TSTP Solution File: NUM923+6 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM923+6 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 13:10:12 EDT 2022
% Result : Unknown 13.34s 13.23s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM923+6 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 09:55:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 13.27/13.17 ----- Otter 3.3f, August 2004 -----
% 13.27/13.17 The process was started by sandbox2 on n020.cluster.edu,
% 13.27/13.17 Wed Jul 27 09:55:38 2022
% 13.27/13.17 The command was "./otter". The process ID is 20609.
% 13.27/13.17
% 13.27/13.17 set(prolog_style_variables).
% 13.27/13.17 set(auto).
% 13.27/13.17 dependent: set(auto1).
% 13.27/13.17 dependent: set(process_input).
% 13.27/13.17 dependent: clear(print_kept).
% 13.27/13.17 dependent: clear(print_new_demod).
% 13.27/13.17 dependent: clear(print_back_demod).
% 13.27/13.17 dependent: clear(print_back_sub).
% 13.27/13.17 dependent: set(control_memory).
% 13.27/13.17 dependent: assign(max_mem, 12000).
% 13.27/13.17 dependent: assign(pick_given_ratio, 4).
% 13.27/13.17 dependent: assign(stats_level, 1).
% 13.27/13.17 dependent: assign(max_seconds, 10800).
% 13.27/13.17 clear(print_given).
% 13.27/13.17
% 13.27/13.17 formula_list(usable).
% 13.27/13.17 all A (A=A).
% 13.27/13.17 ti(fun(int,fun(int,fun(product_prod(int,int),bool))),divmod_int_rel)=divmod_int_rel.
% 13.27/13.17 ti(fun(int,fun(int,product_prod(int,int))),pdivmod)=pdivmod.
% 13.27/13.17 ti(fun(int,fun(int,product_prod(int,int))),posDivAlg)=posDivAlg.
% 13.27/13.17 all X_a (ordere142940540dd_abs(X_a)->ti(fun(X_a,X_a),abs_abs(X_a))=abs_abs(X_a)).
% 13.27/13.17 all X_a (minus(X_a)->ti(fun(X_a,fun(X_a,X_a)),minus_minus(X_a))=minus_minus(X_a)).
% 13.27/13.17 all X_a (one(X_a)->ti(X_a,one_one(X_a))=one_one(X_a)).
% 13.27/13.17 all X_a (monoid_add(X_a)->ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a)).
% 13.27/13.17 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)).
% 13.27/13.17 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)).
% 13.27/13.17 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)).
% 13.27/13.17 all X_a (mult_zero(X_a)->ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a)).
% 13.27/13.17 all X_a (monoid_mult(X_a)->ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a)).
% 13.27/13.17 all X_a (semiring(X_a)->ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a)).
% 13.27/13.17 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)).
% 13.27/13.17 all X_a (zero(X_a)->ti(X_a,zero_zero(X_a))=zero_zero(X_a)).
% 13.27/13.17 all X_a (ti(X_a,undefined(X_a))=undefined(X_a)).
% 13.27/13.17 ti(fun(int,int),zfact)=zfact.
% 13.27/13.17 ti(fun(int,fun(int,product_prod(int,product_prod(int,int)))),xzgcd)=xzgcd.
% 13.27/13.17 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.
% 13.27/13.17 ti(fun(int,fun(int,int)),nat_tsub)=nat_tsub.
% 13.27/13.17 all X_a (ord(X_a)->ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a)).
% 13.27/13.17 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)).
% 13.27/13.17 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)).
% 13.27/13.17 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)).
% 13.27/13.17 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)).
% 13.27/13.17 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)).
% 13.27/13.17 ti(fun(int,bool),twoSqu420862341sum2sq)=twoSqu420862341sum2sq.
% 13.27/13.17 ti(fun(product_prod(int,int),int),twoSqu579703163sum2sq)=twoSqu579703163sum2sq.
% 13.27/13.17 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)).
% 13.27/13.17 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)).
% 13.27/13.17 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)).
% 13.27/13.17 all B_1_1 (hBOOL(ti(bool,B_1_1))<->hBOOL(B_1_1)).
% 13.27/13.17 ti(int,a)=a.
% 13.27/13.17 ti(int,b)=b.
% 13.27/13.17 ti(int,p)=p.
% 13.27/13.17 ti(int,q)=q.
% 13.27/13.17 all A_1 R_1 B M C D N (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_1),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_1),D))),N))=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))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_1),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),N))))).
% 13.27/13.17 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))))).
% 13.27/13.17 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)))))).
% 13.27/13.17 all X_a (ring(X_a)-> (all Aa E_1 C_1 Ba 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),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_1)<->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_1)))).
% 13.27/13.17 all X_a (ring(X_a)-> (all Aa E_1 C_1 Ba 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),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_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),Aa),Ba)),E_1)),C_1)=ti(X_a,D_1)))).
% 13.27/13.17 all X_1 (hBOOL(hAPP(int,bool,twoSqu420862341sum2sq,X_1))<-> (exists A_2 B_2 (hAPP(product_prod(int,int),int,twoSqu579703163sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_2),B_2))=X_1))).
% 13.27/13.17 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)).
% 13.27/13.17 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))).
% 13.27/13.17 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))).
% 13.27/13.17 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))).
% 13.27/13.17 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))).
% 13.27/13.17 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)))).
% 13.27/13.17 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))))).
% 13.27/13.17 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)))).
% 13.27/13.17 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)))).
% 13.27/13.17 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)))).
% 13.27/13.17 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)))).
% 13.27/13.17 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)))).
% 13.27/13.17 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))))).
% 13.27/13.17 all X_a (ab_group_add(X_a)-> (all Aa Ba C_1 D_1 (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_1)-> (ti(X_a,Aa)=ti(X_a,Ba)<->ti(X_a,C_1)=ti(X_a,D_1))))).
% 13.27/13.17 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))).
% 13.27/13.17 all Z W_1 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),W_1)=hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),Z)).
% 13.27/13.17 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))).
% 13.27/13.17 all X Y Z (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))=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))).
% 13.27/13.17 all Z W_1 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),W_1)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),Z)).
% 13.27/13.17 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)))).
% 13.27/13.17 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))))).
% 13.27/13.17 all X_a (real_normed_algebra(X_a)-> (all A_1 A_4 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_4)),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_4),B))))).
% 13.27/13.17 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))))).
% 13.27/13.17 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))))).
% 13.27/13.17 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))))).
% 13.27/13.17 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))))).
% 13.27/13.17 all X_a (real_normed_algebra(X_a)-> (all A_1 A_4 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_4)),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_4),B))))).
% 13.27/13.17 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))))).
% 13.27/13.17 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))))).
% 13.27/13.17 all X_a (ab_group_add(X_a)-> (all A_1 C B D (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))=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))))).
% 13.27/13.17 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)))).
% 13.27/13.17 all X_a (semiri456707255roduct(X_a)-> (all W_2 Y_1 X_1 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),W_2),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),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),W_2),Z_1)),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_2)=ti(X_a,X_1)|ti(X_a,Y_1)=ti(X_a,Z_1)))).
% 13.27/13.17 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)))).
% 13.27/13.17 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))))).
% 13.27/13.17 all X_a (semiri456707255roduct(X_a)-> (all C_1 D_1 Aa Ba (ti(X_a,Aa)!=ti(X_a,Ba)&ti(X_a,C_1)!=ti(X_a,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),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_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),Aa),D_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),C_1))))).
% 13.27/13.17 all X_a (comm_semiring_1(X_a)-> (all X Y Z (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))=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))))).
% 13.27/13.17 all X_b X_a (minus(X_a)-> (all A_5 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_5),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_5,X_1)),hAPP(X_b,X_a,B_4,X_1))))).
% 13.27/13.17 all X_a X_b (minus(X_b)-> (all A_5 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_5),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_5,X_2)),hAPP(X_a,X_b,B_4,X_2))))).
% 13.27/13.17 all X_b X_a A_1 B A_4 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_4),B_1)-> -(ti(X_a,A_1)=ti(X_a,A_4)->ti(X_b,B)!=ti(X_b,B_1))).
% 13.27/13.17 all X_b X_a Aa Ba A_3 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_3),B_3)<->ti(X_a,Aa)=ti(X_a,A_3)&ti(X_b,Ba)=ti(X_b,B_3)).
% 13.27/13.17 all X_a X_b P ((all X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,P,X1)))<-> (all A_2 B_2 hBOOL(hAPP(product_prod(X_a,X_b),bool,P,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))))).
% 13.27/13.17 all X_a (comm_semiring_1(X_a)-> (all A_1 B C D (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))=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))))).
% 13.27/13.17 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)))).
% 13.27/13.17 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)))).
% 13.27/13.17 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)))).
% 13.27/13.17 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)))).
% 13.27/13.17 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))))).
% 13.27/13.17 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)))).
% 13.27/13.17 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))))).
% 13.27/13.17 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)))).
% 13.27/13.17 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)))))).
% 13.27/13.17 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))))).
% 13.27/13.17 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))))).
% 13.27/13.17 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)))).
% 13.27/13.17 all X_a (comm_semiring_1(X_a)-> (all A_1 C D (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))=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))))).
% 13.27/13.17 all X_a (comm_semiring_1(X_a)-> (all A_1 C D (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))=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)))).
% 13.27/13.17 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))))).
% 13.27/13.17 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)))).
% 13.27/13.17 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)).
% 13.27/13.17 all X_a X_b P ((exists X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,P,X1)))<-> (exists A_2 B_2 hBOOL(hAPP(product_prod(X_a,X_b),bool,P,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))))).
% 13.27/13.17 all X_a X_b X_c X_d X_e X_f X_1 P ((all A_2 B_2 C_2 D_2 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,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_2),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,X_1))).
% 13.27/13.18 all X_a X_b X_c X_d X_e X_f Y (-(all A_2 B_2 C_2 D_2 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_2),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)))))))).
% 13.27/13.18 all X_a X_b X_c X_d X_e X_1 P ((all A_2 B_2 C_2 D_2 E hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P,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_2),E)))))))->hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P,X_1))).
% 13.27/13.18 all X_a X_b X_c X_d X_e Y (-(all A_2 B_2 C_2 D_2 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_2),E))))))).
% 13.27/13.18 all X_a X_b X_c X_d X_1 P ((all A_2 B_2 C_2 D_2 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P,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_2))))))->hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P,X_1))).
% 13.27/13.18 all X_a X_b X_c X_d Y (-(all A_2 B_2 C_2 D_2 (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_2)))))).
% 13.27/13.18 all X_a X_b X_c X_1 P ((all A_2 B_2 C_2 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,P,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,X_1))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)).
% 13.27/13.18 all X_a X_b P_2 (-(all X_2 Y_2 (ti(product_prod(X_a,X_b),P_2)!=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)))).
% 13.27/13.18 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)).
% 13.27/13.18 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))).
% 13.27/13.18 all X_a (ordered_ring(X_a)-> (all Aa E_1 C_1 Ba 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),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_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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_1)),C_1)),D_1))))).
