(pls))))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit1(bit1(pls)))),hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))))),B))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit1(bit1(pls)))),A_1)),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls))))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit1(bit1(pls)))))). % 32.58/32.44 all X_a (number_semiring(X_a)-> (all X_1 Y_1 (hAPP(nat,X_a,power_power(X_a,hAPP(X_a,X_a,plus_plus(X_a,X_1),Y_1)),number_number_of(nat,bit0(bit1(pls))))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls)))),X_1)),Y_1))))). % 32.58/32.44 all X_b (monoid_mult(X_b)&number(X_b)-> (all W (hAPP(nat,X_b,power_power(X_b,number_number_of(X_b,W)),number_number_of(nat,bit0(bit1(pls))))=hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,W)),number_number_of(X_b,W))))). % 32.58/32.44 all A_1 (hAPP(int,int,times_times(int,A_1),hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit1(bit1(pls))))). % 32.58/32.44 all X_a (semiring_1(X_a)->hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls))))=one_one(X_a)). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all X_1 (hAPP(X_a,X_a,times_times(X_a,X_1),X_1)=hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))))). % 32.58/32.44 all X_a (monoid_mult(X_a)-> (all A_1 (hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls))))=hAPP(X_a,X_a,times_times(X_a,A_1),A_1)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all X_1 N_1 (hAPP(nat,X_a,power_power(X_a,X_1),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1))=hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,X_1),N_1)),hAPP(nat,X_a,power_power(X_a,X_1),N_1))))). % 32.58/32.44 all X_a (number_ring(X_a)-> (all W (hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,W))=number_number_of(X_a,hAPP(int,int,plus_plus(int,bit1(pls)),W))))). % 32.58/32.44 all X_a (number_ring(X_a)-> (all V (hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),one_one(X_a))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V),bit1(pls)))))). % 32.58/32.44 all X_a (number_ring(X_a)->hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))=number_number_of(X_a,bit0(bit1(pls)))). % 32.58/32.44 -(all T_4 (hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))!=hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),T_4))). % 32.58/32.44 all W hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),W)). % 32.58/32.44 all Z_1 W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z_1))). % 32.58/32.44 all Z_2 W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_2),W_1))&ti(int,Z_2)!=ti(int,W_1)). % 32.58/32.44 all X_1 Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1))|ti(int,X_1)=ti(int,Y_1)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_1),X_1))). % 32.58/32.44 all K_1 I_1 J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),J_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),J_1),K_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),K_1)))). % 32.58/32.44 all Z_1 W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z_1))->ti(int,Z_1)=ti(int,W))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all X_1 P_1 Q_1 (hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,X_1),P_1)),Q_1)=hAPP(nat,X_a,power_power(X_a,X_1),hAPP(nat,nat,times_times(nat,P_1),Q_1))))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all X_1 (hAPP(nat,X_a,power_power(X_a,X_1),one_one(nat))=ti(X_a,X_1)))). % 32.58/32.44 all X_1 Y_1 Z_1 (hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X_1),Y_1)),Z_1)=hAPP(nat,int,power_power(int,X_1),hAPP(nat,nat,times_times(nat,Y_1),Z_1))). % 32.58/32.44 all X_a (number(X_a)&linorder(X_a)-> (all V_2 W_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,V_2)),number_number_of(X_a,W_1)))<-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,W_1)),number_number_of(X_a,V_2)))))). % 32.58/32.44 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X_2 Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X_2)),number_number_of(X_a,Y_2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Y_2))))). % 32.58/32.44 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X_2 Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X_2)),number_number_of(X_a,Y_2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_2),Y_2))))). % 32.58/32.44 all Z_3 Z_1 W_2 W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),W))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_3),Z_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,W_2),Z_3)),hAPP(int,int,plus_plus(int,W),Z_1))))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all X_1 P_1 Q_1 (hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,X_1),P_1)),hAPP(nat,X_a,power_power(X_a,X_1),Q_1))=hAPP(nat,X_a,power_power(X_a,X_1),hAPP(nat,nat,plus_plus(nat,P_1),Q_1))))). % 32.58/32.44 all X_1 Y_1 Z_1 (hAPP(nat,int,power_power(int,X_1),hAPP(nat,nat,plus_plus(nat,Y_1),Z_1))=hAPP(int,int,times_times(int,hAPP(nat,int,power_power(int,X_1),Y_1)),hAPP(nat,int,power_power(int,X_1),Z_1))). % 32.58/32.44 all Z_1 (hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),Z_1)=hAPP(nat,nat,plus_plus(nat,Z_1),Z_1)). % 32.58/32.44 all Z_1 (hAPP(nat,nat,times_times(nat,Z_1),number_number_of(nat,bit0(bit1(pls))))=hAPP(nat,nat,plus_plus(nat,Z_1),Z_1)). % 32.58/32.44 hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))=number_number_of(nat,bit0(bit1(pls))). % 32.58/32.44 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K1)),bit1(K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2))). % 32.58/32.44 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit1(L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))). % 32.58/32.44 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K1)),bit1(K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2))). % 32.58/32.44 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit1(L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L))). % 32.58/32.44 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)). % 32.58/32.44 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K1)),bit0(K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2))). % 32.58/32.44 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit0(L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))). % 32.58/32.44 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),pls)). % 32.58/32.44 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K1)),bit0(K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2))). % 32.58/32.44 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit0(L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L))). % 32.58/32.44 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,K)),number_number_of(int,L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))). % 32.58/32.44 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,K)),number_number_of(int,L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L))). % 32.58/32.44 all K_1 I_1 J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,I_1),K_1)),hAPP(int,int,plus_plus(int,J_1),K_1)))). % 32.58/32.44 all K_1 I_1 J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),J_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,K_1),I_1)),hAPP(int,int,plus_plus(int,K_1),J_1)))). % 32.58/32.44 all V_1 V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=number_number_of(nat,V_1))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=number_number_of(nat,V))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=number_number_of(nat,hAPP(int,int,plus_plus(int,V),V_1))))). % 32.58/32.44 number_number_of(nat,bit1(pls))=one_one(nat). % 32.58/32.44 one_one(nat)=number_number_of(nat,bit1(pls)). % 32.58/32.44 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),pls))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls))). % 32.58/32.44 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit1(K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K))). % 32.58/32.44 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K1)),bit0(K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2))). % 32.58/32.44 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit0(L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))). % 32.58/32.44 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K1)),bit1(K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2))). % 32.58/32.44 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit1(L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L))). % 32.58/32.44 all W Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,W),one_one(int))),Z_1))). % 32.58/32.44 all W_1 Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,W_1),one_one(int))),Z_2))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))). % 32.58/32.44 all W_1 Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_2))). % 32.58/32.44 hBOOL(hAPP(int,bool,zprime,number_number_of(int,bit0(bit1(pls))))). % 32.58/32.44 all Y_1 X_1 (hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,X_1))-> (hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,Y_1))->hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,hAPP(int,int,times_times(int,X_1),Y_1))))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx Ry (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Rx)),hAPP(X_a,X_a,times_times(X_a,Ly),Ry))))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx Ry (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,Rx),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),Ry))))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx Ry (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,Lx),hAPP(X_a,X_a,times_times(X_a,Ly),hAPP(X_a,X_a,times_times(X_a,Rx),Ry)))))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),Rx)=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Rx)),Ly)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),Rx)=hAPP(X_a,X_a,times_times(X_a,Lx),hAPP(X_a,X_a,times_times(X_a,Ly),Rx))))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all Lx Rx Ry (hAPP(X_a,X_a,times_times(X_a,Lx),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Rx)),Ry)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all Lx Rx Ry (hAPP(X_a,X_a,times_times(X_a,Lx),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,Rx),hAPP(X_a,X_a,times_times(X_a,Lx),Ry))))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all A_1 B (hAPP(X_a,X_a,times_times(X_a,A_1),B)=hAPP(X_a,X_a,times_times(X_a,B),A_1)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all A_1 B C D_2 (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),hAPP(X_a,X_a,plus_plus(X_a,C),D_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))))). % 32.58/32.44 all X_a X_2 A_6 (hBOOL(hAPP(fun(X_a,bool),bool,member(X_a,X_2),A_6))<->hBOOL(hAPP(X_a,bool,A_6,X_2))). % 32.58/32.44 all X_a P_2 (collect(X_a,P_2)=ti(fun(X_a,bool),P_2)). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),B)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C))))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all A_1 C D_2 (hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,C),D_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),D_2)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all A_1 C D_2 (hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,C),D_2))=hAPP(X_a,X_a,plus_plus(X_a,C),hAPP(X_a,X_a,plus_plus(X_a,A_1),D_2))))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all A_1 C (hAPP(X_a,X_a,plus_plus(X_a,A_1),C)=hAPP(X_a,X_a,plus_plus(X_a,C),A_1)))). % 32.58/32.44 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)))). % 32.58/32.44 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)))). % 32.58/32.44 all K L (bit1(K)=bit1(L)<->ti(int,K)=ti(int,L)). % 32.58/32.44 all K L (bit0(K)=bit0(L)<->ti(int,K)=ti(int,L)). % 32.58/32.44 all Z1 Z2 Z3 (hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,Z1),Z2)),Z3)=hAPP(int,int,times_times(int,Z1),hAPP(int,int,times_times(int,Z2),Z3))). % 32.58/32.44 all Z_1 W (hAPP(int,int,times_times(int,Z_1),W)=hAPP(int,int,times_times(int,W),Z_1)). % 32.58/32.44 all K_1 (number_number_of(int,K_1)=ti(int,K_1)). % 32.58/32.44 all Z1 Z2 Z3 (hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,Z1),Z2)),Z3)=hAPP(int,int,plus_plus(int,Z1),hAPP(int,int,plus_plus(int,Z2),Z3))). % 32.58/32.44 all X_1 Y_1 Z_1 (hAPP(int,int,plus_plus(int,X_1),hAPP(int,int,plus_plus(int,Y_1),Z_1))=hAPP(int,int,plus_plus(int,Y_1),hAPP(int,int,plus_plus(int,X_1),Z_1))). % 32.58/32.44 all Z_1 W (hAPP(int,int,plus_plus(int,Z_1),W)=hAPP(int,int,plus_plus(int,W),Z_1)). % 32.58/32.44 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),pls))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls))). % 32.58/32.44 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K1)),bit0(K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2))). % 32.58/32.44 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit0(L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))). % 32.58/32.44 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),pls))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls))). % 32.58/32.44 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit0(K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K))). % 32.58/32.44 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit1(K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K))). % 32.58/32.44 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K1)),bit1(K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2))). % 32.58/32.44 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit1(L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L))). % 32.58/32.44 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),pls))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),pls))). % 32.58/32.44 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit0(K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K))). % 32.58/32.44 all W_1 Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))|ti(int,W_1)=ti(int,Z_2)). % 32.58/32.44 all X_a (monoid_mult(X_a)-> (all A_1 N_1 (hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1))=hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N_1)),number_number_of(nat,bit0(bit1(pls))))))). % 32.58/32.44 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X_2)),one_one(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),bit1(pls)))))). % 32.58/32.44 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),number_number_of(X_a,Y_2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(pls)),Y_2))))). % 32.58/32.44 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X_2)),one_one(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_2),bit1(pls)))))). % 32.58/32.44 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),number_number_of(X_a,Y_2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(pls)),Y_2))))). % 32.58/32.44 all X_a (semiri456707255roduct(X_a)-> (all W_1 Y_2 X_2 Z_2 (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,W_1),Y_2)),hAPP(X_a,X_a,times_times(X_a,X_2),Z_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,W_1),Z_2)),hAPP(X_a,X_a,times_times(X_a,X_2),Y_2))<->ti(X_a,W_1)=ti(X_a,X_2)|ti(X_a,Y_2)=ti(X_a,Z_2)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all A_1 M B (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),M)),hAPP(X_a,X_a,times_times(X_a,B),M))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),M)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))))). % 32.58/32.44 all X_a (semiri456707255roduct(X_a)-> (all C_1 D A_3 B_2 (ti(X_a,A_3)!=ti(X_a,B_2)&ti(X_a,C_1)!=ti(X_a,D)<->hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),D))!=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),D)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1))))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all X_1 Y_1 Z_1 (hAPP(X_a,X_a,times_times(X_a,X_1),hAPP(X_a,X_a,plus_plus(X_a,Y_1),Z_1))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Y_1)),hAPP(X_a,X_a,times_times(X_a,X_1),Z_1))))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,A_1),one_one(X_a))=ti(X_a,A_1)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,one_one(X_a)),A_1)=ti(X_a,A_1)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all X_1 Y_1 Q_1 (hAPP(nat,X_a,power_power(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Y_1)),Q_1)=hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,X_1),Q_1)),hAPP(nat,X_a,power_power(X_a,Y_1),Q_1))))). % 32.58/32.44 all K_1 (bit1(K_1)!=pls). % 32.58/32.44 all L_1 (pls!=bit1(L_1)). % 32.58/32.44 all K_1 L_1 (bit1(K_1)!=bit0(L_1)). % 32.58/32.44 all K_1 L_1 (bit0(K_1)!=bit1(L_1)). % 32.58/32.44 all K (bit0(K)=pls<->ti(int,K)=pls). % 32.58/32.44 all L (pls=bit0(L)<->pls=ti(int,L)). % 32.58/32.44 bit0(pls)=pls. % 32.58/32.44 all W (hAPP(int,int,times_times(int,pls),W)=pls). % 32.58/32.44 all K_1 L_1 (hAPP(int,int,times_times(int,bit0(K_1)),L_1)=bit0(hAPP(int,int,times_times(int,K_1),L_1))). % 32.58/32.44 all K_1 (hAPP(int,int,plus_plus(int,K_1),pls)=ti(int,K_1)). % 32.58/32.44 all K_1 (hAPP(int,int,plus_plus(int,pls),K_1)=ti(int,K_1)). % 32.58/32.44 all K_1 L_1 (hAPP(int,int,plus_plus(int,bit0(K_1)),bit0(L_1))=bit0(hAPP(int,int,plus_plus(int,K_1),L_1))). % 32.58/32.44 all K_1 (bit0(K_1)=hAPP(int,int,plus_plus(int,K_1),K_1)). % 32.58/32.44 all Z_1 (hAPP(int,int,times_times(int,Z_1),one_one(int))=ti(int,Z_1)). % 32.58/32.44 all Z_1 (hAPP(int,int,times_times(int,one_one(int)),Z_1)=ti(int,Z_1)). % 32.58/32.44 all V W (hAPP(int,int,times_times(int,number_number_of(int,V)),number_number_of(int,W))=number_number_of(int,hAPP(int,int,times_times(int,V),W))). % 32.58/32.44 all Z1 Z2 W (hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,Z1),Z2)),W)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,Z1),W)),hAPP(int,int,times_times(int,Z2),W))). % 32.58/32.44 all W Z1 Z2 (hAPP(int,int,times_times(int,W),hAPP(int,int,plus_plus(int,Z1),Z2))=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,W),Z1)),hAPP(int,int,times_times(int,W),Z2))). % 32.58/32.44 all V W (hAPP(int,int,plus_plus(int,number_number_of(int,V)),number_number_of(int,W))=number_number_of(int,hAPP(int,int,plus_plus(int,V),W))). % 32.58/32.44 all X_a (number_semiring(X_a)-> (all V_1 V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))->hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,V)),number_number_of(X_a,V_1))=number_number_of(X_a,hAPP(int,int,times_times(int,V),V_1)))))). % 32.58/32.44 all X_a (number_semiring(X_a)-> (all V_1 V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))->hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),number_number_of(X_a,V_1))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V),V_1)))))). % 32.58/32.44 all X_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_1),hAPP(nat,int,power_power(int,X_1),number_number_of(nat,bit0(bit1(pls)))))). % 32.58/32.44 all X_b (number(X_b)&semiring(X_b)-> (all A_1 B V (hAPP(X_b,X_b,times_times(X_b,hAPP(X_b,X_b,plus_plus(X_b,A_1),B)),number_number_of(X_b,V))=hAPP(X_b,X_b,plus_plus(X_b,hAPP(X_b,X_b,times_times(X_b,A_1),number_number_of(X_b,V))),hAPP(X_b,X_b,times_times(X_b,B),number_number_of(X_b,V)))))). % 32.58/32.44 all X_b (number(X_b)&semiring(X_b)-> (all V B C (hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),hAPP(X_b,X_b,plus_plus(X_b,B),C))=hAPP(X_b,X_b,plus_plus(X_b,hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),B)),hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),C))))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all A_1 M (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),M)),M)=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),one_one(X_a))),M)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all M A_1 (hAPP(X_a,X_a,plus_plus(X_a,M),hAPP(X_a,X_a,times_times(X_a,A_1),M))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),one_one(X_a))),M)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all M (hAPP(X_a,X_a,plus_plus(X_a,M),M)=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))),M)))). % 32.58/32.44 all X_a (number_ring(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,pls)),A_1)=ti(X_a,A_1)))). % 32.58/32.44 all X_a (number_ring(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,A_1),number_number_of(X_a,pls))=ti(X_a,A_1)))). % 32.58/32.44 all X_a (number_ring(X_a)-> (all V W Z_1 (hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,V)),hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,W)),Z_1))=hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,hAPP(int,int,times_times(int,V),W))),Z_1)))). % 32.58/32.44 all X_a (number_ring(X_a)-> (all V W (hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,V)),number_number_of(X_a,W))=number_number_of(X_a,hAPP(int,int,times_times(int,V),W))))). % 32.58/32.44 all X_a (number_ring(X_a)-> (all V W (number_number_of(X_a,hAPP(int,int,times_times(int,V),W))=hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,V)),number_number_of(X_a,W))))). % 32.58/32.44 all X_a (number_ring(X_a)-> (all V W Z_1 (hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,W)),Z_1))=hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,hAPP(int,int,plus_plus(int,V),W))),Z_1)))). % 32.58/32.44 all X_a (number_ring(X_a)-> (all V W (hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),number_number_of(X_a,W))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V),W))))). % 32.58/32.44 all X_a (number_ring(X_a)-> (all V W (number_number_of(X_a,hAPP(int,int,plus_plus(int,V),W))=hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),number_number_of(X_a,W))))). % 32.58/32.44 all K_1 L_1 (hAPP(int,int,plus_plus(int,bit1(K_1)),bit0(L_1))=bit1(hAPP(int,int,plus_plus(int,K_1),L_1))). % 32.58/32.44 all K_1 L_1 (hAPP(int,int,plus_plus(int,bit0(K_1)),bit1(L_1))=bit1(hAPP(int,int,plus_plus(int,K_1),L_1))). % 32.58/32.44 all K_1 (bit1(K_1)=hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),K_1)),K_1)). % 32.58/32.44 all X_a (number_ring(X_a)-> (all W (number_number_of(X_a,bit1(W))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,W))),number_number_of(X_a,W))))). % 32.58/32.44 all X_a (number_ring(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit1(pls))),A_1)=ti(X_a,A_1)))). % 32.58/32.44 all X_a (number_ring(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,A_1),number_number_of(X_a,bit1(pls)))=ti(X_a,A_1)))). % 32.58/32.44 all X_a (number_semiring(X_a)->number_number_of(X_a,bit1(pls))=one_one(X_a)). % 32.58/32.44 all X_a (number_ring(X_a)->number_number_of(X_a,bit1(pls))=one_one(X_a)). % 32.58/32.44 all X_a (number_ring(X_a)->one_one(X_a)=number_number_of(X_a,bit1(pls))). % 32.58/32.44 one_one(int)=number_number_of(int,bit1(pls)). % 32.58/32.44 all K_1 L_1 (hAPP(int,int,times_times(int,bit1(K_1)),L_1)=hAPP(int,int,plus_plus(int,bit0(hAPP(int,int,times_times(int,K_1),L_1))),L_1)). % 32.58/32.44 all X_a (number_ring(X_a)-> (all W (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))),number_number_of(X_a,W))=number_number_of(X_a,bit0(W))))). % 32.58/32.44 all X_a (monoid_mult(X_a)-> (all A_1 (hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit1(bit1(pls))))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),A_1)),A_1)))). % 32.58/32.44 all X_1 (hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X_1),number_number_of(nat,bit0(bit1(pls))))),number_number_of(nat,bit0(bit1(pls))))=hAPP(nat,int,power_power(int,X_1),number_number_of(nat,bit0(bit0(bit1(pls)))))). % 32.58/32.44 all X_a (number_semiring(X_a)-> (all Z_1 (hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls)))),Z_1)=hAPP(X_a,X_a,plus_plus(X_a,Z_1),Z_1)))). % 32.58/32.44 all X_a (number_ring(X_a)-> (all Z_1 (hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls)))),Z_1)=hAPP(X_a,X_a,plus_plus(X_a,Z_1),Z_1)))). % 32.58/32.44 all X_a (number_semiring(X_a)-> (all Z_1 (hAPP(X_a,X_a,times_times(X_a,Z_1),number_number_of(X_a,bit0(bit1(pls))))=hAPP(X_a,X_a,plus_plus(X_a,Z_1),Z_1)))). % 32.58/32.44 all X_a (number_ring(X_a)-> (all Z_1 (hAPP(X_a,X_a,times_times(X_a,Z_1),number_number_of(X_a,bit0(bit1(pls))))=hAPP(X_a,X_a,plus_plus(X_a,Z_1),Z_1)))). % 32.58/32.44 all X_a (number_semiring(X_a)->hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))=number_number_of(X_a,bit0(bit1(pls)))). % 32.58/32.44 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.44 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)))). % 32.58/32.44 all P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (ti(int,P_1)!=number_number_of(int,bit0(bit1(pls)))-> (ti(int,P_1)!=number_number_of(int,bit1(bit1(pls)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),P_1))))). % 32.58/32.44 twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))=hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t). % 32.58/32.44 all X_1 Y_1 (hAPP(nat,real,power_power(real,hAPP(real,real,plus_plus(real,X_1),Y_1)),number_number_of(nat,bit0(bit1(pls))))=hAPP(real,real,plus_plus(real,hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,real,power_power(real,Y_1),number_number_of(nat,bit0(bit1(pls)))))),hAPP(real,real,times_times(real,hAPP(real,real,times_times(real,number_number_of(real,bit0(bit1(pls)))),X_1)),Y_1))). % 32.58/32.44 all X_1 (hAPP(real,real,times_times(real,number_number_of(real,bit0(bit0(bit1(pls))))),hAPP(nat,real,power_power(real,X_1),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,real,power_power(real,hAPP(real,real,times_times(real,number_number_of(real,bit0(bit1(pls)))),X_1)),number_number_of(nat,bit0(bit1(pls))))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(nat,X_a,power_power(X_a,A_1),N_1))))))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(nat,X_a,power_power(X_a,A_1),N_1))))))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all M N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)))))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all X_2 Y_2 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,B_2),X_2)),hAPP(nat,X_a,power_power(X_a,B_2),Y_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_2),Y_2)))))). % 32.58/32.44 hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,int,power_power(int,s1),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.44 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),s)). % 32.58/32.44 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),s),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.44 hBOOL(hAPP(int,bool,zcong(s1,s),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.44 exists X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))&hBOOL(hAPP(int,bool,zcong(s1,X),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))& (all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))&hBOOL(hAPP(int,bool,zcong(s1,Y),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))->ti(int,Y)=ti(int,X)))). % 32.58/32.44 -(all S_1 (-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),S_1))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),S_1),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))&hBOOL(hAPP(int,bool,zcong(s1,S_1),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))))). % 32.58/32.44 hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,s1),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.44 all X_a (power(X_a)&mult_zero(X_a)&no_zero_divisors(X_a)&zero_ne_q_one(X_a)-> (all A_3 N (hAPP(nat,X_a,power_power(X_a,A_3),N)=zero_zero(X_a)<->ti(X_a,A_3)=zero_zero(X_a)&N!=zero_zero(nat)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all A_1 M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all N_1 M X_1 Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,X_1),N_1)),hAPP(nat,X_a,power_power(X_a,Y_1),M))))))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all M A_1 N_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),B))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M)),B)))))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all A_1 N_1 B (hAPP(nat,X_a,power_power(X_a,A_1),N_1)=hAPP(nat,X_a,power_power(X_a,B),N_1)-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->ti(X_a,A_1)=ti(X_a,B))))))). % 32.58/32.44 all N_1 M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M),N_1))-> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),M)))). % 32.58/32.44 all N_1 M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),N_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),M))->ti(int,M)=ti(int,N_1))))). % 32.58/32.44 all K_1 M N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,times_times(int,K_1),M)),hAPP(int,int,times_times(int,K_1),N_1)))-> (ti(int,K_1)!=zero_zero(int)->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N_1)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all N_1 X_1 Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,X_1),N_1)),hAPP(nat,X_a,power_power(X_a,Y_1),N_1)))))). % 32.58/32.44 all X_a (ring_11004092258visors(X_a)-> (all N_1 A_1 (ti(X_a,A_1)!=zero_zero(X_a)->hAPP(nat,X_a,power_power(X_a,A_1),N_1)!=zero_zero(X_a)))). % 32.58/32.44 all X_a (power(X_a)&semiring_0(X_a)-> (all N_1 ((N_1=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N_1)=one_one(X_a))& (N_1!=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N_1)=zero_zero(X_a))))). % 32.58/32.44 all Z_1 N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z_1),N_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),N_1)))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,B),N_1)))))))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,zero_zero(X_a)),A_1)=zero_zero(X_a)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a))=zero_zero(X_a)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1)))). % 32.58/32.44 all X_a (semiri456707255roduct(X_a)-> (all B_2 A_3 (ti(X_a,B_2)=hAPP(X_a,X_a,plus_plus(X_a,B_2),A_3)<->ti(X_a,A_3)=zero_zero(X_a)))). % 32.58/32.44 all X_a (linord219039673up_add(X_a)-> (all A_3 (hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)=zero_zero(X_a)<->ti(X_a,A_3)=zero_zero(X_a)))). % 32.58/32.44 pls=zero_zero(int). % 32.58/32.44 zero_zero(int)!=one_one(int). % 32.58/32.44 all Z_1 (hAPP(int,int,plus_plus(int,zero_zero(int)),Z_1)=ti(int,Z_1)). % 32.58/32.44 all Z_1 (hAPP(int,int,plus_plus(int,Z_1),zero_zero(int))=ti(int,Z_1)). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,B),N_1))))))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))))). % 32.58/32.44 all Z_1 X_1 Y_1 P_1 (hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X_1),Y_1),one_one(int)),P_1))->hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X_1),hAPP(nat,nat,times_times(nat,Y_1),Z_1)),one_one(int)),P_1))). % 32.58/32.44 all K N Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,plus_plus(int,N),hAPP(int,int,times_times(int,K),Ma))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N))). % 32.58/32.44 all C_1 X_2 Ta A_3 D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),D))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),hAPP(int,int,plus_plus(int,X_2),Ta)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X_2),hAPP(int,int,times_times(int,C_1),D))),Ta))))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all A_1 N_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,B),N_1)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all A_1 N_1 N_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),N_3))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),one_one(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_3)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))))))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all A_1 N_1 N_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_3))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_3)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))))))). % 32.58/32.44 all X_a (linordered_idom(X_a)-> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),zero_zero(X_a)))))). % 32.58/32.44 all X_a (linord581940658strict(X_a)-> (all X_2 Y_2 (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_2),X_2)),hAPP(X_a,X_a,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)))). % 32.58/32.44 all X_a (semiri456707255roduct(X_a)-> (all C D_2 A_1 B R_1 (ti(X_a,R_1)!=zero_zero(X_a)-> (ti(X_a,A_1)=ti(X_a,B)&ti(X_a,C)!=ti(X_a,D_2)->hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,times_times(X_a,R_1),C))!=hAPP(X_a,X_a,plus_plus(X_a,B),hAPP(X_a,X_a,times_times(X_a,R_1),D_2)))))). % 32.58/32.44 all A_1 N_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),hAPP(nat,int,power_power(int,A_1),N_1)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),A_1)))). % 32.58/32.44 all X_a (number_ring(X_a)->zero_zero(X_a)=number_number_of(X_a,pls)). % 32.58/32.44 all X_a (number_ring(X_a)->number_number_of(X_a,pls)=zero_zero(X_a)). % 32.58/32.44 all X_a (number_semiring(X_a)->number_number_of(X_a,pls)=zero_zero(X_a)). % 32.58/32.44 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(W_1)),zero_zero(int)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int)))). % 32.58/32.44 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))). % 32.58/32.44 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(W_1)),zero_zero(int)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int)))). % 32.58/32.44 zero_zero(int)=number_number_of(int,pls). % 32.58/32.44 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))). % 32.58/32.44 all B A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)))). % 32.58/32.44 all K_1 I_1 J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,K_1),I_1)),hAPP(int,int,times_times(int,K_1),J_1))))). % 32.58/32.44 all Z_1 (hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_1)),Z_1)!=zero_zero(int)). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(nat,X_a,power_power(X_a,A_1),N_1))),hAPP(nat,X_a,power_power(X_a,A_1),N_1))))))). % 32.58/32.44 all N_1 B A_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_1),N_1)),hAPP(int,int,times_times(int,A_1),B)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_1),N_1)),B))))). % 32.58/32.44 all N_1 A_1 B P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),B))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_1),N_1)),hAPP(int,int,times_times(int,A_1),B)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_1),N_1)),A_1))))). % 32.58/32.44 all X_a (linordered_ring(X_a)-> (all X_1 Y_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),X_1)),hAPP(X_a,X_a,times_times(X_a,Y_1),Y_1)))))). % 32.58/32.44 all X_a (linord581940658strict(X_a)-> (all X_2 Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_2),X_2)),hAPP(X_a,X_a,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)))). % 32.58/32.44 all V_2 V_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,V_2)),number_number_of(nat,V_3)))<-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),V_3))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_3)))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),V_3))). % 32.58/32.44 all X_a (linordered_ring(X_a)-> (all X_1 Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),X_1)),hAPP(X_a,X_a,times_times(X_a,Y_1),Y_1))),zero_zero(X_a)))))). % 32.58/32.44 all X_a (linord581940658strict(X_a)-> (all X_2 Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_2),X_2)),hAPP(X_a,X_a,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)))). % 32.58/32.44 all V_2 V_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,V_2)),number_number_of(nat,V_3)))<-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_2),V_3))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_2),pls)))). % 32.58/32.44 all X_a (number_ring(X_a)-> (all W (number_number_of(X_a,bit0(W))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),number_number_of(X_a,W))),number_number_of(X_a,W))))). % 32.58/32.44 all X_a (monoid_mult(X_a)-> (all A_1 (hAPP(nat,X_a,power_power(X_a,A_1),one_one(nat))=ti(X_a,A_1)))). % 32.58/32.44 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_2))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2))). % 32.58/32.44 all N Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))-> (hAPP(int,int,times_times(int,Ma),N)=one_one(int)<->ti(int,Ma)=one_one(int)&ti(int,N)=one_one(int))). % 32.58/32.44 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_2)),Z_2)),zero_zero(int)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int)))). % 32.58/32.44 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),number_number_of(X_a,Y_2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Y_2))))). % 32.58/32.44 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X_2)),zero_zero(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),pls))))). % 32.58/32.44 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),number_number_of(X_a,Y_2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),Y_2))))). % 32.58/32.44 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X_2)),zero_zero(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_2),pls))))). % 32.58/32.44 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),Z_1)))). % 32.58/32.44 all X_a (semiring_1(X_a)->hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,bit0(bit1(pls))))=zero_zero(X_a)). % 32.58/32.44 all X_a (ring_11004092258visors(X_a)-> (all A_3 (hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,bit0(bit1(pls))))=zero_zero(X_a)<->ti(X_a,A_3)=zero_zero(X_a)))). % 32.58/32.44 all X_a (linordered_idom(X_a)-> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls)))))))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all X_1 Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y_1)))))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all X_1 Y_1 (hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))=hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_1))->ti(X_a,X_1)=ti(X_a,Y_1)))))). % 32.58/32.44 all X_a (linordered_idom(X_a)-> (all A_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls))))),zero_zero(X_a)))))). % 32.58/32.44 all X_a (linordered_idom(X_a)-> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,bit0(bit1(pls))))))<->ti(X_a,A_3)!=zero_zero(X_a)))). % 32.58/32.44 all X_a (linordered_idom(X_a)-> (all X_2 Y_2 (hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,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)))). % 32.58/32.44 all X_a (monoid_mult(X_a)-> (all A_1 N_1 (hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N_1)),A_1)=hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(nat,X_a,power_power(X_a,A_1),N_1))))). % 32.58/32.44 all X_a (comm_monoid_mult(X_a)-> (all A_1 B N_1 (hAPP(nat,X_a,power_power(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),N_1)=hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,B),N_1))))). % 32.58/32.44 all X_a (monoid_mult(X_a)-> (all A_1 M N_1 (hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,plus_plus(nat,M),N_1))=hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,A_1),M)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))))). % 32.58/32.44 all X_a (monoid_mult(X_a)-> (all N_1 (hAPP(nat,X_a,power_power(X_a,one_one(X_a)),N_1)=one_one(X_a)))). % 32.58/32.44 all X_a (monoid_mult(X_a)-> (all A_1 M N_1 (hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,times_times(nat,M),N_1))=hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,A_1),M)),N_1)))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all X_1 Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)))))). % 32.58/32.44 all X_a (linordered_idom(X_a)-> (all X_1 Y_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))))))). % 32.58/32.44 all X_a (linordered_idom(X_a)-> (all X_2 Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,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)))). % 32.58/32.44 all X_a (linordered_idom(X_a)-> (all X_1 Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(X_a)))))). % 32.58/32.44 all X_a (linordered_idom(X_a)-> (all X_2 Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,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)))). % 32.58/32.44 all X_a (linordered_idom(X_a)-> (all A_1 N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1)))))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all A_1 N_1 N_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),N_3))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,A_1),N_3))))))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all Ma N A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_3))-> (hAPP(nat,X_a,power_power(X_a,A_3),Ma)=hAPP(nat,X_a,power_power(X_a,A_3),N)<->Ma=N)))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all X_2 Y_2 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,B_2),X_2)),hAPP(nat,X_a,power_power(X_a,B_2),Y_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),Y_2)))))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all M N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)))))). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all A_1 N_1 N_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_3))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,A_1),N_3))))))). % 32.58/32.44 hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.44 all Y_1 X_1 P_1 (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))-> (hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,Y_1),number_number_of(nat,bit0(bit1(pls)))),X_1),P_1))-> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),Y_1)))). % 32.58/32.44 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),number_number_of(int,bit0(bit1(pls)))))->ti(int,X_1)=zero_zero(int)|ti(int,X_1)=one_one(int))). % 32.58/32.44 all X_a (linordered_idom(X_a)-> (all A_1 K_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),K_1))),zero_zero(X_a)))->ti(X_a,A_1)=zero_zero(X_a)))). % 32.58/32.44 all P_3 (hBOOL(hAPP(int,bool,zprime,P_3))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_3))& (all M_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M_2))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M_2),P_3))->ti(int,M_2)=one_one(int)|ti(int,M_2)=ti(int,P_3)))). % 32.58/32.44 all R_1 Q_1 A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (ti(int,A_1)=hAPP(int,int,plus_plus(int,R_1),hAPP(int,int,times_times(int,A_1),Q_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),one_one(int)))))). % 32.58/32.44 all R_1 Q_1 A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (ti(int,A_1)=hAPP(int,int,plus_plus(int,R_1),hAPP(int,int,times_times(int,A_1),Q_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),A_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Q_1))))). % 32.58/32.44 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit0(bit1(pls))))). % 32.58/32.44 -(all S1 (-hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,S1),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))))). % 32.58/32.44 legendre(number_number_of(int,min),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))=one_one(int). % 32.58/32.44 all X_2 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X_2),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_2))|N=zero_zero(nat)). % 32.58/32.44 all X_2 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X_2),N)))<->N=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_2))). % 32.58/32.44 all X_2 W_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X_2),number_number_of(nat,W_1))))<->number_number_of(nat,W_1)=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_2))). % 32.58/32.44 all M N_1 I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),I_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,I_1),M)),hAPP(nat,nat,power_power(nat,I_1),N_1)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)))). % 32.58/32.44 all K (bit1(K)=min<->ti(int,K)=min). % 32.58/32.44 all L (min=bit1(L)<->min=ti(int,L)). % 32.58/32.44 bit1(min)=min. % 32.58/32.44 pls!=min. % 32.58/32.44 min!=pls. % 32.58/32.44 all K_1 (bit0(K_1)!=min). % 32.58/32.44 all L_1 (min!=bit0(L_1)). % 32.58/32.44 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),min)). % 32.58/32.44 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),min)). % 32.58/32.44 all X_2 (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,times_times(real,X_2),X_2)))<->X_2=zero_zero(real)). % 32.58/32.44 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),min))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),min))). % 32.58/32.44 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit1(K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K))). % 32.58/32.44 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),min)). % 32.58/32.44 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),pls)). % 32.58/32.44 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit0(K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K))). % 32.58/32.44 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),zero_zero(int))). % 32.58/32.44 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),min))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min))). % 32.58/32.44 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit1(K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),K))). % 32.58/32.44 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),min)). % 32.58/32.44 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),pls)). % 32.58/32.44 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),min))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min))). % 32.58/32.44 number_number_of(int,pls)!=number_number_of(int,min). % 32.58/32.44 all I_1 M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,I_1),M)),hAPP(nat,nat,power_power(nat,I_1),N_1)))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),I_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all X_1 (hAPP(nat,X_a,power_power(X_a,X_1),zero_zero(nat))=one_one(X_a)))). % 32.58/32.44 all X_a (power(X_a)-> (all A_1 (hAPP(nat,X_a,power_power(X_a,A_1),zero_zero(nat))=one_one(X_a)))). % 32.58/32.44 number_number_of(nat,pls)=zero_zero(nat). % 32.58/32.44 zero_zero(nat)=number_number_of(nat,pls). % 32.58/32.44 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit0(K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K))). % 32.58/32.44 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),min))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min))). % 32.58/32.44 all M N_1 (hAPP(int,int,times_times(int,M),N_1)=one_one(int)->ti(int,M)=one_one(int)|ti(int,M)=number_number_of(int,min)). % 32.58/32.44 all Ma N (hAPP(int,int,times_times(int,Ma),N)=one_one(int)<->ti(int,Ma)=one_one(int)&ti(int,N)=one_one(int)|ti(int,Ma)=number_number_of(int,min)&ti(int,N)=number_number_of(int,min)). % 32.58/32.44 all X_a (linordered_semidom(X_a)-> (all N_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))))))). % 32.58/32.44 all X_a (comm_semiring_1(X_a)-> (all X_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|ti(X_a,X_1)=one_one(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),hAPP(nat,X_a,power_power(X_a,X_1),N_1)))))). % 32.58/32.44 all V_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,V_2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_2))). % 32.58/32.44 all V_2 (number_number_of(nat,V_2)=zero_zero(nat)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_2),pls))). % 32.58/32.44 all V_2 (zero_zero(nat)=number_number_of(nat,V_2)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_2),pls))). % 32.58/32.44 all A_3 B_2 Ma (hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))<->hBOOL(hAPP(int,bool,zcong(B_2,A_3),Ma))). % 32.58/32.44 all K_1 M hBOOL(hAPP(int,bool,zcong(K_1,K_1),M)). % 32.58/32.44 all C A_1 B M (hBOOL(hAPP(int,bool,zcong(A_1,B),M))-> (hBOOL(hAPP(int,bool,zcong(B,C),M))->hBOOL(hAPP(int,bool,zcong(A_1,C),M)))). % 32.58/32.44 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,bit0(bit1(pls))))). % 32.58/32.44 all V_1 K_1 V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,times_times(nat,number_number_of(nat,V)),hAPP(nat,nat,times_times(nat,number_number_of(nat,V_1)),K_1))=zero_zero(nat))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,times_times(nat,number_number_of(nat,V)),hAPP(nat,nat,times_times(nat,number_number_of(nat,V_1)),K_1))=hAPP(nat,nat,times_times(nat,number_number_of(nat,hAPP(int,int,times_times(int,V),V_1))),K_1))). % 32.58/32.44 all V_1 V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,times_times(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=zero_zero(nat))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,times_times(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=number_number_of(nat,hAPP(int,int,times_times(int,V),V_1)))). % 32.58/32.44 all X_a (order(X_a)-> (all X_1 Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y_1))-> (ti(X_a,X_1)!=ti(X_a,Y_1)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)))))). % 32.58/32.44 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),zero_zero(int))). % 32.58/32.44 all B A_1 C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),C))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),A_1)))). % 32.58/32.44 all A_3 B_2 (hBOOL(hAPP(int,bool,zcong(A_3,B_2),zero_zero(int)))<->ti(int,A_3)=ti(int,B_2)). % 32.58/32.44 all A_1 B hBOOL(hAPP(int,bool,zcong(A_1,B),one_one(int))). % 32.58/32.44 all C D_2 A_1 B M (hBOOL(hAPP(int,bool,zcong(A_1,B),M))-> (hBOOL(hAPP(int,bool,zcong(C,D_2),M))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),C),hAPP(int,int,times_times(int,B),D_2)),M)))). % 32.58/32.45 all K_1 A_1 B M (hBOOL(hAPP(int,bool,zcong(A_1,B),M))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,K_1),A_1),hAPP(int,int,times_times(int,K_1),B)),M))). % 32.58/32.45 all K_1 A_1 B M (hBOOL(hAPP(int,bool,zcong(A_1,B),M))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),K_1),hAPP(int,int,times_times(int,B),K_1)),M))). % 32.58/32.45 all A_1 M B hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),M),hAPP(int,int,times_times(int,B),M)),M)). % 32.58/32.45 all C D_2 A_1 B M (hBOOL(hAPP(int,bool,zcong(A_1,B),M))-> (hBOOL(hAPP(int,bool,zcong(C,D_2),M))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,plus_plus(int,A_1),C),hAPP(int,int,plus_plus(int,B),D_2)),M)))). % 32.58/32.45 all X_a (number_ring(X_a)-> (all N_1 (hAPP(nat,X_a,power_power(X_a,number_number_of(X_a,min)),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1))=one_one(X_a)))). % 32.58/32.45 all X_a (power(X_a)&mult_zero(X_a)&no_zero_divisors(X_a)&zero_ne_q_one(X_a)-> (all A_3 W_1 (hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,W_1))=zero_zero(X_a)<->ti(X_a,A_3)=zero_zero(X_a)&number_number_of(nat,W_1)!=zero_zero(nat)))). % 32.58/32.45 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),one_one(int))). % 32.58/32.45 all Y_1 X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,times_times(int,X_1),Y_1))))). % 32.58/32.45 all Y_1 X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,X_1),Y_1))))). % 32.58/32.45 all B M A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1))-> -hBOOL(hAPP(int,bool,zcong(A_1,B),M)))))). % 32.58/32.45 all N_1 X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,power_power(int,X_1),N_1)))). % 32.58/32.45 all A_3 B_2 Ma (hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))<-> (exists K_2 (ti(int,B_2)=hAPP(int,int,plus_plus(int,A_3),hAPP(int,int,times_times(int,Ma),K_2))))). % 32.58/32.45 all X_a (power(X_a)&semiring_0(X_a)-> (all W ((number_number_of(nat,W)=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,W))=one_one(X_a))& (number_number_of(nat,W)!=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,W))=zero_zero(X_a))))). % 32.58/32.45 all B M A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),M))-> (hBOOL(hAPP(int,bool,zcong(A_1,B),M))->ti(int,A_1)=ti(int,B)))))). % 32.58/32.45 all M A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M))-> (hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),M))->ti(int,A_1)=zero_zero(int)))). % 32.58/32.45 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit1(bit1(pls))))). % 32.58/32.45 all B Q_1 R_1 B_3 Q_4 R_3 (hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_1)),R_1)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)),zero_zero(int)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_3),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_4),Q_1)))))))). % 32.58/32.45 all B Q_4 R_3 Q_1 R_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_4)),R_3)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_1)),R_1)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_1),zero_zero(int)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_3))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q_4)))))). % 32.58/32.45 all B Q_1 R_1 B_3 Q_4 R_3 (hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_1)),R_1)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_3),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q_4)))))))). % 32.58/32.45 all B Q_4 R_3 Q_1 R_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_4)),R_3)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_1)),R_1)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_4),Q_1)))))). % 32.58/32.45 all B_3 Q_4 R_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)),zero_zero(int)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_4),zero_zero(int)))))). % 32.58/32.45 all B_3 Q_4 R_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Q_4))))). % 32.58/32.45 all N_1 P_1 M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M))-> (hBOOL(hAPP(int,bool,zprime,P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),hAPP(int,int,times_times(int,M),N_1)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),N_1))))). % 32.58/32.45 hBOOL(hAPP(int,bool,quadRes(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),number_number_of(int,min))). % 32.58/32.45 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)))). % 32.58/32.45 all J_1 K_1 M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),M))-> (hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,number_number_of(int,min)),J_1),hAPP(nat,int,power_power(int,number_number_of(int,min)),K_1)),M))->hAPP(nat,int,power_power(int,number_number_of(int,min)),J_1)=hAPP(nat,int,power_power(int,number_number_of(int,min)),K_1))). % 32.58/32.45 all X_1 P_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))-> (hBOOL(hAPP(int,bool,zcong(X_1,number_number_of(int,min)),P_1))-> -hBOOL(hAPP(int,bool,zcong(X_1,one_one(int)),P_1)))). % 32.58/32.45 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),M))-> -hBOOL(hAPP(int,bool,zcong(one_one(int),number_number_of(int,min)),M))). % 32.58/32.45 hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min))=hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)). % 32.58/32.45 -hBOOL(hAPP(int,bool,quadRes(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),number_number_of(int,min)))->legendre(number_number_of(int,min),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))!