TSTP Solution File: NUM923+7 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM923+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 13:10:13 EDT 2022
% Result : Unknown 23.89s 23.64s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM923+7 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n014.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 09:40:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 23.77/23.58 ----- Otter 3.3f, August 2004 -----
% 23.77/23.58 The process was started by sandbox on n014.cluster.edu,
% 23.77/23.58 Wed Jul 27 09:40:39 2022
% 23.77/23.58 The command was "./otter". The process ID is 9347.
% 23.77/23.58
% 23.77/23.58 set(prolog_style_variables).
% 23.77/23.58 set(auto).
% 23.77/23.58 dependent: set(auto1).
% 23.77/23.58 dependent: set(process_input).
% 23.77/23.58 dependent: clear(print_kept).
% 23.77/23.58 dependent: clear(print_new_demod).
% 23.77/23.58 dependent: clear(print_back_demod).
% 23.77/23.58 dependent: clear(print_back_sub).
% 23.77/23.58 dependent: set(control_memory).
% 23.77/23.58 dependent: assign(max_mem, 12000).
% 23.77/23.58 dependent: assign(pick_given_ratio, 4).
% 23.77/23.58 dependent: assign(stats_level, 1).
% 23.77/23.58 dependent: assign(max_seconds, 10800).
% 23.77/23.58 clear(print_given).
% 23.77/23.58
% 23.77/23.58 formula_list(usable).
% 23.77/23.58 all A (A=A).
% 23.77/23.58 all X_a (archim1727834104eiling(X_a)->ti(fun(X_a,int),archimedean_ceiling(X_a))=archimedean_ceiling(X_a)).
% 23.77/23.58 all X_a (archim1727834104eiling(X_a)->ti(fun(X_a,int),archim2085082626_floor(X_a))=archim2085082626_floor(X_a)).
% 23.77/23.58 ti(fun(int,fun(int,fun(product_prod(int,int),bool))),divmod_int_rel)=divmod_int_rel.
% 23.77/23.58 ti(fun(int,fun(int,product_prod(int,int))),pdivmod)=pdivmod.
% 23.77/23.58 ti(fun(int,fun(int,product_prod(int,int))),posDivAlg)=posDivAlg.
% 23.77/23.58 all X_a X_b (ti(fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),in_rel(X_a,X_b))=in_rel(X_a,X_b)).
% 23.77/23.58 all X_a (ordere142940540dd_abs(X_a)->ti(fun(X_a,X_a),abs_abs(X_a))=abs_abs(X_a)).
% 23.77/23.58 all X_a (minus(X_a)->ti(fun(X_a,fun(X_a,X_a)),minus_minus(X_a))=minus_minus(X_a)).
% 23.77/23.58 all X_a (one(X_a)->ti(X_a,one_one(X_a))=one_one(X_a)).
% 23.77/23.58 all X_a (monoid_add(X_a)->ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a)).
% 23.77/23.58 all X_a (ab_semigroup_add(X_a)->ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a)).
% 23.77/23.58 all X_a (cancel_semigroup_add(X_a)->ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a)).
% 23.77/23.58 all X_a (no_zero_divisors(X_a)->ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a)).
% 23.77/23.58 all X_a (mult_zero(X_a)->ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a)).
% 23.77/23.58 all X_a (monoid_mult(X_a)->ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a)).
% 23.77/23.58 all X_a (semiring(X_a)->ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a)).
% 23.77/23.58 all X_a (ab_semigroup_mult(X_a)->ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a)).
% 23.77/23.58 all X_a (zero(X_a)->ti(X_a,zero_zero(X_a))=zero_zero(X_a)).
% 23.77/23.58 all X_a (ti(X_a,undefined(X_a))=undefined(X_a)).
% 23.77/23.58 all X_a (ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a))=if(X_a)).
% 23.77/23.58 ti(fun(int,int),zfact)=zfact.
% 23.77/23.58 ti(fun(int,fun(int,product_prod(int,product_prod(int,int)))),xzgcd)=xzgcd.
% 23.77/23.58 ti(fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))))),xzgcda)=xzgcda.
% 23.77/23.58 ti(int,pls)=pls.
% 23.77/23.58 all X_a (number(X_a)->ti(fun(int,X_a),number_number_of(X_a))=number_number_of(X_a)).
% 23.77/23.58 ti(fun(int,int),pred)=pred.
% 23.77/23.58 all X_a (ring_1(X_a)->ti(fun(X_a,bool),ring_1_Ints(X_a))=ring_1_Ints(X_a)).
% 23.77/23.58 ti(fun(int,int),succ)=succ.
% 23.77/23.58 ti(fun(nat,nat),suc)=suc.
% 23.77/23.58 all X_a (semiring_1(X_a)->ti(fun(nat,X_a),semiring_1_of_nat(X_a))=semiring_1_of_nat(X_a)).
% 23.77/23.58 ti(fun(int,bool),nat_neg)=nat_neg.
% 23.77/23.58 ti(fun(int,fun(int,int)),nat_tsub)=nat_tsub.
% 23.77/23.58 all X_a (ord(X_a)->ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a)).
% 23.77/23.58 all X_b (ord(X_b)->ti(fun(X_b,fun(X_b,bool)),ord_less_e_q(X_b))=ord_less_e_q(X_b)).
% 23.77/23.58 all X_a X_b (ti(fun(X_a,fun(X_b,product_prod(X_a,X_b))),product_Pair(X_a,X_b))=product_Pair(X_a,X_b)).
% 23.77/23.58 all X_b X_c X_a (ti(fun(fun(product_prod(X_b,X_c),X_a),fun(X_b,fun(X_c,X_a))),product_curry(X_b,X_c,X_a))=product_curry(X_b,X_c,X_a)).
% 23.77/23.58 all X_b X_c X_a (ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),produc1605651328_split(X_b,X_c,X_a))=produc1605651328_split(X_b,X_c,X_a)).
% 23.77/23.58 all X_b X_c X_a (ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),product_prod_rec(X_b,X_c,X_a))=product_prod_rec(X_b,X_c,X_a)).
% 23.77/23.58 ti(fun(real,nat),natceiling)=natceiling.
% 23.77/23.58 ti(fun(real,nat),natfloor)=natfloor.
% 23.77/23.58 ti(fun(int,real),real_1(int))=real_1(int).
% 23.77/23.58 ti(fun(nat,real),real_1(nat))=real_1(nat).
% 23.77/23.58 ti(fun(int,bool),twoSqu658283162sum2sq)=twoSqu658283162sum2sq.
% 23.77/23.58 ti(fun(product_prod(int,int),int),twoSqu1929807760sum2sq)=twoSqu1929807760sum2sq.
% 23.77/23.58 ti(bool,fFalse)=fFalse.
% 23.77/23.58 ti(bool,fTrue)=fTrue.
% 23.77/23.58 all X_c X_a B_1_1 B_2_1 (hAPP(X_c,X_a,ti(fun(X_c,X_a),B_1_1),B_2_1)=hAPP(X_c,X_a,B_1_1,B_2_1)).
% 23.77/23.58 all X_c X_a B_1_1 B_2_1 (hAPP(X_c,X_a,B_1_1,ti(X_c,B_2_1))=hAPP(X_c,X_a,B_1_1,B_2_1)).
% 23.77/23.58 all X_a X_c B_1_1 B_2_1 (ti(X_a,hAPP(X_c,X_a,B_1_1,B_2_1))=hAPP(X_c,X_a,B_1_1,B_2_1)).
% 23.77/23.58 all B_1_1 (hBOOL(ti(bool,B_1_1))<->hBOOL(B_1_1)).
% 23.77/23.58 all X_a (ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a))=member(X_a)).
% 23.77/23.58 ti(int,a)=a.
% 23.77/23.58 ti(int,b)=b.
% 23.77/23.58 ti(int,p)=p.
% 23.77/23.58 ti(int,q)=q.
% 23.77/23.58 all A_1 R B M C D_1 N_1 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R),B))),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R),D_1))),N_1))=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),N_1))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_1),N_1))))).
% 23.77/23.58 all X_a (ring(X_a)-> (all X Y A_1 B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),B))))).
% 23.77/23.58 all X_a (real_normed_algebra(X_a)-> (all X Y A_1 B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B)))))).
% 23.77/23.58 all X_a (ring(X_a)-> (all Aa E_1 C_1 Ba D_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2)<->ti(X_a,C_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ba),Aa)),E_1)),D_2)))).
% 23.77/23.58 all X_a (ring(X_a)-> (all Aa E_1 C_1 Ba D_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2)<->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_1)),C_1)=ti(X_a,D_2)))).
% 23.77/23.58 all X_1 (hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,X_1))<-> (exists A_2 B_2 (hAPP(product_prod(int,int),int,twoSqu1929807760sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_2),B_2))=X_1))).
% 23.77/23.58 all A_1 B C (hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)=C->A_1=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B)).
% 23.77/23.58 all W_1 Z1 Z2 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2))=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),Z2))).
% 23.77/23.58 all Z1 Z2 W_1 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2)),W_1)=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W_1))).
% 23.77/23.58 all W_1 Z1 Z2 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),Z2))).
% 23.77/23.58 all Z1 Z2 W_1 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),W_1)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W_1))).
% 23.77/23.58 all X_a (group_add(X_a)-> (all A_1 B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),B)=ti(X_a,A_1)))).
% 23.77/23.58 all X_a (ab_semigroup_mult(X_a)-> (all A_1 B C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))).
% 23.77/23.58 all X_a (cancel_semigroup_add(X_a)-> (all B A_1 C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)->ti(X_a,B)=ti(X_a,C)))).
% 23.77/23.58 all X_a (cancel146912293up_add(X_a)-> (all A_1 B C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)->ti(X_a,B)=ti(X_a,C)))).
% 23.77/23.58 all X_a (cancel_semigroup_add(X_a)-> (all A_1 B C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)->ti(X_a,B)=ti(X_a,C)))).
% 23.77/23.58 all X_a (cancel_semigroup_add(X_a)-> (all Ba Aa C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)<->ti(X_a,Ba)=ti(X_a,C_1)))).
% 23.77/23.58 all X_a (cancel_semigroup_add(X_a)-> (all Aa Ba C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)<->ti(X_a,Ba)=ti(X_a,C_1)))).
% 23.77/23.58 all X_a (ab_semigroup_add(X_a)-> (all A_1 B C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))).
% 23.77/23.58 all X_a (ab_group_add(X_a)-> (all Aa Ba C_1 D_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_2)-> (ti(X_a,Aa)=ti(X_a,Ba)<->ti(X_a,C_1)=ti(X_a,D_2))))).
% 23.77/23.58 all Z1 Z2 Z3 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),Z2)),Z3)=hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),Z3))).
% 23.77/23.58 all Z_1 W_1 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W_1)=hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),Z_1)).
% 23.77/23.58 all Z1 Z2 Z3 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),Z3)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z2),Z3))).
% 23.77/23.58 all X Y Z_1 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),Z_1))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Z_1))).
% 23.77/23.58 all Z_1 W_1 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),W_1)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),Z_1)).
% 23.77/23.58 all X_a (semiring(X_a)-> (all A_1 E_2 B C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),E_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),E_2)),C))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),E_2)),C)))).
% 23.77/23.58 all X_a (real_normed_algebra(X_a)-> (all X Y Ya (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)),Ya)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Ya))))).
% 23.77/23.58 all X_a (real_normed_algebra(X_a)-> (all A_1 A_5 B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),A_5)),B)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_5),B))))).
% 23.77/23.58 all X_a (comm_semiring(X_a)-> (all A_1 B C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))).
% 23.77/23.58 all X_a (real_normed_algebra(X_a)-> (all Xa X Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),Y))))).
% 23.77/23.58 all X_a (real_normed_algebra(X_a)-> (all A_1 B B_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),B_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B_1))))).
% 23.77/23.58 all X_a (real_normed_algebra(X_a)-> (all X Y Ya (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),Ya)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Ya))))).
% 23.77/23.58 all X_a (real_normed_algebra(X_a)-> (all A_1 A_5 B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_5)),B)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_5),B))))).
% 23.77/23.58 all X_a (real_normed_algebra(X_a)-> (all Xa X Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),Y))))).
% 23.77/23.58 all X_a (real_normed_algebra(X_a)-> (all A_1 B B_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),B_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B_1))))).
% 23.77/23.58 all X_a (ab_group_add(X_a)-> (all A_1 C B D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C),D_1))))).
% 23.77/23.58 all X_a (group_add(X_a)-> (all A_1 B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B)=ti(X_a,A_1)))).
% 23.77/23.58 all X_a (semiri456707255roduct(X_a)-> (all W Y_1 X_1 Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Y_1))<->ti(X_a,W)=ti(X_a,X_1)|ti(X_a,Y_1)=ti(X_a,Z)))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all A_1 M B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),M))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),M)))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))).
% 23.77/23.58 all X_a (semiri456707255roduct(X_a)-> (all C_1 D_2 Aa Ba (ti(X_a,Aa)!=ti(X_a,Ba)&ti(X_a,C_1)!=ti(X_a,D_2)<->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),D_2))!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),D_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),C_1))))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all X Y Z_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z_1))))).
% 23.77/23.58 all X_b X_a (minus(X_a)-> (all A_3 B_4 X_1 (hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),minus_minus(fun(X_b,X_a)),A_3),B_4),X_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_b,X_a,A_3,X_1)),hAPP(X_b,X_a,B_4,X_1))))).
% 23.77/23.58 all X_a X_b (minus(X_b)-> (all A_3 B_4 X_2 (hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),minus_minus(fun(X_a,X_b)),A_3),B_4),X_2)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,A_3,X_2)),hAPP(X_a,X_b,B_4,X_2))))).
% 23.77/23.58 all X_b X_a A_1 B A_5 B_1 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_1),B)=hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_5),B_1)-> -(ti(X_a,A_1)=ti(X_a,A_5)->ti(X_b,B)!=ti(X_b,B_1))).
% 23.77/23.58 all X_b X_a Aa Ba A_4 B_3 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba)=hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_3)<->ti(X_a,Aa)=ti(X_a,A_4)&ti(X_b,Ba)=ti(X_b,B_3)).
% 23.77/23.58 all X_a X_b P_1 ((all X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,X1)))<-> (all A_2 B_2 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_2))))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all A_1 B C D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),B)))).
% 23.77/23.58 all X_a (ab_sem1668676832m_mult(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)=ti(X_a,A_1)))).
% 23.77/23.58 all X_a (ab_sem1668676832m_mult(X_a)-> (all X (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)=ti(X_a,X)))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all A_1 B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)))).
% 23.77/23.58 all X_a (ab_sem1668676832m_mult(X_a)-> (all A_1 B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all Lx Rx Ry (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ry))))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all Lx Rx Ry (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ry)))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Rx))))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ly)))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx Ry (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)))))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx Ry (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Ry))))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all Lx Ly Rx Ry (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Ry))))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all A_1 C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all A_1 C D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),D_1))))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all A_1 C D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),D_1)))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all A_1 B C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))).
% 23.77/23.58 all X_b X_c X_a F1 Aa Ba (hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_rec(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba))=hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,Aa),Ba)).
% 23.77/23.58 all X_a X_b P_1 ((exists X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,X1)))<-> (exists A_2 B_2 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_2))))).
% 23.77/23.58 all X_a X_b X_c X_d X_e X_f X_1 P_1 ((all A_2 B_2 C_2 D E F_1 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_2),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B_2),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C_2),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_1))))))))->hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,P_1,X_1))).
% 23.77/23.58 all X_a X_b X_c X_d X_e X_f Y (-(all A_2 B_2 C_2 D E F_1 (ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),Y)!=hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_2),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B_2),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C_2),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_1)))))))).
% 23.77/23.58 all X_a X_b X_c X_d X_e X_1 P_1 ((all A_2 B_2 C_2 D E hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_2),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B_2),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C_2),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D),E)))))))->hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P_1,X_1))).
% 23.77/23.58 all X_a X_b X_c X_d X_e Y (-(all A_2 B_2 C_2 D E (ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),Y)!=hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_2),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B_2),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C_2),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D),E))))))).
% 23.77/23.58 all X_a X_b X_c X_d X_1 P_1 ((all A_2 B_2 C_2 D hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_2),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B_2),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C_2),D))))))->hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P_1,X_1))).
% 23.77/23.58 all X_a X_b X_c X_d Y (-(all A_2 B_2 C_2 D (ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),Y)!=hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_2),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B_2),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C_2),D)))))).
% 23.77/23.58 all X_a X_b X_c X_1 P_1 ((all A_2 B_2 C_2 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,P_1,hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_2),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B_2),C_2)))))->hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,P_1,X_1))).
% 23.77/23.58 all X_a X_b X_c Y (-(all A_2 B_2 C_2 (ti(product_prod(X_a,product_prod(X_b,X_c)),Y)!=hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_2),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B_2),C_2))))).
% 23.77/23.58 all X_a X_b P_3 (-(all X_2 Y_2 (ti(product_prod(X_a,X_b),P_3)!=hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2)))).
% 23.77/23.58 all X_a X_b F G ((all X_2 (hAPP(X_a,X_b,F,X_2)=hAPP(X_a,X_b,G,X_2)))->ti(fun(X_a,X_b),F)=ti(fun(X_a,X_b),G)).
% 23.77/23.58 all X_a X_1 A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3))<->hBOOL(hAPP(X_a,bool,A_3,X_1))).
% 23.77/23.58 all X_a X_b Y (-(all A_2 B_2 (ti(product_prod(X_a,X_b),Y)!=hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_2)))).
% 23.77/23.58 all X_b X_c X_a C_1 Aa Ba (hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),produc1605651328_split(X_b,X_c,X_a),C_1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba))=hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),C_1,Aa),Ba)).
% 23.77/23.58 all X_a X_b F Aa Ba (hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba)))->hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba))).
% 23.77/23.58 all X_a (ordered_ring(X_a)-> (all Aa E_1 C_1 Ba 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_1)),C_1)),D_2))))).
% 23.77/23.58 all X_a (ordered_ring(X_a)-> (all Aa E_1 C_1 Ba 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2)))<->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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ba),Aa)),E_1)),D_2)))))).
% 23.77/23.58 all X_a (ring_1(X_a)-> (all X (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),one_one(X_a))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a)))))).
% 23.77/23.58 all X_a (ordered_ring(X_a)-> (all Aa E_1 C_1 Ba D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_1)),C_1)),D_2))))).
% 23.77/23.58 all X_a (ordered_ring(X_a)-> (all Aa E_1 C_1 Ba D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ba),Aa)),E_1)),D_2)))))).
% 23.77/23.58 all X_a (number_ring(X_a)-> (all V W_1 C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W_1))),C)))).
% 23.77/23.58 all X_c X_a X_b F Aa Ba (hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),hAPP(fun(product_prod(X_b,X_c),X_a),fun(X_b,fun(X_c,X_a)),product_curry(X_b,X_c,X_a),F),Aa),Ba)=hAPP(product_prod(X_b,X_c),X_a,F,hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba))).
% 23.77/23.58 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M),N_1))))))).
% 23.77/23.58 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a)))))).
% 23.77/23.58 all X_a (ordere223160158up_add(X_a)-> (all C D_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),C),D_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))))))).
% 23.77/23.58 all X_a (ordere223160158up_add(X_a)-> (all C D_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(X_a),C),D_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))))))).
% 23.77/23.58 all X_a (one(X_a)-> (all X_1 (one_one(X_a)=ti(X_a,X_1)<->ti(X_a,X_1)=one_one(X_a)))).
% 23.77/23.58 all W Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z))).
% 23.77/23.58 all X_a (number(X_a)-> (all W X_1 (hAPP(int,X_a,number_number_of(X_a),W)=ti(X_a,X_1)<->ti(X_a,X_1)=hAPP(int,X_a,number_number_of(X_a),W)))).
% 23.77/23.58 all X_a (number(X_a)&linorder(X_a)-> (all V_1 W (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),hAPP(int,X_a,number_number_of(X_a),W)))<-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W)),hAPP(int,X_a,number_number_of(X_a),V_1)))))).
% 23.77/23.58 all X_a (number_ring(X_a)&ring_char_0(X_a)-> (all X_1 Y_1 (hAPP(int,X_a,number_number_of(X_a),X_1)=hAPP(int,X_a,number_number_of(X_a),Y_1)<->X_1=Y_1))).
% 23.77/23.58 all X_a (number_ring(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(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1))))).
% 23.77/23.58 all X_a (number_ring(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),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_1),Y_1))))).
% 23.77/23.58 all W Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),one_one(int))),Z))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z))).
% 23.77/23.58 all X_a (linordered_idom(X_a)-> (all X Y (ti(X_a,X)!=ti(X_a,Y)-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))).
% 23.77/23.58 all W_1 Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),one_one(int))),Z_1))).
% 23.77/23.58 all X_a (order(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))-> (ti(X_a,X)!=ti(X_a,Y)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))).
% 23.77/23.58 all W Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z))).
% 23.77/23.58 all Z_4 Z_1 W_3 W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_3),W_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_4),Z_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_3),Z_4)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),Z_1))))).
% 23.77/23.58 all W Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z))|W=Z).
% 23.77/23.58 all X_a (ordere236663937imp_le(X_a)-> (all Aa C_1 Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),C_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))))).
% 23.77/23.58 all X_a (ordere236663937imp_le(X_a)-> (all C_1 Aa Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Ba)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))))).
% 23.77/23.58 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C)))))).
% 23.77/23.58 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B)))))).
% 23.77/23.58 all X_a (ordere223160158up_add(X_a)-> (all C D_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(X_a),C),D_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))))))).
% 23.77/23.58 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(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))))).
% 23.77/23.58 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(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))))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1)=ti(X_a,A_1)))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a))=ti(X_a,A_1)))).
% 23.77/23.58 all X_a (monoid_mult(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1)=ti(X_a,A_1)))).
% 23.77/23.58 all X_a (comm_monoid_mult(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1)=ti(X_a,A_1)))).
% 23.77/23.58 all X_a (monoid_mult(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a))=ti(X_a,A_1)))).
% 23.77/23.58 all X_a (comm_monoid_mult(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a))=ti(X_a,A_1)))).
% 23.77/23.58 all X_a (ordered_ab_group_add(X_a)-> (all Aa Ba C_1 D_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_2)-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_2)))))).
% 23.77/23.58 all X_a (ordere236663937imp_le(X_a)-> (all Aa C_1 Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),C_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba))))).
% 23.77/23.58 all X_a (ordere236663937imp_le(X_a)-> (all C_1 Aa Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Ba)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba))))).
% 23.77/23.58 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C)))))).
% 23.77/23.58 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B)))))).
% 23.77/23.58 all X_a (ordere779506340up_add(X_a)-> (all C D_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),C),D_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))))))).
% 23.77/23.58 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(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))))).
% 23.77/23.58 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(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))))).
% 23.77/23.58 all X_a (ordered_ab_group_add(X_a)-> (all Aa Ba C_1 D_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_2)-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),D_2)))))).
% 23.77/23.58 all V W_1 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W_1))=hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W_1))).
% 23.77/23.58 all V W_1 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W_1))=hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W_1))).
% 23.77/23.58 all K I J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),J))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),K)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),J),K)))).
% 23.77/23.58 all K I J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I),J))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),I)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),J)))).
% 23.77/23.58 all Z_1 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z_1)=Z_1).
% 23.77/23.58 all Z_1 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),one_one(int))=Z_1).
% 23.77/23.58 all X_b (number(X_b)&semiring(X_b)-> (all V B C (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),C))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C))))).
% 23.77/23.58 all X_b (number(X_b)&semiring(X_b)-> (all A_1 B V (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_1),B)),hAPP(int,X_b,number_number_of(X_b),V))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V)))))).
% 23.77/23.58 all X_b (number(X_b)&ring(X_b)-> (all V B C (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B),C))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C))))).
% 23.77/23.58 all X_b (number(X_b)&ring(X_b)-> (all A_1 B V (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_1),B)),hAPP(int,X_b,number_number_of(X_b),V))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V)))))).
% 23.77/23.58 all X_a (number_ring(X_a)-> (all V W_1 (hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W_1))))).
% 23.77/23.58 all X_a (number_ring(X_a)-> (all V W_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W_1))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W_1))))).
% 23.77/23.58 all X_a (number_ring(X_a)-> (all V W_1 Z_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),Z_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W_1))),Z_1)))).
% 23.77/23.58 all X_a (number_ring(X_a)-> (all V W_1 (hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W_1))))).
% 23.77/23.58 all X_a (number_ring(X_a)-> (all V W_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W_1))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W_1))))).
% 23.77/23.58 all X_a (number_ring(X_a)-> (all V W_1 Z_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),Z_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W_1))),Z_1)))).
% 23.77/23.58 all X_a (number_ring(X_a)-> (all V W_1 (hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),V),W_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W_1))))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all M (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),M)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),M)))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all M A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M)))).
% 23.77/23.58 all X_a (comm_semiring_1(X_a)-> (all A_1 M (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),M)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M)))).
% 23.77/23.58 all X_b X_a F Aa Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba))->hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba)))).
% 23.77/23.58 all X_b X_a F Aa Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba))->hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba)))).
% 23.77/23.58 all X_a (preorder(X_a)-> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),X)))).
% 23.77/23.58 all X_a (order(X_a)-> (all Z_1 Y X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X)))))).
% 23.77/23.58 all X_a (preorder(X_a)-> (all Z_1 X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1)))))).
% 23.77/23.58 all X_a (order(X_a)-> (all Z_1 Y X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Z_1),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X)))))).
% 23.77/23.58 all X_a (preorder(X_a)-> (all Z_1 X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1)))))).
% 23.77/23.58 all X_a (order(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))-> (ti(X_a,A_1)!=ti(X_a,B)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)))))).
% 23.77/23.58 all X_a (order(X_a)-> (all A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (ti(X_a,A_1)!=ti(X_a,B)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))).
% 23.77/23.58 all X_a (order(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y)))).
% 23.77/23.58 all X_a (linorder(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))-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1))<->ti(X_a,X_1)=ti(X_a,Y_1))))).
% 23.77/23.58 all X_a (preorder(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))))).
% 23.77/23.58 all W_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),W_1)).
% 23.77/23.58 all K (hAPP(int,int,number_number_of(int),K)=K).
% 23.77/23.58 all Z_1 W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_1))).
% 23.77/23.58 all Z W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),W))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),W))&Z!=W).
% 23.77/23.58 all X Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),Y))|X=Y|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X))).
% 23.77/23.58 all K_1 L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),K_1)),hAPP(int,int,number_number_of(int),L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),L))).
% 23.77/23.58 all K_1 L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),K_1)),hAPP(int,int,number_number_of(int),L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),L))).
% 23.77/23.58 all K I J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I),J))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),J),K))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I),K)))).
% 23.77/23.58 all Z_1 W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_1))->Z_1=W_1)).
% 23.77/23.58 all X_a X_b (ord(X_b)-> (all F G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G))<-> (all X_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))))))).
% 23.77/23.59 all X_a (linorder(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))))).
% 23.77/23.59 all X_a (order(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_e_q(X_a),X_1),Y_1))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y_1),X_1))))).
% 23.77/23.59 all X_a (preorder(X_a)-> (all X Y (X=Y->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))))).
% 23.77/23.59 all X_a X_b (ord(X_b)-> (all X_1 F G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1)))))).
% 23.77/23.59 all X_a (order(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),Y_1),X_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))))).
% 23.77/23.59 all X_a (ord(X_a)-> (all C A_1 B (A_1=B-> (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),A_1),C)))))).
% 23.77/23.59 all X_a (order(X_a)-> (all C A_1 B (ti(X_a,A_1)=ti(X_a,B)-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),A_1)))))).
% 23.77/23.59 all X_a (ord(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))-> (B=C->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),C)))))).
% 23.77/23.59 all X_a (order(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))-> (ti(X_a,B)=ti(X_a,C)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),A_1)))))).
% 23.77/23.59 all X_a (order(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))->ti(X_a,X)=ti(X_a,Y))))).
% 23.77/23.59 all X_a (preorder(X_a)-> (all Z_1 X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Z_1)))))).
% 23.77/23.59 all X_a (order(X_a)-> (all Y X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))->ti(X_a,X)=ti(X_a,Y))))).
% 23.77/23.59 all X_a (order(X_a)-> (all Z_1 Y X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Z_1),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Z_1),X)))))).
% 23.77/23.59 all X_a X_b (ord(X_b)-> (all X_1 F G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1)))))).
% 23.77/23.59 all X_a (linorder(X_a)-> (all X Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))))).
% 23.77/23.59 all X_a (preorder(X_a)-> (all X (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X))))).
% 23.77/23.59 all X_a (linorder(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))))).
% 23.77/23.59 all X_a (linorder(X_a)-> (all X_1 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))|ti(X_a,X_1)=ti(X_a,Y_1)))).
% 23.77/23.59 all X_a (linorder(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))).
% 23.77/23.59 all X_a (linorder(X_a)-> (all Y_1 X_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1))-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1))<->ti(X_a,X_1)=ti(X_a,Y_1))))).
% 23.77/23.59 all X_a (linorder(X_a)-> (all X Y (ti(X_a,X)!=ti(X_a,Y)-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))).
% 23.77/23.59 all X_a (order(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))->ti(X_a,X)!=ti(X_a,Y)))).
% 23.77/23.59 all X_a (preorder(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))).
% 23.77/23.59 all X_a (preorder(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))).
% 23.77/23.59 all X_a (order(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))->ti(X_a,X)!=ti(X_a,Y)))).
% 23.77/23.59 all X_a (order(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))->ti(X_a,Y)!=ti(X_a,X)))).
% 23.77/23.59 all X_a (preorder(X_a)-> (all P_1 X_1 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))->hBOOL(P_1))))).
% 23.77/23.59 all X_a (preorder(X_a)-> (all 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),B),A_1))))).
% 23.77/23.59 all X_a (order(X_a)-> (all 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),A_1),B))))).
% 23.77/23.59 all X_a (ord(X_a)-> (all C A_1 B (A_1=B-> (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),A_1),C)))))).
% 23.77/23.59 all X_a (order(X_a)-> (all C A_1 B (ti(X_a,A_1)=ti(X_a,B)-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1)))))).
% 23.77/23.59 all X_a (ord(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))-> (B=C->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C)))))).
% 23.77/23.59 all X_a (order(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))-> (ti(X_a,B)=ti(X_a,C)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1)))))).
% 23.77/23.59 all X_a (preorder(X_a)-> (all Z_1 X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1)))))).
% 23.77/23.59 all X_a (order(X_a)-> (all Z_1 Y X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X)))))).
% 23.77/23.59 all X_a (preorder(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))).
% 23.77/23.59 all X_a (linorder(X_a)-> (all X Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))-> (ti(X_a,X)!=ti(X_a,Y)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))).
% 23.77/23.59 all X_a (linorder(X_a)-> (all X_1 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_e_q(X_a),Y_1),X_1))))).
% 23.77/23.59 all X_a (linorder(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))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1))))).
% 23.77/23.59 all X_a (linorder(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))).
% 23.77/23.59 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(X_a),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)))).
% 23.77/23.59 all X_a (preorder(X_a)-> (all X_1 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_e_q(X_a),X_1),Y_1))& -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y_1),X_1))))).
% 23.77/23.59 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))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1))|ti(X_a,X_1)=ti(X_a,Y_1)))).
% 23.77/23.59 all X_a (linorder(X_a)-> (all X Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))))).
% 23.77/23.59 all X_a (linorder(X_a)-> (all Y X (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))))).
% 23.77/23.59 all X_a (linorder(X_a)-> (all X_1 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_e_q(X_a),X_1),Y_1))<->ti(X_a,X_1)=ti(X_a,Y_1))))).
% 23.77/23.59 all X_a (order(X_a)-> (all A_1 B (ti(X_a,A_1)!=ti(X_a,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),A_1),B)))))).
% 23.77/23.59 all X_a (order(X_a)-> (all A_1 B (ti(X_a,A_1)!=ti(X_a,B)-> (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(X_a),B),A_1)))))).
% 23.77/23.59 all X_a (linorder(X_a)-> (all Y X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))))).
% 23.77/23.59 all A_1 B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int))))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B))).
% 23.77/23.59 all P_1 I_1 K_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),K_1))-> (hBOOL(hAPP(int,bool,P_1,K_1))-> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),K_1))-> (hBOOL(hAPP(int,bool,P_1,I_2))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int)))))))->hBOOL(hAPP(int,bool,P_1,I_1))))).
% 23.77/23.59 all P_1 I_1 K_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K_1))-> (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),one_one(int))))-> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),K_1))-> (hBOOL(hAPP(int,bool,P_1,I_2))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int)))))))->hBOOL(hAPP(int,bool,P_1,I_1))))).
% 23.77/23.59 all P_1 K_1 I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),I_1))-> (hBOOL(hAPP(int,bool,P_1,K_1))-> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),I_2))-> (hBOOL(hAPP(int,bool,P_1,I_2))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int)))))))->hBOOL(hAPP(int,bool,P_1,I_1))))).