% 13.27/13.18 all X_a (ordered_ring(X_a)-> (all Aa E_1 C_1 Ba 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),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_1)))<->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_1)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 all X_a (ordered_ring(X_a)-> (all Aa E_1 C_1 Ba 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),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_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),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_1))))).
% 13.27/13.18 all X_a (ordered_ring(X_a)-> (all Aa E_1 C_1 Ba 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),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_1)))<->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_1)))))).
% 13.27/13.18 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)))).
% 13.27/13.18 all W_2 Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_2),Z_1))).
% 13.27/13.18 all W_2 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_2),one_one(int))),Z_1))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),Z_1))).
% 13.27/13.18 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)))))).
% 13.27/13.18 all W_1 Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),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_1),one_one(int))),Z))).
% 13.27/13.18 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)))))).
% 13.27/13.18 all W_2 Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),Z_1))|W_2=Z_1).
% 13.27/13.18 all Z_3 Z 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_3),Z))->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_3)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),Z))))).
% 13.27/13.18 all X_a (ordere223160158up_add(X_a)-> (all C D 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))->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))))))).
% 13.27/13.18 all X_a (ordere223160158up_add(X_a)-> (all C D 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))->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))))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 all X_a (linordered_semidom(X_a)-> (all N M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M),N))))))).
% 13.27/13.18 all W_2 Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_1),one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),Z_1))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 all X_a (ordere223160158up_add(X_a)-> (all C D 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))->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))))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 all X_a (ordered_ab_group_add(X_a)-> (all Aa Ba C_1 D_1 (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_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),D_1)))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 all X_a (ordere779506340up_add(X_a)-> (all C D 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))->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))))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 all X_a (ordered_ab_group_add(X_a)-> (all Aa Ba C_1 D_1 (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_1)-> (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_1)))))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 all Z (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z)=Z).
% 13.27/13.18 all Z (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),one_one(int))=Z).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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))).
% 13.27/13.18 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)))).
% 13.27/13.18 all X_a (order(X_a)-> (all Z 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),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X)))))).
% 13.27/13.18 all X_a (preorder(X_a)-> (all Z 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))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z)))))).
% 13.27/13.18 all X_a (order(X_a)-> (all Z 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),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X)))))).
% 13.27/13.18 all X_a (preorder(X_a)-> (all Z 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))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))).
% 13.27/13.18 all W_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),W_1)).
% 13.27/13.18 all Z W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),W_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z))).
% 13.27/13.18 all Z_1 W_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),W_2))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W_2))&Z_1!=W_2).
% 13.27/13.18 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))).
% 13.27/13.18 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)))).
% 13.27/13.18 all Z W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),W_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z))->Z=W_1)).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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))))).
% 13.27/13.18 all X_a (preorder(X_a)-> (all Z 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))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Z)))))).
% 13.27/13.18 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))))).
% 13.27/13.18 all X_a (order(X_a)-> (all Z 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),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Z),X)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 all X_a (preorder(X_a)-> (all P 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 all X_a (preorder(X_a)-> (all Z 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))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z)))))).
% 13.27/13.18 all X_a (order(X_a)-> (all Z 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),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X)))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))).
% 13.27/13.18 all P 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,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,I_2))->hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int)))))))->hBOOL(hAPP(int,bool,P,I_1))))).
% 13.27/13.18 all P 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,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,I_2))->hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int)))))))->hBOOL(hAPP(int,bool,P,I_1))))).
% 13.27/13.18 all P 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,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,I_2))->hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int)))))))->hBOOL(hAPP(int,bool,P,I_1))))).
% 13.27/13.18 all P 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,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,I_2))->hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int)))))))->hBOOL(hAPP(int,bool,P,I_1))))).
% 13.27/13.18 all X_a (dense_linorder(X_a)-> (all Z 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))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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)))))))).
% 13.27/13.18 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)))))))).
% 13.27/13.18 all X_a (dense_linorder(X_a)-> (all Z X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))-> ((all W (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),W),Z)))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z)))))).
% 13.27/13.18 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)))))))).
% 13.27/13.18 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)))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 all I_1 P K_1 (hBOOL(hAPP(int,bool,P,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,I_2))->hBOOL(hAPP(int,bool,P,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,I_2))->hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int)))))))->hBOOL(hAPP(int,bool,P,I_1))))).
% 13.27/13.18 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)))).
% 13.27/13.18 all X_1 P ((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,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_2),one_one(int)))))->hBOOL(hAPP(int,bool,P,A_2))))->hBOOL(hAPP(int,bool,P,X_1))).
% 13.27/13.18 all X_a (linord626643107strict(X_a)-> (all V U 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))-> (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),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),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1))))))))).
% 13.27/13.18 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(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))))))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 all X_a (zero_ne_q_one(X_a)->one_one(X_a)!=zero_zero(X_a)).
% 13.27/13.18 all X_a (zero_ne_q_one(X_a)->zero_zero(X_a)!=one_one(X_a)).
% 13.27/13.18 zero_zero(int)!=one_one(int).
% 13.27/13.18 all Z (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),zero_zero(int))=Z).
% 13.27/13.18 all Z (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),Z)=Z).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 all X_a (ordered_semiring(X_a)-> (all C D 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))-> (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))))))))).
% 13.27/13.18 all X_a (ordered_semiring(X_a)-> (all C D 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))-> (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))))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))))).
% 13.27/13.18 all X_a (semiri456707255roduct(X_a)-> (all C D A_1 B R_1 (ti(X_a,R_1)!=zero_zero(X_a)-> (ti(X_a,A_1)=ti(X_a,B)&ti(X_a,C)!=ti(X_a,D)->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_1),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_1),D)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))).
% 13.27/13.18 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))))).
% 13.27/13.18 all Z (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)).
% 13.27/13.18 all K_1 L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),L_1))<->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_1)),zero_zero(int)))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 all X_a (linord20386208strict(X_a)-> (all C D 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))-> (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))))))))).
% 13.27/13.18 all X_a (linord20386208strict(X_a)-> (all C D 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))-> (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))))))))).
% 13.27/13.18 all X_a (linord20386208strict(X_a)-> (all C D 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))-> (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))))))))).
% 13.27/13.18 all X_a (linord20386208strict(X_a)-> (all C D 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))-> (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))))))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))))).
% 13.27/13.18 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))))).
% 13.27/13.18 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_1))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1))).
% 13.27/13.18 all N_1 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_1)=one_one(int)<->M_1=one_one(int)&N_1=one_one(int))).
% 13.27/13.18 all 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),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_1)),Z_1)),zero_zero(int)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),zero_zero(int)))).
% 13.27/13.18 all X_a (linord1278240602ring_1(X_a)-> (all V U 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))-> (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),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),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1))))))))).
% 13.27/13.18 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z)))).
% 13.27/13.18 all R_1 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_1),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_1),A_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Q))))).
% 13.27/13.18 all R_1 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_1),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_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q),one_one(int)))))).
% 13.27/13.18 all B_1 Q_1 R_2 (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_2)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Q_1))))).
% 13.27/13.18 all B_1 Q_1 R_2 (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_2)),zero_zero(int)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),zero_zero(int)))))).
% 13.27/13.18 all B Q R_1 B_1 Q_1 R_2 (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_1)=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_2)-> (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_2)),zero_zero(int)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_2))-> (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)))))))).
% 13.27/13.18 all B Q_1 R_2 Q R_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),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_1)),R_2)),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_1)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_1),zero_zero(int)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_2))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q),Q_1)))))).
% 13.27/13.18 all B Q R_1 B_1 Q_1 R_2 (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_1)=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_2)-> (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_2)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_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),B_1),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q),Q_1)))))))).
% 13.27/13.18 all B Q_1 R_2 Q R_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),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_1)),R_2)),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_1)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q)))))).
% 13.27/13.18 all M R_1 S T_3 N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N))-> (hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M),N)=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_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S),T_3))->R_1=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)))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))))).
% 13.27/13.18 all M N R_2 S_1 S T_4 T_3 Rn Sn Tn R_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R_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),R_2),R_1),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_2=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))-> (R_1=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))->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)))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),zero_zero(int))).
% 13.27/13.18 all M N (hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M),N)=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),M),N),one_one(int)),zero_zero(int)),zero_zero(int)),one_one(int))).
% 13.27/13.18 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),one_one(int))).
% 13.27/13.18 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)))).
% 13.27/13.18 all K_1 P D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))-> ((all X_2 (hBOOL(hAPP(int,bool,P,X_2))->hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_1)))))-> (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,X_2))->hBOOL(hAPP(int,bool,P,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_1))))))))).
% 13.27/13.18 all K_1 P D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))-> ((all X_2 (hBOOL(hAPP(int,bool,P,X_2))->hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_1)))))-> (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,X_2))->hBOOL(hAPP(int,bool,P,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_1))))))))).
% 13.27/13.18 all P_1 P X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))-> (hBOOL(P)<->hBOOL(P_1)))-> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))->hBOOL(P))<-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))->hBOOL(P_1)))).
% 13.27/13.18 all P_1 P X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))-> (hBOOL(P)<->hBOOL(P_1)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))&hBOOL(P)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))&hBOOL(P_1))).
% 13.27/13.18 all X_a (linord1117847801e_zero(X_a)-> (all X Y ((all Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Z_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),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_2),X)),Y)))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))))).
% 13.27/13.18 all X_a (linorder(X_a)-> (all T_3 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),T_3),X_2))))).
% 13.27/13.18 all X_a (linorder(X_a)-> (all T_3 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),T_3),X_2))))).
% 13.27/13.18 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))))).
% 13.27/13.18 all X_a (linorder(X_a)-> (all T_3 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_2),T_3))))).
% 13.27/13.18 all X_a (linorder(X_a)-> (all T_3 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_2),T_3))))).
% 13.27/13.18 all A_1 B Q R_1 (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_1)-> ((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_1))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B)))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_1))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_1),zero_zero(int))))->hBOOL(hAPP(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_1))))).
% 13.27/13.18 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))))).
% 13.27/13.18 all A_1 Q R_1 (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_1)))-> (A_1!=zero_zero(int)->R_1=zero_zero(int))).
% 13.27/13.18 all Q_1 R_2 A_1 B Q R_1 (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_1)))-> (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_2)))-> (B!=zero_zero(int)->Q=Q_1))).
% 13.27/13.18 all Q_1 R_2 A_1 B Q R_1 (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_1)))-> (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_2)))-> (B!=zero_zero(int)->R_1=R_2))).
% 13.27/13.18 all A_1 Q R_1 (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_1)))-> (A_1!=zero_zero(int)->Q=one_one(int))).
% 13.27/13.18 all P P1 D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))-> ((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_1))))))-> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Z_2))-> (hBOOL(hAPP(int,bool,P,X_2))<->hBOOL(hAPP(int,bool,P1,X_2)))))-> ((exists X1 hBOOL(hAPP(int,bool,P1,X1)))-> (exists X1 hBOOL(hAPP(int,bool,P,X1))))))).
% 13.27/13.18 all P P_1 D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))-> ((all X_2 K_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_2),D_1))))))-> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),X_2))-> (hBOOL(hAPP(int,bool,P,X_2))<->hBOOL(hAPP(int,bool,P_1,X_2)))))-> ((exists X1 hBOOL(hAPP(int,bool,P_1,X1)))-> (exists X1 hBOOL(hAPP(int,bool,P,X1))))))).