=one_one(int). % 32.58/32.45 all A_1 B C (hAPP(int,int,minus_minus(int,A_1),B)=ti(int,C)->ti(int,A_1)=hAPP(int,int,plus_plus(int,C),B)). % 32.58/32.45 all X_a (number_ring(X_a)-> (all V W (number_number_of(X_a,hAPP(int,int,minus_minus(int,V),W))=hAPP(X_a,X_a,minus_minus(X_a,number_number_of(X_a,V)),number_number_of(X_a,W))))). % 32.58/32.45 all K_1 (hAPP(int,int,minus_minus(int,K_1),pls)=ti(int,K_1)). % 32.58/32.45 all K_1 L_1 (hAPP(int,int,minus_minus(int,bit0(K_1)),bit0(L_1))=bit0(hAPP(int,int,minus_minus(int,K_1),L_1))). % 32.58/32.45 all W Z1 Z2 (hAPP(int,int,times_times(int,W),hAPP(int,int,minus_minus(int,Z1),Z2))=hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,W),Z1)),hAPP(int,int,times_times(int,W),Z2))). % 32.58/32.45 all Z1 Z2 W (hAPP(int,int,times_times(int,hAPP(int,int,minus_minus(int,Z1),Z2)),W)=hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,Z1),W)),hAPP(int,int,times_times(int,Z2),W))). % 32.58/32.45 all C D_2 A_1 B M (hBOOL(hAPP(int,bool,zcong(A_1,B),M))-> (hBOOL(hAPP(int,bool,zcong(C,D_2),M))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,minus_minus(int,A_1),C),hAPP(int,int,minus_minus(int,B),D_2)),M)))). % 32.58/32.45 all K_1 M N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),hAPP(int,int,minus_minus(int,M),N_1)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),N_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),M)))). % 32.58/32.45 all X_b (number(X_b)&ring(X_b)-> (all V B C (hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),hAPP(X_b,X_b,minus_minus(X_b,B),C))=hAPP(X_b,X_b,minus_minus(X_b,hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),B)),hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),C))))). % 32.58/32.45 all X_b (number(X_b)&ring(X_b)-> (all A_1 B V (hAPP(X_b,X_b,times_times(X_b,hAPP(X_b,X_b,minus_minus(X_b,A_1),B)),number_number_of(X_b,V))=hAPP(X_b,X_b,minus_minus(X_b,hAPP(X_b,X_b,times_times(X_b,A_1),number_number_of(X_b,V))),hAPP(X_b,X_b,times_times(X_b,B),number_number_of(X_b,V)))))). % 32.58/32.45 all K_1 L_1 (hAPP(int,int,minus_minus(int,bit1(K_1)),bit0(L_1))=bit1(hAPP(int,int,minus_minus(int,K_1),L_1))). % 32.58/32.45 all K_1 L_1 (hAPP(int,int,minus_minus(int,bit1(K_1)),bit1(L_1))=bit0(hAPP(int,int,minus_minus(int,K_1),L_1))). % 32.58/32.45 all L_1 (hAPP(int,int,minus_minus(int,pls),bit0(L_1))=bit0(hAPP(int,int,minus_minus(int,pls),L_1))). % 32.58/32.45 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,K),L)),zero_zero(int)))). % 32.58/32.45 all A_1 R_1 B M C D_2 N_1 (hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,hAPP(int,int,minus_minus(int,A_1),hAPP(int,int,times_times(int,R_1),B))),M)),hAPP(int,int,times_times(int,hAPP(int,int,minus_minus(int,C),hAPP(int,int,times_times(int,R_1),D_2))),N_1))=hAPP(int,int,minus_minus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A_1),M)),hAPP(int,int,times_times(int,C),N_1))),hAPP(int,int,times_times(int,R_1),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),M)),hAPP(int,int,times_times(int,D_2),N_1))))). % 32.58/32.45 all A_3 B_2 Ma (hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),hAPP(int,int,minus_minus(int,A_3),B_2)))). % 32.58/32.45 all X_a (number_ring(X_a)-> (all V W C (hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),hAPP(X_a,X_a,minus_minus(X_a,number_number_of(X_a,W)),C))=hAPP(X_a,X_a,minus_minus(X_a,number_number_of(X_a,hAPP(int,int,plus_plus(int,V),W))),C)))). % 32.58/32.45 all A_1 X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),A_1))-> (ti(int,X_1)!=hAPP(int,int,minus_minus(int,A_1),one_one(int))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),hAPP(int,int,minus_minus(int,A_1),one_one(int))))))). % 32.58/32.45 all W_1 Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),hAPP(int,int,minus_minus(int,Z_2),one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))). % 32.58/32.45 all L_1 (hAPP(int,int,minus_minus(int,pls),bit1(L_1))=bit1(hAPP(int,int,minus_minus(int,min),L_1))). % 32.58/32.45 all L_1 (hAPP(int,int,minus_minus(int,min),bit0(L_1))=bit1(hAPP(int,int,minus_minus(int,min),L_1))). % 32.58/32.45 all L_1 (hAPP(int,int,minus_minus(int,min),bit1(L_1))=bit0(hAPP(int,int,minus_minus(int,min),L_1))). % 32.58/32.45 all A_3 P_3 (hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_3),hAPP(int,int,minus_minus(int,P_3),one_one(int))),one_one(int)),P_3))<->hBOOL(hAPP(int,bool,zcong(A_3,hAPP(int,int,minus_minus(int,P_3),one_one(int))),P_3))). % 32.58/32.45 all D_2 C A_1 B M (hBOOL(hAPP(int,bool,zcong(A_1,B),M))-> (ti(int,B)=ti(int,C)-> (hBOOL(hAPP(int,bool,zcong(C,D_2),M))->hBOOL(hAPP(int,bool,zcong(A_1,D_2),M))))). % 32.58/32.45 all A_1 B P_1 Q_1 (hAPP(int,int,times_times(int,twoSqu1929807760sum2sq(product_Pair(int,int,A_1,B))),twoSqu1929807760sum2sq(product_Pair(int,int,P_1,Q_1)))=twoSqu1929807760sum2sq(product_Pair(int,int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A_1),P_1)),hAPP(int,int,times_times(int,B),Q_1)),hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,A_1),Q_1)),hAPP(int,int,times_times(int,B),P_1))))). % 32.58/32.45 all A_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),A_1),one_one(int)),P_1))->hBOOL(hAPP(int,bool,zcong(A_1,one_one(int)),P_1))|hBOOL(hAPP(int,bool,zcong(A_1,hAPP(int,int,minus_minus(int,P_1),one_one(int))),P_1))))). % 32.58/32.45 all A_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_1))-> (hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),A_1),one_one(int)),P_1))->ti(int,A_1)=one_one(int)|ti(int,A_1)=hAPP(int,int,minus_minus(int,P_1),one_one(int)))))). % 32.58/32.45 all A_1 B (hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,A_1),B)),hAPP(int,int,minus_minus(int,A_1),B))=hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls)))))). % 32.58/32.45 all M hBOOL(hAPP(int,bool,zcong(M,zero_zero(int)),M)). % 32.58/32.45 all C_1 D A_3 B_2 Ma (hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))-> (hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,A_3),D)),Ma))<->hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,B_2),D)),Ma)))). % 32.58/32.45 all C_1 D A_3 B_2 Ma (hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))-> (hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,D),A_3)),Ma))<->hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,D),B_2)),Ma)))). % 32.58/32.45 all C A_1 B M (hBOOL(hAPP(int,bool,zcong(A_1,B),M))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,plus_plus(int,A_1),C),hAPP(int,int,plus_plus(int,B),C)),M))). % 32.58/32.45 all Z_1 X_1 Y_1 M (hBOOL(hAPP(int,bool,zcong(X_1,Y_1),M))->hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X_1),Z_1),hAPP(nat,int,power_power(int,Y_1),Z_1)),M))). % 32.58/32.45 all X_a (number_ring(X_a)-> (all X_1 Y_1 (hAPP(nat,X_a,power_power(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),Y_1)),number_number_of(nat,bit0(bit1(pls))))=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls)))),X_1)),Y_1))))). % 32.58/32.45 all A_1 B (hAPP(nat,int,power_power(int,hAPP(int,int,minus_minus(int,A_1),B)),number_number_of(nat,bit0(bit1(pls))))=hAPP(int,int,plus_plus(int,hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),A_1)),B))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls)))))). % 32.58/32.45 all A_1 B (hAPP(nat,int,power_power(int,hAPP(int,int,minus_minus(int,A_1),B)),number_number_of(nat,bit1(bit1(pls))))=hAPP(int,int,minus_minus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit1(bit1(pls))))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit1(bit1(pls)))),hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))))),B))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit1(bit1(pls)))),A_1)),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls))))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit1(bit1(pls)))))). % 32.58/32.45 all M Y_1 X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Y_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))-> (hBOOL(hAPP(int,bool,zcong(X_1,Y_1),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_1),M))->ti(int,X_1)=ti(int,Y_1))))))). % 32.58/32.45 all M X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),M))-> -hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),M)))). % 32.58/32.45 all N_1 M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),M))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),M),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_1),M))). % 32.58/32.45 all X_2 P_3 (hBOOL(hAPP(int,bool,zcong(X_2,zero_zero(int)),P_3))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),X_2))). % 32.58/32.45 all A_3 Ma (hBOOL(hAPP(int,bool,zcong(A_3,zero_zero(int)),Ma))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),A_3))). % 32.58/32.45 all M N_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),hAPP(int,int,times_times(int,M),N_1)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),N_1)))). % 32.58/32.45 all M X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),M))-> (hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),M))->ti(int,X_1)=zero_zero(int)))). % 32.58/32.45 all P_1 Y_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),Y_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),hAPP(nat,int,power_power(int,Y_1),N_1))))). % 32.58/32.45 all N_1 (hAPP(nat,int,power_power(int,number_number_of(int,min)),N_1)=one_one(int)|hAPP(nat,int,power_power(int,number_number_of(int,min)),N_1)=number_number_of(int,min)). % 32.58/32.45 all Y_1 X_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))-> (-hBOOL(hAPP(int,bool,zcong(Y_1,zero_zero(int)),P_1))-> -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,X_1),Y_1),zero_zero(int)),P_1))))). % 32.58/32.45 all B A_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),B),zero_zero(int)),P_1))->hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,zcong(B,zero_zero(int)),P_1))))). % 32.58/32.45 all B A_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (-hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_1))& -hBOOL(hAPP(int,bool,zcong(B,zero_zero(int)),P_1))-> -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),B),zero_zero(int)),P_1))))). % 32.58/32.45 all Y_1 N_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),hAPP(nat,int,power_power(int,Y_1),N_1)))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),Y_1))))). % 32.58/32.45 all M (hBOOL(hAPP(int,bool,zprime,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),M)),one_one(int))))->legendre(number_number_of(int,min),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),M)),one_one(int)))=one_one(int)). % 32.58/32.45 all A_1 P_1 ((hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_1))->legendre(A_1,P_1)=zero_zero(int))& (-hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_1))-> (hBOOL(hAPP(int,bool,quadRes(P_1),A_1))->legendre(A_1,P_1)=one_one(int))& (-hBOOL(hAPP(int,bool,quadRes(P_1),A_1))->legendre(A_1,P_1)=number_number_of(int,min)))). % 32.58/32.45 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),M))->M=zero_zero(nat)|M=N_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1)),M))). % 32.58/32.45 all Ma X_2 (hBOOL(hAPP(int,bool,quadRes(Ma),X_2))<-> (exists Y hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,Y),number_number_of(nat,bit0(bit1(pls)))),X_2),Ma)))). % 32.58/32.45 all X_2 Y_2 (hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X_2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,real,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)). % 32.58/32.45 all X_a (linord626643107strict(X_a)-> (all V U_1 Y_1 X_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),U_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),V))-> (hAPP(X_a,X_a,plus_plus(X_a,U_1),V)=one_one(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,U_1),X_1)),hAPP(X_a,X_a,times_times(X_a,V),Y_1))),A_1))))))))). % 32.58/32.45 all X_a (comm_semiring_1(X_a)-> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),zero_zero(X_a))))). % 32.58/32.45 all X_2 Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_2),Y_2))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,minus_minus(real,X_2),Y_2)),zero_zero(real)))). % 32.58/32.45 all X_a (linordered_idom(X_a)-> (all X_1 Y_1 (ti(X_a,X_1)!=ti(X_a,Y_1)-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))). % 32.58/32.45 all X_a (comm_semiring_1(X_a)-> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),A_1)))). % 32.58/32.45 all X_a (comm_semiring_1(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)))))). % 32.58/32.45 zero_zero(real)!=one_one(real). % 32.58/32.45 all X_2 Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_2),Y_2))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_2))|X_2=Y_2). % 32.58/32.45 all X_2 Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_2))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_2),Y_2))&X_2!=Y_2). % 32.58/32.45 all X_2 Y_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2))<->X_2=Y_2). % 32.58/32.45 all Z1 Z2 Z3 (hAPP(real,real,times_times(real,hAPP(real,real,times_times(real,Z1),Z2)),Z3)=hAPP(real,real,times_times(real,Z1),hAPP(real,real,times_times(real,Z2),Z3))). % 32.58/32.45 all Z_1 W (hAPP(real,real,times_times(real,Z_1),W)=hAPP(real,real,times_times(real,W),Z_1)). % 32.58/32.45 all Z_1 (hAPP(real,real,times_times(real,one_one(real)),Z_1)=Z_1). % 32.58/32.45 all Z_1 X_1 Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),Y_1))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,plus_plus(real,Z_1),X_1)),hAPP(real,real,plus_plus(real,Z_1),Y_1)))). % 32.58/32.45 all X_a (monoid_mult(X_a)-> (all X_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,X_1),hAPP(nat,nat,minus_minus(nat,N_1),one_one(nat)))),X_1)=hAPP(nat,X_a,power_power(X_a,X_1),N_1)))). % 32.58/32.45 all N_1 M ((M=zero_zero(nat)->hAPP(nat,nat,times_times(nat,M),N_1)=zero_zero(nat))& (M!=zero_zero(nat)->hAPP(nat,nat,times_times(nat,M),N_1)=hAPP(nat,nat,plus_plus(nat,N_1),hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,M),one_one(nat))),N_1)))). % 32.58/32.45 all P_1 M ((M=zero_zero(nat)->hAPP(nat,nat,power_power(nat,P_1),M)=one_one(nat))& (M!=zero_zero(nat)->hAPP(nat,nat,power_power(nat,P_1),M)=hAPP(nat,nat,times_times(nat,P_1),hAPP(nat,nat,power_power(nat,P_1),hAPP(nat,nat,minus_minus(nat,M),one_one(nat)))))). % 32.58/32.45 all X_1 Y_1 (hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,power_power(nat,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,nat,power_power(nat,Y_1),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,nat,times_times(nat,hAPP(nat,nat,plus_plus(nat,X_1),Y_1)),hAPP(nat,nat,minus_minus(nat,X_1),Y_1))). % 32.58/32.45 all X_a (no_zero_divisors(X_a)-> (all A_1 B (hAPP(X_a,X_a,times_times(X_a,A_1),B)=zero_zero(X_a)->ti(X_a,A_1)=zero_zero(X_a)|ti(X_a,B)=zero_zero(X_a)))). % 32.58/32.45 all X_a (no_zero_divisors(X_a)-> (all B A_1 (ti(X_a,A_1)!=zero_zero(X_a)-> (ti(X_a,B)!=zero_zero(X_a)->hAPP(X_a,X_a,times_times(X_a,A_1),B)!=zero_zero(X_a))))). % 32.58/32.45 all X_a (ring_n68954251visors(X_a)-> (all A_3 B_2 (hAPP(X_a,X_a,times_times(X_a,A_3),B_2)=zero_zero(X_a)<->ti(X_a,A_3)=zero_zero(X_a)|ti(X_a,B_2)=zero_zero(X_a)))). % 32.58/32.45 all X_a (mult_zero(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a))=zero_zero(X_a)))). % 32.58/32.45 all X_a (mult_zero(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,zero_zero(X_a)),A_1)=zero_zero(X_a)))). % 32.58/32.45 all X_a (zero_ne_q_one(X_a)->zero_zero(X_a)!=one_one(X_a)). % 32.58/32.45 all X_a (zero_ne_q_one(X_a)->one_one(X_a)!=zero_zero(X_a)). % 32.58/32.45 all X_a (semiring(X_a)-> (all A_1 E_1 B C (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),E_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B),E_1)),C))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),E_1)),C)))). % 32.58/32.45 all X_a (comm_semiring(X_a)-> (all A_1 B C (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))))). % 32.58/32.45 all X_a (comm_semiring_1(X_a)-> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),zero_zero(X_a)),A_1))->ti(X_a,A_1)=zero_zero(X_a)))). % 32.58/32.45 all X_a (ab_group_add(X_a)-> (all A_1 C B D_2 (hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),hAPP(X_a,X_a,minus_minus(X_a,C),D_2))))). % 32.58/32.45 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),C))))). % 32.58/32.45 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C))))). % 32.58/32.45 all X_a (dvd(X_a)-> (all A_1 B K_1 (A_1=hAPP(X_a,X_a,times_times(X_a,B),K_1)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),A_1))))). % 32.58/32.45 all X_a (comm_semiring_1(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),D_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))))))). % 32.58/32.45 all X_a (comm_semiring_1(X_a)-> (all B A_1 C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,times_times(X_a,B),C)))))). % 32.58/32.45 all X_a (comm_semiring_1(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,times_times(X_a,B),C)))))). % 32.58/32.45 all X_a (comm_semiring_1(X_a)-> (all A_1 B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,times_times(X_a,B),A_1))))). % 32.58/32.45 all X_a (comm_semiring_1(X_a)-> (all A_1 B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,times_times(X_a,A_1),B))))). % 32.58/32.45 all X_a (comm_semiring_1(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C))))))). % 32.58/32.45 all X_a (comm_semiring_1(X_a)-> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),one_one(X_a)),A_1)))). % 32.58/32.45 all X_a (comm_ring_1(X_a)-> (all Z_1 X_1 Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Z_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),hAPP(X_a,X_a,minus_minus(X_a,Y_1),Z_1))))))). % 32.58/32.45 all A_3 B_2 C_1 (C_1!=zero_zero(real)-> (hAPP(real,real,times_times(real,A_3),C_1)=hAPP(real,real,times_times(real,B_2),C_1)<->A_3=B_2)). % 32.58/32.45 all A_3 B_2 C_1 (C_1!=zero_zero(real)-> (hAPP(real,real,times_times(real,C_1),A_3)=hAPP(real,real,times_times(real,C_1),B_2)<->A_3=B_2)). % 32.58/32.45 all B D_2 A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),A_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),hAPP(nat,nat,plus_plus(nat,A_1),B)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),B)))). % 32.58/32.45 all C A_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,C),A_1)),hAPP(nat,nat,times_times(nat,C),B)))). % 32.58/32.45 all C A_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,A_1),C)),hAPP(nat,nat,times_times(nat,B),C)))). % 32.58/32.45 all N Ma (hAPP(nat,nat,times_times(nat,N),Ma)=one_one(nat)<->N=one_one(nat)&Ma=one_one(nat)). % 32.58/32.45 all Z1 Z2 W (hAPP(real,real,times_times(real,hAPP(real,real,plus_plus(real,Z1),Z2)),W)=hAPP(real,real,plus_plus(real,hAPP(real,real,times_times(real,Z1),W)),hAPP(real,real,times_times(real,Z2),W))). % 32.58/32.45 all Ma N (hAPP(nat,nat,power_power(nat,Ma),N)=zero_zero(nat)<->N!=zero_zero(nat)&Ma=zero_zero(nat)). % 32.58/32.45 all N_1 X_1 Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,X_1),N_1)),hAPP(nat,nat,power_power(nat,Y_1),N_1)))). % 32.58/32.45 all X_a (ordere453448008miring(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a)))))). % 32.58/32.45 all X_a (ordered_ring(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B)))))). % 32.58/32.45 all X_a (ordered_semiring(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))))))))). % 32.58/32.45 all X_a (ordered_semiring(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))))))))). % 32.58/32.45 all X_a (ordered_ring(X_a)-> (all C B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))))))). % 32.58/32.45 all X_a (ordered_ring(X_a)-> (all C B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))))))). % 32.58/32.45 all X_a (ordere1490568538miring(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))))))). % 32.58/32.45 all X_a (ordered_semiring(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))))))). % 32.58/32.45 all X_a (ordered_semiring(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))))))). % 32.58/32.45 all X_a (ordered_ring(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))))))). % 32.58/32.45 all X_a (ordere453448008miring(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))))))). % 32.58/32.45 all X_a (ordere453448008miring(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,B),A_1)),zero_zero(X_a))))))). % 32.58/32.45 all X_a (ordere453448008miring(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))))))). % 32.58/32.45 all X_a (ordere453448008miring(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))))))). % 32.58/32.45 all X_a (linord581940658strict(X_a)-> (all A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a)))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_2))))). % 32.58/32.45 all X_a (linord581940658strict(X_a)-> (all A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a)))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),zero_zero(X_a)))))). % 32.58/32.45 all X_a (linordered_ring(X_a)-> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),A_1))))). % 32.58/32.45 all X_a (linord581940658strict(X_a)-> (all C B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))))))). % 32.58/32.45 all X_a (linord581940658strict(X_a)-> (all C B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))))))). % 32.58/32.45 all X_a (linord893533164strict(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))))))). % 32.58/32.45 all X_a (linord20386208strict(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))))))). % 32.58/32.45 all X_a (linord20386208strict(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))))))). % 32.58/32.45 all X_a (linord581940658strict(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))))))). % 32.58/32.45 all X_a (linord20386208strict(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))))))). % 32.58/32.45 all X_a (linord581940658strict(X_a)-> (all A_3 B_2 C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)))))). % 32.58/32.45 all X_a (linord20386208strict(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,B),A_1)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)))))). % 32.58/32.45 all X_a (linord20386208strict(X_a)-> (all A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)))))). % 32.58/32.45 all X_a (linord20386208strict(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,B),A_1)),zero_zero(X_a))))))). % 32.58/32.45 all X_a (linord20386208strict(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))))))). % 32.58/32.45 all X_a (linord20386208strict(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))))))). % 32.58/32.45 all X_a (linord581940658strict(X_a)-> (all A_3 B_2 C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)))))). % 32.58/32.45 all X_a (linord581940658strict(X_a)-> (all C_1 A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3))))). % 32.58/32.45 all X_a (linord581940658strict(X_a)-> (all A_3 C_1 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3))))). % 32.58/32.45 all X_a (linordered_ring(X_a)-> (all A_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),A_1)),zero_zero(X_a)))))). % 32.58/32.45 all X_a (linordered_semidom(X_a)-> (all B C A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))))))). % 32.58/32.45 all X_a (linordered_semidom(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),one_one(X_a)))). % 32.58/32.45 all X_a (linordered_semidom(X_a)-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),zero_zero(X_a)))). % 32.58/32.45 all X_a (linordered_semidom(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a)))). % 32.58/32.45 all X_a (linordered_semidom(X_a)-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a)))). % 32.58/32.45 all X_a (linordered_semidom(X_a)-> (all N_1 M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,times_times(X_a,M),N_1))))))). % 32.58/32.45 all X_a (linordered_semidom(X_a)-> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,plus_plus(X_a,A_1),one_one(X_a)))))). % 32.58/32.45 all X_a (idom(X_a)-> (all C_1 A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))<->ti(X_a,C_1)=zero_zero(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2))))). % 32.58/32.45 all X_a (idom(X_a)-> (all A_3 C_1 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))<->ti(X_a,C_1)=zero_zero(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2))))). % 32.58/32.45 all X_a (ring(X_a)-> (all A_3 E C_1 B_2 D (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)<->hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)=ti(X_a,D)))). % 32.58/32.45 all X_a (ring(X_a)-> (all A_3 E C_1 B_2 D (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)<->ti(X_a,C_1)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D)))). % 32.58/32.45 all X_a (ring(X_a)-> (all X_1 Y_1 A_1 B (hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Y_1)),hAPP(X_a,X_a,times_times(X_a,A_1),B))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),hAPP(X_a,X_a,minus_minus(X_a,Y_1),B))),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),A_1)),B))))). % 32.58/32.45 all A_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))->B=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A_1),B))). % 32.58/32.45 all Ma K N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))<->K=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N))). % 32.58/32.45 all X_2 Y_2 Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,times_times(real,X_2),Z_2)),hAPP(real,real,times_times(real,Y_2),Z_2)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_2)))). % 32.58/32.45 all X_2 Y_2 Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,times_times(real,X_2),Z_2)),hAPP(real,real,times_times(real,Y_2),Z_2)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_2),Y_2)))). % 32.58/32.45 all X_2 Y_2 Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,times_times(real,Z_2),X_2)),hAPP(real,real,times_times(real,Z_2),Y_2)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_2),Y_2)))). % 32.58/32.45 all Y_1 X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,times_times(real,X_1),Y_1))))). % 32.58/32.45 all X_1 Y_1 Z_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_1))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,times_times(real,Z_1),X_1)),hAPP(real,real,times_times(real,Z_1),Y_1))))). % 32.58/32.45 all X_2 Y_2 (hAPP(real,real,plus_plus(real,hAPP(real,real,times_times(real,X_2),X_2)),hAPP(real,real,times_times(real,Y_2),Y_2))=zero_zero(real)<->X_2=zero_zero(real)&Y_2=zero_zero(real)). % 32.58/32.45 all X_1 Y_1 N_1 (N_1!=zero_zero(nat)-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,X_1),N_1)),Y_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))). % 32.58/32.45 all A_1 N_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,A_1),N_1)),hAPP(nat,nat,power_power(nat,B),N_1)))-> (N_1!=zero_zero(nat)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)))). % 32.58/32.45 all X_2 N (hAPP(nat,nat,power_power(nat,X_2),N)=one_one(nat)<->X_2=one_one(nat)|N=zero_zero(nat)). % 32.58/32.45 all X_a (linord581940658strict(X_a)-> (all A_3 B_2 C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2)))))). % 32.58/32.45 all X_a (linord581940658strict(X_a)-> (all A_3 B_2 C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),A_3)))))). % 32.58/32.45 all X_a (linord20386208strict(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))))))))). % 32.58/32.45 all X_a (linord20386208strict(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))))))))). % 32.58/32.45 all X_a (linord20386208strict(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))))))))). % 32.58/32.45 all X_a (linord20386208strict(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))))))))). % 32.58/32.45 all X_a (linordered_semiring(X_a)-> (all A_1 C B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))). % 32.58/32.45 all X_a (linord20386208strict(X_a)-> (all A_1 C B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))). % 32.58/32.45 all X_a (linordered_semiring(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))). % 32.58/32.45 all X_a (linord20386208strict(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))). % 32.58/32.45 all X_a (linord20386208strict(X_a)-> (all A_1 C B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B)))))). % 32.58/32.45 all X_a (linord20386208strict(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B)))))). % 32.58/32.45 all X_a (linordered_idom(X_a)-> (all Y_1 X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y_1),one_one(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,Y_1),X_1)),X_1))))))). % 32.58/32.45 all X_a (linordered_idom(X_a)-> (all Y_1 X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y_1),one_one(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,X_1),Y_1)),X_1))))))). % 32.58/32.45 all X_a (linordered_semidom(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))))). % 32.58/32.45 all X_a (ordered_ring(X_a)-> (all A_3 E C_1 B_2 D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)),D))))). % 32.58/32.45 all X_a (ordered_ring(X_a)-> (all A_3 E C_1 B_2 D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D)))))). % 32.58/32.45 all X_a (ordered_ring(X_a)-> (all A_3 E C_1 B_2 D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)),D))))). % 32.58/32.45 all X_a (ordered_ring(X_a)-> (all A_3 E C_1 B_2 D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D)))))). % 32.58/32.45 all X_a (ring_1(X_a)-> (all X_1 (hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),X_1)),one_one(X_a))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,X_1),one_one(X_a))),hAPP(X_a,X_a,minus_minus(X_a,X_1),one_one(X_a)))))). % 32.58/32.45 all X_a (linord1278240602ring_1(X_a)-> (all V U_1 Y_1 X_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y_1),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),U_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),V))-> (hAPP(X_a,X_a,plus_plus(X_a,U_1),V)=one_one(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,U_1),X_1)),hAPP(X_a,X_a,times_times(X_a,V),Y_1))),A_1))))))))). % 32.58/32.45 all X_1 Q_1 N_1 R_1 (X_1=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,Q_1),N_1)),R_1)-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),R_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_1),N_1))-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),X_1))))). % 32.58/32.45 all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),one_one(real)),hAPP(nat,real,power_power(real,number_number_of(real,bit0(bit1(pls)))),N_1))). % 32.58/32.45 all A_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))-> (exists R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2))&hAPP(nat,real,power_power(real,R_2),N_1)=A_1)))). % 32.58/32.45 all A_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))-> (exists X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X))&hAPP(nat,real,power_power(real,X),N_1)=A_1& (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y))&hAPP(nat,real,power_power(real,Y),N_1)=A_1->Y=X)))))). % 32.58/32.45 all N Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,N),Ma)),Ma))<->N=one_one(nat))). % 32.58/32.45 all N Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,Ma),N)),Ma))<->N=one_one(nat))). % 32.58/32.45 all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N_1)). % 32.58/32.45 all X_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),X_1)). % 32.58/32.45 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))). % 32.58/32.45 all I_1 J_1 K_1 (hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,minus_minus(nat,I_1),J_1)),K_1)=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,minus_minus(nat,I_1),K_1)),J_1)). % 32.58/32.45 all W hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),W)). % 32.58/32.45 all Z_1 W (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z_1),W))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),Z_1))). % 32.58/32.45 all K_1 I_1 J_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I_1),J_1))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),J_1),K_1))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I_1),K_1)))). % 32.58/32.45 all Z_1 W (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z_1),W))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),Z_1))->Z_1=W)). % 32.58/32.45 all N_1 (hAPP(nat,nat,minus_minus(nat,zero_zero(nat)),N_1)=zero_zero(nat)). % 32.58/32.45 all M (hAPP(nat,nat,minus_minus(nat,M),zero_zero(nat))=M). % 32.58/32.45 all M (hAPP(nat,nat,minus_minus(nat,M),M)=zero_zero(nat)). % 32.58/32.45 all M N_1 (hAPP(nat,nat,minus_minus(nat,M),N_1)=zero_zero(nat)-> (hAPP(nat,nat,minus_minus(nat,N_1),M)=zero_zero(nat)->M=N_1)). % 32.58/32.45 all P_2 Ma N ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_2,N),Ma)))-> ((Ma=N->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_2,N),Ma)))-> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),Ma))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_2,N),Ma)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_2,N),Ma))))). % 32.58/32.45 all S T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3))->S!=T_3). % 32.58/32.45 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M))->M!=N_1). % 32.58/32.45 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))). % 32.58/32.45 all X_1 Y_1 (X_1!=Y_1-> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y_1),X_1)))). % 32.58/32.45 all Ma N (Ma!=N<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),Ma))). % 32.58/32.45 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))). % 32.58/32.45 all L_1 M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,L_1),N_1)),hAPP(nat,nat,minus_minus(nat,L_1),M))))). % 32.58/32.45 all N_1 J_1 K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,J_1),N_1)),K_1))). % 32.58/32.45 all X_1 Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))). % 32.58/32.45 all Z_1 X_1 Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),Z_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),Y_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X_1)))). % 32.58/32.45 all A_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)))). % 32.58/32.45 all Z_1 X_1 Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),Z_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X_1)))). % 32.58/32.45 all C A_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1))-> (B=C->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1)))). % 32.58/32.45 all P_2 X_2 Y_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))->hBOOL(P_2))). % 32.58/32.45 all X_1 Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))->Y_1!=X_1). % 32.58/32.45 all X_1 Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))->X_1!=Y_1). % 32.58/32.45 all X_1 Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))). % 32.58/32.45 all X_1 Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))). % 32.58/32.45 all X_1 Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))). % 32.58/32.45 all X_1 Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))->X_1!=Y_1). % 32.58/32.45 all Z_1 X_1 Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),Z_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),Y_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X_1)))). % 32.58/32.45 all C A_1 B (A_1=B-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),B))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1)))). % 32.58/32.45 all Z_1 X_1 Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),Z_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z_1)))). % 32.58/32.45 all X_1 Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))->X_1=Y_1)). % 32.58/32.45 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),M))->M=N_1)). % 32.58/32.45 all C A_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))-> (B=C->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)))). % 32.58/32.45 all C A_1 B (A_1=B-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)))). % 32.58/32.45 all A_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))-> (A_1!=B->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)))). % 32.58/32.45 all X_1 Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))|X_1=Y_1). % 32.58/32.45 all Y_2 X_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))<->X_2=Y_2)). % 32.58/32.45 all X_1 Y_1 (X_1=Y_1->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))). % 32.58/32.45 all A_1 B (A_1!=B-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)))). % 32.58/32.45 all X_2 Y_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2))). % 32.58/32.45 all X_2 Y_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))&X_2!=Y_2). % 32.58/32.45 all X_2 Y_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2))|X_2=Y_2). % 32.58/32.45 all X_2 Y_2 (X_2=Y_2<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2))). % 32.58/32.45 all X_1 (-(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),X_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),X_1)))). % 32.58/32.45 all N_1 K_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),M))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),hAPP(nat,nat,minus_minus(nat,M),N_1))))). % 32.58/32.45 all M N_1 (hAPP(nat,nat,plus_plus(nat,M),N_1)=hAPP(nat,nat,plus_plus(nat,N_1),M)). % 32.58/32.45 all X_1 Y_1 Z_1 (hAPP(nat,nat,plus_plus(nat,X_1),hAPP(nat,nat,plus_plus(nat,Y_1),Z_1))=hAPP(nat,nat,plus_plus(nat,Y_1),hAPP(nat,nat,plus_plus(nat,X_1),Z_1))). % 32.58/32.45 all M N_1 K_1 (hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,plus_plus(nat,M),N_1)),K_1)=hAPP(nat,nat,plus_plus(nat,M),hAPP(nat,nat,plus_plus(nat,N_1),K_1))). % 32.58/32.45 all K Ma N (hAPP(nat,nat,plus_plus(nat,K),Ma)=hAPP(nat,nat,plus_plus(nat,K),N)<->Ma=N). % 32.58/32.45 all Ma K N (hAPP(nat,nat,plus_plus(nat,Ma),K)=hAPP(nat,nat,plus_plus(nat,N),K)<->Ma=N). % 32.58/32.45 all M N_1 (hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,M),N_1)),N_1)=M). % 32.58/32.45 all N_1 M (hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,N_1),M)),N_1)=M). % 32.58/32.45 all I_1 J_1 K_1 (hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,minus_minus(nat,I_1),J_1)),K_1)=hAPP(nat,nat,minus_minus(nat,I_1),hAPP(nat,nat,plus_plus(nat,J_1),K_1))). % 32.58/32.45 all K_1 M N_1 (hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,K_1),M)),hAPP(nat,nat,plus_plus(nat,K_1),N_1))=hAPP(nat,nat,minus_minus(nat,M),N_1)). % 32.58/32.45 all M K_1 N_1 (hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,M),K_1)),hAPP(nat,nat,plus_plus(nat,N_1),K_1))=hAPP(nat,nat,minus_minus(nat,M),N_1)). % 32.58/32.45 all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),N_1)). % 32.58/32.45 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))). % 32.58/32.45 all M N_1 (M=N_1->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))). % 32.58/32.45 all K_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),K_1)))). % 32.58/32.45 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->M=N_1)). % 32.58/32.45 all M N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,M),N_1)),M)). % 32.58/32.45 all L_1 M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,L_1),N_1)),hAPP(nat,nat,minus_minus(nat,L_1),M)))). % 32.58/32.45 all L_1 M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,M),L_1)),hAPP(nat,nat,minus_minus(nat,N_1),L_1)))). % 32.58/32.45 all I_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),N_1))->hAPP(nat,nat,minus_minus(nat,N_1),hAPP(nat,nat,minus_minus(nat,N_1),I_1))=I_1). % 32.58/32.45 all N K Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))-> (hAPP(nat,nat,minus_minus(nat,Ma),K)=hAPP(nat,nat,minus_minus(nat,N),K)<->Ma=N))). % 32.58/32.45 all N_1 K_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))->hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,minus_minus(nat,M),K_1)),hAPP(nat,nat,minus_minus(nat,N_1),K_1))=hAPP(nat,nat,minus_minus(nat,M),N_1))). % 32.58/32.45 all N K Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,Ma),K)),hAPP(nat,nat,minus_minus(nat,N),K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))))). % 32.58/32.45 all M N_1 K_1 (hAPP(nat,nat,times_times(nat,hAPP(nat,nat,times_times(nat,M),N_1)),K_1)=hAPP(nat,nat,times_times(nat,M),hAPP(nat,nat,times_times(nat,N_1),K_1))). % 32.58/32.45 all M N_1 (hAPP(nat,nat,times_times(nat,M),N_1)=hAPP(nat,nat,times_times(nat,N_1),M)). % 32.58/32.45 all M N_1 K_1 (hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),K_1)=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,times_times(nat,M),K_1)),hAPP(nat,nat,times_times(nat,N_1),K_1))). % 32.58/32.45 all K_1 M N_1 (hAPP(nat,nat,times_times(nat,K_1),hAPP(nat,nat,minus_minus(nat,M),N_1))=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,times_times(nat,K_1),M)),hAPP(nat,nat,times_times(nat,K_1),N_1))). % 32.58/32.45 all N_1 (N_1!=zero_zero(nat)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))). % 32.58/32.45 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->N_1!=zero_zero(nat)). % 32.58/32.45 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))). % 32.58/32.45 all N (N!=zero_zero(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))). % 32.58/32.45 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))). % 32.58/32.45 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,M),N_1)),M)))). % 32.58/32.45 all N Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,minus_minus(nat,N),Ma)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))). % 32.58/32.45 all M N_1 (hAPP(nat,nat,plus_plus(nat,M),N_1)=M->N_1=zero_zero(nat)). % 32.58/32.45 all Ma N (hAPP(nat,nat,plus_plus(nat,Ma),N)=zero_zero(nat)<->Ma=zero_zero(nat)&N=zero_zero(nat)). % 32.58/32.45 all M (hAPP(nat,nat,plus_plus(nat,M),zero_zero(nat))=M). % 32.58/32.45 all N_1 (hAPP(nat,nat,plus_plus(nat,zero_zero(nat)),N_1)=N_1). % 32.58/32.45 all N_1 M (hAPP(nat,nat,minus_minus(nat,N_1),hAPP(nat,nat,plus_plus(nat,N_1),M))=zero_zero(nat)). % 32.58/32.45 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),zero_zero(nat)))<->N=zero_zero(nat)). % 32.58/32.45 all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N_1)). % 32.58/32.45 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))->hAPP(nat,nat,minus_minus(nat,M),N_1)=zero_zero(nat)). % 32.58/32.45 all Ma N (hAPP(nat,nat,minus_minus(nat,Ma),N)=zero_zero(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))). % 32.58/32.45 all N_1 (hAPP(nat,nat,times_times(nat,zero_zero(nat)),N_1)=zero_zero(nat)). % 32.58/32.45 all M (hAPP(nat,nat,times_times(nat,M),zero_zero(nat))=zero_zero(nat)). % 32.58/32.45 all Ma N (hAPP(nat,nat,times_times(nat,Ma),N)=zero_zero(nat)<->Ma=zero_zero(nat)|N=zero_zero(nat)). % 32.58/32.45 all K Ma N (hAPP(nat,nat,times_times(nat,K),Ma)=hAPP(nat,nat,times_times(nat,K),N)<->Ma=N|K=zero_zero(nat)). % 32.58/32.45 all Ma K N (hAPP(nat,nat,times_times(nat,Ma),K)=hAPP(nat,nat,times_times(nat,N),K)<->Ma=N|K=zero_zero(nat)). % 32.58/32.45 all I_1 J_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_1),J_1)),I_1))). % 32.58/32.45 all J_1 I_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,J_1),I_1)),I_1))). % 32.58/32.45 all K Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,K),Ma)),hAPP(nat,nat,plus_plus(nat,K),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))). % 32.58/32.45 all M I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,plus_plus(nat,J_1),M)))). % 32.58/32.45 all M I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,plus_plus(nat,M),J_1)))). % 32.58/32.45 all K_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_1),K_1)),hAPP(nat,nat,plus_plus(nat,J_1),K_1)))). % 32.58/32.45 all K_1 L_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_1),K_1)),hAPP(nat,nat,plus_plus(nat,J_1),L_1))))). % 32.58/32.45 all M N_1 K_1 L_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_1))-> (hAPP(nat,nat,plus_plus(nat,M),L_1)=hAPP(nat,nat,plus_plus(nat,K_1),N_1)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)))). % 32.58/32.45 all I_1 J_1 K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_1),J_1)),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K_1))). % 32.58/32.45 all M N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->hAPP(nat,nat,plus_plus(nat,N_1),hAPP(nat,nat,minus_minus(nat,M),N_1))=M). % 32.58/32.45 all I_2 J_2 K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,minus_minus(nat,J_2),K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),J_2))). % 32.58/32.45 all Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))&Ma!=N). % 32.58/32.45 all Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))|Ma=N). % 32.58/32.45 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))). % 32.58/32.45 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))-> (M!=N_1->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)))). % 32.58/32.45 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|M=N_1->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))). % 32.58/32.45 all N K Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,Ma),K)),hAPP(nat,nat,minus_minus(nat,N),K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))))). % 32.58/32.45 all C A_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),A_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,A_1),C)),hAPP(nat,nat,minus_minus(nat,B),C))))). % 32.58/32.45 all K N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,plus_plus(nat,N),K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),N))). % 32.58/32.45 all K_1 M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),hAPP(nat,nat,minus_minus(nat,M),N_1)))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),M))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N_1))))). % 32.58/32.45 all K_1 M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),hAPP(nat,nat,minus_minus(nat,M),N_1)))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),M))))). % 32.58/32.45 all N_1 M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),hAPP(nat,nat,plus_plus(nat,M),N_1))). % 32.58/32.45 all N_1 M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),hAPP(nat,nat,plus_plus(nat,N_1),M))). % 32.58/32.45 all Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))<-> (exists K_2 (N=hAPP(nat,nat,plus_plus(nat,Ma),K_2)))). % 32.58/32.45 all K Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,K),Ma)),hAPP(nat,nat,plus_plus(nat,K),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))). % 32.58/32.45 all M I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),hAPP(nat,nat,plus_plus(nat,J_1),M)))). % 32.58/32.45 all M I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),hAPP(nat,nat,plus_plus(nat,M),J_1)))). % 32.58/32.45 all K_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_1),K_1)),hAPP(nat,nat,plus_plus(nat,J_1),K_1)))). % 32.58/32.45 all K_1 L_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_1),K_1)),hAPP(nat,nat,plus_plus(nat,J_1),L_1))))). % 32.58/32.45 all M K_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M),K_1)),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))). % 32.58/32.45 all M K_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M),K_1)),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))). % 32.58/32.45 all M K_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M),K_1)),N_1))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1)))). % 32.58/32.45 all I_1 K_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))->hAPP(nat,nat,minus_minus(nat,I_1),hAPP(nat,nat,minus_minus(nat,J_1),K_1))=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,I_1),K_1)),J_1)). % 32.58/32.45 all J_2 K I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,J_2),K)),I_2))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),hAPP(nat,nat,plus_plus(nat,I_2),K)))). % 32.58/32.45 all M K_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,N_1),M)),K_1)))). % 32.58/32.45 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hAPP(nat,nat,plus_plus(nat,N_1),hAPP(nat,nat,minus_minus(nat,M),N_1))=M). % 32.58/32.45 all I_1 K_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))->hAPP(nat,nat,plus_plus(nat,I_1),hAPP(nat,nat,minus_minus(nat,J_1),K_1))=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,I_1),J_1)),K_1)). % 32.58/32.45 all I_2 K J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),hAPP(nat,nat,minus_minus(nat,J_2),K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),J_2)))). % 32.58/32.45 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),N_1)=M). % 32.58/32.45 all K I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))-> (hAPP(nat,nat,minus_minus(nat,J_2),I_2)=K<->J_2=hAPP(nat,nat,plus_plus(nat,K),I_2))). % 32.58/32.45 all I_1 K_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))->hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,I_1),J_1)),K_1)=hAPP(nat,nat,plus_plus(nat,I_1),hAPP(nat,nat,minus_minus(nat,J_1),K_1))). % 32.58/32.45 all I_1 K_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))->hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,minus_minus(nat,J_1),K_1)),I_1)=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,J_1),I_1)),K_1)). % 32.58/32.45 all I_1 K_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))->hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,J_1),I_1)),K_1)=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,minus_minus(nat,J_1),K_1)),I_1)). % 32.58/32.45 all M N_1 K_1 (hAPP(nat,nat,times_times(nat,hAPP(nat,nat,plus_plus(nat,M),N_1)),K_1)=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,M),K_1)),hAPP(nat,nat,times_times(nat,N_1),K_1))). % 32.58/32.45 all K_1 M N_1 (hAPP(nat,nat,times_times(nat,K_1),hAPP(nat,nat,plus_plus(nat,M),N_1))=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,K_1),M)),hAPP(nat,nat,times_times(nat,K_1),N_1))). % 32.58/32.45 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),one_one(nat)))<->Ma=one_one(nat)). % 32.58/32.45 all K_1 L_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,I_1),K_1)),hAPP(nat,nat,times_times(nat,J_1),L_1))))). % 32.58/32.45 all K_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K_1),I_1)),hAPP(nat,nat,times_times(nat,K_1),J_1)))). % 32.58/32.45 all K_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,I_1),K_1)),hAPP(nat,nat,times_times(nat,J_1),K_1)))). % 32.58/32.45 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,times_times(nat,M),hAPP(nat,nat,times_times(nat,M),M)))). % 32.58/32.45 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,times_times(nat,M),M))). % 32.58/32.45 all Ma N (hAPP(nat,nat,times_times(nat,Ma),N)=one_one(nat)<->Ma=one_one(nat)&N=one_one(nat)). % 32.58/32.45 all N_1 (hAPP(nat,nat,times_times(nat,N_1),one_one(nat))=N_1). % 32.58/32.45 all Ma N (one_one(nat)=hAPP(nat,nat,times_times(nat,Ma),N)<->Ma=one_one(nat)&N=one_one(nat)). % 32.58/32.45 all N_1 (hAPP(nat,nat,times_times(nat,one_one(nat)),N_1)=N_1). % 32.58/32.45 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),M)))). % 32.58/32.45 all Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,Ma),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))). % 32.58/32.45 all P_2 A_3 B_2 (hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))<-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2))->hBOOL(hAPP(nat,bool,P_2,zero_zero(nat))))& (all D_4 (A_3=hAPP(nat,nat,plus_plus(nat,B_2),D_4)->hBOOL(hAPP(nat,bool,P_2,D_4))))). % 32.58/32.45 all P_2 A_3 B_2 (hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))<-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2))& -hBOOL(hAPP(nat,bool,P_2,zero_zero(nat)))| (exists D_4 (A_3=hAPP(nat,nat,plus_plus(nat,B_2),D_4)& -hBOOL(hAPP(nat,bool,P_2,D_4)))))). % 32.58/32.45 all K_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K_1),I_1)),hAPP(nat,nat,times_times(nat,K_1),J_1))))). % 32.58/32.45 all K_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,I_1),K_1)),hAPP(nat,nat,times_times(nat,J_1),K_1))))). % 32.58/32.45 all Ma K N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))). % 32.58/32.45 all K Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))). % 32.58/32.45 all Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,times_times(nat,Ma),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))). % 32.58/32.45 all M N_1 (M=hAPP(nat,nat,times_times(nat,M),N_1)->N_1=one_one(nat)|M=zero_zero(nat)). % 32.58/32.45 all K_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1)))). % 32.58/32.45 all K_1 M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K_1),M)),hAPP(nat,nat,times_times(nat,K_1),N_1)))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N_1)))). % 32.58/32.45 all K Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))<-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)))). % 32.58/32.45 all Ma K N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))<-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)))). % 32.58/32.45 all X_a (power(X_a)-> (all M N_1 ((N_1=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,M),N_1)=one_one(X_a))& (N_1!