% 23.77/23.59 all P_1 K_1 I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),I_1))-> (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),one_one(int))))-> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),I_2))-> (hBOOL(hAPP(int,bool,P_1,I_2))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int)))))))->hBOOL(hAPP(int,bool,P_1,I_1))))).
% 23.77/23.59 all X_a (dense_linorder(X_a)-> (all Z_1 Y ((all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_2),Z_1))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1))))).
% 23.77/23.59 all X_a (dense_linorder(X_a)-> (all Z_1 X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))-> ((all W_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W_2),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),W_2),Z_1)))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1)))))).
% 23.77/23.59 all X_b X_a (order(X_a)&order(X_b)-> (all C_1 F Ba Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C_1),hAPP(X_a,X_b,F,Ba)))-> ((all X_2 Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_2))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_2)))))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Aa)))))))).
% 23.77/23.59 all X_a X_b (ord(X_b)-> (all F G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G))<->hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G))& -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),G),F))))).
% 23.77/23.59 all X_a X_b (ord(X_b)-> (all F G ((all X_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))))->hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G))))).
% 23.77/23.59 all X_b X_a (order(X_a)&ord(X_b)-> (all C_1 F Ba Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_b,X_a,F,Ba)),Aa))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),Ba))-> ((all X_2 Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_2)))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),Aa))))))).
% 23.77/23.59 all X_b X_a (order(X_a)&order(X_b)-> (all C_1 F Ba Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ba)),Aa))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C_1),Ba))-> ((all X_2 Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_2),X_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_2)))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),Aa))))))).
% 23.77/23.59 all X_a X_b (order(X_b)&order(X_a)-> (all C_1 Aa F Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),hAPP(X_b,X_a,F,Ba)))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),C_1))-> ((all X_2 Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2)))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,C_1)))))))).
% 23.77/23.59 all X_a X_b (order(X_b)&order(X_a)-> (all C_1 Aa F Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ba)))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Ba),C_1))-> ((all X_2 Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Y_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2)))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,C_1)))))))).
% 23.77/23.59 all X_a X_b (order(X_b)&order(X_a)-> (all F C_1 Aa Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Ba)),C_1))-> ((all X_2 Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_2),Y_2))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2)))))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),C_1))))))).
% 23.77/23.59 all X_a X_b (order(X_b)&order(X_a)-> (all F C_1 Aa Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,Ba)),C_1))-> ((all X_2 Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_2))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2)))))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),C_1))))))).
% 23.77/23.59 all X_b X_a (order(X_a)&order(X_b)-> (all C_1 F Ba Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ba),Aa))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Ba)))-> ((all X_2 Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y_2),X_2))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_2)))))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Aa)))))))).
% 23.77/23.59 all I_1 P_1 K_1 (hBOOL(hAPP(int,bool,P_1,K_1))-> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),I_2))-> (hBOOL(hAPP(int,bool,P_1,I_2))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int)))))))-> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),K_1))-> (hBOOL(hAPP(int,bool,P_1,I_2))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int)))))))->hBOOL(hAPP(int,bool,P_1,I_1))))).
% 23.77/23.59 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)))).
% 23.77/23.59 all X_1 P_1 ((all A_2 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_2))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_2),one_one(int)))))->hBOOL(hAPP(int,bool,P_1,A_2))))->hBOOL(hAPP(int,bool,P_1,X_1))).
% 23.77/23.59 all X_a (linord626643107strict(X_a)-> (all V U_1 Y X A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),U_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),V))-> (hAPP(X_a,X_a,hAPP(X_a,fun(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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1))))))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all V_1 X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))),X_1))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X_1 V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1))))).
% 23.77/23.59 all X_a (zero(X_a)-> (all X_1 (zero_zero(X_a)=ti(X_a,X_1)<->ti(X_a,X_1)=zero_zero(X_a)))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)->hAPP(X_a,int,archimedean_ceiling(X_a),zero_zero(X_a))=zero_zero(int)).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),zero_zero(int)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),zero_zero(X_a)))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),one_one(int)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),zero_zero(X_a)))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1))))).
% 23.77/23.59 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1)=zero_zero(X_a)))).
% 23.77/23.59 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a))=zero_zero(X_a)))).
% 23.77/23.59 all X_a (mult_zero(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1)=zero_zero(X_a)))).
% 23.77/23.59 all X_a (real_normed_algebra(X_a)-> (all B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),B)=zero_zero(X_a)))).
% 23.77/23.59 all X_a (real_normed_algebra(X_a)-> (all Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),Y)=zero_zero(X_a)))).
% 23.77/23.59 all X_a (mult_zero(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a))=zero_zero(X_a)))).
% 23.77/23.59 all X_a (real_normed_algebra(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a))=zero_zero(X_a)))).
% 23.77/23.59 all X_a (real_normed_algebra(X_a)-> (all X (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),zero_zero(X_a))=zero_zero(X_a)))).
% 23.77/23.59 all X_a (ring_n68954251visors(X_a)-> (all Aa Ba (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)=zero_zero(X_a)<->ti(X_a,Aa)=zero_zero(X_a)|ti(X_a,Ba)=zero_zero(X_a)))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)!=zero_zero(X_a))))).
% 23.77/23.59 all X_a (no_zero_divisors(X_a)-> (all A_1 B (hAPP(X_a,X_a,hAPP(X_a,fun(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)))).
% 23.77/23.59 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1)=ti(X_a,A_1)))).
% 23.77/23.59 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a))=ti(X_a,A_1)))).
% 23.77/23.59 all X_a (semiri456707255roduct(X_a)-> (all Ba Aa (ti(X_a,Ba)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa)<->ti(X_a,Aa)=zero_zero(X_a)))).
% 23.77/23.59 all X_a (monoid_add(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1)=ti(X_a,A_1)))).
% 23.77/23.59 all X_a (comm_monoid_add(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1)=ti(X_a,A_1)))).
% 23.77/23.59 all X_a (linord219039673up_add(X_a)-> (all Aa (zero_zero(X_a)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)<->ti(X_a,Aa)=zero_zero(X_a)))).
% 23.77/23.59 all X_a (monoid_add(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a))=ti(X_a,A_1)))).
% 23.77/23.59 all X_a (comm_monoid_add(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a))=ti(X_a,A_1)))).
% 23.77/23.59 all X_a (linord219039673up_add(X_a)-> (all Aa (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)=zero_zero(X_a)<->ti(X_a,Aa)=zero_zero(X_a)))).
% 23.77/23.59 all X_a (zero_ne_q_one(X_a)->one_one(X_a)!=zero_zero(X_a)).
% 23.77/23.59 all X_a (zero_ne_q_one(X_a)->zero_zero(X_a)!=one_one(X_a)).
% 23.77/23.59 all X_a (group_add(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),zero_zero(X_a))=ti(X_a,A_1)))).
% 23.77/23.59 all X_a (group_add(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_1)=zero_zero(X_a)))).
% 23.77/23.59 all X_a (ab_group_add(X_a)-> (all Aa Ba (ti(X_a,Aa)=ti(X_a,Ba)<->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)=zero_zero(X_a)))).
% 23.77/23.59 all X_a (group_add(X_a)-> (all Aa Ba (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)=zero_zero(X_a)<->ti(X_a,Aa)=ti(X_a,Ba)))).
% 23.77/23.59 zero_zero(int)!=one_one(int).
% 23.77/23.59 all Z_1 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),Z_1)=Z_1).
% 23.77/23.59 all Z_1 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),zero_zero(int))=Z_1).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(X_a,int,archimedean_ceiling(X_a),Y)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all Y X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archimedean_ceiling(X_a),Y)),hAPP(X_a,int,archimedean_ceiling(X_a),X)))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)->hAPP(X_a,int,archimedean_ceiling(X_a),one_one(X_a))=one_one(int)).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all V (hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(int,X_a,number_number_of(X_a),V))=hAPP(int,int,number_number_of(int),V)))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1))))).
% 23.77/23.59 all X_a (linord581940658strict(X_a)-> (all Aa Ba (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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Aa))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Ba))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),zero_zero(X_a)))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ba),zero_zero(X_a)))))).
% 23.77/23.59 all X_a (linord581940658strict(X_a)-> (all Aa Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),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)),Aa))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ba),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),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)),Ba))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),zero_zero(X_a))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))))))).
% 23.77/23.59 all X_a (ordered_semiring(X_a)-> (all C D_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),C),D_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1))))))))).
% 23.77/23.59 all X_a (ordered_semiring(X_a)-> (all C D_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),C),D_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))-> (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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1))))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)),zero_zero(X_a)))))).
% 23.77/23.59 all X_a (linord581940658strict(X_a)-> (all Aa C_1 Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),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),Aa),Ba))|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),Ba),Aa))))).
% 23.77/23.59 all X_a (linord581940658strict(X_a)-> (all C_1 Aa Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))<->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),Aa),Ba))|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),Ba),Aa))))).
% 23.77/23.59 all X_a (linord581940658strict(X_a)-> (all Aa Ba 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),zero_zero(X_a))))))).
% 23.77/23.59 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,hAPP(X_a,fun(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)))))).
% 23.77/23.59 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,hAPP(X_a,fun(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)))))).
% 23.77/23.59 all X_a (linord581940658strict(X_a)-> (all Aa Ba 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa)))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))))))).
% 23.77/23.59 all X_a (linord219039673up_add(X_a)-> (all Aa (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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Aa))))).
% 23.77/23.59 all X_a (linord219039673up_add(X_a)-> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),zero_zero(X_a)))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))))))).
% 23.77/23.59 all X_a (ordere216010020id_add(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))-> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1)=zero_zero(X_a)<->ti(X_a,X_1)=zero_zero(X_a)&ti(X_a,Y_1)=zero_zero(X_a)))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a))))))).
% 23.77/23.59 all X_a (linord219039673up_add(X_a)-> (all Aa (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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa))))).
% 23.77/23.59 all X_a (linordered_idom(X_a)-> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a)))))).
% 23.77/23.59 all X_a (linord219039673up_add(X_a)-> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a)))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a))))))).
% 23.77/23.59 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)))).
% 23.77/23.59 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)))).
% 23.77/23.59 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)))).
% 23.77/23.59 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)))).
% 23.77/23.59 all X_a (ordered_ab_group_add(X_a)-> (all Aa Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),zero_zero(X_a)))))).
% 23.77/23.59 all X_a (semiri456707255roduct(X_a)-> (all C D_1 A_1 B R (ti(X_a,R)!=zero_zero(X_a)-> (ti(X_a,A_1)=ti(X_a,B)&ti(X_a,C)!=ti(X_a,D_1)->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R),C))!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R),D_1)))))).
% 23.77/23.59 all X_a (ordered_ab_group_add(X_a)-> (all Aa Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),zero_zero(X_a)))))).
% 23.77/23.59 all A_1 X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),A_1))-> (X!=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),one_one(int))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),one_one(int))))))).
% 23.77/23.59 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))).
% 23.77/23.59 all K I J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),J))-> (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),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),J))))).
% 23.77/23.59 all Z_1 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_1)),Z_1)!=zero_zero(int)).
% 23.77/23.59 all K_1 L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),L))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),L)),zero_zero(int)))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),X_1))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),one_one(int)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),one_one(X_a)))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all V_1 X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),X_1))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X_1 V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),V_1)))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X (hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a)))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),one_one(int))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X V (hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V)))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(int,int,number_number_of(int),V))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X (hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a)))=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),one_one(int))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X V (hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V)))=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(int,int,number_number_of(int),V))))).
% 23.77/23.59 all X_a (linord581940658strict(X_a)-> (all Aa Ba 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba)))))).
% 23.77/23.59 all X_a (linord581940658strict(X_a)-> (all Aa Ba 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ba),Aa)))))).
% 23.77/23.59 all X_a (linord20386208strict(X_a)-> (all C D_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(X_a),C),D_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))-> (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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1))))))))).
% 23.77/23.59 all X_a (linord20386208strict(X_a)-> (all C D_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(X_a),C),D_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1))))))))).
% 23.77/23.59 all X_a (linord20386208strict(X_a)-> (all C D_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),C),D_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1))))))))).
% 23.77/23.59 all X_a (linord20386208strict(X_a)-> (all C D_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(X_a),C),D_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1))))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(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)))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(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)))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(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)))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(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)))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(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)))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(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)))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a))))))).
% 23.77/23.59 all X_a (linordered_idom(X_a)-> (all Y X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),one_one(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),X))))))).
% 23.77/23.59 all X_a (linordered_idom(X_a)-> (all Y X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),one_one(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X)),X))))))).
% 23.77/23.59 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))))).
% 23.77/23.59 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z))).
% 23.77/23.59 all N_2 M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M_1))-> (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N_2)=one_one(int)<->M_1=one_one(int)&N_2=one_one(int))).
% 23.77/23.59 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z)),Z)),zero_zero(int)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),zero_zero(int)))).
% 23.77/23.59 all X_a (linord1278240602ring_1(X_a)-> (all V U_1 Y X A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),U_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),V))-> (hAPP(X_a,X_a,hAPP(X_a,fun(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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1))))))))).
% 23.77/23.59 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,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_1)))).
% 23.77/23.59 all R Q A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (A_1=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q),one_one(int)))))).
% 23.77/23.59 all R Q A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))-> (A_1=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R),A_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Q))))).
% 23.77/23.59 all B Q R B_1 Q_1 R_3 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q)),R)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),R_3)-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),R_3)),zero_zero(int)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R),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_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_1),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q)))))))).
% 23.77/23.59 all B Q_1 R_3 Q R (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_1)),R_3)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q)),R)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R),zero_zero(int)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R))-> (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),Q_1)))))).
% 23.77/23.59 all B Q R B_1 Q_1 R_3 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q)),R)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),R_3)-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),R_3)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R))-> (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),B_1),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q),Q_1)))))))).
% 23.77/23.59 all B Q_1 R_3 Q R (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_1)),R_3)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q)),R)))-> (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),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q)))))).
% 23.77/23.59 all B_1 Q_1 R_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),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_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),zero_zero(int)))))).
% 23.77/23.59 all B_1 Q_1 R_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),R_3)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),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_e_q(int),zero_zero(int)),Q_1))))).
% 23.77/23.59 all M R S T_3 N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1))-> (hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M),N_1)=hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),R),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S),T_3))->R=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_3),N_1)))).
% 23.77/23.59 all X_a (linord581940658strict(X_a)-> (all X_1 Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))))<->ti(X_a,X_1)!=zero_zero(X_a)|ti(X_a,Y_1)!=zero_zero(X_a)))).
% 23.77/23.59 all X_a (linordered_ring(X_a)-> (all X Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y))),zero_zero(X_a)))))).
% 23.77/23.59 all X_a (linord581940658strict(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(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))),zero_zero(X_a)))<->ti(X_a,X_1)=zero_zero(X_a)&ti(X_a,Y_1)=zero_zero(X_a)))).
% 23.77/23.59 all X_a (linordered_ring(X_a)-> (all X Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y)))))).
% 23.77/23.59 all X_a (linord581940658strict(X_a)-> (all X_1 Y_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))=zero_zero(X_a)<->ti(X_a,X_1)=zero_zero(X_a)&ti(X_a,Y_1)=zero_zero(X_a)))).
% 23.77/23.59 all M N_1 R_3 S_1 S T_4 T_3 Rn Sn Tn R (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R))-> (hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N_1),R_3),R),S_1),S),T_4),T_3)=hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),Rn),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Sn),Tn))-> (R_3=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_4),N_1))-> (R=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_3),N_1))->Rn=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Sn),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Tn),N_1)))))).
% 23.77/23.59 all Y X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y))))).
% 23.77/23.59 all Y X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y))))).
% 23.77/23.59 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,hAPP(int,fun(int,int),times_times(int),A_1),B)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)))).
% 23.77/23.59 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),one_one(int))).
% 23.77/23.59 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),zero_zero(int))).
% 23.77/23.59 all M N_1 (hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M),N_1)=hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N_1),M),N_1),one_one(int)),zero_zero(int)),zero_zero(int)),one_one(int))).
% 23.77/23.59 all K_1 P_1 D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))-> ((all X_2 (hBOOL(hAPP(int,bool,P_1,X_2))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)))))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K_1))-> (all X_2 (hBOOL(hAPP(int,bool,P_1,X_2))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_2))))))))).
% 23.77/23.59 all K_1 P_1 D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))-> ((all X_2 (hBOOL(hAPP(int,bool,P_1,X_2))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)))))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K_1))-> (all X_2 (hBOOL(hAPP(int,bool,P_1,X_2))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_2))))))))).
% 23.77/23.59 all X_a (linord1117847801e_zero(X_a)-> (all X Y ((all Z_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Z_3))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_3),X)),Y)))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))))).
% 23.77/23.59 all A_1 B Q R (A_1=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q)),R)-> ((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)),R))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R),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),B),R))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R),zero_zero(int))))->hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q),R))))).
% 23.77/23.59 all Y X ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Y),X))->hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Y),X))->hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)=zero_zero(int))).
% 23.77/23.59 all B (B!=zero_zero(int)->hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,zero_zero(int)),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int))))).
% 23.77/23.59 all A_1 Q R (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),A_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q),R)))-> (A_1!=zero_zero(int)->R=zero_zero(int))).
% 23.77/23.59 all Q_1 R_3 A_1 B Q R (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q),R)))-> (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_1),R_3)))-> (B!=zero_zero(int)->Q=Q_1))).
% 23.77/23.59 all Q_1 R_3 A_1 B Q R (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q),R)))-> (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_1),R_3)))-> (B!=zero_zero(int)->R=R_3))).
% 23.77/23.59 all A_1 Q R (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),A_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q),R)))-> (A_1!=zero_zero(int)->Q=one_one(int))).
% 23.77/23.59 all Y X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y))))).
% 23.77/23.59 all Y X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Y),X))->hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y)).
% 23.77/23.59 all P_2 P_1 X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))-> (hBOOL(P_1)<->hBOOL(P_2)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))&hBOOL(P_1)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))&hBOOL(P_2))).
% 23.77/23.59 all P_2 P_1 X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))-> (hBOOL(P_1)<->hBOOL(P_2)))-> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))->hBOOL(P_1))<-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))->hBOOL(P_2)))).
% 23.77/23.59 all X_a (linordered_field(X_a)-> (all X Y ((all E (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),E))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),E)))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))))).
% 23.77/23.59 all X_a (linorder(X_a)-> (all T_3 exists Z_3 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),X_2))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_2),T_3))))).
% 23.77/23.59 all X_a (linorder(X_a)-> (all T_3 exists Z_3 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_3))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_2),T_3))))).
% 23.77/23.59 all X_a (linorder(X_a)-> (all T_3 exists Z_3 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),X_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),T_3),X_2))))).
% 23.77/23.59 all X_a (linorder(X_a)-> (all T_3 exists Z_3 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_3))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),T_3),X_2))))).
% 23.77/23.59 all P_1 P1 D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))-> ((all X_2 K_2 (hBOOL(hAPP(int,bool,P1,X_2))<->hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_2),D_2))))))-> ((exists Z_3 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Z_3))-> (hBOOL(hAPP(int,bool,P_1,X_2))<->hBOOL(hAPP(int,bool,P1,X_2)))))-> ((exists X1 hBOOL(hAPP(int,bool,P1,X1)))-> (exists X1 hBOOL(hAPP(int,bool,P_1,X1))))))).
% 23.77/23.59 all P_1 P_2 D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))-> ((all X_2 K_2 (hBOOL(hAPP(int,bool,P_2,X_2))<->hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_2),D_2))))))-> ((exists Z_3 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_3),X_2))-> (hBOOL(hAPP(int,bool,P_1,X_2))<->hBOOL(hAPP(int,bool,P_2,X_2)))))-> ((exists X1 hBOOL(hAPP(int,bool,P_2,X1)))-> (exists X1 hBOOL(hAPP(int,bool,P_1,X1))))))).
% 23.77/23.59 all N_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_1),zero_zero(int)))->hAPP(int,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)))->hAPP(int,int,zfact,N_1)=hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N_1),hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N_1),one_one(int)))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X_1 V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all V_1 X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))),X_1))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)->hAPP(X_a,int,archim2085082626_floor(X_a),zero_zero(X_a))=zero_zero(int)).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(X_a,int,archim2085082626_floor(X_a),Y)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(X_a,int,archim2085082626_floor(X_a),Y)))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)->hAPP(X_a,int,archim2085082626_floor(X_a),one_one(X_a))=one_one(int)).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all V (hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(int,X_a,number_number_of(X_a),V))=hAPP(int,int,number_number_of(int),V)))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),zero_zero(int)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),zero_zero(X_a)))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(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)),X_1))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),X_1))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),zero_zero(int)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a)))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),one_one(int)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a)))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),X_1))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X_1 V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),V_1)))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all V_1 X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),X_1))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X (hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a)))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X V (hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V)))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(int,int,number_number_of(int),V))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X (hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a)))=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int))))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all X V (hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V)))=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(int,int,number_number_of(int),V))))).
% 23.77/23.59 all B A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),A_1))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(real,int,archim2085082626_floor(real),A_1)),hAPP(real,int,archim2085082626_floor(real),B))),hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B)))))).
% 23.77/23.59 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),zero_zero(int)),B))->hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B))))).
% 23.77/23.59 all Z_1 X D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Z_1))),one_one(int))),D_1))))).
% 23.77/23.59 all X Z_1 D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Z_1))),one_one(int))),D_1))),Z_1))).
% 23.77/23.59 all X_a (linordered_idom(X_a)-> (all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))))))).
% 23.77/23.59 all W_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W_1),W_1)).
% 23.77/23.59 all Z_1 W_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z_1),W_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W_1),Z_1))).
% 23.77/23.59 all Z_1 X Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z_1),X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z_1),Y)))).
% 23.77/23.59 all K I J (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I),J))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),J),K))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I),K)))).
% 23.77/23.59 all Z_1 W_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z_1),W_1))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W_1),Z_1))->Z_1=W_1)).
% 23.77/23.59 all Z1 Z2 W_1 (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z1),Z2)),W_1)=hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),W_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z2),W_1))).
% 23.77/23.59 all Z1 Z2 Z3 (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),Z2)),Z3)=hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z2),Z3))).
% 23.77/23.59 all Z_1 W_1 (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),W_1)=hAPP(real,real,hAPP(real,fun(real,real),times_times(real),W_1),Z_1)).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 (hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1))=hAPP(X_a,X_a,abs_abs(X_a),A_1)))).
% 23.77/23.59 all Z_1 (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),one_one(real)),Z_1)=Z_1).
% 23.77/23.59 all 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(real),X_1),Y_1))|X_1=Y_1).
% 23.77/23.59 all X_1 Y_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_e_q(real),X_1),Y_1))&X_1!=Y_1).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 B (hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))=hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))))).
% 23.77/23.59 all X_a (linordered_idom(X_a)->hAPP(X_a,X_a,abs_abs(X_a),one_one(X_a))=one_one(X_a)).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 B (hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))).
% 23.77/23.59 all X_a (linordered_idom(X_a)-> (all A_1 B (hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))).
% 23.77/23.59 all X_a (linordered_idom(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),A_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)))).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),hAPP(X_a,X_a,abs_abs(X_a),A_1))))).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all 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,abs_abs(X_a),A_1)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))))).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)->hAPP(X_a,X_a,abs_abs(X_a),zero_zero(X_a))=zero_zero(X_a)).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all Aa (hAPP(X_a,X_a,abs_abs(X_a),Aa)=zero_zero(X_a)<->ti(X_a,Aa)=zero_zero(X_a)))).
% 23.77/23.59 all 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,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_1)),zero_zero(real)))).
% 23.77/23.59 all Aa Ba C_1 (C_1!=zero_zero(real)-> (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),Aa)=hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),Ba)<->Aa=Ba)).
% 23.77/23.59 all Aa Ba C_1 (C_1!=zero_zero(real)-> (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Aa),C_1)=hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Ba),C_1)<->Aa=Ba)).
% 23.77/23.59 all X_1 Y_1 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),X_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Y_1))=zero_zero(real)<->X_1=zero_zero(real)&Y_1=zero_zero(real)).
% 23.77/23.59 zero_zero(real)!=one_one(real).
% 23.77/23.59 all X_1 Y_1 Z (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),Z)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Z)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)))).
% 23.77/23.59 all Y X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y))))).
% 23.77/23.59 all X Y Z_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_1))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),Y))))).
% 23.77/23.59 all X_1 Y_1 Z (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),X_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),Y_1)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),Y_1)))).
% 23.77/23.59 all X_1 Y_1 Z (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),Z)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Z)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),Y_1)))).
% 23.77/23.59 all X_a (ring_1(X_a)->hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),zero_zero(X_a)),ring_1_Ints(X_a)))).
% 23.77/23.59 all X_a (ring_1(X_a)-> (all Ba Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))-> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a)))->hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),ring_1_Ints(X_a))))))).
% 23.77/23.59 all X_a (ring_1(X_a)-> (all Ba Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))-> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a)))->hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba)),ring_1_Ints(X_a))))))).
% 23.77/23.59 all X_a (number_ring(X_a)-> (all W hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,number_number_of(X_a),W)),ring_1_Ints(X_a))))).
% 23.77/23.59 all X_a (ring_1(X_a)->hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),one_one(X_a)),ring_1_Ints(X_a)))).
% 23.77/23.59 all X_a (ring_1(X_a)-> (all Ba Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))-> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a)))->hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),ring_1_Ints(X_a))))))).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,abs_abs(X_a),A_1))))).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,abs_abs(X_a),Aa)),zero_zero(X_a)))<->ti(X_a,Aa)=zero_zero(X_a)))).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))->hAPP(X_a,X_a,abs_abs(X_a),A_1)=ti(X_a,A_1)))).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),zero_zero(X_a)))))).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all Aa (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,abs_abs(X_a),Aa)))<->ti(X_a,Aa)!=zero_zero(X_a)))).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))->hAPP(X_a,X_a,abs_abs(X_a),A_1)=ti(X_a,A_1)))).
% 23.77/23.59 all X_a (linordered_idom(X_a)-> (all B D_1 A_1 C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),C))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),B)),D_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),D_1))))))).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all 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,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))))).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all 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,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1)))))).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all 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,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)))))).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all 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,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)))))).
% 23.77/23.59 all X_a (linordered_idom(X_a)-> (all X_1 Aa R_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),Aa))),R_2))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),R_2)),X_1))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),R_2)))))).
% 23.77/23.59 all M N_1 (hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N_1))=one_one(int)->hAPP(int,int,abs_abs(int),M)=one_one(int)).
% 23.77/23.59 all X_a (ordered_ring_abs(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),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),B),zero_zero(X_a))))->hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))).
% 23.77/23.59 all X_a (linordered_idom(X_a)-> (all Y X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X))->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),Y)),X)=hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X))))).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 B C D_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1)))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),C))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),D_1))))))).
% 23.77/23.59 all X_a (ordere142940540dd_abs(X_a)-> (all 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,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))))).
% 23.77/23.59 all X_a (ring_char_0(X_a)-> (all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))-> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)=zero_zero(X_a)<->ti(X_a,Aa)=zero_zero(X_a))))).
% 23.77/23.59 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z)),one_one(int)))<->Z=zero_zero(int)).
% 23.77/23.59 all B (hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,zero_zero(int)),B)=hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int))).
% 23.77/23.59 all X_a (ring_char_0(X_a)-> (all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa)!=zero_zero(X_a)))).
% 23.77/23.59 all K L_1 ((L_1=zero_zero(int)->hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L_1)=hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),hAPP(int,int,abs_abs(int),K)))& (L_1!=zero_zero(int)->hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L_1)=hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,abs_abs(int),K)),hAPP(int,int,abs_abs(int),L_1)))).
% 23.77/23.59 all K_1 F N_2 M_1 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),I_2))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_2))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int)))))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M_1)),K_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))-> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),I_2))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),N_2))&hAPP(nat,int,F,I_2)=K_1)))))).
% 23.77/23.59 all K_1 F N_2 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_2))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int)))))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))-> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),N_2))&hAPP(nat,int,F,I_2)=K_1))))).
% 23.77/23.59 all K_1 F N_2 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_2))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int)))))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))-> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),N_2))&hAPP(nat,int,F,I_2)=K_1))))).
% 23.77/23.59 all N_1 M ((M=zero_zero(nat)->hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)=zero_zero(nat))& (M!=zero_zero(nat)->hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_1)))).
% 23.77/23.59 all X (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),X)),one_one(real))),X))).
% 23.77/23.59 all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(real,real,abs_abs(real),X)))).
% 23.77/23.59 all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N_1)).
% 23.77/23.59 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))).
% 23.77/23.59 all U_1 V X Y (X=Y-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,abs_abs(real),U_1)),V))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),U_1)),Y))),V)))).
% 23.77/23.59 all U M_1 N_2 I_1 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_2))))).
% 23.77/23.59 all K M N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))).
% 23.77/23.59 all M N_1 K (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))).
% 23.77/23.59 all I J K (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),K)),J)).
% 23.77/23.59 all M N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),M)).
% 23.77/23.59 all M N_1 K (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))).
% 23.77/23.59 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N_1)=zero_zero(nat)).
% 23.77/23.59 all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),zero_zero(nat))=zero_zero(nat)).
% 23.77/23.59 all M_1 N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)=zero_zero(nat)<->M_1=zero_zero(nat)|N_2=zero_zero(nat)).
% 23.77/23.59 all K_1 M_1 N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)<->K_1=zero_zero(nat)|M_1=N_2).
% 23.77/23.59 all K_1 M_1 N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)<->M_1=N_2|K_1=zero_zero(nat)).
% 23.77/23.59 all M_1 K_1 N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_1)<->M_1=N_2|K_1=zero_zero(nat)).
% 23.77/23.59 all M N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)=zero_zero(nat)-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M)=zero_zero(nat)->M=N_1)).
% 23.77/23.59 all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M)=zero_zero(nat)).
% 23.77/23.59 all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat))=M).
% 23.77/23.59 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N_1)=zero_zero(nat)).
% 23.77/23.59 all P_1 M_1 N_2 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1)))-> ((M_1=N_2->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1)))-> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1))))).
% 23.77/23.59 all S T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3))->S!=T_3).
% 23.77/23.59 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M))->M!=N_1).
% 23.77/23.59 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))).
% 23.77/23.59 all X Y (X!=Y-> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X)))).
% 23.77/23.59 all M_1 N_2 (M_1!=N_2<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))).
% 23.77/23.59 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))).
% 23.77/23.59 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,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M))))).
% 23.77/23.59 all N_1 J K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),N_1)),K))).
% 23.77/23.59 all M N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),N_1)=M).
% 23.77/23.59 all N_1 M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)),N_1)=M).
% 23.77/23.59 all I J K (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))).
% 23.77/23.59 all K M N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)).
% 23.77/23.59 all M K N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)).
% 23.77/23.59 all M_1 K_1 N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K_1)<->M_1=N_2).
% 23.77/23.59 all K_1 M_1 N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2)<->M_1=N_2).
% 23.77/23.59 all M N_1 K (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))).
% 23.77/23.59 all X Y Z_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Z_1))).
% 23.77/23.59 all M N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)).
% 23.77/23.59 all K M N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))).
% 23.77/23.59 all M N_1 K (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))).
% 23.77/23.59 all I U_1 J K (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),U_1)),K)).
% 23.77/23.59 all M N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),M)).
% 23.77/23.59 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,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M)))).
% 23.77/23.59 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,hAPP(nat,fun(nat,nat),minus_minus(nat),M),L_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),L_1)))).
% 23.77/23.59 all I N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),N_1))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),I))=I).
% 23.77/23.59 all N_2 K_1 M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_2))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_1)<->M_1=N_2))).
% 23.77/23.59 all N_1 K M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),M))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N_1))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1))).
% 23.77/23.59 all N_2 K_1 M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))))).
% 23.77/23.59 all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),N_1)).
% 23.77/23.59 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))).
% 23.77/23.59 all M N_1 (M=N_1->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))).
% 23.77/23.59 all K I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),K))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),K)))).
% 23.77/23.59 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)).
% 23.77/23.59 all K L_1 I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),L_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),L_1))))).
% 23.77/23.59 all K I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),I)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),J)))).
% 23.77/23.59 all K I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K)))).
% 23.77/23.59 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M)))).
% 23.77/23.59 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M))).
% 23.77/23.59 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N_1)=N_1).
% 23.77/23.59 all M_1 N_2 (one_one(nat)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)<->M_1=one_one(nat)&N_2=one_one(nat)).
% 23.77/23.59 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),one_one(nat))=N_1).
% 23.77/23.59 all M_1 N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)=one_one(nat)<->M_1=one_one(nat)&N_2=one_one(nat)).
% 23.77/23.59 all N_2 M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),M_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))).
% 23.77/23.59 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,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),M)))).
% 23.77/23.59 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))).
% 23.77/23.59 all N_2 (N_2!=zero_zero(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2))).
% 23.77/23.59 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))).
% 23.77/23.59 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->N_1!=zero_zero(nat)).
% 23.77/23.59 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))).
% 23.77/23.59 all K I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))-> (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,hAPP(nat,fun(nat,nat),times_times(nat),K),I)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),J))))).
% 23.77/23.59 all K I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))-> (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,hAPP(nat,fun(nat,nat),times_times(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K))))).
% 23.77/23.59 all M_1 N_2 K_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,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)))).