% 13.27/13.18 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))).
% 13.27/13.18 all N ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N),zero_zero(int)))->hAPP(int,int,zfact,N)=one_one(int))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N),zero_zero(int)))->hAPP(int,int,zfact,N)=hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N),hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N),one_one(int)))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)).
% 13.27/13.18 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))))).
% 13.27/13.18 all X Z D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(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))),one_one(int))),D))),Z))).
% 13.27/13.18 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)))).
% 13.27/13.18 all X_a (ordere142940540dd_abs(X_a)->hAPP(X_a,X_a,abs_abs(X_a),zero_zero(X_a))=zero_zero(X_a)).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))).
% 13.27/13.18 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)))))).
% 13.27/13.18 all X_a (linordered_idom(X_a)-> (all B D 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))->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))))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 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)))))).
% 13.27/13.18 all M N (hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))=one_one(int)->hAPP(int,int,abs_abs(int),M)=one_one(int)).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))).
% 13.27/13.18 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))))).
% 13.27/13.18 all X_a (linordered_idom(X_a)->hAPP(X_a,X_a,abs_abs(X_a),one_one(X_a))=one_one(X_a)).
% 13.27/13.18 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))))).
% 13.27/13.18 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)))).
% 13.27/13.18 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))))).
% 13.27/13.19 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))))).
% 13.27/13.19 all X_a (ordere142940540dd_abs(X_a)-> (all A_1 B C D 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)))),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))))))).
% 13.27/13.19 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)))))).
% 13.27/13.19 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z_1)),one_one(int)))<->Z_1=zero_zero(int)).
% 13.27/13.19 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))).
% 13.27/13.19 all Z X D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),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))),one_one(int))),D))))).
% 13.27/13.19 all X_a (linordered_idom(X_a)-> (all X_1 Aa R (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))<->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)),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)))))).
% 13.27/13.19 all K L ((L=zero_zero(int)->hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)=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!=zero_zero(int)->hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)=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)))).
% 13.27/13.19 all K_1 F N_1 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_1))->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_1)))-> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),N_1))&hAPP(nat,int,F,I_2)=K_1))))).
% 13.27/13.19 all K_1 F N_1 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_1))->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_1)))-> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),N_1))&hAPP(nat,int,F,I_2)=K_1))))).
% 13.27/13.19 all N M ((M=zero_zero(nat)->hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)=zero_zero(nat))& (M!=zero_zero(nat)->hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),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)))).
% 13.27/13.19 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N)).
% 13.27/13.19 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))).
% 13.27/13.19 all M N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M)).
% 13.27/13.19 all M N 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)),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),K))).
% 13.27/13.19 all M N 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)),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),K))).
% 13.27/13.19 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)).
% 13.27/13.19 all K M N (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))=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))).
% 13.27/13.19 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N)=zero_zero(nat)).
% 13.27/13.19 all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),zero_zero(nat))=zero_zero(nat)).
% 13.27/13.19 all M_1 N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)=zero_zero(nat)<->M_1=zero_zero(nat)|N_1=zero_zero(nat)).
% 13.27/13.19 all K_1 M_1 N_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_1)<->M_1=N_1|K_1=zero_zero(nat)).
% 13.27/13.19 all M_1 K_1 N_1 (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_1),K_1)<->M_1=N_1|K_1=zero_zero(nat)).
% 13.27/13.19 all M N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)=zero_zero(nat)-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M)=zero_zero(nat)->M=N)).
% 13.27/13.19 all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M)=zero_zero(nat)).
% 13.27/13.19 all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat))=M).
% 13.27/13.19 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N)=zero_zero(nat)).
% 13.27/13.19 all N 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)),K))).
% 13.27/13.19 all L M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M))))).
% 13.27/13.19 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))).
% 13.27/13.19 all M_1 N_1 (M_1!=N_1<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1))).
% 13.27/13.19 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)))).
% 13.27/13.19 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))).
% 13.27/13.19 all N M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M))->M!=N).
% 13.27/13.19 all S T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3))->S!=T_3).
% 13.27/13.19 all P M_1 N_1 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P,N_1),M_1)))-> ((M_1=N_1->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P,N_1),M_1)))-> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P,N_1),M_1)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P,N_1),M_1))))).
% 13.27/13.19 all M N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)).
% 13.27/13.19 all X Y Z (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))=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))).
% 13.27/13.19 all K M N (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))=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))).
% 13.27/13.19 all M N 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)),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),K))).
% 13.27/13.19 all M N 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)),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),K))).
% 13.27/13.19 all K_1 M_1 N_1 (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_1)<->M_1=N_1).
% 13.27/13.19 all M_1 K_1 N_1 (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_1),K_1)<->M_1=N_1).
% 13.27/13.19 all M K N (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),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)).
% 13.27/13.19 all K M N (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))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)).
% 13.27/13.19 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))).
% 13.27/13.19 all N M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),N)=M).
% 13.27/13.19 all M N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),N)=M).
% 13.27/13.19 all M N 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)),M)).
% 13.27/13.19 all L M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M)))).
% 13.27/13.19 all L M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),L)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),L)))).
% 13.27/13.19 all I N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),N))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),I))=I).
% 13.27/13.19 all N_1 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_1))-> (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_1),K_1)<->M_1=N_1))).
% 13.27/13.19 all N 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))->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),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))).
% 13.27/13.19 all N_1 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_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_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))))).
% 13.27/13.19 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),N)).
% 13.27/13.19 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M))).
% 13.27/13.19 all M N (M=N->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))).
% 13.27/13.19 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)))).
% 13.27/13.19 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M))->M=N)).
% 13.27/13.19 all K L 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))->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))))).
% 13.27/13.19 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)))).
% 13.27/13.19 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)))).
% 13.27/13.19 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)))).
% 13.27/13.19 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))).
% 13.27/13.19 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N)=N).
% 13.27/13.19 all M_1 N_1 (one_one(nat)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)<->M_1=one_one(nat)&N_1=one_one(nat)).
% 13.27/13.19 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),one_one(nat))=N).
% 13.27/13.19 all M_1 N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)=one_one(nat)<->M_1=one_one(nat)&N_1=one_one(nat)).
% 13.27/13.19 all N_1 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_1),M_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))).
% 13.27/13.19 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),M)))).
% 13.27/13.19 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))).
% 13.27/13.19 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))).
% 13.27/13.19 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))).
% 13.27/13.19 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))->N!=zero_zero(nat)).
% 13.27/13.19 all N (N!=zero_zero(nat)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))).
% 13.27/13.19 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))))).
% 13.27/13.19 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))))).
% 13.27/13.19 all M_1 K_1 N_1 (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_1),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_1))).
% 13.27/13.19 all K_1 M_1 N_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_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_1))).
% 13.27/13.19 all M_1 N_1 (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_1)))<->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_1))).
% 13.27/13.19 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N)=N).
% 13.27/13.19 all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),zero_zero(nat))=M).
% 13.27/13.19 all M_1 N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)=zero_zero(nat)<->M_1=zero_zero(nat)&N_1=zero_zero(nat)).
% 13.27/13.19 all M N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)=M->N=zero_zero(nat)).
% 13.27/13.19 all N M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M))=zero_zero(nat)).
% 13.27/13.19 all M_1 N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)=zero_zero(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))).
% 13.27/13.19 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)=zero_zero(nat)).
% 13.27/13.19 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N)).
% 13.27/13.19 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),zero_zero(nat)))<->N_1=zero_zero(nat)).
% 13.27/13.19 all I_1 J_1 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_1),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_1))).
% 13.27/13.19 all M N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))=M).
% 13.27/13.19 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))).
% 13.27/13.19 all M N K L (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))).
% 13.27/13.19 all K L 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))->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))))).
% 13.27/13.19 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)))).
% 13.27/13.19 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)))).
% 13.27/13.19 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)))).
% 13.27/13.19 all T_2 T_1 (preorder(T_1)->preorder(fun(T_2,T_1))).
% 13.27/13.19 all T_2 T_1 (order(T_1)->order(fun(T_2,T_1))).
% 13.27/13.19 all T_2 T_1 (ord(T_1)->ord(fun(T_2,T_1))).
% 13.27/13.19 all T_2 T_1 (minus(T_1)->minus(fun(T_2,T_1))).
% 13.27/13.19 semiri456707255roduct(int).
% 13.27/13.19 ordere223160158up_add(int).
% 13.27/13.19 ordere236663937imp_le(int).
% 13.27/13.19 linord893533164strict(int).
% 13.27/13.19 linord626643107strict(int).
% 13.27/13.19 linord20386208strict(int).
% 13.27/13.19 ordere779506340up_add(int).
% 13.27/13.19 ordere142940540dd_abs(int).
% 13.27/13.19 ordere216010020id_add(int).
% 13.27/13.19 linord219039673up_add(int).
% 13.27/13.19 cancel146912293up_add(int).
% 13.27/13.19 ordere453448008miring(int).
% 13.27/13.19 linord581940658strict(int).
% 13.27/13.19 ring_n68954251visors(int).
% 13.27/13.19 ordere1490568538miring(int).
% 13.27/13.19 linord1278240602ring_1(int).
% 13.27/13.19 ordered_ab_group_add(int).
% 13.27/13.19 cancel_semigroup_add(int).
% 13.27/13.19 linordered_semiring(int).
% 13.27/13.19 linordered_semidom(int).
% 13.27/13.19 ab_semigroup_mult(int).
% 13.27/13.19 comm_monoid_mult(int).
% 13.27/13.19 ab_semigroup_add(int).
% 13.27/13.19 ordered_semiring(int).
% 13.27/13.19 ordered_ring_abs(int).
% 13.27/13.19 no_zero_divisors(int).
% 13.27/13.19 comm_monoid_add(int).
% 13.27/13.19 linordered_ring(int).
% 13.27/13.19 linordered_idom(int).
% 13.27/13.19 comm_semiring_1(int).
% 13.27/13.19 comm_semiring(int).
% 13.27/13.19 ab_group_add(int).
% 13.27/13.19 zero_ne_q_one(int).
% 13.27/13.19 ordered_ring(int).
% 13.27/13.19 preorder(int).
% 13.27/13.19 linorder(int).
% 13.27/13.19 monoid_mult(int).
% 13.27/13.19 monoid_add(int).
% 13.27/13.19 group_add(int).
% 13.27/13.19 mult_zero(int).
% 13.27/13.19 order(int).
% 13.27/13.19 semiring(int).
% 13.27/13.19 ord(int).
% 13.27/13.19 ring_1(int).
% 13.27/13.19 minus(int).
% 13.27/13.19 zero(int).
% 13.27/13.19 ring(int).
% 13.27/13.19 one(int).
% 13.27/13.19 semiri456707255roduct(nat).
% 13.27/13.19 ordere223160158up_add(nat).
% 13.27/13.19 ordere236663937imp_le(nat).
% 13.27/13.19 linord893533164strict(nat).
% 13.27/13.19 linord20386208strict(nat).
% 13.27/13.19 ordere779506340up_add(nat).