=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,M),N_1)=hAPP(X_a,X_a,times_times(X_a,M),hAPP(nat,X_a,power_power(X_a,M),hAPP(nat,nat,minus_minus(nat,N_1),one_one(nat)))))))). % 32.58/32.45 all N P_2 (-hBOOL(hAPP(nat,bool,P_2,zero_zero(nat)))-> (hBOOL(hAPP(nat,bool,P_2,N))-> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),N))& (all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),K_2))-> -hBOOL(hAPP(nat,bool,P_2,I))))&hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,plus_plus(nat,K_2),one_one(nat)))))))). % 32.58/32.45 all U Ma N I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N))))). % 32.58/32.45 all K Ma N (hAPP(nat,nat,times_times(nat,K),Ma)=hAPP(nat,nat,times_times(nat,K),N)<->K=zero_zero(nat)|Ma=N). % 32.58/32.45 all I_1 U_1 J_1 K_1 (hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_1),U_1)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_1),U_1)),K_1))=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,plus_plus(nat,I_1),J_1)),U_1)),K_1)). % 32.58/32.45 all Ma N K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))-> (hAPP(nat,nat,times_times(nat,K),Ma)=hAPP(nat,nat,times_times(nat,K),N)<->Ma=N)). % 32.58/32.45 all Ma N K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)))). % 32.58/32.45 all K Ma N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))<->K=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N))). % 32.58/32.45 all Ma N K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N)))). % 32.58/32.45 all Ma N K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)))). % 32.58/32.45 all U Ma N J_2 I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)),N)))). % 32.58/32.45 all U_1 M N_1 J_1 I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),I_1))->hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_1),U_1)),M)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_1),U_1)),N_1))=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_1),J_1)),U_1)),M)),N_1)). % 32.58/32.45 all U Ma N J_2 I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))-> (hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)<->hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)=N)). % 32.58/32.45 all U Ma N I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N))))). % 32.58/32.45 all U_1 M N_1 I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))->hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_1),U_1)),M)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_1),U_1)),N_1))=hAPP(nat,nat,minus_minus(nat,M),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_1),I_1)),U_1)),N_1))). % 32.58/32.45 all U Ma N I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))-> (hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)<->Ma=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N))). % 32.58/32.45 all U Ma N J_2 I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)),N)))). % 32.58/32.45 all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,N_1)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit0(N_1))))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit1(N_1))))). % 32.58/32.45 all X_2 (hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,X_2))<-> (exists A_5 B_4 (twoSqu1929807760sum2sq(product_Pair(int,int,A_5,B_4))=ti(int,X_2)))). % 32.58/32.45 all P_5 P_2 X_2 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_2))-> (hBOOL(P_2)<->hBOOL(P_5)))-> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_2))->hBOOL(P_2))<-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_2))->hBOOL(P_5)))). % 32.58/32.45 all P_5 P_2 X_2 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_2))-> (hBOOL(P_2)<->hBOOL(P_5)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_2))&hBOOL(P_2)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_2))&hBOOL(P_5))). % 32.58/32.45 all Ma Ta K (ti(int,K)!=zero_zero(int)-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),Ta))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,times_times(int,K),Ma)),hAPP(int,int,times_times(int,K),Ta))))). % 32.58/32.45 all X_a (dvd(X_a)&semiring_0(X_a)-> (all P_2 L ((exists X hBOOL(hAPP(X_a,bool,P_2,hAPP(X_a,X_a,times_times(X_a,L),X))))<-> (exists X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L),hAPP(X_a,X_a,plus_plus(X_a,X),zero_zero(X_a))))&hBOOL(hAPP(X_a,bool,P_2,X))))))). % 32.58/32.45 all X_a (comm_ring(X_a)&dvd(X_a)-> (all Ta D D_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),D_3))-> (all X K_2 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X),Ta)))<-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,X),hAPP(X_a,X_a,times_times(X_a,K_2),D_3))),Ta)))))))). % 32.58/32.45 all X_a (comm_ring(X_a)&dvd(X_a)-> (all Ta D D_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),D_3))-> (all X K_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X),Ta)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,X),hAPP(X_a,X_a,times_times(X_a,K_2),D_3))),Ta)))))))). % 32.58/32.45 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,pls))). % 32.58/32.45 all K P_2 D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))-> ((all X (hBOOL(hAPP(int,bool,P_2,X))->hBOOL(hAPP(int,bool,P_2,hAPP(int,int,minus_minus(int,X),D)))))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))-> (all X (hBOOL(hAPP(int,bool,P_2,X))->hBOOL(hAPP(int,bool,P_2,hAPP(int,int,minus_minus(int,X),hAPP(int,int,times_times(int,K),D))))))))). % 32.58/32.45 all K P_2 D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))-> ((all X (hBOOL(hAPP(int,bool,P_2,X))->hBOOL(hAPP(int,bool,P_2,hAPP(int,int,plus_plus(int,X),D)))))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))-> (all X (hBOOL(hAPP(int,bool,P_2,X))->hBOOL(hAPP(int,bool,P_2,hAPP(int,int,plus_plus(int,X),hAPP(int,int,times_times(int,K),D))))))))). % 32.58/32.45 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))-> (exists P_4 (hBOOL(hAPP(int,bool,zprime,P_4))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),A_1))))). % 32.58/32.45 all A_1 M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))-> (exists X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M))&hBOOL(hAPP(int,bool,zcong(A_1,X),M))& (all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),M))&hBOOL(hAPP(int,bool,zcong(A_1,Y),M))->ti(int,Y)=ti(int,X)))))). % 32.58/32.45 all A_1 B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),hAPP(int,int,minus_minus(int,B),one_one(int))))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B))). % 32.58/32.45 all P_1 (hBOOL(hAPP(int,bool,zprime,P_1))->hBOOL(hAPP(int,bool,zcong(zfact(hAPP(int,int,minus_minus(int,P_1),one_one(int))),number_number_of(int,min)),P_1))). % 32.58/32.45 all N_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_1),zero_zero(int)))->zfact(N_1)=one_one(int))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_1),zero_zero(int)))->zfact(N_1)=hAPP(int,int,times_times(int,N_1),zfact(hAPP(int,int,minus_minus(int,N_1),one_one(int)))))). % 32.58/32.45 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))))))). % 32.58/32.45 all X_a (zero(X_a)-> (all X_2 (zero_zero(X_a)=ti(X_a,X_2)<->ti(X_a,X_2)=zero_zero(X_a)))). % 32.58/32.45 all X_a (ab_semigroup_mult(X_a)-> (all A_1 B C (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,times_times(X_a,B),C))))). % 32.58/32.45 all X_a (ab_semigroup_add(X_a)-> (all A_1 B C (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C))))). % 32.58/32.45 all X_a (cancel_semigroup_add(X_a)-> (all A_3 B_2 C_1 (hAPP(X_a,X_a,plus_plus(X_a,A_3),B_2)=hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)<->ti(X_a,B_2)=ti(X_a,C_1)))). % 32.58/32.45 all X_a (cancel_semigroup_add(X_a)-> (all B_2 A_3 C_1 (hAPP(X_a,X_a,plus_plus(X_a,B_2),A_3)=hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)<->ti(X_a,B_2)=ti(X_a,C_1)))). % 32.58/32.45 all X_a (cancel_semigroup_add(X_a)-> (all A_1 B C (hAPP(X_a,X_a,plus_plus(X_a,A_1),B)=hAPP(X_a,X_a,plus_plus(X_a,A_1),C)->ti(X_a,B)=ti(X_a,C)))). % 32.58/32.45 all X_a (cancel146912293up_add(X_a)-> (all A_1 B C (hAPP(X_a,X_a,plus_plus(X_a,A_1),B)=hAPP(X_a,X_a,plus_plus(X_a,A_1),C)->ti(X_a,B)=ti(X_a,C)))). % 32.58/32.45 all X_a (cancel_semigroup_add(X_a)-> (all B A_1 C (hAPP(X_a,X_a,plus_plus(X_a,B),A_1)=hAPP(X_a,X_a,plus_plus(X_a,C),A_1)->ti(X_a,B)=ti(X_a,C)))). % 32.58/32.45 all X_a (one(X_a)-> (all X_2 (one_one(X_a)=ti(X_a,X_2)<->ti(X_a,X_2)=one_one(X_a)))). % 32.58/32.45 all X_a (ab_group_add(X_a)-> (all A_3 B_2 C_1 D (hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)-> (ti(X_a,A_3)=ti(X_a,B_2)<->ti(X_a,C_1)=ti(X_a,D))))). % 32.58/32.45 all X_a (monoid_add(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1)))). % 32.58/32.45 all X_a (comm_monoid_add(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1)))). % 32.58/32.45 all X_a (linord219039673up_add(X_a)-> (all A_3 (zero_zero(X_a)=hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)<->ti(X_a,A_3)=zero_zero(X_a)))). % 32.58/32.45 all X_a (monoid_add(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1)))). % 32.58/32.45 all X_a (comm_monoid_add(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1)))). % 32.58/32.45 all X_a (ordere236663937imp_le(X_a)-> (all A_3 C_1 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B_2),C_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2))))). % 32.58/32.45 all X_a (ordere236663937imp_le(X_a)-> (all C_1 A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2))))). % 32.58/32.45 all X_a (ordere779506340up_add(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),C)))))). % 32.58/32.45 all X_a (ordere779506340up_add(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C),B)))))). % 32.58/32.45 all X_a (ordere779506340up_add(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))))))). % 32.58/32.45 all X_a (ordere236663937imp_le(X_a)-> (all A_1 C B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),C)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))))). % 32.58/32.45 all X_a (ordere236663937imp_le(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C),B)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))))). % 32.58/32.45 all X_a (ordere236663937imp_le(X_a)-> (all A_3 C_1 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B_2),C_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))))). % 32.58/32.45 all X_a (ordere236663937imp_le(X_a)-> (all C_1 A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))))). % 32.58/32.45 all X_a (ordere223160158up_add(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),C)))))). % 32.58/32.45 all X_a (ordere223160158up_add(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C),B)))))). % 32.58/32.45 all X_a (ordere223160158up_add(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))))))). % 32.58/32.45 all X_a (ordere236663937imp_le(X_a)-> (all A_1 C B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),C)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))). % 32.58/32.45 all X_a (ordere236663937imp_le(X_a)-> (all C A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C),B)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))). % 32.58/32.45 all X_a (group_add(X_a)-> (all A_3 B_2 (hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)=zero_zero(X_a)<->ti(X_a,A_3)=ti(X_a,B_2)))). % 32.58/32.45 all X_a (ab_group_add(X_a)-> (all A_3 B_2 (ti(X_a,A_3)=ti(X_a,B_2)<->hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)=zero_zero(X_a)))). % 32.58/32.45 all X_a (group_add(X_a)-> (all A_1 (hAPP(X_a,X_a,minus_minus(X_a,A_1),A_1)=zero_zero(X_a)))). % 32.58/32.45 all X_a (group_add(X_a)-> (all A_1 (hAPP(X_a,X_a,minus_minus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1)))). % 32.58/32.45 all X_a (ordered_ab_group_add(X_a)-> (all A_3 B_2 C_1 D (hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),D)))))). % 32.58/32.45 all X_a (ordered_ab_group_add(X_a)-> (all A_3 B_2 C_1 D (hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D)))))). % 32.58/32.45 all X_a (monoid_mult(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,one_one(X_a)),A_1)=ti(X_a,A_1)))). % 32.58/32.45 all X_a (comm_monoid_mult(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,one_one(X_a)),A_1)=ti(X_a,A_1)))). % 32.58/32.45 all X_a (monoid_mult(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,A_1),one_one(X_a))=ti(X_a,A_1)))). % 32.58/32.45 all X_a (comm_monoid_mult(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,A_1),one_one(X_a))=ti(X_a,A_1)))). % 32.58/32.45 all X_a (group_add(X_a)-> (all A_1 B (hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),B)=ti(X_a,A_1)))). % 32.58/32.45 all X_a (group_add(X_a)-> (all A_1 B (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),B)=ti(X_a,A_1)))). % 32.58/32.45 all X_a (linord219039673up_add(X_a)-> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))))). % 32.58/32.45 all X_a (linord219039673up_add(X_a)-> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a)))))). % 32.58/32.45 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))))))). % 32.58/32.45 all X_a (ordere216010020id_add(X_a)-> (all Y_2 X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_2))-> (hAPP(X_a,X_a,plus_plus(X_a,X_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)))))). % 32.58/32.45 all X_a (ordere216010020id_add(X_a)-> (all B C A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))))))). % 32.58/32.45 all X_a (ordere216010020id_add(X_a)-> (all B A_1 C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))))))). % 32.58/32.45 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))))))). % 32.58/32.45 all X_a (linord219039673up_add(X_a)-> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_3))))). % 32.58/32.45 all X_a (linord219039673up_add(X_a)-> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),zero_zero(X_a)))))). % 32.58/32.45 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))))))). % 32.58/32.45 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))))))). % 32.58/32.45 all X_a (ordere223160158up_add(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))))))). % 32.58/32.45 all X_a (ordere223160158up_add(X_a)-> (all C D_2 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))))))). % 32.58/32.45 all X_a (ordered_ab_group_add(X_a)-> (all A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),zero_zero(X_a)))))). % 32.58/32.45 all X_a (ordered_ab_group_add(X_a)-> (all A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),zero_zero(X_a)))))). % 32.58/32.45 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))))))). % 32.58/32.45 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))))))). % 32.58/32.45 all X_a (ordere216010020id_add(X_a)-> (all B C A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))))))). % 32.58/32.45 all X_a (ordere216010020id_add(X_a)-> (all B C A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))))))). % 32.58/32.45 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))))))). % 32.58/32.45 all A_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_1))->inv(P_1,inv(P_1,A_1))=ti(int,A_1))))). % 32.58/32.45 all J_1 A_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))-> (-hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_1))-> (-hBOOL(hAPP(int,bool,zcong(J_1,zero_zero(int)),P_1))-> (-hBOOL(hAPP(int,bool,quadRes(P_1),A_1))-> -hBOOL(hAPP(int,bool,zcong(J_1,hAPP(int,int,times_times(int,A_1),multInv(P_1,J_1))),P_1))))))). % 32.58/32.45 all J_1 K_1 A_1 P_1 (hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,J_1),K_1),A_1),P_1))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,multInv(P_1,J_1)),J_1)),K_1),hAPP(int,int,times_times(int,multInv(P_1,J_1)),A_1)),P_1))). % 32.58/32.45 all J_1 A_1 P_1 K_1 (hBOOL(hAPP(int,bool,zcong(J_1,hAPP(int,int,times_times(int,A_1),multInv(P_1,K_1))),P_1))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,J_1),K_1),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,A_1),multInv(P_1,K_1))),K_1)),P_1))). % 32.58/32.45 all A_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_1),one_one(int))))->ti(int,A_1)!=inv(P_1,A_1)))). % 32.58/32.45 all A_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_1),one_one(int))))->inv(P_1,A_1)!=one_one(int)))). % 32.58/32.45 all A_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_1),one_one(int))))->inv(P_1,A_1)!=hAPP(int,int,minus_minus(int,P_1),one_one(int))))). % 32.58/32.45 all A_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_1),one_one(int))))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),inv(P_1,A_1)))))). % 32.58/32.45 all A_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_1),one_one(int))))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),inv(P_1,A_1)),hAPP(int,int,minus_minus(int,P_1),one_one(int))))))). % 32.58/32.45 all X_1 Y_1 P_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))-> (hBOOL(hAPP(int,bool,zcong(X_1,Y_1),P_1))->hBOOL(hAPP(int,bool,zcong(multInv(P_1,X_1),multInv(P_1,Y_1)),P_1)))). % 32.58/32.45 all A_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_1),one_one(int))))->inv(P_1,A_1)!=zero_zero(int)))). % 32.58/32.45 all A_1 J_1 K_1 P_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))-> (hBOOL(hAPP(int,bool,zcong(J_1,K_1),P_1))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),multInv(P_1,J_1)),hAPP(int,int,times_times(int,A_1),multInv(P_1,K_1))),P_1)))). % 32.58/32.45 all Y_1 X_1 P_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))-> (hBOOL(hAPP(int,bool,zprime,P_1))-> (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))-> (-hBOOL(hAPP(int,bool,zcong(Y_1,zero_zero(int)),P_1))-> (hBOOL(hAPP(int,bool,zcong(multInv(P_1,X_1),multInv(P_1,Y_1)),P_1))->hBOOL(hAPP(int,bool,zcong(X_1,Y_1),P_1))))))). % 32.58/32.45 all X_1 P_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))-> (hBOOL(hAPP(int,bool,zprime,P_1))-> (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))->hBOOL(hAPP(int,bool,zcong(multInv(P_1,multInv(P_1,X_1)),X_1),P_1))))). % 32.58/32.45 all X_1 P_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))-> (hBOOL(hAPP(int,bool,zprime,P_1))-> (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))-> -hBOOL(hAPP(int,bool,zcong(multInv(P_1,X_1),zero_zero(int)),P_1))))). % 32.58/32.45 all A_1 P_1 (hBOOL(hAPP(int,bool,zprime,P_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_1))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),inv(P_1,A_1)),one_one(int)),P_1))))). % 32.58/32.45 all K_1 A_1 J_1 P_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))-> (hBOOL(hAPP(int,bool,zprime,P_1))-> (-hBOOL(hAPP(int,bool,zcong(J_1,zero_zero(int)),P_1))-> (hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,multInv(P_1,J_1)),J_1)),K_1),hAPP(int,int,times_times(int,multInv(P_1,J_1)),A_1)),P_1))->hBOOL(hAPP(int,bool,zcong(K_1,hAPP(int,int,times_times(int,A_1),multInv(P_1,J_1))),P_1)))))). % 32.58/32.45 all J_1 A_1 K_1 P_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))-> (hBOOL(hAPP(int,bool,zprime,P_1))-> (-hBOOL(hAPP(int,bool,zcong(K_1,zero_zero(int)),P_1))-> (hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,J_1),K_1),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,A_1),multInv(P_1,K_1))),K_1)),P_1))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,J_1),K_1),A_1),P_1)))))). % 32.58/32.45 all A_1 J_1 K_1 P_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))-> (hBOOL(hAPP(int,bool,zprime,P_1))-> (-hBOOL(hAPP(int,bool,zcong(K_1,zero_zero(int)),P_1))-> (-hBOOL(hAPP(int,bool,zcong(J_1,zero_zero(int)),P_1))-> (hBOOL(hAPP(int,bool,zcong(J_1,hAPP(int,int,times_times(int,A_1),multInv(P_1,K_1))),P_1))->hBOOL(hAPP(int,bool,zcong(K_1,hAPP(int,int,times_times(int,A_1),multInv(P_1,J_1))),P_1))))))). % 32.58/32.45 all J_1 K_1 A_1 P_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))-> (hBOOL(hAPP(int,bool,zprime,P_1))-> (-hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_1))-> (-hBOOL(hAPP(int,bool,zcong(K_1,zero_zero(int)),P_1))-> (-hBOOL(hAPP(int,bool,zcong(J_1,zero_zero(int)),P_1))-> (hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),multInv(P_1,J_1)),hAPP(int,int,times_times(int,A_1),multInv(P_1,K_1))),P_1))->hBOOL(hAPP(int,bool,zcong(J_1,K_1),P_1)))))))). % 32.58/32.45 all X_1 P_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))-> (hBOOL(hAPP(int,bool,zprime,P_1))-> (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,X_1),multInv(P_1,X_1))),multInv(P_1,multInv(P_1,X_1))),X_1),P_1))))). % 32.58/32.45 all X_1 P_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))-> (hBOOL(hAPP(int,bool,zprime,P_1))-> (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))->hBOOL(hAPP(int,bool,zcong(multInv(P_1,multInv(P_1,X_1)),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,X_1),multInv(P_1,X_1))),multInv(P_1,multInv(P_1,X_1)))),P_1))))). % 32.58/32.45 all X_1 P_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))-> (hBOOL(hAPP(int,bool,zprime,P_1))-> (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,multInv(P_1,X_1)),X_1),one_one(int)),P_1))))). % 32.58/32.45 all X_1 P_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))-> (hBOOL(hAPP(int,bool,zprime,P_1))-> (-hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,X_1),multInv(P_1,X_1)),one_one(int)),P_1))))). % 32.58/32.45 all B_2 A_3 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_3),one_one(int))))-> (hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_3)))->hBOOL(hAPP(fun(int,bool),bool,member(int,inv(P_3,B_2)),wset(A_3,P_3))))))). % 32.58/32.45 all B_2 A_3 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_3),one_one(int))))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_2),hAPP(int,int,minus_minus(int,P_3),one_one(int))))-> (hBOOL(hAPP(fun(int,bool),bool,member(int,inv(P_3,B_2)),wset(A_3,P_3)))->hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_3))))))))). % 32.58/32.45 all P_3 A_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_3))->hBOOL(hAPP(fun(int,bool),bool,member(int,A_3),wset(A_3,P_3)))). % 32.58/32.45 all B_2 P_3 A_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_3))-> (hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(hAPP(int,int,minus_minus(int,A_3),one_one(int)),P_3)))->hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_3))))). % 32.58/32.45 all B_2 A_3 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_3),one_one(int))))-> (hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_3)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_2),hAPP(int,int,minus_minus(int,P_3),one_one(int))))))). % 32.58/32.45 all B_2 A_3 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_3),one_one(int))))-> (hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_3)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2))))). % 32.58/32.45 all B_2 P_3 A_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_3))-> (-hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(hAPP(int,int,minus_minus(int,A_3),one_one(int)),P_3)))-> (hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_3)))->ti(int,B_2)=ti(int,A_3)|ti(int,B_2)=inv(P_3,A_3)))). % 32.58/32.45 all B_2 A_3 P_3 (hBOOL(hAPP(int,bool,zprime,P_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_3),one_one(int))))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),A_3))->hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_3))))))). % 32.58/32.45 all P_2 I_2 K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),K))-> (hBOOL(hAPP(int,bool,P_2,K))-> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I),K))-> (hBOOL(hAPP(int,bool,P_2,I))->hBOOL(hAPP(int,bool,P_2,hAPP(int,int,minus_minus(int,I),one_one(int)))))))->hBOOL(hAPP(int,bool,P_2,I_2))))). % 32.58/32.45 all P_2 I_2 K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),K))-> (hBOOL(hAPP(int,bool,P_2,hAPP(int,int,minus_minus(int,K),one_one(int))))-> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),K))-> (hBOOL(hAPP(int,bool,P_2,I))->hBOOL(hAPP(int,bool,P_2,hAPP(int,int,minus_minus(int,I),one_one(int)))))))->hBOOL(hAPP(int,bool,P_2,I_2))))). % 32.58/32.45 all X_2 P_2 ((all A_5 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_5))->hBOOL(hAPP(int,bool,P_2,hAPP(int,int,minus_minus(int,A_5),one_one(int)))))->hBOOL(hAPP(int,bool,P_2,A_5))))->hBOOL(hAPP(int,bool,P_2,X_2))). % 32.58/32.45 all P_2 K I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),I_2))-> (hBOOL(hAPP(int,bool,P_2,K))-> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),I))-> (hBOOL(hAPP(int,bool,P_2,I))->hBOOL(hAPP(int,bool,P_2,hAPP(int,int,plus_plus(int,I),one_one(int)))))))->hBOOL(hAPP(int,bool,P_2,I_2))))). % 32.58/32.45 all P_2 K I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_2))-> (hBOOL(hAPP(int,bool,P_2,hAPP(int,int,plus_plus(int,K),one_one(int))))-> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I))-> (hBOOL(hAPP(int,bool,P_2,I))->hBOOL(hAPP(int,bool,P_2,hAPP(int,int,plus_plus(int,I),one_one(int)))))))->hBOOL(hAPP(int,bool,P_2,I_2))))). % 32.58/32.45 all Ma K F_1 ((all M_2 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F_1,M_2)),hAPP(nat,nat,F_1,N_2)))))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,F_1,Ma)),K)),hAPP(nat,nat,F_1,hAPP(nat,nat,plus_plus(nat,Ma),K))))). % 32.58/32.45 all P_3 (hBOOL(hAPP(int,bool,zprime,P_3))->d22set(hAPP(int,int,minus_minus(int,P_3),number_number_of(int,bit0(bit1(pls)))))=wset(hAPP(int,int,minus_minus(int,P_3),number_number_of(int,bit0(bit1(pls)))),P_3)). % 32.58/32.45 all N P_2 (-hBOOL(hAPP(nat,bool,P_2,zero_zero(nat)))-> (hBOOL(hAPP(nat,bool,P_2,N))-> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),N))& (all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_2))-> -hBOOL(hAPP(nat,bool,P_2,I))))&hBOOL(hAPP(nat,bool,P_2,K_2)))))). % 32.58/32.45 all B_2 A_3 (hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),d22set(A_3)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),A_3))). % 32.58/32.45 all A_3 B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),B_2))-> -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),d22set(A_3)))). % 32.58/32.45 all B_2 A_3 (hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),d22set(A_3)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2))). % 32.58/32.45 all A_3 B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),A_3))->hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),d22set(A_3))))). % 32.58/32.45 all I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))-> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2))&hAPP(nat,nat,plus_plus(nat,I_1),K_2)=J_1))). % 32.58/32.45 all X_a (plus(X_a)&linorder(X_a)&dvd(X_a)-> (all D Sa exists Z all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X),Sa)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X),Sa))))))). % 32.58/32.45 all X_a (plus(X_a)&linorder(X_a)&dvd(X_a)-> (all D Sa exists Z all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X),Sa)))<-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X),Sa))))))). % 32.58/32.45 all X_a (plus(X_a)&linorder(X_a)&dvd(X_a)-> (all D Sa exists Z all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X),Sa)))<-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X),Sa))))))). % 32.58/32.45 all X_a (plus(X_a)&linorder(X_a)&dvd(X_a)-> (all D Sa exists Z all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X),Sa)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X),Sa))))))). % 32.58/32.45 all A_3 B_2 N (N!=zero_zero(nat)-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A_3),N)),hAPP(nat,int,power_power(int,B_2),N)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),B_2)))). % 32.58/32.45 all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_1))->A_1=zero_zero(nat)). % 32.58/32.45 all A_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_3))<->A_3=zero_zero(nat)). % 32.58/32.45 all A_3 (A_3!=zero_zero(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),zero_zero(nat)))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_3))). % 32.58/32.45 all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),zero_zero(nat))). % 32.58/32.45 all A_1 (-(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_1))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),zero_zero(nat))))). % 32.58/32.45 all A_1 (-(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),one_one(nat)))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_1)))). % 32.58/32.45 all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_1)). % 32.58/32.45 all A_3 (A_3!=one_one(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_3))& -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),one_one(nat)))). % 32.58/32.45 all A_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),one_one(nat)))<->A_3=one_one(nat)). % 32.58/32.45 all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),one_one(nat)))->A_1=one_one(nat)). % 32.58/32.45 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)))). % 32.58/32.45 all A_3 B_2 N (N!=zero_zero(nat)-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,A_3),N)),hAPP(nat,nat,power_power(nat,B_2),N)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),B_2)))). % 32.58/32.45 all A_1 N_1 B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A_1),N_1)),hAPP(nat,int,power_power(int,B),N_1)))-> (N_1!=zero_zero(nat)->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_1),B)))). % 32.58/32.45 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|N_1=zero_zero(nat)). % 32.58/32.45 all N_1 M K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))-> (hAPP(nat,nat,times_times(nat,K_1),N_1)=hAPP(nat,nat,times_times(nat,K_1),M)->N_1=M)). % 32.58/32.45 all X_a (real_normed_algebra(X_a)-> (all X_1 Y_1 A_1 B (hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Y_1)),hAPP(X_a,X_a,times_times(X_a,A_1),B))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),A_1)),hAPP(X_a,X_a,minus_minus(X_a,Y_1),B))),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),A_1)),B))),hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,minus_minus(X_a,Y_1),B)))))). % 32.58/32.45 all P_3 (sr(P_3)=collect(int,combs(int,bool,bool,combb(bool,fun(bool,bool),int,fconj,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int))),combc(int,int,bool,ord_less(int),P_3)))). % 32.58/32.45 all X_a (real_normed_algebra(X_a)-> (all X_1 (hAPP(X_a,X_a,times_times(X_a,X_1),zero_zero(X_a))=zero_zero(X_a)))). % 32.58/32.45 all X_a (real_normed_algebra(X_a)-> (all A_1 (hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a))=zero_zero(X_a)))). % 32.58/32.45 all X_a (real_normed_algebra(X_a)-> (all Y_1 (hAPP(X_a,X_a,times_times(X_a,zero_zero(X_a)),Y_1)=zero_zero(X_a)))). % 32.58/32.45 all X_a (real_normed_algebra(X_a)-> (all B (hAPP(X_a,X_a,times_times(X_a,zero_zero(X_a)),B)=zero_zero(X_a)))). % 32.58/32.45 all X_a (real_normed_algebra(X_a)-> (all X_1 Y_1 Ya (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,X_1),Y_1)),Ya)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Ya)),hAPP(X_a,X_a,times_times(X_a,Y_1),Ya))))). % 32.58/32.45 all X_a (real_normed_algebra(X_a)-> (all A_1 A_4 B (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),A_4)),B)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),hAPP(X_a,X_a,times_times(X_a,A_4),B))))). % 32.58/32.45 all X_a (real_normed_algebra(X_a)-> (all Xa X_1 Y_1 (hAPP(X_a,X_a,times_times(X_a,Xa),hAPP(X_a,X_a,plus_plus(X_a,X_1),Y_1))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,Xa),X_1)),hAPP(X_a,X_a,times_times(X_a,Xa),Y_1))))). % 32.58/32.45 all X_a (real_normed_algebra(X_a)-> (all A_1 B B_3 (hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),B_3))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),hAPP(X_a,X_a,times_times(X_a,A_1),B_3))))). % 32.58/32.45 all X_a (real_normed_algebra(X_a)-> (all A_1 B B_3 (hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,minus_minus(X_a,B),B_3))=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),hAPP(X_a,X_a,times_times(X_a,A_1),B_3))))). % 32.58/32.45 all X_a (real_normed_algebra(X_a)-> (all Xa X_1 Y_1 (hAPP(X_a,X_a,times_times(X_a,Xa),hAPP(X_a,X_a,minus_minus(X_a,X_1),Y_1))=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,Xa),X_1)),hAPP(X_a,X_a,times_times(X_a,Xa),Y_1))))). % 32.58/32.45 all X_a (real_normed_algebra(X_a)-> (all A_1 A_4 B (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),A_4)),B)=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),hAPP(X_a,X_a,times_times(X_a,A_4),B))))). % 32.58/32.45 all X_a (real_normed_algebra(X_a)-> (all X_1 Y_1 Ya (hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),Y_1)),Ya)=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Ya)),hAPP(X_a,X_a,times_times(X_a,Y_1),Ya))))). % 32.58/32.45 all B A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),zero_zero(int)))->hAPP(int,int,div_mod(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),B))),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),A_1))=hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,hAPP(int,int,plus_plus(int,B),one_one(int))),A_1))),one_one(int))). % 32.58/32.45 all V W ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,W)))->hAPP(int,int,div_mod(int,number_number_of(int,bit1(V))),number_number_of(int,bit0(W)))=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,number_number_of(int,V)),number_number_of(int,W)))),one_one(int)))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,W)))->hAPP(int,int,div_mod(int,number_number_of(int,bit1(V))),number_number_of(int,bit0(W)))=hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,hAPP(int,int,plus_plus(int,number_number_of(int,V)),one_one(int))),number_number_of(int,W)))),one_one(int)))). % 32.58/32.45 all X_2 Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),number_number_of(int,X_2)),number_number_of(int,Y_2)))<->hAPP(int,int,div_mod(int,number_number_of(int,Y_2)),number_number_of(int,X_2))=zero_zero(int)). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all B A_1 (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,B),A_1)),B)=zero_zero(X_a)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 B (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),B)=zero_zero(X_a)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 (hAPP(X_a,X_a,div_mod(X_a,A_1),one_one(X_a))=zero_zero(X_a)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 C B (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,times_times(X_a,C),B))),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,times_times(X_a,B),C))),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_3 B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2))<->hAPP(X_a,X_a,div_mod(X_a,B_2),A_3)=zero_zero(X_a)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))->hAPP(X_a,X_a,div_mod(X_a,B),A_1)=zero_zero(X_a)))). % 32.58/32.45 all A_1 B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,div_mod(int,A_1),B)))). % 32.58/32.45 all A_1 B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,div_mod(int,A_1),B)),B))). % 32.58/32.45 all Y_1 X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,div_mod(int,X_1),Y_1))))). % 32.58/32.45 all K_1 M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,div_mod(int,M),K_1)),M))). % 32.58/32.45 all Ma D (hAPP(int,int,div_mod(int,Ma),D)=zero_zero(int)<-> (exists Q_2 (ti(int,Ma)=hAPP(int,int,times_times(int,D),Q_2)))). % 32.58/32.45 all X_2 N Y_2 (hAPP(int,int,div_mod(int,X_2),N)=hAPP(int,int,div_mod(int,Y_2),N)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),hAPP(int,int,minus_minus(int,X_2),Y_2)))). % 32.58/32.45 all X_1 M Y_1 (hAPP(int,int,div_mod(int,X_1),M)=hAPP(int,int,div_mod(int,Y_1),M)->hBOOL(hAPP(int,bool,zcong(X_1,Y_1),M))). % 32.58/32.45 all X_1 M hBOOL(hAPP(int,bool,zcong(X_1,hAPP(int,int,div_mod(int,X_1),M)),M)). % 32.58/32.45 all A_3 B_2 Ma (hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))<->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,div_mod(int,A_3),Ma),hAPP(int,int,div_mod(int,B_2),Ma)),Ma))). % 32.58/32.45 all K_1 M N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),hAPP(int,int,div_mod(int,M),N_1)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),N_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),M)))). % 32.58/32.45 all N_1 F M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F),N_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F),hAPP(int,int,div_mod(int,M),N_1))))). % 32.58/32.45 all X_1 M Y_1 (hAPP(int,int,div_mod(int,hAPP(nat,int,power_power(int,hAPP(int,int,div_mod(int,X_1),M)),Y_1)),M)=hAPP(int,int,div_mod(int,hAPP(nat,int,power_power(int,X_1),Y_1)),M)). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 B (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),B)),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B)))). % 32.58/32.45 all A_1 B C (hAPP(int,int,div_mod(int,hAPP(int,int,times_times(int,A_1),B)),C)=hAPP(int,int,div_mod(int,hAPP(int,int,times_times(int,A_1),hAPP(int,int,div_mod(int,B),C))),C)). % 32.58/32.45 all A_1 B C (hAPP(int,int,div_mod(int,hAPP(int,int,times_times(int,A_1),hAPP(int,int,div_mod(int,B),C))),C)=hAPP(int,int,div_mod(int,hAPP(int,int,times_times(int,A_1),B)),C)). % 32.58/32.45 all A_1 (hAPP(int,int,div_mod(int,A_1),A_1)=zero_zero(int)). % 32.58/32.45 all B (hAPP(int,int,div_mod(int,zero_zero(int)),B)=zero_zero(int)). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all K_1 M N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),hAPP(X_a,X_a,div_mod(X_a,M),N_1)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),N_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),M)))))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all N_1 K_1 M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),M))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),N_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),hAPP(X_a,X_a,div_mod(X_a,M),N_1))))))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 C B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),B))->hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,A_1),C)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all Ma K N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),N))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),hAPP(X_a,X_a,div_mod(X_a,Ma),N)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),Ma)))))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 B (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all B A_1 (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,B),A_1)),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,div_mod(X_a,B),C))),C)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),hAPP(X_a,X_a,div_mod(X_a,B),C))),C)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,div_mod(X_a,B),C))),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 C B (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all B B_3 A_1 C A_4 (hAPP(X_a,X_a,div_mod(X_a,A_1),C)=hAPP(X_a,X_a,div_mod(X_a,A_4),C)-> (hAPP(X_a,X_a,div_mod(X_a,B),C)=hAPP(X_a,X_a,div_mod(X_a,B_3),C)->hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_4),B_3)),C))))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,div_mod(X_a,B),C))),C)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),hAPP(X_a,X_a,div_mod(X_a,B),C))),C)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all C A_1 B (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))=hAPP(X_a,X_a,times_times(X_a,C),hAPP(X_a,X_a,div_mod(X_a,A_1),B))))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 C B (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),B)),C)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 C B (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all B B_3 A_1 C A_4 (hAPP(X_a,X_a,div_mod(X_a,A_1),C)=hAPP(X_a,X_a,div_mod(X_a,A_4),C)-> (hAPP(X_a,X_a,div_mod(X_a,B),C)=hAPP(X_a,X_a,div_mod(X_a,B_3),C)->hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_4),B_3)),C))))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 (hAPP(X_a,X_a,div_mod(X_a,A_1),A_1)=zero_zero(X_a)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 (hAPP(X_a,X_a,div_mod(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1)))). % 32.58/32.45 all X_a (semiring_div(X_a)-> (all A_1 (hAPP(X_a,X_a,div_mod(X_a,zero_zero(X_a)),A_1)=zero_zero(X_a)))). % 32.58/32.45 all X_1 Y_1 M (hAPP(int,int,div_mod(int,hAPP(int,int,minus_minus(int,X_1),hAPP(int,int,div_mod(int,Y_1),M))),M)=hAPP(int,int,div_mod(int,hAPP(int,int,minus_minus(int,X_1),Y_1)),M)). % 32.58/32.45 all X_1 M Y_1 (hAPP(int,int,div_mod(int,hAPP(int,int,minus_minus(int,hAPP(int,int,div_mod(int,X_1),M)),Y_1)),M)=hAPP(int,int,div_mod(int,hAPP(int,int,minus_minus(int,X_1),Y_1)),M)). % 32.58/32.45 all X_a (ring_div(X_a)-> (all B B_3 A_1 C A_4 (hAPP(X_a,X_a,div_mod(X_a,A_1),C)=hAPP(X_a,X_a,div_mod(X_a,A_4),C)-> (hAPP(X_a,X_a,div_mod(X_a,B),C)=hAPP(X_a,X_a,div_mod(X_a,B_3),C)->hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_4),B_3)),C))))). % 32.58/32.45 all X_a (ring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),hAPP(X_a,X_a,div_mod(X_a,B),C))),C)))). % 32.58/32.45 all X_a (ring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C)))). % 32.58/32.45 all X_a (ring_div(X_a)-> (all A_1 B C (hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),hAPP(X_a,X_a,div_mod(X_a,B),C))),C)))). % 32.58/32.45 all X_a (semiring_div(X_a)&number(X_a)-> (all X_2 Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),number_number_of(X_a,X_2)),number_number_of(X_a,Y_2)))<->hAPP(X_a,X_a,div_mod(X_a,number_number_of(X_a,Y_2)),number_number_of(X_a,X_2))=zero_zero(X_a)))). % 32.58/32.45 all A_1 (hAPP(int,int,div_mod(int,A_1),number_number_of(int,min))=zero_zero(int)). % 32.58/32.45 all A_1 B M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),B))->hAPP(int,int,div_mod(int,hAPP(int,int,div_mod(int,A_1),B)),M)=hAPP(int,int,div_mod(int,A_1),M))). % 32.58/32.45 all A_3 B_2 Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))-> (hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))<->hAPP(int,int,div_mod(int,A_3),Ma)=hAPP(int,int,div_mod(int,B_2),Ma))). % 32.58/32.45 all A_1 B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,div_mod(int,A_1),B)))). % 32.58/32.45 all A_1 B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,div_mod(int,A_1),B)))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,div_mod(int,A_1),B)),B))). % 32.58/32.45 all B A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B))->hAPP(int,int,div_mod(int,A_1),B)=ti(int,A_1))). % 32.58/32.45 all A_1 B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,div_mod(int,A_1),B)),zero_zero(int)))). % 32.58/32.45 all A_1 B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,div_mod(int,A_1),B)),zero_zero(int)))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,div_mod(int,A_1),B)))). % 32.58/32.45 all B A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),zero_zero(int)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1))->hAPP(int,int,div_mod(int,A_1),B)=ti(int,A_1))). % 32.58/32.45 all B A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,A_1),B)),zero_zero(int)))->hAPP(int,int,div_mod(int,A_1),B)=hAPP(int,int,plus_plus(int,A_1),B))). % 32.58/32.45 all V W (hAPP(int,int,div_mod(int,number_number_of(int,bit0(V))),number_number_of(int,bit0(W)))=hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,number_number_of(int,V)),number_number_of(int,W)))). % 32.58/32.45 all P_2 N K (hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))<-> (ti(int,K)=zero_zero(int)->hBOOL(hAPP(int,bool,P_2,N)))& (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))-> (all I J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),J))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J),K))&ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),I)),J)->hBOOL(hAPP(int,bool,P_2,J)))))& (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int)))-> (all I J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),J))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),J),zero_zero(int)))&ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),I)),J)->hBOOL(hAPP(int,bool,P_2,J)))))). % 32.58/32.45 all Q_1 B R_1 C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),hAPP(int,int,div_mod(int,Q_1),C))),R_1)))))). % 32.58/32.45 all Q_1 B R_1 C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),hAPP(int,int,div_mod(int,Q_1),C))),R_1)),hAPP(int,int,times_times(int,B),C)))))). % 32.58/32.45 all Q_1 B R_1 C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_1),zero_zero(int)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,B),C)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),hAPP(int,int,div_mod(int,Q_1),C))),R_1)))))). % 32.58/32.45 all Q_1 B R_1 C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_1),zero_zero(int)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),hAPP(int,int,div_mod(int,Q_1),C))),R_1)),zero_zero(int)))))). % 32.58/32.45 all A_2 B_1 Q_3 Y_1 (ti(int,A_2)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_1),Q_3)),Y_1)-> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y_1))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_1),B_1)))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),Y_1))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Y_1),zero_zero(int))))-> (ti(int,B_1)!=zero_zero(int)->hAPP(int,int,div_mod(int,A_2),B_1)=ti(int,Y_1)))). % 32.58/32.45 all X_2 (hAPP(int,int,div_mod(int,X_2),number_number_of(int,bit0(bit1(pls))))!=zero_zero(int)<->hAPP(int,int,div_mod(int,X_2),number_number_of(int,bit0(bit1(pls))))=one_one(int)). % 32.58/32.45 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))->hAPP(int,int,div_mod(int,number_number_of(int,min)),B)=hAPP(int,int,minus_minus(int,B),one_one(int))). % 32.58/32.45 all B A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A_1))->hAPP(int,int,div_mod(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),B))),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),A_1))=hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,B),A_1)))). % 32.58/32.45 all M_1 D_1 (hAPP(int,int,div_mod(int,M_1),D_1)=zero_zero(int)-> (exists Q_2 (ti(int,M_1)=hAPP(int,int,times_times(int,D_1),Q_2)))). % 32.58/32.45 all X_1 Y_1 M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),M))->hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,standardRes(M,X_1)),standardRes(M,Y_1)),hAPP(int,int,times_times(int,X_1),Y_1)),M))). % 32.58/32.45 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,div_mod(nat,M),N_1)),N_1))). % 32.58/32.45 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,div_mod(nat,M),N_1)),N_1))). % 32.58/32.45 all Ma D (hAPP(nat,nat,div_mod(nat,Ma),D)=zero_zero(nat)<-> (exists Q_2 (Ma=hAPP(nat,nat,times_times(nat,D),Q_2)))). % 32.58/32.45 all M N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->hAPP(nat,nat,div_mod(nat,M),N_1)=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),N_1)). % 32.58/32.46 all M N_1 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->hAPP(nat,nat,div_mod(nat,M),N_1)=M)& (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->hAPP(nat,nat,div_mod(nat,M),N_1)=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),N_1))). % 32.58/32.46 all K_1 N_1 M (hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,K_1),N_1)),M)),N_1)=hAPP(nat,nat,div_mod(nat,M),N_1)). % 32.58/32.46 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hAPP(nat,nat,div_mod(nat,M),N_1)=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),N_1)). % 32.58/32.46 all M X_1 (standardRes(M,X_1)=hAPP(int,int,div_mod(int,X_1),M)). % 32.58/32.46 all M N_1 K_1 (hAPP(nat,nat,times_times(nat,hAPP(nat,nat,div_mod(nat,M),N_1)),K_1)=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,times_times(nat,M),K_1)),hAPP(nat,nat,times_times(nat,N_1),K_1))). % 32.58/32.46 all K_1 M N_1 (hAPP(nat,nat,times_times(nat,K_1),hAPP(nat,nat,div_mod(nat,M),N_1))=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,times_times(nat,K_1),M)),hAPP(nat,nat,times_times(nat,K_1),N_1))). % 32.58/32.46 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->hAPP(nat,nat,div_mod(nat,M),N_1)=M). % 32.58/32.46 all M N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,div_mod(nat,M),N_1)),M)). % 32.58/32.46 all Ma X_2 (standardRes(Ma,X_2)=zero_zero(int)<->hBOOL(hAPP(int,bool,zcong(X_2,zero_zero(int)),Ma))). % 32.58/32.46 all X_2 P_3 (-hBOOL(hAPP(int,bool,zcong(X_2,zero_zero(int)),P_3))<->standardRes(P_3,X_2)!=zero_zero(int)). % 32.58/32.46 all X_1 M hBOOL(hAPP(int,bool,zcong(X_1,standardRes(M,X_1)),M)). % 32.58/32.46 all X_1 P_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),standardRes(P_1,X_1)),P_1))). % 32.58/32.46 all X_2 P_3 (hBOOL(hAPP(fun(int,bool),bool,member(int,X_2),sr(P_3)))->standardRes(P_3,X_2)=ti(int,X_2)). % 32.58/32.46 all P_2 N K (hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,div_mod(nat,N),K)))<-> (K=zero_zero(nat)->hBOOL(hAPP(nat,bool,P_2,N)))& (K!