% 23.77/23.59 all M_1 N_2 K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)<->M_1=N_2)).
% 23.77/23.59 all M_1 K_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_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),M_1),N_2))).
% 23.77/23.59 all K_1 M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)))<->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),M_1),N_2))).
% 23.77/23.59 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2))).
% 23.77/23.59 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N_1)=N_1).
% 23.77/23.59 all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),zero_zero(nat))=M).
% 23.77/23.59 all M_1 N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)=zero_zero(nat)<->M_1=zero_zero(nat)&N_2=zero_zero(nat)).
% 23.77/23.59 all M N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)=M->N_1=zero_zero(nat)).
% 23.77/23.59 all N_1 M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M))=zero_zero(nat)).
% 23.77/23.59 all M_1 N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_2)=zero_zero(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))).
% 23.77/23.59 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)=zero_zero(nat)).
% 23.77/23.59 all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N_1)).
% 23.77/23.59 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),zero_zero(nat)))<->N_2=zero_zero(nat)).
% 23.77/23.59 all I J (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),I))).
% 23.77/23.59 all J I (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),I))).
% 23.77/23.59 all K_1 M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))).
% 23.77/23.59 all M I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M)))).
% 23.77/23.59 all M I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J)))).
% 23.77/23.59 all K I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K)))).
% 23.77/23.59 all K L_1 I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1))))).
% 23.77/23.59 all M N_1 K L_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L_1))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)))).
% 23.77/23.59 all I J K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K))).
% 23.77/23.59 all M N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1))=M).
% 23.77/23.59 all I_1 J_2 K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2))).
% 23.77/23.59 all M N_1 (M=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)->N_1=one_one(nat)|M=zero_zero(nat)).
% 23.77/23.59 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))).
% 23.77/23.59 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)))).
% 23.77/23.59 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))).
% 23.77/23.59 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|M_1=N_2).
% 23.77/23.59 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))&M_1!=N_2).
% 23.77/23.59 all N_2 K_1 M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))))).
% 23.77/23.59 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,hAPP(nat,fun(nat,nat),minus_minus(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),C))))).
% 23.77/23.59 all I K J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),J)).
% 23.77/23.59 all J_2 K_1 I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)),I_1))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)))).
% 23.77/23.59 all M K N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)),K)))).
% 23.77/23.59 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1))=M).
% 23.77/23.59 all I K J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K)).
% 23.77/23.59 all I_1 K_1 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2)))).
% 23.77/23.59 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),N_1)=M).
% 23.77/23.59 all K_1 I_1 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)=K_1<->J_2=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),I_1))).
% 23.77/23.59 all I K J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))).
% 23.77/23.59 all I K J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),K)).
% 23.77/23.59 all I K J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I)).
% 23.77/23.59 all U M_1 N_2 I_1 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)<->M_1=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_2))).
% 23.77/23.59 all U_1 M N_1 I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I)),U_1)),N_1))).
% 23.77/23.59 all U M_1 N_2 I_1 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_2))))).
% 23.77/23.59 all U M_1 N_2 J_2 I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_1))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)<->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M_1)=N_2)).
% 23.77/23.59 all U_1 M N_1 J I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),I))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),U_1)),M)),N_1)).
% 23.77/23.59 all U M_1 N_2 J_2 I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M_1)),N_2)))).
% 23.77/23.59 all M K N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),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),N_1)))).
% 23.77/23.59 all M K N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))).
% 23.77/23.59 all M K N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N_1))).
% 23.77/23.59 all K L_1 I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),L_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1))))).
% 23.77/23.59 all K I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K)))).
% 23.77/23.59 all M I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J)))).
% 23.77/23.59 all M I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M)))).
% 23.77/23.59 all K_1 M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))).
% 23.77/23.59 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))<-> (exists K_2 (N_2=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2)))).
% 23.77/23.59 all N_1 M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M))).
% 23.77/23.59 all N_1 M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))).
% 23.77/23.59 all X_1 Y_1 Z (X_1=hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y_1),Z)<->Y_1=hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Z)).
% 23.77/23.59 all P_1 Aa Ba (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))<-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba))& -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| (exists D (Aa=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),D)& -hBOOL(hAPP(nat,bool,P_1,D)))))).
% 23.77/23.59 all P_1 Aa Ba (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))<-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba))->hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))))& (all D (Aa=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),D)->hBOOL(hAPP(nat,bool,P_1,D))))).
% 23.77/23.59 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2))).
% 23.77/23.59 all K_1 M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)))<-> (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_e_q(nat),M_1),N_2)))).
% 23.77/23.59 all M_1 K_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_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_e_q(nat),M_1),N_2)))).
% 23.77/23.59 all M_1 N_2 K_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_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)))).
% 23.77/23.59 all U M_1 N_2 J_2 I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M_1)),N_2)))).
% 23.77/23.59 all N_2 P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))-> (hBOOL(hAPP(nat,bool,P_1,N_2))-> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),N_2))& (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),K_2))-> -hBOOL(hAPP(nat,bool,P_1,I_2))))&hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),one_one(nat)))))))).
% 23.77/23.59 all X Y C (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),C),zero_zero(real)))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,abs_abs(real),Y))))->X=zero_zero(real))).
% 23.77/23.59 all M_1 K_1 F ((all M_2 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_2)),hAPP(nat,nat,F,N)))))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,M_1)),K_1)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1))))).
% 23.77/23.59 all N_2 P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))-> (hBOOL(hAPP(nat,bool,P_1,N_2))-> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),N_2))& (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_2))-> -hBOOL(hAPP(nat,bool,P_1,I_2))))&hBOOL(hAPP(nat,bool,P_1,K_2)))))).
% 23.77/23.59 all K_1 L (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L))<-> (exists N (L=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N)))).
% 23.77/23.59 all I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))-> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2))&hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_2)=J))).
% 23.77/23.59 all X_1 (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),X_1)))<->X_1=zero_zero(real)).
% 23.77/23.59 all N_1 M K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)->N_1=M)).
% 23.77/23.59 all B A_1 X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B))-> (exists D (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D))& (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y_2))),D))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),A_1),Y_2))&hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Y_2),B)))))))).
% 23.77/23.59 all K L_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),L_1))-> (exists N (L_1=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N)))).
% 23.77/23.59 all I_1 J_2 F ((all I_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_2)),hAPP(nat,nat,F,J_1)))))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_2))))).
% 23.77/23.59 all B A_1 X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B))-> (exists D (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D))& (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y_2))),D))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),Y_2))&hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),B)))))))).
% 23.77/23.59 all D2 D1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D1))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D2))-> (exists E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E))&hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),E),D1))&hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),E),D2)))))).
% 23.77/23.59 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X))->hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),one_one(nat))).
% 23.77/23.59 all N_1 (hAPP(real,nat,natceiling,hAPP(int,real,number_number_of(real),N_1))=hAPP(int,nat,number_number_of(nat),N_1)).
% 23.77/23.59 hAPP(real,nat,natceiling,zero_zero(real))=zero_zero(nat).
% 23.77/23.59 all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),hAPP(real,nat,natceiling,X))).
% 23.77/23.59 all X Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(real,nat,natceiling,X)),hAPP(real,nat,natceiling,Y)))).
% 23.77/23.59 hAPP(real,nat,natceiling,one_one(real))=one_one(nat).
% 23.77/23.59 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),zero_zero(real)))->hAPP(real,nat,natceiling,X)=zero_zero(nat)).
% 23.77/23.59 all X_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(real,nat,natceiling,X_1)),one_one(nat)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),one_one(real)))).
% 23.77/23.59 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X))->hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),one_one(nat))).
% 23.77/23.59 all N_2 M_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),M_1)=one_one(nat)<->N_2=one_one(nat)&M_1=one_one(nat)).
% 23.77/23.59 all N_1 X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_1)),X))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_1)),one_one(real))))->hAPP(real,nat,natceiling,X)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat)))).
% 23.77/23.59 all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),hAPP(nat,real,real_1(nat),N_1))).
% 23.77/23.59 all N_1 (hAPP(real,nat,natceiling,hAPP(nat,real,real_1(nat),N_1))=N_1).
% 23.77/23.59 all N_2 M_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(nat,real,real_1(nat),M_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))).
% 23.77/23.59 hAPP(nat,real,real_1(nat),zero_zero(nat))=zero_zero(real).
% 23.77/23.59 all N_2 (hAPP(nat,real,real_1(nat),N_2)=zero_zero(real)<->N_2=zero_zero(nat)).
% 23.77/23.59 all X (hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X))=hAPP(nat,real,real_1(nat),X)).
% 23.77/23.59 all N_1 (hAPP(real,nat,natfloor,hAPP(nat,real,real_1(nat),N_1))=N_1).
% 23.77/23.59 all N_2 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,real_1(nat),N_2)),ring_1_Ints(real))).
% 23.77/23.59 all N_1 (hAPP(real,nat,natfloor,hAPP(int,real,number_number_of(real),N_1))=hAPP(int,nat,number_number_of(nat),N_1)).
% 23.77/23.59 all N_2 M_1 (hAPP(nat,real,real_1(nat),N_2)=hAPP(nat,real,real_1(nat),M_1)<->N_2=M_1).
% 23.77/23.59 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))),X))).
% 23.77/23.59 all X A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),X)),A_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),hAPP(real,nat,natfloor,A_1)))).
% 23.77/23.59 all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),one_one(real))),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X)))).
% 23.77/23.59 all A_1 X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),A_1)),X))->hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,real_1(nat),A_1)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(real,nat,natfloor,X)),A_1)).
% 23.77/23.59 all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))),one_one(real)))).
% 23.77/23.59 all Aa X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Aa),hAPP(real,nat,natfloor,X_1)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),Aa)),X_1)))).
% 23.77/23.59 all N_1 (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_1)),zero_zero(real)))).
% 23.77/23.59 all N_2 M_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(nat,real,real_1(nat),M_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M_1))).
% 23.77/23.59 all N_1 X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),N_1)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(real,nat,natfloor,X)),N_1)))).
% 23.77/23.59 all M N_1 (hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))=hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N_1))).
% 23.77/23.59 all A_1 X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X))->hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(nat,real,real_1(nat),A_1)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),A_1)).
% 23.77/23.59 all M N_1 (hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))=hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N_1))).
% 23.77/23.59 all Z_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,Z_1)),one_one(nat))),N_1))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Z_1),hAPP(nat,real,real_1(nat),N_1)))).
% 23.77/23.59 all N_1 X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),N_1)),X))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_1)),one_one(real))))->hAPP(real,nat,natfloor,X)=N_1)).
% 23.77/23.59 hAPP(nat,real,real_1(nat),one_one(nat))=one_one(real).
% 23.77/23.59 all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),hAPP(nat,real,real_1(nat),hAPP(real,nat,natceiling,X)))).
% 23.77/23.59 hAPP(real,nat,natfloor,zero_zero(real))=zero_zero(nat).
% 23.77/23.59 all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),hAPP(real,nat,natfloor,X))).
% 23.77/23.59 all X Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(real,nat,natfloor,X)),hAPP(real,nat,natfloor,Y)))).
% 23.77/23.59 hAPP(real,nat,natfloor,one_one(real))=one_one(nat).
% 23.77/23.59 all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),N_2)),zero_zero(real)))<->N_2=zero_zero(nat)).
% 23.77/23.59 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1))=hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N_1))).
% 23.77/23.59 all X A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),hAPP(nat,real,real_1(nat),A_1)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(real,nat,natceiling,X)),A_1))).
% 23.77/23.59 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),zero_zero(real)))->hAPP(real,nat,natfloor,X)=zero_zero(nat)).
% 23.77/23.59 all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2))).
% 23.77/23.59 all N_2 M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_2)),one_one(real))),hAPP(nat,real,real_1(nat),M_1)))).
% 23.77/23.59 all N_2 M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M_1))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),M_1)),one_one(real))))).
% 23.77/23.59 all Aa X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(real,nat,natceiling,X_1)),Aa))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),hAPP(nat,real,real_1(nat),Aa))))).
% 23.77/23.59 all A_1 X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),A_1)),X))->hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,real_1(nat),A_1)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(real,nat,natceiling,X)),A_1)).
% 23.77/23.59 all X_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),one_one(nat)),hAPP(real,nat,natfloor,X_1)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),one_one(real)),X_1))).
% 23.77/23.59 all A_1 X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X))->hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(nat,real,real_1(nat),A_1)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),A_1)).
% 23.77/23.59 all B A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),A_1))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),B))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(real,nat,natfloor,A_1)),hAPP(real,nat,natfloor,B))),hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B)))))).
% 23.77/23.59 all R (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),R))-> (exists N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))),R))&hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(nat,real,real_1(nat),N)))))).
% 23.77/23.59 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X))-> (all Y_2 exists N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),X))))).
% 23.77/23.59 all X N_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_1)))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X))->hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,number_number_of(real),N_1)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),hAPP(int,nat,number_number_of(nat),N_1)))).
% 23.77/23.59 -hBOOL(hAPP(int,bool,nat_neg,zero_zero(int))).
% 23.77/23.59 -hBOOL(hAPP(int,bool,nat_neg,one_one(int))).
% 23.77/23.59 all Z_2 (hBOOL(hAPP(int,bool,nat_neg,Z_2))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int)))).
% 23.77/23.59 all X_1 (-hBOOL(hAPP(int,bool,nat_neg,X_1))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))).
% 23.77/23.59 all V (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(int,nat,number_number_of(nat),V)=zero_zero(nat)).
% 23.77/23.59 all V_1 V_3 (hAPP(int,nat,number_number_of(nat),V_1)=hAPP(int,nat,number_number_of(nat),V_3)<-> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_3)),zero_zero(int))))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1)))-> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3)))->hAPP(int,int,number_number_of(int),V_1)=zero_zero(int))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3)))->V_1=V_3))).
% 23.77/23.59 all V_2 K V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_2)),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_2)),K))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))-> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2)))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_2)),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),K))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2)))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_2)),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_2))),K)))).
% 23.77/23.59 all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,real,real_1(nat),hAPP(int,nat,number_number_of(nat),V))=zero_zero(real))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,real,real_1(nat),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,real,number_number_of(real),V))).
% 23.77/23.59 all X_1 N_2 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_2)))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(int,nat,number_number_of(nat),N_2)),hAPP(real,nat,natfloor,X_1)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,number_number_of(real),N_2)),X_1))))).
% 23.77/23.59 all X_1 N_2 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_2)))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(real,nat,natceiling,X_1)),hAPP(int,nat,number_number_of(nat),N_2)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),hAPP(int,real,number_number_of(real),N_2)))))).
% 23.77/23.59 all X N_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_1)))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X))->hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,number_number_of(real),N_1)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),hAPP(int,nat,number_number_of(nat),N_1)))).
% 23.77/23.59 all X exists N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),N))).
% 23.77/23.59 all Y X Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),Z_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1)))).
% 23.77/23.59 all Z_1 X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1)))).
% 23.77/23.59 all Y X Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1)))).
% 23.77/23.59 all Z_1 X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1)))).
% 23.77/23.59 all X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),Y))).
% 23.77/23.59 all X_b X_a R_1 X_1 Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),in_rel(X_a,X_b),R_1),X_1),Y_1))<->hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1)),R_1))).
% 23.77/23.59 all N_1 X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),X))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real))))->hAPP(real,int,archimedean_ceiling(real),X)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_1),one_one(int)))).
% 23.77/23.59 all X Y (hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y))=hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y))).
% 23.77/23.59 all X A_1 (hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,real_1(int),A_1)))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)).
% 23.77/23.59 all X_1 (hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),X_1))=X_1<-> (exists N (X_1=hAPP(int,real,real_1(int),N)))).
% 23.77/23.59 all N_1 (hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),N_1))=N_1).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all R (hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(X_a,int,archim2085082626_floor(X_a),R)))=hAPP(X_a,int,archim2085082626_floor(X_a),R)))).
% 23.77/23.59 all X_1 (hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),X_1))=X_1<-> (exists N (X_1=hAPP(int,real,real_1(int),N)))).
% 23.77/23.59 all N_1 (hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N_1))=N_1).
% 23.77/23.59 all V (hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V))=hAPP(int,real,number_number_of(real),V)).
% 23.77/23.59 all X_1 Y_1 (hAPP(int,real,real_1(int),X_1)=hAPP(int,real,real_1(int),Y_1)<->X_1=Y_1).
% 23.77/23.59 all R hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),R),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R)))).
% 23.77/23.59 hAPP(int,real,real_1(int),one_one(int))=one_one(real).
% 23.77/23.59 all X Y (hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y))=hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y))).
% 23.77/23.59 all X_1 Aa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(real,int,archimedean_ceiling(real),X_1)),Aa))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),hAPP(int,real,real_1(int),Aa)))).
% 23.77/23.59 all X A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),hAPP(int,real,real_1(int),A_1)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1))).
% 23.77/23.59 all X A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),hAPP(int,real,real_1(int),A_1)))).
% 23.77/23.59 all X_1 Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),X_1)),hAPP(int,real,real_1(int),Y_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_1),Y_1))).
% 23.77/23.59 all X_1 Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),X_1)),hAPP(int,real,real_1(int),Y_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1))).
% 23.77/23.59 all Aa X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),hAPP(real,int,archimedean_ceiling(real),X_1)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),Aa)),X_1))).
% 23.77/23.59 all X_1 (hAPP(int,real,real_1(int),X_1)=zero_zero(real)<->X_1=zero_zero(int)).
% 23.77/23.59 hAPP(int,real,real_1(int),zero_zero(int))=zero_zero(real).
% 23.77/23.59 all X A_1 (hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(int,real,real_1(int),A_1)))=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)).
% 23.77/23.59 all X Y (hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y))=hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all R (hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(X_a,int,archimedean_ceiling(X_a),R)))=hAPP(X_a,int,archimedean_ceiling(X_a),R)))).
% 23.77/23.59 all R hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R))),R)).
% 23.77/23.59 all X (hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X))=hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X))).
% 23.77/23.59 all X_1 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,real_1(int),X_1)),ring_1_Ints(real))).
% 23.77/23.59 all R hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R),one_one(real)))).
% 23.77/23.59 all R hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R))),one_one(real))),R)).
% 23.77/23.59 all X_1 Aa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),X_1)),Aa))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(int,real,real_1(int),Aa)))).
% 23.77/23.59 all A_1 X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),A_1)),X))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),hAPP(real,int,archim2085082626_floor(real),X)))).
% 23.77/23.59 all Aa X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Aa),hAPP(real,int,archim2085082626_floor(real),X_1)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),Aa)),X_1))).
% 23.77/23.59 all A_1 X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),hAPP(real,int,archim2085082626_floor(real),X)))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),A_1)),X))).
% 23.77/23.59 all X A_1 (hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,real_1(int),A_1)))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),X)),A_1)).
% 23.77/23.59 all X A_1 (hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(int,real,real_1(int),A_1)))=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),X)),A_1)).
% 23.77/23.59 all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,real_1(int),N_2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_2))).
% 23.77/23.59 all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_2)),zero_zero(real)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N_2),zero_zero(int)))).
% 23.77/23.59 all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),hAPP(int,real,real_1(int),N_2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),N_2))).
% 23.77/23.59 all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),N_2)),zero_zero(real)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_2),zero_zero(int)))).
% 23.77/23.59 all N_2 M_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),N_2)),hAPP(int,real,real_1(int),M_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),N_2)),M_1))).
% 23.77/23.59 all M_1 N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),M_1)),hAPP(int,real,number_number_of(real),N_2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M_1),hAPP(int,int,number_number_of(int),N_2)))).
% 23.77/23.59 all N_2 M_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,number_number_of(real),N_2)),hAPP(int,real,real_1(int),M_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),N_2)),M_1))).
% 23.77/23.59 all M_1 N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),M_1)),hAPP(int,real,number_number_of(real),N_2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),M_1),hAPP(int,int,number_number_of(int),N_2)))).
% 23.77/23.59 all N_2 M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N_2),M_1))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_2)),one_one(real))),hAPP(int,real,real_1(int),M_1)))).
% 23.77/23.59 all N_2 M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_2),M_1))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_2)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),M_1)),one_one(real))))).
% 23.77/23.59 all N_1 X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),X)),one_one(real))))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_1),X))).
% 23.77/23.59 all N_1 X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),N_1)),one_one(real))),X))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),hAPP(int,real,real_1(int),N_1)))->hAPP(real,int,archimedean_ceiling(real),X)=N_1)).
% 23.77/23.59 all X_1 Aa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),X_1)),Aa))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),Aa)),one_one(real))))).
% 23.77/23.59 all Aa X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Aa),hAPP(real,int,archimedean_ceiling(real),X_1)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),Aa)),one_one(real))),X_1))).
% 23.77/23.59 all R hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),R),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R))),one_one(real)))).
% 23.77/23.59 all R hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R))),one_one(real)))).
% 23.77/23.59 all N_1 X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),X))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real))))->hAPP(real,int,archim2085082626_floor(real),X)=N_1)).
% 23.77/23.59 all R hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R),one_one(real))),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R)))).
% 23.77/23.59 all R hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R),one_one(real))),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R)))).
% 23.77/23.59 all N_1 M R (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),M)),R))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real))))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),M),N_1)))).
% 23.77/23.59 all N_1 X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),X))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real))))->hAPP(real,int,archimedean_ceiling(real),X)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_1),one_one(int)))).
% 23.77/23.59 all N_1 X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),N_1)),X))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real))))->hAPP(real,int,archim2085082626_floor(real),X)=N_1)).
% 23.77/23.59 all Aa X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),hAPP(real,int,archim2085082626_floor(real),X_1)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),Aa)),one_one(real))),X_1))).
% 23.77/23.59 all X_1 Aa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(real,int,archim2085082626_floor(real),X_1)),Aa))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),Aa)),one_one(real))))).
% 23.77/23.59 all R (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),R))-> (exists N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),N)),R))&hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int)))))))).
% 23.77/23.59 all R (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),zero_zero(real)))-> (exists N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),N)),R))&hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int)))))))).
% 23.77/23.59 all R exists N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),N)),R))&hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int)))))).
% 23.77/23.59 all X_a (number_ring(X_a)-> (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V)))->hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,X_a,number_number_of(X_a),V))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V)))->hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))=zero_zero(X_a))))).
% 23.77/23.59 all N_1 (hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,real_1(nat),N_1))=hAPP(nat,int,semiring_1_of_nat(int),N_1)).
% 23.77/23.59 all X_a (number_semiring(X_a)-> (all N_1 (hAPP(int,X_a,number_number_of(X_a),hAPP(nat,int,semiring_1_of_nat(int),N_1))=hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))).
% 23.77/23.59 all K (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K)),zero_zero(int)))).
% 23.77/23.59 all N_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N_1))).
% 23.77/23.59 all P_1 ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_2))->hBOOL(hAPP(int,bool,P_1,X_2))))<-> (all X_2 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_2))))).
% 23.77/23.59 all P_1 ((exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_2))&hBOOL(hAPP(int,bool,P_1,X_2))))<-> (exists X_2 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_2))))).
% 23.77/23.59 all Z_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Z_1))).
% 23.77/23.59 all X_1 Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1))).
% 23.77/23.59 all M_1 N_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))).
% 23.77/23.59 all X_a (linordered_semidom(X_a)-> (all 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,semiring_1_of_nat(X_a),N_1))))).
% 23.77/23.59 all X_a (linordered_semidom(X_a)-> (all M hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M))))).
% 23.77/23.59 all X_a (linordered_semidom(X_a)-> (all M (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),zero_zero(X_a)))))).
% 23.77/23.59 all X_a (semiring_1(X_a)->hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat))=zero_zero(X_a)).
% 23.77/23.59 all X_a (linordered_semidom(X_a)-> (all M N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))))).
% 23.77/23.59 all X_a (linordered_semidom(X_a)-> (all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))))).
% 23.77/23.59 all X_a (linordered_semidom(X_a)-> (all M_1 N_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))))).
% 23.77/23.59 all X_a (linordered_semidom(X_a)-> (all M_1 N_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))))).
% 23.77/23.59 all X_a (semiring_1(X_a)-> (all M N_1 (hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))).
% 23.77/23.59 all X_a (semiring_1(X_a)-> (all M N_1 (hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))).
% 23.77/23.59 all X_a (semiring_1(X_a)->hAPP(nat,X_a,semiring_1_of_nat(X_a),one_one(nat))=one_one(X_a)).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all N_1 (hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))=hAPP(nat,int,semiring_1_of_nat(int),N_1)))).
% 23.77/23.59 all X_a (semiring_char_0(X_a)-> (all M_1 N_2 (hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)=hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)<->M_1=N_2))).
% 23.77/23.59 all M (hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),M))=hAPP(nat,int,semiring_1_of_nat(int),M)).
% 23.77/23.59 all X_a (linordered_idom(X_a)-> (all N_1 (hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))=hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))).
% 23.77/23.59 all N_2 (hAPP(nat,int,semiring_1_of_nat(int),N_2)=zero_zero(int)<->N_2=zero_zero(nat)).
% 23.77/23.59 hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat))=zero_zero(int).
% 23.77/23.59 zero_zero(int)=hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)).
% 23.77/23.59 one_one(int)=hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)).
% 23.77/23.59 hAPP(nat,int,semiring_1_of_nat(int),one_one(nat))=one_one(int).
% 23.77/23.59 all X Y (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Y))).
% 23.77/23.59 all M N_1 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))).
% 23.77/23.59 all M N_1 Z_1 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),Z_1))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))),Z_1)).
% 23.77/23.59 all W Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z))<-> (exists N (Z=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),hAPP(nat,int,semiring_1_of_nat(int),N))))).
% 23.77/23.59 all M N_1 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))).
% 23.77/23.59 all M N_1 (hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))=hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1))).
% 23.77/23.59 all X Y (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y))).
% 23.77/23.59 all M_1 N_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))).
% 23.77/23.59 all X_1 Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_1),Y_1))).
% 23.77/23.59 all X_a (ring_1(X_a)-> (all N_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)),ring_1_Ints(X_a))))).
% 23.77/23.59 all N_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),N_1)))).
% 23.77/23.59 all X_a (archim1727834104eiling(X_a)-> (all N_1 (hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))=hAPP(nat,int,semiring_1_of_nat(int),N_1)))).
% 23.77/23.59 real_1(nat)=semiring_1_of_nat(real).
% 23.77/23.59 all N_1 (hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N_1))=hAPP(nat,real,real_1(nat),N_1)).
% 23.77/23.59 real_1(nat)=semiring_1_of_nat(real).
% 23.77/23.59 all N_1 (hAPP(real,int,archim2085082626_floor(real),hAPP(nat,real,real_1(nat),N_1))=hAPP(nat,int,semiring_1_of_nat(int),N_1)).
% 23.77/23.59 all X Y (hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X),Y))).
% 23.77/23.59 all X_a (ring_1(X_a)-> (all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))).
% 23.77/23.59 all N_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),N_2)),zero_zero(int)))<->N_2=zero_zero(nat)).
% 23.77/23.59 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1))).
% 23.77/23.59 all X_a (linordered_semidom(X_a)-> (all N_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2))))).
% 23.77/23.59 all N_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2))).
% 23.77/23.59 all K I J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K)),I)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K)),J))))).
% 23.77/23.59 all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V))=zero_zero(int))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,int,number_number_of(int),V))).
% 23.77/23.59 all X_a (number_ring(X_a)-> (all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))=zero_zero(X_a))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,X_a,number_number_of(X_a),V))))).
% 23.77/23.59 all P_1 X_1 Y_1 (hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_1))))<-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Y_1),X_1))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1)))))& (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1))->hBOOL(hAPP(int,bool,P_1,zero_zero(int))))).
% 23.77/23.60 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))-> (exists N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))&K=hAPP(nat,int,semiring_1_of_nat(int),N)))).
% 23.77/23.60 all X_a (archim1804426504_field(X_a)-> (all Y X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X))-> (exists N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)),X))))))).
% 23.77/23.60 all M_1 N_2 (hAPP(nat,int,semiring_1_of_nat(int),M_1)=hAPP(nat,int,semiring_1_of_nat(int),N_2)<->M_1=N_2).
% 23.77/23.60 all X_1 Y_1 P_1 ((hBOOL(P_1)->hAPP(nat,int,semiring_1_of_nat(int),X_1)=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),P_1),X_1),Y_1)))& (-hBOOL(P_1)->hAPP(nat,int,semiring_1_of_nat(int),Y_1)=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),P_1),X_1),Y_1)))).
% 23.77/23.60 all X_1 Y_1 (hAPP(nat,int,semiring_1_of_nat(int),X_1)=hAPP(nat,int,semiring_1_of_nat(int),Y_1)<->X_1=Y_1).
% 23.77/23.60 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))-> (exists N (K=hAPP(nat,int,semiring_1_of_nat(int),N)))).
% 23.77/23.60 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1))-> -(all M_2 (Z_1!=hAPP(nat,int,semiring_1_of_nat(int),M_2)))).
% 23.77/23.60 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))-> -(all N (K!=hAPP(nat,int,semiring_1_of_nat(int),N)))).
% 23.77/23.60 all Z_1 (-(all M_2 N (Z_1!=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_2)),hAPP(nat,int,semiring_1_of_nat(int),N))))).
% 23.77/23.60 all X_a (archim1804426504_field(X_a)-> (all X exists N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))).
% 23.77/23.60 all X_a (archim1804426504_field(X_a)-> (all X exists N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))).
% 23.77/23.60 all V_2 V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_2))=zero_zero(nat))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_2))=hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_2)))).
% 23.77/23.60 all V_2 K V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V_2)),K))=zero_zero(nat))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V_2)),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_2))),K))).
% 23.77/23.60 all X_a (number_ring(X_a)->hAPP(int,X_a,number_number_of(X_a),pls)=zero_zero(X_a)).
% 23.77/23.60 all X_a (number_semiring(X_a)->hAPP(int,X_a,number_number_of(X_a),pls)=zero_zero(X_a)).
% 23.77/23.60 all X_a (number_ring(X_a)->zero_zero(X_a)=hAPP(int,X_a,number_number_of(X_a),pls)).
% 23.77/23.60 all X_a (number_ring(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),pls)),A_1)=ti(X_a,A_1)))).
% 23.77/23.60 all X_a (number_ring(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),pls))=ti(X_a,A_1)))).
% 23.77/23.60 all K (hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),pls)=K).
% 23.77/23.60 all W_1 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),W_1)=pls).
% 23.77/23.60 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)).
% 23.77/23.60 all K (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),K)=K).
% 23.77/23.60 all K (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),pls)=K).
% 23.77/23.60 pls=zero_zero(int).
% 23.77/23.60 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),pls)).
% 23.77/23.60 zero_zero(int)=hAPP(int,int,number_number_of(int),pls).
% 23.77/23.60 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))).
% 23.77/23.60 hAPP(int,nat,number_number_of(nat),pls)=zero_zero(nat).
% 23.77/23.60 zero_zero(nat)=hAPP(int,nat,number_number_of(nat),pls).
% 23.77/23.60 -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),pls))).
% 23.77/23.60 all V_1 (zero_zero(nat)=hAPP(int,nat,number_number_of(nat),V_1)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_1),pls))).
% 23.77/23.60 all V_1 (hAPP(int,nat,number_number_of(nat),V_1)=zero_zero(nat)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_1),pls))).
% 23.77/23.60 all V_1 V_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_3)))<-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),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_1),V_3))).
% 23.77/23.60 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,number_number_of(int),pls))).
% 23.77/23.60 all V_1 V_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_3)))<-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_1),V_3))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_1),pls)))).
% 23.77/23.60 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Y_1))))).
% 23.77/23.60 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),zero_zero(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),pls))))).
% 23.77/23.60 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),Y_1))))).
% 23.77/23.60 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),zero_zero(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_1),pls))))).
% 23.77/23.60 all X_a (number_semiring(X_a)-> (all V_2 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_2))->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),V_2))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_2)))))).
% 23.77/23.60 all X_a (number_semiring(X_a)-> (all V_2 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_2))->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),V_2))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_2)))))).
% 23.77/23.60 all V_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_1))).
% 23.77/23.60 all V_2 V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_2))=hAPP(int,nat,number_number_of(nat),V_2))& (-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_2),pls))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_2))=hAPP(int,nat,number_number_of(nat),V))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_2))=hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_2))))).
% 23.77/23.60 all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V))=one_one(nat))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V)))).
% 23.77/23.60 all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))=one_one(nat))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))=hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V)))).
% 23.77/23.60 all K (hAPP(int,int,succ,K)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),one_one(int))).
% 23.77/23.60 all X_a (number_ring(X_a)-> (all K (hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,K))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),K))))).
% 23.77/23.60 all X_a (number_semiring(X_a)-> (all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V))->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),V))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,V))))).
% 23.77/23.60 all X_a (number_semiring(X_a)-> (all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V))->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,V))))).
% 23.77/23.60 all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V),pls))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))=zero_zero(nat))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V),pls))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))=hAPP(int,nat,number_number_of(nat),hAPP(int,int,pred,V)))).
% 23.77/23.60 all N_1 V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N_1))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))),N_1))).
% 23.77/23.60 all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,N_1))).