% 13.27/13.19 ordere216010020id_add(nat).
% 13.27/13.19 cancel146912293up_add(nat).
% 13.27/13.19 ordere453448008miring(nat).
% 13.27/13.19 ordere1490568538miring(nat).
% 13.27/13.19 cancel_semigroup_add(nat).
% 13.27/13.19 linordered_semiring(nat).
% 13.27/13.19 linordered_semidom(nat).
% 13.27/13.19 ab_semigroup_mult(nat).
% 13.27/13.19 comm_monoid_mult(nat).
% 13.27/13.19 ab_semigroup_add(nat).
% 13.27/13.19 ordered_semiring(nat).
% 13.27/13.19 no_zero_divisors(nat).
% 13.27/13.19 comm_monoid_add(nat).
% 13.27/13.19 comm_semiring_1(nat).
% 13.27/13.19 comm_semiring(nat).
% 13.27/13.19 zero_ne_q_one(nat).
% 13.27/13.19 preorder(nat).
% 13.27/13.19 linorder(nat).
% 13.27/13.19 monoid_mult(nat).
% 13.27/13.19 monoid_add(nat).
% 13.27/13.19 mult_zero(nat).
% 13.27/13.19 order(nat).
% 13.27/13.19 semiring(nat).
% 13.27/13.19 ord(nat).
% 13.27/13.19 minus(nat).
% 13.27/13.19 zero(nat).
% 13.27/13.19 one(nat).
% 13.27/13.19 preorder(bool).
% 13.27/13.19 order(bool).
% 13.27/13.19 ord(bool).
% 13.27/13.19 minus(bool).
% 13.27/13.19 all T A (ti(T,ti(T,A))=ti(T,A)).
% 13.27/13.19 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,twoSqu579703163sum2sq,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,twoSqu579703163sum2sq,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,twoSqu579703163sum2sq,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)))).
% 13.27/13.19 end_of_list.
% 13.27/13.19
% 13.27/13.19 -------> usable clausifies to:
% 13.27/13.19
% 13.27/13.19 list(usable).
% 13.27/13.19 0 [] A=A.
% 13.27/13.19 0 [] ti(fun(int,fun(int,fun(product_prod(int,int),bool))),divmod_int_rel)=divmod_int_rel.
% 13.27/13.19 0 [] ti(fun(int,fun(int,product_prod(int,int))),pdivmod)=pdivmod.
% 13.27/13.19 0 [] ti(fun(int,fun(int,product_prod(int,int))),posDivAlg)=posDivAlg.
% 13.27/13.19 0 [] -ordere142940540dd_abs(X_a)|ti(fun(X_a,X_a),abs_abs(X_a))=abs_abs(X_a).
% 13.27/13.19 0 [] -minus(X_a)|ti(fun(X_a,fun(X_a,X_a)),minus_minus(X_a))=minus_minus(X_a).
% 13.27/13.19 0 [] -one(X_a)|ti(X_a,one_one(X_a))=one_one(X_a).
% 13.27/13.19 0 [] -monoid_add(X_a)|ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a).
% 13.27/13.19 0 [] -ab_semigroup_add(X_a)|ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a).
% 13.27/13.19 0 [] -cancel_semigroup_add(X_a)|ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a).
% 13.27/13.19 0 [] -no_zero_divisors(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 13.27/13.19 0 [] -mult_zero(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 13.27/13.19 0 [] -monoid_mult(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 13.27/13.19 0 [] -semiring(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 13.27/13.19 0 [] -ab_semigroup_mult(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 13.27/13.19 0 [] -zero(X_a)|ti(X_a,zero_zero(X_a))=zero_zero(X_a).
% 13.27/13.19 0 [] ti(X_a,undefined(X_a))=undefined(X_a).
% 13.27/13.19 0 [] ti(fun(int,int),zfact)=zfact.
% 13.27/13.19 0 [] ti(fun(int,fun(int,product_prod(int,product_prod(int,int)))),xzgcd)=xzgcd.
% 13.27/13.19 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.
% 13.27/13.19 0 [] ti(fun(int,fun(int,int)),nat_tsub)=nat_tsub.
% 13.27/13.19 0 [] -ord(X_a)|ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a).
% 13.27/13.19 0 [] -ord(X_b)|ti(fun(X_b,fun(X_b,bool)),ord_less_e_q(X_b))=ord_less_e_q(X_b).
% 13.27/13.19 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).
% 13.27/13.19 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).
% 13.27/13.19 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).
% 13.27/13.19 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).
% 13.27/13.19 0 [] ti(fun(int,bool),twoSqu420862341sum2sq)=twoSqu420862341sum2sq.
% 13.27/13.19 0 [] ti(fun(product_prod(int,int),int),twoSqu579703163sum2sq)=twoSqu579703163sum2sq.
% 13.27/13.19 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).
% 13.27/13.19 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).
% 13.27/13.19 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).
% 13.27/13.19 0 [] -hBOOL(ti(bool,B_1_1))|hBOOL(B_1_1).
% 13.27/13.19 0 [] hBOOL(ti(bool,B_1_1))| -hBOOL(B_1_1).
% 13.27/13.19 0 [] ti(int,a)=a.
% 13.27/13.19 0 [] ti(int,b)=b.
% 13.27/13.19 0 [] ti(int,p)=p.
% 13.27/13.19 0 [] ti(int,q)=q.
% 13.27/13.19 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_1),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_1),D))),N))=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))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_1),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),N)))).
% 13.27/13.19 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)).
% 13.27/13.19 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))).
% 13.27/13.19 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_1)|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_1).
% 13.27/13.19 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_1)|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_1).
% 13.27/13.19 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_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),Aa),Ba)),E_1)),C_1)=ti(X_a,D_1).
% 13.27/13.19 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_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),Aa),Ba)),E_1)),C_1)!=ti(X_a,D_1).
% 13.27/13.19 0 [] -hBOOL(hAPP(int,bool,twoSqu420862341sum2sq,X_1))|hAPP(product_prod(int,int),int,twoSqu579703163sum2sq,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.
% 13.27/13.19 0 [] hBOOL(hAPP(int,bool,twoSqu420862341sum2sq,X_1))|hAPP(product_prod(int,int),int,twoSqu579703163sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_2),B_2))!=X_1.
% 13.27/13.19 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).
% 13.27/13.19 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)).
% 13.27/13.19 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)).
% 13.27/13.19 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)).
% 13.27/13.19 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)).
% 13.27/13.19 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).
% 13.27/13.19 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)).
% 13.27/13.19 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).
% 13.27/13.19 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).
% 13.27/13.19 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).
% 13.27/13.19 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).
% 13.27/13.19 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).
% 13.27/13.19 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).
% 13.27/13.19 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).
% 13.27/13.19 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)).
% 13.27/13.19 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_1)|ti(X_a,Aa)!=ti(X_a,Ba)|ti(X_a,C_1)=ti(X_a,D_1).
% 13.27/13.19 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_1)|ti(X_a,Aa)=ti(X_a,Ba)|ti(X_a,C_1)!=ti(X_a,D_1).
% 13.27/13.19 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)).
% 13.27/13.19 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),W_1)=hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),Z).
% 13.27/13.19 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)).
% 13.27/13.19 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))=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)).
% 13.27/13.19 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),W_1)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),Z).
% 13.27/13.19 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).
% 13.27/13.19 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)).
% 13.27/13.19 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_4)),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_4),B)).
% 13.27/13.19 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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_4)),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_4),B)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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))=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)).
% 13.27/13.20 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).
% 13.27/13.20 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_2),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),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),W_2),Z_1)),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_2)=ti(X_a,X_1)|ti(X_a,Y_1)=ti(X_a,Z_1).
% 13.27/13.20 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_2),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),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),W_2),Z_1)),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_2)!=ti(X_a,X_1).
% 13.27/13.20 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_2),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),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),W_2),Z_1)),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_1).
% 13.27/13.20 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).
% 13.27/13.20 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)).
% 13.27/13.20 0 [] -semiri456707255roduct(X_a)|ti(X_a,Aa)=ti(X_a,Ba)|ti(X_a,C_1)=ti(X_a,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),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_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),Aa),D_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),C_1)).
% 13.27/13.20 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_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),Aa),D_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),C_1)).
% 13.27/13.20 0 [] -semiri456707255roduct(X_a)|ti(X_a,C_1)!=ti(X_a,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),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_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),Aa),D_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),C_1)).
% 13.27/13.20 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))=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)).
% 13.27/13.20 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_5),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_5,X_1)),hAPP(X_b,X_a,B_4,X_1)).
% 13.27/13.20 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_5),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_5,X_2)),hAPP(X_a,X_b,B_4,X_2)).
% 13.27/13.20 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_4),B_1)|ti(X_a,A_1)=ti(X_a,A_4).
% 13.27/13.20 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_4),B_1)|ti(X_b,B)=ti(X_b,B_1).
% 13.27/13.20 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_3),B_3)|ti(X_a,Aa)=ti(X_a,A_3).
% 13.27/13.20 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_3),B_3)|ti(X_b,Ba)=ti(X_b,B_3).
% 13.27/13.20 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_3),B_3)|ti(X_a,Aa)!=ti(X_a,A_3)|ti(X_b,Ba)!=ti(X_b,B_3).
% 13.27/13.20 0 [] -hBOOL(hAPP(product_prod(X_a,X_b),bool,P,$f3(X_a,X_b,P)))|hBOOL(hAPP(product_prod(X_a,X_b),bool,P,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_2))).
% 13.27/13.20 0 [] hBOOL(hAPP(product_prod(X_a,X_b),bool,P,X1))| -hBOOL(hAPP(product_prod(X_a,X_b),bool,P,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),$f5(X_a,X_b,P)),$f4(X_a,X_b,P)))).
% 13.27/13.20 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))=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)).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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)).
% 13.27/13.20 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).
% 13.27/13.20 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)).
% 13.27/13.20 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).
% 13.27/13.20 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))).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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).
% 13.27/13.20 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))=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)).
% 13.27/13.20 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))=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).
% 13.27/13.20 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)).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 0 [] -hBOOL(hAPP(product_prod(X_a,X_b),bool,P,X1))|hBOOL(hAPP(product_prod(X_a,X_b),bool,P,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)),$f6(X_a,X_b,P)))).
% 13.27/13.20 0 [] hBOOL(hAPP(product_prod(X_a,X_b),bool,P,$f8(X_a,X_b,P)))| -hBOOL(hAPP(product_prod(X_a,X_b),bool,P,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))).
% 13.27/13.20 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,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))))),$f14(X_a,X_b,X_c,X_d,X_e,X_f,X_1,P)),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),$f13(X_a,X_b,X_c,X_d,X_e,X_f,X_1,P)),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))),$f12(X_a,X_b,X_c,X_d,X_e,X_f,X_1,P)),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),$f11(X_a,X_b,X_c,X_d,X_e,X_f,X_1,P)),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),$f10(X_a,X_b,X_c,X_d,X_e,X_f,X_1,P)),$f9(X_a,X_b,X_c,X_d,X_e,X_f,X_1,P))))))))|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,X_1)).
% 13.27/13.20 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)))))).