=zero_zero(nat)-> (all I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K))-> (N=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,K),I)),J)->hBOOL(hAPP(nat,bool,P_2,J))))))). % 32.58/32.46 all Q_1 R_1 B C (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_1),B))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,B),hAPP(nat,nat,div_mod(nat,Q_1),C))),R_1)),hAPP(nat,nat,times_times(nat,B),C))))). % 32.58/32.46 all X_1 P_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),standardRes(P_1,X_1)))). % 32.58/32.46 all X1 X2 Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))-> (standardRes(Ma,X1)=standardRes(Ma,X2)<->hBOOL(hAPP(int,bool,zcong(X1,X2),Ma)))). % 32.58/32.46 all T_2 T_1 (order(T_1)->order(fun(T_2,T_1))). % 32.58/32.46 semiri456707255roduct(int). % 32.58/32.46 ordere223160158up_add(int). % 32.58/32.46 ordere236663937imp_le(int). % 32.58/32.46 linord893533164strict(int). % 32.58/32.46 linord626643107strict(int). % 32.58/32.46 linord20386208strict(int). % 32.58/32.46 ordere779506340up_add(int). % 32.58/32.46 ordere216010020id_add(int). % 32.58/32.46 linord219039673up_add(int). % 32.58/32.46 cancel146912293up_add(int). % 32.58/32.46 ring_11004092258visors(int). % 32.58/32.46 ordere453448008miring(int). % 32.58/32.46 linord581940658strict(int). % 32.58/32.46 ring_n68954251visors(int). % 32.58/32.46 ordere1490568538miring(int). % 32.58/32.46 linord1278240602ring_1(int). % 32.58/32.46 ordered_ab_group_add(int). % 32.58/32.46 cancel_semigroup_add(int). % 32.58/32.46 linordered_semiring(int). % 32.58/32.46 linordered_semidom(int). % 32.58/32.46 ab_semigroup_mult(int). % 32.58/32.46 comm_monoid_mult(int). % 32.58/32.46 ab_semigroup_add(int). % 32.58/32.46 ordered_semiring(int). % 32.58/32.46 no_zero_divisors(int). % 32.58/32.46 comm_monoid_add(int). % 32.58/32.46 linordered_ring(int). % 32.58/32.46 linordered_idom(int). % 32.58/32.46 comm_semiring_1(int). % 32.58/32.46 semiring_div(int). % 32.58/32.46 comm_semiring(int). % 32.58/32.46 number_semiring(int). % 32.58/32.46 ab_group_add(int). % 32.58/32.46 zero_ne_q_one(int). % 32.58/32.46 ordered_ring(int). % 32.58/32.46 linorder(int). % 32.58/32.46 monoid_mult(int). % 32.58/32.46 comm_ring_1(int). % 32.58/32.46 monoid_add(int). % 32.58/32.46 semiring_1(int). % 32.58/32.46 semiring_0(int). % 32.58/32.46 group_add(int). % 32.58/32.46 ring_div(int). % 32.58/32.46 mult_zero(int). % 32.58/32.46 comm_ring(int). % 32.58/32.46 order(int). % 32.58/32.46 ring_char_0(int). % 32.58/32.46 number_ring(int). % 32.58/32.46 semiring(int). % 32.58/32.46 ring_1(int). % 32.58/32.46 power(int). % 32.58/32.46 zero(int). % 32.58/32.46 plus(int). % 32.58/32.46 ring(int). % 32.58/32.46 idom(int). % 32.58/32.46 number(int). % 32.58/32.46 one(int). % 32.58/32.46 dvd(int). % 32.58/32.46 semiri456707255roduct(nat). % 32.58/32.46 ordere223160158up_add(nat). % 32.58/32.46 ordere236663937imp_le(nat). % 32.58/32.46 linord893533164strict(nat). % 32.58/32.46 linord20386208strict(nat). % 32.58/32.46 ordere779506340up_add(nat). % 32.58/32.46 ordere216010020id_add(nat). % 32.58/32.46 cancel146912293up_add(nat). % 32.58/32.46 ordere453448008miring(nat). % 32.58/32.46 ordere1490568538miring(nat). % 32.58/32.46 cancel_semigroup_add(nat). % 32.58/32.46 linordered_semiring(nat). % 32.58/32.46 linordered_semidom(nat). % 32.58/32.46 ab_semigroup_mult(nat). % 32.58/32.46 comm_monoid_mult(nat). % 32.58/32.46 ab_semigroup_add(nat). % 32.58/32.46 ordered_semiring(nat). % 32.58/32.46 no_zero_divisors(nat). % 32.58/32.46 comm_monoid_add(nat). % 32.58/32.46 comm_semiring_1(nat). % 32.58/32.46 semiring_div(nat). % 32.58/32.46 comm_semiring(nat). % 32.58/32.46 number_semiring(nat). % 32.58/32.46 zero_ne_q_one(nat). % 32.58/32.46 linorder(nat). % 32.58/32.46 monoid_mult(nat). % 32.58/32.46 monoid_add(nat). % 32.58/32.46 semiring_1(nat). % 32.58/32.46 semiring_0(nat). % 32.58/32.46 mult_zero(nat). % 32.58/32.46 order(nat). % 32.58/32.46 semiring(nat). % 32.58/32.46 power(nat). % 32.58/32.46 zero(nat). % 32.58/32.46 plus(nat). % 32.58/32.46 number(nat). % 32.58/32.46 one(nat). % 32.58/32.46 dvd(nat). % 32.58/32.46 order(bool). % 32.58/32.46 semiri456707255roduct(real). % 32.58/32.46 ordere223160158up_add(real). % 32.58/32.46 ordere236663937imp_le(real). % 32.58/32.46 linord893533164strict(real). % 32.58/32.46 linord626643107strict(real). % 32.58/32.46 linord20386208strict(real). % 32.58/32.46 ordere779506340up_add(real). % 32.58/32.46 real_normed_algebra(real). % 32.58/32.46 ordere216010020id_add(real). % 32.58/32.46 linord219039673up_add(real). % 32.58/32.46 cancel146912293up_add(real). % 32.58/32.46 ring_11004092258visors(real). % 32.58/32.46 ordere453448008miring(real). % 32.58/32.46 linord581940658strict(real). % 32.58/32.46 ring_n68954251visors(real). % 32.58/32.46 ordere1490568538miring(real). % 32.58/32.46 linord1278240602ring_1(real). % 32.58/32.46 ordered_ab_group_add(real). % 32.58/32.46 cancel_semigroup_add(real). % 32.58/32.46 linordered_semiring(real). % 32.58/32.46 linordered_semidom(real). % 32.58/32.46 ab_semigroup_mult(real). % 32.58/32.46 comm_monoid_mult(real). % 32.58/32.46 ab_semigroup_add(real). % 32.58/32.46 ordered_semiring(real). % 32.58/32.46 no_zero_divisors(real). % 32.58/32.46 comm_monoid_add(real). % 32.58/32.46 linordered_ring(real). % 32.58/32.46 linordered_idom(real). % 32.58/32.46 comm_semiring_1(real). % 32.58/32.46 comm_semiring(real). % 32.58/32.46 number_semiring(real). % 32.58/32.46 ab_group_add(real). % 32.58/32.46 zero_ne_q_one(real). % 32.58/32.46 ordered_ring(real). % 32.58/32.46 linorder(real). % 32.58/32.46 monoid_mult(real). % 32.58/32.46 comm_ring_1(real). % 32.58/32.46 monoid_add(real). % 32.58/32.46 semiring_1(real). % 32.58/32.46 semiring_0(real). % 32.58/32.46 group_add(real). % 32.58/32.46 mult_zero(real). % 32.58/32.46 comm_ring(real). % 32.58/32.46 order(real). % 32.58/32.46 ring_char_0(real). % 32.58/32.46 number_ring(real). % 32.58/32.46 semiring(real). % 32.58/32.46 ring_1(real). % 32.58/32.46 power(real). % 32.58/32.46 zero(real). % 32.58/32.46 plus(real). % 32.58/32.46 ring(real). % 32.58/32.46 idom(real). % 32.58/32.46 number(real). % 32.58/32.46 one(real). % 32.58/32.46 dvd(real). % 32.58/32.46 all T A (ti(T,ti(T,A))=ti(T,A)). % 32.58/32.46 all X_a X_c X_b P Q R (hAPP(X_a,X_c,combb(X_b,X_c,X_a,P,Q),R)=hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R))). % 32.58/32.46 all X_a X_c X_b P Q R (hAPP(X_a,X_c,combc(X_a,X_b,X_c,P,Q),R)=hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)). % 32.58/32.46 all X_a X_c X_b P Q R (hAPP(X_a,X_c,combs(X_a,X_b,X_c,P,Q),R)=hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R))). % 32.58/32.46 all Q P (-hBOOL(P)| -hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))). % 32.58/32.46 all P Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(P)). % 32.58/32.46 all P Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(Q)). % 32.58/32.46 -(exists X Y (hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,Y),number_number_of(nat,bit0(bit1(pls)))))=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.46 end_of_list. % 32.58/32.46 % 32.58/32.46 -------> usable clausifies to: % 32.58/32.46 % 32.58/32.46 list(usable). % 32.58/32.46 0 [] A=A. % 32.58/32.46 0 [] combb(X_b,X_c,X_a,ti(fun(X_b,X_c),B_1_1),B_2_1)=combb(X_b,X_c,X_a,B_1_1,B_2_1). % 32.58/32.46 0 [] combb(X_b,X_c,X_a,B_1_1,ti(fun(X_a,X_b),B_2_1))=combb(X_b,X_c,X_a,B_1_1,B_2_1). % 32.58/32.46 0 [] ti(fun(X_a,X_c),combb(X_b,X_c,X_a,B_1_1,B_2_1))=combb(X_b,X_c,X_a,B_1_1,B_2_1). % 32.58/32.46 0 [] combc(X_a,X_b,X_c,ti(fun(X_a,fun(X_b,X_c)),B_1_1),B_2_1)=combc(X_a,X_b,X_c,B_1_1,B_2_1). % 32.58/32.46 0 [] combc(X_a,X_b,X_c,B_1_1,ti(X_b,B_2_1))=combc(X_a,X_b,X_c,B_1_1,B_2_1). % 32.58/32.46 0 [] ti(fun(X_a,X_c),combc(X_a,X_b,X_c,B_1_1,B_2_1))=combc(X_a,X_b,X_c,B_1_1,B_2_1). % 32.58/32.46 0 [] combs(X_a,X_b,X_c,ti(fun(X_a,fun(X_b,X_c)),B_1_1),B_2_1)=combs(X_a,X_b,X_c,B_1_1,B_2_1). % 32.58/32.46 0 [] combs(X_a,X_b,X_c,B_1_1,ti(fun(X_a,X_b),B_2_1))=combs(X_a,X_b,X_c,B_1_1,B_2_1). % 32.58/32.46 0 [] ti(fun(X_a,X_c),combs(X_a,X_b,X_c,B_1_1,B_2_1))=combs(X_a,X_b,X_c,B_1_1,B_2_1). % 32.58/32.46 0 [] -semiring_div(X_a)|div_mod(X_a,ti(X_a,B_1_1))=div_mod(X_a,B_1_1). % 32.58/32.46 0 [] -semiring_div(X_a)|ti(fun(X_a,X_a),div_mod(X_a,B_1_1))=div_mod(X_a,B_1_1). % 32.58/32.46 0 [] -group_add(X_a)|minus_minus(X_a,ti(X_a,B_1_1))=minus_minus(X_a,B_1_1). % 32.58/32.46 0 [] -group_add(X_a)|ti(fun(X_a,X_a),minus_minus(X_a,B_1_1))=minus_minus(X_a,B_1_1). % 32.58/32.46 0 [] minus_minus(nat,ti(nat,B_1_1))=minus_minus(nat,B_1_1). % 32.58/32.46 0 [] ti(fun(nat,nat),minus_minus(nat,B_1_1))=minus_minus(nat,B_1_1). % 32.58/32.46 0 [] -one(X_a)|ti(X_a,one_one(X_a))=one_one(X_a). % 32.58/32.46 0 [] -plus(X_a)| -linorder(X_a)| -dvd(X_a)|plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1). % 32.58/32.46 0 [] -plus(X_a)| -linorder(X_a)| -dvd(X_a)|ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1). % 32.58/32.46 0 [] -monoid_add(X_a)|plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1). % 32.58/32.46 0 [] -monoid_add(X_a)|ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1). % 32.58/32.46 0 [] -cancel_semigroup_add(X_a)|plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1). % 32.58/32.46 0 [] -cancel_semigroup_add(X_a)|ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1). % 32.58/32.46 0 [] -ab_semigroup_add(X_a)|plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1). % 32.58/32.46 0 [] -ab_semigroup_add(X_a)|ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1). % 32.58/32.46 0 [] -ab_semigroup_mult(X_a)|times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1). % 32.58/32.46 0 [] -ab_semigroup_mult(X_a)|ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1). % 32.58/32.46 0 [] -power(X_a)|times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1). % 32.58/32.46 0 [] -power(X_a)|ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1). % 32.58/32.46 0 [] -dvd(X_a)|times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1). % 32.58/32.46 0 [] -dvd(X_a)|ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1). % 32.58/32.46 0 [] -semiring(X_a)|times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1). % 32.58/32.46 0 [] -semiring(X_a)|ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1). % 32.58/32.46 0 [] -mult_zero(X_a)|times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1). % 32.58/32.46 0 [] -mult_zero(X_a)|ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1). % 32.58/32.46 0 [] -no_zero_divisors(X_a)|times_times(X_a,ti(X_a,B_1_1))=times_times(X_a,B_1_1). % 32.58/32.46 0 [] -no_zero_divisors(X_a)|ti(fun(X_a,X_a),times_times(X_a,B_1_1))=times_times(X_a,B_1_1). % 32.58/32.46 0 [] -zero(X_a)|ti(X_a,zero_zero(X_a))=zero_zero(X_a). % 32.58/32.46 0 [] ti(X_a,undefined(X_a))=undefined(X_a). % 32.58/32.47 0 [] multInv(ti(int,B_1_1),B_2_1)=multInv(B_1_1,B_2_1). % 32.58/32.47 0 [] multInv(B_1_1,ti(int,B_2_1))=multInv(B_1_1,B_2_1). % 32.58/32.47 0 [] ti(int,multInv(B_1_1,B_2_1))=multInv(B_1_1,B_2_1). % 32.58/32.47 0 [] d22set(ti(int,B_1_1))=d22set(B_1_1). % 32.58/32.47 0 [] ti(fun(int,bool),d22set(B_1_1))=d22set(B_1_1). % 32.58/32.47 0 [] zfact(ti(int,B_1_1))=zfact(B_1_1). % 32.58/32.47 0 [] ti(int,zfact(B_1_1))=zfact(B_1_1). % 32.58/32.47 0 [] zcong(ti(int,B_1_1),B_2_1)=zcong(B_1_1,B_2_1). % 32.58/32.47 0 [] zcong(B_1_1,ti(int,B_2_1))=zcong(B_1_1,B_2_1). % 32.58/32.47 0 [] ti(fun(int,bool),zcong(B_1_1,B_2_1))=zcong(B_1_1,B_2_1). % 32.58/32.47 0 [] ti(fun(int,bool),zprime)=zprime. % 32.58/32.47 0 [] bit0(ti(int,B_1_1))=bit0(B_1_1). % 32.58/32.47 0 [] ti(int,bit0(B_1_1))=bit0(B_1_1). % 32.58/32.47 0 [] bit1(ti(int,B_1_1))=bit1(B_1_1). % 32.58/32.47 0 [] ti(int,bit1(B_1_1))=bit1(B_1_1). % 32.58/32.47 0 [] ti(int,min)=min. % 32.58/32.47 0 [] ti(int,pls)=pls. % 32.58/32.47 0 [] -number(X_a)|number_number_of(X_a,ti(int,B_1_1))=number_number_of(X_a,B_1_1). % 32.58/32.47 0 [] -number(X_a)|ti(X_a,number_number_of(X_a,B_1_1))=number_number_of(X_a,B_1_1). % 32.58/32.47 0 [] -order(X_a)|ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a). % 32.58/32.47 0 [] -order(X_a)|ti(fun(X_a,fun(X_a,bool)),ord_less_e_q(X_a))=ord_less_e_q(X_a). % 32.58/32.47 0 [] -power(X_a)|power_power(X_a,ti(X_a,B_1_1))=power_power(X_a,B_1_1). % 32.58/32.47 0 [] -power(X_a)|ti(fun(nat,X_a),power_power(X_a,B_1_1))=power_power(X_a,B_1_1). % 32.58/32.47 0 [] product_Pair(int,int,ti(int,B_1_1),B_2_1)=product_Pair(int,int,B_1_1,B_2_1). % 32.58/32.47 0 [] product_Pair(int,int,B_1_1,ti(int,B_2_1))=product_Pair(int,int,B_1_1,B_2_1). % 32.58/32.47 0 [] ti(product_prod(int,int),product_Pair(int,int,B_1_1,B_2_1))=product_Pair(int,int,B_1_1,B_2_1). % 32.58/32.47 0 [] legendre(ti(int,B_1_1),B_2_1)=legendre(B_1_1,B_2_1). % 32.58/32.47 0 [] legendre(B_1_1,ti(int,B_2_1))=legendre(B_1_1,B_2_1). % 32.58/32.47 0 [] ti(int,legendre(B_1_1,B_2_1))=legendre(B_1_1,B_2_1). % 32.58/32.47 0 [] quadRes(ti(int,B_1_1))=quadRes(B_1_1). % 32.58/32.47 0 [] ti(fun(int,bool),quadRes(B_1_1))=quadRes(B_1_1). % 32.58/32.47 0 [] sr(ti(int,B_1_1))=sr(B_1_1). % 32.58/32.47 0 [] ti(fun(int,bool),sr(B_1_1))=sr(B_1_1). % 32.58/32.47 0 [] standardRes(ti(int,B_1_1),B_2_1)=standardRes(B_1_1,B_2_1). % 32.58/32.47 0 [] standardRes(B_1_1,ti(int,B_2_1))=standardRes(B_1_1,B_2_1). % 32.58/32.47 0 [] ti(int,standardRes(B_1_1,B_2_1))=standardRes(B_1_1,B_2_1). % 32.58/32.47 0 [] -dvd(X_a)|ti(fun(X_a,fun(X_a,bool)),dvd_dvd(X_a))=dvd_dvd(X_a). % 32.58/32.47 0 [] collect(X_a,ti(fun(X_a,bool),B_1_1))=collect(X_a,B_1_1). % 32.58/32.47 0 [] ti(fun(X_a,bool),collect(X_a,B_1_1))=collect(X_a,B_1_1). % 32.58/32.47 0 [] ti(fun(int,bool),twoSqu658283162sum2sq)=twoSqu658283162sum2sq. % 32.58/32.47 0 [] twoSqu1929807760sum2sq(ti(product_prod(int,int),B_1_1))=twoSqu1929807760sum2sq(B_1_1). % 32.58/32.47 0 [] ti(int,twoSqu1929807760sum2sq(B_1_1))=twoSqu1929807760sum2sq(B_1_1). % 32.58/32.47 0 [] inv(ti(int,B_1_1),B_2_1)=inv(B_1_1,B_2_1). % 32.58/32.47 0 [] inv(B_1_1,ti(int,B_2_1))=inv(B_1_1,B_2_1). % 32.58/32.47 0 [] ti(int,inv(B_1_1,B_2_1))=inv(B_1_1,B_2_1). % 32.58/32.47 0 [] wset(ti(int,B_1_1),B_2_1)=wset(B_1_1,B_2_1). % 32.58/32.47 0 [] wset(B_1_1,ti(int,B_2_1))=wset(B_1_1,B_2_1). % 32.58/32.47 0 [] ti(fun(int,bool),wset(B_1_1,B_2_1))=wset(B_1_1,B_2_1). % 32.58/32.47 0 [] ti(fun(bool,fun(bool,bool)),fconj)=fconj. % 32.58/32.47 0 [] hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1)=hAPP(X_a,X_c,B_1_1,B_2_1). % 32.58/32.47 0 [] hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1))=hAPP(X_a,X_c,B_1_1,B_2_1). % 32.58/32.47 0 [] ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1))=hAPP(X_a,X_c,B_1_1,B_2_1). % 32.58/32.47 0 [] -hBOOL(ti(bool,B_1_1))|hBOOL(B_1_1). % 32.58/32.47 0 [] hBOOL(ti(bool,B_1_1))| -hBOOL(B_1_1). % 32.58/32.47 0 [] member(X_a,ti(X_a,B_1_1))=member(X_a,B_1_1). % 32.58/32.47 0 [] ti(fun(fun(X_a,bool),bool),member(X_a,B_1_1))=member(X_a,B_1_1). % 32.58/32.47 0 [] ti(int,m)=m. % 32.58/32.47 0 [] ti(int,s1)=s1. % 32.58/32.47 0 [] ti(int,s)=s. % 32.58/32.47 0 [] ti(int,t)=t. % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),t)). % 32.58/32.47 0 [] t!=one_one(int)|hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,$c2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,$c1),number_number_of(nat,bit0(bit1(pls)))))=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t))|hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,$c4),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,$c3),number_number_of(nat,bit0(bit1(pls)))))=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zprime,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.47 0 [] hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))=hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))). % 32.58/32.47 0 [] hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,A_1),B)),number_number_of(nat,bit0(bit1(pls))))=hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),A_1)),B))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls))))). % 32.58/32.47 0 [] hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,A_1),B)),number_number_of(nat,bit1(bit1(pls))))=hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit1(bit1(pls))))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit1(bit1(pls)))),hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))))),B))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit1(bit1(pls)))),A_1)),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls))))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit1(bit1(pls))))). % 32.58/32.47 0 [] -number_semiring(X_a)|hAPP(nat,X_a,power_power(X_a,hAPP(X_a,X_a,plus_plus(X_a,X_1),Y_1)),number_number_of(nat,bit0(bit1(pls))))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls)))),X_1)),Y_1)). % 32.58/32.47 0 [] -monoid_mult(X_b)| -number(X_b)|hAPP(nat,X_b,power_power(X_b,number_number_of(X_b,W)),number_number_of(nat,bit0(bit1(pls))))=hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,W)),number_number_of(X_b,W)). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,A_1),hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit1(bit1(pls)))). % 32.58/32.47 0 [] -semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls))))=one_one(X_a). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,X_1),X_1)=hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls)))). % 32.58/32.47 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls))))=hAPP(X_a,X_a,times_times(X_a,A_1),A_1). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,X_1),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1))=hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,X_1),N_1)),hAPP(nat,X_a,power_power(X_a,X_1),N_1)). % 32.58/32.47 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,W))=number_number_of(X_a,hAPP(int,int,plus_plus(int,bit1(pls)),W)). % 32.58/32.47 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),one_one(X_a))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V),bit1(pls))). % 32.58/32.47 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))=number_number_of(X_a,bit0(bit1(pls))). % 32.58/32.47 0 [] hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))=hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),$c5). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),W)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_2),W_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))|ti(int,Z_2)!=ti(int,W_1). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_2),W_1))|ti(int,Z_2)=ti(int,W_1). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1))|ti(int,X_1)=ti(int,Y_1)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_1),X_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),J_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),J_1),K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),K_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z_1))|ti(int,Z_1)=ti(int,W). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,X_1),P_1)),Q_1)=hAPP(nat,X_a,power_power(X_a,X_1),hAPP(nat,nat,times_times(nat,P_1),Q_1)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,X_1),one_one(nat))=ti(X_a,X_1). % 32.58/32.47 0 [] hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X_1),Y_1)),Z_1)=hAPP(nat,int,power_power(int,X_1),hAPP(nat,nat,times_times(nat,Y_1),Z_1)). % 32.58/32.47 0 [] -number(X_a)| -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,V_2)),number_number_of(X_a,W_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,W_1)),number_number_of(X_a,V_2))). % 32.58/32.47 0 [] -number(X_a)| -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,V_2)),number_number_of(X_a,W_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,W_1)),number_number_of(X_a,V_2))). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X_2)),number_number_of(X_a,Y_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Y_2)). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X_2)),number_number_of(X_a,Y_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Y_2)). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X_2)),number_number_of(X_a,Y_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_2),Y_2)). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X_2)),number_number_of(X_a,Y_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_2),Y_2)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),W))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_3),Z_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,W_2),Z_3)),hAPP(int,int,plus_plus(int,W),Z_1))). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,X_1),P_1)),hAPP(nat,X_a,power_power(X_a,X_1),Q_1))=hAPP(nat,X_a,power_power(X_a,X_1),hAPP(nat,nat,plus_plus(nat,P_1),Q_1)). % 32.58/32.47 0 [] hAPP(nat,int,power_power(int,X_1),hAPP(nat,nat,plus_plus(nat,Y_1),Z_1))=hAPP(int,int,times_times(int,hAPP(nat,int,power_power(int,X_1),Y_1)),hAPP(nat,int,power_power(int,X_1),Z_1)). % 32.58/32.47 0 [] hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),Z_1)=hAPP(nat,nat,plus_plus(nat,Z_1),Z_1). % 32.58/32.47 0 [] hAPP(nat,nat,times_times(nat,Z_1),number_number_of(nat,bit0(bit1(pls))))=hAPP(nat,nat,plus_plus(nat,Z_1),Z_1). % 32.58/32.47 0 [] hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))=number_number_of(nat,bit0(bit1(pls))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K1)),bit1(K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K1)),bit1(K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit1(L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit1(L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K1)),bit1(K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K1)),bit1(K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit1(L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit1(L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K1)),bit0(K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K1)),bit0(K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit0(L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit0(L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),pls)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K1)),bit0(K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K1)),bit0(K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit0(L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit0(L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,K)),number_number_of(int,L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,K)),number_number_of(int,L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,K)),number_number_of(int,L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,K)),number_number_of(int,L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,I_1),K_1)),hAPP(int,int,plus_plus(int,J_1),K_1))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),J_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,K_1),I_1)),hAPP(int,int,plus_plus(int,K_1),J_1))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=number_number_of(nat,V_1). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=number_number_of(nat,V). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=number_number_of(nat,hAPP(int,int,plus_plus(int,V),V_1)). % 32.58/32.47 0 [] number_number_of(nat,bit1(pls))=one_one(nat). % 32.58/32.47 0 [] one_one(nat)=number_number_of(nat,bit1(pls)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit1(K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit1(K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K1)),bit0(K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K1)),bit0(K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit0(L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),bit0(L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K1)),bit1(K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K1)),bit1(K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit1(L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),bit1(L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,W),one_one(int))),Z_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,W_1),one_one(int))),Z_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,W_1),one_one(int))),Z_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_2)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_2)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zprime,number_number_of(int,bit0(bit1(pls))))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,X_1))| -hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,Y_1))|hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,hAPP(int,int,times_times(int,X_1),Y_1))). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Rx)),hAPP(X_a,X_a,times_times(X_a,Ly),Ry)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,Rx),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),Ry)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,Lx),hAPP(X_a,X_a,times_times(X_a,Ly),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),Rx)=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Rx)),Ly). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Ly)),Rx)=hAPP(X_a,X_a,times_times(X_a,Lx),hAPP(X_a,X_a,times_times(X_a,Ly),Rx)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,Lx),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,Lx),Rx)),Ry). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,Lx),hAPP(X_a,X_a,times_times(X_a,Rx),Ry))=hAPP(X_a,X_a,times_times(X_a,Rx),hAPP(X_a,X_a,times_times(X_a,Lx),Ry)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),B)=hAPP(X_a,X_a,times_times(X_a,B),A_1). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),hAPP(X_a,X_a,plus_plus(X_a,C),D_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2)). % 32.58/32.47 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,member(X_a,X_2),A_6))|hBOOL(hAPP(X_a,bool,A_6,X_2)). % 32.58/32.47 0 [] hBOOL(hAPP(fun(X_a,bool),bool,member(X_a,X_2),A_6))| -hBOOL(hAPP(X_a,bool,A_6,X_2)). % 32.58/32.47 0 [] collect(X_a,P_2)=ti(fun(X_a,bool),P_2). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),B). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,C),D_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),D_2). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,C),D_2))=hAPP(X_a,X_a,plus_plus(X_a,C),hAPP(X_a,X_a,plus_plus(X_a,A_1),D_2)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),C)=hAPP(X_a,X_a,plus_plus(X_a,C),A_1). % 32.58/32.47 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). % 32.58/32.47 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). % 32.58/32.47 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). % 32.58/32.47 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). % 32.58/32.47 0 [] bit1(K)!=bit1(L)|ti(int,K)=ti(int,L). % 32.58/32.47 0 [] bit1(K)=bit1(L)|ti(int,K)!=ti(int,L). % 32.58/32.47 0 [] bit0(K)!=bit0(L)|ti(int,K)=ti(int,L). % 32.58/32.47 0 [] bit0(K)=bit0(L)|ti(int,K)!=ti(int,L). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,Z1),Z2)),Z3)=hAPP(int,int,times_times(int,Z1),hAPP(int,int,times_times(int,Z2),Z3)). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,Z_1),W)=hAPP(int,int,times_times(int,W),Z_1). % 32.58/32.47 0 [] number_number_of(int,K_1)=ti(int,K_1). % 32.58/32.47 0 [] hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,Z1),Z2)),Z3)=hAPP(int,int,plus_plus(int,Z1),hAPP(int,int,plus_plus(int,Z2),Z3)). % 32.58/32.47 0 [] hAPP(int,int,plus_plus(int,X_1),hAPP(int,int,plus_plus(int,Y_1),Z_1))=hAPP(int,int,plus_plus(int,Y_1),hAPP(int,int,plus_plus(int,X_1),Z_1)). % 32.58/32.47 0 [] hAPP(int,int,plus_plus(int,Z_1),W)=hAPP(int,int,plus_plus(int,W),Z_1). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K1)),bit0(K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K1)),bit0(K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit0(L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),bit0(L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit0(K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit0(K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit1(K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit1(K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K1)),bit1(K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K1)),bit1(K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit1(L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),bit1(L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),pls)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),pls)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit0(K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit0(K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))|ti(int,W_1)=ti(int,Z_2). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))|ti(int,W_1)!=ti(int,Z_2). % 32.58/32.47 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1))=hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N_1)),number_number_of(nat,bit0(bit1(pls)))). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X_2)),one_one(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),bit1(pls))). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X_2)),one_one(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),bit1(pls))). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),number_number_of(X_a,Y_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(pls)),Y_2)). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),number_number_of(X_a,Y_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(pls)),Y_2)). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X_2)),one_one(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_2),bit1(pls))). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X_2)),one_one(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_2),bit1(pls))). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),number_number_of(X_a,Y_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(pls)),Y_2)). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),number_number_of(X_a,Y_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(pls)),Y_2)). % 32.58/32.47 0 [] -semiri456707255roduct(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,W_1),Y_2)),hAPP(X_a,X_a,times_times(X_a,X_2),Z_2))!=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,W_1),Z_2)),hAPP(X_a,X_a,times_times(X_a,X_2),Y_2))|ti(X_a,W_1)=ti(X_a,X_2)|ti(X_a,Y_2)=ti(X_a,Z_2). % 32.58/32.47 0 [] -semiri456707255roduct(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,W_1),Y_2)),hAPP(X_a,X_a,times_times(X_a,X_2),Z_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,W_1),Z_2)),hAPP(X_a,X_a,times_times(X_a,X_2),Y_2))|ti(X_a,W_1)!=ti(X_a,X_2). % 32.58/32.47 0 [] -semiri456707255roduct(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,W_1),Y_2)),hAPP(X_a,X_a,times_times(X_a,X_2),Z_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,W_1),Z_2)),hAPP(X_a,X_a,times_times(X_a,X_2),Y_2))|ti(X_a,Y_2)!=ti(X_a,Z_2). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),M)),hAPP(X_a,X_a,times_times(X_a,B),M))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),M). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C)). % 32.58/32.47 0 [] -semiri456707255roduct(X_a)|ti(X_a,A_3)=ti(X_a,B_2)|ti(X_a,C_1)=ti(X_a,D)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),D))!=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),D)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)). % 32.58/32.47 0 [] -semiri456707255roduct(X_a)|ti(X_a,A_3)!=ti(X_a,B_2)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),D))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),D)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)). % 32.58/32.47 0 [] -semiri456707255roduct(X_a)|ti(X_a,C_1)!=ti(X_a,D)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),D))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),D)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,X_1),hAPP(X_a,X_a,plus_plus(X_a,Y_1),Z_1))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Y_1)),hAPP(X_a,X_a,times_times(X_a,X_1),Z_1)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),one_one(X_a))=ti(X_a,A_1). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,one_one(X_a)),A_1)=ti(X_a,A_1). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Y_1)),Q_1)=hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,X_1),Q_1)),hAPP(nat,X_a,power_power(X_a,Y_1),Q_1)). % 32.58/32.47 0 [] bit1(K_1)!=pls. % 32.58/32.47 0 [] pls!=bit1(L_1). % 32.58/32.47 0 [] bit1(K_1)!=bit0(L_1). % 32.58/32.47 0 [] bit0(K_1)!=bit1(L_1). % 32.58/32.47 0 [] bit0(K)!=pls|ti(int,K)=pls. % 32.58/32.47 0 [] bit0(K)=pls|ti(int,K)!=pls. % 32.58/32.47 0 [] pls!=bit0(L)|pls=ti(int,L). % 32.58/32.47 0 [] pls=bit0(L)|pls!=ti(int,L). % 32.58/32.47 0 [] bit0(pls)=pls. % 32.58/32.47 0 [] hAPP(int,int,times_times(int,pls),W)=pls. % 32.58/32.47 0 [] hAPP(int,int,times_times(int,bit0(K_1)),L_1)=bit0(hAPP(int,int,times_times(int,K_1),L_1)). % 32.58/32.47 0 [] hAPP(int,int,plus_plus(int,K_1),pls)=ti(int,K_1). % 32.58/32.47 0 [] hAPP(int,int,plus_plus(int,pls),K_1)=ti(int,K_1). % 32.58/32.47 0 [] hAPP(int,int,plus_plus(int,bit0(K_1)),bit0(L_1))=bit0(hAPP(int,int,plus_plus(int,K_1),L_1)). % 32.58/32.47 0 [] bit0(K_1)=hAPP(int,int,plus_plus(int,K_1),K_1). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,Z_1),one_one(int))=ti(int,Z_1). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,one_one(int)),Z_1)=ti(int,Z_1). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,number_number_of(int,V)),number_number_of(int,W))=number_number_of(int,hAPP(int,int,times_times(int,V),W)). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,Z1),Z2)),W)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,Z1),W)),hAPP(int,int,times_times(int,Z2),W)). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,W),hAPP(int,int,plus_plus(int,Z1),Z2))=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,W),Z1)),hAPP(int,int,times_times(int,W),Z2)). % 32.58/32.47 0 [] hAPP(int,int,plus_plus(int,number_number_of(int,V)),number_number_of(int,W))=number_number_of(int,hAPP(int,int,plus_plus(int,V),W)). % 32.58/32.47 0 [] -number_semiring(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))|hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,V)),number_number_of(X_a,V_1))=number_number_of(X_a,hAPP(int,int,times_times(int,V),V_1)). % 32.58/32.47 0 [] -number_semiring(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),number_number_of(X_a,V_1))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V),V_1)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_1),hAPP(nat,int,power_power(int,X_1),number_number_of(nat,bit0(bit1(pls)))))). % 32.58/32.47 0 [] -number(X_b)| -semiring(X_b)|hAPP(X_b,X_b,times_times(X_b,hAPP(X_b,X_b,plus_plus(X_b,A_1),B)),number_number_of(X_b,V))=hAPP(X_b,X_b,plus_plus(X_b,hAPP(X_b,X_b,times_times(X_b,A_1),number_number_of(X_b,V))),hAPP(X_b,X_b,times_times(X_b,B),number_number_of(X_b,V))). % 32.58/32.47 0 [] -number(X_b)| -semiring(X_b)|hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),hAPP(X_b,X_b,plus_plus(X_b,B),C))=hAPP(X_b,X_b,plus_plus(X_b,hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),B)),hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),C)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),M)),M)=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),one_one(X_a))),M). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,M),hAPP(X_a,X_a,times_times(X_a,A_1),M))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),one_one(X_a))),M). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,M),M)=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))),M). % 32.58/32.47 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,pls)),A_1)=ti(X_a,A_1). % 32.58/32.47 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),number_number_of(X_a,pls))=ti(X_a,A_1). % 32.58/32.47 0 [] -number_ring(X_a)|hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,V)),hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,W)),Z_1))=hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,hAPP(int,int,times_times(int,V),W))),Z_1). % 32.58/32.47 0 [] -number_ring(X_a)|hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,V)),number_number_of(X_a,W))=number_number_of(X_a,hAPP(int,int,times_times(int,V),W)). % 32.58/32.47 0 [] -number_ring(X_a)|number_number_of(X_a,hAPP(int,int,times_times(int,V),W))=hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,V)),number_number_of(X_a,W)). % 32.58/32.47 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,W)),Z_1))=hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,hAPP(int,int,plus_plus(int,V),W))),Z_1). % 32.58/32.47 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),number_number_of(X_a,W))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V),W)). % 32.58/32.47 0 [] -number_ring(X_a)|number_number_of(X_a,hAPP(int,int,plus_plus(int,V),W))=hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),number_number_of(X_a,W)). % 32.58/32.47 0 [] hAPP(int,int,plus_plus(int,bit1(K_1)),bit0(L_1))=bit1(hAPP(int,int,plus_plus(int,K_1),L_1)). % 32.58/32.47 0 [] hAPP(int,int,plus_plus(int,bit0(K_1)),bit1(L_1))=bit1(hAPP(int,int,plus_plus(int,K_1),L_1)). % 32.58/32.47 0 [] bit1(K_1)=hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),K_1)),K_1). % 32.58/32.47 0 [] -number_ring(X_a)|number_number_of(X_a,bit1(W))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,W))),number_number_of(X_a,W)). % 32.58/32.47 0 [] -number_ring(X_a)|hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit1(pls))),A_1)=ti(X_a,A_1). % 32.58/32.47 0 [] -number_ring(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),number_number_of(X_a,bit1(pls)))=ti(X_a,A_1). % 32.58/32.47 0 [] -number_semiring(X_a)|number_number_of(X_a,bit1(pls))=one_one(X_a). % 32.58/32.47 0 [] -number_ring(X_a)|number_number_of(X_a,bit1(pls))=one_one(X_a). % 32.58/32.47 0 [] -number_ring(X_a)|one_one(X_a)=number_number_of(X_a,bit1(pls)). % 32.58/32.47 0 [] one_one(int)=number_number_of(int,bit1(pls)). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,bit1(K_1)),L_1)=hAPP(int,int,plus_plus(int,bit0(hAPP(int,int,times_times(int,K_1),L_1))),L_1). % 32.58/32.47 0 [] -number_ring(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))),number_number_of(X_a,W))=number_number_of(X_a,bit0(W)). % 32.58/32.47 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit1(bit1(pls))))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),A_1)),A_1). % 32.58/32.47 0 [] hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X_1),number_number_of(nat,bit0(bit1(pls))))),number_number_of(nat,bit0(bit1(pls))))=hAPP(nat,int,power_power(int,X_1),number_number_of(nat,bit0(bit0(bit1(pls))))). % 32.58/32.47 0 [] -number_semiring(X_a)|hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls)))),Z_1)=hAPP(X_a,X_a,plus_plus(X_a,Z_1),Z_1). % 32.58/32.47 0 [] -number_ring(X_a)|hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls)))),Z_1)=hAPP(X_a,X_a,plus_plus(X_a,Z_1),Z_1). % 32.58/32.47 0 [] -number_semiring(X_a)|hAPP(X_a,X_a,times_times(X_a,Z_1),number_number_of(X_a,bit0(bit1(pls))))=hAPP(X_a,X_a,plus_plus(X_a,Z_1),Z_1). % 32.58/32.47 0 [] -number_ring(X_a)|hAPP(X_a,X_a,times_times(X_a,Z_1),number_number_of(X_a,bit0(bit1(pls))))=hAPP(X_a,X_a,plus_plus(X_a,Z_1),Z_1). % 32.58/32.47 0 [] -number_semiring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))=number_number_of(X_a,bit0(bit1(pls))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))|ti(int,P_1)=number_number_of(int,bit0(bit1(pls)))|ti(int,P_1)=number_number_of(int,bit1(bit1(pls)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),P_1)). % 32.58/32.47 0 [] twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))=hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t). % 32.58/32.47 0 [] hAPP(nat,real,power_power(real,hAPP(real,real,plus_plus(real,X_1),Y_1)),number_number_of(nat,bit0(bit1(pls))))=hAPP(real,real,plus_plus(real,hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,real,power_power(real,Y_1),number_number_of(nat,bit0(bit1(pls)))))),hAPP(real,real,times_times(real,hAPP(real,real,times_times(real,number_number_of(real,bit0(bit1(pls)))),X_1)),Y_1)). % 32.58/32.47 0 [] hAPP(real,real,times_times(real,number_number_of(real,bit0(bit0(bit1(pls))))),hAPP(nat,real,power_power(real,X_1),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,real,power_power(real,hAPP(real,real,times_times(real,number_number_of(real,bit0(bit1(pls)))),X_1)),number_number_of(nat,bit0(bit1(pls)))). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,B_2),X_2)),hAPP(nat,X_a,power_power(X_a,B_2),Y_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_2),Y_2)). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,B_2),X_2)),hAPP(nat,X_a,power_power(X_a,B_2),Y_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_2),Y_2)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,int,power_power(int,s1),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),s)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),s),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(s1,s),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$c6)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$c6),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(s1,$c6),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))| -hBOOL(hAPP(int,bool,zcong(s1,Y),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))|ti(int,Y)=ti(int,$c6). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$c7)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$c7),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(s1,$c7),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,s1),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.47 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_3),N)!=zero_zero(X_a)|ti(X_a,A_3)=zero_zero(X_a). % 32.58/32.47 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_3),N)!=zero_zero(X_a)|N!=zero_zero(nat). % 32.58/32.47 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_3),N)=zero_zero(X_a)|ti(X_a,A_3)!=zero_zero(X_a)|N=zero_zero(nat). % 32.58/32.47 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))). % 32.58/32.47 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,X_1),N_1)),hAPP(nat,X_a,power_power(X_a,Y_1),M))). % 32.58/32.47 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M)),B)). % 32.58/32.47 0 [] -linordered_semidom(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),N_1)!=hAPP(nat,X_a,power_power(X_a,B),N_1)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|ti(X_a,A_1)=ti(X_a,B). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M),N_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),M)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),N_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),M))|ti(int,M)=ti(int,N_1). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,times_times(int,K_1),M)),hAPP(int,int,times_times(int,K_1),N_1)))|ti(int,K_1)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N_1)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,power_power(X_a,X_1),N_1)),hAPP(nat,X_a,power_power(X_a,Y_1),N_1))). % 32.58/32.47 0 [] -ring_11004092258visors(X_a)|ti(X_a,A_1)=zero_zero(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),N_1)!=zero_zero(X_a). % 32.58/32.47 0 [] -power(X_a)| -semiring_0(X_a)|N_1!=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N_1)=one_one(X_a). % 32.58/32.47 0 [] -power(X_a)| -semiring_0(X_a)|N_1=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N_1)=zero_zero(X_a). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z_1),N_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),N_1)). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,B),N_1))). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,zero_zero(X_a)),A_1)=zero_zero(X_a). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a))=zero_zero(X_a). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1). % 32.58/32.47 0 [] -semiri456707255roduct(X_a)|ti(X_a,B_2)!=hAPP(X_a,X_a,plus_plus(X_a,B_2),A_3)|ti(X_a,A_3)=zero_zero(X_a). % 32.58/32.47 0 [] -semiri456707255roduct(X_a)|ti(X_a,B_2)=hAPP(X_a,X_a,plus_plus(X_a,B_2),A_3)|ti(X_a,A_3)!=zero_zero(X_a). % 32.58/32.47 0 [] -linord219039673up_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)!=zero_zero(X_a)|ti(X_a,A_3)=zero_zero(X_a). % 32.58/32.47 0 [] -linord219039673up_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)=zero_zero(X_a)|ti(X_a,A_3)!=zero_zero(X_a). % 32.58/32.47 0 [] pls=zero_zero(int). % 32.58/32.47 0 [] zero_zero(int)!=one_one(int). % 32.58/32.47 0 [] hAPP(int,int,plus_plus(int,zero_zero(int)),Z_1)=ti(int,Z_1). % 32.58/32.47 0 [] hAPP(int,int,plus_plus(int,Z_1),zero_zero(int))=ti(int,Z_1). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,B),N_1))). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X_1),Y_1),one_one(int)),P_1))|hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X_1),hAPP(nat,nat,times_times(nat,Y_1),Z_1)),one_one(int)),P_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,plus_plus(int,N),hAPP(int,int,times_times(int,K),Ma))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,plus_plus(int,N),hAPP(int,int,times_times(int,K),Ma))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),D))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),hAPP(int,int,plus_plus(int,X_2),Ta)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X_2),hAPP(int,int,times_times(int,C_1),D))),Ta))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),D))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),hAPP(int,int,plus_plus(int,X_2),Ta)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X_2),hAPP(int,int,times_times(int,C_1),D))),Ta))). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,B),N_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),N_3))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),one_one(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_3)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_3))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_3)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))). % 32.58/32.47 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),zero_zero(X_a))). % 32.58/32.47 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),zero_zero(X_a))). % 32.58/32.47 0 [] -linord581940658strict(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_2),X_2)),hAPP(X_a,X_a,times_times(X_a,Y_2),Y_2))!=zero_zero(X_a)|ti(X_a,X_2)=zero_zero(X_a). % 32.58/32.47 0 [] -linord581940658strict(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_2),X_2)),hAPP(X_a,X_a,times_times(X_a,Y_2),Y_2))!=zero_zero(X_a)|ti(X_a,Y_2)=zero_zero(X_a). % 32.58/32.47 0 [] -linord581940658strict(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_2),X_2)),hAPP(X_a,X_a,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). % 32.58/32.47 0 [] -semiri456707255roduct(X_a)|ti(X_a,R_1)=zero_zero(X_a)|ti(X_a,A_1)!=ti(X_a,B)|ti(X_a,C)=ti(X_a,D_2)|hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,times_times(X_a,R_1),C))!=hAPP(X_a,X_a,plus_plus(X_a,B),hAPP(X_a,X_a,times_times(X_a,R_1),D_2)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),hAPP(nat,int,power_power(int,A_1),N_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),A_1)). % 32.58/32.47 0 [] -number_ring(X_a)|zero_zero(X_a)=number_number_of(X_a,pls). % 32.58/32.47 0 [] -number_ring(X_a)|number_number_of(X_a,pls)=zero_zero(X_a). % 32.58/32.47 0 [] -number_semiring(X_a)|number_number_of(X_a,pls)=zero_zero(X_a). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(W_1)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(W_1)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(W_1)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(W_1)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int))). % 32.58/32.47 0 [] zero_zero(int)=number_number_of(int,pls). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,K_1),I_1)),hAPP(int,int,times_times(int,K_1),J_1))). % 32.58/32.47 0 [] hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_1)),Z_1)!=zero_zero(int). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(nat,X_a,power_power(X_a,A_1),N_1))),hAPP(nat,X_a,power_power(X_a,A_1),N_1))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_1),N_1)),hAPP(int,int,times_times(int,A_1),B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_1),N_1)),B)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_1),N_1)),hAPP(int,int,times_times(int,A_1),B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,P_1),N_1)),A_1)). % 32.58/32.47 0 [] -linordered_ring(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),X_1)),hAPP(X_a,X_a,times_times(X_a,Y_1),Y_1)))). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_2),X_2)),hAPP(X_a,X_a,times_times(X_a,Y_2),Y_2))),zero_zero(X_a)))|ti(X_a,X_2)=zero_zero(X_a). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_2),X_2)),hAPP(X_a,X_a,times_times(X_a,Y_2),Y_2))),zero_zero(X_a)))|ti(X_a,Y_2)=zero_zero(X_a). % 32.58/32.47 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_2),X_2)),hAPP(X_a,X_a,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). % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,V_2)),number_number_of(nat,V_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),V_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_3)). % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,V_2)),number_number_of(nat,V_3)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),V_3)). % 32.58/32.47 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,V_2)),number_number_of(nat,V_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),V_3)). % 32.58/32.47 0 [] -linordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),X_1)),hAPP(X_a,X_a,times_times(X_a,Y_1),Y_1))),zero_zero(X_a))). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_2),X_2)),hAPP(X_a,X_a,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). % 32.58/32.47 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_2),X_2)),hAPP(X_a,X_a,times_times(X_a,Y_2),Y_2))))|ti(X_a,X_2)=zero_zero(X_a). % 32.58/32.47 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_2),X_2)),hAPP(X_a,X_a,times_times(X_a,Y_2),Y_2))))|ti(X_a,Y_2)=zero_zero(X_a). % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,V_2)),number_number_of(nat,V_3)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_2),V_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_2),pls)). % 32.58/32.47 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,V_2)),number_number_of(nat,V_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_2),V_3)). % 32.58/32.47 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,V_2)),number_number_of(nat,V_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_2),pls)). % 32.58/32.47 0 [] -number_ring(X_a)|number_number_of(X_a,bit0(W))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),number_number_of(X_a,W))),number_number_of(X_a,W)). % 32.58/32.47 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),one_one(nat))=ti(X_a,A_1). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))|hAPP(int,int,times_times(int,Ma),N)!=one_one(int)|ti(int,Ma)=one_one(int). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))|hAPP(int,int,times_times(int,Ma),N)!=one_one(int)|ti(int,N)=one_one(int). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))|hAPP(int,int,times_times(int,Ma),N)=one_one(int)|ti(int,Ma)!=one_one(int)|ti(int,N)!=one_one(int). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_2)),Z_2)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_2)),Z_2)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int))). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),number_number_of(X_a,Y_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Y_2)). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),number_number_of(X_a,Y_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Y_2)). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X_2)),zero_zero(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),pls)). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,X_2)),zero_zero(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),pls)). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),number_number_of(X_a,Y_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),Y_2)). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),number_number_of(X_a,Y_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),Y_2)). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X_2)),zero_zero(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_2),pls)). % 32.58/32.47 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,X_2)),zero_zero(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_2),pls)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),Z_1))). % 32.58/32.47 0 [] -semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,bit0(bit1(pls))))=zero_zero(X_a). % 32.58/32.47 0 [] -ring_11004092258visors(X_a)|hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,bit0(bit1(pls))))!=zero_zero(X_a)|ti(X_a,A_3)=zero_zero(X_a). % 32.58/32.47 0 [] -ring_11004092258visors(X_a)|hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,bit0(bit1(pls))))=zero_zero(X_a)|ti(X_a,A_3)!=zero_zero(X_a). % 32.58/32.47 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls)))))). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y_1)). % 32.58/32.47 0 [] -linordered_semidom(X_a)|hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))!=hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_1))|ti(X_a,X_1)=ti(X_a,Y_1). % 32.58/32.47 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,bit0(bit1(pls))))),zero_zero(X_a))). % 32.58/32.47 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,bit0(bit1(pls))))))|ti(X_a,A_3)!=zero_zero(X_a). % 32.58/32.47 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,bit0(bit1(pls))))))|ti(X_a,A_3)=zero_zero(X_a). % 32.58/32.47 0 [] -linordered_idom(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,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). % 32.58/32.47 0 [] -linordered_idom(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,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). % 32.58/32.47 0 [] -linordered_idom(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,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). % 32.58/32.47 0 [] -monoid_mult(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N_1)),A_1)=hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(nat,X_a,power_power(X_a,A_1),N_1)). % 32.58/32.47 0 [] -comm_monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),N_1)=hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,B),N_1)). % 32.58/32.47 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,plus_plus(nat,M),N_1))=hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,A_1),M)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)). % 32.58/32.47 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,one_one(X_a)),N_1)=one_one(X_a). % 32.58/32.47 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,times_times(nat,M),N_1))=hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,power_power(X_a,A_1),M)),N_1). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)). % 32.58/32.47 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))))). % 32.58/32.47 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,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). % 32.58/32.47 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,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). % 32.58/32.47 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,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). % 32.58/32.47 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(X_a))). % 32.58/32.47 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,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). % 32.58/32.47 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_2),number_number_of(nat,bit0(bit1(pls)))))))|ti(X_a,X_2)=zero_zero(X_a). % 32.58/32.47 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_2),number_number_of(nat,bit0(bit1(pls)))))))|ti(X_a,Y_2)=zero_zero(X_a). % 32.58/32.47 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1)))). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),N_3))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,A_1),N_3))). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_3))|hAPP(nat,X_a,power_power(X_a,A_3),Ma)!=hAPP(nat,X_a,power_power(X_a,A_3),N)|Ma=N. % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_3))|hAPP(nat,X_a,power_power(X_a,A_3),Ma)=hAPP(nat,X_a,power_power(X_a,A_3),N)|Ma!=N. % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,B_2),X_2)),hAPP(nat,X_a,power_power(X_a,B_2),Y_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),Y_2)). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,B_2),X_2)),hAPP(nat,X_a,power_power(X_a,B_2),Y_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),Y_2)). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M)),hAPP(nat,X_a,power_power(X_a,A_1),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_3))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_1)),hAPP(nat,X_a,power_power(X_a,A_1),N_3))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))| -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,Y_1),number_number_of(nat,bit0(bit1(pls)))),X_1),P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),Y_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),number_number_of(int,bit0(bit1(pls)))))|ti(int,X_1)=zero_zero(int)|ti(int,X_1)=one_one(int). % 32.58/32.47 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),K_1))),zero_zero(X_a)))|ti(X_a,A_1)=zero_zero(X_a). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_3)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M_2),P_3))|ti(int,M_2)=one_one(int)|ti(int,M_2)=ti(int,P_3). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f1(P_3))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),$f1(P_3)),P_3)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_3))|ti(int,$f1(P_3))!