% 23.77/23.60 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(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_1)))).
% 23.77/23.60 all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1))).
% 23.77/23.60 all X (hAPP(int,int,succ,hAPP(int,int,pred,X))=X).
% 23.77/23.60 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))<->M_1=zero_zero(nat)| (exists J_1 (M_1=hAPP(nat,nat,suc,J_1)&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),N_2))))).
% 23.77/23.60 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,zero_zero(nat))))<->N_2=zero_zero(nat)).
% 23.77/23.60 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2))<-> (exists M_2 (N_2=hAPP(nat,nat,suc,M_2)))).
% 23.77/23.60 all M_1 N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)=hAPP(nat,nat,suc,zero_zero(nat))<->M_1=hAPP(nat,nat,suc,zero_zero(nat))&N_2=zero_zero(nat)|M_1=zero_zero(nat)&N_2=hAPP(nat,nat,suc,zero_zero(nat))).
% 23.77/23.60 all M_1 N_2 (hAPP(nat,nat,suc,zero_zero(nat))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)<->M_1=hAPP(nat,nat,suc,zero_zero(nat))&N_2=zero_zero(nat)|M_1=zero_zero(nat)&N_2=hAPP(nat,nat,suc,zero_zero(nat))).
% 23.77/23.60 all M_1 N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)=hAPP(nat,nat,suc,zero_zero(nat))<->M_1=hAPP(nat,nat,suc,zero_zero(nat))&N_2=hAPP(nat,nat,suc,zero_zero(nat))).
% 23.77/23.60 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))<-> (exists K_2 (N_2=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2))))).
% 23.77/23.60 all I M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),I)))).
% 23.77/23.60 all I M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),M)))).
% 23.77/23.60 one_one(nat)=hAPP(nat,nat,suc,zero_zero(nat)).
% 23.77/23.60 all N_2 M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_2)),M_1))).
% 23.77/23.60 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))).
% 23.77/23.60 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M_1)),N_2))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))).
% 23.77/23.60 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(nat),M),hAPP(nat,nat,suc,N_1)))).
% 23.77/23.60 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),hAPP(nat,nat,suc,M)),N_1))).
% 23.77/23.60 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1)))<->N_2=M_1)).
% 23.77/23.60 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M)),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))).
% 23.77/23.60 all K_1 M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))).
% 23.77/23.60 all M N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),hAPP(nat,nat,suc,M))).
% 23.77/23.60 all M N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,M)),N_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))).
% 23.77/23.60 all M N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,suc,N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))).
% 23.77/23.60 all K_1 M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))).
% 23.77/23.60 all N_1 (hAPP(nat,nat,suc,N_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N_1)).
% 23.77/23.60 all N_1 (hAPP(nat,nat,suc,N_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat))).
% 23.77/23.60 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N_1)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1))).
% 23.77/23.60 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N_1)),one_one(nat))=N_1).
% 23.77/23.60 all M N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_1)).
% 23.77/23.60 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M)),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))).
% 23.77/23.60 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,suc,N_1)))-> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))->M=hAPP(nat,nat,suc,N_1))).
% 23.77/23.60 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),M),hAPP(nat,nat,suc,N_1)))).
% 23.77/23.60 all N_2 M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_2)),hAPP(nat,nat,suc,M_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M_1))).
% 23.77/23.60 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,suc,N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))|M_1=hAPP(nat,nat,suc,N_2)).
% 23.77/23.60 all M_1 N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_2)),M_1))).
% 23.77/23.60 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_1)),N_1))).
% 23.77/23.60 all M (zero_zero(nat)!=hAPP(nat,nat,suc,M)).
% 23.77/23.60 all Nat_3 (zero_zero(nat)!=hAPP(nat,nat,suc,Nat_3)).
% 23.77/23.60 all M (hAPP(nat,nat,suc,M)!=zero_zero(nat)).
% 23.77/23.60 all Nat_2 (hAPP(nat,nat,suc,Nat_2)!=zero_zero(nat)).
% 23.77/23.60 all M (zero_zero(nat)!=hAPP(nat,nat,suc,M)).
% 23.77/23.60 all M (hAPP(nat,nat,suc,M)!=zero_zero(nat)).
% 23.77/23.60 all M_1 N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1)))).
% 23.77/23.60 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|M_1=N_2).
% 23.77/23.60 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))).
% 23.77/23.60 all N_2 M_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1)))<->N_2=M_1)).
% 23.77/23.60 all N_1 M (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M)))->M=N_1)).
% 23.77/23.60 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(nat),M),hAPP(nat,nat,suc,N_1)))).
% 23.77/23.60 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))-> (hAPP(nat,nat,suc,M)!=N_1->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N_1)))).
% 23.77/23.60 all K I J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K)))).
% 23.77/23.60 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N_1)))-> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))->M=N_1)).
% 23.77/23.60 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))).
% 23.77/23.60 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_1)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))).
% 23.77/23.60 all M N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N_1))=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))).
% 23.77/23.60 all M N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N_1)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))).
% 23.77/23.60 all M N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N_1))).
% 23.77/23.60 all M N_1 K (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N_1)),hAPP(nat,nat,suc,K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),K)).
% 23.77/23.60 all M N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)).
% 23.77/23.60 all N_1 (N_1!=hAPP(nat,nat,suc,N_1)).
% 23.77/23.60 all N_1 (hAPP(nat,nat,suc,N_1)!=N_1).
% 23.77/23.60 all Nat_1 Nat (hAPP(nat,nat,suc,Nat_1)=hAPP(nat,nat,suc,Nat)<->Nat_1=Nat).
% 23.77/23.60 all X Y (hAPP(nat,nat,suc,X)=hAPP(nat,nat,suc,Y)->X=Y).
% 23.77/23.60 all K_1 M_1 N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_2)<->M_1=N_2).
% 23.77/23.60 all K (hAPP(int,int,pred,K)=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),one_one(int))).
% 23.77/23.60 all K_1 L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),L))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,pred,K_1)),L))).
% 23.77/23.60 all M V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(int,nat,number_number_of(nat),V))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,pred,V)))).
% 23.77/23.60 all X_a (semiring_1(X_a)-> (all M (hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,M))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M))))).
% 23.77/23.60 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))))).
% 23.77/23.60 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),M))))).
% 23.77/23.60 all M N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))))).
% 23.77/23.60 all N_1 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)=M->N_1=hAPP(nat,nat,suc,zero_zero(nat)))).
% 23.77/23.60 all M K 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)),K))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)=K->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),K)))))).
% 23.77/23.60 all M K (M!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),K)))).
% 23.77/23.60 all M K (M!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)-> (M!=hAPP(nat,nat,suc,zero_zero(nat))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)))).
% 23.77/23.60 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))=N_1).
% 23.77/23.60 all I 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,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,I))),N_1))).
% 23.77/23.60 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_2))).
% 23.77/23.60 all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_1)))).
% 23.77/23.60 hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,zero_zero(nat)))=one_one(int).
% 23.77/23.60 hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,zero_zero(nat)))=one_one(real).
% 23.77/23.60 all M K J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,suc,J))).
% 23.77/23.60 all M K J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))),M)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M))).
% 23.77/23.60 all W Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z))<-> (exists N (Z=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N)))))).
% 23.77/23.60 all M (hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M))).
% 23.77/23.60 all N_1 (hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_1))=hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_1)),one_one(real))).
% 23.77/23.60 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->N_1=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat)))).
% 23.77/23.60 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))->hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat)))=N_1).
% 23.77/23.60 all N_1 M ((M=zero_zero(nat)->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)=N_1)& (M!=zero_zero(nat)->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_1)))).
% 23.77/23.60 all V (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V)))->hAPP(int,nat,number_number_of(nat),V)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)))).
% 23.77/23.60 all V_1 (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))))<->hAPP(int,nat,number_number_of(nat),V_1)=zero_zero(nat)).
% 23.77/23.60 all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V))=one_one(nat))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V))=hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V)))).
% 23.77/23.60 all R (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),R))-> (exists N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),N)),R))&hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N))))))).
% 23.77/23.61 all T_2 T_1 (preorder(T_1)->preorder(fun(T_2,T_1))).
% 23.77/23.61 all T_2 T_1 (order(T_1)->order(fun(T_2,T_1))).
% 23.77/23.61 all T_2 T_1 (ord(T_1)->ord(fun(T_2,T_1))).
% 23.77/23.61 all T_2 T_1 (minus(T_1)->minus(fun(T_2,T_1))).
% 23.77/23.61 semiri456707255roduct(int).
% 23.77/23.61 ordere223160158up_add(int).
% 23.77/23.61 ordere236663937imp_le(int).
% 23.77/23.61 linord893533164strict(int).
% 23.77/23.61 linord626643107strict(int).
% 23.77/23.61 linord20386208strict(int).
% 23.77/23.61 ordere779506340up_add(int).
% 23.77/23.61 ordere142940540dd_abs(int).
% 23.77/23.61 ordere216010020id_add(int).
% 23.77/23.61 linord219039673up_add(int).
% 23.77/23.61 cancel146912293up_add(int).
% 23.77/23.61 ordere453448008miring(int).
% 23.77/23.61 linord581940658strict(int).
% 23.77/23.61 ring_n68954251visors(int).
% 23.77/23.61 ordere1490568538miring(int).
% 23.77/23.61 linord1278240602ring_1(int).
% 23.77/23.61 ordered_ab_group_add(int).
% 23.77/23.61 cancel_semigroup_add(int).
% 23.77/23.61 linordered_semiring(int).
% 23.77/23.61 linordered_semidom(int).
% 23.77/23.61 ab_semigroup_mult(int).
% 23.77/23.61 comm_monoid_mult(int).
% 23.77/23.61 ab_semigroup_add(int).
% 23.77/23.61 ordered_semiring(int).
% 23.77/23.61 ordered_ring_abs(int).
% 23.77/23.61 no_zero_divisors(int).
% 23.77/23.61 comm_monoid_add(int).
% 23.77/23.61 linordered_ring(int).
% 23.77/23.61 linordered_idom(int).
% 23.77/23.61 comm_semiring_1(int).
% 23.77/23.61 comm_semiring(int).
% 23.77/23.61 semiring_char_0(int).
% 23.77/23.61 number_semiring(int).
% 23.77/23.61 ab_group_add(int).
% 23.77/23.61 zero_ne_q_one(int).
% 23.77/23.61 ordered_ring(int).
% 23.77/23.61 preorder(int).
% 23.77/23.61 linorder(int).
% 23.77/23.61 monoid_mult(int).
% 23.77/23.61 monoid_add(int).
% 23.77/23.61 semiring_1(int).
% 23.77/23.61 group_add(int).
% 23.77/23.61 mult_zero(int).
% 23.77/23.61 order(int).
% 23.77/23.61 ring_char_0(int).
% 23.77/23.61 number_ring(int).
% 23.77/23.61 semiring(int).
% 23.77/23.61 ord(int).
% 23.77/23.61 ring_1(int).
% 23.77/23.61 minus(int).
% 23.77/23.61 zero(int).
% 23.77/23.61 ring(int).
% 23.77/23.61 number(int).
% 23.77/23.61 one(int).
% 23.77/23.61 semiri456707255roduct(nat).
% 23.77/23.61 ordere223160158up_add(nat).
% 23.77/23.61 ordere236663937imp_le(nat).
% 23.77/23.61 linord893533164strict(nat).
% 23.77/23.61 linord20386208strict(nat).
% 23.77/23.61 ordere779506340up_add(nat).
% 23.77/23.61 ordere216010020id_add(nat).
% 23.77/23.61 cancel146912293up_add(nat).
% 23.77/23.61 ordere453448008miring(nat).
% 23.77/23.61 ordere1490568538miring(nat).
% 23.77/23.61 cancel_semigroup_add(nat).
% 23.77/23.61 linordered_semiring(nat).
% 23.77/23.61 linordered_semidom(nat).
% 23.77/23.61 ab_semigroup_mult(nat).
% 23.77/23.61 comm_monoid_mult(nat).
% 23.77/23.61 ab_semigroup_add(nat).
% 23.77/23.61 ordered_semiring(nat).
% 23.77/23.61 no_zero_divisors(nat).
% 23.77/23.61 comm_monoid_add(nat).
% 23.77/23.61 comm_semiring_1(nat).
% 23.77/23.61 comm_semiring(nat).
% 23.77/23.61 semiring_char_0(nat).
% 23.77/23.61 number_semiring(nat).
% 23.77/23.61 zero_ne_q_one(nat).
% 23.77/23.61 preorder(nat).
% 23.77/23.61 linorder(nat).
% 23.77/23.61 monoid_mult(nat).
% 23.77/23.61 monoid_add(nat).
% 23.77/23.61 semiring_1(nat).
% 23.77/23.61 mult_zero(nat).
% 23.77/23.61 order(nat).
% 23.77/23.61 semiring(nat).
% 23.77/23.61 ord(nat).
% 23.77/23.61 minus(nat).
% 23.77/23.61 zero(nat).
% 23.77/23.61 number(nat).
% 23.77/23.61 one(nat).
% 23.77/23.61 preorder(bool).
% 23.77/23.61 order(bool).
% 23.77/23.61 ord(bool).
% 23.77/23.61 minus(bool).
% 23.77/23.61 semiri456707255roduct(real).
% 23.77/23.61 ordere223160158up_add(real).
% 23.77/23.61 ordere236663937imp_le(real).
% 23.77/23.61 linord893533164strict(real).
% 23.77/23.61 linord1117847801e_zero(real).
% 23.77/23.61 archim1804426504_field(real).
% 23.77/23.61 linord626643107strict(real).
% 23.77/23.61 linord20386208strict(real).
% 23.77/23.61 ordere779506340up_add(real).
% 23.77/23.61 ordere142940540dd_abs(real).
% 23.77/23.61 archim1727834104eiling(real).
% 23.77/23.61 real_normed_algebra(real).
% 23.77/23.61 ordere216010020id_add(real).
% 23.77/23.61 linord219039673up_add(real).
% 23.77/23.61 cancel146912293up_add(real).
% 23.77/23.61 ordere453448008miring(real).
% 23.77/23.61 linord581940658strict(real).
% 23.77/23.61 ring_n68954251visors(real).
% 23.77/23.61 ordere1490568538miring(real).
% 23.77/23.61 linord1278240602ring_1(real).
% 23.77/23.61 ordered_ab_group_add(real).
% 23.77/23.61 cancel_semigroup_add(real).
% 23.77/23.61 linordered_semiring(real).
% 23.77/23.61 linordered_semidom(real).
% 23.77/23.61 dense_linorder(real).
% 23.77/23.61 ab_semigroup_mult(real).
% 23.77/23.61 comm_monoid_mult(real).
% 23.77/23.61 ab_semigroup_add(real).
% 23.77/23.61 linordered_field(real).
% 23.77/23.61 ordered_semiring(real).
% 23.77/23.61 ordered_ring_abs(real).
% 23.77/23.61 no_zero_divisors(real).
% 23.77/23.61 comm_monoid_add(real).
% 23.77/23.61 linordered_ring(real).
% 23.77/23.61 linordered_idom(real).
% 23.77/23.61 comm_semiring_1(real).
% 23.77/23.61 comm_semiring(real).
% 23.77/23.61 semiring_char_0(real).
% 23.77/23.61 number_semiring(real).
% 23.77/23.61 ab_group_add(real).
% 23.77/23.61 zero_ne_q_one(real).
% 23.77/23.61 ordered_ring(real).
% 23.77/23.61 preorder(real).
% 23.77/23.61 linorder(real).
% 23.77/23.61 monoid_mult(real).
% 23.77/23.61 monoid_add(real).
% 23.77/23.61 semiring_1(real).
% 23.77/23.61 group_add(real).
% 23.77/23.61 mult_zero(real).
% 23.77/23.61 order(real).
% 23.77/23.61 ring_char_0(real).
% 23.77/23.61 number_ring(real).
% 23.77/23.61 semiring(real).
% 23.77/23.61 ord(real).
% 23.77/23.61 ring_1(real).
% 23.77/23.61 minus(real).
% 23.77/23.61 zero(real).
% 23.77/23.61 ring(real).
% 23.77/23.61 number(real).
% 23.77/23.61 one(real).
% 23.77/23.61 all T A (ti(T,ti(T,A))=ti(T,A)).
% 23.77/23.61 all X_a X Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y)=ti(X_a,X)).
% 23.77/23.61 all X_a X Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y)=ti(X_a,Y)).
% 23.77/23.61 all P (ti(bool,P)=fTrue|ti(bool,P)=fFalse).
% 23.77/23.61 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,twoSqu1929807760sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),a),b))),hAPP(product_prod(int,int),int,twoSqu1929807760sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),p),q)))!=hAPP(product_prod(int,int),int,twoSqu1929807760sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),a),p)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),b),q))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),a),q)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),b),p)))).
% 23.77/23.61 end_of_list.
% 23.77/23.61
% 23.77/23.61 -------> usable clausifies to:
% 23.77/23.61
% 23.77/23.61 list(usable).
% 23.77/23.61 0 [] A=A.
% 23.77/23.61 0 [] -archim1727834104eiling(X_a)|ti(fun(X_a,int),archimedean_ceiling(X_a))=archimedean_ceiling(X_a).
% 23.77/23.61 0 [] -archim1727834104eiling(X_a)|ti(fun(X_a,int),archim2085082626_floor(X_a))=archim2085082626_floor(X_a).
% 23.77/23.61 0 [] ti(fun(int,fun(int,fun(product_prod(int,int),bool))),divmod_int_rel)=divmod_int_rel.
% 23.77/23.61 0 [] ti(fun(int,fun(int,product_prod(int,int))),pdivmod)=pdivmod.
% 23.77/23.61 0 [] ti(fun(int,fun(int,product_prod(int,int))),posDivAlg)=posDivAlg.
% 23.77/23.61 0 [] ti(fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),in_rel(X_a,X_b))=in_rel(X_a,X_b).
% 23.77/23.61 0 [] -ordere142940540dd_abs(X_a)|ti(fun(X_a,X_a),abs_abs(X_a))=abs_abs(X_a).
% 23.77/23.61 0 [] -minus(X_a)|ti(fun(X_a,fun(X_a,X_a)),minus_minus(X_a))=minus_minus(X_a).
% 23.77/23.61 0 [] -one(X_a)|ti(X_a,one_one(X_a))=one_one(X_a).
% 23.77/23.61 0 [] -monoid_add(X_a)|ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a).
% 23.77/23.61 0 [] -ab_semigroup_add(X_a)|ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a).
% 23.77/23.61 0 [] -cancel_semigroup_add(X_a)|ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a).
% 23.77/23.61 0 [] -no_zero_divisors(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 23.77/23.61 0 [] -mult_zero(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 23.77/23.61 0 [] -monoid_mult(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 23.77/23.61 0 [] -semiring(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 23.77/23.61 0 [] -ab_semigroup_mult(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 23.77/23.61 0 [] -zero(X_a)|ti(X_a,zero_zero(X_a))=zero_zero(X_a).
% 23.77/23.61 0 [] ti(X_a,undefined(X_a))=undefined(X_a).
% 23.77/23.61 0 [] ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a))=if(X_a).
% 23.77/23.61 0 [] ti(fun(int,int),zfact)=zfact.
% 23.77/23.61 0 [] ti(fun(int,fun(int,product_prod(int,product_prod(int,int)))),xzgcd)=xzgcd.
% 23.77/23.61 0 [] ti(fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))))),xzgcda)=xzgcda.
% 23.77/23.61 0 [] ti(int,pls)=pls.
% 23.77/23.61 0 [] -number(X_a)|ti(fun(int,X_a),number_number_of(X_a))=number_number_of(X_a).
% 23.77/23.61 0 [] ti(fun(int,int),pred)=pred.
% 23.77/23.61 0 [] -ring_1(X_a)|ti(fun(X_a,bool),ring_1_Ints(X_a))=ring_1_Ints(X_a).
% 23.77/23.61 0 [] ti(fun(int,int),succ)=succ.
% 23.77/23.61 0 [] ti(fun(nat,nat),suc)=suc.
% 23.77/23.61 0 [] -semiring_1(X_a)|ti(fun(nat,X_a),semiring_1_of_nat(X_a))=semiring_1_of_nat(X_a).
% 23.77/23.61 0 [] ti(fun(int,bool),nat_neg)=nat_neg.
% 23.77/23.61 0 [] ti(fun(int,fun(int,int)),nat_tsub)=nat_tsub.
% 23.77/23.61 0 [] -ord(X_a)|ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a).
% 23.77/23.61 0 [] -ord(X_b)|ti(fun(X_b,fun(X_b,bool)),ord_less_e_q(X_b))=ord_less_e_q(X_b).
% 23.77/23.61 0 [] ti(fun(X_a,fun(X_b,product_prod(X_a,X_b))),product_Pair(X_a,X_b))=product_Pair(X_a,X_b).
% 23.77/23.61 0 [] ti(fun(fun(product_prod(X_b,X_c),X_a),fun(X_b,fun(X_c,X_a))),product_curry(X_b,X_c,X_a))=product_curry(X_b,X_c,X_a).
% 23.77/23.61 0 [] ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),produc1605651328_split(X_b,X_c,X_a))=produc1605651328_split(X_b,X_c,X_a).
% 23.77/23.61 0 [] ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),product_prod_rec(X_b,X_c,X_a))=product_prod_rec(X_b,X_c,X_a).
% 23.77/23.61 0 [] ti(fun(real,nat),natceiling)=natceiling.
% 23.77/23.61 0 [] ti(fun(real,nat),natfloor)=natfloor.
% 23.77/23.61 0 [] ti(fun(int,real),real_1(int))=real_1(int).
% 23.77/23.61 0 [] ti(fun(nat,real),real_1(nat))=real_1(nat).
% 23.77/23.61 0 [] ti(fun(int,bool),twoSqu658283162sum2sq)=twoSqu658283162sum2sq.
% 23.77/23.61 0 [] ti(fun(product_prod(int,int),int),twoSqu1929807760sum2sq)=twoSqu1929807760sum2sq.
% 23.77/23.61 0 [] ti(bool,fFalse)=fFalse.
% 23.77/23.61 0 [] ti(bool,fTrue)=fTrue.
% 23.77/23.61 0 [] hAPP(X_c,X_a,ti(fun(X_c,X_a),B_1_1),B_2_1)=hAPP(X_c,X_a,B_1_1,B_2_1).
% 23.77/23.61 0 [] hAPP(X_c,X_a,B_1_1,ti(X_c,B_2_1))=hAPP(X_c,X_a,B_1_1,B_2_1).
% 23.77/23.61 0 [] ti(X_a,hAPP(X_c,X_a,B_1_1,B_2_1))=hAPP(X_c,X_a,B_1_1,B_2_1).
% 23.77/23.61 0 [] -hBOOL(ti(bool,B_1_1))|hBOOL(B_1_1).
% 23.77/23.61 0 [] hBOOL(ti(bool,B_1_1))| -hBOOL(B_1_1).
% 23.77/23.61 0 [] ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a))=member(X_a).
% 23.77/23.61 0 [] ti(int,a)=a.
% 23.77/23.61 0 [] ti(int,b)=b.
% 23.77/23.61 0 [] ti(int,p)=p.
% 23.77/23.61 0 [] ti(int,q)=q.
% 23.77/23.61 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R),B))),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R),D_1))),N_1))=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),N_1))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_1),N_1)))).
% 23.77/23.61 0 [] -ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),B)).
% 23.77/23.61 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))).
% 23.77/23.61 0 [] -ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2)|ti(X_a,C_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ba),Aa)),E_1)),D_2).
% 23.77/23.61 0 [] -ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2)|ti(X_a,C_1)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ba),Aa)),E_1)),D_2).
% 23.77/23.61 0 [] -ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_1)),C_1)=ti(X_a,D_2).
% 23.77/23.61 0 [] -ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_1)),C_1)!=ti(X_a,D_2).
% 23.77/23.61 0 [] -hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,X_1))|hAPP(product_prod(int,int),int,twoSqu1929807760sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),$f2(X_1)),$f1(X_1)))=X_1.
% 23.77/23.61 0 [] hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,X_1))|hAPP(product_prod(int,int),int,twoSqu1929807760sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_2),B_2))!=X_1.
% 23.77/23.61 0 [] hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)!=C|A_1=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B).
% 23.77/23.61 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2))=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),Z2)).
% 23.77/23.61 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2)),W_1)=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W_1)).
% 23.77/23.61 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),Z2)).
% 23.77/23.61 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),W_1)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W_1)).
% 23.77/23.61 0 [] -group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),B)=ti(X_a,A_1).
% 23.77/23.61 0 [] -ab_semigroup_mult(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)).
% 23.77/23.61 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)|ti(X_a,B)=ti(X_a,C).
% 23.77/23.61 0 [] -cancel146912293up_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)|ti(X_a,B)=ti(X_a,C).
% 23.77/23.61 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)|ti(X_a,B)=ti(X_a,C).
% 23.77/23.61 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)|ti(X_a,Ba)=ti(X_a,C_1).
% 23.77/23.61 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)|ti(X_a,Ba)!=ti(X_a,C_1).
% 23.77/23.61 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)|ti(X_a,Ba)=ti(X_a,C_1).
% 23.77/23.61 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)|ti(X_a,Ba)!=ti(X_a,C_1).
% 23.77/23.61 0 [] -ab_semigroup_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C)).
% 23.77/23.61 0 [] -ab_group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_2)|ti(X_a,Aa)!=ti(X_a,Ba)|ti(X_a,C_1)=ti(X_a,D_2).
% 23.77/23.61 0 [] -ab_group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_2)|ti(X_a,Aa)=ti(X_a,Ba)|ti(X_a,C_1)!=ti(X_a,D_2).
% 23.77/23.61 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),Z2)),Z3)=hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),Z3)).
% 23.77/23.61 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W_1)=hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),Z_1).
% 23.77/23.61 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),Z3)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z2),Z3)).
% 23.77/23.61 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),Z_1))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Z_1)).
% 23.77/23.61 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),W_1)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),Z_1).
% 23.77/23.61 0 [] -semiring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),E_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),E_2)),C))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),E_2)),C).
% 23.77/23.61 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)),Ya)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Ya)).
% 23.77/23.61 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),A_5)),B)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_5),B)).
% 23.77/23.61 0 [] -comm_semiring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)).
% 23.77/23.61 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),Y)).
% 23.77/23.61 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),B_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B_1)).
% 23.77/23.61 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),Ya)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Ya)).
% 23.77/23.61 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_5)),B)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_5),B)).
% 23.77/23.61 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),Y)).
% 23.77/23.61 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),B_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B_1)).
% 23.77/23.61 0 [] -ab_group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C),D_1)).
% 23.77/23.61 0 [] -group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B)=ti(X_a,A_1).
% 23.77/23.61 0 [] -semiri456707255roduct(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Z))!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Y_1))|ti(X_a,W)=ti(X_a,X_1)|ti(X_a,Y_1)=ti(X_a,Z).
% 23.77/23.61 0 [] -semiri456707255roduct(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Y_1))|ti(X_a,W)!=ti(X_a,X_1).
% 23.77/23.61 0 [] -semiri456707255roduct(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Y_1))|ti(X_a,Y_1)!=ti(X_a,Z).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),M))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),M).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)).
% 23.77/23.61 0 [] -semiri456707255roduct(X_a)|ti(X_a,Aa)=ti(X_a,Ba)|ti(X_a,C_1)=ti(X_a,D_2)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),D_2))!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),D_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),C_1)).
% 23.77/23.61 0 [] -semiri456707255roduct(X_a)|ti(X_a,Aa)!=ti(X_a,Ba)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),D_2))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),D_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),C_1)).
% 23.77/23.61 0 [] -semiri456707255roduct(X_a)|ti(X_a,C_1)!=ti(X_a,D_2)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),D_2))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),D_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),C_1)).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z_1)).
% 23.77/23.61 0 [] -minus(X_a)|hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),minus_minus(fun(X_b,X_a)),A_3),B_4),X_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_b,X_a,A_3,X_1)),hAPP(X_b,X_a,B_4,X_1)).
% 23.77/23.61 0 [] -minus(X_b)|hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),minus_minus(fun(X_a,X_b)),A_3),B_4),X_2)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,A_3,X_2)),hAPP(X_a,X_b,B_4,X_2)).
% 23.77/23.61 0 [] hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_1),B)!=hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_5),B_1)|ti(X_a,A_1)=ti(X_a,A_5).
% 23.77/23.61 0 [] hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_1),B)!=hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_5),B_1)|ti(X_b,B)=ti(X_b,B_1).
% 23.77/23.61 0 [] hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba)!=hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_3)|ti(X_a,Aa)=ti(X_a,A_4).
% 23.77/23.61 0 [] hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba)!=hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_3)|ti(X_b,Ba)=ti(X_b,B_3).
% 23.77/23.61 0 [] hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba)=hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_3)|ti(X_a,Aa)!=ti(X_a,A_4)|ti(X_b,Ba)!=ti(X_b,B_3).
% 23.77/23.61 0 [] -hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,$f3(X_a,X_b,P_1)))|hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_2))).
% 23.77/23.61 0 [] hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,X1))| -hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),$f5(X_a,X_b,P_1)),$f4(X_a,X_b,P_1)))).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),B).
% 23.77/23.61 0 [] -ab_sem1668676832m_mult(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)=ti(X_a,A_1).
% 23.77/23.61 0 [] -ab_sem1668676832m_mult(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)=ti(X_a,X).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1).
% 23.77/23.61 0 [] -ab_sem1668676832m_mult(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ry)).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ry).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Rx)).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ly).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Ry)).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Ry)).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),D_1)).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),D_1).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C)).
% 23.77/23.61 0 [] hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_rec(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba))=hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,Aa),Ba).
% 23.77/23.61 0 [] -hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,X1))|hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),$f7(X_a,X_b,P_1)),$f6(X_a,X_b,P_1)))).
% 23.77/23.61 0 [] hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,$f8(X_a,X_b,P_1)))| -hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_2))).
% 23.77/23.61 0 [] -hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),$f14(X_a,X_b,X_c,X_d,X_e,X_f,X_1,P_1)),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),$f13(X_a,X_b,X_c,X_d,X_e,X_f,X_1,P_1)),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),$f12(X_a,X_b,X_c,X_d,X_e,X_f,X_1,P_1)),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),$f11(X_a,X_b,X_c,X_d,X_e,X_f,X_1,P_1)),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),$f10(X_a,X_b,X_c,X_d,X_e,X_f,X_1,P_1)),$f9(X_a,X_b,X_c,X_d,X_e,X_f,X_1,P_1))))))))|hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,P_1,X_1)).
% 23.77/23.61 0 [] ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),Y)=hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),$f20(X_a,X_b,X_c,X_d,X_e,X_f,Y)),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),$f19(X_a,X_b,X_c,X_d,X_e,X_f,Y)),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),$f18(X_a,X_b,X_c,X_d,X_e,X_f,Y)),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),$f17(X_a,X_b,X_c,X_d,X_e,X_f,Y)),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),$f16(X_a,X_b,X_c,X_d,X_e,X_f,Y)),$f15(X_a,X_b,X_c,X_d,X_e,X_f,Y)))))).
% 23.77/23.61 0 [] -hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),$f25(X_a,X_b,X_c,X_d,X_e,X_1,P_1)),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),$f24(X_a,X_b,X_c,X_d,X_e,X_1,P_1)),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),$f23(X_a,X_b,X_c,X_d,X_e,X_1,P_1)),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),$f22(X_a,X_b,X_c,X_d,X_e,X_1,P_1)),$f21(X_a,X_b,X_c,X_d,X_e,X_1,P_1)))))))|hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P_1,X_1)).
% 23.77/23.61 0 [] ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),Y)=hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),$f30(X_a,X_b,X_c,X_d,X_e,Y)),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),$f29(X_a,X_b,X_c,X_d,X_e,Y)),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),$f28(X_a,X_b,X_c,X_d,X_e,Y)),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),$f27(X_a,X_b,X_c,X_d,X_e,Y)),$f26(X_a,X_b,X_c,X_d,X_e,Y))))).
% 23.77/23.61 0 [] -hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),$f34(X_a,X_b,X_c,X_d,X_1,P_1)),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),$f33(X_a,X_b,X_c,X_d,X_1,P_1)),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),$f32(X_a,X_b,X_c,X_d,X_1,P_1)),$f31(X_a,X_b,X_c,X_d,X_1,P_1))))))|hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P_1,X_1)).
% 23.77/23.61 0 [] ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),Y)=hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),$f38(X_a,X_b,X_c,X_d,Y)),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),$f37(X_a,X_b,X_c,X_d,Y)),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),$f36(X_a,X_b,X_c,X_d,Y)),$f35(X_a,X_b,X_c,X_d,Y)))).
% 23.77/23.61 0 [] -hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,P_1,hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),$f41(X_a,X_b,X_c,X_1,P_1)),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),$f40(X_a,X_b,X_c,X_1,P_1)),$f39(X_a,X_b,X_c,X_1,P_1)))))|hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,P_1,X_1)).