% 13.27/13.20 0 [] -hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P,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)))),$f25(X_a,X_b,X_c,X_d,X_e,X_1,P)),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),$f24(X_a,X_b,X_c,X_d,X_e,X_1,P)),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)),$f23(X_a,X_b,X_c,X_d,X_e,X_1,P)),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),$f22(X_a,X_b,X_c,X_d,X_e,X_1,P)),$f21(X_a,X_b,X_c,X_d,X_e,X_1,P)))))))|hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P,X_1)).
% 13.27/13.20 0 [] ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),Y)=hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),$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))))).
% 13.27/13.20 0 [] -hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P,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))),$f34(X_a,X_b,X_c,X_d,X_1,P)),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),$f33(X_a,X_b,X_c,X_d,X_1,P)),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),$f32(X_a,X_b,X_c,X_d,X_1,P)),$f31(X_a,X_b,X_c,X_d,X_1,P))))))|hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P,X_1)).
% 13.27/13.20 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)))).
% 13.27/13.20 0 [] -hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,P,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)),$f41(X_a,X_b,X_c,X_1,P)),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),$f40(X_a,X_b,X_c,X_1,P)),$f39(X_a,X_b,X_c,X_1,P)))))|hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,P,X_1)).
% 13.27/13.20 0 [] ti(product_prod(X_a,product_prod(X_b,X_c)),Y)=hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),$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))).
% 13.27/13.20 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),$f46(X_a,X_b,Y)),$f45(X_a,X_b,Y)).
% 13.27/13.20 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).
% 13.27/13.20 0 [] ti(product_prod(X_a,X_b),P_2)=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),$f49(X_a,X_b,P_2)),$f48(X_a,X_b,P_2)).
% 13.27/13.20 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).
% 13.27/13.20 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)).
% 13.27/13.20 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_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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_1)),C_1)),D_1)).
% 13.27/13.20 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_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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_1)),C_1)),D_1)).
% 13.27/13.20 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_1)))|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_1))).
% 13.27/13.20 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_1)))| -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_1))).
% 13.27/13.20 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))).
% 13.27/13.20 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_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),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_1)).
% 13.27/13.20 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_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),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_1)).
% 13.27/13.20 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_1)))|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_1))).
% 13.27/13.20 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_1)))| -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_1))).
% 13.27/13.20 0 [] -one(X_a)|one_one(X_a)!=ti(X_a,X_1)|ti(X_a,X_1)=one_one(X_a).
% 13.27/13.20 0 [] -one(X_a)|one_one(X_a)=ti(X_a,X_1)|ti(X_a,X_1)!=one_one(X_a).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_2),Z_1)).
% 13.27/13.20 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_2),Z_1)).
% 13.27/13.20 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_2),one_one(int))),Z_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),Z_1)).
% 13.27/13.20 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_2),one_one(int))),Z_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),Z_1)).
% 13.27/13.20 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)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),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_1),one_one(int))),Z)).
% 13.27/13.20 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)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),Z_1))|W_2=Z_1.
% 13.27/13.20 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),Z_1)).
% 13.27/13.20 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),one_one(int))))|W_2!=Z_1.
% 13.27/13.20 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_3),Z))|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_3)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),Z))).
% 13.27/13.20 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))|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))).
% 13.27/13.20 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))|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))).
% 13.27/13.20 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)))).
% 13.27/13.20 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M),N))).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_1),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),Z_1)).
% 13.27/13.20 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_1),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),Z_1)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))|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))).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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_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),D_1)).
% 13.27/13.20 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_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),D_1)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))|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))).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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_1)| -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_1)).
% 13.27/13.20 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_1)|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_1)).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z)=Z.
% 13.27/13.20 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),one_one(int))=Z.
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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)).
% 13.27/13.20 0 [] -preorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),X)).
% 13.27/13.20 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),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X)).
% 13.27/13.20 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))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z)).
% 13.27/13.20 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),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X)).
% 13.27/13.20 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))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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).
% 13.27/13.20 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),W_1)).
% 13.27/13.20 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),W_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),W_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W_2)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),W_2))|Z_1!=W_2.
% 13.27/13.20 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),W_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W_2))|Z_1=W_2.
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),W_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z))|Z=W_1.
% 13.27/13.20 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))).
% 13.27/13.20 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)))).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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))).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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).
% 13.27/13.20 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))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Z)).
% 13.27/13.20 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).
% 13.27/13.20 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),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Z),X)).
% 13.27/13.20 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))).
% 13.27/13.20 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)).
% 13.27/13.20 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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).
% 13.27/13.20 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)).
% 13.27/13.20 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).
% 13.27/13.20 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)).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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)).
% 13.27/13.20 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).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z)).
% 13.27/13.20 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),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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).
% 13.27/13.20 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)).
% 13.27/13.20 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).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),K_1))| -hBOOL(hAPP(int,bool,P,K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f51(P,I_1,K_1)),K_1))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),K_1))| -hBOOL(hAPP(int,bool,P,K_1))|hBOOL(hAPP(int,bool,P,$f51(P,I_1,K_1)))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),K_1))| -hBOOL(hAPP(int,bool,P,K_1))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f51(P,I_1,K_1)),one_one(int))))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K_1))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f52(P,I_1,K_1)),K_1))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K_1))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),one_one(int))))|hBOOL(hAPP(int,bool,P,$f52(P,I_1,K_1)))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K_1))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),one_one(int))))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f52(P,I_1,K_1)),one_one(int))))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),I_1))| -hBOOL(hAPP(int,bool,P,K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),$f53(P,K_1,I_1)))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),I_1))| -hBOOL(hAPP(int,bool,P,K_1))|hBOOL(hAPP(int,bool,P,$f53(P,K_1,I_1)))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),I_1))| -hBOOL(hAPP(int,bool,P,K_1))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f53(P,K_1,I_1)),one_one(int))))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),I_1))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),$f54(P,K_1,I_1)))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),I_1))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),one_one(int))))|hBOOL(hAPP(int,bool,P,$f54(P,K_1,I_1)))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),I_1))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),one_one(int))))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f54(P,K_1,I_1)),one_one(int))))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -dense_linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f55(X_a,Z,Y)),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z)).
% 13.27/13.20 0 [] -dense_linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),$f55(X_a,Z,Y)),Z))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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,$f56(X_a,X_b,F,G))),hAPP(X_a,X_b,G,$f56(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)).
% 13.27/13.20 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),$f57(X_b,X_a,C_1,F,Ba,Aa)),$f58(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)).
% 13.27/13.20 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,$f57(X_b,X_a,C_1,F,Ba,Aa))),hAPP(X_b,X_a,F,$f58(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)).
% 13.27/13.20 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),$f59(X_b,X_a,C_1,F,Ba,Aa)),$f60(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)).
% 13.27/13.20 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,$f59(X_b,X_a,C_1,F,Ba,Aa))),hAPP(X_b,X_a,F,$f60(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)).
% 13.27/13.20 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),$f62(X_a,X_b,C_1,Aa,F,Ba)),$f61(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))).
% 13.27/13.20 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,$f62(X_a,X_b,C_1,Aa,F,Ba))),hAPP(X_b,X_a,F,$f61(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))).
% 13.27/13.20 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),$f64(X_a,X_b,C_1,Aa,F,Ba)),$f63(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))).
% 13.27/13.20 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,$f64(X_a,X_b,C_1,Aa,F,Ba))),hAPP(X_b,X_a,F,$f63(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))).
% 13.27/13.20 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),$f65(X_a,Z,X,Y)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z)).
% 13.27/13.20 0 [] -dense_linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f65(X_a,Z,X,Y)),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z)).
% 13.27/13.20 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),$f65(X_a,Z,X,Y)),Z))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z)).
% 13.27/13.20 0 [] -order(X_a)| -order(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C_1),hAPP(X_a,X_b,F,Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f66(X_b,X_a,C_1,F,Ba,Aa)),$f67(X_b,X_a,C_1,F,Ba,Aa)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Aa))).
% 13.27/13.20 0 [] -order(X_a)| -order(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C_1),hAPP(X_a,X_b,F,Ba)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,$f66(X_b,X_a,C_1,F,Ba,Aa))),hAPP(X_a,X_b,F,$f67(X_b,X_a,C_1,F,Ba,Aa))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Aa))).
% 13.27/13.20 0 [] -order(X_a)| -order(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ba),Aa))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),$f68(X_b,X_a,C_1,F,Ba,Aa)),$f69(X_b,X_a,C_1,F,Ba,Aa)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Aa))).
% 13.27/13.20 0 [] -order(X_a)| -order(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ba),Aa))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Ba)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,$f68(X_b,X_a,C_1,F,Ba,Aa))),hAPP(X_a,X_b,F,$f69(X_b,X_a,C_1,F,Ba,Aa))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Aa))).
% 13.27/13.20 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,Ba)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f71(X_a,X_b,F,C_1,Aa,Ba)),$f70(X_a,X_b,F,C_1,Aa,Ba)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),C_1)).
% 13.27/13.20 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,Ba)),C_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,$f71(X_a,X_b,F,C_1,Aa,Ba))),hAPP(X_a,X_b,F,$f70(X_a,X_b,F,C_1,Aa,Ba))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),C_1)).
% 13.27/13.20 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Ba)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),$f73(X_a,X_b,F,C_1,Aa,Ba)),$f72(X_a,X_b,F,C_1,Aa,Ba)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),C_1)).
% 13.27/13.20 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Aa),Ba))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Ba)),C_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,$f73(X_a,X_b,F,C_1,Aa,Ba))),hAPP(X_a,X_b,F,$f72(X_a,X_b,F,C_1,Aa,Ba))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),C_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,P,K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),$f74(I_1,P,K_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f75(I_1,P,K_1)),K_1))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,P,K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),$f74(I_1,P,K_1)))|hBOOL(hAPP(int,bool,P,$f75(I_1,P,K_1)))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,P,K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),$f74(I_1,P,K_1)))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f75(I_1,P,K_1)),one_one(int))))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,P,K_1))|hBOOL(hAPP(int,bool,P,$f74(I_1,P,K_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f75(I_1,P,K_1)),K_1))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,P,K_1))|hBOOL(hAPP(int,bool,P,$f74(I_1,P,K_1)))|hBOOL(hAPP(int,bool,P,$f75(I_1,P,K_1)))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,P,K_1))|hBOOL(hAPP(int,bool,P,$f74(I_1,P,K_1)))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f75(I_1,P,K_1)),one_one(int))))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,P,K_1))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f74(I_1,P,K_1)),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f75(I_1,P,K_1)),K_1))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,P,K_1))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f74(I_1,P,K_1)),one_one(int))))|hBOOL(hAPP(int,bool,P,$f75(I_1,P,K_1)))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,P,K_1))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f74(I_1,P,K_1)),one_one(int))))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f75(I_1,P,K_1)),one_one(int))))|hBOOL(hAPP(int,bool,P,I_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),C))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A_1),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),A_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),$f76(X_1,P)))|hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f76(X_1,P)),one_one(int))))|hBOOL(hAPP(int,bool,P,X_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,P,$f76(X_1,P)))|hBOOL(hAPP(int,bool,P,X_1)).