=one_one(int). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_3))|ti(int,$f1(P_3))!=ti(int,P_3). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))|ti(int,A_1)!=hAPP(int,int,plus_plus(int,R_1),hAPP(int,int,times_times(int,A_1),Q_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),one_one(int))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))|ti(int,A_1)!=hAPP(int,int,plus_plus(int,R_1),hAPP(int,int,times_times(int,A_1),Q_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),A_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Q_1)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit0(bit1(pls))))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,$c8),number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))). % 32.58/32.47 0 [] legendre(number_number_of(int,min),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))=one_one(int). % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X_2),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_2))|N=zero_zero(nat). % 32.58/32.47 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X_2),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_2)). % 32.58/32.47 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X_2),N)))|N!=zero_zero(nat). % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X_2),N)))|N=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_2)). % 32.58/32.47 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X_2),N)))|N!=zero_zero(nat). % 32.58/32.47 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X_2),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_2)). % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X_2),number_number_of(nat,W_1))))|number_number_of(nat,W_1)=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_2)). % 32.58/32.47 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X_2),number_number_of(nat,W_1))))|number_number_of(nat,W_1)!=zero_zero(nat). % 32.58/32.47 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X_2),number_number_of(nat,W_1))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_2)). % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),I_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,I_1),M)),hAPP(nat,nat,power_power(nat,I_1),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)). % 32.58/32.47 0 [] bit1(K)!=min|ti(int,K)=min. % 32.58/32.47 0 [] bit1(K)=min|ti(int,K)!=min. % 32.58/32.47 0 [] min!=bit1(L)|min=ti(int,L). % 32.58/32.47 0 [] min=bit1(L)|min!=ti(int,L). % 32.58/32.47 0 [] bit1(min)=min. % 32.58/32.47 0 [] pls!=min. % 32.58/32.47 0 [] min!=pls. % 32.58/32.47 0 [] bit0(K_1)!=min. % 32.58/32.47 0 [] min!=bit0(L_1). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),min)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),min)). % 32.58/32.47 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,times_times(real,X_2),X_2)))|X_2=zero_zero(real). % 32.58/32.47 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,times_times(real,X_2),X_2)))|X_2!=zero_zero(real). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),min))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),min)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(K)),min))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),min)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit1(K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit1(K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),min)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),pls)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit0(K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit0(K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),zero_zero(int))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),min))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(K)),min))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit1(K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),K)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit1(K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),K)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),min)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),pls)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),min))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(K)),min))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min)). % 32.58/32.47 0 [] number_number_of(int,pls)!=number_number_of(int,min). % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,I_1),M)),hAPP(nat,nat,power_power(nat,I_1),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),I_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,X_1),zero_zero(nat))=one_one(X_a). % 32.58/32.47 0 [] -power(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),zero_zero(nat))=one_one(X_a). % 32.58/32.47 0 [] number_number_of(nat,pls)=zero_zero(nat). % 32.58/32.47 0 [] zero_zero(nat)=number_number_of(nat,pls). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit0(K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit0(K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),min))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(K)),min))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),min)). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,M),N_1)!=one_one(int)|ti(int,M)=one_one(int)|ti(int,M)=number_number_of(int,min). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,Ma),N)!=one_one(int)|ti(int,Ma)=one_one(int)|ti(int,Ma)=number_number_of(int,min). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,Ma),N)!=one_one(int)|ti(int,Ma)=one_one(int)|ti(int,N)=number_number_of(int,min). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,Ma),N)!=one_one(int)|ti(int,N)=one_one(int)|ti(int,Ma)=number_number_of(int,min). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,Ma),N)!=one_one(int)|ti(int,N)=one_one(int)|ti(int,N)=number_number_of(int,min). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,Ma),N)=one_one(int)|ti(int,Ma)!=one_one(int)|ti(int,N)!=one_one(int). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,Ma),N)=one_one(int)|ti(int,Ma)!=number_number_of(int,min)|ti(int,N)!=number_number_of(int,min). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N_1))). % 32.58/32.47 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),hAPP(nat,X_a,power_power(X_a,X_1),N_1))). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|ti(X_a,X_1)!=one_one(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),hAPP(nat,X_a,power_power(X_a,X_1),N_1))). % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,V_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_2)). % 32.58/32.47 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,V_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_2)). % 32.58/32.47 0 [] number_number_of(nat,V_2)!=zero_zero(nat)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_2),pls)). % 32.58/32.47 0 [] number_number_of(nat,V_2)=zero_zero(nat)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_2),pls)). % 32.58/32.47 0 [] zero_zero(nat)!=number_number_of(nat,V_2)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_2),pls)). % 32.58/32.47 0 [] zero_zero(nat)=number_number_of(nat,V_2)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_2),pls)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|hBOOL(hAPP(int,bool,zcong(B_2,A_3),Ma)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))| -hBOOL(hAPP(int,bool,zcong(B_2,A_3),Ma)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(K_1,K_1),M)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B),M))| -hBOOL(hAPP(int,bool,zcong(B,C),M))|hBOOL(hAPP(int,bool,zcong(A_1,C),M)). % 32.58/32.47 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,bit0(bit1(pls))))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,times_times(nat,number_number_of(nat,V)),hAPP(nat,nat,times_times(nat,number_number_of(nat,V_1)),K_1))=zero_zero(nat). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,times_times(nat,number_number_of(nat,V)),hAPP(nat,nat,times_times(nat,number_number_of(nat,V_1)),K_1))=hAPP(nat,nat,times_times(nat,number_number_of(nat,hAPP(int,int,times_times(int,V),V_1))),K_1). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,times_times(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=zero_zero(nat). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,times_times(nat,number_number_of(nat,V)),number_number_of(nat,V_1))=number_number_of(nat,hAPP(int,int,times_times(int,V),V_1)). % 32.58/32.47 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y_1))|ti(X_a,X_1)=ti(X_a,Y_1)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),zero_zero(int))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),A_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),zero_zero(int)))|ti(int,A_3)=ti(int,B_2). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(A_3,B_2),zero_zero(int)))|ti(int,A_3)!=ti(int,B_2). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(A_1,B),one_one(int))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B),M))| -hBOOL(hAPP(int,bool,zcong(C,D_2),M))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),C),hAPP(int,int,times_times(int,B),D_2)),M)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B),M))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,K_1),A_1),hAPP(int,int,times_times(int,K_1),B)),M)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B),M))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),K_1),hAPP(int,int,times_times(int,B),K_1)),M)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),M),hAPP(int,int,times_times(int,B),M)),M)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B),M))| -hBOOL(hAPP(int,bool,zcong(C,D_2),M))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,plus_plus(int,A_1),C),hAPP(int,int,plus_plus(int,B),D_2)),M)). % 32.58/32.47 0 [] -number_ring(X_a)|hAPP(nat,X_a,power_power(X_a,number_number_of(X_a,min)),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1))=one_one(X_a). % 32.58/32.47 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,W_1))!=zero_zero(X_a)|ti(X_a,A_3)=zero_zero(X_a). % 32.58/32.47 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,W_1))!=zero_zero(X_a)|number_number_of(nat,W_1)!=zero_zero(nat). % 32.58/32.47 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_3),number_number_of(nat,W_1))=zero_zero(X_a)|ti(X_a,A_3)!=zero_zero(X_a)|number_number_of(nat,W_1)=zero_zero(nat). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),one_one(int))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,times_times(int,X_1),Y_1))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,X_1),Y_1))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1))| -hBOOL(hAPP(int,bool,zcong(A_1,B),M)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,power_power(int,X_1),N_1))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|ti(int,B_2)=hAPP(int,int,plus_plus(int,A_3),hAPP(int,int,times_times(int,Ma),$f2(A_3,B_2,Ma))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|ti(int,B_2)!=hAPP(int,int,plus_plus(int,A_3),hAPP(int,int,times_times(int,Ma),K_2)). % 32.58/32.47 0 [] -power(X_a)| -semiring_0(X_a)|number_number_of(nat,W)!=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,W))=one_one(X_a). % 32.58/32.47 0 [] -power(X_a)| -semiring_0(X_a)|number_number_of(nat,W)=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,W))=zero_zero(X_a). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),M))| -hBOOL(hAPP(int,bool,zcong(A_1,B),M))|ti(int,A_1)=ti(int,B). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M))| -hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),M))|ti(int,A_1)=zero_zero(int). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit1(bit1(pls))))). % 32.58/32.47 0 [] hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_1)),R_1)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_3),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_4),Q_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_4)),R_3)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_1)),R_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_1),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q_4)). % 32.58/32.47 0 [] hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_1)),R_1)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_3),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q_4)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_4)),R_3)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),Q_1)),R_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_4),Q_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_4),zero_zero(int))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_3),Q_4)),R_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Q_4)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M))| -hBOOL(hAPP(int,bool,zprime,P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),hAPP(int,int,times_times(int,M),N_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),N_1)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,quadRes(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),number_number_of(int,min))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),M))| -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,number_number_of(int,min)),J_1),hAPP(nat,int,power_power(int,number_number_of(int,min)),K_1)),M))|hAPP(nat,int,power_power(int,number_number_of(int,min)),J_1)=hAPP(nat,int,power_power(int,number_number_of(int,min)),K_1). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))| -hBOOL(hAPP(int,bool,zcong(X_1,number_number_of(int,min)),P_1))| -hBOOL(hAPP(int,bool,zcong(X_1,one_one(int)),P_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),M))| -hBOOL(hAPP(int,bool,zcong(one_one(int),number_number_of(int,min)),M)). % 32.58/32.47 0 [] hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min))=hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,quadRes(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),number_number_of(int,min)))|legendre(number_number_of(int,min),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))!=one_one(int). % 32.58/32.47 0 [] hAPP(int,int,minus_minus(int,A_1),B)!=ti(int,C)|ti(int,A_1)=hAPP(int,int,plus_plus(int,C),B). % 32.58/32.47 0 [] -number_ring(X_a)|number_number_of(X_a,hAPP(int,int,minus_minus(int,V),W))=hAPP(X_a,X_a,minus_minus(X_a,number_number_of(X_a,V)),number_number_of(X_a,W)). % 32.58/32.47 0 [] hAPP(int,int,minus_minus(int,K_1),pls)=ti(int,K_1). % 32.58/32.47 0 [] hAPP(int,int,minus_minus(int,bit0(K_1)),bit0(L_1))=bit0(hAPP(int,int,minus_minus(int,K_1),L_1)). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,W),hAPP(int,int,minus_minus(int,Z1),Z2))=hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,W),Z1)),hAPP(int,int,times_times(int,W),Z2)). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,hAPP(int,int,minus_minus(int,Z1),Z2)),W)=hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,Z1),W)),hAPP(int,int,times_times(int,Z2),W)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B),M))| -hBOOL(hAPP(int,bool,zcong(C,D_2),M))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,minus_minus(int,A_1),C),hAPP(int,int,minus_minus(int,B),D_2)),M)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),hAPP(int,int,minus_minus(int,M),N_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),N_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),M)). % 32.58/32.47 0 [] -number(X_b)| -ring(X_b)|hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),hAPP(X_b,X_b,minus_minus(X_b,B),C))=hAPP(X_b,X_b,minus_minus(X_b,hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),B)),hAPP(X_b,X_b,times_times(X_b,number_number_of(X_b,V)),C)). % 32.58/32.47 0 [] -number(X_b)| -ring(X_b)|hAPP(X_b,X_b,times_times(X_b,hAPP(X_b,X_b,minus_minus(X_b,A_1),B)),number_number_of(X_b,V))=hAPP(X_b,X_b,minus_minus(X_b,hAPP(X_b,X_b,times_times(X_b,A_1),number_number_of(X_b,V))),hAPP(X_b,X_b,times_times(X_b,B),number_number_of(X_b,V))). % 32.58/32.47 0 [] hAPP(int,int,minus_minus(int,bit1(K_1)),bit0(L_1))=bit1(hAPP(int,int,minus_minus(int,K_1),L_1)). % 32.58/32.47 0 [] hAPP(int,int,minus_minus(int,bit1(K_1)),bit1(L_1))=bit0(hAPP(int,int,minus_minus(int,K_1),L_1)). % 32.58/32.47 0 [] hAPP(int,int,minus_minus(int,pls),bit0(L_1))=bit0(hAPP(int,int,minus_minus(int,pls),L_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,K),L)),zero_zero(int))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,K),L)),zero_zero(int))). % 32.58/32.47 0 [] hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,hAPP(int,int,minus_minus(int,A_1),hAPP(int,int,times_times(int,R_1),B))),M)),hAPP(int,int,times_times(int,hAPP(int,int,minus_minus(int,C),hAPP(int,int,times_times(int,R_1),D_2))),N_1))=hAPP(int,int,minus_minus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A_1),M)),hAPP(int,int,times_times(int,C),N_1))),hAPP(int,int,times_times(int,R_1),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),M)),hAPP(int,int,times_times(int,D_2),N_1)))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),hAPP(int,int,minus_minus(int,A_3),B_2))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),hAPP(int,int,minus_minus(int,A_3),B_2))). % 32.58/32.47 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V)),hAPP(X_a,X_a,minus_minus(X_a,number_number_of(X_a,W)),C))=hAPP(X_a,X_a,minus_minus(X_a,number_number_of(X_a,hAPP(int,int,plus_plus(int,V),W))),C). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),A_1))|ti(int,X_1)=hAPP(int,int,minus_minus(int,A_1),one_one(int))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),hAPP(int,int,minus_minus(int,A_1),one_one(int)))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),hAPP(int,int,minus_minus(int,Z_2),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),hAPP(int,int,minus_minus(int,Z_2),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)). % 32.58/32.47 0 [] hAPP(int,int,minus_minus(int,pls),bit1(L_1))=bit1(hAPP(int,int,minus_minus(int,min),L_1)). % 32.58/32.47 0 [] hAPP(int,int,minus_minus(int,min),bit0(L_1))=bit1(hAPP(int,int,minus_minus(int,min),L_1)). % 32.58/32.47 0 [] hAPP(int,int,minus_minus(int,min),bit1(L_1))=bit0(hAPP(int,int,minus_minus(int,min),L_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_3),hAPP(int,int,minus_minus(int,P_3),one_one(int))),one_one(int)),P_3))|hBOOL(hAPP(int,bool,zcong(A_3,hAPP(int,int,minus_minus(int,P_3),one_one(int))),P_3)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_3),hAPP(int,int,minus_minus(int,P_3),one_one(int))),one_one(int)),P_3))| -hBOOL(hAPP(int,bool,zcong(A_3,hAPP(int,int,minus_minus(int,P_3),one_one(int))),P_3)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B),M))|ti(int,B)!=ti(int,C)| -hBOOL(hAPP(int,bool,zcong(C,D_2),M))|hBOOL(hAPP(int,bool,zcong(A_1,D_2),M)). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,twoSqu1929807760sum2sq(product_Pair(int,int,A_1,B))),twoSqu1929807760sum2sq(product_Pair(int,int,P_1,Q_1)))=twoSqu1929807760sum2sq(product_Pair(int,int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A_1),P_1)),hAPP(int,int,times_times(int,B),Q_1)),hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,A_1),Q_1)),hAPP(int,int,times_times(int,B),P_1)))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),A_1),one_one(int)),P_1))|hBOOL(hAPP(int,bool,zcong(A_1,one_one(int)),P_1))|hBOOL(hAPP(int,bool,zcong(A_1,hAPP(int,int,minus_minus(int,P_1),one_one(int))),P_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_1))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),A_1),one_one(int)),P_1))|ti(int,A_1)=one_one(int)|ti(int,A_1)=hAPP(int,int,minus_minus(int,P_1),one_one(int)). % 32.58/32.47 0 [] hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,A_1),B)),hAPP(int,int,minus_minus(int,A_1),B))=hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls))))). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(M,zero_zero(int)),M)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))| -hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,A_3),D)),Ma))|hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,B_2),D)),Ma)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,A_3),D)),Ma))| -hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,B_2),D)),Ma)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))| -hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,D),A_3)),Ma))|hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,D),B_2)),Ma)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,D),A_3)),Ma))| -hBOOL(hAPP(int,bool,zcong(C_1,hAPP(int,int,times_times(int,D),B_2)),Ma)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,B),M))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,plus_plus(int,A_1),C),hAPP(int,int,plus_plus(int,B),C)),M)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(X_1,Y_1),M))|hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,X_1),Z_1),hAPP(nat,int,power_power(int,Y_1),Z_1)),M)). % 32.58/32.47 0 [] -number_ring(X_a)|hAPP(nat,X_a,power_power(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),Y_1)),number_number_of(nat,bit0(bit1(pls))))=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls)))))),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls)))),X_1)),Y_1)). % 32.58/32.47 0 [] hAPP(nat,int,power_power(int,hAPP(int,int,minus_minus(int,A_1),B)),number_number_of(nat,bit0(bit1(pls))))=hAPP(int,int,plus_plus(int,hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),A_1)),B))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls))))). % 32.58/32.47 0 [] hAPP(nat,int,power_power(int,hAPP(int,int,minus_minus(int,A_1),B)),number_number_of(nat,bit1(bit1(pls))))=hAPP(int,int,minus_minus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit1(bit1(pls))))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit1(bit1(pls)))),hAPP(nat,int,power_power(int,A_1),number_number_of(nat,bit0(bit1(pls)))))),B))),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,number_number_of(int,bit1(bit1(pls)))),A_1)),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit0(bit1(pls))))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,bit1(bit1(pls))))). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Y_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))| -hBOOL(hAPP(int,bool,zcong(X_1,Y_1),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_1),M))|ti(int,X_1)=ti(int,Y_1). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),M))| -hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),M)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),M),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_1),M)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(X_2,zero_zero(int)),P_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),X_2)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(X_2,zero_zero(int)),P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_3),X_2)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,zero_zero(int)),Ma))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),A_3)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(A_3,zero_zero(int)),Ma))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),A_3)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),hAPP(int,int,times_times(int,M),N_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),N_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),M))| -hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),M))|ti(int,X_1)=zero_zero(int). % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),Y_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),hAPP(nat,int,power_power(int,Y_1),N_1))). % 32.58/32.47 0 [] hAPP(nat,int,power_power(int,number_number_of(int,min)),N_1)=one_one(int)|hAPP(nat,int,power_power(int,number_number_of(int,min)),N_1)=number_number_of(int,min). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))|hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,zcong(Y_1,zero_zero(int)),P_1))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,X_1),Y_1),zero_zero(int)),P_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),B),zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,zcong(B,zero_zero(int)),P_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))|hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,zcong(B,zero_zero(int)),P_1))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),B),zero_zero(int)),P_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),hAPP(nat,int,power_power(int,Y_1),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_1),Y_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zprime,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),M)),one_one(int))))|legendre(number_number_of(int,min),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),M)),one_one(int)))=one_one(int). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_1))|legendre(A_1,P_1)=zero_zero(int). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_1))| -hBOOL(hAPP(int,bool,quadRes(P_1),A_1))|legendre(A_1,P_1)=one_one(int). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,quadRes(P_1),A_1))|legendre(A_1,P_1)=number_number_of(int,min). % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),M))|M=zero_zero(nat)|M=N_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),N_1)),M)). % 32.58/32.47 0 [] -hBOOL(hAPP(int,bool,quadRes(Ma),X_2))|hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,$f3(Ma,X_2)),number_number_of(nat,bit0(bit1(pls)))),X_2),Ma)). % 32.58/32.47 0 [] hBOOL(hAPP(int,bool,quadRes(Ma),X_2))| -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,Y),number_number_of(nat,bit0(bit1(pls)))),X_2),Ma)). % 32.58/32.47 0 [] hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X_2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,real,power_power(real,Y_2),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(real)|X_2=zero_zero(real). % 32.58/32.47 0 [] hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X_2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,real,power_power(real,Y_2),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(real)|Y_2=zero_zero(real). % 32.58/32.47 0 [] hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X_2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,real,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). % 32.58/32.47 0 [] -linord626643107strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),U_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),V))|hAPP(X_a,X_a,plus_plus(X_a,U_1),V)!=one_one(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,U_1),X_1)),hAPP(X_a,X_a,times_times(X_a,V),Y_1))),A_1)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),zero_zero(X_a))). % 32.58/32.47 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_2),Y_2))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,minus_minus(real,X_2),Y_2)),zero_zero(real))). % 32.58/32.47 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_2),Y_2))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,minus_minus(real,X_2),Y_2)),zero_zero(real))). % 32.58/32.47 0 [] -linordered_idom(X_a)|ti(X_a,X_1)=ti(X_a,Y_1)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),A_1)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)). % 32.58/32.47 0 [] zero_zero(real)!=one_one(real). % 32.58/32.47 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_2),Y_2))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_2))|X_2=Y_2. % 32.58/32.47 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_2),Y_2))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_2)). % 32.58/32.47 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_2),Y_2))|X_2!=Y_2. % 32.58/32.47 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_2))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_2),Y_2)). % 32.58/32.47 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_2))|X_2!=Y_2. % 32.58/32.47 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_2))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_2),Y_2))|X_2=Y_2. % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2))|X_2=Y_2. % 32.58/32.47 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))|X_2!=Y_2. % 32.58/32.47 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2))|X_2!=Y_2. % 32.58/32.47 0 [] hAPP(real,real,times_times(real,hAPP(real,real,times_times(real,Z1),Z2)),Z3)=hAPP(real,real,times_times(real,Z1),hAPP(real,real,times_times(real,Z2),Z3)). % 32.58/32.47 0 [] hAPP(real,real,times_times(real,Z_1),W)=hAPP(real,real,times_times(real,W),Z_1). % 32.58/32.47 0 [] hAPP(real,real,times_times(real,one_one(real)),Z_1)=Z_1. % 32.58/32.47 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),Y_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,plus_plus(real,Z_1),X_1)),hAPP(real,real,plus_plus(real,Z_1),Y_1))). % 32.58/32.47 0 [] -monoid_mult(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hAPP(X_a,X_a,times_times(X_a,hAPP(nat,X_a,power_power(X_a,X_1),hAPP(nat,nat,minus_minus(nat,N_1),one_one(nat)))),X_1)=hAPP(nat,X_a,power_power(X_a,X_1),N_1). % 32.58/32.47 0 [] M!=zero_zero(nat)|hAPP(nat,nat,times_times(nat,M),N_1)=zero_zero(nat). % 32.58/32.47 0 [] M=zero_zero(nat)|hAPP(nat,nat,times_times(nat,M),N_1)=hAPP(nat,nat,plus_plus(nat,N_1),hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,M),one_one(nat))),N_1)). % 32.58/32.47 0 [] M!=zero_zero(nat)|hAPP(nat,nat,power_power(nat,P_1),M)=one_one(nat). % 32.58/32.47 0 [] M=zero_zero(nat)|hAPP(nat,nat,power_power(nat,P_1),M)=hAPP(nat,nat,times_times(nat,P_1),hAPP(nat,nat,power_power(nat,P_1),hAPP(nat,nat,minus_minus(nat,M),one_one(nat)))). % 32.58/32.47 0 [] hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,power_power(nat,X_1),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,nat,power_power(nat,Y_1),number_number_of(nat,bit0(bit1(pls)))))=hAPP(nat,nat,times_times(nat,hAPP(nat,nat,plus_plus(nat,X_1),Y_1)),hAPP(nat,nat,minus_minus(nat,X_1),Y_1)). % 32.58/32.47 0 [] -no_zero_divisors(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),B)!=zero_zero(X_a)|ti(X_a,A_1)=zero_zero(X_a)|ti(X_a,B)=zero_zero(X_a). % 32.58/32.47 0 [] -no_zero_divisors(X_a)|ti(X_a,A_1)=zero_zero(X_a)|ti(X_a,B)=zero_zero(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),B)!=zero_zero(X_a). % 32.58/32.47 0 [] -ring_n68954251visors(X_a)|hAPP(X_a,X_a,times_times(X_a,A_3),B_2)!=zero_zero(X_a)|ti(X_a,A_3)=zero_zero(X_a)|ti(X_a,B_2)=zero_zero(X_a). % 32.58/32.47 0 [] -ring_n68954251visors(X_a)|hAPP(X_a,X_a,times_times(X_a,A_3),B_2)=zero_zero(X_a)|ti(X_a,A_3)!=zero_zero(X_a). % 32.58/32.47 0 [] -ring_n68954251visors(X_a)|hAPP(X_a,X_a,times_times(X_a,A_3),B_2)=zero_zero(X_a)|ti(X_a,B_2)!=zero_zero(X_a). % 32.58/32.47 0 [] -mult_zero(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a))=zero_zero(X_a). % 32.58/32.47 0 [] -mult_zero(X_a)|hAPP(X_a,X_a,times_times(X_a,zero_zero(X_a)),A_1)=zero_zero(X_a). % 32.58/32.47 0 [] -zero_ne_q_one(X_a)|zero_zero(X_a)!=one_one(X_a). % 32.58/32.47 0 [] -zero_ne_q_one(X_a)|one_one(X_a)!=zero_zero(X_a). % 32.58/32.47 0 [] -semiring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),E_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B),E_1)),C))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),E_1)),C). % 32.58/32.47 0 [] -comm_semiring(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),zero_zero(X_a)),A_1))|ti(X_a,A_1)=zero_zero(X_a). % 32.58/32.47 0 [] -ab_group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),hAPP(X_a,X_a,minus_minus(X_a,C),D_2)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),C)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)). % 32.58/32.47 0 [] -dvd(X_a)|A_1!=hAPP(X_a,X_a,times_times(X_a,B),K_1)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),A_1)). % 32.58/32.47 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),D_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))). % 32.58/32.47 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,times_times(X_a,B),C))). % 32.58/32.47 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,times_times(X_a,B),C))). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,times_times(X_a,B),A_1))). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,times_times(X_a,A_1),B))). % 32.58/32.47 0 [] -comm_semiring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C))). % 32.58/32.47 0 [] -comm_semiring_1(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),one_one(X_a)),A_1)). % 32.58/32.47 0 [] -comm_ring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Z_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),hAPP(X_a,X_a,minus_minus(X_a,Y_1),Z_1))). % 32.58/32.47 0 [] C_1=zero_zero(real)|hAPP(real,real,times_times(real,A_3),C_1)!=hAPP(real,real,times_times(real,B_2),C_1)|A_3=B_2. % 32.58/32.47 0 [] C_1=zero_zero(real)|hAPP(real,real,times_times(real,A_3),C_1)=hAPP(real,real,times_times(real,B_2),C_1)|A_3!=B_2. % 32.58/32.47 0 [] C_1=zero_zero(real)|hAPP(real,real,times_times(real,C_1),A_3)!=hAPP(real,real,times_times(real,C_1),B_2)|A_3=B_2. % 32.58/32.47 0 [] C_1=zero_zero(real)|hAPP(real,real,times_times(real,C_1),A_3)=hAPP(real,real,times_times(real,C_1),B_2)|A_3!=B_2. % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),A_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),hAPP(nat,nat,plus_plus(nat,A_1),B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),B)). % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,C),A_1)),hAPP(nat,nat,times_times(nat,C),B))). % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,A_1),C)),hAPP(nat,nat,times_times(nat,B),C))). % 32.58/32.47 0 [] hAPP(nat,nat,times_times(nat,N),Ma)!=one_one(nat)|N=one_one(nat). % 32.58/32.47 0 [] hAPP(nat,nat,times_times(nat,N),Ma)!=one_one(nat)|Ma=one_one(nat). % 32.58/32.47 0 [] hAPP(nat,nat,times_times(nat,N),Ma)=one_one(nat)|N!=one_one(nat)|Ma!=one_one(nat). % 32.58/32.47 0 [] hAPP(real,real,times_times(real,hAPP(real,real,plus_plus(real,Z1),Z2)),W)=hAPP(real,real,plus_plus(real,hAPP(real,real,times_times(real,Z1),W)),hAPP(real,real,times_times(real,Z2),W)). % 32.58/32.47 0 [] hAPP(nat,nat,power_power(nat,Ma),N)!=zero_zero(nat)|N!=zero_zero(nat). % 32.58/32.47 0 [] hAPP(nat,nat,power_power(nat,Ma),N)!=zero_zero(nat)|Ma=zero_zero(nat). % 32.58/32.47 0 [] hAPP(nat,nat,power_power(nat,Ma),N)=zero_zero(nat)|N=zero_zero(nat)|Ma!=zero_zero(nat). % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,X_1),N_1)),hAPP(nat,nat,power_power(nat,Y_1),N_1))). % 32.58/32.47 0 [] -ordere453448008miring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))). % 32.58/32.47 0 [] -ordere453448008miring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))). % 32.58/32.47 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))). % 32.58/32.47 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))). % 32.58/32.47 0 [] -ordered_semiring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))). % 32.58/32.47 0 [] -ordered_semiring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))). % 32.58/32.47 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))). % 32.58/32.47 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))). % 32.58/32.47 0 [] -ordere1490568538miring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))). % 32.58/32.47 0 [] -ordered_semiring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))). % 32.58/32.47 0 [] -ordered_semiring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))). % 32.58/32.47 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))). % 32.58/32.47 0 [] -ordere453448008miring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))). % 32.58/32.47 0 [] -ordere453448008miring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,B),A_1)),zero_zero(X_a))). % 32.58/32.47 0 [] -ordere453448008miring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))). % 32.58/32.47 0 [] -ordere453448008miring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a))). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_2)). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a))). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_2)). % 32.58/32.47 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),zero_zero(X_a))). % 32.58/32.47 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_2)). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a))). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),zero_zero(X_a))). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a))). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),zero_zero(X_a))). % 32.58/32.47 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B_2)). % 32.58/32.47 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_3),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),zero_zero(X_a))). % 32.58/32.47 0 [] -linordered_ring(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),A_1))). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))). % 32.58/32.47 0 [] -linord893533164strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))). % 32.58/32.47 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))). % 32.58/32.47 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))). % 32.58/32.47 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)). % 32.58/32.47 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,B),A_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)). % 32.58/32.47 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)). % 32.58/32.47 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,B),A_1)),zero_zero(X_a))). % 32.58/32.47 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),B)),zero_zero(X_a))). % 32.58/32.47 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,times_times(X_a,A_1),B))). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)). % 32.58/32.47 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)). % 32.58/32.47 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)). % 32.58/32.47 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)). % 32.58/32.47 0 [] -linord581940658strict(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)). % 32.58/32.47 0 [] -linordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),A_1)),zero_zero(X_a))). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))). % 32.58/32.47 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),one_one(X_a))). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),zero_zero(X_a))). % 32.58/32.47 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a))). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a))). % 32.58/32.47 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,times_times(X_a,M),N_1))). % 32.58/32.47 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,plus_plus(X_a,A_1),one_one(X_a)))). % 32.58/32.47 0 [] -idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|ti(X_a,C_1)=zero_zero(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2)). % 32.58/32.47 0 [] -idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|ti(X_a,C_1)!=zero_zero(X_a). % 32.58/32.47 0 [] -idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2)). % 32.58/32.47 0 [] -idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))|ti(X_a,C_1)=zero_zero(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2)). % 32.58/32.47 0 [] -idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))|ti(X_a,C_1)!=zero_zero(X_a). % 32.58/32.47 0 [] -idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,times_times(X_a,A_3),C_1)),hAPP(X_a,X_a,times_times(X_a,B_2),C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2)). % 32.58/32.47 0 [] -ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)!=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)=ti(X_a,D). % 32.58/32.47 0 [] -ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)!=ti(X_a,D). % 32.58/32.47 0 [] -ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)!=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)|ti(X_a,C_1)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D). % 32.58/32.47 0 [] -ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)|ti(X_a,C_1)!=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D). % 32.58/32.47 0 [] -ring(X_a)|hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Y_1)),hAPP(X_a,X_a,times_times(X_a,A_1),B))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),hAPP(X_a,X_a,minus_minus(X_a,Y_1),B))),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),A_1)),B)). % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))|B=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A_1),B)). % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))|K=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N)). % 32.58/32.47 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))|K!=zero_zero(nat). % 32.58/32.47 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N)). % 32.58/32.47 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,times_times(real,X_2),Z_2)),hAPP(real,real,times_times(real,Y_2),Z_2)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_2)). % 32.58/32.47 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,times_times(real,X_2),Z_2)),hAPP(real,real,times_times(real,Y_2),Z_2)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_2)). % 32.58/32.47 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,times_times(real,X_2),Z_2)),hAPP(real,real,times_times(real,Y_2),Z_2)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_2),Y_2)). % 32.58/32.47 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,times_times(real,X_2),Z_2)),hAPP(real,real,times_times(real,Y_2),Z_2)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_2),Y_2)). % 32.58/32.47 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,times_times(real,Z_2),X_2)),hAPP(real,real,times_times(real,Z_2),Y_2)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_2),Y_2)). % 32.58/32.47 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_2))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,times_times(real,Z_2),X_2)),hAPP(real,real,times_times(real,Z_2),Y_2)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_2),Y_2)). % 32.58/32.47 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,times_times(real,X_1),Y_1))). % 32.58/32.47 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,times_times(real,Z_1),X_1)),hAPP(real,real,times_times(real,Z_1),Y_1))). % 32.58/32.47 0 [] hAPP(real,real,plus_plus(real,hAPP(real,real,times_times(real,X_2),X_2)),hAPP(real,real,times_times(real,Y_2),Y_2))!=zero_zero(real)|X_2=zero_zero(real). % 32.58/32.47 0 [] hAPP(real,real,plus_plus(real,hAPP(real,real,times_times(real,X_2),X_2)),hAPP(real,real,times_times(real,Y_2),Y_2))!=zero_zero(real)|Y_2=zero_zero(real). % 32.58/32.47 0 [] hAPP(real,real,plus_plus(real,hAPP(real,real,times_times(real,X_2),X_2)),hAPP(real,real,times_times(real,Y_2),Y_2))=zero_zero(real)|X_2!=zero_zero(real)|Y_2!=zero_zero(real). % 32.58/32.47 0 [] N_1=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,X_1),N_1)),Y_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)). % 32.58/32.47 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,A_1),N_1)),hAPP(nat,nat,power_power(nat,B),N_1)))|N_1=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)). % 32.58/32.47 0 [] hAPP(nat,nat,power_power(nat,X_2),N)!=one_one(nat)|X_2=one_one(nat)|N=zero_zero(nat). % 32.58/32.47 0 [] hAPP(nat,nat,power_power(nat,X_2),N)=one_one(nat)|X_2!=one_one(nat). % 32.58/32.47 0 [] hAPP(nat,nat,power_power(nat,X_2),N)=one_one(nat)|N!=zero_zero(nat). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2)). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2)). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),A_3)). % 32.58/32.47 0 [] -linord581940658strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C_1),A_3)),hAPP(X_a,X_a,times_times(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_2),A_3)). % 32.58/32.47 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))). % 32.58/32.47 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))). % 32.58/32.47 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))). % 32.58/32.48 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),D_2))). % 32.58/32.48 0 [] -linordered_semiring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)). % 32.58/32.48 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)). % 32.58/32.48 0 [] -linordered_semiring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)). % 32.58/32.48 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)). % 32.58/32.48 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B)). % 32.58/32.48 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B)). % 32.58/32.48 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y_1),one_one(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,Y_1),X_1)),X_1)). % 32.58/32.48 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y_1),one_one(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,times_times(X_a,X_1),Y_1)),X_1)). % 32.58/32.48 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a)))). % 32.58/32.48 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)),D)). % 32.58/32.48 0 [] -ordered_ring(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)),D)). % 32.58/32.48 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D))). % 32.58/32.48 0 [] -ordered_ring(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D))). % 32.58/32.48 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)),D)). % 32.58/32.48 0 [] -ordered_ring(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),E)),C_1)),D)). % 32.58/32.48 0 [] -ordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D))). % 32.58/32.48 0 [] -ordered_ring(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_3),E)),C_1)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,B_2),E)),D)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,B_2),A_3)),E)),D))). % 32.58/32.48 0 [] -ring_1(X_a)|hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),X_1)),one_one(X_a))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,X_1),one_one(X_a))),hAPP(X_a,X_a,minus_minus(X_a,X_1),one_one(X_a))). % 32.58/32.48 0 [] -linord1278240602ring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y_1),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),U_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),V))|hAPP(X_a,X_a,plus_plus(X_a,U_1),V)!=one_one(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,U_1),X_1)),hAPP(X_a,X_a,times_times(X_a,V),Y_1))),A_1)). % 32.58/32.48 0 [] X_1!=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,Q_1),N_1)),R_1)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),R_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_1),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),X_1)). % 32.58/32.48 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),one_one(real)),hAPP(nat,real,power_power(real,number_number_of(real,bit0(bit1(pls)))),N_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),$f4(A_1,N_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))|hAPP(nat,real,power_power(real,$f4(A_1,N_1)),N_1)=A_1. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),$f5(A_1,N_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))|hAPP(nat,real,power_power(real,$f5(A_1,N_1)),N_1)=A_1. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y))|hAPP(nat,real,power_power(real,Y),N_1)!=A_1|Y=$f5(A_1,N_1). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,N),Ma)),Ma))|N=one_one(nat). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,N),Ma)),Ma))|N!=one_one(nat). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,Ma),N)),Ma))|N=one_one(nat). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,Ma),N)),Ma))|N!=one_one(nat). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N_1)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),X_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))). % 32.58/32.48 0 [] hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,minus_minus(nat,I_1),J_1)),K_1)=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,minus_minus(nat,I_1),K_1)),J_1). % 32.58/32.48 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),W)). % 32.58/32.48 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z_1),W))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),Z_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I_1),J_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),J_1),K_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I_1),K_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z_1),W))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W),Z_1))|Z_1=W. % 32.58/32.48 0 [] hAPP(nat,nat,minus_minus(nat,zero_zero(nat)),N_1)=zero_zero(nat). % 32.58/32.48 0 [] hAPP(nat,nat,minus_minus(nat,M),zero_zero(nat))=M. % 32.58/32.48 0 [] hAPP(nat,nat,minus_minus(nat,M),M)=zero_zero(nat). % 32.58/32.48 0 [] hAPP(nat,nat,minus_minus(nat,M),N_1)!=zero_zero(nat)|hAPP(nat,nat,minus_minus(nat,N_1),M)!=zero_zero(nat)|M=N_1. % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))|Ma=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),Ma))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_2,N),Ma)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3))|S!=T_3. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M))|M!=N_1. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1)). % 32.58/32.48 0 [] X_1=Y_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y_1),X_1)). % 32.58/32.48 0 [] Ma=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),Ma)). % 32.58/32.48 0 [] Ma!=N| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)). % 32.58/32.48 0 [] Ma!=N| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),Ma)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,L_1),N_1)),hAPP(nat,nat,minus_minus(nat,L_1),M))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,J_1),N_1)),K_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),Z_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),Y_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),Z_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),Y_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),Z_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),Z_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1))|B!=C|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1))|B!=C| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))|Y_1!=X_1. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))|X_1!=Y_1. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))|X_1!=Y_1. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),Z_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),Y_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),Z_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),Y_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X_1)). % 32.58/32.48 0 [] A_1!=B| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)). % 32.58/32.48 0 [] A_1!=B| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),Z_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))|X_1=Y_1. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),M))|M=N_1. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))|B!=C|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)). % 32.58/32.48 0 [] A_1!=B| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))|A_1=B| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1))|X_1=Y_1. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))|X_2=Y_2. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))|X_2!=Y_2. % 32.58/32.48 0 [] X_1!=Y_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)). % 32.58/32.48 0 [] A_1=B| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2))|X_2!=Y_2. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))|X_2=Y_2. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2))|X_2=Y_2. % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))|X_2!=Y_2. % 32.58/32.48 0 [] X_2!=Y_2|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2)). % 32.58/32.48 0 [] X_2!=Y_2|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2)). % 32.58/32.48 0 [] X_2=Y_2| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),M))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),hAPP(nat,nat,minus_minus(nat,M),N_1))). % 32.58/32.48 0 [] hAPP(nat,nat,plus_plus(nat,M),N_1)=hAPP(nat,nat,plus_plus(nat,N_1),M). % 32.58/32.48 0 [] hAPP(nat,nat,plus_plus(nat,X_1),hAPP(nat,nat,plus_plus(nat,Y_1),Z_1))=hAPP(nat,nat,plus_plus(nat,Y_1),hAPP(nat,nat,plus_plus(nat,X_1),Z_1)). % 32.58/32.48 0 [] hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,plus_plus(nat,M),N_1)),K_1)=hAPP(nat,nat,plus_plus(nat,M),hAPP(nat,nat,plus_plus(nat,N_1),K_1)). % 32.58/32.48 0 [] hAPP(nat,nat,plus_plus(nat,K),Ma)!=hAPP(nat,nat,plus_plus(nat,K),N)|Ma=N. % 32.58/32.48 0 [] hAPP(nat,nat,plus_plus(nat,K),Ma)=hAPP(nat,nat,plus_plus(nat,K),N)|Ma!=N. % 32.58/32.48 0 [] hAPP(nat,nat,plus_plus(nat,Ma),K)!=hAPP(nat,nat,plus_plus(nat,N),K)|Ma=N. % 32.58/32.48 0 [] hAPP(nat,nat,plus_plus(nat,Ma),K)=hAPP(nat,nat,plus_plus(nat,N),K)|Ma!=N. % 32.58/32.48 0 [] hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,M),N_1)),N_1)=M. % 32.58/32.48 0 [] hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,N_1),M)),N_1)=M. % 32.58/32.48 0 [] hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,minus_minus(nat,I_1),J_1)),K_1)=hAPP(nat,nat,minus_minus(nat,I_1),hAPP(nat,nat,plus_plus(nat,J_1),K_1)). % 32.58/32.48 0 [] hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,K_1),M)),hAPP(nat,nat,plus_plus(nat,K_1),N_1))=hAPP(nat,nat,minus_minus(nat,M),N_1). % 32.58/32.48 0 [] hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,M),K_1)),hAPP(nat,nat,plus_plus(nat,N_1),K_1))=hAPP(nat,nat,minus_minus(nat,M),N_1). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),N_1)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M)). % 32.58/32.48 0 [] M!=N_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),K_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|M=N_1. % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,M),N_1)),M)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,L_1),N_1)),hAPP(nat,nat,minus_minus(nat,L_1),M))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,M),L_1)),hAPP(nat,nat,minus_minus(nat,N_1),L_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),N_1))|hAPP(nat,nat,minus_minus(nat,N_1),hAPP(nat,nat,minus_minus(nat,N_1),I_1))=I_1. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))|hAPP(nat,nat,minus_minus(nat,Ma),K)!=hAPP(nat,nat,minus_minus(nat,N),K)|Ma=N. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))|hAPP(nat,nat,minus_minus(nat,Ma),K)=hAPP(nat,nat,minus_minus(nat,N),K)|Ma!=N. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))|hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,minus_minus(nat,M),K_1)),hAPP(nat,nat,minus_minus(nat,N_1),K_1))=hAPP(nat,nat,minus_minus(nat,M),N_1). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,Ma),K)),hAPP(nat,nat,minus_minus(nat,N),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,Ma),K)),hAPP(nat,nat,minus_minus(nat,N),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,hAPP(nat,nat,times_times(nat,M),N_1)),K_1)=hAPP(nat,nat,times_times(nat,M),hAPP(nat,nat,times_times(nat,N_1),K_1)). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,M),N_1)=hAPP(nat,nat,times_times(nat,N_1),M). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),K_1)=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,times_times(nat,M),K_1)),hAPP(nat,nat,times_times(nat,N_1),K_1)). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,K_1),hAPP(nat,nat,minus_minus(nat,M),N_1))=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,times_times(nat,K_1),M)),hAPP(nat,nat,times_times(nat,K_1),N_1)). % 32.58/32.48 0 [] N_1=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|N_1!=zero_zero(nat). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))). % 32.58/32.48 0 [] N=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)). % 32.58/32.48 0 [] N!=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,M),N_1)),M)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,minus_minus(nat,N),Ma)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,minus_minus(nat,N),Ma)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)). % 32.58/32.48 0 [] hAPP(nat,nat,plus_plus(nat,M),N_1)!=M|N_1=zero_zero(nat). % 32.58/32.48 0 [] hAPP(nat,nat,plus_plus(nat,Ma),N)!=zero_zero(nat)|Ma=zero_zero(nat). % 32.58/32.48 0 [] hAPP(nat,nat,plus_plus(nat,Ma),N)!=zero_zero(nat)|N=zero_zero(nat). % 32.58/32.48 0 [] hAPP(nat,nat,plus_plus(nat,Ma),N)=zero_zero(nat)|Ma!=zero_zero(nat)|N!=zero_zero(nat). % 32.58/32.48 0 [] hAPP(nat,nat,plus_plus(nat,M),zero_zero(nat))=M. % 32.58/32.48 0 [] hAPP(nat,nat,plus_plus(nat,zero_zero(nat)),N_1)=N_1. % 32.58/32.48 0 [] hAPP(nat,nat,minus_minus(nat,N_1),hAPP(nat,nat,plus_plus(nat,N_1),M))=zero_zero(nat). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),zero_zero(nat)))|N=zero_zero(nat). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),zero_zero(nat)))|N!=zero_zero(nat). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|hAPP(nat,nat,minus_minus(nat,M),N_1)=zero_zero(nat). % 32.58/32.48 0 [] hAPP(nat,nat,minus_minus(nat,Ma),N)!=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)). % 32.58/32.48 0 [] hAPP(nat,nat,minus_minus(nat,Ma),N)=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,zero_zero(nat)),N_1)=zero_zero(nat). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,M),zero_zero(nat))=zero_zero(nat). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,Ma),N)!=zero_zero(nat)|Ma=zero_zero(nat)|N=zero_zero(nat). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,Ma),N)=zero_zero(nat)|Ma!=zero_zero(nat). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,Ma),N)=zero_zero(nat)|N!=zero_zero(nat). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,K),Ma)!=hAPP(nat,nat,times_times(nat,K),N)|Ma=N|K=zero_zero(nat). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,K),Ma)=hAPP(nat,nat,times_times(nat,K),N)|Ma!=N. % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,K),Ma)=hAPP(nat,nat,times_times(nat,K),N)|K!=zero_zero(nat). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,Ma),K)!=hAPP(nat,nat,times_times(nat,N),K)|Ma=N|K=zero_zero(nat). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,Ma),K)=hAPP(nat,nat,times_times(nat,N),K)|Ma!=N. % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,Ma),K)=hAPP(nat,nat,times_times(nat,N),K)|K!=zero_zero(nat). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_1),J_1)),I_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,J_1),I_1)),I_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,K),Ma)),hAPP(nat,nat,plus_plus(nat,K),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,K),Ma)),hAPP(nat,nat,plus_plus(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,plus_plus(nat,J_1),M))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,plus_plus(nat,M),J_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_1),K_1)),hAPP(nat,nat,plus_plus(nat,J_1),K_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_1),K_1)),hAPP(nat,nat,plus_plus(nat,J_1),L_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_1))|hAPP(nat,nat,plus_plus(nat,M),L_1)!=hAPP(nat,nat,plus_plus(nat,K_1),N_1)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_1),J_1)),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K_1)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|hAPP(nat,nat,plus_plus(nat,N_1),hAPP(nat,nat,minus_minus(nat,M),N_1))=M. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,minus_minus(nat,J_2),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),J_2)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,minus_minus(nat,J_2),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),J_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))|Ma!=N. % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))|Ma=N. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N))|Ma=N. % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))|Ma!=N. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|M=N_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)). % 32.58/32.48 0 [] M!=N_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,Ma),K)),hAPP(nat,nat,minus_minus(nat,N),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,Ma),K)),hAPP(nat,nat,minus_minus(nat,N),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),A_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,minus_minus(nat,A_1),C)),hAPP(nat,nat,minus_minus(nat,B),C))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,plus_plus(nat,N),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),N)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,plus_plus(nat,N),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),hAPP(nat,nat,minus_minus(nat,M),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),M))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),hAPP(nat,nat,minus_minus(nat,M),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),M)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),hAPP(nat,nat,plus_plus(nat,M),N_1))). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),hAPP(nat,nat,plus_plus(nat,N_1),M))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))|N=hAPP(nat,nat,plus_plus(nat,Ma),$f6(Ma,N)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N))|N!=hAPP(nat,nat,plus_plus(nat,Ma),K_2). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,K),Ma)),hAPP(nat,nat,plus_plus(nat,K),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,K),Ma)),hAPP(nat,nat,plus_plus(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),hAPP(nat,nat,plus_plus(nat,J_1),M))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),hAPP(nat,nat,plus_plus(nat,M),J_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_1),K_1)),hAPP(nat,nat,plus_plus(nat,J_1),K_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_1),K_1)),hAPP(nat,nat,plus_plus(nat,J_1),L_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M),K_1)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M),K_1)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M),K_1)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M),K_1)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))|hAPP(nat,nat,minus_minus(nat,I_1),hAPP(nat,nat,minus_minus(nat,J_1),K_1))=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,I_1),K_1)),J_1). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,J_2),K)),I_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),hAPP(nat,nat,plus_plus(nat,I_2),K))). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,minus_minus(nat,J_2),K)),I_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),hAPP(nat,nat,plus_plus(nat,I_2),K))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,N_1),M)),K_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hAPP(nat,nat,plus_plus(nat,N_1),hAPP(nat,nat,minus_minus(nat,M),N_1))=M. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))|hAPP(nat,nat,plus_plus(nat,I_1),hAPP(nat,nat,minus_minus(nat,J_1),K_1))=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,I_1),J_1)),K_1). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),hAPP(nat,nat,minus_minus(nat,J_2),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),J_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),hAPP(nat,nat,minus_minus(nat,J_2),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),J_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),N_1)=M. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))|hAPP(nat,nat,minus_minus(nat,J_2),I_2)!=K|J_2=hAPP(nat,nat,plus_plus(nat,K),I_2). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))|hAPP(nat,nat,minus_minus(nat,J_2),I_2)=K|J_2!=hAPP(nat,nat,plus_plus(nat,K),I_2). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))|hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,I_1),J_1)),K_1)=hAPP(nat,nat,plus_plus(nat,I_1),hAPP(nat,nat,minus_minus(nat,J_1),K_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))|hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,minus_minus(nat,J_1),K_1)),I_1)=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,J_1),I_1)),K_1). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_1))|hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,J_1),I_1)),K_1)=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,minus_minus(nat,J_1),K_1)),I_1). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,hAPP(nat,nat,plus_plus(nat,M),N_1)),K_1)=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,M),K_1)),hAPP(nat,nat,times_times(nat,N_1),K_1)). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,K_1),hAPP(nat,nat,plus_plus(nat,M),N_1))=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,K_1),M)),hAPP(nat,nat,times_times(nat,K_1),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),one_one(nat)))|Ma=one_one(nat). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),one_one(nat)))|Ma!=one_one(nat). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,I_1),K_1)),hAPP(nat,nat,times_times(nat,J_1),L_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K_1),I_1)),hAPP(nat,nat,times_times(nat,K_1),J_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,I_1),K_1)),hAPP(nat,nat,times_times(nat,J_1),K_1))). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,times_times(nat,M),hAPP(nat,nat,times_times(nat,M),M)))). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,times_times(nat,M),M))). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,Ma),N)!=one_one(nat)|Ma=one_one(nat). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,Ma),N)!=one_one(nat)|N=one_one(nat). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,Ma),N)=one_one(nat)|Ma!=one_one(nat)|N!=one_one(nat). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,N_1),one_one(nat))=N_1. % 32.58/32.48 0 [] one_one(nat)!=hAPP(nat,nat,times_times(nat,Ma),N)|Ma=one_one(nat). % 32.58/32.48 0 [] one_one(nat)!=hAPP(nat,nat,times_times(nat,Ma),N)|N=one_one(nat). % 32.58/32.48 0 [] one_one(nat)=hAPP(nat,nat,times_times(nat,Ma),N)|Ma!=one_one(nat)|N!=one_one(nat). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,one_one(nat)),N_1)=N_1. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),M)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,Ma),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,Ma),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,Ma),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2))|hBOOL(hAPP(nat,bool,P_2,zero_zero(nat))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))|A_3!=hAPP(nat,nat,plus_plus(nat,B_2),D_4)|hBOOL(hAPP(nat,bool,P_2,D_4)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2))|A_3=hAPP(nat,nat,plus_plus(nat,B_2),$f7(P_2,A_3,B_2)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2))| -hBOOL(hAPP(nat,bool,P_2,$f7(P_2,A_3,B_2))). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))| -hBOOL(hAPP(nat,bool,P_2,zero_zero(nat)))|A_3=hAPP(nat,nat,plus_plus(nat,B_2),$f7(P_2,A_3,B_2)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))| -hBOOL(hAPP(nat,bool,P_2,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_2,$f7(P_2,A_3,B_2))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2))|hBOOL(hAPP(nat,bool,P_2,zero_zero(nat))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))|A_3!=hAPP(nat,nat,plus_plus(nat,B_2),D_4)|hBOOL(hAPP(nat,bool,P_2,D_4)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2))|A_3=hAPP(nat,nat,plus_plus(nat,B_2),$f8(P_2,A_3,B_2)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2))| -hBOOL(hAPP(nat,bool,P_2,$f8(P_2,A_3,B_2))). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))| -hBOOL(hAPP(nat,bool,P_2,zero_zero(nat)))|A_3=hAPP(nat,nat,plus_plus(nat,B_2),$f8(P_2,A_3,B_2)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,minus_minus(nat,A_3),B_2)))| -hBOOL(hAPP(nat,bool,P_2,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_2,$f8(P_2,A_3,B_2))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K_1),I_1)),hAPP(nat,nat,times_times(nat,K_1),J_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,I_1),K_1)),hAPP(nat,nat,times_times(nat,J_1),K_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,times_times(nat,Ma),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,times_times(nat,Ma),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,times_times(nat,Ma),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)). % 32.58/32.48 0 [] M!=hAPP(nat,nat,times_times(nat,M),N_1)|N_1=one_one(nat)|M=zero_zero(nat). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_1),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K_1),M)),hAPP(nat,nat,times_times(nat,K_1),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,Ma),K)),hAPP(nat,nat,times_times(nat,N),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)). % 32.58/32.48 0 [] -power(X_a)|N_1!=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,M),N_1)=one_one(X_a). % 32.58/32.48 0 [] -power(X_a)|N_1=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,M),N_1)=hAPP(X_a,X_a,times_times(X_a,M),hAPP(nat,X_a,power_power(X_a,M),hAPP(nat,nat,minus_minus(nat,N_1),one_one(nat)))). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_2,N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f9(N,P_2)),N)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_2,N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),$f9(N,P_2)))| -hBOOL(hAPP(nat,bool,P_2,I)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_2,N))|hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,plus_plus(nat,$f9(N,P_2)),one_one(nat)))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N))). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,K),Ma)!=hAPP(nat,nat,times_times(nat,K),N)|K=zero_zero(nat)|Ma=N. % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,K),Ma)=hAPP(nat,nat,times_times(nat,K),N)|K!=zero_zero(nat). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,K),Ma)=hAPP(nat,nat,times_times(nat,K),N)|Ma!=N. % 32.58/32.48 0 [] hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_1),U_1)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_1),U_1)),K_1))=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,plus_plus(nat,I_1),J_1)),U_1)),K_1). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hAPP(nat,nat,times_times(nat,K),Ma)!=hAPP(nat,nat,times_times(nat,K),N)|Ma=N. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hAPP(nat,nat,times_times(nat,K),Ma)=hAPP(nat,nat,times_times(nat,K),N)|Ma!=N. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))|K=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))|K!=zero_zero(nat). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,K),Ma)),hAPP(nat,nat,times_times(nat,K),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),I_1))|hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_1),U_1)),M)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_1),U_1)),N_1))=hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_1),J_1)),U_1)),M)),N_1). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))|hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)!=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)|hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)=N. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))|hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)|hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)!=N. % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hAPP(nat,nat,minus_minus(nat,hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_1),U_1)),M)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_1),U_1)),N_1))=hAPP(nat,nat,minus_minus(nat,M),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_1),I_1)),U_1)),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))|hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)!=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)|Ma=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))|hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)|Ma!=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,J_2),I_2)),U)),N). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,I_2),U)),Ma)),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,J_2),U)),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,hAPP(nat,nat,minus_minus(nat,I_2),J_2)),U)),Ma)),N)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,N_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit0(N_1)))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,N_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,bit1(N_1)))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,X_2))|twoSqu1929807760sum2sq(product_Pair(int,int,$f11(X_2),$f10(X_2)))=ti(int,X_2). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,X_2))|twoSqu1929807760sum2sq(product_Pair(int,int,A_5,B_4))!=ti(int,X_2). % 32.58/32.48 0 [] ti(int,K)=zero_zero(int)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),Ta))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,times_times(int,K),Ma)),hAPP(int,int,times_times(int,K),Ta))). % 32.58/32.48 0 [] ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),Ta))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,times_times(int,K),Ma)),hAPP(int,int,times_times(int,K),Ta))). % 32.58/32.48 0 [] -dvd(X_a)| -semiring_0(X_a)| -hBOOL(hAPP(X_a,bool,P_2,hAPP(X_a,X_a,times_times(X_a,L),X)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L),hAPP(X_a,X_a,plus_plus(X_a,$f12(X_a,P_2,L)),zero_zero(X_a)))). % 32.58/32.48 0 [] -dvd(X_a)| -semiring_0(X_a)| -hBOOL(hAPP(X_a,bool,P_2,hAPP(X_a,X_a,times_times(X_a,L),X)))|hBOOL(hAPP(X_a,bool,P_2,$f12(X_a,P_2,L))). % 32.58/32.48 0 [] -dvd(X_a)| -semiring_0(X_a)|hBOOL(hAPP(X_a,bool,P_2,hAPP(X_a,X_a,times_times(X_a,L),$f13(X_a,P_2,L))))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L),hAPP(X_a,X_a,plus_plus(X_a,X3),zero_zero(X_a))))| -hBOOL(hAPP(X_a,bool,P_2,X3)). % 32.58/32.48 0 [] -comm_ring(X_a)| -dvd(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),D_3))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X),Ta)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,X),hAPP(X_a,X_a,times_times(X_a,K_2),D_3))),Ta))). % 32.58/32.48 0 [] -comm_ring(X_a)| -dvd(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),D_3))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X),Ta)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,X),hAPP(X_a,X_a,times_times(X_a,K_2),D_3))),Ta))). % 32.58/32.48 0 [] -comm_ring(X_a)| -dvd(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),D_3))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X),Ta)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,X),hAPP(X_a,X_a,times_times(X_a,K_2),D_3))),Ta))). % 32.58/32.48 0 [] -comm_ring(X_a)| -dvd(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),D_3))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,X),Ta)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D),hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,X),hAPP(X_a,X_a,times_times(X_a,K_2),D_3))),Ta))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,pls))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))|hBOOL(hAPP(int,bool,P_2,$f14(K,P_2,D)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,P_2,X))|hBOOL(hAPP(int,bool,P_2,hAPP(int,int,minus_minus(int,X),hAPP(int,int,times_times(int,K),D)))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))| -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,minus_minus(int,$f14(K,P_2,D)),D)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,P_2,X))|hBOOL(hAPP(int,bool,P_2,hAPP(int,int,minus_minus(int,X),hAPP(int,int,times_times(int,K),D)))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))|hBOOL(hAPP(int,bool,P_2,$f15(K,P_2,D)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,P_2,X))|hBOOL(hAPP(int,bool,P_2,hAPP(int,int,plus_plus(int,X),hAPP(int,int,times_times(int,K),D)))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))| -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,plus_plus(int,$f15(K,P_2,D)),D)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,P_2,X))|hBOOL(hAPP(int,bool,P_2,hAPP(int,int,plus_plus(int,X),hAPP(int,int,times_times(int,K),D)))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))|hBOOL(hAPP(int,bool,zprime,$f16(A_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),$f16(A_1)),A_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f17(A_1,M))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f17(A_1,M)),M)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))|hBOOL(hAPP(int,bool,zcong(A_1,$f17(A_1,M)),M)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),M))| -hBOOL(hAPP(int,bool,zcong(A_1,Y),M))|ti(int,Y)=ti(int,$f17(A_1,M)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),hAPP(int,int,minus_minus(int,B),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))|hBOOL(hAPP(int,bool,zcong(zfact(hAPP(int,int,minus_minus(int,P_1),one_one(int))),number_number_of(int,min)),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_1),zero_zero(int)))|zfact(N_1)=one_one(int). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_1),zero_zero(int)))|zfact(N_1)=hAPP(int,int,times_times(int,N_1),zfact(hAPP(int,int,minus_minus(int,N_1),one_one(int)))). % 32.58/32.48 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))). % 32.58/32.48 0 [] -zero(X_a)|zero_zero(X_a)!=ti(X_a,X_2)|ti(X_a,X_2)=zero_zero(X_a). % 32.58/32.48 0 [] -zero(X_a)|zero_zero(X_a)=ti(X_a,X_2)|ti(X_a,X_2)!=zero_zero(X_a). % 32.58/32.48 0 [] -ab_semigroup_mult(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,times_times(X_a,B),C)). % 32.58/32.48 0 [] -ab_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C)). % 32.58/32.48 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_3),B_2)!=hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)|ti(X_a,B_2)=ti(X_a,C_1). % 32.58/32.48 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_3),B_2)=hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)|ti(X_a,B_2)!=ti(X_a,C_1). % 32.58/32.48 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,B_2),A_3)!=hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)|ti(X_a,B_2)=ti(X_a,C_1). % 32.58/32.48 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,B_2),A_3)=hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)|ti(X_a,B_2)!=ti(X_a,C_1). % 32.58/32.48 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),B)!=hAPP(X_a,X_a,plus_plus(X_a,A_1),C)|ti(X_a,B)=ti(X_a,C). % 32.58/32.48 0 [] -cancel146912293up_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),B)!=hAPP(X_a,X_a,plus_plus(X_a,A_1),C)|ti(X_a,B)=ti(X_a,C). % 32.58/32.48 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,B),A_1)!=hAPP(X_a,X_a,plus_plus(X_a,C),A_1)|ti(X_a,B)=ti(X_a,C). % 32.58/32.48 0 [] -one(X_a)|one_one(X_a)!=ti(X_a,X_2)|ti(X_a,X_2)=one_one(X_a). % 32.58/32.48 0 [] -one(X_a)|one_one(X_a)=ti(X_a,X_2)|ti(X_a,X_2)!=one_one(X_a). % 32.58/32.48 0 [] -ab_group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)!=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)|ti(X_a,A_3)!=ti(X_a,B_2)|ti(X_a,C_1)=ti(X_a,D). % 32.58/32.48 0 [] -ab_group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)!=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)|ti(X_a,A_3)=ti(X_a,B_2)|ti(X_a,C_1)!=ti(X_a,D). % 32.58/32.48 0 [] -monoid_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1). % 32.58/32.48 0 [] -comm_monoid_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1). % 32.58/32.48 0 [] -linord219039673up_add(X_a)|zero_zero(X_a)!=hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)|ti(X_a,A_3)=zero_zero(X_a). % 32.58/32.48 0 [] -linord219039673up_add(X_a)|zero_zero(X_a)=hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)|ti(X_a,A_3)!=zero_zero(X_a). % 32.58/32.48 0 [] -monoid_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1). % 32.58/32.48 0 [] -comm_monoid_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1). % 32.58/32.48 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B_2),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2)). % 32.58/32.48 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B_2),C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2)). % 32.58/32.48 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2)). % 32.58/32.48 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2)). % 32.58/32.48 0 [] -ordere779506340up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),C))). % 32.58/32.48 0 [] -ordere779506340up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C),B))). % 32.58/32.48 0 [] -ordere779506340up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))). % 32.58/32.48 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),C)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B)). % 32.58/32.48 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C),B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B)). % 32.58/32.48 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B_2),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)). % 32.58/32.48 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B_2),C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)). % 32.58/32.48 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)). % 32.58/32.48 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_3)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)). % 32.58/32.48 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),C))). % 32.58/32.48 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C),B))). % 32.58/32.48 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))). % 32.58/32.48 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),C)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)). % 32.58/32.48 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C),B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)). % 32.58/32.48 0 [] -group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)!=zero_zero(X_a)|ti(X_a,A_3)=ti(X_a,B_2). % 32.58/32.48 0 [] -group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)=zero_zero(X_a)|ti(X_a,A_3)!=ti(X_a,B_2). % 32.58/32.48 0 [] -ab_group_add(X_a)|ti(X_a,A_3)!=ti(X_a,B_2)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)=zero_zero(X_a). % 32.58/32.48 0 [] -ab_group_add(X_a)|ti(X_a,A_3)=ti(X_a,B_2)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)!=zero_zero(X_a). % 32.58/32.48 0 [] -group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_1),A_1)=zero_zero(X_a). % 32.58/32.48 0 [] -group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1). % 32.58/32.48 0 [] -ordered_ab_group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)!=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),D)). % 32.58/32.48 0 [] -ordered_ab_group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)!=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),D)). % 32.58/32.48 0 [] -ordered_ab_group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)!=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D)). % 32.58/32.48 0 [] -ordered_ab_group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)!=hAPP(X_a,X_a,minus_minus(X_a,C_1),D)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D)). % 32.58/32.48 0 [] -monoid_mult(X_a)|hAPP(X_a,X_a,times_times(X_a,one_one(X_a)),A_1)=ti(X_a,A_1). % 32.58/32.48 0 [] -comm_monoid_mult(X_a)|hAPP(X_a,X_a,times_times(X_a,one_one(X_a)),A_1)=ti(X_a,A_1). % 32.58/32.48 0 [] -monoid_mult(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),one_one(X_a))=ti(X_a,A_1). % 32.58/32.48 0 [] -comm_monoid_mult(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),one_one(X_a))=ti(X_a,A_1). % 32.58/32.48 0 [] -group_add(X_a)|hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),B)=ti(X_a,A_1). % 32.58/32.48 0 [] -group_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),B)=ti(X_a,A_1). % 32.58/32.48 0 [] -linord219039673up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3)). % 32.58/32.48 0 [] -linord219039673up_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_3)). % 32.58/32.48 0 [] -linord219039673up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a))). % 32.58/32.48 0 [] -linord219039673up_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),zero_zero(X_a))). % 32.58/32.48 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))). % 32.58/32.48 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_2))|hAPP(X_a,X_a,plus_plus(X_a,X_2),Y_2)!=zero_zero(X_a)|ti(X_a,X_2)=zero_zero(X_a). % 32.58/32.48 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_2))|hAPP(X_a,X_a,plus_plus(X_a,X_2),Y_2)!=zero_zero(X_a)|ti(X_a,Y_2)=zero_zero(X_a). % 32.58/32.48 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y_2))|hAPP(X_a,X_a,plus_plus(X_a,X_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). % 32.58/32.48 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))). % 32.58/32.48 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))). % 32.58/32.48 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))). % 32.58/32.48 0 [] -linord219039673up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_3)). % 32.58/32.48 0 [] -linord219039673up_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_3)). % 32.58/32.48 0 [] -linord219039673up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),zero_zero(X_a))). % 32.58/32.48 0 [] -linord219039673up_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_3),A_3)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),zero_zero(X_a))). % 32.58/32.48 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))). % 32.58/32.48 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))). % 32.58/32.48 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))). % 32.58/32.48 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C)),hAPP(X_a,X_a,plus_plus(X_a,B),D_2))). % 32.58/32.48 0 [] -ordered_ab_group_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),zero_zero(X_a))). % 32.58/32.48 0 [] -ordered_ab_group_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_3),B_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),zero_zero(X_a))). % 32.58/32.48 0 [] -ordered_ab_group_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),zero_zero(X_a))). % 32.58/32.48 0 [] -ordered_ab_group_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,minus_minus(X_a,A_3),B_2)),zero_zero(X_a))). % 32.58/32.48 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))). % 32.58/32.48 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))). % 32.58/32.48 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))). % 32.58/32.48 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C))). % 32.58/32.48 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_1))|inv(P_1,inv(P_1,A_1))=ti(int,A_1). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))|hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,zcong(J_1,zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,quadRes(P_1),A_1))| -hBOOL(hAPP(int,bool,zcong(J_1,hAPP(int,int,times_times(int,A_1),multInv(P_1,J_1))),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,J_1),K_1),A_1),P_1))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,multInv(P_1,J_1)),J_1)),K_1),hAPP(int,int,times_times(int,multInv(P_1,J_1)),A_1)),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zcong(J_1,hAPP(int,int,times_times(int,A_1),multInv(P_1,K_1))),P_1))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,J_1),K_1),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,A_1),multInv(P_1,K_1))),K_1)),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_1),one_one(int))))|ti(int,A_1)!=inv(P_1,A_1). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_1),one_one(int))))|inv(P_1,A_1)!=one_one(int). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_1),one_one(int))))|inv(P_1,A_1)!=hAPP(int,int,minus_minus(int,P_1),one_one(int)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_1),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),inv(P_1,A_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_1),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),inv(P_1,A_1)),hAPP(int,int,minus_minus(int,P_1),one_one(int)))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))| -hBOOL(hAPP(int,bool,zcong(X_1,Y_1),P_1))|hBOOL(hAPP(int,bool,zcong(multInv(P_1,X_1),multInv(P_1,Y_1)),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,minus_minus(int,P_1),one_one(int))))|inv(P_1,A_1)!=zero_zero(int). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))| -hBOOL(hAPP(int,bool,zcong(J_1,K_1),P_1))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),multInv(P_1,J_1)),hAPP(int,int,times_times(int,A_1),multInv(P_1,K_1))),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))| -hBOOL(hAPP(int,bool,zprime,P_1))|hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,zcong(Y_1,zero_zero(int)),P_1))| -hBOOL(hAPP(int,bool,zcong(multInv(P_1,X_1),multInv(P_1,Y_1)),P_1))|hBOOL(hAPP(int,bool,zcong(X_1,Y_1),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))| -hBOOL(hAPP(int,bool,zprime,P_1))|hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,zcong(multInv(P_1,multInv(P_1,X_1)),X_1),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))| -hBOOL(hAPP(int,bool,zprime,P_1))|hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))| -hBOOL(hAPP(int,bool,zcong(multInv(P_1,X_1),zero_zero(int)),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zprime,P_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_1))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),inv(P_1,A_1)),one_one(int)),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))| -hBOOL(hAPP(int,bool,zprime,P_1))|hBOOL(hAPP(int,bool,zcong(J_1,zero_zero(int)),P_1))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,multInv(P_1,J_1)),J_1)),K_1),hAPP(int,int,times_times(int,multInv(P_1,J_1)),A_1)),P_1))|hBOOL(hAPP(int,bool,zcong(K_1,hAPP(int,int,times_times(int,A_1),multInv(P_1,J_1))),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))| -hBOOL(hAPP(int,bool,zprime,P_1))|hBOOL(hAPP(int,bool,zcong(K_1,zero_zero(int)),P_1))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,J_1),K_1),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,A_1),multInv(P_1,K_1))),K_1)),P_1))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,J_1),K_1),A_1),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))| -hBOOL(hAPP(int,bool,zprime,P_1))|hBOOL(hAPP(int,bool,zcong(K_1,zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,zcong(J_1,zero_zero(int)),P_1))| -hBOOL(hAPP(int,bool,zcong(J_1,hAPP(int,int,times_times(int,A_1),multInv(P_1,K_1))),P_1))|hBOOL(hAPP(int,bool,zcong(K_1,hAPP(int,int,times_times(int,A_1),multInv(P_1,J_1))),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))| -hBOOL(hAPP(int,bool,zprime,P_1))|hBOOL(hAPP(int,bool,zcong(A_1,zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,zcong(K_1,zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,zcong(J_1,zero_zero(int)),P_1))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A_1),multInv(P_1,J_1)),hAPP(int,int,times_times(int,A_1),multInv(P_1,K_1))),P_1))|hBOOL(hAPP(int,bool,zcong(J_1,K_1),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))| -hBOOL(hAPP(int,bool,zprime,P_1))|hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,X_1),multInv(P_1,X_1))),multInv(P_1,multInv(P_1,X_1))),X_1),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))| -hBOOL(hAPP(int,bool,zprime,P_1))|hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,zcong(multInv(P_1,multInv(P_1,X_1)),hAPP(int,int,times_times(int,hAPP(int,int,times_times(int,X_1),multInv(P_1,X_1))),multInv(P_1,multInv(P_1,X_1)))),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))| -hBOOL(hAPP(int,bool,zprime,P_1))|hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,multInv(P_1,X_1)),X_1),one_one(int)),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),P_1))| -hBOOL(hAPP(int,bool,zprime,P_1))|hBOOL(hAPP(int,bool,zcong(X_1,zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,X_1),multInv(P_1,X_1)),one_one(int)),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_3),one_one(int))))| -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_3)))|hBOOL(hAPP(fun(int,bool),bool,member(int,inv(P_3,B_2)),wset(A_3,P_3))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_3),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_2),hAPP(int,int,minus_minus(int,P_3),one_one(int))))| -hBOOL(hAPP(fun(int,bool),bool,member(int,inv(P_3,B_2)),wset(A_3,P_3)))|hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_3))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_3))|hBOOL(hAPP(fun(int,bool),bool,member(int,A_3),wset(A_3,P_3))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_3))| -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(hAPP(int,int,minus_minus(int,A_3),one_one(int)),P_3)))|hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_3))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_3),one_one(int))))| -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_3)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_2),hAPP(int,int,minus_minus(int,P_3),one_one(int)))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_3),one_one(int))))| -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_3)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_3))|hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(hAPP(int,int,minus_minus(int,A_3),one_one(int)),P_3)))| -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_3)))|ti(int,B_2)=ti(int,A_3)|ti(int,B_2)=inv(P_3,A_3). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(int,int,minus_minus(int,P_3),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),A_3))|hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),wset(A_3,P_3))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),K))| -hBOOL(hAPP(int,bool,P_2,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f18(P_2,I_2,K)),K))|hBOOL(hAPP(int,bool,P_2,I_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),K))| -hBOOL(hAPP(int,bool,P_2,K))|hBOOL(hAPP(int,bool,P_2,$f18(P_2,I_2,K)))|hBOOL(hAPP(int,bool,P_2,I_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),K))| -hBOOL(hAPP(int,bool,P_2,K))| -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,minus_minus(int,$f18(P_2,I_2,K)),one_one(int))))|hBOOL(hAPP(int,bool,P_2,I_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),K))| -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,minus_minus(int,K),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f19(P_2,I_2,K)),K))|hBOOL(hAPP(int,bool,P_2,I_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),K))| -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,minus_minus(int,K),one_one(int))))|hBOOL(hAPP(int,bool,P_2,$f19(P_2,I_2,K)))|hBOOL(hAPP(int,bool,P_2,I_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),K))| -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,minus_minus(int,K),one_one(int))))| -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,minus_minus(int,$f19(P_2,I_2,K)),one_one(int))))|hBOOL(hAPP(int,bool,P_2,I_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),$f20(X_2,P_2)))|hBOOL(hAPP(int,bool,P_2,hAPP(int,int,minus_minus(int,$f20(X_2,P_2)),one_one(int))))|hBOOL(hAPP(int,bool,P_2,X_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,P_2,$f20(X_2,P_2)))|hBOOL(hAPP(int,bool,P_2,X_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),I_2))| -hBOOL(hAPP(int,bool,P_2,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),$f21(P_2,K,I_2)))|hBOOL(hAPP(int,bool,P_2,I_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),I_2))| -hBOOL(hAPP(int,bool,P_2,K))|hBOOL(hAPP(int,bool,P_2,$f21(P_2,K,I_2)))|hBOOL(hAPP(int,bool,P_2,I_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),I_2))| -hBOOL(hAPP(int,bool,P_2,K))| -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,plus_plus(int,$f21(P_2,K,I_2)),one_one(int))))|hBOOL(hAPP(int,bool,P_2,I_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_2))| -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,plus_plus(int,K),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f22(P_2,K,I_2)))|hBOOL(hAPP(int,bool,P_2,I_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_2))| -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,plus_plus(int,K),one_one(int))))|hBOOL(hAPP(int,bool,P_2,$f22(P_2,K,I_2)))|hBOOL(hAPP(int,bool,P_2,I_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_2))| -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,plus_plus(int,K),one_one(int))))| -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,plus_plus(int,$f22(P_2,K,I_2)),one_one(int))))|hBOOL(hAPP(int,bool,P_2,I_2)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f24(Ma,K,F_1)),$f23(Ma,K,F_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,F_1,Ma)),K)),hAPP(nat,nat,F_1,hAPP(nat,nat,plus_plus(nat,Ma),K)))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F_1,$f24(Ma,K,F_1))),hAPP(nat,nat,F_1,$f23(Ma,K,F_1))))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,F_1,Ma)),K)),hAPP(nat,nat,F_1,hAPP(nat,nat,plus_plus(nat,Ma),K)))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zprime,P_3))|d22set(hAPP(int,int,minus_minus(int,P_3),number_number_of(int,bit0(bit1(pls)))))=wset(hAPP(int,int,minus_minus(int,P_3),number_number_of(int,bit0(bit1(pls)))),P_3). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_2,N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f25(N,P_2)),N)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_2,N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),$f25(N,P_2)))| -hBOOL(hAPP(nat,bool,P_2,I)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_2,N))|hBOOL(hAPP(nat,bool,P_2,$f25(N,P_2))). % 32.58/32.48 0 [] -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),d22set(A_3)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),A_3)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),B_2))| -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),d22set(A_3))). % 32.58/32.48 0 [] -hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),d22set(A_3)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),A_3))|hBOOL(hAPP(fun(int,bool),bool,member(int,B_2),d22set(A_3))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),$f26(I_1,J_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))|hAPP(nat,nat,plus_plus(nat,I_1),$f26(I_1,J_1))=J_1. % 32.58/32.48 0 [] N=zero_zero(nat)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A_3),N)),hAPP(nat,int,power_power(int,B_2),N)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),B_2)). % 32.58/32.48 0 [] N=zero_zero(nat)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A_3),N)),hAPP(nat,int,power_power(int,B_2),N)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),B_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_1))|A_1=zero_zero(nat). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_3))|A_3=zero_zero(nat). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_3))|A_3!=zero_zero(nat). % 32.58/32.48 0 [] A_3=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),zero_zero(nat))). % 32.58/32.48 0 [] A_3=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_3)). % 32.58/32.48 0 [] A_3!=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),zero_zero(nat)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_3)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),zero_zero(nat))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),zero_zero(nat))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),one_one(nat)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_1)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_1)). % 32.58/32.48 0 [] A_3=one_one(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_3)). % 32.58/32.48 0 [] A_3=one_one(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),one_one(nat))). % 32.58/32.48 0 [] A_3!=one_one(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_3))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),one_one(nat))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),one_one(nat)))|A_3=one_one(nat). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),one_one(nat)))|A_3!=one_one(nat). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),one_one(nat)))|A_1=one_one(nat). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)). % 32.58/32.48 0 [] N=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,A_3),N)),hAPP(nat,nat,power_power(nat,B_2),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),B_2)). % 32.58/32.48 0 [] N=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,A_3),N)),hAPP(nat,nat,power_power(nat,B_2),N)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),B_2)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A_1),N_1)),hAPP(nat,int,power_power(int,B),N_1)))|N_1=zero_zero(nat)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_1),B)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|N_1=zero_zero(nat). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))|hAPP(nat,nat,times_times(nat,K_1),N_1)!=hAPP(nat,nat,times_times(nat,K_1),M)|N_1=M. % 32.58/32.48 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Y_1)),hAPP(X_a,X_a,times_times(X_a,A_1),B))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),A_1)),hAPP(X_a,X_a,minus_minus(X_a,Y_1),B))),hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),A_1)),B))),hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,minus_minus(X_a,Y_1),B))). % 32.58/32.48 0 [] sr(P_3)=collect(int,combs(int,bool,bool,combb(bool,fun(bool,bool),int,fconj,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int))),combc(int,int,bool,ord_less(int),P_3))). % 32.58/32.48 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,X_1),zero_zero(X_a))=zero_zero(X_a). % 32.58/32.48 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a))=zero_zero(X_a). % 32.58/32.48 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,zero_zero(X_a)),Y_1)=zero_zero(X_a). % 32.58/32.48 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,zero_zero(X_a)),B)=zero_zero(X_a). % 32.58/32.48 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,X_1),Y_1)),Ya)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Ya)),hAPP(X_a,X_a,times_times(X_a,Y_1),Ya)). % 32.58/32.48 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),A_4)),B)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),hAPP(X_a,X_a,times_times(X_a,A_4),B)). % 32.58/32.48 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,Xa),hAPP(X_a,X_a,plus_plus(X_a,X_1),Y_1))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,Xa),X_1)),hAPP(X_a,X_a,times_times(X_a,Xa),Y_1)). % 32.58/32.48 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),B_3))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),hAPP(X_a,X_a,times_times(X_a,A_1),B_3)). % 32.58/32.48 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,minus_minus(X_a,B),B_3))=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),hAPP(X_a,X_a,times_times(X_a,A_1),B_3)). % 32.58/32.48 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,Xa),hAPP(X_a,X_a,minus_minus(X_a,X_1),Y_1))=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,Xa),X_1)),hAPP(X_a,X_a,times_times(X_a,Xa),Y_1)). % 32.58/32.48 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),A_4)),B)=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),hAPP(X_a,X_a,times_times(X_a,A_4),B)). % 32.58/32.48 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,minus_minus(X_a,X_1),Y_1)),Ya)=hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,times_times(X_a,X_1),Ya)),hAPP(X_a,X_a,times_times(X_a,Y_1),Ya)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),zero_zero(int)))|hAPP(int,int,div_mod(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),B))),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),A_1))=hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,hAPP(int,int,plus_plus(int,B),one_one(int))),A_1))),one_one(int)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,W)))|hAPP(int,int,div_mod(int,number_number_of(int,bit1(V))),number_number_of(int,bit0(W)))=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,number_number_of(int,V)),number_number_of(int,W)))),one_one(int)). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,W)))|hAPP(int,int,div_mod(int,number_number_of(int,bit1(V))),number_number_of(int,bit0(W)))=hAPP(int,int,minus_minus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,hAPP(int,int,plus_plus(int,number_number_of(int,V)),one_one(int))),number_number_of(int,W)))),one_one(int)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),number_number_of(int,X_2)),number_number_of(int,Y_2)))|hAPP(int,int,div_mod(int,number_number_of(int,Y_2)),number_number_of(int,X_2))=zero_zero(int). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),number_number_of(int,X_2)),number_number_of(int,Y_2)))|hAPP(int,int,div_mod(int,number_number_of(int,Y_2)),number_number_of(int,X_2))!=zero_zero(int). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,B),A_1)),B)=zero_zero(X_a). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),B)=zero_zero(X_a). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,A_1),one_one(X_a))=zero_zero(X_a). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,times_times(X_a,C),B))),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,times_times(X_a,B),C))),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B). % 32.58/32.48 0 [] -semiring_div(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2))|hAPP(X_a,X_a,div_mod(X_a,B_2),A_3)=zero_zero(X_a). % 32.58/32.48 0 [] -semiring_div(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2))|hAPP(X_a,X_a,div_mod(X_a,B_2),A_3)!=zero_zero(X_a). % 32.58/32.48 0 [] -semiring_div(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B))|hAPP(X_a,X_a,div_mod(X_a,B),A_1)=zero_zero(X_a). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,div_mod(int,A_1),B))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,div_mod(int,A_1),B)),B)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,div_mod(int,X_1),Y_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),M))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,div_mod(int,M),K_1)),M)). % 32.58/32.48 0 [] hAPP(int,int,div_mod(int,Ma),D)!=zero_zero(int)|ti(int,Ma)=hAPP(int,int,times_times(int,D),$f31(Ma,D)). % 32.58/32.48 0 [] hAPP(int,int,div_mod(int,Ma),D)=zero_zero(int)|ti(int,Ma)!=hAPP(int,int,times_times(int,D),Q_2). % 32.58/32.48 0 [] hAPP(int,int,div_mod(int,X_2),N)!=hAPP(int,int,div_mod(int,Y_2),N)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),hAPP(int,int,minus_minus(int,X_2),Y_2))). % 32.58/32.48 0 [] hAPP(int,int,div_mod(int,X_2),N)=hAPP(int,int,div_mod(int,Y_2),N)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),hAPP(int,int,minus_minus(int,X_2),Y_2))). % 32.58/32.48 0 [] hAPP(int,int,div_mod(int,X_1),M)!=hAPP(int,int,div_mod(int,Y_1),M)|hBOOL(hAPP(int,bool,zcong(X_1,Y_1),M)). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,zcong(X_1,hAPP(int,int,div_mod(int,X_1),M)),M)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,div_mod(int,A_3),Ma),hAPP(int,int,div_mod(int,B_2),Ma)),Ma)). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,div_mod(int,A_3),Ma),hAPP(int,int,div_mod(int,B_2),Ma)),Ma)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),hAPP(int,int,div_mod(int,M),N_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),N_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_1),M)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F),N_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F),hAPP(int,int,div_mod(int,M),N_1))). % 32.58/32.48 0 [] hAPP(int,int,div_mod(int,hAPP(nat,int,power_power(int,hAPP(int,int,div_mod(int,X_1),M)),Y_1)),M)=hAPP(int,int,div_mod(int,hAPP(nat,int,power_power(int,X_1),Y_1)),M). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),B)),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B). % 32.58/32.48 0 [] hAPP(int,int,div_mod(int,hAPP(int,int,times_times(int,A_1),B)),C)=hAPP(int,int,div_mod(int,hAPP(int,int,times_times(int,A_1),hAPP(int,int,div_mod(int,B),C))),C). % 32.58/32.48 0 [] hAPP(int,int,div_mod(int,hAPP(int,int,times_times(int,A_1),hAPP(int,int,div_mod(int,B),C))),C)=hAPP(int,int,div_mod(int,hAPP(int,int,times_times(int,A_1),B)),C). % 32.58/32.48 0 [] hAPP(int,int,div_mod(int,A_1),A_1)=zero_zero(int). % 32.58/32.48 0 [] hAPP(int,int,div_mod(int,zero_zero(int)),B)=zero_zero(int). % 32.58/32.48 0 [] -semiring_div(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),hAPP(X_a,X_a,div_mod(X_a,M),N_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),N_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),M)). % 32.58/32.48 0 [] -semiring_div(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),M))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),N_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_1),hAPP(X_a,X_a,div_mod(X_a,M),N_1))). % 32.58/32.48 0 [] -semiring_div(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),B))|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,A_1),C). % 32.58/32.48 0 [] -semiring_div(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),N))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),hAPP(X_a,X_a,div_mod(X_a,Ma),N)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),Ma)). % 32.58/32.48 0 [] -semiring_div(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),N))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),hAPP(X_a,X_a,div_mod(X_a,Ma),N)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),Ma)). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,B),A_1)),B)=hAPP(X_a,X_a,div_mod(X_a,A_1),B). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,div_mod(X_a,B),C))),C). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),hAPP(X_a,X_a,div_mod(X_a,B),C))),C). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,div_mod(X_a,B),C))),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,A_1),C)!=hAPP(X_a,X_a,div_mod(X_a,A_4),C)|hAPP(X_a,X_a,div_mod(X_a,B),C)!=hAPP(X_a,X_a,div_mod(X_a,B_3),C)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_4),B_3)),C). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),hAPP(X_a,X_a,div_mod(X_a,B),C))),C). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),hAPP(X_a,X_a,div_mod(X_a,B),C))),C). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,C),A_1)),hAPP(X_a,X_a,times_times(X_a,C),B))=hAPP(X_a,X_a,times_times(X_a,C),hAPP(X_a,X_a,div_mod(X_a,A_1),B)). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),C)),hAPP(X_a,X_a,times_times(X_a,B),C))=hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),B)),C). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,A_1),C)!=hAPP(X_a,X_a,div_mod(X_a,A_4),C)|hAPP(X_a,X_a,div_mod(X_a,B),C)!=hAPP(X_a,X_a,div_mod(X_a,B_3),C)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,times_times(X_a,A_4),B_3)),C). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,A_1),A_1)=zero_zero(X_a). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1). % 32.58/32.48 0 [] -semiring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,zero_zero(X_a)),A_1)=zero_zero(X_a). % 32.58/32.48 0 [] hAPP(int,int,div_mod(int,hAPP(int,int,minus_minus(int,X_1),hAPP(int,int,div_mod(int,Y_1),M))),M)=hAPP(int,int,div_mod(int,hAPP(int,int,minus_minus(int,X_1),Y_1)),M). % 32.58/32.48 0 [] hAPP(int,int,div_mod(int,hAPP(int,int,minus_minus(int,hAPP(int,int,div_mod(int,X_1),M)),Y_1)),M)=hAPP(int,int,div_mod(int,hAPP(int,int,minus_minus(int,X_1),Y_1)),M). % 32.58/32.48 0 [] -ring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,A_1),C)!=hAPP(X_a,X_a,div_mod(X_a,A_4),C)|hAPP(X_a,X_a,div_mod(X_a,B),C)!=hAPP(X_a,X_a,div_mod(X_a,B_3),C)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_4),B_3)),C). % 32.58/32.48 0 [] -ring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),hAPP(X_a,X_a,div_mod(X_a,B),C))),C). % 32.58/32.48 0 [] -ring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,hAPP(X_a,X_a,div_mod(X_a,A_1),C)),B)),C). % 32.58/32.48 0 [] -ring_div(X_a)|hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),B)),C)=hAPP(X_a,X_a,div_mod(X_a,hAPP(X_a,X_a,minus_minus(X_a,A_1),hAPP(X_a,X_a,div_mod(X_a,B),C))),C). % 32.58/32.48 0 [] -semiring_div(X_a)| -number(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),number_number_of(X_a,X_2)),number_number_of(X_a,Y_2)))|hAPP(X_a,X_a,div_mod(X_a,number_number_of(X_a,Y_2)),number_number_of(X_a,X_2))=zero_zero(X_a). % 32.58/32.48 0 [] -semiring_div(X_a)| -number(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),number_number_of(X_a,X_2)),number_number_of(X_a,Y_2)))|hAPP(X_a,X_a,div_mod(X_a,number_number_of(X_a,Y_2)),number_number_of(X_a,X_2))!=zero_zero(X_a). % 32.58/32.48 0 [] hAPP(int,int,div_mod(int,A_1),number_number_of(int,min))=zero_zero(int). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),B))|hAPP(int,int,div_mod(int,hAPP(int,int,div_mod(int,A_1),B)),M)=hAPP(int,int,div_mod(int,A_1),M). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))| -hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|hAPP(int,int,div_mod(int,A_3),Ma)=hAPP(int,int,div_mod(int,B_2),Ma). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))|hBOOL(hAPP(int,bool,zcong(A_3,B_2),Ma))|hAPP(int,int,div_mod(int,A_3),Ma)!=hAPP(int,int,div_mod(int,B_2),Ma). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,div_mod(int,A_1),B))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,div_mod(int,A_1),B))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,div_mod(int,A_1),B)),B)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B))|hAPP(int,int,div_mod(int,A_1),B)=ti(int,A_1). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,div_mod(int,A_1),B)),zero_zero(int))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,div_mod(int,A_1),B)),zero_zero(int))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,div_mod(int,A_1),B))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1))|hAPP(int,int,div_mod(int,A_1),B)=ti(int,A_1). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,A_1),B)),zero_zero(int)))|hAPP(int,int,div_mod(int,A_1),B)=hAPP(int,int,plus_plus(int,A_1),B). % 32.58/32.48 0 [] hAPP(int,int,div_mod(int,number_number_of(int,bit0(V))),number_number_of(int,bit0(W)))=hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,number_number_of(int,V)),number_number_of(int,W))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)!=zero_zero(int)|hBOOL(hAPP(int,bool,P_2,N)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),J))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J),K))|ti(int,N)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),I)),J)|hBOOL(hAPP(int,bool,P_2,J)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),X5))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X5),zero_zero(int)))|ti(int,N)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),X4)),X5)|hBOOL(hAPP(int,bool,P_2,X5)). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_2,N,K)),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_2,N,K))),$f34(P_2,N,K)). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,P_2,$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_2,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_2,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_2,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_2,N,K)),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_2,N,K)))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_2,N,K))),$f34(P_2,N,K)). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_2,N,K)))| -hBOOL(hAPP(int,bool,P_2,$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_2,N,K)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_2,N,K)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_2,N,K)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_2,N,K)),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_2,N,K)),K))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_2,N,K))),$f34(P_2,N,K)). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_2,N,K)),K))| -hBOOL(hAPP(int,bool,P_2,$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_2,N,K))),$f32(P_2,N,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_2,N,K))),$f32(P_2,N,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_2,N,K))),$f32(P_2,N,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_2,N,K)),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_2,N,K))),$f32(P_2,N,K))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_2,N,K))),$f34(P_2,N,K)). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_2,N,K))),$f32(P_2,N,K))| -hBOOL(hAPP(int,bool,P_2,$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)| -hBOOL(hAPP(int,bool,P_2,$f32(P_2,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)| -hBOOL(hAPP(int,bool,P_2,$f32(P_2,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)| -hBOOL(hAPP(int,bool,P_2,$f32(P_2,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_2,N,K)),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)| -hBOOL(hAPP(int,bool,P_2,$f32(P_2,N,K)))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_2,N,K))),$f34(P_2,N,K)). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))|ti(int,K)=zero_zero(int)| -hBOOL(hAPP(int,bool,P_2,$f32(P_2,N,K)))| -hBOOL(hAPP(int,bool,P_2,$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_2,N,K)),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_2,N,K))),$f34(P_2,N,K)). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,P_2,$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_2,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_2,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_2,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_2,N,K)),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_2,N,K)))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_2,N,K))),$f34(P_2,N,K)). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f32(P_2,N,K)))| -hBOOL(hAPP(int,bool,P_2,$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_2,N,K)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_2,N,K)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_2,N,K)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_2,N,K)),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_2,N,K)),K))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_2,N,K))),$f34(P_2,N,K)). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f32(P_2,N,K)),K))| -hBOOL(hAPP(int,bool,P_2,$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_2,N,K))),$f32(P_2,N,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_2,N,K))),$f32(P_2,N,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_2,N,K))),$f32(P_2,N,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_2,N,K)),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_2,N,K))),$f32(P_2,N,K))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_2,N,K))),$f34(P_2,N,K)). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f33(P_2,N,K))),$f32(P_2,N,K))| -hBOOL(hAPP(int,bool,P_2,$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))| -hBOOL(hAPP(int,bool,P_2,$f32(P_2,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))| -hBOOL(hAPP(int,bool,P_2,$f32(P_2,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f34(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))| -hBOOL(hAPP(int,bool,P_2,$f32(P_2,N,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f34(P_2,N,K)),zero_zero(int))). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))| -hBOOL(hAPP(int,bool,P_2,$f32(P_2,N,K)))|ti(int,N)=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,K),$f35(P_2,N,K))),$f34(P_2,N,K)). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,P_2,hAPP(int,int,div_mod(int,N),K)))| -hBOOL(hAPP(int,bool,P_2,N))| -hBOOL(hAPP(int,bool,P_2,$f32(P_2,N,K)))| -hBOOL(hAPP(int,bool,P_2,$f34(P_2,N,K))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),hAPP(int,int,div_mod(int,Q_1),C))),R_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),hAPP(int,int,div_mod(int,Q_1),C))),R_1)),hAPP(int,int,times_times(int,B),C))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_1),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,B),C)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),hAPP(int,int,div_mod(int,Q_1),C))),R_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_1),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B),hAPP(int,int,div_mod(int,Q_1),C))),R_1)),zero_zero(int))). % 32.58/32.48 0 [] ti(int,A_2)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_1),Q_3)),Y_1)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),Y_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Y_1),zero_zero(int)))|ti(int,B_1)=zero_zero(int)|hAPP(int,int,div_mod(int,A_2),B_1)=ti(int,Y_1). % 32.58/32.48 0 [] ti(int,A_2)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_1),Q_3)),Y_1)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_1),B_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1))|ti(int,B_1)=zero_zero(int)|hAPP(int,int,div_mod(int,A_2),B_1)=ti(int,Y_1). % 32.58/32.48 0 [] ti(int,A_2)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,B_1),Q_3)),Y_1)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_1),B_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),Y_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Y_1),zero_zero(int)))|ti(int,B_1)=zero_zero(int)|hAPP(int,int,div_mod(int,A_2),B_1)=ti(int,Y_1). % 32.58/32.48 0 [] hAPP(int,int,div_mod(int,X_2),number_number_of(int,bit0(bit1(pls))))=zero_zero(int)|hAPP(int,int,div_mod(int,X_2),number_number_of(int,bit0(bit1(pls))))=one_one(int). % 32.58/32.48 0 [] hAPP(int,int,div_mod(int,X_2),number_number_of(int,bit0(bit1(pls))))!=zero_zero(int)|hAPP(int,int,div_mod(int,X_2),number_number_of(int,bit0(bit1(pls))))!=one_one(int). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))|hAPP(int,int,div_mod(int,number_number_of(int,min)),B)=hAPP(int,int,minus_minus(int,B),one_one(int)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A_1))|hAPP(int,int,div_mod(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),B))),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),A_1))=hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit1(pls)))),hAPP(int,int,div_mod(int,B),A_1))). % 32.58/32.48 0 [] hAPP(int,int,div_mod(int,M_1),D_1)!=zero_zero(int)|ti(int,M_1)=hAPP(int,int,times_times(int,D_1),$f36(M_1,D_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),M))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,standardRes(M,X_1)),standardRes(M,Y_1)),hAPP(int,int,times_times(int,X_1),Y_1)),M)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,div_mod(nat,M),N_1)),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,div_mod(nat,M),N_1)),N_1)). % 32.58/32.48 0 [] hAPP(nat,nat,div_mod(nat,Ma),D)!=zero_zero(nat)|Ma=hAPP(nat,nat,times_times(nat,D),$f37(Ma,D)). % 32.58/32.48 0 [] hAPP(nat,nat,div_mod(nat,Ma),D)=zero_zero(nat)|Ma!=hAPP(nat,nat,times_times(nat,D),Q_2). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|hAPP(nat,nat,div_mod(nat,M),N_1)=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),N_1). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|hAPP(nat,nat,div_mod(nat,M),N_1)=M. % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|hAPP(nat,nat,div_mod(nat,M),N_1)=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),N_1). % 32.58/32.48 0 [] hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,K_1),N_1)),M)),N_1)=hAPP(nat,nat,div_mod(nat,M),N_1). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hAPP(nat,nat,div_mod(nat,M),N_1)=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,minus_minus(nat,M),N_1)),N_1). % 32.58/32.48 0 [] standardRes(M,X_1)=hAPP(int,int,div_mod(int,X_1),M). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,hAPP(nat,nat,div_mod(nat,M),N_1)),K_1)=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,times_times(nat,M),K_1)),hAPP(nat,nat,times_times(nat,N_1),K_1)). % 32.58/32.48 0 [] hAPP(nat,nat,times_times(nat,K_1),hAPP(nat,nat,div_mod(nat,M),N_1))=hAPP(nat,nat,div_mod(nat,hAPP(nat,nat,times_times(nat,K_1),M)),hAPP(nat,nat,times_times(nat,K_1),N_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|hAPP(nat,nat,div_mod(nat,M),N_1)=M. % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,div_mod(nat,M),N_1)),M)). % 32.58/32.48 0 [] standardRes(Ma,X_2)!=zero_zero(int)|hBOOL(hAPP(int,bool,zcong(X_2,zero_zero(int)),Ma)). % 32.58/32.48 0 [] standardRes(Ma,X_2)=zero_zero(int)| -hBOOL(hAPP(int,bool,zcong(X_2,zero_zero(int)),Ma)). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,zcong(X_2,zero_zero(int)),P_3))|standardRes(P_3,X_2)!=zero_zero(int). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,zcong(X_2,zero_zero(int)),P_3))|standardRes(P_3,X_2)=zero_zero(int). % 32.58/32.48 0 [] hBOOL(hAPP(int,bool,zcong(X_1,standardRes(M,X_1)),M)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),standardRes(P_1,X_1)),P_1)). % 32.58/32.48 0 [] -hBOOL(hAPP(fun(int,bool),bool,member(int,X_2),sr(P_3)))|standardRes(P_3,X_2)=ti(int,X_2). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,div_mod(nat,N),K)))|K!=zero_zero(nat)|hBOOL(hAPP(nat,bool,P_2,N)). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,div_mod(nat,N),K)))|K=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K))|N!=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,K),I)),J)|hBOOL(hAPP(nat,bool,P_2,J)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,div_mod(nat,N),K)))|K=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f38(P_2,N,K)),K)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,div_mod(nat,N),K)))|K=zero_zero(nat)|N=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,K),$f39(P_2,N,K))),$f38(P_2,N,K)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,div_mod(nat,N),K)))|K=zero_zero(nat)| -hBOOL(hAPP(nat,bool,P_2,$f38(P_2,N,K))). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,div_mod(nat,N),K)))| -hBOOL(hAPP(nat,bool,P_2,N))|K!=zero_zero(nat). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,div_mod(nat,N),K)))| -hBOOL(hAPP(nat,bool,P_2,N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f38(P_2,N,K)),K)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,div_mod(nat,N),K)))| -hBOOL(hAPP(nat,bool,P_2,N))|N=hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,K),$f39(P_2,N,K))),$f38(P_2,N,K)). % 32.58/32.48 0 [] hBOOL(hAPP(nat,bool,P_2,hAPP(nat,nat,div_mod(nat,N),K)))| -hBOOL(hAPP(nat,bool,P_2,N))| -hBOOL(hAPP(nat,bool,P_2,$f38(P_2,N,K))). % 32.58/32.48 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_1),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,times_times(nat,B),hAPP(nat,nat,div_mod(nat,Q_1),C))),R_1)),hAPP(nat,nat,times_times(nat,B),C))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),standardRes(P_1,X_1))). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))|standardRes(Ma,X1)!=standardRes(Ma,X2)|hBOOL(hAPP(int,bool,zcong(X1,X2),Ma)). % 32.58/32.48 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma))|standardRes(Ma,X1)=standardRes(Ma,X2)| -hBOOL(hAPP(int,bool,zcong(X1,X2),Ma)). % 32.58/32.48 0 [] -order(T_1)|order(fun(T_2,T_1)). % 32.58/32.48 0 [] semiri456707255roduct(int). % 32.58/32.48 0 [] ordere223160158up_add(int). % 32.58/32.48 0 [] ordere236663937imp_le(int). % 32.58/32.48 0 [] linord893533164strict(int). % 32.58/32.48 0 [] linord626643107strict(int). % 32.58/32.48 0 [] linord20386208strict(int). % 32.58/32.49 0 [] ordere779506340up_add(int). % 32.58/32.49 0 [] ordere216010020id_add(int). % 32.58/32.49 0 [] linord219039673up_add(int). % 32.58/32.49 0 [] cancel146912293up_add(int). % 32.58/32.49 0 [] ring_11004092258visors(int). % 32.58/32.49 0 [] ordere453448008miring(int). % 32.58/32.49 0 [] linord581940658strict(int). % 32.58/32.49 0 [] ring_n68954251visors(int). % 32.58/32.49 0 [] ordere1490568538miring(int). % 32.58/32.49 0 [] linord1278240602ring_1(int). % 32.58/32.49 0 [] ordered_ab_group_add(int). % 32.58/32.49 0 [] cancel_semigroup_add(int). % 32.58/32.49 0 [] linordered_semiring(int). % 32.58/32.49 0 [] linordered_semidom(int). % 32.58/32.49 0 [] ab_semigroup_mult(int). % 32.58/32.49 0 [] comm_monoid_mult(int). % 32.58/32.49 0 [] ab_semigroup_add(int). % 32.58/32.49 0 [] ordered_semiring(int). % 32.58/32.49 0 [] no_zero_divisors(int). % 32.58/32.49 0 [] comm_monoid_add(int). % 32.58/32.49 0 [] linordered_ring(int). % 32.58/32.49 0 [] linordered_idom(int). % 32.58/32.49 0 [] comm_semiring_1(int). % 32.58/32.49 0 [] semiring_div(int). % 32.58/32.49 0 [] comm_semiring(int). % 32.58/32.49 0 [] number_semiring(int). % 32.58/32.49 0 [] ab_group_add(int). % 32.58/32.49 0 [] zero_ne_q_one(int). % 32.58/32.49 0 [] ordered_ring(int). % 32.58/32.49 0 [] linorder(int). % 32.58/32.49 0 [] monoid_mult(int). % 32.58/32.49 0 [] comm_ring_1(int). % 32.58/32.49 0 [] monoid_add(int). % 32.58/32.49 0 [] semiring_1(int). % 32.58/32.49 0 [] semiring_0(int). % 32.58/32.49 0 [] group_add(int). % 32.58/32.49 0 [] ring_div(int). % 32.58/32.49 0 [] mult_zero(int). % 32.58/32.49 0 [] comm_ring(int). % 32.58/32.49 0 [] order(int). % 32.58/32.49 0 [] ring_char_0(int). % 32.58/32.49 0 [] number_ring(int). % 32.58/32.49 0 [] semiring(int). % 32.58/32.49 0 [] ring_1(int). % 32.58/32.49 0 [] power(int). % 32.58/32.49 0 [] zero(int). % 32.58/32.49 0 [] plus(int). % 32.58/32.49 0 [] ring(int). % 32.58/32.49 0 [] idom(int). % 32.58/32.49 0 [] number(int). % 32.58/32.49 0 [] one(int). % 32.58/32.49 0 [] dvd(int). % 32.58/32.49 0 [] semiri456707255roduct(nat). % 32.58/32.49 0 [] ordere223160158up_add(nat). % 32.58/32.49 0 [] ordere236663937imp_le(nat). % 32.58/32.49 0 [] linord893533164strict(nat). % 32.58/32.49 0 [] linord20386208strict(nat). % 32.58/32.49 0 [] ordere779506340up_add(nat). % 32.58/32.49 0 [] ordere216010020id_add(nat). % 32.58/32.49 0 [] cancel146912293up_add(nat). % 32.58/32.49 0 [] ordere453448008miring(nat). % 32.58/32.49 0 [] ordere1490568538miring(nat). % 32.58/32.49 0 [] cancel_semigroup_add(nat). % 32.58/32.49 0 [] linordered_semiring(nat). % 32.58/32.49 0 [] linordered_semidom(nat). % 32.58/32.49 0 [] ab_semigroup_mult(nat). % 32.58/32.49 0 [] comm_monoid_mult(nat). % 32.58/32.49 0 [] ab_semigroup_add(nat). % 32.58/32.49 0 [] ordered_semiring(nat). % 32.58/32.49 0 [] no_zero_divisors(nat). % 32.58/32.49 0 [] comm_monoid_add(nat). % 32.58/32.49 0 [] comm_semiring_1(nat). % 32.58/32.49 0 [] semiring_div(nat). % 32.58/32.49 0 [] comm_semiring(nat). % 32.58/32.49 0 [] number_semiring(nat). % 32.58/32.49 0 [] zero_ne_q_one(nat). % 32.58/32.49 0 [] linorder(nat). % 32.58/32.49 0 [] monoid_mult(nat). % 32.58/32.49 0 [] monoid_add(nat). % 32.58/32.49 0 [] semiring_1(nat). % 32.58/32.49 0 [] semiring_0(nat). % 32.58/32.49 0 [] mult_zero(nat). % 32.58/32.49 0 [] order(nat). % 32.58/32.49 0 [] semiring(nat). % 32.58/32.49 0 [] power(nat). % 32.58/32.49 0 [] zero(nat). % 32.58/32.49 0 [] plus(nat). % 32.58/32.49 0 [] number(nat). % 32.58/32.49 0 [] one(nat). % 32.58/32.49 0 [] dvd(nat). % 32.58/32.49 0 [] order(bool). % 32.58/32.49 0 [] semiri456707255roduct(real). % 32.58/32.49 0 [] ordere223160158up_add(real). % 32.58/32.49 0 [] ordere236663937imp_le(real). % 32.58/32.49 0 [] linord893533164strict(real). % 32.58/32.49 0 [] linord626643107strict(real). % 32.58/32.49 0 [] linord20386208strict(real). % 32.58/32.49 0 [] ordere779506340up_add(real). % 32.58/32.49 0 [] real_normed_algebra(real). % 32.58/32.49 0 [] ordere216010020id_add(real). % 32.58/32.49 0 [] linord219039673up_add(real). % 32.58/32.49 0 [] cancel146912293up_add(real). % 32.58/32.49 0 [] ring_11004092258visors(real). % 32.58/32.49 0 [] ordere453448008miring(real). % 32.58/32.49 0 [] linord581940658strict(real). % 32.58/32.49 0 [] ring_n68954251visors(real). % 32.58/32.49 0 [] ordere1490568538miring(real). % 32.58/32.49 0 [] linord1278240602ring_1(real). % 32.58/32.49 0 [] ordered_ab_group_add(real). % 32.58/32.49 0 [] cancel_semigroup_add(real). % 32.58/32.49 0 [] linordered_semiring(real). % 32.58/32.49 0 [] linordered_semidom(real). % 32.58/32.49 0 [] ab_semigroup_mult(real). % 32.58/32.49 0 [] comm_monoid_mult(real). % 32.58/32.49 0 [] ab_semigroup_add(real). % 32.58/32.49 0 [] ordered_semiring(real). % 32.58/32.49 0 [] no_zero_divisors(real). % 32.58/32.49 0 [] comm_monoid_add(real). % 32.58/32.49 0 [] linordered_ring(real). % 32.58/32.49 0 [] linordered_idom(real). % 32.58/32.49 0 [] comm_semiring_1(real). % 32.58/32.49 0 [] comm_semiring(real). % 32.58/32.49 0 [] number_semiring(real). % 32.58/32.49 0 [] ab_group_add(real). % 32.58/32.49 0 [] zero_ne_q_one(real). % 32.58/32.49 0 [] ordered_ring(real). % 32.58/32.49 0 [] linorder(real). % 32.58/32.49 0 [] monoid_mult(real). % 32.58/32.49 0 [] comm_ring_1(real). % 32.58/32.49 0 [] monoid_add(real). % 32.58/32.49 0 [] semiring_1(real). % 32.58/32.49 0 [] semiring_0(real). % 32.58/32.49 0 [] group_add(real). % 32.58/32.49 0 [] mult_zero(real). % 32.58/32.49 0 [] comm_ring(real). % 32.58/32.49 0 [] order(real). % 32.58/32.49 0 [] ring_char_0(real). % 32.58/32.49 0 [] number_ring(real). % 32.58/32.49 0 [] semiring(real). % 32.58/32.49 0 [] ring_1(real). % 32.58/32.49 0 [] power(real). % 32.58/32.49 0 [] zero(real). % 32.58/32.49 0 [] plus(real). % 32.58/32.49 0 [] ring(real). % 32.58/32.49 0 [] idom(real). % 32.58/32.49 0 [] number(real). % 32.58/32.49 0 [] one(real). % 32.58/32.49 0 [] dvd(real). % 32.58/32.49 0 [] ti(T,ti(T,A))=ti(T,A). % 32.58/32.49 0 [] hAPP(X_a,X_c,combb(X_b,X_c,X_a,P,Q),R)=hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R)). % 32.58/32.49 0 [] hAPP(X_a,X_c,combc(X_a,X_b,X_c,P,Q),R)=hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q). % 32.58/32.49 0 [] hAPP(X_a,X_c,combs(X_a,X_b,X_c,P,Q),R)=hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R)). % 32.69/32.49 0 [] -hBOOL(P)| -hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)). % 32.69/32.49 0 [] -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(P). % 32.69/32.49 0 [] -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(Q). % 32.69/32.49 0 [] hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,Y),number_number_of(nat,bit0(bit1(pls)))))!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)). % 32.69/32.49 end_of_list. % 32.69/32.49 % 32.69/32.49 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7. % 32.69/32.49 % 32.69/32.49 This ia a non-Horn set with equality. The strategy will be % 32.69/32.49 Knuth-Bendix, ordered hyper_res, factoring, and unit % 32.69/32.49 deletion, with positive clauses in sos and nonpositive % 32.69/32.49 clauses in usable. % 32.69/32.49 % 32.69/32.49 dependent: set(knuth_bendix). % 32.69/32.49 dependent: set(anl_eq). % 32.69/32.49 dependent: set(para_from). % 32.69/32.49 dependent: set(para_into). % 32.69/32.49 dependent: clear(para_from_right). % 32.69/32.49 dependent: clear(para_into_right). % 32.69/32.49 dependent: set(para_from_vars). % 32.69/32.49 dependent: set(eq_units_both_ways). % 32.69/32.49 dependent: set(dynamic_demod_all). % 32.69/32.49 dependent: set(dynamic_demod). % 32.69/32.49 dependent: set(order_eq). % 32.69/32.49 dependent: set(back_demod). % 32.69/32.49 dependent: set(lrpo). % 32.69/32.49 dependent: set(hyper_res). % 32.69/32.49 dependent: set(unit_deletion). % 32.69/32.49 dependent: set(factor). % 32.69/32.49 % 32.69/32.49 ------------> process usable: % 32.69/32.49 ** KEPT (pick-wt=11): 1 [] -semiring_div(A)|div_mod(A,ti(A,B))=div_mod(A,B). % 32.69/32.49 ** KEPT (pick-wt=13): 2 [] -semiring_div(A)|ti(fun(A,A),div_mod(A,B))=div_mod(A,B). % 32.69/32.49 ** KEPT (pick-wt=11): 3 [] -group_add(A)|minus_minus(A,ti(A,B))=minus_minus(A,B). % 32.69/32.49 ** KEPT (pick-wt=13): 4 [] -group_add(A)|ti(fun(A,A),minus_minus(A,B))=minus_minus(A,B). % 32.69/32.49 ** KEPT (pick-wt=9): 5 [] -one(A)|ti(A,one_one(A))=one_one(A). % 32.69/32.49 ** KEPT (pick-wt=15): 6 [] -plus(A)| -linorder(A)| -dvd(A)|plus_plus(A,ti(A,B))=plus_plus(A,B). % 32.69/32.49 ** KEPT (pick-wt=17): 7 [] -plus(A)| -linorder(A)| -dvd(A)|ti(fun(A,A),plus_plus(A,B))=plus_plus(A,B). % 32.69/32.49 ** KEPT (pick-wt=11): 8 [] -monoid_add(A)|plus_plus(A,ti(A,B))=plus_plus(A,B). % 32.69/32.49 ** KEPT (pick-wt=13): 9 [] -monoid_add(A)|ti(fun(A,A),plus_plus(A,B))=plus_plus(A,B). % 32.69/32.49 ** KEPT (pick-wt=11): 10 [] -cancel_semigroup_add(A)|plus_plus(A,ti(A,B))=plus_plus(A,B). % 32.69/32.49 ** KEPT (pick-wt=13): 11 [] -cancel_semigroup_add(A)|ti(fun(A,A),plus_plus(A,B))=plus_plus(A,B). % 32.69/32.49 ** KEPT (pick-wt=11): 12 [] -ab_semigroup_add(A)|plus_plus(A,ti(A,B))=plus_plus(A,B). % 32.69/32.49 ** KEPT (pick-wt=13): 13 [] -ab_semigroup_add(A)|ti(fun(A,A),plus_plus(A,B))=plus_plus(A,B). % 32.69/32.49 ** KEPT (pick-wt=11): 14 [] -ab_semigroup_mult(A)|times_times(A,ti(A,B))=times_times(A,B). % 32.69/32.49 ** KEPT (pick-wt=13): 15 [] -ab_semigroup_mult(A)|ti(fun(A,A),times_times(A,B))=times_times(A,B). % 32.69/32.49 ** KEPT (pick-wt=11): 16 [] -power(A)|times_times(A,ti(A,B))=times_times(A,B). % 32.69/32.49 ** KEPT (pick-wt=13): 17 [] -power(A)|ti(fun(A,A),times_times(A,B))=times_times(A,B). % 32.69/32.49 ** KEPT (pick-wt=11): 18 [] -dvd(A)|times_times(A,ti(A,B))=times_times(A,B). % 32.69/32.49 ** KEPT (pick-wt=13): 19 [] -dvd(A)|ti(fun(A,A),times_times(A,B))=times_times(A,B). % 32.69/32.49 ** KEPT (pick-wt=11): 20 [] -semiring(A)|times_times(A,ti(A,B))=times_times(A,B). % 32.69/32.49 ** KEPT (pick-wt=13): 21 [] -semiring(A)|ti(fun(A,A),times_times(A,B))=times_times(A,B). % 32.69/32.49 ** KEPT (pick-wt=11): 22 [] -mult_zero(A)|times_times(A,ti(A,B))=times_times(A,B). % 32.69/32.49 ** KEPT (pick-wt=13): 23 [] -mult_zero(A)|ti(fun(A,A),times_times(A,B))=times_times(A,B). % 32.69/32.49 ** KEPT (pick-wt=11): 24 [] -no_zero_divisors(A)|times_times(A,ti(A,B))=times_times(A,B). % 32.69/32.49 ** KEPT (pick-wt=13): 25 [] -no_zero_divisors(A)|ti(fun(A,A),times_times(A,B))=times_times(A,B). % 32.69/32.49 ** KEPT (pick-wt=9): 26 [] -zero(A)|ti(A,zero_zero(A))=zero_zero(A). % 32.69/32.49 ** KEPT (pick-wt=11): 27 [] -number(A)|number_number_of(A,ti(int,B))=number_number_of(A,B). % 32.69/32.49 ** KEPT (pick-wt=11): 28 [] -number(A)|ti(A,number_number_of(A,B))=number_number_of(A,B). % 32.69/32.49 ** KEPT (pick-wt=13): 29 [] -order(A)|ti(fun(A,fun(A,bool)),ord_less(A))=ord_less(A). % 32.69/32.49 ** KEPT (pick-wt=13): 30 [] -order(A)|ti(fun(A,fun(A,bool)),ord_less_e_q(A))=ord_less_e_q(A). % 32.69/32.49 ** KEPT (pick-wt=11): 31 [] -power(A)|power_power(A,ti(A,B))=power_power(A,B). % 32.69/32.49 ** KEPT (pick-wt=13): 32 [] -power(A)|ti(fun(nat,A),power_power(A,B))=power_power(A,B). % 32.69/32.49 ** KEPT (pick-wt=13): 33 [] -dvd(A)|ti(fun(A,fun(A,bool)),dvd_dvd(A))=dvd_dvd(A). % 32.69/32.49 ** KEPT (pick-wt=6): 34 [] -hBOOL(ti(bool,A))|hBOOL(A). % 32.69/32.49 ** KEPT (pick-wt=6): 35 [] hBOOL(ti(bool,A))| -hBOOL(A). % 32.69/32.49 ** KEPT (pick-wt=51): 37 [copy,36,flip.1,flip.2] one_one(int)!=t|hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))=hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,$c2),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,$c1),number_number_of(nat,bit0(bit1(pls))))). % 32.69/32.49 ** KEPT (pick-wt=61): 39 [copy,38,flip.2] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t))|hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))=hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,$c4),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,$c3),number_number_of(nat,bit0(bit1(pls))))). % 32.69/32.49 ** KEPT (pick-wt=69): 40 [] -number_semiring(A)|hAPP(nat,A,power_power(A,hAPP(A,A,plus_plus(A,B),C)),number_number_of(nat,bit0(bit1(pls))))=hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))),hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,number_number_of(A,bit0(bit1(pls)))),B)),C)). % 32.69/32.49 ** KEPT (pick-wt=29): 41 [] -monoid_mult(A)| -number(A)|hAPP(nat,A,power_power(A,number_number_of(A,B)),number_number_of(nat,bit0(bit1(pls))))=hAPP(A,A,times_times(A,number_number_of(A,B)),number_number_of(A,B)). % 32.69/32.49 ** KEPT (pick-wt=17): 42 [] -semiring_1(A)|hAPP(nat,A,power_power(A,one_one(A)),number_number_of(nat,bit0(bit1(pls))))=one_one(A). % 32.69/32.49 ** KEPT (pick-wt=21): 43 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,B),B)=hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls)))). % 32.69/32.49 ** KEPT (pick-wt=21): 44 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))=hAPP(A,A,times_times(A,B),B). % 32.69/32.49 ** KEPT (pick-wt=39): 45 [] -comm_semiring_1(A)|hAPP(nat,A,power_power(A,B),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),C))=hAPP(A,A,times_times(A,hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),C)). % 32.69/32.49 ** KEPT (pick-wt=23): 46 [] -number_ring(A)|hAPP(A,A,plus_plus(A,one_one(A)),number_number_of(A,B))=number_number_of(A,hAPP(int,int,plus_plus(int,bit1(pls)),B)). % 32.69/32.49 ** KEPT (pick-wt=23): 47 [] -number_ring(A)|hAPP(A,A,plus_plus(A,number_number_of(A,B)),one_one(A))=number_number_of(A,hAPP(int,int,plus_plus(int,B),bit1(pls))). % 32.69/32.49 ** KEPT (pick-wt=17): 48 [] -number_ring(A)|hAPP(A,A,plus_plus(A,one_one(A)),one_one(A))=number_number_of(A,bit0(bit1(pls))). % 32.69/32.49 ** KEPT (pick-wt=26): 49 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=20): 50 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|ti(int,A)!=ti(int,B). % 32.69/32.49 ** KEPT (pick-wt=33): 51 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))|ti(int,A)=ti(int,B). % 32.69/32.49 ** KEPT (pick-wt=39): 52 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),C)). % 32.69/32.49 ** KEPT (pick-wt=33): 53 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),A))|ti(int,A)=ti(int,B). % 32.69/32.49 ** KEPT (pick-wt=29): 54 [] -comm_semiring_1(A)|hAPP(nat,A,power_power(A,hAPP(nat,A,power_power(A,B),C)),D)=hAPP(nat,A,power_power(A,B),hAPP(nat,nat,times_times(nat,C),D)). % 32.69/32.49 ** KEPT (pick-wt=14): 55 [] -comm_semiring_1(A)|hAPP(nat,A,power_power(A,B),one_one(nat))=ti(A,B). % 32.69/32.49 ** KEPT (pick-wt=38): 56 [] -number(A)| -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),number_number_of(A,C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,C)),number_number_of(A,B))). % 32.69/32.49 ** KEPT (pick-wt=38): 57 [] -number(A)| -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),number_number_of(A,C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,C)),number_number_of(A,B))). % 32.69/32.49 ** KEPT (pick-wt=34): 58 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),number_number_of(A,C)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). % 32.69/32.49 ** KEPT (pick-wt=34): 59 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),number_number_of(A,C)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). % 32.69/32.49 ** KEPT (pick-wt=34): 60 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),number_number_of(A,C)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),C)). % 32.69/32.49 ** KEPT (pick-wt=34): 61 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),number_number_of(A,C)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),C)). % 32.69/32.49 ** KEPT (pick-wt=51): 62 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),C),D))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,A),C)),hAPP(int,int,plus_plus(int,B),D))). % 32.69/32.49 ** KEPT (pick-wt=35): 63 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D))=hAPP(nat,A,power_power(A,B),hAPP(nat,nat,plus_plus(nat,C),D)). % 32.69/32.49 ** KEPT (pick-wt=28): 64 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),bit1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=28): 65 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),bit1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 Following clause subsumed by 64 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),bit1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 Following clause subsumed by 65 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),bit1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=28): 66 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),bit1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=28): 67 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),bit1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 Following clause subsumed by 66 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),bit1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 Following clause subsumed by 67 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),bit1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=13): 68 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)). % 32.69/32.49 ** KEPT (pick-wt=28): 69 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),bit0(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=28): 70 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),bit0(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 Following clause subsumed by 69 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),bit0(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 Following clause subsumed by 70 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),bit0(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=28): 71 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),bit0(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=28): 72 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),bit0(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 Following clause subsumed by 71 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),bit0(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 Following clause subsumed by 72 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),bit0(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=30): 73 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,A)),number_number_of(int,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=30): 74 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,A)),number_number_of(int,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=30): 75 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,A)),number_number_of(int,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=30): 76 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,A)),number_number_of(int,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=38): 77 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,A),C)),hAPP(int,int,plus_plus(int,B),C))). % 32.69/32.49 ** KEPT (pick-wt=38): 78 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,C),A)),hAPP(int,int,plus_plus(int,C),B))). % 32.69/32.49 ** KEPT (pick-wt=28): 79 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,A)),number_number_of(nat,B))=number_number_of(nat,B). % 32.69/32.49 ** KEPT (pick-wt=41): 80 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,A)),number_number_of(nat,B))=number_number_of(nat,A). % 32.69/32.49 ** KEPT (pick-wt=27): 81 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). % 32.69/32.49 ** KEPT (pick-wt=27): 82 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). % 32.69/32.49 ** KEPT (pick-wt=27): 83 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit1(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)). % 32.69/32.49 ** KEPT (pick-wt=27): 84 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit1(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)). % 32.69/32.49 ** KEPT (pick-wt=28): 85 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),bit0(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=28): 86 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),bit0(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 Following clause subsumed by 85 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),bit0(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 Following clause subsumed by 86 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),bit0(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=28): 87 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),bit1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=28): 88 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),bit1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 Following clause subsumed by 87 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),bit1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 Following clause subsumed by 88 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),bit1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=33): 89 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,A),one_one(int))),B)). % 32.69/32.49 ** KEPT (pick-wt=33): 90 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,A),one_one(int))),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 Following clause subsumed by 89 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,A),one_one(int))),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=33): 91 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,B),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=33): 92 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,B),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=24): 93 [] -hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,A))| -hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,B))|hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,hAPP(int,int,times_times(int,A),B))). % 32.69/32.49 ** KEPT (pick-wt=41): 94 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),E))=hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),E)). % 32.69/32.49 ** KEPT (pick-wt=41): 95 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),E))=hAPP(A,A,times_times(A,D),hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),C)),E)). % 32.69/32.49 ** KEPT (pick-wt=41): 96 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),E))=hAPP(A,A,times_times(A,B),hAPP(A,A,times_times(A,C),hAPP(A,A,times_times(A,D),E))). % 32.69/32.49 ** KEPT (pick-wt=29): 97 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),C)),D)=hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),D)),C). % 32.69/32.49 ** KEPT (pick-wt=29): 98 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),C)),D)=hAPP(A,A,times_times(A,B),hAPP(A,A,times_times(A,C),D)). % 32.69/32.49 Following clause subsumed by 98 during input processing: 0 [flip.2] -comm_semiring_1(A)|hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),C)),D)=hAPP(A,A,times_times(A,B),hAPP(A,A,times_times(A,C),D)). % 32.69/32.49 ** KEPT (pick-wt=29): 99 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,B),hAPP(A,A,times_times(A,C),D))=hAPP(A,A,times_times(A,C),hAPP(A,A,times_times(A,B),D)). % 32.69/32.49 ** KEPT (pick-wt=17): 100 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,B),C)=hAPP(A,A,times_times(A,C),B). % 32.69/32.49 ** KEPT (pick-wt=41): 101 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,D),E))=hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),E)). % 32.69/32.49 ** KEPT (pick-wt=16): 102 [] -hBOOL(hAPP(fun(A,bool),bool,member(A,B),C))|hBOOL(hAPP(A,bool,C,B)). % 32.69/32.49 ** KEPT (pick-wt=16): 103 [] hBOOL(hAPP(fun(A,bool),bool,member(A,B),C))| -hBOOL(hAPP(A,bool,C,B)). % 32.69/32.49 ** KEPT (pick-wt=29): 104 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),D)=hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),D)),C). % 32.69/32.49 ** KEPT (pick-wt=29): 105 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),D)=hAPP(A,A,plus_plus(A,B),hAPP(A,A,plus_plus(A,C),D)). % 32.69/32.49 Following clause subsumed by 105 during input processing: 0 [flip.2] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),D)=hAPP(A,A,plus_plus(A,B),hAPP(A,A,plus_plus(A,C),D)). % 32.69/32.49 ** KEPT (pick-wt=29): 106 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,B),hAPP(A,A,plus_plus(A,C),D))=hAPP(A,A,plus_plus(A,C),hAPP(A,A,plus_plus(A,B),D)). % 32.69/32.49 ** KEPT (pick-wt=17): 107 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,B),C)=hAPP(A,A,plus_plus(A,C),B). % 32.69/32.49 ** KEPT (pick-wt=18): 108 [] -number_ring(A)| -ring_char_0(A)|number_number_of(A,B)!=number_number_of(A,C)|ti(int,B)=ti(int,C). % 32.69/32.49 ** KEPT (pick-wt=18): 109 [] -number_ring(A)| -ring_char_0(A)|number_number_of(A,B)=number_number_of(A,C)|ti(int,B)!=ti(int,C). % 32.69/32.49 ** KEPT (pick-wt=16): 110 [] -number(A)|number_number_of(A,B)!=ti(A,C)|ti(A,C)=number_number_of(A,B). % 32.69/32.49 ** KEPT (pick-wt=16): 111 [] -number(A)|number_number_of(A,B)=ti(A,C)|ti(A,C)!=number_number_of(A,B). % 32.69/32.49 ** KEPT (pick-wt=12): 112 [] bit1(A)!=bit1(B)|ti(int,A)=ti(int,B). % 32.69/32.49 ** KEPT (pick-wt=12): 113 [] bit1(A)=bit1(B)|ti(int,A)!=ti(int,B). % 32.69/32.49 ** KEPT (pick-wt=12): 114 [] bit0(A)!=bit0(B)|ti(int,A)=ti(int,B). % 32.69/32.49 ** KEPT (pick-wt=12): 115 [] bit0(A)=bit0(B)|ti(int,A)!=ti(int,B). % 32.69/32.49 ** KEPT (pick-wt=27): 116 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). % 32.69/32.49 ** KEPT (pick-wt=27): 117 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). % 32.69/32.49 ** KEPT (pick-wt=28): 118 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),bit0(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=28): 119 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),bit0(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 Following clause subsumed by 118 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),bit0(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 Following clause subsumed by 119 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),bit0(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=27): 120 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). % 32.69/32.49 ** KEPT (pick-wt=27): 121 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). % 32.69/32.49 ** KEPT (pick-wt=27): 122 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit0(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). % 32.69/32.49 ** KEPT (pick-wt=27): 123 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),bit0(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). % 32.69/32.49 ** KEPT (pick-wt=27): 124 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit1(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)). % 32.69/32.49 ** KEPT (pick-wt=27): 125 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit1(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)). % 32.69/32.49 ** KEPT (pick-wt=28): 126 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),bit1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=28): 127 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),bit1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 Following clause subsumed by 126 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),bit1(B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 Following clause subsumed by 127 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),bit1(B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=27): 128 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)). % 32.69/32.49 ** KEPT (pick-wt=27): 129 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)). % 32.69/32.49 ** KEPT (pick-wt=27): 130 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit0(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)). % 32.69/32.49 ** KEPT (pick-wt=27): 131 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),bit0(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)). % 32.69/32.49 ** KEPT (pick-wt=40): 132 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,B),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|ti(int,A)=ti(int,B). % 32.69/32.49 ** KEPT (pick-wt=33): 133 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,B),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.49 ** KEPT (pick-wt=27): 134 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,B),one_one(int))))|ti(int,A)!=ti(int,B). % 32.69/32.49 ** KEPT (pick-wt=37): 135 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,B),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),C))=hAPP(nat,A,power_power(A,hAPP(nat,A,power_power(A,B),C)),number_number_of(nat,bit0(bit1(pls)))). % 32.69/32.49 ** KEPT (pick-wt=34): 136 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),one_one(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),bit1(pls))). % 32.69/32.49 ** KEPT (pick-wt=34): 137 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),one_one(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),bit1(pls))). % 32.69/32.49 ** KEPT (pick-wt=34): 138 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),number_number_of(A,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(pls)),B)). % 32.69/32.49 ** KEPT (pick-wt=34): 139 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),number_number_of(A,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(pls)),B)). % 32.69/32.49 ** KEPT (pick-wt=34): 140 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),one_one(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),bit1(pls))). % 32.69/32.49 ** KEPT (pick-wt=34): 141 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),one_one(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),bit1(pls))). % 32.69/32.49 ** KEPT (pick-wt=34): 142 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),number_number_of(A,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(pls)),B)). % 32.69/32.49 ** KEPT (pick-wt=34): 143 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),number_number_of(A,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(pls)),B)). % 32.69/32.49 ** KEPT (pick-wt=55): 144 [] -semiri456707255roduct(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),E))!=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),E)),hAPP(A,A,times_times(A,D),C))|ti(A,B)=ti(A,D)|ti(A,C)=ti(A,E). % 32.69/32.49 ** KEPT (pick-wt=48): 145 [] -semiri456707255roduct(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),E))=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),E)),hAPP(A,A,times_times(A,D),C))|ti(A,B)!=ti(A,D). % 32.69/32.49 ** KEPT (pick-wt=48): 146 [] -semiri456707255roduct(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),E))=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),E)),hAPP(A,A,times_times(A,D),C))|ti(A,C)!=ti(A,E). % 32.69/32.49 ** KEPT (pick-wt=35): 147 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,D),C))=hAPP(A,A,times_times(A,hAPP(A,A,plus_plus(A,B),D)),C). % 32.69/32.49 ** KEPT (pick-wt=35): 148 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,hAPP(A,A,plus_plus(A,B),C)),D)=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),D)). % 32.69/32.49 Following clause subsumed by 144 during input processing: 0 [] -semiri456707255roduct(A)|ti(A,B)=ti(A,C)|ti(A,D)=ti(A,E)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),E))!=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),E)),hAPP(A,A,times_times(A,C),D)). % 32.69/32.49 Following clause subsumed by 145 during input processing: 0 [] -semiri456707255roduct(A)|ti(A,B)!=ti(A,C)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),D)),hAPP(A,A,times_times(A,C),E))=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),E)),hAPP(A,A,times_times(A,C),D)). % 32.69/32.49 Following clause subsumed by 146 during input processing: 0 [] -semiri456707255roduct(A)|ti(A,B)!=ti(A,C)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,D),B)),hAPP(A,A,times_times(A,E),C))=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,D),C)),hAPP(A,A,times_times(A,E),B)). % 32.69/32.49 ** KEPT (pick-wt=35): 150 [copy,149,flip.2] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),hAPP(A,A,times_times(A,B),D))=hAPP(A,A,times_times(A,B),hAPP(A,A,plus_plus(A,C),D)). % 32.69/32.49 ** KEPT (pick-wt=14): 151 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,B),one_one(A))=ti(A,B). % 32.69/32.49 ** KEPT (pick-wt=14): 152 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,one_one(A)),B)=ti(A,B). % 32.69/32.49 ** KEPT (pick-wt=35): 153 [] -comm_semiring_1(A)|hAPP(nat,A,power_power(A,hAPP(A,A,times_times(A,B),C)),D)=hAPP(A,A,times_times(A,hAPP(nat,A,power_power(A,B),D)),hAPP(nat,A,power_power(A,C),D)). % 32.69/32.49 ** KEPT (pick-wt=4): 154 [] bit1(A)!=pls. % 32.69/32.49 Following clause subsumed by 154 during input processing: 0 [flip.1] bit1(A)!=pls. % 32.69/32.49 ** KEPT (pick-wt=5): 155 [] bit1(A)!=bit0(B). % 32.69/32.49 ** KEPT (pick-wt=5): 156 [] bit0(A)!=bit1(B). % 32.69/32.49 ** KEPT (pick-wt=9): 157 [] bit0(A)!=pls|ti(int,A)=pls. % 32.69/32.49 ** KEPT (pick-wt=9): 158 [] bit0(A)=pls|ti(int,A)!=pls. % 32.69/32.49 Following clause subsumed by 157 during input processing: 0 [flip.1,flip.2] bit0(A)!=pls|ti(int,A)=pls. % 32.69/32.49 Following clause subsumed by 158 during input processing: 0 [flip.1,flip.2] bit0(A)=pls|ti(int,A)!