% 23.77/23.61 0 [] ti(product_prod(X_a,product_prod(X_b,X_c)),Y)=hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),$f44(X_a,X_b,X_c,Y)),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),$f43(X_a,X_b,X_c,Y)),$f42(X_a,X_b,X_c,Y))).
% 23.77/23.61 0 [] ti(product_prod(X_a,X_b),P_3)=hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),$f46(X_a,X_b,P_3)),$f45(X_a,X_b,P_3)).
% 23.77/23.61 0 [] hAPP(X_a,X_b,F,$f47(X_a,X_b,F,G))!=hAPP(X_a,X_b,G,$f47(X_a,X_b,F,G))|ti(fun(X_a,X_b),F)=ti(fun(X_a,X_b),G).
% 23.77/23.61 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3))|hBOOL(hAPP(X_a,bool,A_3,X_1)).
% 23.77/23.61 0 [] hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3))| -hBOOL(hAPP(X_a,bool,A_3,X_1)).
% 23.77/23.61 0 [] ti(product_prod(X_a,X_b),Y)=hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),$f49(X_a,X_b,Y)),$f48(X_a,X_b,Y)).
% 23.77/23.61 0 [] hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),produc1605651328_split(X_b,X_c,X_a),C_1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba))=hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),C_1,Aa),Ba).
% 23.77/23.61 0 [] -hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba)))|hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba)).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_1)),C_1)),D_2)).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_1)),C_1)),D_2)).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2)))|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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ba),Aa)),E_1)),D_2))).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2)))| -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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ba),Aa)),E_1)),D_2))).
% 23.77/23.61 0 [] -ring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),one_one(X_a))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a))).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_1)),C_1)),D_2)).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_1)),C_1)),D_2)).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ba),Aa)),E_1)),D_2))).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ba),Aa)),E_1)),D_2))).
% 23.77/23.61 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W_1))),C).
% 23.77/23.61 0 [] hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),hAPP(fun(product_prod(X_b,X_c),X_a),fun(X_b,fun(X_c,X_a)),product_curry(X_b,X_c,X_a),F),Aa),Ba)=hAPP(product_prod(X_b,X_c),X_a,F,hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M),N_1))).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a)))).
% 23.77/23.61 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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))).
% 23.77/23.61 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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))).
% 23.77/23.61 0 [] -one(X_a)|one_one(X_a)!=ti(X_a,X_1)|ti(X_a,X_1)=one_one(X_a).
% 23.77/23.61 0 [] -one(X_a)|one_one(X_a)=ti(X_a,X_1)|ti(X_a,X_1)!=one_one(X_a).
% 23.77/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z)).
% 23.77/23.61 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z)).
% 23.77/23.61 0 [] -number(X_a)|hAPP(int,X_a,number_number_of(X_a),W)!=ti(X_a,X_1)|ti(X_a,X_1)=hAPP(int,X_a,number_number_of(X_a),W).
% 23.77/23.61 0 [] -number(X_a)|hAPP(int,X_a,number_number_of(X_a),W)=ti(X_a,X_1)|ti(X_a,X_1)!=hAPP(int,X_a,number_number_of(X_a),W).
% 23.77/23.61 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),hAPP(int,X_a,number_number_of(X_a),V_1)),hAPP(int,X_a,number_number_of(X_a),W)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W)),hAPP(int,X_a,number_number_of(X_a),V_1))).
% 23.77/23.61 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),hAPP(int,X_a,number_number_of(X_a),V_1)),hAPP(int,X_a,number_number_of(X_a),W)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W)),hAPP(int,X_a,number_number_of(X_a),V_1))).
% 23.77/23.61 0 [] -number_ring(X_a)| -ring_char_0(X_a)|hAPP(int,X_a,number_number_of(X_a),X_1)!=hAPP(int,X_a,number_number_of(X_a),Y_1)|X_1=Y_1.
% 23.77/23.61 0 [] -number_ring(X_a)| -ring_char_0(X_a)|hAPP(int,X_a,number_number_of(X_a),X_1)=hAPP(int,X_a,number_number_of(X_a),Y_1)|X_1!=Y_1.
% 23.77/23.61 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)).
% 23.77/23.61 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)).
% 23.77/23.61 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),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_1),Y_1)).
% 23.77/23.61 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),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_1),Y_1)).
% 23.77/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),one_one(int))),Z))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z)).
% 23.77/23.61 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),one_one(int))),Z))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z)).
% 23.77/23.61 0 [] -linordered_idom(X_a)|ti(X_a,X)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)).
% 23.77/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),one_one(int))),Z_1)).
% 23.77/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)).
% 23.77/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z)).
% 23.77/23.61 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z)).
% 23.77/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_3),W_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_4),Z_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_3),Z_4)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),Z_1))).
% 23.77/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z))|W=Z.
% 23.77/23.61 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z)).
% 23.77/23.61 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),one_one(int))))|W!=Z.
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Ba)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))).
% 23.77/23.61 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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(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)).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(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)).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1)=ti(X_a,A_1).
% 23.77/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a))=ti(X_a,A_1).
% 23.77/23.61 0 [] -monoid_mult(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1)=ti(X_a,A_1).
% 23.77/23.61 0 [] -comm_monoid_mult(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1)=ti(X_a,A_1).
% 23.77/23.61 0 [] -monoid_mult(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a))=ti(X_a,A_1).
% 23.77/23.61 0 [] -comm_monoid_mult(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a))=ti(X_a,A_1).
% 23.77/23.61 0 [] -ordered_ab_group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_2)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_2)).
% 23.77/23.61 0 [] -ordered_ab_group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_2)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_2)).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba)).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba)).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba)).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Ba)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba)).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))).
% 23.77/23.61 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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(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)).
% 23.77/23.61 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(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)).
% 23.77/23.61 0 [] -ordered_ab_group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_2)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),D_2)).
% 23.77/23.61 0 [] -ordered_ab_group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_2)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),D_2)).
% 23.77/23.61 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W_1))=hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W_1)).
% 23.77/23.61 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W_1))=hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W_1)).
% 23.77/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),J))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),K)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),J),K))).
% 23.77/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I),J))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),I)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),J))).
% 23.77/23.61 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z_1)=Z_1.
% 23.77/23.61 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),one_one(int))=Z_1.
% 23.77/23.61 0 [] -number(X_b)| -semiring(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),C))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C)).
% 23.89/23.61 0 [] -number(X_b)| -semiring(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_1),B)),hAPP(int,X_b,number_number_of(X_b),V))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V))).
% 23.89/23.61 0 [] -number(X_b)| -ring(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B),C))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C)).
% 23.89/23.61 0 [] -number(X_b)| -ring(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_1),B)),hAPP(int,X_b,number_number_of(X_b),V))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V))).
% 23.89/23.61 0 [] -number_ring(X_a)|hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W_1)).
% 23.89/23.61 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W_1))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W_1)).
% 23.89/23.61 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),Z_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W_1))),Z_1).
% 23.89/23.61 0 [] -number_ring(X_a)|hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W_1)).
% 23.89/23.61 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W_1))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W_1)).
% 23.89/23.61 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),Z_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W_1))),Z_1).
% 23.89/23.61 0 [] -number_ring(X_a)|hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),V),W_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W_1)).
% 23.89/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),M)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),M).
% 23.89/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M).
% 23.89/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),M)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M).
% 23.89/23.61 0 [] -hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba))|hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))).
% 23.89/23.61 0 [] -hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba))|hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))).
% 23.89/23.61 0 [] -preorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),X)).
% 23.89/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X)).
% 23.89/23.61 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1)).
% 23.89/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Z_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X)).
% 23.89/23.61 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1)).
% 23.89/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))|ti(X_a,A_1)=ti(X_a,B)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)).
% 23.89/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))|ti(X_a,A_1)=ti(X_a,B)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)).
% 23.89/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y).
% 23.89/23.61 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1))|ti(X_a,X_1)=ti(X_a,Y_1).
% 23.89/23.61 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1))|ti(X_a,X_1)!=ti(X_a,Y_1).
% 23.89/23.61 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)).
% 23.89/23.61 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),W_1)).
% 23.89/23.61 0 [] hAPP(int,int,number_number_of(int),K)=K.
% 23.89/23.61 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),W))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),W)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),W))|Z!=W.
% 23.89/23.61 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),W))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),W))|Z=W.
% 23.89/23.61 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),Y))|X=Y|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),K_1)),hAPP(int,int,number_number_of(int),L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),L)).
% 23.89/23.61 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),K_1)),hAPP(int,int,number_number_of(int),L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),L)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),K_1)),hAPP(int,int,number_number_of(int),L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),L)).
% 23.89/23.61 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),K_1)),hAPP(int,int,number_number_of(int),L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),L)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I),J))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),J),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I),K)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_1))|Z_1=W_1.
% 23.89/23.61 0 [] -ord(X_b)| -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))).
% 23.89/23.61 0 [] -ord(X_b)|hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,$f50(X_a,X_b,F,G))),hAPP(X_a,X_b,G,$f50(X_a,X_b,F,G)))).
% 23.89/23.61 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X)).
% 23.89/23.61 0 [] -order(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_e_q(X_a),X_1),Y_1)).
% 23.89/23.61 0 [] -order(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_e_q(X_a),Y_1),X_1)).
% 23.89/23.61 0 [] -order(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_e_q(X_a),X_1),Y_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y_1),X_1)).
% 23.89/23.61 0 [] -preorder(X_a)|X!=Y|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)).
% 23.89/23.61 0 [] -ord(X_b)| -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))).
% 23.89/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y_1),X_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).
% 23.89/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y_1),X_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).
% 23.89/23.61 0 [] -ord(X_a)|A_1!=B| -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),A_1),C)).
% 23.89/23.61 0 [] -order(X_a)|ti(X_a,A_1)!=ti(X_a,B)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),A_1)).
% 23.89/23.61 0 [] -ord(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))|B!=C|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),C)).
% 23.89/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))|ti(X_a,B)!=ti(X_a,C)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),A_1)).
% 23.89/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))|ti(X_a,X)=ti(X_a,Y).
% 23.89/23.61 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Z_1)).
% 23.89/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y).
% 23.89/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Z_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Z_1),X)).
% 23.89/23.61 0 [] -ord(X_b)| -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))).
% 23.89/23.61 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X)).
% 23.89/23.61 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X)).
% 23.89/23.61 0 [] -linorder(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)).
% 23.89/23.61 0 [] -linorder(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)).
% 23.89/23.61 0 [] -linorder(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),Y_1),X_1)).
% 23.89/23.61 0 [] -linorder(X_a)|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))|ti(X_a,X_1)=ti(X_a,Y_1).
% 23.89/23.61 0 [] -linorder(X_a)| -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)).
% 23.89/23.61 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1))|ti(X_a,X_1)!=ti(X_a,Y_1).
% 23.89/23.61 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)).
% 23.89/23.61 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1))|ti(X_a,X_1)=ti(X_a,Y_1).
% 23.89/23.61 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1))|ti(X_a,X_1)!=ti(X_a,Y_1).
% 23.89/23.61 0 [] -linorder(X_a)|ti(X_a,X)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)).
% 23.89/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|ti(X_a,X)!=ti(X_a,Y).
% 23.89/23.61 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)).
% 23.89/23.61 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)).
% 23.89/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|ti(X_a,X)!=ti(X_a,Y).
% 23.89/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|ti(X_a,Y)!=ti(X_a,X).
% 23.89/23.61 0 [] -preorder(X_a)| -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))|hBOOL(P_1).
% 23.89/23.61 0 [] -preorder(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),B),A_1)).
% 23.89/23.61 0 [] -order(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),A_1),B)).
% 23.89/23.61 0 [] -ord(X_a)|A_1!=B| -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),A_1),C)).
% 23.89/23.61 0 [] -order(X_a)|ti(X_a,A_1)!=ti(X_a,B)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1)).
% 23.89/23.61 0 [] -ord(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))|B!=C|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C)).
% 23.89/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))|ti(X_a,B)!=ti(X_a,C)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1)).
% 23.89/23.61 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1)).
% 23.89/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X)).
% 23.89/23.61 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)).
% 23.89/23.61 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)).
% 23.89/23.61 0 [] -linorder(X_a)|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_e_q(X_a),Y_1),X_1)).
% 23.89/23.61 0 [] -linorder(X_a)| -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_e_q(X_a),Y_1),X_1)).
% 23.89/23.61 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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)).
% 23.89/23.61 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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)).
% 23.89/23.61 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)).
% 23.89/23.61 0 [] -order(X_a)| -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_e_q(X_a),X_1),Y_1)).
% 23.89/23.61 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1))|ti(X_a,X_1)!=ti(X_a,Y_1).
% 23.89/23.61 0 [] -order(X_a)|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_e_q(X_a),X_1),Y_1))|ti(X_a,X_1)=ti(X_a,Y_1).
% 23.89/23.61 0 [] -preorder(X_a)| -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_e_q(X_a),X_1),Y_1)).
% 23.89/23.61 0 [] -preorder(X_a)| -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_e_q(X_a),Y_1),X_1)).
% 23.89/23.61 0 [] -preorder(X_a)|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_e_q(X_a),X_1),Y_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y_1),X_1)).
% 23.89/23.61 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))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1))|ti(X_a,X_1)=ti(X_a,Y_1).
% 23.89/23.61 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))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)).
% 23.89/23.61 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).
% 23.89/23.61 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X)).
% 23.89/23.61 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)).
% 23.89/23.61 0 [] -linorder(X_a)|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_e_q(X_a),X_1),Y_1))|ti(X_a,X_1)=ti(X_a,Y_1).
% 23.89/23.61 0 [] -linorder(X_a)|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_e_q(X_a),X_1),Y_1))|ti(X_a,X_1)!=ti(X_a,Y_1).
% 23.89/23.61 0 [] -order(X_a)|ti(X_a,A_1)=ti(X_a,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),A_1),B)).
% 23.89/23.61 0 [] -order(X_a)|ti(X_a,A_1)=ti(X_a,B)| -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(X_a),B),A_1)).
% 23.89/23.61 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),K_1))| -hBOOL(hAPP(int,bool,P_1,K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f51(P_1,I_1,K_1)),K_1))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),K_1))| -hBOOL(hAPP(int,bool,P_1,K_1))|hBOOL(hAPP(int,bool,P_1,$f51(P_1,I_1,K_1)))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),K_1))| -hBOOL(hAPP(int,bool,P_1,K_1))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f51(P_1,I_1,K_1)),one_one(int))))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K_1))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f52(P_1,I_1,K_1)),K_1))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K_1))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),one_one(int))))|hBOOL(hAPP(int,bool,P_1,$f52(P_1,I_1,K_1)))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K_1))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),one_one(int))))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f52(P_1,I_1,K_1)),one_one(int))))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),I_1))| -hBOOL(hAPP(int,bool,P_1,K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),$f53(P_1,K_1,I_1)))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),I_1))| -hBOOL(hAPP(int,bool,P_1,K_1))|hBOOL(hAPP(int,bool,P_1,$f53(P_1,K_1,I_1)))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),I_1))| -hBOOL(hAPP(int,bool,P_1,K_1))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f53(P_1,K_1,I_1)),one_one(int))))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),I_1))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),$f54(P_1,K_1,I_1)))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),I_1))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),one_one(int))))|hBOOL(hAPP(int,bool,P_1,$f54(P_1,K_1,I_1)))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),I_1))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),one_one(int))))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f54(P_1,K_1,I_1)),one_one(int))))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -dense_linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f55(X_a,Z_1,Y)),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1)).
% 23.89/23.61 0 [] -dense_linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),$f55(X_a,Z_1,Y)),Z_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1)).
% 23.89/23.61 0 [] -dense_linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),$f56(X_a,Z_1,X,Y)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1)).
% 23.89/23.61 0 [] -dense_linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f56(X_a,Z_1,X,Y)),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1)).
% 23.89/23.61 0 [] -dense_linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),$f56(X_a,Z_1,X,Y)),Z_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1)).
% 23.89/23.61 0 [] -order(X_a)| -order(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C_1),hAPP(X_a,X_b,F,Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f57(X_b,X_a,C_1,F,Ba,Aa)),$f58(X_b,X_a,C_1,F,Ba,Aa)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Aa))).
% 23.89/23.61 0 [] -order(X_a)| -order(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C_1),hAPP(X_a,X_b,F,Ba)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,$f57(X_b,X_a,C_1,F,Ba,Aa))),hAPP(X_a,X_b,F,$f58(X_b,X_a,C_1,F,Ba,Aa))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Aa))).
% 23.89/23.61 0 [] -ord(X_b)| -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G))|hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G)).
% 23.89/23.61 0 [] -ord(X_b)| -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G))| -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),G),F)).
% 23.89/23.61 0 [] -ord(X_b)|hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G))| -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G))|hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),G),F)).
% 23.89/23.61 0 [] -ord(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,$f59(X_a,X_b,F,G))),hAPP(X_a,X_b,G,$f59(X_a,X_b,F,G))))|hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G)).
% 23.89/23.61 0 [] -order(X_a)| -ord(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_b,X_a,F,Ba)),Aa))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),Ba))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),$f60(X_b,X_a,C_1,F,Ba,Aa)),$f61(X_b,X_a,C_1,F,Ba,Aa)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),Aa)).
% 23.89/23.61 0 [] -order(X_a)| -ord(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_b,X_a,F,Ba)),Aa))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),Ba))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,$f60(X_b,X_a,C_1,F,Ba,Aa))),hAPP(X_b,X_a,F,$f61(X_b,X_a,C_1,F,Ba,Aa))))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),Aa)).
% 23.89/23.61 0 [] -order(X_a)| -order(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ba)),Aa))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C_1),Ba))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),$f62(X_b,X_a,C_1,F,Ba,Aa)),$f63(X_b,X_a,C_1,F,Ba,Aa)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),Aa)).
% 23.89/23.61 0 [] -order(X_a)| -order(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ba)),Aa))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C_1),Ba))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_b,X_a,F,$f62(X_b,X_a,C_1,F,Ba,Aa))),hAPP(X_b,X_a,F,$f63(X_b,X_a,C_1,F,Ba,Aa))))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),Aa)).
% 23.89/23.61 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),hAPP(X_b,X_a,F,Ba)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),C_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),$f65(X_a,X_b,C_1,Aa,F,Ba)),$f64(X_a,X_b,C_1,Aa,F,Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,C_1))).
% 23.89/23.61 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),hAPP(X_b,X_a,F,Ba)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),C_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,$f65(X_a,X_b,C_1,Aa,F,Ba))),hAPP(X_b,X_a,F,$f64(X_a,X_b,C_1,Aa,F,Ba))))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,C_1))).
% 23.89/23.61 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ba)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Ba),C_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),$f67(X_a,X_b,C_1,Aa,F,Ba)),$f66(X_a,X_b,C_1,Aa,F,Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,C_1))).
% 23.89/23.61 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ba)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Ba),C_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_b,X_a,F,$f67(X_a,X_b,C_1,Aa,F,Ba))),hAPP(X_b,X_a,F,$f66(X_a,X_b,C_1,Aa,F,Ba))))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,C_1))).
% 23.89/23.61 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Ba)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),$f69(X_a,X_b,F,C_1,Aa,Ba)),$f68(X_a,X_b,F,C_1,Aa,Ba)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),C_1)).
% 23.89/23.61 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Ba)),C_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,$f69(X_a,X_b,F,C_1,Aa,Ba))),hAPP(X_a,X_b,F,$f68(X_a,X_b,F,C_1,Aa,Ba))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),C_1)).
% 23.89/23.61 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,Ba)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f71(X_a,X_b,F,C_1,Aa,Ba)),$f70(X_a,X_b,F,C_1,Aa,Ba)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),C_1)).
% 23.89/23.61 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,Ba)),C_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,$f71(X_a,X_b,F,C_1,Aa,Ba))),hAPP(X_a,X_b,F,$f70(X_a,X_b,F,C_1,Aa,Ba))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),C_1)).
% 23.89/23.61 0 [] -order(X_a)| -order(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ba),Aa))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),$f72(X_b,X_a,C_1,F,Ba,Aa)),$f73(X_b,X_a,C_1,F,Ba,Aa)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Aa))).
% 23.89/23.61 0 [] -order(X_a)| -order(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ba),Aa))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Ba)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,$f72(X_b,X_a,C_1,F,Ba,Aa))),hAPP(X_a,X_b,F,$f73(X_b,X_a,C_1,F,Ba,Aa))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Aa))).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,P_1,K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),$f74(I_1,P_1,K_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f75(I_1,P_1,K_1)),K_1))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,P_1,K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),$f74(I_1,P_1,K_1)))|hBOOL(hAPP(int,bool,P_1,$f75(I_1,P_1,K_1)))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,P_1,K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),$f74(I_1,P_1,K_1)))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f75(I_1,P_1,K_1)),one_one(int))))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,P_1,K_1))|hBOOL(hAPP(int,bool,P_1,$f74(I_1,P_1,K_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f75(I_1,P_1,K_1)),K_1))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,P_1,K_1))|hBOOL(hAPP(int,bool,P_1,$f74(I_1,P_1,K_1)))|hBOOL(hAPP(int,bool,P_1,$f75(I_1,P_1,K_1)))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,P_1,K_1))|hBOOL(hAPP(int,bool,P_1,$f74(I_1,P_1,K_1)))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f75(I_1,P_1,K_1)),one_one(int))))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,P_1,K_1))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f74(I_1,P_1,K_1)),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f75(I_1,P_1,K_1)),K_1))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,P_1,K_1))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f74(I_1,P_1,K_1)),one_one(int))))|hBOOL(hAPP(int,bool,P_1,$f75(I_1,P_1,K_1)))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,P_1,K_1))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f74(I_1,P_1,K_1)),one_one(int))))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f75(I_1,P_1,K_1)),one_one(int))))|hBOOL(hAPP(int,bool,P_1,I_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),A_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),$f76(X_1,P_1)))|hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f76(X_1,P_1)),one_one(int))))|hBOOL(hAPP(int,bool,P_1,X_1)).
% 23.89/23.61 0 [] -hBOOL(hAPP(int,bool,P_1,$f76(X_1,P_1)))|hBOOL(hAPP(int,bool,P_1,X_1)).
% 23.89/23.61 0 [] -linord626643107strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),U_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),V))|hAPP(X_a,X_a,hAPP(X_a,fun(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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)).
% 23.89/23.61 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))),X_1)).
% 23.89/23.61 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))),X_1)).
% 23.89/23.61 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a)))).
% 23.89/23.61 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a)))).
% 23.89/23.61 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)).
% 23.89/23.61 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)).
% 23.89/23.61 0 [] -zero(X_a)|zero_zero(X_a)!=ti(X_a,X_1)|ti(X_a,X_1)=zero_zero(X_a).
% 23.89/23.61 0 [] -zero(X_a)|zero_zero(X_a)=ti(X_a,X_1)|ti(X_a,X_1)!=zero_zero(X_a).
% 23.89/23.61 0 [] -archim1727834104eiling(X_a)|hAPP(X_a,int,archimedean_ceiling(X_a),zero_zero(X_a))=zero_zero(int).
% 23.89/23.61 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),zero_zero(int)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),zero_zero(X_a))).
% 23.89/23.61 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),zero_zero(int)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),zero_zero(X_a))).
% 23.89/23.61 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),one_one(int)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),zero_zero(X_a))).
% 23.89/23.61 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),one_one(int)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),zero_zero(X_a))).
% 23.89/23.61 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)).
% 23.89/23.61 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)).
% 23.89/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1)=zero_zero(X_a).
% 23.89/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a))=zero_zero(X_a).
% 23.89/23.61 0 [] -mult_zero(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1)=zero_zero(X_a).
% 23.89/23.61 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),B)=zero_zero(X_a).
% 23.89/23.61 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),Y)=zero_zero(X_a).
% 23.89/23.61 0 [] -mult_zero(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a))=zero_zero(X_a).
% 23.89/23.61 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a))=zero_zero(X_a).
% 23.89/23.61 0 [] -real_normed_algebra(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),zero_zero(X_a))=zero_zero(X_a).
% 23.89/23.61 0 [] -ring_n68954251visors(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)!=zero_zero(X_a)|ti(X_a,Aa)=zero_zero(X_a)|ti(X_a,Ba)=zero_zero(X_a).
% 23.89/23.61 0 [] -ring_n68954251visors(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)=zero_zero(X_a)|ti(X_a,Aa)!=zero_zero(X_a).
% 23.89/23.61 0 [] -ring_n68954251visors(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)=zero_zero(X_a)|ti(X_a,Ba)!=zero_zero(X_a).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)!=zero_zero(X_a).
% 23.89/23.61 0 [] -no_zero_divisors(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(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).
% 23.89/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1)=ti(X_a,A_1).
% 23.89/23.61 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a))=ti(X_a,A_1).
% 23.89/23.61 0 [] -semiri456707255roduct(X_a)|ti(X_a,Ba)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa)|ti(X_a,Aa)=zero_zero(X_a).
% 23.89/23.61 0 [] -semiri456707255roduct(X_a)|ti(X_a,Ba)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa)|ti(X_a,Aa)!=zero_zero(X_a).
% 23.89/23.61 0 [] -monoid_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1)=ti(X_a,A_1).
% 23.89/23.61 0 [] -comm_monoid_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1)=ti(X_a,A_1).
% 23.89/23.61 0 [] -linord219039673up_add(X_a)|zero_zero(X_a)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)|ti(X_a,Aa)=zero_zero(X_a).
% 23.89/23.61 0 [] -linord219039673up_add(X_a)|zero_zero(X_a)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)|ti(X_a,Aa)!=zero_zero(X_a).
% 23.89/23.61 0 [] -monoid_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a))=ti(X_a,A_1).
% 23.89/23.61 0 [] -comm_monoid_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a))=ti(X_a,A_1).
% 23.89/23.61 0 [] -linord219039673up_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)!=zero_zero(X_a)|ti(X_a,Aa)=zero_zero(X_a).
% 23.89/23.61 0 [] -linord219039673up_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)=zero_zero(X_a)|ti(X_a,Aa)!=zero_zero(X_a).
% 23.89/23.61 0 [] -zero_ne_q_one(X_a)|one_one(X_a)!=zero_zero(X_a).
% 23.89/23.61 0 [] -zero_ne_q_one(X_a)|zero_zero(X_a)!=one_one(X_a).
% 23.89/23.61 0 [] -group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),zero_zero(X_a))=ti(X_a,A_1).
% 23.89/23.61 0 [] -group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_1)=zero_zero(X_a).
% 23.89/23.61 0 [] -ab_group_add(X_a)|ti(X_a,Aa)!=ti(X_a,Ba)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)=zero_zero(X_a).
% 23.89/23.61 0 [] -ab_group_add(X_a)|ti(X_a,Aa)=ti(X_a,Ba)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)!=zero_zero(X_a).
% 23.89/23.61 0 [] -group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)!=zero_zero(X_a)|ti(X_a,Aa)=ti(X_a,Ba).
% 23.89/23.61 0 [] -group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)=zero_zero(X_a)|ti(X_a,Aa)!=ti(X_a,Ba).
% 23.89/23.61 0 [] zero_zero(int)!=one_one(int).
% 23.89/23.61 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),Z_1)=Z_1.
% 23.89/23.61 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),zero_zero(int))=Z_1.
% 23.89/23.61 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(X_a,int,archimedean_ceiling(X_a),Y)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)).
% 23.89/23.61 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archimedean_ceiling(X_a),Y)),hAPP(X_a,int,archimedean_ceiling(X_a),X))).
% 23.89/23.61 0 [] -archim1727834104eiling(X_a)|hAPP(X_a,int,archimedean_ceiling(X_a),one_one(X_a))=one_one(int).
% 23.89/23.61 0 [] -archim1727834104eiling(X_a)|hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(int,X_a,number_number_of(X_a),V))=hAPP(int,int,number_number_of(int),V).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Aa))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),zero_zero(X_a))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Aa))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ba),zero_zero(X_a))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Ba))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),zero_zero(X_a))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Ba))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ba),zero_zero(X_a))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Aa))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Ba)).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ba),zero_zero(X_a))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),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)),Aa))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),zero_zero(X_a))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),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)),Aa))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Ba)).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ba),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),zero_zero(X_a))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ba),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)),Ba)).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),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)),Aa))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ba),zero_zero(X_a))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),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)),Ba)).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),zero_zero(X_a))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))).
% 23.89/23.61 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_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1))).
% 23.89/23.61 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_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)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)),zero_zero(X_a))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),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))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),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),Ba),Aa)).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa)).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),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),Aa),Ba)).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),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),Ba),Aa)).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))|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))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))|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),Ba),Aa)).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))).
% 23.89/23.61 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))| -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),Aa),Ba)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))| -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),Ba),Aa)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),zero_zero(X_a))).
% 23.89/23.62 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,hAPP(X_a,fun(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)).
% 23.89/23.62 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,hAPP(X_a,fun(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)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Aa)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Aa)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),zero_zero(X_a))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),zero_zero(X_a))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))).
% 23.89/23.62 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_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))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1)!=zero_zero(X_a)|ti(X_a,X_1)=zero_zero(X_a).
% 23.89/23.62 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_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))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1)!=zero_zero(X_a)|ti(X_a,Y_1)=zero_zero(X_a).
% 23.89/23.62 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_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))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1)=zero_zero(X_a)|ti(X_a,X_1)!=zero_zero(X_a)|ti(X_a,Y_1)!=zero_zero(X_a).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a))).
% 23.89/23.62 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))).
% 23.89/23.62 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))).
% 23.89/23.62 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))).
% 23.89/23.62 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))).
% 23.89/23.62 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),Aa),Ba))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),zero_zero(X_a))).
% 23.89/23.62 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),Aa),Ba))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),zero_zero(X_a))).
% 23.89/23.62 0 [] -semiri456707255roduct(X_a)|ti(X_a,R)=zero_zero(X_a)|ti(X_a,A_1)!=ti(X_a,B)|ti(X_a,C)=ti(X_a,D_1)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R),C))!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R),D_1)).
% 23.89/23.62 0 [] -ordered_ab_group_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),zero_zero(X_a))).
% 23.89/23.62 0 [] -ordered_ab_group_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),zero_zero(X_a))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),A_1))|X=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),one_one(int))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),one_one(int)))).
% 23.89/23.62 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),J))| -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),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),J))).
% 23.89/23.62 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_1)),Z_1)!=zero_zero(int).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),L))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),L)),zero_zero(int))).
% 23.89/23.62 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),L))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),L)),zero_zero(int))).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),X_1)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),X_1)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),one_one(int)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),one_one(X_a))).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),one_one(int)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),one_one(X_a))).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),X_1)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),X_1)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),V_1))).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),V_1))).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a)))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),one_one(int)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V)))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(int,int,number_number_of(int),V)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a)))=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),one_one(int)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V)))=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(int,int,number_number_of(int),V)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ba),Aa)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ba),Aa)).
% 23.89/23.62 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_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_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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1))).
% 23.89/23.62 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_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1))).
% 23.89/23.62 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_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1))).
% 23.89/23.62 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_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(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)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(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)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(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)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(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)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(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)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(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)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a))).
% 23.89/23.62 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),one_one(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),X)).
% 23.89/23.62 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),one_one(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X)),X)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)).
% 23.89/23.62 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M_1))|hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N_2)!=one_one(int)|M_1=one_one(int).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M_1))|hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N_2)!=one_one(int)|N_2=one_one(int).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M_1))|hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N_2)=one_one(int)|M_1!=one_one(int)|N_2!=one_one(int).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z)),Z)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),zero_zero(int))).
% 23.89/23.62 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z)),Z)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),zero_zero(int))).
% 23.89/23.62 0 [] -linord1278240602ring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),U_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),V))|hAPP(X_a,X_a,hAPP(X_a,fun(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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)).
% 23.89/23.62 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,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_1))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))|A_1!=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q),one_one(int))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))|A_1!=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R),A_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Q)).
% 23.89/23.62 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q)),R)!=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),R_3)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),R_3)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R),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_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_1),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q)).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_1)),R_3)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q)),R)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R))| -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),Q_1)).
% 23.89/23.62 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q)),R)!=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),R_3)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),R_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R))| -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),B_1),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q),Q_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_1)),R_3)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q)),R)))| -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),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q)).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),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_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),zero_zero(int))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),R_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),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_e_q(int),zero_zero(int)),Q_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1))|hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M),N_1)!=hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),R),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S),T_3))|R=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_3),N_1)).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))))|ti(X_a,X_1)!=zero_zero(X_a)|ti(X_a,Y_1)!=zero_zero(X_a).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))))|ti(X_a,X_1)=zero_zero(X_a).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))))|ti(X_a,Y_1)=zero_zero(X_a).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y))),zero_zero(X_a))).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))),zero_zero(X_a)))|ti(X_a,X_1)=zero_zero(X_a).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))),zero_zero(X_a)))|ti(X_a,Y_1)=zero_zero(X_a).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))),zero_zero(X_a)))|ti(X_a,X_1)!=zero_zero(X_a)|ti(X_a,Y_1)!=zero_zero(X_a).
% 23.89/23.62 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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y)))).