% 13.27/13.20 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))| -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),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),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)).
% 13.27/13.20 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(X_b),C_1),Ba))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),$f77(X_b,X_a,C_1,F,Ba,Aa)),$f78(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)).
% 13.27/13.20 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(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,$f77(X_b,X_a,C_1,F,Ba,Aa))),hAPP(X_b,X_a,F,$f78(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)).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 0 [] -zero(X_a)|zero_zero(X_a)!=ti(X_a,X_1)|ti(X_a,X_1)=zero_zero(X_a).
% 13.27/13.20 0 [] -zero(X_a)|zero_zero(X_a)=ti(X_a,X_1)|ti(X_a,X_1)!=zero_zero(X_a).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 0 [] -zero_ne_q_one(X_a)|one_one(X_a)!=zero_zero(X_a).
% 13.27/13.20 0 [] -zero_ne_q_one(X_a)|zero_zero(X_a)!=one_one(X_a).
% 13.27/13.20 0 [] zero_zero(int)!=one_one(int).
% 13.27/13.20 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),zero_zero(int))=Z.
% 13.27/13.20 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),Z)=Z.
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))| -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))).
% 13.27/13.20 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))| -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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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)).
% 13.27/13.20 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))).
% 13.27/13.20 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)).
% 13.27/13.20 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))).
% 13.27/13.20 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)).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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)).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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))).
% 13.27/13.20 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)).
% 13.27/13.20 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))).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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))).
% 13.27/13.20 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)).
% 13.27/13.20 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))).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 0 [] -semiri456707255roduct(X_a)|ti(X_a,R_1)=zero_zero(X_a)|ti(X_a,A_1)!=ti(X_a,B)|ti(X_a,C)=ti(X_a,D)|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_1),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_1),D)).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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)))).
% 13.27/13.20 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))).
% 13.27/13.20 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))).
% 13.27/13.20 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)),Z)!=zero_zero(int).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),L_1))|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_1)),zero_zero(int))).
% 13.27/13.20 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),L_1))| -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_1)),zero_zero(int))).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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))| -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))).
% 13.27/13.20 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))| -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))).
% 13.27/13.20 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))| -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))).
% 13.27/13.20 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))| -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))).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 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)).
% 13.27/13.20 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)).
% 13.27/13.20 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)))).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)).
% 13.27/13.20 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)).
% 13.27/13.20 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_1)!=one_one(int)|M_1=one_one(int).
% 13.27/13.20 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_1)!=one_one(int)|N_1=one_one(int).
% 13.27/13.20 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_1)=one_one(int)|M_1!=one_one(int)|N_1!=one_one(int).
% 13.27/13.20 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_1)),Z_1)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),zero_zero(int))).
% 13.27/13.20 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_1)),Z_1)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),zero_zero(int))).
% 13.27/13.20 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))| -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),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),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z))).
% 13.27/13.20 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_1),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_1),A_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Q)).
% 13.27/13.20 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_1),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_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q),one_one(int))).
% 13.27/13.20 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_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Q_1)).
% 13.27/13.20 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_2)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),zero_zero(int))).
% 13.27/13.20 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_1)!=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_2)| -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_2)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_2))| -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)).
% 13.27/13.20 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_2)),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_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_1),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q),Q_1)).
% 13.27/13.20 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_1)!=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_2)| -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_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_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),B_1),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q),Q_1)).
% 13.27/13.20 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_2)),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_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N))|hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M),N)!=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_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S),T_3))|R_1=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)).
% 13.27/13.20 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))).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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).
% 13.27/13.20 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)))).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R_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),R_2),R_1),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_2!=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))|R_1!=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))|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)).
% 13.27/13.20 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))).
% 13.27/13.20 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))).
% 13.27/13.20 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),zero_zero(int))).
% 13.27/13.20 0 [] hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M),N)=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),M),N),one_one(int)),zero_zero(int)),zero_zero(int)),one_one(int)).
% 13.27/13.20 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),one_one(int))).
% 13.27/13.20 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)).
% 13.27/13.20 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,P,$f79(K_1,P,D_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K_1))| -hBOOL(hAPP(int,bool,P,X_2))|hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_1)))).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f79(K_1,P,D_1)),D_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K_1))| -hBOOL(hAPP(int,bool,P,X_2))|hBOOL(hAPP(int,bool,P,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_1)))).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,P,$f80(K_1,P,D_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K_1))| -hBOOL(hAPP(int,bool,P,X_2))|hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_1)))).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))| -hBOOL(hAPP(int,bool,P,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f80(K_1,P,D_1)),D_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K_1))| -hBOOL(hAPP(int,bool,P,X_2))|hBOOL(hAPP(int,bool,P,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_1)))).
% 13.27/13.21 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)),$f81(X_a,X,Y)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)).
% 13.27/13.21 0 [] -linord1117847801e_zero(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f81(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)).
% 13.27/13.21 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),$f81(X_a,X,Y)),X)),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)).
% 13.27/13.21 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),$f82(X_a,T_3)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),T_3),X_2)).
% 13.27/13.21 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f83(X_a,T_3)),X_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),T_3),X_2)).
% 13.27/13.21 0 [] -linordered_field(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),$f84(X_a,X,Y)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)).
% 13.27/13.21 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),$f84(X_a,X,Y))))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)).
% 13.27/13.21 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f85(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)).
% 13.27/13.21 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),$f86(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)).
% 13.27/13.21 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_1)|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_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_1),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_1))).
% 13.27/13.21 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_1)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),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_1))).
% 13.27/13.21 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_1)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_1),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_1),zero_zero(int)))|hBOOL(hAPP(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_1))).
% 13.27/13.21 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)))).
% 13.27/13.21 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_1)))|A_1=zero_zero(int)|R_1=zero_zero(int).
% 13.27/13.21 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_1)))| -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_2)))|B=zero_zero(int)|Q=Q_1.
% 13.27/13.21 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_1)))| -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_2)))|B=zero_zero(int)|R_1=R_2.
% 13.27/13.21 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_1)))|A_1=zero_zero(int)|Q=one_one(int).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,P1,$f88(P,P1,D_1)))|hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f88(P,P1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f87(P,P1,D_1)),D_1))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f89(P,P1,D_1,Z_2)),Z_2))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,P,$f90(P,P1,D_1))).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,P1,$f88(P,P1,D_1)))|hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f88(P,P1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f87(P,P1,D_1)),D_1))))|hBOOL(hAPP(int,bool,P,$f89(P,P1,D_1,Z_2)))|hBOOL(hAPP(int,bool,P1,$f89(P,P1,D_1,Z_2)))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,P,$f90(P,P1,D_1))).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,P1,$f88(P,P1,D_1)))|hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f88(P,P1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f87(P,P1,D_1)),D_1))))| -hBOOL(hAPP(int,bool,P,$f89(P,P1,D_1,Z_2)))| -hBOOL(hAPP(int,bool,P1,$f89(P,P1,D_1,Z_2)))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,P,$f90(P,P1,D_1))).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))| -hBOOL(hAPP(int,bool,P1,$f88(P,P1,D_1)))| -hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f88(P,P1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f87(P,P1,D_1)),D_1))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f89(P,P1,D_1,Z_2)),Z_2))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,P,$f90(P,P1,D_1))).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))| -hBOOL(hAPP(int,bool,P1,$f88(P,P1,D_1)))| -hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f88(P,P1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f87(P,P1,D_1)),D_1))))|hBOOL(hAPP(int,bool,P,$f89(P,P1,D_1,Z_2)))|hBOOL(hAPP(int,bool,P1,$f89(P,P1,D_1,Z_2)))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,P,$f90(P,P1,D_1))).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))| -hBOOL(hAPP(int,bool,P1,$f88(P,P1,D_1)))| -hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f88(P,P1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f87(P,P1,D_1)),D_1))))| -hBOOL(hAPP(int,bool,P,$f89(P,P1,D_1,Z_2)))| -hBOOL(hAPP(int,bool,P1,$f89(P,P1,D_1,Z_2)))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,P,$f90(P,P1,D_1))).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,P_1,$f92(P,P_1,D_1)))|hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f92(P,P_1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f91(P,P_1,D_1)),D_1))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),$f93(P,P_1,D_1,Z_2)))| -hBOOL(hAPP(int,bool,P_1,X1))|hBOOL(hAPP(int,bool,P,$f94(P,P_1,D_1))).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,P_1,$f92(P,P_1,D_1)))|hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f92(P,P_1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f91(P,P_1,D_1)),D_1))))|hBOOL(hAPP(int,bool,P,$f93(P,P_1,D_1,Z_2)))|hBOOL(hAPP(int,bool,P_1,$f93(P,P_1,D_1,Z_2)))| -hBOOL(hAPP(int,bool,P_1,X1))|hBOOL(hAPP(int,bool,P,$f94(P,P_1,D_1))).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,P_1,$f92(P,P_1,D_1)))|hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f92(P,P_1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f91(P,P_1,D_1)),D_1))))| -hBOOL(hAPP(int,bool,P,$f93(P,P_1,D_1,Z_2)))| -hBOOL(hAPP(int,bool,P_1,$f93(P,P_1,D_1,Z_2)))| -hBOOL(hAPP(int,bool,P_1,X1))|hBOOL(hAPP(int,bool,P,$f94(P,P_1,D_1))).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))| -hBOOL(hAPP(int,bool,P_1,$f92(P,P_1,D_1)))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f92(P,P_1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f91(P,P_1,D_1)),D_1))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),$f93(P,P_1,D_1,Z_2)))| -hBOOL(hAPP(int,bool,P_1,X1))|hBOOL(hAPP(int,bool,P,$f94(P,P_1,D_1))).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))| -hBOOL(hAPP(int,bool,P_1,$f92(P,P_1,D_1)))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f92(P,P_1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f91(P,P_1,D_1)),D_1))))|hBOOL(hAPP(int,bool,P,$f93(P,P_1,D_1,Z_2)))|hBOOL(hAPP(int,bool,P_1,$f93(P,P_1,D_1,Z_2)))| -hBOOL(hAPP(int,bool,P_1,X1))|hBOOL(hAPP(int,bool,P,$f94(P,P_1,D_1))).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))| -hBOOL(hAPP(int,bool,P_1,$f92(P,P_1,D_1)))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f92(P,P_1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f91(P,P_1,D_1)),D_1))))| -hBOOL(hAPP(int,bool,P,$f93(P,P_1,D_1,Z_2)))| -hBOOL(hAPP(int,bool,P_1,$f93(P,P_1,D_1,Z_2)))| -hBOOL(hAPP(int,bool,P_1,X1))|hBOOL(hAPP(int,bool,P,$f94(P,P_1,D_1))).
% 13.27/13.21 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).
% 13.27/13.21 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).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N),zero_zero(int)))|hAPP(int,int,zfact,N)=one_one(int).
% 13.27/13.21 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),N),zero_zero(int)))|hAPP(int,int,zfact,N)=hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N),hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N),one_one(int)))).
% 13.27/13.21 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))).
% 13.27/13.21 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).
% 13.27/13.21 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))).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(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))),one_one(int))),D))),Z)).
% 13.27/13.21 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).