=pls. % 32.69/32.49 ** KEPT (pick-wt=49): 159 [] -number_semiring(A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),C))|hAPP(A,A,times_times(A,number_number_of(A,B)),number_number_of(A,C))=number_number_of(A,hAPP(int,int,times_times(int,B),C)). % 32.69/32.49 ** KEPT (pick-wt=49): 160 [] -number_semiring(A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),C))|hAPP(A,A,plus_plus(A,number_number_of(A,B)),number_number_of(A,C))=number_number_of(A,hAPP(int,int,plus_plus(int,B),C)). % 32.69/32.49 ** KEPT (pick-wt=43): 161 [] -number(A)| -semiring(A)|hAPP(A,A,times_times(A,hAPP(A,A,plus_plus(A,B),C)),number_number_of(A,D))=hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),number_number_of(A,D))),hAPP(A,A,times_times(A,C),number_number_of(A,D))). % 32.69/32.49 ** KEPT (pick-wt=43): 163 [copy,162,flip.3] -number(A)| -semiring(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,number_number_of(A,B)),C)),hAPP(A,A,times_times(A,number_number_of(A,B)),D))=hAPP(A,A,times_times(A,number_number_of(A,B)),hAPP(A,A,plus_plus(A,C),D)). % 32.69/32.49 ** KEPT (pick-wt=30): 164 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),C)),C)=hAPP(A,A,times_times(A,hAPP(A,A,plus_plus(A,B),one_one(A))),C). % 32.69/32.49 ** KEPT (pick-wt=30): 165 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,B),hAPP(A,A,times_times(A,C),B))=hAPP(A,A,times_times(A,hAPP(A,A,plus_plus(A,C),one_one(A))),B). % 32.69/32.49 ** KEPT (pick-wt=25): 166 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,B),B)=hAPP(A,A,times_times(A,hAPP(A,A,plus_plus(A,one_one(A)),one_one(A))),B). % 32.69/32.49 ** KEPT (pick-wt=15): 168 [copy,167,flip.2] -number_ring(A)|ti(A,B)=hAPP(A,A,plus_plus(A,number_number_of(A,pls)),B). % 32.69/32.49 ** KEPT (pick-wt=15): 170 [copy,169,flip.2] -number_ring(A)|ti(A,B)=hAPP(A,A,plus_plus(A,B),number_number_of(A,pls)). % 32.69/32.49 ** KEPT (pick-wt=35): 172 [copy,171,flip.2] -number_ring(A)|hAPP(A,A,times_times(A,number_number_of(A,hAPP(int,int,times_times(int,B),C))),D)=hAPP(A,A,times_times(A,number_number_of(A,B)),hAPP(A,A,times_times(A,number_number_of(A,C)),D)). % 32.69/32.49 ** KEPT (pick-wt=23): 173 [] -number_ring(A)|hAPP(A,A,times_times(A,number_number_of(A,B)),number_number_of(A,C))=number_number_of(A,hAPP(int,int,times_times(int,B),C)). % 32.69/32.49 ** KEPT (pick-wt=23): 174 [] -number_ring(A)|number_number_of(A,hAPP(int,int,times_times(int,B),C))=hAPP(A,A,times_times(A,number_number_of(A,B)),number_number_of(A,C)). % 32.69/32.49 ** KEPT (pick-wt=35): 176 [copy,175,flip.2] -number_ring(A)|hAPP(A,A,plus_plus(A,number_number_of(A,hAPP(int,int,plus_plus(int,B),C))),D)=hAPP(A,A,plus_plus(A,number_number_of(A,B)),hAPP(A,A,plus_plus(A,number_number_of(A,C)),D)). % 32.69/32.49 ** KEPT (pick-wt=23): 177 [] -number_ring(A)|hAPP(A,A,plus_plus(A,number_number_of(A,B)),number_number_of(A,C))=number_number_of(A,hAPP(int,int,plus_plus(int,B),C)). % 32.69/32.49 ** KEPT (pick-wt=23): 178 [] -number_ring(A)|number_number_of(A,hAPP(int,int,plus_plus(int,B),C))=hAPP(A,A,plus_plus(A,number_number_of(A,B)),number_number_of(A,C)). % 32.69/32.49 ** KEPT (pick-wt=25): 179 [] -number_ring(A)|number_number_of(A,bit1(B))=hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,one_one(A)),number_number_of(A,B))),number_number_of(A,B)). % 32.69/32.49 ** KEPT (pick-wt=16): 180 [] -number_ring(A)|hAPP(A,A,times_times(A,number_number_of(A,bit1(pls))),B)=ti(A,B). % 32.69/32.49 ** KEPT (pick-wt=16): 181 [] -number_ring(A)|hAPP(A,A,times_times(A,B),number_number_of(A,bit1(pls)))=ti(A,B). % 32.69/32.49 ** KEPT (pick-wt=9): 183 [copy,182,flip.2] -number_semiring(A)|one_one(A)=number_number_of(A,bit1(pls)). % 32.69/32.49 ** KEPT (pick-wt=9): 185 [copy,184,flip.2] -number_ring(A)|one_one(A)=number_number_of(A,bit1(pls)). % 32.69/32.49 Following clause subsumed by 185 during input processing: 0 [] -number_ring(A)|one_one(A)=number_number_of(A,bit1(pls)). % 32.69/32.49 ** KEPT (pick-wt=24): 186 [] -number_ring(A)|hAPP(A,A,times_times(A,hAPP(A,A,plus_plus(A,one_one(A)),one_one(A))),number_number_of(A,B))=number_number_of(A,bit0(B)). % 32.69/32.49 ** KEPT (pick-wt=27): 187 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,bit1(bit1(pls))))=hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,B),B)),B). % 32.69/32.49 ** KEPT (pick-wt=21): 188 [] -number_semiring(A)|hAPP(A,A,times_times(A,number_number_of(A,bit0(bit1(pls)))),B)=hAPP(A,A,plus_plus(A,B),B). % 32.69/32.49 ** KEPT (pick-wt=21): 189 [] -number_ring(A)|hAPP(A,A,times_times(A,number_number_of(A,bit0(bit1(pls)))),B)=hAPP(A,A,plus_plus(A,B),B). % 32.69/32.49 ** KEPT (pick-wt=21): 190 [] -number_semiring(A)|hAPP(A,A,times_times(A,B),number_number_of(A,bit0(bit1(pls))))=hAPP(A,A,plus_plus(A,B),B). % 32.69/32.49 ** KEPT (pick-wt=21): 191 [] -number_ring(A)|hAPP(A,A,times_times(A,B),number_number_of(A,bit0(bit1(pls))))=hAPP(A,A,plus_plus(A,B),B). % 32.69/32.49 ** KEPT (pick-wt=17): 192 [] -number_semiring(A)|hAPP(A,A,plus_plus(A,one_one(A)),one_one(A))=number_number_of(A,bit0(bit1(pls))). % 32.69/32.49 ** KEPT (pick-wt=42): 193 [] -hBOOL(hAPP(int,bool,zprime,A))|ti(int,A)=number_number_of(int,bit0(bit1(pls)))|ti(int,A)=number_number_of(int,bit1(bit1(pls)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,bit1(bit0(bit1(pls))))),A)). % 32.69/32.49 ** KEPT (pick-wt=47): 194 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),C)),hAPP(A,A,times_times(A,B),hAPP(nat,A,power_power(A,B),C)))). % 32.69/32.49 ** KEPT (pick-wt=42): 195 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,times_times(A,B),hAPP(nat,A,power_power(A,B),C)))). % 32.69/32.49 ** KEPT (pick-wt=54): 196 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),D)). % 32.69/32.49 Following clause subsumed by 196 during input processing: 0 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),D)). % 32.69/32.50 ** KEPT (pick-wt=54): 197 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),D)). % 32.69/32.50 ** KEPT (pick-wt=78): 198 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))| -hBOOL(hAPP(int,bool,zcong(s1,A),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))|ti(int,A)=ti(int,$c6). % 32.69/32.50 ** KEPT (pick-wt=24): 199 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),C)!=zero_zero(A)|ti(A,B)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=22): 200 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),C)!=zero_zero(A)|C!=zero_zero(nat). % 32.69/32.50 ** KEPT (pick-wt=28): 201 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),C)=zero_zero(A)|ti(A,B)!=zero_zero(A)|C=zero_zero(nat). % 32.69/32.50 ** KEPT (pick-wt=40): 202 [] -comm_semiring_1(A)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,power_power(A,D),B)),hAPP(nat,A,power_power(A,D),C))). % 32.69/32.50 ** KEPT (pick-wt=53): 203 [] -comm_semiring_1(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),D),E))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,power_power(A,B),D)),hAPP(nat,A,power_power(A,C),E))). % 32.69/32.50 ** KEPT (pick-wt=53): 204 [] -comm_semiring_1(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,power_power(A,B),C)),D))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),E),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,power_power(A,B),E)),D)). % 32.69/32.50 ** KEPT (pick-wt=66): 205 [] -linordered_semidom(A)|hAPP(nat,A,power_power(A,B),C)!=hAPP(nat,A,power_power(A,D),C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),D))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C))|ti(A,B)=ti(A,D). % 32.69/32.50 ** KEPT (pick-wt=40): 206 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A)). % 32.69/32.50 ** KEPT (pick-wt=61): 207 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A))|ti(int,A)=ti(int,B). % 32.69/32.50 ** KEPT (pick-wt=44): 208 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,times_times(int,A),B)),hAPP(int,int,times_times(int,A),C)))|ti(int,A)=zero_zero(int)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)). % 32.69/32.50 ** KEPT (pick-wt=40): 209 [] -comm_semiring_1(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,power_power(A,B),D)),hAPP(nat,A,power_power(A,C),D))). % 32.69/32.50 ** KEPT (pick-wt=18): 210 [] -ring_11004092258visors(A)|ti(A,B)=zero_zero(A)|hAPP(nat,A,power_power(A,B),C)!=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=19): 211 [] -power(A)| -semiring_0(A)|B!=zero_zero(nat)|hAPP(nat,A,power_power(A,zero_zero(A)),B)=one_one(A). % 32.69/32.50 ** KEPT (pick-wt=19): 212 [] -power(A)| -semiring_0(A)|B=zero_zero(nat)|hAPP(nat,A,power_power(A,zero_zero(A)),B)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=40): 213 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.50 ** KEPT (pick-wt=68): 214 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),D)),hAPP(nat,A,power_power(A,C),D))). % 32.69/32.50 ** KEPT (pick-wt=13): 215 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,zero_zero(A)),B)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=13): 216 [] -comm_semiring_1(A)|hAPP(A,A,times_times(A,B),zero_zero(A))=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=14): 217 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,zero_zero(A)),B)=ti(A,B). % 32.69/32.50 ** KEPT (pick-wt=14): 218 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,B),zero_zero(A))=ti(A,B). % 32.69/32.50 ** KEPT (pick-wt=19): 219 [] -semiri456707255roduct(A)|ti(A,B)!=hAPP(A,A,plus_plus(A,B),C)|ti(A,C)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=19): 220 [] -semiri456707255roduct(A)|ti(A,B)=hAPP(A,A,plus_plus(A,B),C)|ti(A,C)!=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=18): 221 [] -linord219039673up_add(A)|hAPP(A,A,plus_plus(A,B),B)!=zero_zero(A)|ti(A,B)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=18): 222 [] -linord219039673up_add(A)|hAPP(A,A,plus_plus(A,B),B)=zero_zero(A)|ti(A,B)!=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=5): 223 [] zero_zero(int)!=one_one(int). % 32.69/32.50 ** KEPT (pick-wt=36): 224 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),C))). % 32.69/32.50 ** KEPT (pick-wt=54): 225 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,B),D)),hAPP(nat,A,power_power(A,C),D))). % 32.69/32.50 ** KEPT (pick-wt=36): 226 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),C))). % 32.69/32.50 ** KEPT (pick-wt=36): 227 [] -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,A),B),one_one(int)),C))|hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,A),hAPP(nat,nat,times_times(nat,B),D)),one_one(int)),C)). % 32.69/32.50 ** KEPT (pick-wt=38): 228 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,plus_plus(int,B),hAPP(int,int,times_times(int,A),C))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). % 32.69/32.50 ** KEPT (pick-wt=38): 229 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,plus_plus(int,B),hAPP(int,int,times_times(int,A),C))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). % 32.69/32.50 ** KEPT (pick-wt=63): 230 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,plus_plus(int,C),D)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,C),hAPP(int,int,times_times(int,E),B))),D))). % 32.69/32.50 ** KEPT (pick-wt=63): 231 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,plus_plus(int,C),D)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,C),hAPP(int,int,times_times(int,E),B))),D))). % 32.69/32.50 ** KEPT (pick-wt=54): 232 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,D),C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)). % 32.69/32.50 ** KEPT (pick-wt=68): 233 [] -linordered_semidom(A)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),D))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),one_one(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,D),C)),hAPP(nat,A,power_power(A,D),B))). % 32.69/32.50 ** KEPT (pick-wt=68): 234 [] -linordered_semidom(A)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),one_one(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,D),C)),hAPP(nat,A,power_power(A,D),B))). % 32.69/32.50 ** KEPT (pick-wt=36): 235 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),B)),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))). % 32.69/32.50 ** KEPT (pick-wt=36): 236 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),B)),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))). % 32.69/32.50 ** KEPT (pick-wt=30): 237 [] -linord581940658strict(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))!=zero_zero(A)|ti(A,B)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=30): 238 [] -linord581940658strict(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))!=zero_zero(A)|ti(A,C)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=36): 239 [] -linord581940658strict(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))=zero_zero(A)|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=49): 240 [] -semiri456707255roduct(A)|ti(A,B)=zero_zero(A)|ti(A,C)!=ti(A,D)|ti(A,E)=ti(A,F)|hAPP(A,A,plus_plus(A,C),hAPP(A,A,times_times(A,B),E))!=hAPP(A,A,plus_plus(A,D),hAPP(A,A,times_times(A,B),F)). % 32.69/32.50 ** KEPT (pick-wt=38): 241 [] -hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(nat,int,power_power(int,B),C)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). % 32.69/32.50 ** KEPT (pick-wt=8): 242 [] -number_ring(A)|zero_zero(A)=number_number_of(A,pls). % 32.69/32.50 Following clause subsumed by 242 during input processing: 0 [flip.2] -number_ring(A)|zero_zero(A)=number_number_of(A,pls). % 32.69/32.50 ** KEPT (pick-wt=8): 244 [copy,243,flip.2] -number_semiring(A)|zero_zero(A)=number_number_of(A,pls). % 32.69/32.50 ** KEPT (pick-wt=29): 245 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). % 32.69/32.50 ** KEPT (pick-wt=29): 246 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). % 32.69/32.50 ** KEPT (pick-wt=14): 247 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))). % 32.69/32.50 ** KEPT (pick-wt=29): 248 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). % 32.69/32.50 ** KEPT (pick-wt=29): 249 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). % 32.69/32.50 ** KEPT (pick-wt=48): 250 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A),B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)). % 32.69/32.50 ** KEPT (pick-wt=52): 251 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,C),A)),hAPP(int,int,times_times(int,C),B))). % 32.69/32.50 ** KEPT (pick-wt=17): 252 [] hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),A)),A)!=zero_zero(int). % 32.69/32.50 ** KEPT (pick-wt=61): 253 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,times_times(A,B),hAPP(nat,A,power_power(A,B),C))),hAPP(nat,A,power_power(A,B),C))). % 32.69/32.50 ** KEPT (pick-wt=63): 254 [] -hBOOL(hAPP(int,bool,zprime,A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A),C)),hAPP(int,int,times_times(int,B),D)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A),C)),D)). % 32.69/32.50 ** KEPT (pick-wt=63): 255 [] -hBOOL(hAPP(int,bool,zprime,A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A),C)),hAPP(int,int,times_times(int,D),B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,power_power(int,A),C)),D)). % 32.69/32.50 ** KEPT (pick-wt=34): 256 [] -linordered_ring(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C)))). % 32.69/32.50 ** KEPT (pick-wt=40): 257 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))),zero_zero(A)))|ti(A,B)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=40): 258 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))),zero_zero(A)))|ti(A,C)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=46): 259 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))),zero_zero(A)))|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=43): 260 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,A)),number_number_of(nat,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)). % 32.69/32.50 ** KEPT (pick-wt=30): 261 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,A)),number_number_of(nat,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.50 ** KEPT (pick-wt=43): 262 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,A)),number_number_of(nat,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.50 ** KEPT (pick-wt=34): 263 [] -linordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))),zero_zero(A))). % 32.69/32.50 ** KEPT (pick-wt=46): 264 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))))|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=40): 265 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))))|ti(A,B)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=40): 266 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,B),B)),hAPP(A,A,times_times(A,C),C))))|ti(A,C)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=43): 267 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,A)),number_number_of(nat,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)). % 32.69/32.50 ** KEPT (pick-wt=30): 268 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,A)),number_number_of(nat,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.50 ** KEPT (pick-wt=30): 269 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,A)),number_number_of(nat,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)). % 32.69/32.50 ** KEPT (pick-wt=25): 270 [] -number_ring(A)|number_number_of(A,bit0(B))=hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,zero_zero(A)),number_number_of(A,B))),number_number_of(A,B)). % 32.69/32.50 ** KEPT (pick-wt=14): 271 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,B),one_one(nat))=ti(A,B). % 32.69/32.50 ** KEPT (pick-wt=28): 272 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). % 32.69/32.50 ** KEPT (pick-wt=28): 273 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). % 32.69/32.50 ** KEPT (pick-wt=30): 274 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hAPP(int,int,times_times(int,A),B)!=one_one(int)|ti(int,A)=one_one(int). % 32.69/32.50 ** KEPT (pick-wt=30): 275 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hAPP(int,int,times_times(int,A),B)!=one_one(int)|ti(int,B)=one_one(int). % 32.69/32.50 ** KEPT (pick-wt=36): 276 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hAPP(int,int,times_times(int,A),B)=one_one(int)|ti(int,A)!=one_one(int)|ti(int,B)!=one_one(int). % 32.69/32.50 ** KEPT (pick-wt=41): 277 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),A)),A)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). % 32.69/32.50 ** KEPT (pick-wt=41): 278 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),A)),A)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). % 32.69/32.50 ** KEPT (pick-wt=33): 279 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),number_number_of(A,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)). % 32.69/32.50 ** KEPT (pick-wt=33): 280 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),number_number_of(A,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)). % 32.69/32.50 ** KEPT (pick-wt=33): 281 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),zero_zero(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)). % 32.69/32.50 ** KEPT (pick-wt=33): 282 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),zero_zero(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)). % 32.69/32.50 ** KEPT (pick-wt=33): 283 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),number_number_of(A,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),B)). % 32.69/32.50 ** KEPT (pick-wt=33): 284 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),number_number_of(A,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),B)). % 32.69/32.50 ** KEPT (pick-wt=33): 285 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),zero_zero(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),pls)). % 32.69/32.50 ** KEPT (pick-wt=33): 286 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),zero_zero(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),pls)). % 32.69/32.50 ** KEPT (pick-wt=35): 287 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),A))). % 32.69/32.50 ** KEPT (pick-wt=17): 288 [] -semiring_1(A)|hAPP(nat,A,power_power(A,zero_zero(A)),number_number_of(nat,bit0(bit1(pls))))=zero_zero(A). % 32.69/32.50 Following clause subsumed by 210 during input processing: 0 [] -ring_11004092258visors(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))!=zero_zero(A)|ti(A,B)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=22): 289 [] -ring_11004092258visors(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))=zero_zero(A)|ti(A,B)!=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=26): 290 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls)))))). % 32.69/32.50 ** KEPT (pick-wt=62): 291 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls))))))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C)). % 32.69/32.50 ** KEPT (pick-wt=60): 292 [] -linordered_semidom(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))!=hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls))))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|ti(A,B)=ti(A,C). % 32.69/32.50 ** KEPT (pick-wt=26): 293 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),zero_zero(A))). % 32.69/32.50 ** KEPT (pick-wt=32): 294 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))))|ti(A,B)!=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=32): 295 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))))|ti(A,B)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=38): 296 [] -linordered_idom(A)|hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(A)|ti(A,B)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=38): 297 [] -linordered_idom(A)|hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(A)|ti(A,C)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=44): 298 [] -linordered_idom(A)|hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))=zero_zero(A)|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=29): 299 [] -monoid_mult(A)|hAPP(A,A,times_times(A,hAPP(nat,A,power_power(A,B),C)),B)=hAPP(A,A,times_times(A,B),hAPP(nat,A,power_power(A,B),C)). % 32.69/32.50 ** KEPT (pick-wt=35): 300 [] -comm_monoid_mult(A)|hAPP(nat,A,power_power(A,hAPP(A,A,times_times(A,B),C)),D)=hAPP(A,A,times_times(A,hAPP(nat,A,power_power(A,B),D)),hAPP(nat,A,power_power(A,C),D)). % 32.69/32.50 ** KEPT (pick-wt=35): 301 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,B),hAPP(nat,nat,plus_plus(nat,C),D))=hAPP(A,A,times_times(A,hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)). % 32.69/32.50 ** KEPT (pick-wt=13): 302 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,one_one(A)),B)=one_one(A). % 32.69/32.50 ** KEPT (pick-wt=29): 303 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,B),hAPP(nat,nat,times_times(nat,C),D))=hAPP(nat,A,power_power(A,hAPP(nat,A,power_power(A,B),C)),D). % 32.69/32.50 Following clause subsumed by 232 during input processing: 0 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls))))))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)). % 32.69/32.50 ** KEPT (pick-wt=42): 304 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls))))))). % 32.69/32.50 ** KEPT (pick-wt=48): 305 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(A)))|ti(A,B)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=48): 306 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(A)))|ti(A,C)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=54): 307 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(A)))|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=42): 308 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))),zero_zero(A))). % 32.69/32.50 ** KEPT (pick-wt=54): 309 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))))|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=48): 310 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))))|ti(A,B)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=48): 311 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))))|ti(A,C)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=32): 312 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),C)))). % 32.69/32.50 ** KEPT (pick-wt=36): 313 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),hAPP(nat,A,power_power(A,B),C))). % 32.69/32.50 ** KEPT (pick-wt=54): 314 [] -linordered_semidom(A)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,D),B)),hAPP(nat,A,power_power(A,D),C))). % 32.69/32.50 ** KEPT (pick-wt=34): 315 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))|hAPP(nat,A,power_power(A,B),C)!=hAPP(nat,A,power_power(A,B),D)|C=D. % 32.69/32.50 ** KEPT (pick-wt=34): 316 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))|hAPP(nat,A,power_power(A,B),C)=hAPP(nat,A,power_power(A,B),D)|C!=D. % 32.69/32.50 ** KEPT (pick-wt=54): 317 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)). % 32.69/32.50 ** KEPT (pick-wt=54): 318 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)). % 32.69/32.50 Following clause subsumed by 317 during input processing: 0 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)). % 32.69/32.50 Following clause subsumed by 318 during input processing: 0 [] -linordered_semidom(A)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,D),B)),hAPP(nat,A,power_power(A,D),C))). % 32.69/32.50 ** KEPT (pick-wt=40): 319 [] hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B))| -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,C),number_number_of(nat,bit0(bit1(pls)))),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)). % 32.69/32.50 ** KEPT (pick-wt=43): 320 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),number_number_of(int,bit0(bit1(pls)))))|ti(int,A)=zero_zero(int)|ti(int,A)=one_one(int). % 32.69/32.50 ** KEPT (pick-wt=38): 321 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,B),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),C))),zero_zero(A)))|ti(A,B)=zero_zero(A). % 32.69/32.50 ** KEPT (pick-wt=20): 322 [] -hBOOL(hAPP(int,bool,zprime,A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)). % 32.69/32.50 ** KEPT (pick-wt=46): 323 [] -hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A))|ti(int,B)=one_one(int)|ti(int,B)=ti(int,A). % 32.69/32.50 ** KEPT (pick-wt=35): 324 [] hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f1(A))). % 32.69/32.50 ** KEPT (pick-wt=34): 325 [] hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),$f1(A)),A)). % 32.69/32.50 ** KEPT (pick-wt=27): 326 [] hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A))|ti(int,$f1(A))!=one_one(int). % 32.69/32.50 ** KEPT (pick-wt=28): 327 [] hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A))|ti(int,$f1(A))!=ti(int,A). % 32.69/32.50 ** KEPT (pick-wt=59): 329 [copy,328,flip.2] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hAPP(int,int,plus_plus(int,B),hAPP(int,int,times_times(int,A),C))!=ti(int,A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),C),one_one(int))). % 32.69/32.50 ** KEPT (pick-wt=58): 331 [copy,330,flip.2] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hAPP(int,int,plus_plus(int,B),hAPP(int,int,times_times(int,A),C))!=ti(int,A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),C)). % 32.69/32.50 ** KEPT (pick-wt=38): 332 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))|B=zero_zero(nat). % 32.69/32.50 ** KEPT (pick-wt=34): 333 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). % 32.69/32.50 ** KEPT (pick-wt=24): 334 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))|B!=zero_zero(nat). % 32.69/32.50 Following clause subsumed by 332 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))|B=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). % 32.69/32.50 Following clause subsumed by 334 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))|B!=zero_zero(nat). % 32.69/32.50 Following clause subsumed by 333 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). % 32.69/32.50 Following clause subsumed by 332 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),number_number_of(nat,B))))|number_number_of(nat,B)=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). % 32.69/32.50 Following clause subsumed by 334 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),number_number_of(nat,B))))|number_number_of(nat,B)!=zero_zero(nat). % 32.69/32.50 Following clause subsumed by 333 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),number_number_of(nat,B))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). % 32.69/32.50 ** KEPT (pick-wt=52): 335 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,A),B)),hAPP(nat,nat,power_power(nat,A),C)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). % 32.69/32.50 ** KEPT (pick-wt=9): 336 [] bit1(A)!=min|ti(int,A)=min. % 32.69/32.50 ** KEPT (pick-wt=9): 337 [] bit1(A)=min|ti(int,A)!=min. % 32.69/32.50 Following clause subsumed by 336 during input processing: 0 [flip.1,flip.2] bit1(A)!=min|ti(int,A)=min. % 32.69/32.50 Following clause subsumed by 337 during input processing: 0 [flip.1,flip.2] bit1(A)=min|ti(int,A)!=min. % 32.69/32.50 ** KEPT (pick-wt=3): 338 [] pls!=min. % 32.69/32.50 Following clause subsumed by 338 during input processing: 0 [flip.1] pls!=min. % 32.69/32.50 ** KEPT (pick-wt=4): 339 [] bit0(A)!=min. % 32.69/32.50 Following clause subsumed by 339 during input processing: 0 [flip.1] bit0(A)!=min. % 32.69/32.50 ** KEPT (pick-wt=13): 340 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),min)). % 32.69/32.50 ** KEPT (pick-wt=24): 341 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,times_times(real,A),A)))|A!=zero_zero(real). % 32.69/32.50 ** KEPT (pick-wt=27): 342 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),min))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),min)). % 32.69/32.50 ** KEPT (pick-wt=27): 343 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit1(A)),min))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),min)). % 32.69/32.50 ** KEPT (pick-wt=27): 344 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit1(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),A)). % 32.69/32.50 ** KEPT (pick-wt=27): 345 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit1(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),A)). % 32.69/32.50 ** KEPT (pick-wt=13): 346 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),min)). % 32.69/32.50 ** KEPT (pick-wt=27): 347 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit0(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),A)). % 32.69/32.50 ** KEPT (pick-wt=27): 348 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),bit0(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),A)). % 32.69/32.50 ** KEPT (pick-wt=27): 349 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),min))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),min)). % 32.69/32.50 ** KEPT (pick-wt=27): 350 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit1(A)),min))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),min)). % 32.69/32.50 ** KEPT (pick-wt=27): 351 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit1(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),A)). % 32.69/32.50 ** KEPT (pick-wt=27): 352 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit1(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),A)). % 32.69/32.50 ** KEPT (pick-wt=13): 353 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),min)). % 32.69/32.50 ** KEPT (pick-wt=27): 354 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),min))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),min)). % 32.69/32.50 ** KEPT (pick-wt=27): 355 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),bit0(A)),min))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),min)). % 32.69/32.50 ** KEPT (pick-wt=7): 356 [] number_number_of(int,pls)!=number_number_of(int,min). % 32.69/32.50 ** KEPT (pick-wt=52): 357 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,power_power(nat,A),B)),hAPP(nat,nat,power_power(nat,A),C)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C)). % 32.69/32.50 ** KEPT (pick-wt=13): 358 [] -comm_semiring_1(A)|hAPP(nat,A,power_power(A,B),zero_zero(nat))=one_one(A). % 32.69/32.50 ** KEPT (pick-wt=13): 359 [] -power(A)|hAPP(nat,A,power_power(A,B),zero_zero(nat))=one_one(A). % 32.69/32.50 ** KEPT (pick-wt=27): 360 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit0(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),A)). % 32.69/32.50 ** KEPT (pick-wt=27): 361 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),min),bit0(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),A)). % 32.69/32.50 ** KEPT (pick-wt=27): 362 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),min))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),min)). % 32.69/32.50 ** KEPT (pick-wt=27): 363 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),bit0(A)),min))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),min)). % 32.69/32.50 ** KEPT (pick-wt=23): 364 [] hAPP(int,int,times_times(int,A),B)!=one_one(int)|ti(int,A)=one_one(int)|ti(int,A)=number_number_of(int,min). % 32.69/32.50 Following clause subsumed by 364 during input processing: 0 [] hAPP(int,int,times_times(int,A),B)!=one_one(int)|ti(int,A)=one_one(int)|ti(int,A)=number_number_of(int,min). % 32.69/32.50 ** KEPT (pick-wt=23): 365 [] hAPP(int,int,times_times(int,A),B)!=one_one(int)|ti(int,A)=one_one(int)|ti(int,B)=number_number_of(int,min). % 32.69/32.50 ** KEPT (pick-wt=23): 366 [] hAPP(int,int,times_times(int,A),B)!=one_one(int)|ti(int,B)=one_one(int)|ti(int,A)=number_number_of(int,min). % 32.69/32.50 ** KEPT (pick-wt=23): 367 [] hAPP(int,int,times_times(int,A),B)!=one_one(int)|ti(int,B)=one_one(int)|ti(int,B)=number_number_of(int,min). % 32.69/32.50 ** KEPT (pick-wt=22): 368 [] hAPP(int,int,times_times(int,A),B)=one_one(int)|ti(int,A)!=one_one(int)|ti(int,B)!=one_one(int). % 32.69/32.50 ** KEPT (pick-wt=24): 369 [] hAPP(int,int,times_times(int,A),B)=one_one(int)|ti(int,A)!=number_number_of(int,min)|ti(int,B)!=number_number_of(int,min). % 32.69/32.50 ** KEPT (pick-wt=50): 370 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(nat,A,power_power(A,B),C))). % 32.69/32.50 ** KEPT (pick-wt=35): 371 [] -comm_semiring_1(A)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),hAPP(nat,A,power_power(A,C),B))). % 32.69/32.50 ** KEPT (pick-wt=27): 372 [] -comm_semiring_1(A)|ti(A,B)!=one_one(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(nat,A,power_power(A,B),C))). % 32.69/32.50 ** KEPT (pick-wt=29): 373 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). % 32.69/32.50 ** KEPT (pick-wt=29): 374 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). % 32.69/32.50 ** KEPT (pick-wt=19): 375 [] number_number_of(nat,A)!=zero_zero(nat)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)). % 32.69/32.50 ** KEPT (pick-wt=19): 376 [] number_number_of(nat,A)=zero_zero(nat)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)). % 32.69/32.50 ** KEPT (pick-wt=19): 377 [] zero_zero(nat)!=number_number_of(nat,A)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)). % 32.69/32.51 ** KEPT (pick-wt=19): 378 [] zero_zero(nat)=number_number_of(nat,A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)). % 32.69/32.51 ** KEPT (pick-wt=16): 379 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|hBOOL(hAPP(int,bool,zcong(B,A),C)). % 32.69/32.51 Following clause subsumed by 379 during input processing: 0 [] hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,zcong(B,A),C)). % 32.69/32.51 ** KEPT (pick-wt=24): 380 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,zcong(B,D),C))|hBOOL(hAPP(int,bool,zcong(A,D),C)). % 32.69/32.51 ** KEPT (pick-wt=33): 381 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls))|hAPP(nat,nat,times_times(nat,number_number_of(nat,A)),hAPP(nat,nat,times_times(nat,number_number_of(nat,B)),C))=zero_zero(nat). % 32.69/32.51 ** KEPT (pick-wt=27): 382 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls))|hAPP(nat,nat,times_times(nat,number_number_of(nat,A)),number_number_of(nat,B))=zero_zero(nat). % 32.69/32.51 ** KEPT (pick-wt=35): 383 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|ti(A,B)=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)). % 32.69/32.51 ** KEPT (pick-wt=52): 384 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),C),A)). % 32.69/32.51 ** KEPT (pick-wt=16): 385 [] -hBOOL(hAPP(int,bool,zcong(A,B),zero_zero(int)))|ti(int,A)=ti(int,B). % 32.69/32.51 ** KEPT (pick-wt=16): 386 [] hBOOL(hAPP(int,bool,zcong(A,B),zero_zero(int)))|ti(int,A)!=ti(int,B). % 32.69/32.51 ** KEPT (pick-wt=36): 387 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,zcong(D,E),C))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A),D),hAPP(int,int,times_times(int,B),E)),C)). % 32.69/32.51 ** KEPT (pick-wt=28): 388 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,D),A),hAPP(int,int,times_times(int,D),B)),C)). % 32.69/32.51 ** KEPT (pick-wt=28): 389 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A),D),hAPP(int,int,times_times(int,B),D)),C)). % 32.69/32.51 ** KEPT (pick-wt=36): 390 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,zcong(D,E),C))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,plus_plus(int,A),D),hAPP(int,int,plus_plus(int,B),E)),C)). % 32.69/32.51 ** KEPT (pick-wt=24): 391 [] -number_ring(A)|hAPP(nat,A,power_power(A,number_number_of(A,min)),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),B))=one_one(A). % 32.69/32.51 Following clause subsumed by 199 during input processing: 0 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,C))!=zero_zero(A)|ti(A,B)=zero_zero(A). % 32.69/32.51 Following clause subsumed by 200 during input processing: 0 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,C))!=zero_zero(A)|number_number_of(nat,C)!=zero_zero(nat). % 32.69/32.51 Following clause subsumed by 201 during input processing: 0 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,C))=zero_zero(A)|ti(A,B)!=zero_zero(A)|number_number_of(nat,C)=zero_zero(nat). % 32.69/32.51 ** KEPT (pick-wt=48): 392 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,times_times(int,A),B))). % 32.69/32.51 ** KEPT (pick-wt=48): 393 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,A),B))). % 32.69/32.51 ** KEPT (pick-wt=62): 394 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),A))| -hBOOL(hAPP(int,bool,zcong(A,C),B)). % 32.69/32.51 ** KEPT (pick-wt=34): 395 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,power_power(int,A),B))). % 32.69/32.51 ** KEPT (pick-wt=28): 396 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|ti(int,B)=hAPP(int,int,plus_plus(int,A),hAPP(int,int,times_times(int,C),$f2(A,B,C))). % 32.69/32.51 ** KEPT (pick-wt=25): 397 [] hBOOL(hAPP(int,bool,zcong(A,B),C))|ti(int,B)!=hAPP(int,int,plus_plus(int,A),hAPP(int,int,times_times(int,C),D)). % 32.69/32.51 Following clause subsumed by 211 during input processing: 0 [] -power(A)| -semiring_0(A)|number_number_of(nat,B)!=zero_zero(nat)|hAPP(nat,A,power_power(A,zero_zero(A)),number_number_of(nat,B))=one_one(A). % 32.69/32.51 Following clause subsumed by 212 during input processing: 0 [] -power(A)| -semiring_0(A)|number_number_of(nat,B)=zero_zero(nat)|hAPP(nat,A,power_power(A,zero_zero(A)),number_number_of(nat,B))=zero_zero(A). % 32.69/32.51 ** KEPT (pick-wt=69): 398 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B))| -hBOOL(hAPP(int,bool,zcong(A,C),B))|ti(int,A)=ti(int,C). % 32.69/32.51 ** KEPT (pick-wt=42): 399 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B))|ti(int,A)=zero_zero(int). % 32.69/32.51 ** KEPT (pick-wt=120): 400 [] hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A),B)),C)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,D),E)),F)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,D),E)),F)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),F))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),D),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),E),B)). % 32.69/32.51 ** KEPT (pick-wt=90): 401 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A),B)),C)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A),D)),E)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),E),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),E))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),D),B)). % 32.69/32.51 ** KEPT (pick-wt=120): 402 [] hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A),B)),C)!=hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,D),E)),F)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,D),E)),F)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),F),D))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),D),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),E)). % 32.69/32.51 ** KEPT (pick-wt=90): 403 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A),B)),C)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A),D)),E)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),E),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),D)). % 32.69/32.51 ** KEPT (pick-wt=68): 404 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A),B)),C)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),zero_zero(int))). % 32.69/32.51 ** KEPT (pick-wt=67): 405 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,A),B)),C)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B)). % 32.69/32.51 ** KEPT (pick-wt=65): 406 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,zprime,B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),hAPP(int,int,times_times(int,A),C)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)). % 32.69/32.51 ** KEPT (pick-wt=60): 407 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),A))| -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,number_number_of(int,min)),B),hAPP(nat,int,power_power(int,number_number_of(int,min)),C)),A))|hAPP(nat,int,power_power(int,number_number_of(int,min)),B)=hAPP(nat,int,power_power(int,number_number_of(int,min)),C). % 32.69/32.51 ** KEPT (pick-wt=36): 408 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),A))| -hBOOL(hAPP(int,bool,zcong(B,number_number_of(int,min)),A))| -hBOOL(hAPP(int,bool,zcong(B,one_one(int)),A)). % 32.69/32.51 ** KEPT (pick-wt=28): 409 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,bit0(bit1(pls)))),A))| -hBOOL(hAPP(int,bool,zcong(one_one(int),number_number_of(int,min)),A)). % 32.69/32.51 ** KEPT (pick-wt=53): 410 [] hBOOL(hAPP(int,bool,quadRes(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),number_number_of(int,min)))|legendre(number_number_of(int,min),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))!=one_one(int). % 32.69/32.51 ** KEPT (pick-wt=22): 411 [] hAPP(int,int,minus_minus(int,A),B)!=ti(int,C)|ti(int,A)=hAPP(int,int,plus_plus(int,C),B). % 32.69/32.51 ** KEPT (pick-wt=23): 412 [] -number_ring(A)|number_number_of(A,hAPP(int,int,minus_minus(int,B),C))=hAPP(A,A,minus_minus(A,number_number_of(A,B)),number_number_of(A,C)). % 32.69/32.51 ** KEPT (pick-wt=36): 413 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,zcong(D,E),C))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,minus_minus(int,A),D),hAPP(int,int,minus_minus(int,B),E)),C)). % 32.69/32.51 ** KEPT (pick-wt=45): 414 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,minus_minus(int,B),C)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). % 32.69/32.51 ** KEPT (pick-wt=43): 416 [copy,415,flip.3] -number(A)| -ring(A)|hAPP(A,A,minus_minus(A,hAPP(A,A,times_times(A,number_number_of(A,B)),C)),hAPP(A,A,times_times(A,number_number_of(A,B)),D))=hAPP(A,A,times_times(A,number_number_of(A,B)),hAPP(A,A,minus_minus(A,C),D)). % 32.69/32.51 ** KEPT (pick-wt=43): 417 [] -number(A)| -ring(A)|hAPP(A,A,times_times(A,hAPP(A,A,minus_minus(A,B),C)),number_number_of(A,D))=hAPP(A,A,minus_minus(A,hAPP(A,A,times_times(A,B),number_number_of(A,D))),hAPP(A,A,times_times(A,C),number_number_of(A,D))). % 32.69/32.51 ** KEPT (pick-wt=33): 418 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,A),B)),zero_zero(int))). % 32.69/32.51 ** KEPT (pick-wt=33): 419 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,A),B)),zero_zero(int))). % 32.69/32.51 ** KEPT (pick-wt=27): 420 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),C),hAPP(int,int,minus_minus(int,A),B))). % 32.69/32.51 ** KEPT (pick-wt=27): 421 [] hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),C),hAPP(int,int,minus_minus(int,A),B))). % 32.69/32.51 ** KEPT (pick-wt=35): 422 [] -number_ring(A)|hAPP(A,A,plus_plus(A,number_number_of(A,B)),hAPP(A,A,minus_minus(A,number_number_of(A,C)),D))=hAPP(A,A,minus_minus(A,number_number_of(A,hAPP(int,int,plus_plus(int,B),C))),D). % 32.69/32.51 ** KEPT (pick-wt=59): 423 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|ti(int,A)=hAPP(int,int,minus_minus(int,B),one_one(int))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,minus_minus(int,B),one_one(int)))). % 32.69/32.51 ** KEPT (pick-wt=33): 424 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),hAPP(int,int,minus_minus(int,B),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.51 ** KEPT (pick-wt=33): 425 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),hAPP(int,int,minus_minus(int,B),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 32.69/32.51 ** KEPT (pick-wt=37): 426 [] -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A),hAPP(int,int,minus_minus(int,B),one_one(int))),one_one(int)),B))|hBOOL(hAPP(int,bool,zcong(A,hAPP(int,int,minus_minus(int,B),one_one(int))),B)). % 32.69/32.51 ** KEPT (pick-wt=37): 427 [] hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,A),hAPP(int,int,minus_minus(int,B),one_one(int))),one_one(int)),B))| -hBOOL(hAPP(int,bool,zcong(A,hAPP(int,int,minus_minus(int,B),one_one(int))),B)). % 32.69/32.51 ** KEPT (pick-wt=31): 428 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|ti(int,B)!=ti(int,D)| -hBOOL(hAPP(int,bool,zcong(D,E),C))|hBOOL(hAPP(int,bool,zcong(A,E),C)). % 32.69/32.51 ** KEPT (pick-wt=59): 429 [] -hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,B),B),one_one(int)),A))|hBOOL(hAPP(int,bool,zcong(B,one_one(int)),A))|hBOOL(hAPP(int,bool,zcong(B,hAPP(int,int,minus_minus(int,A),one_one(int))),A)). % 32.69/32.51 ** KEPT (pick-wt=66): 430 [] -hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,B),B),one_one(int)),A))|ti(int,B)=one_one(int)|ti(int,B)=hAPP(int,int,minus_minus(int,A),one_one(int)). % 32.69/32.51 ** KEPT (pick-wt=36): 431 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,zcong(D,hAPP(int,int,times_times(int,A),E)),C))|hBOOL(hAPP(int,bool,zcong(D,hAPP(int,int,times_times(int,B),E)),C)). % 32.69/32.51 ** KEPT (pick-wt=36): 432 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|hBOOL(hAPP(int,bool,zcong(D,hAPP(int,int,times_times(int,A),E)),C))| -hBOOL(hAPP(int,bool,zcong(D,hAPP(int,int,times_times(int,B),E)),C)). % 32.69/32.51 ** KEPT (pick-wt=36): 433 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,zcong(D,hAPP(int,int,times_times(int,E),A)),C))|hBOOL(hAPP(int,bool,zcong(D,hAPP(int,int,times_times(int,E),B)),C)). % 32.69/32.51 ** KEPT (pick-wt=36): 434 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|hBOOL(hAPP(int,bool,zcong(D,hAPP(int,int,times_times(int,E),A)),C))| -hBOOL(hAPP(int,bool,zcong(D,hAPP(int,int,times_times(int,E),B)),C)). % 32.69/32.51 ** KEPT (pick-wt=28): 435 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|hBOOL(hAPP(int,bool,zcong(hAPP(int,int,plus_plus(int,A),D),hAPP(int,int,plus_plus(int,B),D)),C)). % 32.69/32.51 ** KEPT (pick-wt=28): 436 [] -hBOOL(hAPP(int,bool,zcong(A,B),C))|hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,A),D),hAPP(nat,int,power_power(int,B),D)),C)). % 32.69/32.51 ** KEPT (pick-wt=69): 437 [] -number_ring(A)|hAPP(nat,A,power_power(A,hAPP(A,A,minus_minus(A,B),C)),number_number_of(nat,bit0(bit1(pls))))=hAPP(A,A,minus_minus(A,hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,bit0(bit1(pls)))))),hAPP(A,A,times_times(A,hAPP(A,A,times_times(A,number_number_of(A,bit0(bit1(pls)))),B)),C)). % 32.69/32.51 ** KEPT (pick-wt=83): 438 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C))| -hBOOL(hAPP(int,bool,zcong(A,B),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C))|ti(int,A)=ti(int,B). % 32.69/32.51 ** KEPT (pick-wt=36): 439 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B)). % 32.69/32.51 ** KEPT (pick-wt=40): 440 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 32.69/32.51 ** KEPT (pick-wt=22): 441 [] -hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A)). % 32.69/32.51 ** KEPT (pick-wt=22): 442 [] hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A)). % 32.69/32.51 Following clause subsumed by 441 during input processing: 0 [] -hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A)). % 32.69/32.51 Following clause subsumed by 442 during input processing: 0 [] hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A)). % 32.69/32.51 ** KEPT (pick-wt=51): 443 [] -hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,times_times(int,B),C)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)). % 32.69/32.51 Following clause subsumed by 399 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B))|ti(int,A)=zero_zero(int). % 32.69/32.51 ** KEPT (pick-wt=46): 444 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),hAPP(nat,int,power_power(int,C),A))). % 32.69/32.51 ** KEPT (pick-wt=39): 445 [] -hBOOL(hAPP(int,bool,zprime,A))|hBOOL(hAPP(int,bool,zcong(B,zero_zero(int)),A))|hBOOL(hAPP(int,bool,zcong(C,zero_zero(int)),A))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,B),C),zero_zero(int)),A)). % 32.69/32.51 Following clause subsumed by 445 during input processing: 0 [] -hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,B),C),zero_zero(int)),A))|hBOOL(hAPP(int,bool,zcong(B,zero_zero(int)),A))|hBOOL(hAPP(int,bool,zcong(C,zero_zero(int)),A)). % 32.69/32.51 Following clause subsumed by 445 during input processing: 0 [] -hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,zcong(B,zero_zero(int)),A))|hBOOL(hAPP(int,bool,zcong(C,zero_zero(int)),A))| -hBOOL(hAPP(int,bool,zcong(hAPP(int,int,times_times(int,B),C),zero_zero(int)),A)). % 32.69/32.51 Following clause subsumed by 241 during input processing: 0 [] -hBOOL(hAPP(int,bool,zprime,A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(nat,int,power_power(int,B),C)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). % 32.69/32.51 ** KEPT (pick-wt=50): 446 [] -hBOOL(hAPP(int,bool,zprime,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),A)),one_one(int))))|legendre(number_number_of(int,min),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),A)),one_one(int)))=one_one(int) % 32.69/32.51 Search stopped in tp_alloc by max_mem option. % 32.69/32.51 . % 32.69/32.51 ** KEPT (pick-wt=15): 447 [] -hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B))|legendre(A,B)=zero_zero(int). % 32.69/32.51 ** KEPT (pick-wt=22): 448 [] hBOOL(hAPP(int,bool,zcong(A,zero_zero(int)),B))| -hBOOL(hAPP(int,bool,quadRes(B),A))|legendre(A,B)=one_one(int). % 32.69/32.51 ** KEPT (pick-wt=43): 449 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B))|B=zero_zero(nat)|B=A|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,times_times(nat,number_number_of(nat,bit0(bit1(pls)))),A)),B)). % 32.69/32.51 ** KEPT (pick-wt=27): 450 [] -hBOOL(hAPP(int,bool,quadRes(A),B))|hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,$f3(A,B)),number_number_of(nat,bit0(bit1(pls)))),B),A)). % 32.69/32.51 ** KEPT (pick-wt=25): 451 [] hBOOL(hAPP(int,bool,quadRes(A),B))| -hBOOL(hAPP(int,bool,zcong(hAPP(nat,int,power_power(int,C),number_number_of(nat,bit0(bit1(pls)))),B),A)). % 32.69/32.51 ** KEPT (pick-wt=34): 452 [] hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,A),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,real,power_power(real,B),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(real)|A=zero_zero(real). % 32.69/32.51 ** KEPT (pick-wt=34): 453 [] hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,A),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,real,power_power(real,B),number_number_of(nat,bit0(bit1(pls)))))!=zero_zero(real)|B=zero_zero(real). % 32.69/32.51 ** KEPT (pick-wt=38): 454 [] hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,A),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,real,power_power(real,B),number_number_of(nat,bit0(bit1(pls)))))=zero_zero(real)|A!=zero_zero(real)|B!=zero_zero(real). % 32.69/32.51 ** KEPT (pick-wt=97): 455 [] -linord626643107strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),E))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),F))|hAPP(A,A,plus_plus(A,E),F)!=one_one(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,hAPP(A,A,times_times(A,E),B)),hAPP(A,A,times_times(A,F),D))),C)). % 32.69/32.51 ** KEPT (pick-wt=16): 456 [] -comm_semiring_1(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),zero_zero(A))). % 32.69/32.51 % 32.69/32.51 Search stopped in tp_alloc by max_mem option. % 32.69/32.51 % 32.69/32.51 ============ end of search ============ % 32.69/32.51 % 32.69/32.51 -------------- statistics ------------- % 32.69/32.51 clauses given 0 % 32.69/32.51 clauses generated 0 % 32.69/32.51 clauses kept 442 % 32.69/32.51 clauses forward subsumed 55 % 32.69/32.51 clauses back subsumed 0 % 32.69/32.51 Kbytes malloced 11718 % 32.69/32.51 % 32.69/32.51 ----------- times (seconds) ----------- % 32.69/32.51 user CPU time 0.23 (0 hr, 0 min, 0 sec) % 32.69/32.51 system CPU time 0.01 (0 hr, 0 min, 0 sec) % 32.69/32.51 wall-clock time 32 (0 hr, 0 min, 32 sec) % 32.69/32.51 % 32.69/32.51 Process 20062 finished Wed Jul 27 09:44:19 2022 % 32.69/32.51 Otter interrupted % 32.69/32.51 PROOF NOT FOUND %------------------------------------------------------------------------------