% 23.89/23.62 0 [] -linord581940658strict(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))!=zero_zero(X_a)|ti(X_a,X_1)=zero_zero(X_a).
% 23.89/23.62 0 [] -linord581940658strict(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))!=zero_zero(X_a)|ti(X_a,Y_1)=zero_zero(X_a).
% 23.89/23.62 0 [] -linord581940658strict(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))=zero_zero(X_a)|ti(X_a,X_1)!=zero_zero(X_a)|ti(X_a,Y_1)!=zero_zero(X_a).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R))|hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N_1),R_3),R),S_1),S),T_4),T_3)!=hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),Rn),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Sn),Tn))|R_3!=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_4),N_1))|R!=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_3),N_1))|Rn=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Sn),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Tn),N_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y))).
% 23.89/23.62 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,hAPP(int,fun(int,int),times_times(int),A_1),B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)).
% 23.89/23.62 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),one_one(int))).
% 23.89/23.62 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),zero_zero(int))).
% 23.89/23.62 0 [] hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M),N_1)=hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N_1),M),N_1),one_one(int)),zero_zero(int)),zero_zero(int)),one_one(int)).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))|hBOOL(hAPP(int,bool,P_1,$f77(K_1,P_1,D_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K_1))| -hBOOL(hAPP(int,bool,P_1,X_2))|hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_2)))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f77(K_1,P_1,D_2)),D_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K_1))| -hBOOL(hAPP(int,bool,P_1,X_2))|hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_2)))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))|hBOOL(hAPP(int,bool,P_1,$f78(K_1,P_1,D_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K_1))| -hBOOL(hAPP(int,bool,P_1,X_2))|hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_2)))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f78(K_1,P_1,D_2)),D_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K_1))| -hBOOL(hAPP(int,bool,P_1,X_2))|hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_2)))).
% 23.89/23.62 0 [] -linord1117847801e_zero(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),$f79(X_a,X,Y)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)).
% 23.89/23.62 0 [] -linord1117847801e_zero(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f79(X_a,X,Y)),one_one(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)).
% 23.89/23.62 0 [] -linord1117847801e_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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),$f79(X_a,X,Y)),X)),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)).
% 23.89/23.62 0 [] A_1!=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q)),R)|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),R))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R),zero_zero(int)))|hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q),R))).
% 23.89/23.62 0 [] A_1!=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q)),R)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))|hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q),R))).
% 23.89/23.62 0 [] A_1!=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q)),R)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R),zero_zero(int)))|hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q),R))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Y),X))|hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y).
% 23.89/23.62 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Y),X))|hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)=zero_zero(int).
% 23.89/23.62 0 [] B=zero_zero(int)|hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,zero_zero(int)),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int)))).
% 23.89/23.62 0 [] -hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),A_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q),R)))|A_1=zero_zero(int)|R=zero_zero(int).
% 23.89/23.62 0 [] -hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q),R)))| -hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_1),R_3)))|B=zero_zero(int)|Q=Q_1.
% 23.89/23.62 0 [] -hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q),R)))| -hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_1),R_3)))|B=zero_zero(int)|R=R_3.
% 23.89/23.62 0 [] -hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),A_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q),R)))|A_1=zero_zero(int)|Q=one_one(int).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Y),X))|hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y).
% 23.89/23.62 0 [] -linordered_field(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),$f80(X_a,X,Y)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)).
% 23.89/23.62 0 [] -linordered_field(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),$f80(X_a,X,Y))))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)).
% 23.89/23.62 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f81(X_a,T_3)),X_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_2),T_3)).
% 23.89/23.62 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),$f82(X_a,T_3)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_2),T_3)).
% 23.89/23.62 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f83(X_a,T_3)),X_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),T_3),X_2)).
% 23.89/23.62 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),$f84(X_a,T_3)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),T_3),X_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))|hBOOL(hAPP(int,bool,P1,$f86(P_1,P1,D_2)))|hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f86(P_1,P1,D_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f85(P_1,P1,D_2)),D_2))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f87(P_1,P1,D_2,Z_3)),Z_3))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,P_1,$f88(P_1,P1,D_2))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))|hBOOL(hAPP(int,bool,P1,$f86(P_1,P1,D_2)))|hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f86(P_1,P1,D_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f85(P_1,P1,D_2)),D_2))))|hBOOL(hAPP(int,bool,P_1,$f87(P_1,P1,D_2,Z_3)))|hBOOL(hAPP(int,bool,P1,$f87(P_1,P1,D_2,Z_3)))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,P_1,$f88(P_1,P1,D_2))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))|hBOOL(hAPP(int,bool,P1,$f86(P_1,P1,D_2)))|hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f86(P_1,P1,D_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f85(P_1,P1,D_2)),D_2))))| -hBOOL(hAPP(int,bool,P_1,$f87(P_1,P1,D_2,Z_3)))| -hBOOL(hAPP(int,bool,P1,$f87(P_1,P1,D_2,Z_3)))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,P_1,$f88(P_1,P1,D_2))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))| -hBOOL(hAPP(int,bool,P1,$f86(P_1,P1,D_2)))| -hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f86(P_1,P1,D_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f85(P_1,P1,D_2)),D_2))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f87(P_1,P1,D_2,Z_3)),Z_3))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,P_1,$f88(P_1,P1,D_2))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))| -hBOOL(hAPP(int,bool,P1,$f86(P_1,P1,D_2)))| -hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f86(P_1,P1,D_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f85(P_1,P1,D_2)),D_2))))|hBOOL(hAPP(int,bool,P_1,$f87(P_1,P1,D_2,Z_3)))|hBOOL(hAPP(int,bool,P1,$f87(P_1,P1,D_2,Z_3)))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,P_1,$f88(P_1,P1,D_2))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))| -hBOOL(hAPP(int,bool,P1,$f86(P_1,P1,D_2)))| -hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f86(P_1,P1,D_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f85(P_1,P1,D_2)),D_2))))| -hBOOL(hAPP(int,bool,P_1,$f87(P_1,P1,D_2,Z_3)))| -hBOOL(hAPP(int,bool,P1,$f87(P_1,P1,D_2,Z_3)))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,P_1,$f88(P_1,P1,D_2))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))|hBOOL(hAPP(int,bool,P_2,$f90(P_1,P_2,D_2)))|hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f90(P_1,P_2,D_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f89(P_1,P_2,D_2)),D_2))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_3),$f91(P_1,P_2,D_2,Z_3)))| -hBOOL(hAPP(int,bool,P_2,X1))|hBOOL(hAPP(int,bool,P_1,$f92(P_1,P_2,D_2))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))|hBOOL(hAPP(int,bool,P_2,$f90(P_1,P_2,D_2)))|hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f90(P_1,P_2,D_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f89(P_1,P_2,D_2)),D_2))))|hBOOL(hAPP(int,bool,P_1,$f91(P_1,P_2,D_2,Z_3)))|hBOOL(hAPP(int,bool,P_2,$f91(P_1,P_2,D_2,Z_3)))| -hBOOL(hAPP(int,bool,P_2,X1))|hBOOL(hAPP(int,bool,P_1,$f92(P_1,P_2,D_2))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))|hBOOL(hAPP(int,bool,P_2,$f90(P_1,P_2,D_2)))|hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f90(P_1,P_2,D_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f89(P_1,P_2,D_2)),D_2))))| -hBOOL(hAPP(int,bool,P_1,$f91(P_1,P_2,D_2,Z_3)))| -hBOOL(hAPP(int,bool,P_2,$f91(P_1,P_2,D_2,Z_3)))| -hBOOL(hAPP(int,bool,P_2,X1))|hBOOL(hAPP(int,bool,P_1,$f92(P_1,P_2,D_2))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))| -hBOOL(hAPP(int,bool,P_2,$f90(P_1,P_2,D_2)))| -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f90(P_1,P_2,D_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f89(P_1,P_2,D_2)),D_2))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_3),$f91(P_1,P_2,D_2,Z_3)))| -hBOOL(hAPP(int,bool,P_2,X1))|hBOOL(hAPP(int,bool,P_1,$f92(P_1,P_2,D_2))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))| -hBOOL(hAPP(int,bool,P_2,$f90(P_1,P_2,D_2)))| -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f90(P_1,P_2,D_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f89(P_1,P_2,D_2)),D_2))))|hBOOL(hAPP(int,bool,P_1,$f91(P_1,P_2,D_2,Z_3)))|hBOOL(hAPP(int,bool,P_2,$f91(P_1,P_2,D_2,Z_3)))| -hBOOL(hAPP(int,bool,P_2,X1))|hBOOL(hAPP(int,bool,P_1,$f92(P_1,P_2,D_2))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2))| -hBOOL(hAPP(int,bool,P_2,$f90(P_1,P_2,D_2)))| -hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f90(P_1,P_2,D_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f89(P_1,P_2,D_2)),D_2))))| -hBOOL(hAPP(int,bool,P_1,$f91(P_1,P_2,D_2,Z_3)))| -hBOOL(hAPP(int,bool,P_2,$f91(P_1,P_2,D_2,Z_3)))| -hBOOL(hAPP(int,bool,P_2,X1))|hBOOL(hAPP(int,bool,P_1,$f92(P_1,P_2,D_2))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_1),zero_zero(int)))|hAPP(int,int,zfact,N_1)=one_one(int).
% 23.89/23.62 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_1),zero_zero(int)))|hAPP(int,int,zfact,N_1)=hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N_1),hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N_1),one_one(int)))).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a)))).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a)))).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))),X_1)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))),X_1)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hAPP(X_a,int,archim2085082626_floor(X_a),zero_zero(X_a))=zero_zero(int).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(X_a,int,archim2085082626_floor(X_a),Y)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(X_a,int,archim2085082626_floor(X_a),Y))).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hAPP(X_a,int,archim2085082626_floor(X_a),one_one(X_a))=one_one(int).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(int,X_a,number_number_of(X_a),V))=hAPP(int,int,number_number_of(int),V).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),zero_zero(int)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),zero_zero(X_a))).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),zero_zero(int)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),zero_zero(X_a))).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(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)),X_1)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(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)),X_1)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),X_1)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),X_1)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),zero_zero(int)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),zero_zero(int)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),one_one(int)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),one_one(int)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),X_1)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),X_1)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),V_1))).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),V_1))).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),X_1)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),X_1)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a)))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V)))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(int,int,number_number_of(int),V)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a)))=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int)).
% 23.89/23.62 0 [] -archim1727834104eiling(X_a)|hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V)))=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(int,int,number_number_of(int),V)).
% 23.89/23.62 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),A_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(real,int,archim2085082626_floor(real),A_1)),hAPP(real,int,archim2085082626_floor(real),B))),hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B)))).
% 23.89/23.62 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),zero_zero(int)),B))|hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Z_1))),one_one(int))),D_1)))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Z_1))),one_one(int))),D_1))),Z_1)).
% 23.89/23.62 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))).
% 23.89/23.62 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))).
% 23.89/23.62 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W_1),W_1)).
% 23.89/23.62 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z_1),W_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W_1),Z_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z_1),X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z_1),Y))).
% 23.89/23.62 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I),J))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),J),K))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I),K)).
% 23.89/23.62 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z_1),W_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W_1),Z_1))|Z_1=W_1.
% 23.89/23.62 0 [] hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z1),Z2)),W_1)=hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),W_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z2),W_1)).
% 23.89/23.62 0 [] hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),Z2)),Z3)=hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z2),Z3)).
% 23.89/23.62 0 [] hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),W_1)=hAPP(real,real,hAPP(real,fun(real,real),times_times(real),W_1),Z_1).
% 23.89/23.62 0 [] -ordere142940540dd_abs(X_a)|hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1))=hAPP(X_a,X_a,abs_abs(X_a),A_1).
% 23.89/23.62 0 [] hAPP(real,real,hAPP(real,fun(real,real),times_times(real),one_one(real)),Z_1)=Z_1.
% 23.89/23.62 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(real),X_1),Y_1))|X_1=Y_1.
% 23.89/23.62 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(real),X_1),Y_1)).
% 23.89/23.62 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),Y_1))|X_1!=Y_1.
% 23.89/23.62 0 [] -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_e_q(real),X_1),Y_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1))|X_1!=Y_1.
% 23.89/23.62 0 [] 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_e_q(real),X_1),Y_1))|X_1=Y_1.
% 23.89/23.62 0 [] -ordere142940540dd_abs(X_a)|hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))=hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1)).
% 23.89/23.62 0 [] -linordered_idom(X_a)|hAPP(X_a,X_a,abs_abs(X_a),one_one(X_a))=one_one(X_a).
% 23.89/23.62 0 [] -ordere142940540dd_abs(X_a)|hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)).
% 23.89/23.62 0 [] -linordered_idom(X_a)|hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)).
% 23.89/23.62 0 [] -linordered_idom(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),A_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1).
% 23.89/23.62 0 [] -ordere142940540dd_abs(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),hAPP(X_a,X_a,abs_abs(X_a),A_1))).
% 23.89/23.62 0 [] -ordere142940540dd_abs(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,abs_abs(X_a),A_1)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B)).
% 23.89/23.62 0 [] -ordere142940540dd_abs(X_a)|hAPP(X_a,X_a,abs_abs(X_a),zero_zero(X_a))=zero_zero(X_a).
% 23.89/23.62 0 [] -ordere142940540dd_abs(X_a)|hAPP(X_a,X_a,abs_abs(X_a),Aa)!=zero_zero(X_a)|ti(X_a,Aa)=zero_zero(X_a).
% 23.89/23.62 0 [] -ordere142940540dd_abs(X_a)|hAPP(X_a,X_a,abs_abs(X_a),Aa)=zero_zero(X_a)|ti(X_a,Aa)!=zero_zero(X_a).
% 23.89/23.62 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,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_1)),zero_zero(real))).
% 23.89/23.62 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,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_1)),zero_zero(real))).
% 23.89/23.62 0 [] C_1=zero_zero(real)|hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),Aa)!=hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),Ba)|Aa=Ba.
% 23.89/23.62 0 [] C_1=zero_zero(real)|hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),Aa)=hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),Ba)|Aa!=Ba.
% 23.89/23.62 0 [] C_1=zero_zero(real)|hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Aa),C_1)!=hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Ba),C_1)|Aa=Ba.
% 23.89/23.62 0 [] C_1=zero_zero(real)|hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Aa),C_1)=hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Ba),C_1)|Aa!=Ba.
% 23.89/23.62 0 [] hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),X_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Y_1))!=zero_zero(real)|X_1=zero_zero(real).
% 23.89/23.62 0 [] hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),X_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Y_1))!=zero_zero(real)|Y_1=zero_zero(real).
% 23.89/23.62 0 [] hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),X_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Y_1))=zero_zero(real)|X_1!=zero_zero(real)|Y_1!=zero_zero(real).
% 23.89/23.62 0 [] zero_zero(real)!=one_one(real).
% 23.89/23.62 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),Z)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Z)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),Z)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Z)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y))).
% 23.89/23.62 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),Y))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),Y))).
% 23.89/23.62 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),X_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),Y_1)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),Y_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),X_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),Y_1)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),Y_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),Z)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Z)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),Y_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),Z)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Z)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),Y_1)).
% 23.89/23.62 0 [] -ring_1(X_a)|hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),zero_zero(X_a)),ring_1_Ints(X_a))).
% 23.89/23.62 0 [] -ring_1(X_a)| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a)))|hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),ring_1_Ints(X_a))).
% 23.89/23.62 0 [] -ring_1(X_a)| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a)))|hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba)),ring_1_Ints(X_a))).
% 23.89/23.62 0 [] -number_ring(X_a)|hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,number_number_of(X_a),W)),ring_1_Ints(X_a))).
% 23.89/23.62 0 [] -ring_1(X_a)|hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),one_one(X_a)),ring_1_Ints(X_a))).
% 23.89/23.62 0 [] -ring_1(X_a)| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a)))|hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),ring_1_Ints(X_a))).
% 23.89/23.62 0 [] -ordere142940540dd_abs(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,abs_abs(X_a),A_1))).
% 23.89/23.62 0 [] -ordere142940540dd_abs(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,abs_abs(X_a),Aa)),zero_zero(X_a)))|ti(X_a,Aa)=zero_zero(X_a).
% 23.89/23.62 0 [] -ordere142940540dd_abs(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,abs_abs(X_a),Aa)),zero_zero(X_a)))|ti(X_a,Aa)!=zero_zero(X_a).
% 23.89/23.62 0 [] -ordere142940540dd_abs(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))|hAPP(X_a,X_a,abs_abs(X_a),A_1)=ti(X_a,A_1).
% 23.89/23.62 0 [] -ordere142940540dd_abs(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),zero_zero(X_a))).
% 23.89/23.62 0 [] -ordere142940540dd_abs(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,abs_abs(X_a),Aa)))|ti(X_a,Aa)!=zero_zero(X_a).
% 23.89/23.62 0 [] -ordere142940540dd_abs(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,abs_abs(X_a),Aa)))|ti(X_a,Aa)=zero_zero(X_a).
% 23.89/23.62 0 [] -ordere142940540dd_abs(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))|hAPP(X_a,X_a,abs_abs(X_a),A_1)=ti(X_a,A_1).
% 23.89/23.62 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,abs_abs(X_a),A_1)),C))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),B)),D_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),D_1))).
% 23.89/23.62 0 [] -ordere142940540dd_abs(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,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))).
% 23.89/23.62 0 [] -ordere142940540dd_abs(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,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1)))).
% 23.89/23.62 0 [] -ordere142940540dd_abs(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,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)))).
% 23.89/23.62 0 [] -ordere142940540dd_abs(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,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)))).
% 23.89/23.62 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,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),Aa))),R_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),R_2)),X_1)).
% 23.89/23.62 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,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),Aa))),R_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),R_2))).
% 23.89/23.62 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,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),Aa))),R_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),R_2)),X_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),R_2))).
% 23.89/23.62 0 [] hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N_1))!=one_one(int)|hAPP(int,int,abs_abs(int),M)=one_one(int).
% 23.89/23.62 0 [] -ordered_ring_abs(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)).
% 23.89/23.62 0 [] -ordered_ring_abs(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)).
% 23.89/23.62 0 [] -ordered_ring_abs(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)).
% 23.89/23.62 0 [] -ordered_ring_abs(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)).
% 23.89/23.62 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))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),Y)),X)=hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X)).
% 23.89/23.62 0 [] -ordere142940540dd_abs(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,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1)))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),C))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),D_1))))).
% 23.89/23.62 0 [] -ordere142940540dd_abs(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,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))).
% 23.89/23.62 0 [] -ring_char_0(X_a)| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)!=zero_zero(X_a)|ti(X_a,Aa)=zero_zero(X_a).
% 23.89/23.62 0 [] -ring_char_0(X_a)| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)=zero_zero(X_a)|ti(X_a,Aa)!=zero_zero(X_a).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z)),one_one(int)))|Z=zero_zero(int).
% 23.89/23.62 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z)),one_one(int)))|Z!=zero_zero(int).
% 23.89/23.62 0 [] hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,zero_zero(int)),B)=hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int)).
% 23.89/23.62 0 [] -ring_char_0(X_a)| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa)!=zero_zero(X_a).
% 23.89/23.62 0 [] L_1!=zero_zero(int)|hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L_1)=hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),hAPP(int,int,abs_abs(int),K)).
% 23.89/23.62 0 [] L_1=zero_zero(int)|hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L_1)=hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,abs_abs(int),K)),hAPP(int,int,abs_abs(int),L_1)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),$f93(K_1,F,N_2,M_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M_1)),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),$f94(K_1,F,N_2,M_1))).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),$f93(K_1,F,N_2,M_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M_1)),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f94(K_1,F,N_2,M_1)),N_2)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),$f93(K_1,F,N_2,M_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M_1)),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))|hAPP(nat,int,F,$f94(K_1,F,N_2,M_1))=K_1.
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f93(K_1,F,N_2,M_1)),N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M_1)),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),$f94(K_1,F,N_2,M_1))).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f93(K_1,F,N_2,M_1)),N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M_1)),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f94(K_1,F,N_2,M_1)),N_2)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f93(K_1,F,N_2,M_1)),N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M_1)),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))|hAPP(nat,int,F,$f94(K_1,F,N_2,M_1))=K_1.
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),$f93(K_1,F,N_2,M_1)),one_one(nat)))),hAPP(nat,int,F,$f93(K_1,F,N_2,M_1))))),one_one(int)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M_1)),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),$f94(K_1,F,N_2,M_1))).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),$f93(K_1,F,N_2,M_1)),one_one(nat)))),hAPP(nat,int,F,$f93(K_1,F,N_2,M_1))))),one_one(int)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M_1)),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f94(K_1,F,N_2,M_1)),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),$f93(K_1,F,N_2,M_1)),one_one(nat)))),hAPP(nat,int,F,$f93(K_1,F,N_2,M_1))))),one_one(int)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M_1)),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))|hAPP(nat,int,F,$f94(K_1,F,N_2,M_1))=K_1.
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f95(K_1,F,N_2)),N_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f96(K_1,F,N_2)),N_2)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f95(K_1,F,N_2)),N_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))|hAPP(nat,int,F,$f96(K_1,F,N_2))=K_1.
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),$f95(K_1,F,N_2)),one_one(nat)))),hAPP(nat,int,F,$f95(K_1,F,N_2))))),one_one(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f96(K_1,F,N_2)),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),$f95(K_1,F,N_2)),one_one(nat)))),hAPP(nat,int,F,$f95(K_1,F,N_2))))),one_one(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))|hAPP(nat,int,F,$f96(K_1,F,N_2))=K_1.
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f97(K_1,F,N_2)),N_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f98(K_1,F,N_2)),N_2)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f97(K_1,F,N_2)),N_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))|hAPP(nat,int,F,$f98(K_1,F,N_2))=K_1.
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),$f97(K_1,F,N_2)),one_one(nat)))),hAPP(nat,int,F,$f97(K_1,F,N_2))))),one_one(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f98(K_1,F,N_2)),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),$f97(K_1,F,N_2)),one_one(nat)))),hAPP(nat,int,F,$f97(K_1,F,N_2))))),one_one(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_2)))|hAPP(nat,int,F,$f98(K_1,F,N_2))=K_1.
% 23.89/23.62 0 [] M!=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)=zero_zero(nat).
% 23.89/23.62 0 [] M=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),X)),one_one(real))),X)).
% 23.89/23.62 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(real,real,abs_abs(real),X)))).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))).
% 23.89/23.62 0 [] X!=Y| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,abs_abs(real),U_1)),V))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),U_1)),Y))),V)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_2))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_2))).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1)).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K)).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),K)),J).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),M).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K)).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N_1)=zero_zero(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),zero_zero(nat))=zero_zero(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)!=zero_zero(nat)|M_1=zero_zero(nat)|N_2=zero_zero(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)=zero_zero(nat)|M_1!=zero_zero(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)=zero_zero(nat)|N_2!=zero_zero(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)|K_1=zero_zero(nat)|M_1=N_2.
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)|K_1!=zero_zero(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)|M_1!=N_2.
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)|M_1=N_2|K_1=zero_zero(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)|M_1!=N_2.
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)|K_1!=zero_zero(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_1)|M_1=N_2|K_1=zero_zero(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_1)|M_1!=N_2.
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_1)|K_1!=zero_zero(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)!=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M)!=zero_zero(nat)|M=N_1.
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M)=zero_zero(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat))=M.
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N_1)=zero_zero(nat).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|M_1=N_2|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3))|S!=T_3.
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M))|M!=N_1.
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1)).
% 23.89/23.62 0 [] X=Y|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X)).
% 23.89/23.62 0 [] M_1=N_2|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)).
% 23.89/23.62 0 [] M_1!=N_2| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.62 0 [] M_1!=N_2| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1)).
% 23.89/23.62 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,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),N_1)),K)).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),N_1)=M.
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)),N_1)=M.
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K)).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K_1)|M_1=N_2.
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K_1)|M_1!=N_2.
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2)|M_1=N_2.
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2)|M_1!=N_2.
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K)).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Z_1)).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1)).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K)).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),U_1)),K).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),M)).
% 23.89/23.62 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,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M))).
% 23.89/23.62 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,hAPP(nat,fun(nat,nat),minus_minus(nat),M),L_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),L_1))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),N_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),I))=I.
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_2))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_1)|M_1=N_2.
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_2))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_1)|M_1!=N_2.
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),M))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),N_1)).
% 23.89/23.62 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)).
% 23.89/23.62 0 [] M!=N_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),K)).
% 23.89/23.62 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.
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),L_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),L_1))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),I)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),J))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K))).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M)))).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M))).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N_1)=N_1.
% 23.89/23.62 0 [] one_one(nat)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)|M_1=one_one(nat).
% 23.89/23.62 0 [] one_one(nat)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)|N_2=one_one(nat).
% 23.89/23.62 0 [] one_one(nat)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)|M_1!=one_one(nat)|N_2!=one_one(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),one_one(nat))=N_1.
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)!=one_one(nat)|M_1=one_one(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)!=one_one(nat)|N_2=one_one(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)=one_one(nat)|M_1!=one_one(nat)|N_2!=one_one(nat).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),M_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),M_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.62 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,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),M)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))).
% 23.89/23.62 0 [] N_2=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)).
% 23.89/23.62 0 [] N_2!=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|N_1!=zero_zero(nat).
% 23.89/23.62 0 [] N_1=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))| -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,hAPP(nat,fun(nat,nat),times_times(nat),K),I)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),J))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))| -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,hAPP(nat,fun(nat,nat),times_times(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K))).
% 23.89/23.62 0 [] -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,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.62 0 [] -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,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)|M_1=N_2.
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)|M_1!=N_2.
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_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),M_1),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)))| -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),M_1),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N_1)=N_1.
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),zero_zero(nat))=M.
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)!=zero_zero(nat)|M_1=zero_zero(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)!=zero_zero(nat)|N_2=zero_zero(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)=zero_zero(nat)|M_1!=zero_zero(nat)|N_2!=zero_zero(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)!=M|N_1=zero_zero(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M))=zero_zero(nat).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_2)!=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.62 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_2)=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)=zero_zero(nat).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),zero_zero(nat)))|N_2=zero_zero(nat).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),zero_zero(nat)))|N_2!=zero_zero(nat).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),I)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),I)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1))=M.
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2)).
% 23.89/23.62 0 [] M!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)|N_1=one_one(nat)|M=zero_zero(nat).
% 23.89/23.62 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)).
% 23.89/23.62 0 [] M!=N_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)).
% 23.89/23.62 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)).
% 23.89/23.62 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)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|M_1=N_2.
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))|M_1!=N_2.
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|M_1!=N_2.
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))|M_1=N_2.
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.62 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,hAPP(nat,fun(nat,nat),minus_minus(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),C))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),J).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)),I_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1))).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)),I_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)),K))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1))=M.
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),N_1)=M.
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)!=K_1|J_2=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),I_1).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)=K_1|J_2!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),I_1).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),K).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)|M_1=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_2).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)|M_1!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_2).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I)),U_1)),N_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_2))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_2))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M_1)=N_2.
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M_1)!=N_2.
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),I))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),U_1)),M)),N_1).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M_1)),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M_1)),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N_1)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),L_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))|N_2=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),$f99(M_1,N_2)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))|N_2!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M))).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))).
% 23.89/23.62 0 [] X_1!=hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y_1),Z)|Y_1=hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Z).
% 23.89/23.62 0 [] X_1=hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y_1),Z)|Y_1!=hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Z).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba))|hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))|Aa!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),D)|hBOOL(hAPP(nat,bool,P_1,D)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba))|Aa=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),$f100(P_1,Aa,Ba)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba))| -hBOOL(hAPP(nat,bool,P_1,$f100(P_1,Aa,Ba))).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))|Aa=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),$f100(P_1,Aa,Ba)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,$f100(P_1,Aa,Ba))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba))|hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))|Aa!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),D)|hBOOL(hAPP(nat,bool,P_1,D)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba))|Aa=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),$f101(P_1,Aa,Ba)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba))| -hBOOL(hAPP(nat,bool,P_1,$f101(P_1,Aa,Ba))).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))|Aa=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),$f101(P_1,Aa,Ba)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,$f101(P_1,Aa,Ba))).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)))| -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_e_q(nat),M_1),N_2)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_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_e_q(nat),M_1),N_2)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)).
% 23.89/23.62 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.62 0 [] -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_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.62 0 [] -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_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.62 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M_1)),N_2)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M_1)),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f102(N_2,P_1)),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),$f102(N_2,P_1)))| -hBOOL(hAPP(nat,bool,P_1,I_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,N_2))|hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),$f102(N_2,P_1)),one_one(nat)))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),C),zero_zero(real)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,abs_abs(real),Y))))|X=zero_zero(real).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f104(M_1,K_1,F)),$f103(M_1,K_1,F)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,M_1)),K_1)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,$f104(M_1,K_1,F))),hAPP(nat,nat,F,$f103(M_1,K_1,F))))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,M_1)),K_1)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)))).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f105(N_2,P_1)),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),$f105(N_2,P_1)))| -hBOOL(hAPP(nat,bool,P_1,I_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,N_2))|hBOOL(hAPP(nat,bool,P_1,$f105(N_2,P_1))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L))|L=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),$f106(K_1,L)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L))|L!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),$f107(I,J))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),$f107(I,J))=J.
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),X_1)))|X_1=zero_zero(real).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),X_1)))|X_1!=zero_zero(real).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)|N_1=M.
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),$f108(B,A_1,X))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y_2))),$f108(B,A_1,X)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),A_1),Y_2)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y_2))),$f108(B,A_1,X)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Y_2),B)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),L_1))|L_1=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),$f109(K,L_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f111(I_1,J_2,F)),$f110(I_1,J_2,F)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_2))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,$f111(I_1,J_2,F))),hAPP(nat,nat,F,$f110(I_1,J_2,F))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_2))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),$f112(B,A_1,X))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y_2))),$f112(B,A_1,X)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),Y_2)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y_2))),$f112(B,A_1,X)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),B)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D2))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),$f113(D2,D1))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D2))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),$f113(D2,D1)),D1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D2))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),$f113(D2,D1)),D2)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X))|hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),one_one(nat)).
% 23.89/23.63 0 [] hAPP(real,nat,natceiling,hAPP(int,real,number_number_of(real),N_1))=hAPP(int,nat,number_number_of(nat),N_1).
% 23.89/23.63 0 [] hAPP(real,nat,natceiling,zero_zero(real))=zero_zero(nat).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),hAPP(real,nat,natceiling,X))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(real,nat,natceiling,X)),hAPP(real,nat,natceiling,Y))).
% 23.89/23.63 0 [] hAPP(real,nat,natceiling,one_one(real))=one_one(nat).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),zero_zero(real)))|hAPP(real,nat,natceiling,X)=zero_zero(nat).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(real,nat,natceiling,X_1)),one_one(nat)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),one_one(real))).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(real,nat,natceiling,X_1)),one_one(nat)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),one_one(real))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X))|hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),one_one(nat)).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),M_1)!=one_one(nat)|N_2=one_one(nat).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),M_1)!=one_one(nat)|M_1=one_one(nat).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),M_1)=one_one(nat)|N_2!=one_one(nat)|M_1!=one_one(nat).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_1)),X))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_1)),one_one(real))))|hAPP(real,nat,natceiling,X)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat)).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),hAPP(nat,real,real_1(nat),N_1))).
% 23.89/23.63 0 [] hAPP(real,nat,natceiling,hAPP(nat,real,real_1(nat),N_1))=N_1.
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(nat,real,real_1(nat),M_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(nat,real,real_1(nat),M_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)).
% 23.89/23.63 0 [] hAPP(nat,real,real_1(nat),zero_zero(nat))=zero_zero(real).
% 23.89/23.63 0 [] hAPP(nat,real,real_1(nat),N_2)!=zero_zero(real)|N_2=zero_zero(nat).
% 23.89/23.63 0 [] hAPP(nat,real,real_1(nat),N_2)=zero_zero(real)|N_2!=zero_zero(nat).
% 23.89/23.63 0 [] hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X))=hAPP(nat,real,real_1(nat),X).
% 23.89/23.63 0 [] hAPP(real,nat,natfloor,hAPP(nat,real,real_1(nat),N_1))=N_1.
% 23.89/23.63 0 [] hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,real_1(nat),N_2)),ring_1_Ints(real))).
% 23.89/23.63 0 [] hAPP(real,nat,natfloor,hAPP(int,real,number_number_of(real),N_1))=hAPP(int,nat,number_number_of(nat),N_1).
% 23.89/23.63 0 [] hAPP(nat,real,real_1(nat),N_2)!=hAPP(nat,real,real_1(nat),M_1)|N_2=M_1.
% 23.89/23.63 0 [] hAPP(nat,real,real_1(nat),N_2)=hAPP(nat,real,real_1(nat),M_1)|N_2!=M_1.
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))),X)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),X)),A_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),hAPP(real,nat,natfloor,A_1))).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),one_one(real))),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X)))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),A_1)),X))|hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,real_1(nat),A_1)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(real,nat,natfloor,X)),A_1).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))),one_one(real)))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Aa),hAPP(real,nat,natfloor,X_1)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),Aa)),X_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Aa),hAPP(real,nat,natfloor,X_1)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),Aa)),X_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_1)),zero_zero(real))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(nat,real,real_1(nat),M_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(nat,real,real_1(nat),M_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(real,nat,natfloor,X)),N_1)).