% 13.27/13.21 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).
% 13.27/13.21 0 [] -ordere142940540dd_abs(X_a)|hAPP(X_a,X_a,abs_abs(X_a),zero_zero(X_a))=zero_zero(X_a).
% 13.27/13.21 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).
% 13.27/13.21 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).
% 13.27/13.21 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).
% 13.27/13.21 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))).
% 13.27/13.21 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).
% 13.27/13.21 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).
% 13.27/13.21 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).
% 13.27/13.21 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))).
% 13.27/13.21 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))|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))).
% 13.27/13.21 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)))).
% 13.27/13.21 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)))).
% 13.27/13.21 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)))).
% 13.27/13.21 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)))).
% 13.27/13.21 0 [] hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))!=one_one(int)|hAPP(int,int,abs_abs(int),M)=one_one(int).
% 13.27/13.21 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))).
% 13.27/13.21 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)).
% 13.27/13.21 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)).
% 13.27/13.21 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).
% 13.27/13.21 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)).
% 13.27/13.21 0 [] -linordered_idom(X_a)|hAPP(X_a,X_a,abs_abs(X_a),one_one(X_a))=one_one(X_a).
% 13.27/13.21 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)).
% 13.27/13.21 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).
% 13.27/13.21 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)).
% 13.27/13.21 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)).
% 13.27/13.21 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)).
% 13.27/13.21 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)).
% 13.27/13.21 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)).
% 13.27/13.21 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)))),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))))).
% 13.27/13.21 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)))).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z_1)),one_one(int)))|Z_1=zero_zero(int).
% 13.27/13.21 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z_1)),one_one(int)))|Z_1!=zero_zero(int).
% 13.27/13.21 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)).
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),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))),one_one(int))),D)))).
% 13.27/13.21 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))|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)),X_1)).
% 13.27/13.21 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))|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))).
% 13.27/13.21 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))| -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)),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))).
% 13.27/13.21 0 [] L!=zero_zero(int)|hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)=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)).
% 13.27/13.21 0 [] L=zero_zero(int)|hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)=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)).
% 13.27/13.21 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f95(K_1,F,N_1)),N_1))| -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_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f96(K_1,F,N_1)),N_1)).
% 13.27/13.21 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f95(K_1,F,N_1)),N_1))| -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_1)))|hAPP(nat,int,F,$f96(K_1,F,N_1))=K_1.
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),$f95(K_1,F,N_1)),one_one(nat)))),hAPP(nat,int,F,$f95(K_1,F,N_1))))),one_one(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f96(K_1,F,N_1)),N_1)).
% 13.27/13.21 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),$f95(K_1,F,N_1)),one_one(nat)))),hAPP(nat,int,F,$f95(K_1,F,N_1))))),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_1)))|hAPP(nat,int,F,$f96(K_1,F,N_1))=K_1.
% 13.27/13.21 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f97(K_1,F,N_1)),N_1))| -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_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f98(K_1,F,N_1)),N_1)).
% 13.27/13.21 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f97(K_1,F,N_1)),N_1))| -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_1)))|hAPP(nat,int,F,$f98(K_1,F,N_1))=K_1.
% 13.27/13.21 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),$f97(K_1,F,N_1)),one_one(nat)))),hAPP(nat,int,F,$f97(K_1,F,N_1))))),one_one(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_1),hAPP(nat,int,F,N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f98(K_1,F,N_1)),N_1)).
% 13.27/13.21 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),$f97(K_1,F,N_1)),one_one(nat)))),hAPP(nat,int,F,$f97(K_1,F,N_1))))),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_1)))|hAPP(nat,int,F,$f98(K_1,F,N_1))=K_1.
% 13.27/13.21 0 [] M!=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)=zero_zero(nat).
% 13.27/13.21 0 [] M=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),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)).
% 13.27/13.21 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N)).
% 13.27/13.21 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M).
% 13.27/13.21 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)),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),K)).
% 13.27/13.21 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)),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),K)).
% 13.27/13.21 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).
% 13.27/13.21 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))=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)).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N)=zero_zero(nat).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),zero_zero(nat))=zero_zero(nat).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)!=zero_zero(nat)|M_1=zero_zero(nat)|N_1=zero_zero(nat).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)=zero_zero(nat)|M_1!=zero_zero(nat).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)=zero_zero(nat)|N_1!=zero_zero(nat).
% 13.27/13.21 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_1)|M_1=N_1|K_1=zero_zero(nat).
% 13.27/13.21 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_1)|M_1!=N_1.
% 13.27/13.21 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_1)|K_1!=zero_zero(nat).
% 13.27/13.21 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_1),K_1)|M_1=N_1|K_1=zero_zero(nat).
% 13.27/13.21 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_1),K_1)|M_1!=N_1.
% 13.27/13.21 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_1),K_1)|K_1!=zero_zero(nat).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)!=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M)!=zero_zero(nat)|M=N.
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M)=zero_zero(nat).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat))=M.
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N)=zero_zero(nat).
% 13.27/13.21 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)),K)).
% 13.27/13.21 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M))).
% 13.27/13.21 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)).
% 13.27/13.21 0 [] M_1=N_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1)).
% 13.27/13.21 0 [] M_1!=N_1| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 13.27/13.21 0 [] M_1!=N_1| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1)).
% 13.27/13.21 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)).
% 13.27/13.21 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)).
% 13.27/13.21 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M))|M!=N.
% 13.27/13.21 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3))|S!=T_3.
% 13.27/13.21 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))|M_1=N_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P,N_1),M_1)).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M).
% 13.27/13.21 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))=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)).
% 13.27/13.21 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))=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)).
% 13.27/13.21 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)),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),K)).
% 13.27/13.21 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)),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),K)).
% 13.27/13.21 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_1)|M_1=N_1.
% 13.27/13.21 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_1)|M_1!=N_1.
% 13.27/13.21 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_1),K_1)|M_1=N_1.
% 13.27/13.21 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_1),K_1)|M_1!=N_1.
% 13.27/13.21 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),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N).
% 13.27/13.21 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))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N).
% 13.27/13.21 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)).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),N)=M.
% 13.27/13.21 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)),N)=M.
% 13.27/13.21 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)),M)).
% 13.27/13.21 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M))).
% 13.27/13.21 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),L)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),L))).
% 13.27/13.21 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),N))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),I))=I.
% 13.27/13.21 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_1))|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_1),K_1)|M_1=N_1.
% 13.27/13.21 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_1))|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_1),K_1)|M_1!=N_1.
% 13.27/13.21 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))|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),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N).
% 13.27/13.21 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_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_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1)).
% 13.27/13.21 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_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_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1)).
% 13.27/13.21 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),N)).
% 13.27/13.21 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M)).
% 13.27/13.21 0 [] M!=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N)).
% 13.27/13.21 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)).
% 13.27/13.21 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M))|M=N.
% 13.27/13.21 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))|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))).
% 13.27/13.21 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))).
% 13.27/13.21 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))).
% 13.27/13.21 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)))).
% 13.27/13.21 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))).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N)=N.
% 13.27/13.21 0 [] one_one(nat)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)|M_1=one_one(nat).
% 13.27/13.21 0 [] one_one(nat)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)|N_1=one_one(nat).
% 13.27/13.21 0 [] one_one(nat)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)|M_1!=one_one(nat)|N_1!=one_one(nat).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),one_one(nat))=N.
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)!=one_one(nat)|M_1=one_one(nat).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)!=one_one(nat)|N_1=one_one(nat).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)=one_one(nat)|M_1!=one_one(nat)|N_1!=one_one(nat).
% 13.27/13.21 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_1),M_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 13.27/13.21 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_1),M_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 13.27/13.21 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),M)).
% 13.27/13.21 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))).
% 13.27/13.21 0 [] N_1=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)).
% 13.27/13.21 0 [] N_1!=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)).
% 13.27/13.21 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))).
% 13.27/13.21 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))|N!=zero_zero(nat).
% 13.27/13.21 0 [] N=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)).
% 13.27/13.21 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))).
% 13.27/13.21 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))).
% 13.27/13.21 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_1),K_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)).
% 13.27/13.21 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_1),K_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 13.27/13.21 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_1),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_1)).
% 13.27/13.21 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_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)).
% 13.27/13.21 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_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 13.27/13.21 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_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_1)).
% 13.27/13.21 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_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)).
% 13.27/13.21 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_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)).
% 13.27/13.21 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_1)))| -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_1)).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N)=N.
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),zero_zero(nat))=M.
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)!=zero_zero(nat)|M_1=zero_zero(nat).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)!=zero_zero(nat)|N_1=zero_zero(nat).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)=zero_zero(nat)|M_1!=zero_zero(nat)|N_1!=zero_zero(nat).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)!=M|N=zero_zero(nat).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M))=zero_zero(nat).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)!=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1)).
% 13.27/13.21 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1)).
% 13.27/13.21 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)=zero_zero(nat).
% 13.27/13.21 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N)).
% 13.27/13.21 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),zero_zero(nat)))|N_1=zero_zero(nat).
% 13.27/13.21 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),zero_zero(nat)))|N_1!=zero_zero(nat).
% 13.27/13.21 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_1),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_1)).
% 13.27/13.21 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_1),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_1)).
% 13.27/13.21 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))=M.
% 13.27/13.21 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)).
% 13.27/13.21 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)).
% 13.27/13.21 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))|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))).
% 13.27/13.21 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))).
% 13.27/13.21 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))).
% 13.27/13.21 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))).
% 13.27/13.21 0 [] -preorder(T_1)|preorder(fun(T_2,T_1)).
% 13.27/13.21 0 [] -order(T_1)|order(fun(T_2,T_1)).
% 13.27/13.21 0 [] -ord(T_1)|ord(fun(T_2,T_1)).
% 13.27/13.21 0 [] -minus(T_1)|minus(fun(T_2,T_1)).
% 13.27/13.21 0 [] semiri456707255roduct(int).
% 13.27/13.21 0 [] ordere223160158up_add(int).
% 13.27/13.21 0 [] ordere236663937imp_le(int).
% 13.27/13.21 0 [] linord893533164strict(int).
% 13.27/13.21 0 [] linord626643107strict(int).
% 13.27/13.21 0 [] linord20386208strict(int).
% 13.27/13.21 0 [] ordere779506340up_add(int).
% 13.27/13.21 0 [] ordere142940540dd_abs(int).
% 13.27/13.21 0 [] ordere216010020id_add(int).
% 13.27/13.21 0 [] linord219039673up_add(int).
% 13.27/13.21 0 [] cancel146912293up_add(int).
% 13.27/13.21 0 [] ordere453448008miring(int).
% 13.27/13.21 0 [] linord581940658strict(int).
% 13.27/13.21 0 [] ring_n68954251visors(int).
% 13.27/13.21 0 [] ordere1490568538miring(int).
% 13.27/13.21 0 [] linord1278240602ring_1(int).
% 13.27/13.21 0 [] ordered_ab_group_add(int).
% 13.27/13.21 0 [] cancel_semigroup_add(int).
% 13.27/13.21 0 [] linordered_semiring(int).
% 13.27/13.21 0 [] linordered_semidom(int).