% 23.89/23.63 0 [] hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))=hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X))|hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(nat,real,real_1(nat),A_1)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),A_1).
% 23.89/23.63 0 [] hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))=hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,Z_1)),one_one(nat))),N_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Z_1),hAPP(nat,real,real_1(nat),N_1))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),N_1)),X))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_1)),one_one(real))))|hAPP(real,nat,natfloor,X)=N_1.
% 23.89/23.63 0 [] hAPP(nat,real,real_1(nat),one_one(nat))=one_one(real).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),hAPP(nat,real,real_1(nat),hAPP(real,nat,natceiling,X)))).
% 23.89/23.63 0 [] hAPP(real,nat,natfloor,zero_zero(real))=zero_zero(nat).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),hAPP(real,nat,natfloor,X))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(real,nat,natfloor,X)),hAPP(real,nat,natfloor,Y))).
% 23.89/23.63 0 [] hAPP(real,nat,natfloor,one_one(real))=one_one(nat).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),N_2)),zero_zero(real)))|N_2=zero_zero(nat).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),N_2)),zero_zero(real)))|N_2!=zero_zero(nat).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1))=hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),hAPP(nat,real,real_1(nat),A_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(real,nat,natceiling,X)),A_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),zero_zero(real)))|hAPP(real,nat,natfloor,X)=zero_zero(nat).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_2)),one_one(real))),hAPP(nat,real,real_1(nat),M_1))).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_2)),one_one(real))),hAPP(nat,real,real_1(nat),M_1))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),M_1)),one_one(real)))).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),M_1)),one_one(real)))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(real,nat,natceiling,X_1)),Aa))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),hAPP(nat,real,real_1(nat),Aa))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(real,nat,natceiling,X_1)),Aa))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),hAPP(nat,real,real_1(nat),Aa))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),A_1)),X))|hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,real_1(nat),A_1)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(real,nat,natceiling,X)),A_1).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),one_one(nat)),hAPP(real,nat,natfloor,X_1)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),one_one(real)),X_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),one_one(nat)),hAPP(real,nat,natfloor,X_1)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),one_one(real)),X_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X))|hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(nat,real,real_1(nat),A_1)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),A_1).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),A_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(real,nat,natfloor,A_1)),hAPP(real,nat,natfloor,B))),hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B)))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),R))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),$f114(R)),one_one(nat)))),R)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),R))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(nat,real,real_1(nat),$f114(R)))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),$f115(X,Y_2))),X))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_1)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X))|hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,number_number_of(real),N_1)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),hAPP(int,nat,number_number_of(nat),N_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,nat_neg,zero_zero(int))).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,nat_neg,one_one(int))).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,nat_neg,Z_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,nat_neg,Z_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,nat_neg,X_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,nat_neg,X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(int,nat,number_number_of(nat),V)=zero_zero(nat).
% 23.89/23.63 0 [] hAPP(int,nat,number_number_of(nat),V_1)!=hAPP(int,nat,number_number_of(nat),V_3)| -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_3)),zero_zero(int))).
% 23.89/23.63 0 [] hAPP(int,nat,number_number_of(nat),V_1)!=hAPP(int,nat,number_number_of(nat),V_3)|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1)))| -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3)))|hAPP(int,int,number_number_of(int),V_1)=zero_zero(int).
% 23.89/23.63 0 [] hAPP(int,nat,number_number_of(nat),V_1)!=hAPP(int,nat,number_number_of(nat),V_3)|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1)))|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3)))|V_1=V_3.
% 23.89/23.63 0 [] hAPP(int,nat,number_number_of(nat),V_1)=hAPP(int,nat,number_number_of(nat),V_3)|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1)))|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3)))|V_1!=V_3.
% 23.89/23.63 0 [] hAPP(int,nat,number_number_of(nat),V_1)=hAPP(int,nat,number_number_of(nat),V_3)|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1)))|hAPP(int,int,number_number_of(int),V_1)!=zero_zero(int)| -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))).
% 23.89/23.63 0 [] hAPP(int,nat,number_number_of(nat),V_1)=hAPP(int,nat,number_number_of(nat),V_3)|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1)))|hAPP(int,int,number_number_of(int),V_1)!=zero_zero(int)|V_1!=V_3.
% 23.89/23.63 0 [] hAPP(int,nat,number_number_of(nat),V_1)=hAPP(int,nat,number_number_of(nat),V_3)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_3)),zero_zero(int)))| -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1))).
% 23.89/23.63 0 [] hAPP(int,nat,number_number_of(nat),V_1)=hAPP(int,nat,number_number_of(nat),V_3)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_3)),zero_zero(int)))|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3)))|V_1!=V_3.
% 23.89/23.63 0 [] hAPP(int,nat,number_number_of(nat),V_1)=hAPP(int,nat,number_number_of(nat),V_3)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_3)),zero_zero(int)))|hAPP(int,int,number_number_of(int),V_1)!=zero_zero(int)| -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))).
% 23.89/23.63 0 [] hAPP(int,nat,number_number_of(nat),V_1)=hAPP(int,nat,number_number_of(nat),V_3)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_3)),zero_zero(int)))|hAPP(int,int,number_number_of(int),V_1)!=zero_zero(int)|V_1!=V_3.
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_2)),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_2)),K).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))| -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2)))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_2)),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),K).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2)))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_2)),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_2))),K).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,real,real_1(nat),hAPP(int,nat,number_number_of(nat),V))=zero_zero(real).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,real,real_1(nat),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,real,number_number_of(real),V).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_2)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(int,nat,number_number_of(nat),N_2)),hAPP(real,nat,natfloor,X_1)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,number_number_of(real),N_2)),X_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_2)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(int,nat,number_number_of(nat),N_2)),hAPP(real,nat,natfloor,X_1)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,number_number_of(real),N_2)),X_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_2)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(real,nat,natceiling,X_1)),hAPP(int,nat,number_number_of(nat),N_2)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),hAPP(int,real,number_number_of(real),N_2))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_2)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(real,nat,natceiling,X_1)),hAPP(int,nat,number_number_of(nat),N_2)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),hAPP(int,real,number_number_of(real),N_2))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_1)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),X))|hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,number_number_of(real),N_1)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),hAPP(int,nat,number_number_of(nat),N_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),$f116(X)))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),Z_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),Y)).
% 23.89/23.63 0 [] -hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),in_rel(X_a,X_b),R_1),X_1),Y_1))|hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1)),R_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),in_rel(X_a,X_b),R_1),X_1),Y_1))| -hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1)),R_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),X))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real))))|hAPP(real,int,archimedean_ceiling(real),X)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_1),one_one(int)).
% 23.89/23.63 0 [] hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y))=hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y)).
% 23.89/23.63 0 [] hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,real_1(int),A_1)))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1).
% 23.89/23.63 0 [] hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),X_1))!=X_1|X_1=hAPP(int,real,real_1(int),$f117(X_1)).
% 23.89/23.63 0 [] hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),X_1))=X_1|X_1!=hAPP(int,real,real_1(int),N).
% 23.89/23.63 0 [] hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),N_1))=N_1.
% 23.89/23.63 0 [] -archim1727834104eiling(X_a)|hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(X_a,int,archim2085082626_floor(X_a),R)))=hAPP(X_a,int,archim2085082626_floor(X_a),R).
% 23.89/23.63 0 [] hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),X_1))!=X_1|X_1=hAPP(int,real,real_1(int),$f118(X_1)).
% 23.89/23.63 0 [] hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),X_1))=X_1|X_1!=hAPP(int,real,real_1(int),N).
% 23.89/23.63 0 [] hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N_1))=N_1.
% 23.89/23.63 0 [] hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V))=hAPP(int,real,number_number_of(real),V).
% 23.89/23.63 0 [] hAPP(int,real,real_1(int),X_1)!=hAPP(int,real,real_1(int),Y_1)|X_1=Y_1.
% 23.89/23.63 0 [] hAPP(int,real,real_1(int),X_1)=hAPP(int,real,real_1(int),Y_1)|X_1!=Y_1.
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),R),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R)))).
% 23.89/23.63 0 [] hAPP(int,real,real_1(int),one_one(int))=one_one(real).
% 23.89/23.63 0 [] hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y))=hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(real,int,archimedean_ceiling(real),X_1)),Aa))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),hAPP(int,real,real_1(int),Aa))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(real,int,archimedean_ceiling(real),X_1)),Aa))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),hAPP(int,real,real_1(int),Aa))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),hAPP(int,real,real_1(int),A_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),hAPP(int,real,real_1(int),A_1))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),X_1)),hAPP(int,real,real_1(int),Y_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_1),Y_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),X_1)),hAPP(int,real,real_1(int),Y_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_1),Y_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),X_1)),hAPP(int,real,real_1(int),Y_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),X_1)),hAPP(int,real,real_1(int),Y_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),hAPP(real,int,archimedean_ceiling(real),X_1)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),Aa)),X_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),hAPP(real,int,archimedean_ceiling(real),X_1)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),Aa)),X_1)).
% 23.89/23.63 0 [] hAPP(int,real,real_1(int),X_1)!=zero_zero(real)|X_1=zero_zero(int).
% 23.89/23.63 0 [] hAPP(int,real,real_1(int),X_1)=zero_zero(real)|X_1!=zero_zero(int).
% 23.89/23.63 0 [] hAPP(int,real,real_1(int),zero_zero(int))=zero_zero(real).
% 23.89/23.63 0 [] hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(int,real,real_1(int),A_1)))=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1).
% 23.89/23.63 0 [] hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y))=hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y)).
% 23.89/23.63 0 [] -archim1727834104eiling(X_a)|hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(X_a,int,archimedean_ceiling(X_a),R)))=hAPP(X_a,int,archimedean_ceiling(X_a),R).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R))),R)).
% 23.89/23.63 0 [] hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X))=hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)).
% 23.89/23.63 0 [] hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,real_1(int),X_1)),ring_1_Ints(real))).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R),one_one(real)))).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R))),one_one(real))),R)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),X_1)),Aa))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(int,real,real_1(int),Aa))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),X_1)),Aa))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(int,real,real_1(int),Aa))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),A_1)),X))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),hAPP(real,int,archim2085082626_floor(real),X))).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Aa),hAPP(real,int,archim2085082626_floor(real),X_1)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),Aa)),X_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Aa),hAPP(real,int,archim2085082626_floor(real),X_1)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),Aa)),X_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),hAPP(real,int,archim2085082626_floor(real),X)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),A_1)),X)).
% 23.89/23.63 0 [] hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,real_1(int),A_1)))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),X)),A_1).
% 23.89/23.63 0 [] hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(int,real,real_1(int),A_1)))=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),X)),A_1).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,real_1(int),N_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,real_1(int),N_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_2)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_2)),zero_zero(real)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N_2),zero_zero(int))).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_2)),zero_zero(real)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N_2),zero_zero(int))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),hAPP(int,real,real_1(int),N_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),hAPP(int,real,real_1(int),N_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),N_2)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),N_2)),zero_zero(real)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_2),zero_zero(int))).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),N_2)),zero_zero(real)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_2),zero_zero(int))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),N_2)),hAPP(int,real,real_1(int),M_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),N_2)),M_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),N_2)),hAPP(int,real,real_1(int),M_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),N_2)),M_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),M_1)),hAPP(int,real,number_number_of(real),N_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M_1),hAPP(int,int,number_number_of(int),N_2))).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),M_1)),hAPP(int,real,number_number_of(real),N_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M_1),hAPP(int,int,number_number_of(int),N_2))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,number_number_of(real),N_2)),hAPP(int,real,real_1(int),M_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),N_2)),M_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,number_number_of(real),N_2)),hAPP(int,real,real_1(int),M_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),N_2)),M_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),M_1)),hAPP(int,real,number_number_of(real),N_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),M_1),hAPP(int,int,number_number_of(int),N_2))).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),M_1)),hAPP(int,real,number_number_of(real),N_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),M_1),hAPP(int,int,number_number_of(int),N_2))).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N_2),M_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_2)),one_one(real))),hAPP(int,real,real_1(int),M_1))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N_2),M_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_2)),one_one(real))),hAPP(int,real,real_1(int),M_1))).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_2),M_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_2)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),M_1)),one_one(real)))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_2),M_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_2)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),M_1)),one_one(real)))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),X)),one_one(real))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N_1),X)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),N_1)),one_one(real))),X))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),hAPP(int,real,real_1(int),N_1)))|hAPP(real,int,archimedean_ceiling(real),X)=N_1.
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),X_1)),Aa))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),Aa)),one_one(real)))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),X_1)),Aa))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),Aa)),one_one(real)))).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Aa),hAPP(real,int,archimedean_ceiling(real),X_1)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),Aa)),one_one(real))),X_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Aa),hAPP(real,int,archimedean_ceiling(real),X_1)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),Aa)),one_one(real))),X_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),R),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R))),one_one(real)))).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R))),one_one(real)))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),X))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real))))|hAPP(real,int,archim2085082626_floor(real),X)=N_1.
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R),one_one(real))),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R)))).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R),one_one(real))),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R)))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),M)),R))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),M),N_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),X))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real))))|hAPP(real,int,archimedean_ceiling(real),X)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_1),one_one(int)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),N_1)),X))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real))))|hAPP(real,int,archim2085082626_floor(real),X)=N_1.
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),hAPP(real,int,archim2085082626_floor(real),X_1)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),Aa)),one_one(real))),X_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),hAPP(real,int,archim2085082626_floor(real),X_1)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),Aa)),one_one(real))),X_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(real,int,archim2085082626_floor(real),X_1)),Aa))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),Aa)),one_one(real)))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(real,int,archim2085082626_floor(real),X_1)),Aa))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),Aa)),one_one(real)))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),R))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),$f119(R))),R)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),R))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f119(R)),one_one(int))))).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),zero_zero(real)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),$f120(R))),R)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),zero_zero(real)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f120(R)),one_one(int))))).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(int,real,real_1(int),$f121(R))),R)).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f121(R)),one_one(int))))).
% 23.89/23.63 0 [] -number_ring(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V)))|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,X_a,number_number_of(X_a),V).
% 23.89/23.63 0 [] -number_ring(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V)))|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))=zero_zero(X_a).
% 23.89/23.63 0 [] hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,real_1(nat),N_1))=hAPP(nat,int,semiring_1_of_nat(int),N_1).
% 23.89/23.63 0 [] -number_semiring(X_a)|hAPP(int,X_a,number_number_of(X_a),hAPP(nat,int,semiring_1_of_nat(int),N_1))=hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K)),zero_zero(int))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N_1))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f122(P_1)))|hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_2))).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,P_1,$f122(P_1)))|hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_2))).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X2))|hBOOL(hAPP(int,bool,P_1,X2))| -hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),$f123(P_1)))).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_2))| -hBOOL(hAPP(int,bool,P_1,X_2))|hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),$f124(P_1)))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f125(P_1)))| -hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X3))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,P_1,$f125(P_1)))| -hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X3))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Z_1))).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.63 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))).
% 23.89/23.63 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M))).
% 23.89/23.63 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),zero_zero(X_a))).
% 23.89/23.63 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat))=zero_zero(X_a).
% 23.89/23.63 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)).
% 23.89/23.63 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))).
% 23.89/23.63 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.63 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.63 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.63 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.63 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)).
% 23.89/23.63 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)).
% 23.89/23.63 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),one_one(nat))=one_one(X_a).
% 23.89/23.63 0 [] -archim1727834104eiling(X_a)|hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))=hAPP(nat,int,semiring_1_of_nat(int),N_1).
% 23.89/23.63 0 [] -semiring_char_0(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)!=hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)|M_1=N_2.
% 23.89/23.63 0 [] -semiring_char_0(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)=hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)|M_1!=N_2.
% 23.89/23.63 0 [] hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),M))=hAPP(nat,int,semiring_1_of_nat(int),M).
% 23.89/23.63 0 [] -linordered_idom(X_a)|hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))=hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1).
% 23.89/23.63 0 [] hAPP(nat,int,semiring_1_of_nat(int),N_2)!=zero_zero(int)|N_2=zero_zero(nat).
% 23.89/23.63 0 [] hAPP(nat,int,semiring_1_of_nat(int),N_2)=zero_zero(int)|N_2!=zero_zero(nat).
% 23.89/23.63 0 [] hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat))=zero_zero(int).
% 23.89/23.63 0 [] zero_zero(int)=hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)).
% 23.89/23.63 0 [] one_one(int)=hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)).
% 23.89/23.63 0 [] hAPP(nat,int,semiring_1_of_nat(int),one_one(nat))=one_one(int).
% 23.89/23.63 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Y)).
% 23.89/23.63 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)).
% 23.89/23.63 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),Z_1))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))),Z_1).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z))|Z=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),hAPP(nat,int,semiring_1_of_nat(int),$f126(W,Z))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z))|Z!=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),hAPP(nat,int,semiring_1_of_nat(int),N)).
% 23.89/23.63 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)).
% 23.89/23.63 0 [] hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))=hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1)).
% 23.89/23.63 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_1),Y_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_1),Y_1)).
% 23.89/23.63 0 [] -ring_1(X_a)|hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)),ring_1_Ints(X_a))).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),N_1))).
% 23.89/23.63 0 [] -archim1727834104eiling(X_a)|hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))=hAPP(nat,int,semiring_1_of_nat(int),N_1).
% 23.89/23.63 0 [] real_1(nat)=semiring_1_of_nat(real).
% 23.89/23.63 0 [] hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N_1))=hAPP(nat,real,real_1(nat),N_1).
% 23.89/23.63 0 [] real_1(nat)=semiring_1_of_nat(real).
% 23.89/23.63 0 [] hAPP(real,int,archim2085082626_floor(real),hAPP(nat,real,real_1(nat),N_1))=hAPP(nat,int,semiring_1_of_nat(int),N_1).
% 23.89/23.63 0 [] hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X),Y)).
% 23.89/23.63 0 [] -ring_1(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),N_2)),zero_zero(int)))|N_2=zero_zero(nat).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),N_2)),zero_zero(int)))|N_2!=zero_zero(nat).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)).
% 23.89/23.63 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)).
% 23.89/23.63 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K)),I)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K)),J))).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V))=zero_zero(int).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,int,number_number_of(int),V).
% 23.89/23.63 0 [] -number_ring(X_a)| -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))=zero_zero(X_a).
% 23.89/23.63 0 [] -number_ring(X_a)|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,X_a,number_number_of(X_a),V).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_1))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Y_1),X_1))|hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1)))).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_1))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1))|hBOOL(hAPP(int,bool,P_1,zero_zero(int))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_1))))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Y_1),X_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_1))))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Y_1),X_1))| -hBOOL(hAPP(int,bool,P_1,zero_zero(int))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_1))))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_1))))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))))| -hBOOL(hAPP(int,bool,P_1,zero_zero(int))).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),$f127(K))).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|K=hAPP(nat,int,semiring_1_of_nat(int),$f127(K)).
% 23.89/23.63 0 [] -archim1804426504_field(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),$f128(X_a,Y,X))),X))).
% 23.89/23.63 0 [] hAPP(nat,int,semiring_1_of_nat(int),M_1)!=hAPP(nat,int,semiring_1_of_nat(int),N_2)|M_1=N_2.
% 23.89/23.63 0 [] hAPP(nat,int,semiring_1_of_nat(int),M_1)=hAPP(nat,int,semiring_1_of_nat(int),N_2)|M_1!=N_2.
% 23.89/23.63 0 [] -hBOOL(P_1)|hAPP(nat,int,semiring_1_of_nat(int),X_1)=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),P_1),X_1),Y_1)).
% 23.89/23.63 0 [] hBOOL(P_1)|hAPP(nat,int,semiring_1_of_nat(int),Y_1)=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),P_1),X_1),Y_1)).
% 23.89/23.63 0 [] hAPP(nat,int,semiring_1_of_nat(int),X_1)!=hAPP(nat,int,semiring_1_of_nat(int),Y_1)|X_1=Y_1.
% 23.89/23.63 0 [] hAPP(nat,int,semiring_1_of_nat(int),X_1)=hAPP(nat,int,semiring_1_of_nat(int),Y_1)|X_1!=Y_1.
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))|K=hAPP(nat,int,semiring_1_of_nat(int),$f129(K)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1))|Z_1=hAPP(nat,int,semiring_1_of_nat(int),$f130(Z_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))|K=hAPP(nat,int,semiring_1_of_nat(int),$f131(K)).
% 23.89/23.63 0 [] Z_1=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),$f133(Z_1))),hAPP(nat,int,semiring_1_of_nat(int),$f132(Z_1))).
% 23.89/23.63 0 [] -archim1804426504_field(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(nat,X_a,semiring_1_of_nat(X_a),$f134(X_a,X)))).
% 23.89/23.63 0 [] -archim1804426504_field(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),hAPP(nat,X_a,semiring_1_of_nat(X_a),$f135(X_a,X)))).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_2))=zero_zero(nat).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_2))=hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_2)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V_2)),K))=zero_zero(nat).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V_2)),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_2))),K).
% 23.89/23.63 0 [] -number_ring(X_a)|hAPP(int,X_a,number_number_of(X_a),pls)=zero_zero(X_a).
% 23.89/23.63 0 [] -number_semiring(X_a)|hAPP(int,X_a,number_number_of(X_a),pls)=zero_zero(X_a).
% 23.89/23.63 0 [] -number_ring(X_a)|zero_zero(X_a)=hAPP(int,X_a,number_number_of(X_a),pls).
% 23.89/23.63 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),pls)),A_1)=ti(X_a,A_1).
% 23.89/23.63 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),pls))=ti(X_a,A_1).
% 23.89/23.63 0 [] hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),pls)=K.
% 23.89/23.63 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),W_1)=pls.
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)).
% 23.89/23.63 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),K)=K.
% 23.89/23.63 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),pls)=K.
% 23.89/23.63 0 [] pls=zero_zero(int).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),pls)).
% 23.89/23.63 0 [] zero_zero(int)=hAPP(int,int,number_number_of(int),pls).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))).
% 23.89/23.63 0 [] hAPP(int,nat,number_number_of(nat),pls)=zero_zero(nat).
% 23.89/23.63 0 [] zero_zero(nat)=hAPP(int,nat,number_number_of(nat),pls).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),pls))).
% 23.89/23.63 0 [] zero_zero(nat)!=hAPP(int,nat,number_number_of(nat),V_1)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_1),pls)).
% 23.89/23.63 0 [] zero_zero(nat)=hAPP(int,nat,number_number_of(nat),V_1)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_1),pls)).
% 23.89/23.63 0 [] hAPP(int,nat,number_number_of(nat),V_1)!=zero_zero(nat)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_1),pls)).
% 23.89/23.63 0 [] hAPP(int,nat,number_number_of(nat),V_1)=zero_zero(nat)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_1),pls)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),V_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_3)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_3)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),V_3)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,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_1),V_3)).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,number_number_of(int),pls))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_3)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_1),V_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_1),pls)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_1),V_3)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V_1),pls)).
% 23.89/23.63 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)),hAPP(int,X_a,number_number_of(X_a),Y_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Y_1)).
% 23.89/23.63 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)),hAPP(int,X_a,number_number_of(X_a),Y_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Y_1)).
% 23.89/23.63 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),zero_zero(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),pls)).
% 23.89/23.63 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),zero_zero(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),pls)).
% 23.89/23.63 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)),hAPP(int,X_a,number_number_of(X_a),Y_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),Y_1)).
% 23.89/23.63 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)),hAPP(int,X_a,number_number_of(X_a),Y_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),Y_1)).
% 23.89/23.63 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),hAPP(int,X_a,number_number_of(X_a),X_1)),zero_zero(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_1),pls)).
% 23.89/23.63 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),hAPP(int,X_a,number_number_of(X_a),X_1)),zero_zero(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_1),pls)).
% 23.89/23.63 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_2))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),V_2))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_2)).
% 23.89/23.63 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_2))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),V_2))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_2)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_2))=hAPP(int,nat,number_number_of(nat),V_2).
% 23.89/23.63 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_2),pls))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_2))=hAPP(int,nat,number_number_of(nat),V).
% 23.89/23.63 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_2),pls))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_2))=hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_2)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V))=one_one(nat).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))=one_one(nat).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))=hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V)).
% 23.89/23.63 0 [] hAPP(int,int,succ,K)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),one_one(int)).
% 23.89/23.63 0 [] -number_ring(X_a)|hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,K))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),K)).
% 23.89/23.63 0 [] -number_semiring(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),V))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,V)).
% 23.89/23.63 0 [] -number_semiring(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,V)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V),pls))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))=zero_zero(nat).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),V),pls))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))=hAPP(int,nat,number_number_of(nat),hAPP(int,int,pred,V)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N_1).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))),N_1).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,N_1))).
% 23.89/23.63 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),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_1))).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1))).
% 23.89/23.63 0 [] hAPP(int,int,succ,hAPP(int,int,pred,X))=X.
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))|M_1=zero_zero(nat)|M_1=hAPP(nat,nat,suc,$f136(M_1,N_2)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))|M_1=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f136(M_1,N_2)),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))|M_1!=zero_zero(nat).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))|M_1!=hAPP(nat,nat,suc,J_1)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),N_2)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,zero_zero(nat))))|N_2=zero_zero(nat).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,zero_zero(nat))))|N_2!=zero_zero(nat).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2))|N_2=hAPP(nat,nat,suc,$f137(N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2))|N_2!=hAPP(nat,nat,suc,M_2).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)!=hAPP(nat,nat,suc,zero_zero(nat))|M_1=hAPP(nat,nat,suc,zero_zero(nat))|M_1=zero_zero(nat).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)!=hAPP(nat,nat,suc,zero_zero(nat))|M_1=hAPP(nat,nat,suc,zero_zero(nat))|N_2=hAPP(nat,nat,suc,zero_zero(nat)).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)!=hAPP(nat,nat,suc,zero_zero(nat))|N_2=zero_zero(nat)|M_1=zero_zero(nat).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)!=hAPP(nat,nat,suc,zero_zero(nat))|N_2=zero_zero(nat)|N_2=hAPP(nat,nat,suc,zero_zero(nat)).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)=hAPP(nat,nat,suc,zero_zero(nat))|M_1!=hAPP(nat,nat,suc,zero_zero(nat))|N_2!=zero_zero(nat).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)=hAPP(nat,nat,suc,zero_zero(nat))|M_1!=zero_zero(nat)|N_2!=hAPP(nat,nat,suc,zero_zero(nat)).
% 23.89/23.63 0 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)|M_1=hAPP(nat,nat,suc,zero_zero(nat))|M_1=zero_zero(nat).
% 23.89/23.63 0 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)|M_1=hAPP(nat,nat,suc,zero_zero(nat))|N_2=hAPP(nat,nat,suc,zero_zero(nat)).
% 23.89/23.63 0 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)|N_2=zero_zero(nat)|M_1=zero_zero(nat).
% 23.89/23.63 0 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)|N_2=zero_zero(nat)|N_2=hAPP(nat,nat,suc,zero_zero(nat)).
% 23.89/23.63 0 [] hAPP(nat,nat,suc,zero_zero(nat))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)|M_1!=hAPP(nat,nat,suc,zero_zero(nat))|N_2!=zero_zero(nat).
% 23.89/23.63 0 [] hAPP(nat,nat,suc,zero_zero(nat))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)|M_1!=zero_zero(nat)|N_2!=hAPP(nat,nat,suc,zero_zero(nat)).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)!=hAPP(nat,nat,suc,zero_zero(nat))|M_1=hAPP(nat,nat,suc,zero_zero(nat)).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)!=hAPP(nat,nat,suc,zero_zero(nat))|N_2=hAPP(nat,nat,suc,zero_zero(nat)).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)=hAPP(nat,nat,suc,zero_zero(nat))|M_1!=hAPP(nat,nat,suc,zero_zero(nat))|N_2!=hAPP(nat,nat,suc,zero_zero(nat)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|N_2=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),$f138(M_1,N_2))).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|N_2!=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),I)))).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),M)))).
% 23.89/23.63 0 [] one_one(nat)=hAPP(nat,nat,suc,zero_zero(nat)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_2)),M_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_2)),M_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M_1)),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M_1)),N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.63 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(nat),M),hAPP(nat,nat,suc,N_1))).
% 23.89/23.63 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),hAPP(nat,nat,suc,M)),N_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1)))|N_2=M_1.
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1)))|N_2!=M_1.
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),hAPP(nat,nat,suc,M))).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,M)),N_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,suc,N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.63 0 [] hAPP(nat,nat,suc,N_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N_1).
% 23.89/23.63 0 [] hAPP(nat,nat,suc,N_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N_1)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N_1)),one_one(nat))=N_1.
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_1).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,suc,N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_1))|M=hAPP(nat,nat,suc,N_1).
% 23.89/23.63 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),M),hAPP(nat,nat,suc,N_1))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_2)),hAPP(nat,nat,suc,M_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M_1)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_2)),hAPP(nat,nat,suc,M_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,suc,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))|M_1=hAPP(nat,nat,suc,N_2).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,suc,N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,suc,N_2)))|M_1!=hAPP(nat,nat,suc,N_2).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_2)),M_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_2)),M_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_1)),N_1)).
% 23.89/23.63 0 [] zero_zero(nat)!=hAPP(nat,nat,suc,M).
% 23.89/23.63 0 [] zero_zero(nat)!=hAPP(nat,nat,suc,Nat_3).
% 23.89/23.63 0 [] hAPP(nat,nat,suc,M)!=zero_zero(nat).
% 23.89/23.63 0 [] hAPP(nat,nat,suc,Nat_2)!=zero_zero(nat).
% 23.89/23.63 0 [] zero_zero(nat)!=hAPP(nat,nat,suc,M).
% 23.89/23.63 0 [] hAPP(nat,nat,suc,M)!=zero_zero(nat).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|M_1=N_2.
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))|M_1!=N_2.
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1)))|N_2=M_1.
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1)))|N_2!=M_1.
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M)))|M=N_1.
% 23.89/23.63 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),hAPP(nat,nat,suc,N_1))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|hAPP(nat,nat,suc,M)=N_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))|M=N_1.
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N_1))=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N_1)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N_1)).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N_1)),hAPP(nat,nat,suc,K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),K).
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1).
% 23.89/23.63 0 [] N_1!=hAPP(nat,nat,suc,N_1).
% 23.89/23.63 0 [] hAPP(nat,nat,suc,N_1)!=N_1.
% 23.89/23.63 0 [] hAPP(nat,nat,suc,Nat_1)!=hAPP(nat,nat,suc,Nat)|Nat_1=Nat.
% 23.89/23.63 0 [] hAPP(nat,nat,suc,Nat_1)=hAPP(nat,nat,suc,Nat)|Nat_1!=Nat.
% 23.89/23.63 0 [] hAPP(nat,nat,suc,X)!=hAPP(nat,nat,suc,Y)|X=Y.
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_2)|M_1=N_2.
% 23.89/23.63 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_2)|M_1!=N_2.
% 23.89/23.63 0 [] hAPP(int,int,pred,K)=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),one_one(int)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),L))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,pred,K_1)),L)).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),L))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,pred,K_1)),L)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(int,nat,number_number_of(nat),V))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,pred,V))).
% 23.89/23.63 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,M))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),M))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)!=M|N_1=hAPP(nat,nat,suc,zero_zero(nat)).
% 23.89/23.63 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)),K))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)!=K|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),K)).
% 23.89/23.63 0 [] M=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),K)).
% 23.89/23.63 0 [] M=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)|M=hAPP(nat,nat,suc,zero_zero(nat))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))=N_1.
% 23.89/23.63 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,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,I))),N_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_2)).
% 23.89/23.63 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_1)))).
% 23.89/23.63 0 [] hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,zero_zero(nat)))=one_one(int).
% 23.89/23.63 0 [] hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,zero_zero(nat)))=one_one(real).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,suc,J)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))),M)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z))|Z=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,$f139(W,Z)))).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z))|Z!=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N))).
% 23.89/23.63 0 [] hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M)).
% 23.89/23.63 0 [] hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_1))=hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_1)),one_one(real)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|N_1=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat)))=N_1.
% 23.89/23.63 0 [] M!=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)=N_1.
% 23.89/23.63 0 [] M=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_1)).
% 23.89/23.63 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V)))|hAPP(int,nat,number_number_of(nat),V)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))))|hAPP(int,nat,number_number_of(nat),V_1)=zero_zero(nat).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))))|hAPP(int,nat,number_number_of(nat),V_1)!=zero_zero(nat).
% 23.89/23.63 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V))=one_one(nat).
% 23.89/23.63 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V))=hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),R))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(nat,real,real_1(nat),$f140(R))),R)).
% 23.89/23.63 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),R))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,$f140(R))))).
% 23.89/23.63 0 [] -preorder(T_1)|preorder(fun(T_2,T_1)).
% 23.89/23.63 0 [] -order(T_1)|order(fun(T_2,T_1)).
% 23.89/23.63 0 [] -ord(T_1)|ord(fun(T_2,T_1)).
% 23.89/23.63 0 [] -minus(T_1)|minus(fun(T_2,T_1)).
% 23.89/23.63 0 [] semiri456707255roduct(int).
% 23.89/23.63 0 [] ordere223160158up_add(int).
% 23.89/23.63 0 [] ordere236663937imp_le(int).
% 23.89/23.63 0 [] linord893533164strict(int).
% 23.89/23.63 0 [] linord626643107strict(int).
% 23.89/23.63 0 [] linord20386208strict(int).
% 23.89/23.63 0 [] ordere779506340up_add(int).
% 23.89/23.63 0 [] ordere142940540dd_abs(int).
% 23.89/23.63 0 [] ordere216010020id_add(int).
% 23.89/23.63 0 [] linord219039673up_add(int).
% 23.89/23.63 0 [] cancel146912293up_add(int).
% 23.89/23.63 0 [] ordere453448008miring(int).
% 23.89/23.63 0 [] linord581940658strict(int).
% 23.89/23.63 0 [] ring_n68954251visors(int).
% 23.89/23.63 0 [] ordere1490568538miring(int).
% 23.89/23.63 0 [] linord1278240602ring_1(int).
% 23.89/23.63 0 [] ordered_ab_group_add(int).
% 23.89/23.63 0 [] cancel_semigroup_add(int).
% 23.89/23.63 0 [] linordered_semiring(int).
% 23.89/23.63 0 [] linordered_semidom(int).
% 23.89/23.63 0 [] ab_semigroup_mult(int).
% 23.89/23.63 0 [] comm_monoid_mult(int).
% 23.89/23.63 0 [] ab_semigroup_add(int).
% 23.89/23.63 0 [] ordered_semiring(int).
% 23.89/23.63 0 [] ordered_ring_abs(int).
% 23.89/23.63 0 [] no_zero_divisors(int).
% 23.89/23.63 0 [] comm_monoid_add(int).
% 23.89/23.63 0 [] linordered_ring(int).
% 23.89/23.63 0 [] linordered_idom(int).
% 23.89/23.63 0 [] comm_semiring_1(int).
% 23.89/23.63 0 [] comm_semiring(int).
% 23.89/23.63 0 [] semiring_char_0(int).
% 23.89/23.63 0 [] number_semiring(int).
% 23.89/23.63 0 [] ab_group_add(int).
% 23.89/23.63 0 [] zero_ne_q_one(int).
% 23.89/23.63 0 [] ordered_ring(int).
% 23.89/23.63 0 [] preorder(int).
% 23.89/23.63 0 [] linorder(int).
% 23.89/23.63 0 [] monoid_mult(int).
% 23.89/23.63 0 [] monoid_add(int).
% 23.89/23.63 0 [] semiring_1(int).
% 23.89/23.63 0 [] group_add(int).
% 23.89/23.63 0 [] mult_zero(int).
% 23.89/23.63 0 [] order(int).
% 23.89/23.63 0 [] ring_char_0(int).
% 23.89/23.63 0 [] number_ring(int).
% 23.89/23.63 0 [] semiring(int).
% 23.89/23.63 0 [] ord(int).
% 23.89/23.63 0 [] ring_1(int).
% 23.89/23.63 0 [] minus(int).
% 23.89/23.63 0 [] zero(int).
% 23.89/23.63 0 [] ring(int).
% 23.89/23.63 0 [] number(int).
% 23.89/23.63 0 [] one(int).
% 23.89/23.63 0 [] semiri456707255roduct(nat).
% 23.89/23.63 0 [] ordere223160158up_add(nat).
% 23.89/23.63 0 [] ordere236663937imp_le(nat).
% 23.89/23.63 0 [] linord893533164strict(nat).
% 23.89/23.63 0 [] linord20386208strict(nat).
% 23.89/23.63 0 [] ordere779506340up_add(nat).
% 23.89/23.63 0 [] ordere216010020id_add(nat).
% 23.89/23.63 0 [] cancel146912293up_add(nat).
% 23.89/23.63 0 [] ordere453448008miring(nat).
% 23.89/23.63 0 [] ordere1490568538miring(nat).
% 23.89/23.63 0 [] cancel_semigroup_add(nat).
% 23.89/23.63 0 [] linordered_semiring(nat).
% 23.89/23.63 0 [] linordered_semidom(nat).
% 23.89/23.63 0 [] ab_semigroup_mult(nat).
% 23.89/23.63 0 [] comm_monoid_mult(nat).
% 23.89/23.63 0 [] ab_semigroup_add(nat).
% 23.89/23.63 0 [] ordered_semiring(nat).
% 23.89/23.63 0 [] no_zero_divisors(nat).
% 23.89/23.63 0 [] comm_monoid_add(nat).
% 23.89/23.63 0 [] comm_semiring_1(nat).
% 23.89/23.63 0 [] comm_semiring(nat).
% 23.89/23.63 0 [] semiring_char_0(nat).
% 23.89/23.63 0 [] number_semiring(nat).
% 23.89/23.63 0 [] zero_ne_q_one(nat).
% 23.89/23.63 0 [] preorder(nat).
% 23.89/23.63 0 [] linorder(nat).
% 23.89/23.63 0 [] monoid_mult(nat).
% 23.89/23.63 0 [] monoid_add(nat).
% 23.89/23.63 0 [] semiring_1(nat).
% 23.89/23.63 0 [] mult_zero(nat).
% 23.89/23.63 0 [] order(nat).
% 23.89/23.63 0 [] semiring(nat).
% 23.89/23.63 0 [] ord(nat).
% 23.89/23.63 0 [] minus(nat).
% 23.89/23.63 0 [] zero(nat).
% 23.89/23.63 0 [] number(nat).
% 23.89/23.63 0 [] one(nat).
% 23.89/23.63 0 [] preorder(bool).
% 23.89/23.63 0 [] order(bool).
% 23.89/23.63 0 [] ord(bool).
% 23.89/23.63 0 [] minus(bool).
% 23.89/23.63 0 [] semiri456707255roduct(real).
% 23.89/23.63 0 [] ordere223160158up_add(real).
% 23.89/23.63 0 [] ordere236663937imp_le(real).
% 23.89/23.63 0 [] linord893533164strict(real).
% 23.89/23.63 0 [] linord1117847801e_zero(real).
% 23.89/23.63 0 [] archim1804426504_field(real).
% 23.89/23.63 0 [] linord626643107strict(real).
% 23.89/23.63 0 [] linord20386208strict(real).
% 23.89/23.63 0 [] ordere779506340up_add(real).
% 23.89/23.63 0 [] ordere142940540dd_abs(real).
% 23.89/23.63 0 [] archim1727834104eiling(real).
% 23.89/23.63 0 [] real_normed_algebra(real).
% 23.89/23.63 0 [] ordere216010020id_add(real).
% 23.89/23.63 0 [] linord219039673up_add(real).
% 23.89/23.63 0 [] cancel146912293up_add(real).
% 23.89/23.63 0 [] ordere453448008miring(real).
% 23.89/23.63 0 [] linord581940658strict(real).
% 23.89/23.63 0 [] ring_n68954251visors(real).
% 23.89/23.63 0 [] ordere1490568538miring(real).
% 23.89/23.63 0 [] linord1278240602ring_1(real).
% 23.89/23.63 0 [] ordered_ab_group_add(real).
% 23.89/23.63 0 [] cancel_semigroup_add(real).
% 23.89/23.63 0 [] linordered_semiring(real).
% 23.89/23.63 0 [] linordered_semidom(real).
% 23.89/23.63 0 [] dense_linorder(real).
% 23.89/23.63 0 [] ab_semigroup_mult(real).
% 23.89/23.63 0 [] comm_monoid_mult(real).
% 23.89/23.63 0 [] ab_semigroup_add(real).
% 23.89/23.63 0 [] linordered_field(real).
% 23.89/23.63 0 [] ordered_semiring(real).
% 23.89/23.63 0 [] ordered_ring_abs(real).
% 23.89/23.63 0 [] no_zero_divisors(real).
% 23.89/23.63 0 [] comm_monoid_add(real).
% 23.89/23.63 0 [] linordered_ring(real).
% 23.89/23.63 0 [] linordered_idom(real).
% 23.89/23.63 0 [] comm_semiring_1(real).
% 23.89/23.63 0 [] comm_semiring(real).
% 23.89/23.63 0 [] semiring_char_0(real).
% 23.89/23.63 0 [] number_semiring(real).
% 23.89/23.63 0 [] ab_group_add(real).
% 23.89/23.63 0 [] zero_ne_q_one(real).
% 23.89/23.63 0 [] ordered_ring(real).
% 23.89/23.63 0 [] preorder(real).
% 23.89/23.63 0 [] linorder(real).
% 23.89/23.63 0 [] monoid_mult(real).
% 23.89/23.63 0 [] monoid_add(real).
% 23.89/23.63 0 [] semiring_1(real).
% 23.89/23.63 0 [] group_add(real).
% 23.89/23.63 0 [] mult_zero(real).
% 23.89/23.63 0 [] order(real).
% 23.89/23.63 0 [] ring_char_0(real).
% 23.89/23.63 0 [] number_ring(real).
% 23.89/23.63 0 [] semiring(real).
% 23.89/23.63 0 [] ord(real).
% 23.89/23.63 0 [] ring_1(real).
% 23.89/23.63 0 [] minus(real).
% 23.89/23.63 0 [] zero(real).
% 23.89/23.63 0 [] ring(real).
% 23.89/23.63 0 [] number(real).
% 23.89/23.63 0 [] one(real).
% 23.89/23.63 0 [] ti(T,ti(T,A))=ti(T,A).
% 23.89/23.63 0 [] hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y)=ti(X_a,X).
% 23.89/23.63 0 [] hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y)=ti(X_a,Y).
% 23.89/23.63 0 [] ti(bool,P)=fTrue|ti(bool,P)=fFalse.
% 23.89/23.63 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,twoSqu1929807760sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),a),b))),hAPP(product_prod(int,int),int,twoSqu1929807760sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),p),q)))!=hAPP(product_prod(int,int),int,twoSqu1929807760sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),a),p)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),b),q))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),a),q)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),b),p)))).
% 23.89/23.64 end_of_list.
% 23.89/23.64
% 23.89/23.64 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 23.89/23.64
% 23.89/23.64 This ia a non-Horn set with equality. The strategy will be
% 23.89/23.64 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 23.89/23.64 deletion, with positive clauses in sos and nonpositive
% 23.89/23.64 clauses in usable.
% 23.89/23.64
% 23.89/23.64 dependent: set(knuth_bendix).
% 23.89/23.64 dependent: set(anl_eq).
% 23.89/23.64 dependent: set(para_from).
% 23.89/23.64 dependent: set(para_into).
% 23.89/23.64 dependent: clear(para_from_right).
% 23.89/23.64 dependent: clear(para_into_right).
% 23.89/23.64 dependent: set(para_from_vars).
% 23.89/23.64 dependent: set(eq_units_both_ways).
% 23.89/23.64 dependent: set(dynamic_demod_all).
% 23.89/23.64 dependent: set(dynamic_demod).
% 23.89/23.64 dependent: set(order_eq).
% 23.89/23.64 dependent: set(back_demod).
% 23.89/23.64 dependent: set(lrpo).
% 23.89/23.64 dependent: set(hyper_res).
% 23.89/23.64 dependent: set(unit_deletion).
% 23.89/23.64 dependent: set(factor).
% 23.89/23.64
% 23.89/23.64 ------------> process usable:
% 23.89/23.64 ** KEPT (pick-wt=11): 1 [] -archim1727834104eiling(A)|ti(fun(A,int),archimedean_ceiling(A))=archimedean_ceiling(A).
% 23.89/23.64 ** KEPT (pick-wt=11): 2 [] -archim1727834104eiling(A)|ti(fun(A,int),archim2085082626_floor(A))=archim2085082626_floor(A).
% 23.89/23.64 ** KEPT (pick-wt=11): 3 [] -ordere142940540dd_abs(A)|ti(fun(A,A),abs_abs(A))=abs_abs(A).
% 23.89/23.64 ** KEPT (pick-wt=13): 4 [] -minus(A)|ti(fun(A,fun(A,A)),minus_minus(A))=minus_minus(A).
% 23.89/23.64 ** KEPT (pick-wt=9): 5 [] -one(A)|ti(A,one_one(A))=one_one(A).
% 23.89/23.64 ** KEPT (pick-wt=13): 6 [] -monoid_add(A)|ti(fun(A,fun(A,A)),plus_plus(A))=plus_plus(A).
% 23.89/23.64 ** KEPT (pick-wt=13): 7 [] -ab_semigroup_add(A)|ti(fun(A,fun(A,A)),plus_plus(A))=plus_plus(A).
% 23.89/23.64 ** KEPT (pick-wt=13): 8 [] -cancel_semigroup_add(A)|ti(fun(A,fun(A,A)),plus_plus(A))=plus_plus(A).
% 23.89/23.64 ** KEPT (pick-wt=13): 9 [] -no_zero_divisors(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 23.89/23.64 ** KEPT (pick-wt=13): 10 [] -mult_zero(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 23.89/23.64 ** KEPT (pick-wt=13): 11 [] -monoid_mult(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 23.89/23.64 ** KEPT (pick-wt=13): 12 [] -semiring(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 23.89/23.64 ** KEPT (pick-wt=13): 13 [] -ab_semigroup_mult(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 23.89/23.64 ** KEPT (pick-wt=9): 14 [] -zero(A)|ti(A,zero_zero(A))=zero_zero(A).
% 23.89/23.64 ** KEPT (pick-wt=11): 15 [] -number(A)|ti(fun(int,A),number_number_of(A))=number_number_of(A).
% 23.89/23.64 ** KEPT (pick-wt=11): 16 [] -ring_1(A)|ti(fun(A,bool),ring_1_Ints(A))=ring_1_Ints(A).
% 23.89/23.64 ** KEPT (pick-wt=11): 17 [] -semiring_1(A)|ti(fun(nat,A),semiring_1_of_nat(A))=semiring_1_of_nat(A).
% 23.89/23.64 ** KEPT (pick-wt=13): 18 [] -ord(A)|ti(fun(A,fun(A,bool)),ord_less(A))=ord_less(A).
% 23.89/23.64 ** KEPT (pick-wt=13): 19 [] -ord(A)|ti(fun(A,fun(A,bool)),ord_less_e_q(A))=ord_less_e_q(A).
% 23.89/23.64 ** KEPT (pick-wt=6): 20 [] -hBOOL(ti(bool,A))|hBOOL(A).
% 23.89/23.64 ** KEPT (pick-wt=6): 21 [] hBOOL(ti(bool,A))| -hBOOL(A).
% 23.89/23.64 ** KEPT (pick-wt=93): 23 [copy,22,flip.2] -ring(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),D))=hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),D)).
% 23.89/23.64 ** KEPT (pick-wt=137): 25 [copy,24,flip.2] -real_normed_algebra(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E)))=hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)).
% 23.89/23.64 ** KEPT (pick-wt=87): 26 [] -ring(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)!=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F)|ti(A,D)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F).
% 23.89/23.64 ** KEPT (pick-wt=87): 27 [] -ring(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F)|ti(A,D)!=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F).
% 23.89/23.64 ** KEPT (pick-wt=87): 28 [] -ring(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)!=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D)=ti(A,F).
% 23.89/23.64 ** KEPT (pick-wt=87): 29 [] -ring(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D)!=ti(A,F).
% 23.89/23.64 ** KEPT (pick-wt=33): 30 [] -hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,A))|hAPP(product_prod(int,int),int,twoSqu1929807760sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),$f2(A)),$f1(A)))=A.
% 23.89/23.64 ** KEPT (pick-wt=31): 31 [] hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,A))|hAPP(product_prod(int,int),int,twoSqu1929807760sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),B),C))!=A.
% 23.89/23.64 ** KEPT (pick-wt=28): 32 [] hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)!=C|A=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B).
% 23.89/23.64 ** KEPT (pick-wt=29): 33 [] -group_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),C)=ti(A,B).
% 23.89/23.64 ** KEPT (pick-wt=49): 34 [] -ab_semigroup_mult(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)).
% 23.89/23.64 ** KEPT (pick-wt=34): 35 [] -cancel_semigroup_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)!=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C)|ti(A,B)=ti(A,D).
% 23.89/23.64 ** KEPT (pick-wt=34): 36 [] -cancel146912293up_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)!=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)|ti(A,C)=ti(A,D).
% 23.89/23.64 ** KEPT (pick-wt=34): 37 [] -cancel_semigroup_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)!=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)|ti(A,C)=ti(A,D).
% 23.89/23.64 Following clause subsumed by 35 during input processing: 0 [] -cancel_semigroup_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)!=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C)|ti(A,B)=ti(A,D).
% 23.89/23.64 ** KEPT (pick-wt=34): 38 [] -cancel_semigroup_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C)|ti(A,B)!=ti(A,D).
% 23.89/23.64 Following clause subsumed by 37 during input processing: 0 [] -cancel_semigroup_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)!=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)|ti(A,C)=ti(A,D).
% 23.89/23.64 ** KEPT (pick-wt=34): 39 [] -cancel_semigroup_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)|ti(A,C)!=ti(A,D).
% 23.89/23.64 ** KEPT (pick-wt=49): 40 [] -ab_semigroup_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)).
% 23.89/23.64 ** KEPT (pick-wt=41): 41 [] -ab_group_add(A)|hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)!=hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E)|ti(A,B)!=ti(A,C)|ti(A,D)=ti(A,E).
% 23.89/23.64 ** KEPT (pick-wt=41): 42 [] -ab_group_add(A)|hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)!=hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E)|ti(A,B)=ti(A,C)|ti(A,D)!=ti(A,E).
% 23.89/23.64 ** KEPT (pick-wt=82): 44 [copy,43,flip.2] -semiring(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D)),E)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),E)).
% 23.89/23.64 ** KEPT (pick-wt=60): 45 [] -real_normed_algebra(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)).
% 23.89/23.64 Following clause subsumed by 45 during input processing: 0 [] -real_normed_algebra(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)).
% 23.89/23.64 ** KEPT (pick-wt=60): 46 [] -comm_semiring(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)).
% 23.89/23.64 ** KEPT (pick-wt=60): 48 [copy,47,flip.2] -real_normed_algebra(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)).
% 23.89/23.64 Following clause subsumed by 48 during input processing: 0 [flip.2] -real_normed_algebra(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)).
% 23.89/23.64 ** KEPT (pick-wt=60): 49 [] -real_normed_algebra(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)).
% 23.89/23.64 Following clause subsumed by 49 during input processing: 0 [] -real_normed_algebra(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)).
% 23.89/23.64 ** KEPT (pick-wt=60): 51 [copy,50,flip.2] -real_normed_algebra(A)|hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)).
% 23.89/23.64 Following clause subsumed by 51 during input processing: 0 [flip.2] -real_normed_algebra(A)|hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)).
% 23.89/23.64 ** KEPT (pick-wt=71): 52 [] -ab_group_add(A)|hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E))=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E)).
% 23.89/23.64 ** KEPT (pick-wt=29): 53 [] -group_add(A)|hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),C)=ti(A,B).
% 23.89/23.64 ** KEPT (pick-wt=85): 54 [] -semiri456707255roduct(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E))!=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))|ti(A,B)=ti(A,D)|ti(A,C)=ti(A,E).
% 23.89/23.64 ** KEPT (pick-wt=78): 55 [] -semiri456707255roduct(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E))=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))|ti(A,B)!=ti(A,D).
% 23.89/23.64 ** KEPT (pick-wt=78): 56 [] -semiri456707255roduct(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E))=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))|ti(A,C)!=ti(A,E).
% 23.89/23.64 ** KEPT (pick-wt=60): 57 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C).
% 23.89/23.64 ** KEPT (pick-wt=60): 58 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)).
% 23.89/23.64 Following clause subsumed by 54 during input processing: 0 [] -semiri456707255roduct(A)|ti(A,B)=ti(A,C)|ti(A,D)=ti(A,E)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))!=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)).
% 23.89/23.64 Following clause subsumed by 55 during input processing: 0 [] -semiri456707255roduct(A)|ti(A,B)!=ti(A,C)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)).
% 23.89/23.64 Following clause subsumed by 56 during input processing: 0 [] -semiri456707255roduct(A)|ti(A,B)!=ti(A,C)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C))=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),B)).
% 23.89/23.64 ** KEPT (pick-wt=60): 60 [copy,59,flip.2] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)).
% 23.89/23.64 ** KEPT (pick-wt=51): 61 [] -minus(A)|hAPP(B,A,hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),minus_minus(fun(B,A)),C),D),E)=hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(B,A,C,E)),hAPP(B,A,D,E)).
% 23.89/23.64 Following clause subsumed by 61 during input processing: 0 [] -minus(A)|hAPP(B,A,hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),minus_minus(fun(B,A)),C),D),E)=hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(B,A,C,E)),hAPP(B,A,D,E)).
% 23.89/23.64 ** KEPT (pick-wt=42): 62 [] hAPP(A,product_prod(B,A),hAPP(B,fun(A,product_prod(B,A)),product_Pair(B,A),C),D)!=hAPP(A,product_prod(B,A),hAPP(B,fun(A,product_prod(B,A)),product_Pair(B,A),E),F)|ti(B,C)=ti(B,E).
% 23.89/23.64 ** KEPT (pick-wt=42): 63 [] hAPP(A,product_prod(B,A),hAPP(B,fun(A,product_prod(B,A)),product_Pair(B,A),C),D)!=hAPP(A,product_prod(B,A),hAPP(B,fun(A,product_prod(B,A)),product_Pair(B,A),E),F)|ti(A,D)=ti(A,F).
% 23.89/23.64 Following clause subsumed by 62 during input processing: 0 [] hAPP(A,product_prod(B,A),hAPP(B,fun(A,product_prod(B,A)),product_Pair(B,A),C),D)!=hAPP(A,product_prod(B,A),hAPP(B,fun(A,product_prod(B,A)),product_Pair(B,A),E),F)|ti(B,C)=ti(B,E).
% 23.89/23.64 Following clause subsumed by 63 during input processing: 0 [] hAPP(A,product_prod(B,A),hAPP(B,fun(A,product_prod(B,A)),product_Pair(B,A),C),D)!=hAPP(A,product_prod(B,A),hAPP(B,fun(A,product_prod(B,A)),product_Pair(B,A),E),F)|ti(A,D)=ti(A,F).
% 23.89/23.64 ** KEPT (pick-wt=49): 64 [] hAPP(A,product_prod(B,A),hAPP(B,fun(A,product_prod(B,A)),product_Pair(B,A),C),D)=hAPP(A,product_prod(B,A),hAPP(B,fun(A,product_prod(B,A)),product_Pair(B,A),E),F)|ti(B,C)!=ti(B,E)|ti(A,D)!=ti(A,F).
% 23.89/23.64 ** KEPT (pick-wt=35): 65 [] -hBOOL(hAPP(product_prod(A,B),bool,C,$f3(A,B,C)))|hBOOL(hAPP(product_prod(A,B),bool,C,hAPP(B,product_prod(A,B),hAPP(A,fun(B,product_prod(A,B)),product_Pair(A,B),D),E))).
% 23.89/23.64 ** KEPT (pick-wt=38): 66 [] hBOOL(hAPP(product_prod(A,B),bool,C,D))| -hBOOL(hAPP(product_prod(A,B),bool,C,hAPP(B,product_prod(A,B),hAPP(A,fun(B,product_prod(A,B)),product_Pair(A,B),$f5(A,B,C)),$f4(A,B,C)))).
% 23.89/23.64 ** KEPT (pick-wt=71): 67 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E))=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E)).
% 23.89/23.64 ** KEPT (pick-wt=49): 68 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C).
% 23.89/23.64 ** KEPT (pick-wt=18): 69 [] -ab_sem1668676832m_mult(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)=ti(A,B).
% 23.89/23.64 Following clause subsumed by 69 during input processing: 0 [] -ab_sem1668676832m_mult(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)=ti(A,B).
% 23.89/23.64 ** KEPT (pick-wt=27): 70 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B).
% 23.89/23.64 ** KEPT (pick-wt=38): 71 [] -ab_sem1668676832m_mult(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C).
% 23.89/23.64 ** KEPT (pick-wt=49): 72 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)).
% 23.89/23.64 ** KEPT (pick-wt=49): 74 [copy,73,flip.2] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)).
% 23.89/23.64 Following clause subsumed by 74 during input processing: 0 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)).
% 23.89/23.64 ** KEPT (pick-wt=49): 75 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C).
% 23.89/23.64 Following clause subsumed by 74 during input processing: 0 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E))=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E))).
% 23.89/23.64 Following clause subsumed by 72 during input processing: 0 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E))=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),E)).
% 23.89/23.64 ** KEPT (pick-wt=71): 76 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E))=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)).
% 23.89/23.64 ** KEPT (pick-wt=27): 77 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B).
% 23.89/23.64 ** KEPT (pick-wt=49): 78 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)).
% 23.89/23.64 ** KEPT (pick-wt=49): 80 [copy,79,flip.2] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)).
% 23.89/23.64 Following clause subsumed by 80 during input processing: 0 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)).
% 23.89/23.64 ** KEPT (pick-wt=38): 81 [] -hBOOL(hAPP(product_prod(A,B),bool,C,D))|hBOOL(hAPP(product_prod(A,B),bool,C,hAPP(B,product_prod(A,B),hAPP(A,fun(B,product_prod(A,B)),product_Pair(A,B),$f7(A,B,C)),$f6(A,B,C)))).
% 23.89/23.64 ** KEPT (pick-wt=35): 82 [] hBOOL(hAPP(product_prod(A,B),bool,C,$f8(A,B,C)))| -hBOOL(hAPP(product_prod(A,B),bool,C,hAPP(B,product_prod(A,B),hAPP(A,fun(B,product_prod(A,B)),product_Pair(A,B),D),E))).
% 23.89/23.64 ** KEPT (pick-wt=260): 83 [] -hBOOL(hAPP(product_prod(A,product_prod(B,product_prod(C,product_prod(D,product_prod(E,F))))),bool,G,hAPP(product_prod(B,product_prod(C,product_prod(D,product_prod(E,F)))),product_prod(A,product_prod(B,product_prod(C,product_prod(D,product_prod(E,F))))),hAPP(A,fun(product_prod(B,product_prod(C,product_prod(D,product_prod(E,F)))),product_prod(A,product_prod(B,product_prod(C,product_prod(D,product_prod(E,F)))))),product_Pair(A,product_prod(B,product_prod(C,product_prod(D,product_prod(E,F))))),$f14(A,B,C,D,E,F,H,G)),hAPP(product_prod(C,product_prod(D,product_prod(E,F))),product_prod(B,product_prod(C,product_prod(D,product_prod(E,F)))),hAPP(B,fun(product_prod(C,product_prod(D,product_prod(E,F))),product_prod(B,product_prod(C,product_prod(D,product_prod(E,F))))),product_Pair(B,product_prod(C,product_prod(D,product_prod(E,F)))),$f13(A,B,C,D,E,F,H,G)),hAPP(product_prod(D,product_prod(E,F)),product_prod(C,product_prod(D,product_prod(E,F))),hAPP(C,fun(product_prod(D,product_prod(E,F)),product_prod(C,product_prod(D,product_prod(E,F)))),product_Pair(C,product_prod(D,product_prod(E,F))),$f12(A,B,C,D,E,F,H,G)),hAPP(product_prod(E,F),product_prod(D,product_prod(E,F)),hAPP(D,fun(product_prod(E,F),product_prod(D,product_prod(E,F))),product_Pair(D,product_prod(E,F)),$f11(A,B,C,D,E,F,H,G)),hAPP(F,product_prod(E,F),hAPP(E,fun(F,product_prod(E,F)),product_Pair(E,F),$f10(A,B,C,D,E,F,H,G)),$f9(A,B,C,D,E,F,H,G))))))))|hBOOL(hAPP(product_prod(A,product_prod(B,product_prod(C,product_prod(D,product_prod(E,F))))),bool,G,H)).
% 23.89/23.64 ** KEPT (pick-wt=187): 84 [] -hBOOL(hAPP(product_prod(A,product_prod(B,product_prod(C,product_prod(D,E)))),bool,F,hAPP(product_prod(B,product_prod(C,product_prod(D,E))),product_prod(A,product_prod(B,product_prod(C,product_prod(D,E)))),hAPP(A,fun(product_prod(B,product_prod(C,product_prod(D,E))),product_prod(A,product_prod(B,product_prod(C,product_prod(D,E))))),product_Pair(A,product_prod(B,product_prod(C,product_prod(D,E)))),$f25(A,B,C,D,E,G,F)),hAPP(product_prod(C,product_prod(D,E)),product_prod(B,product_prod(C,product_prod(D,E))),hAPP(B,fun(product_prod(C,product_prod(D,E)),product_prod(B,product_prod(C,product_prod(D,E)))),product_Pair(B,product_prod(C,product_prod(D,E))),$f24(A,B,C,D,E,G,F)),hAPP(product_prod(D,E),product_prod(C,product_prod(D,E)),hAPP(C,fun(product_prod(D,E),product_prod(C,product_prod(D,E))),product_Pair(C,product_prod(D,E)),$f23(A,B,C,D,E,G,F)),hAPP(E,product_prod(D,E),hAPP(D,fun(E,product_prod(D,E)),product_Pair(D,E),$f22(A,B,C,D,E,G,F)),$f21(A,B,C,D,E,G,F)))))))|hBOOL(hAPP(product_prod(A,product_prod(B,product_prod(C,product_prod(D,E)))),bool,F,G)).
% 23.89/23.64 ** KEPT (pick-wt=126): 85 [] -hBOOL(hAPP(product_prod(A,product_prod(B,product_prod(C,D))),bool,E,hAPP(product_prod(B,product_prod(C,D)),product_prod(A,product_prod(B,product_prod(C,D))),hAPP(A,fun(product_prod(B,product_prod(C,D)),product_prod(A,product_prod(B,product_prod(C,D)))),product_Pair(A,product_prod(B,product_prod(C,D))),$f34(A,B,C,D,F,E)),hAPP(product_prod(C,D),product_prod(B,product_prod(C,D)),hAPP(B,fun(product_prod(C,D),product_prod(B,product_prod(C,D))),product_Pair(B,product_prod(C,D)),$f33(A,B,C,D,F,E)),hAPP(D,product_prod(C,D),hAPP(C,fun(D,product_prod(C,D)),product_Pair(C,D),$f32(A,B,C,D,F,E)),$f31(A,B,C,D,F,E))))))|hBOOL(hAPP(product_prod(A,product_prod(B,product_prod(C,D))),bool,E,F)).
% 23.89/23.64 ** KEPT (pick-wt=77): 86 [] -hBOOL(hAPP(product_prod(A,product_prod(B,C)),bool,D,hAPP(product_prod(B,C),product_prod(A,product_prod(B,C)),hAPP(A,fun(product_prod(B,C),product_prod(A,product_prod(B,C))),product_Pair(A,product_prod(B,C)),$f41(A,B,C,E,D)),hAPP(C,product_prod(B,C),hAPP(B,fun(C,product_prod(B,C)),product_Pair(B,C),$f40(A,B,C,E,D)),$f39(A,B,C,E,D)))))|hBOOL(hAPP(product_prod(A,product_prod(B,C)),bool,D,E)).
% 23.89/23.64 ** KEPT (pick-wt=30): 87 [] hAPP(A,B,C,$f47(A,B,C,D))!=hAPP(A,B,D,$f47(A,B,C,D))|ti(fun(A,B),C)=ti(fun(A,B),D).
% 23.89/23.64 ** KEPT
% 23.89/23.64 Search stopped in tp_alloc by max_mem option.
% 23.89/23.64 (pick-wt=23): 88 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|hBOOL(hAPP(A,bool,C,B)).
% 23.89/23.64 ** KEPT (pick-wt=23): 89 [] hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))| -hBOOL(hAPP(A,bool,C,B)).
% 23.89/23.64
% 23.89/23.64 Search stopped in tp_alloc by max_mem option.
% 23.89/23.64
% 23.89/23.64 ============ end of search ============
% 23.89/23.64
% 23.89/23.64 -------------- statistics -------------
% 23.89/23.64 clauses given 0
% 23.89/23.64 clauses generated 0
% 23.89/23.64 clauses kept 81
% 23.89/23.64 clauses forward subsumed 17
% 23.89/23.64 clauses back subsumed 0
% 23.89/23.64 Kbytes malloced 11718
% 23.89/23.64
% 23.89/23.64 ----------- times (seconds) -----------
% 23.89/23.64 user CPU time 0.25 (0 hr, 0 min, 0 sec)
% 23.89/23.64 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 23.89/23.64 wall-clock time 23 (0 hr, 0 min, 23 sec)
% 23.89/23.64
% 23.89/23.64 Process 9347 finished Wed Jul 27 09:41:02 2022
% 23.89/23.64 Otter interrupted
% 23.89/23.64 PROOF NOT FOUND
%------------------------------------------------------------------------------