% 13.27/13.21 0 [] ab_semigroup_mult(int).
% 13.27/13.21 0 [] comm_monoid_mult(int).
% 13.27/13.21 0 [] ab_semigroup_add(int).
% 13.27/13.21 0 [] ordered_semiring(int).
% 13.27/13.21 0 [] ordered_ring_abs(int).
% 13.27/13.21 0 [] no_zero_divisors(int).
% 13.27/13.21 0 [] comm_monoid_add(int).
% 13.27/13.21 0 [] linordered_ring(int).
% 13.27/13.21 0 [] linordered_idom(int).
% 13.27/13.21 0 [] comm_semiring_1(int).
% 13.27/13.21 0 [] comm_semiring(int).
% 13.27/13.21 0 [] ab_group_add(int).
% 13.27/13.21 0 [] zero_ne_q_one(int).
% 13.27/13.21 0 [] ordered_ring(int).
% 13.27/13.21 0 [] preorder(int).
% 13.27/13.21 0 [] linorder(int).
% 13.27/13.21 0 [] monoid_mult(int).
% 13.27/13.21 0 [] monoid_add(int).
% 13.27/13.21 0 [] group_add(int).
% 13.27/13.21 0 [] mult_zero(int).
% 13.27/13.21 0 [] order(int).
% 13.27/13.21 0 [] semiring(int).
% 13.27/13.21 0 [] ord(int).
% 13.27/13.21 0 [] ring_1(int).
% 13.27/13.21 0 [] minus(int).
% 13.27/13.21 0 [] zero(int).
% 13.27/13.21 0 [] ring(int).
% 13.27/13.21 0 [] one(int).
% 13.27/13.21 0 [] semiri456707255roduct(nat).
% 13.27/13.21 0 [] ordere223160158up_add(nat).
% 13.27/13.21 0 [] ordere236663937imp_le(nat).
% 13.27/13.21 0 [] linord893533164strict(nat).
% 13.27/13.21 0 [] linord20386208strict(nat).
% 13.27/13.21 0 [] ordere779506340up_add(nat).
% 13.27/13.21 0 [] ordere216010020id_add(nat).
% 13.27/13.21 0 [] cancel146912293up_add(nat).
% 13.27/13.21 0 [] ordere453448008miring(nat).
% 13.27/13.21 0 [] ordere1490568538miring(nat).
% 13.27/13.21 0 [] cancel_semigroup_add(nat).
% 13.27/13.21 0 [] linordered_semiring(nat).
% 13.27/13.21 0 [] linordered_semidom(nat).
% 13.27/13.21 0 [] ab_semigroup_mult(nat).
% 13.27/13.21 0 [] comm_monoid_mult(nat).
% 13.27/13.21 0 [] ab_semigroup_add(nat).
% 13.27/13.21 0 [] ordered_semiring(nat).
% 13.27/13.21 0 [] no_zero_divisors(nat).
% 13.27/13.21 0 [] comm_monoid_add(nat).
% 13.27/13.21 0 [] comm_semiring_1(nat).
% 13.27/13.21 0 [] comm_semiring(nat).
% 13.27/13.21 0 [] zero_ne_q_one(nat).
% 13.27/13.21 0 [] preorder(nat).
% 13.27/13.21 0 [] linorder(nat).
% 13.27/13.21 0 [] monoid_mult(nat).
% 13.27/13.21 0 [] monoid_add(nat).
% 13.27/13.21 0 [] mult_zero(nat).
% 13.27/13.21 0 [] order(nat).
% 13.27/13.21 0 [] semiring(nat).
% 13.27/13.21 0 [] ord(nat).
% 13.27/13.21 0 [] minus(nat).
% 13.27/13.21 0 [] zero(nat).
% 13.27/13.21 0 [] one(nat).
% 13.27/13.21 0 [] preorder(bool).
% 13.27/13.21 0 [] order(bool).
% 13.27/13.21 0 [] ord(bool).
% 13.27/13.21 0 [] minus(bool).
% 13.27/13.21 0 [] ti(T,ti(T,A))=ti(T,A).
% 13.27/13.21 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,twoSqu579703163sum2sq,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,twoSqu579703163sum2sq,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,twoSqu579703163sum2sq,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)))).
% 13.27/13.21 end_of_list.
% 13.27/13.21
% 13.27/13.21 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 13.27/13.21
% 13.27/13.21 This ia a non-Horn set with equality. The strategy will be
% 13.27/13.21 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 13.27/13.21 deletion, with positive clauses in sos and nonpositive
% 13.27/13.21 clauses in usable.
% 13.27/13.21
% 13.27/13.21 dependent: set(knuth_bendix).
% 13.27/13.21 dependent: set(anl_eq).
% 13.27/13.21 dependent: set(para_from).
% 13.27/13.21 dependent: set(para_into).
% 13.27/13.21 dependent: clear(para_from_right).
% 13.27/13.21 dependent: clear(para_into_right).
% 13.27/13.21 dependent: set(para_from_vars).
% 13.27/13.21 dependent: set(eq_units_both_ways).
% 13.27/13.21 dependent: set(dynamic_demod_all).
% 13.27/13.21 dependent: set(dynamic_demod).
% 13.27/13.21 dependent: set(order_eq).
% 13.27/13.21 dependent: set(back_demod).
% 13.27/13.21 dependent: set(lrpo).
% 13.27/13.21 dependent: set(hyper_res).
% 13.27/13.21 dependent: set(unit_deletion).
% 13.27/13.21 dependent: set(factor).
% 13.27/13.21
% 13.27/13.21 ------------> process usable:
% 13.27/13.21 ** KEPT (pick-wt=11): 1 [] -ordere142940540dd_abs(A)|ti(fun(A,A),abs_abs(A))=abs_abs(A).
% 13.27/13.21 ** KEPT (pick-wt=13): 2 [] -minus(A)|ti(fun(A,fun(A,A)),minus_minus(A))=minus_minus(A).
% 13.27/13.21 ** KEPT (pick-wt=9): 3 [] -one(A)|ti(A,one_one(A))=one_one(A).
% 13.27/13.21 ** KEPT (pick-wt=13): 4 [] -monoid_add(A)|ti(fun(A,fun(A,A)),plus_plus(A))=plus_plus(A).
% 13.27/13.21 ** KEPT (pick-wt=13): 5 [] -ab_semigroup_add(A)|ti(fun(A,fun(A,A)),plus_plus(A))=plus_plus(A).
% 13.27/13.21 ** KEPT (pick-wt=13): 6 [] -cancel_semigroup_add(A)|ti(fun(A,fun(A,A)),plus_plus(A))=plus_plus(A).
% 13.27/13.21 ** KEPT (pick-wt=13): 7 [] -no_zero_divisors(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 13.27/13.21 ** KEPT (pick-wt=13): 8 [] -mult_zero(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 13.27/13.21 ** KEPT (pick-wt=13): 9 [] -monoid_mult(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 13.27/13.21 ** KEPT (pick-wt=13): 10 [] -semiring(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 13.27/13.21 ** KEPT (pick-wt=13): 11 [] -ab_semigroup_mult(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 13.27/13.21 ** KEPT (pick-wt=9): 12 [] -zero(A)|ti(A,zero_zero(A))=zero_zero(A).
% 13.27/13.21 ** KEPT (pick-wt=13): 13 [] -ord(A)|ti(fun(A,fun(A,bool)),ord_less(A))=ord_less(A).
% 13.27/13.21 ** KEPT (pick-wt=13): 14 [] -ord(A)|ti(fun(A,fun(A,bool)),ord_less_e_q(A))=ord_less_e_q(A).
% 13.27/13.21 ** KEPT (pick-wt=6): 15 [] -hBOOL(ti(bool,A))|hBOOL(A).
% 13.27/13.21 ** KEPT (pick-wt=6): 16 [] hBOOL(ti(bool,A))| -hBOOL(A).
% 13.27/13.21 ** KEPT (pick-wt=93): 18 [copy,17,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)).
% 13.27/13.21 ** KEPT (pick-wt=137): 20 [copy,19,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)).
% 13.27/13.21 ** KEPT (pick-wt=87): 21 [] -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).
% 13.27/13.21 ** KEPT (pick-wt=87): 22 [] -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).
% 13.27/13.21 ** KEPT (pick-wt=87): 23 [] -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).
% 13.27/13.21 ** KEPT (pick-wt=87): 24 [] -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).
% 13.27/13.21 ** KEPT (pick-wt=33): 25 [] -hBOOL(hAPP(int,bool,twoSqu420862341sum2sq,A))|hAPP(product_prod(int,int),int,twoSqu579703163sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),$f2(A)),$f1(A)))=A.
% 13.27/13.21 ** KEPT (pick-wt=31): 26 [] hBOOL(hAPP(int,bool,twoSqu420862341sum2sq,A))|hAPP(product_prod(int,int),int,twoSqu579703163sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),B),C))!=A.
% 13.27/13.21 ** KEPT (pick-wt=28): 27 [] 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).
% 13.27/13.21 ** KEPT (pick-wt=29): 28 [] -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).
% 13.27/13.21 ** KEPT (pick-wt=49): 29 [] -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)).
% 13.27/13.21 ** KEPT (pick-wt=34): 30 [] -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).
% 13.27/13.21 ** KEPT (pick-wt=34): 31 [] -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).
% 13.27/13.21 ** KEPT (pick-wt=34): 32 [] -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).
% 13.27/13.21 Following clause subsumed by 30 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).
% 13.27/13.21 ** KEPT (pick-wt=34): 33 [] -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).
% 13.27/13.21 Following clause subsumed by 32 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).
% 13.27/13.21 ** KEPT (pick-wt=34): 34 [] -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).
% 13.27/13.21 ** KEPT (pick-wt=49): 35 [] -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)).
% 13.27/13.21 ** KEPT (pick-wt=41): 36 [] -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).
% 13.27/13.21 ** KEPT (pick-wt=41): 37 [] -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).
% 13.27/13.21 ** KEPT (pick-wt=82): 39 [copy,38,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)).
% 13.27/13.21 ** KEPT (pick-wt=60): 40 [] -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)).
% 13.27/13.21 Following clause subsumed by 40 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)).
% 13.27/13.21 ** KEPT (pick-wt=60): 41 [] -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)).
% 13.27/13.21 ** KEPT (pick-wt=60): 43 [copy,42,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)).
% 13.27/13.21 Following clause subsumed by 43 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)).
% 13.27/13.21 ** KEPT (pick-wt=60): 44 [] -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)).
% 13.27/13.21 Following clause subsumed by 44 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)).
% 13.27/13.21 ** KEPT (pick-wt=60): 46 [copy,45,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)).
% 13.27/13.21 Following clause subsumed by 46 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)).
% 13.27/13.21 ** KEPT (pick-wt=71): 47 [] -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)).
% 13.27/13.21 ** KEPT (pick-wt=29): 48 [] -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).
% 13.27/13.21 ** KEPT (pick-wt=85): 49 [] -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).
% 13.27/13.21 ** KEPT (pick-wt=78): 50 [] -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).
% 13.27/13.21 ** KEPT (pick-wt=78): 51 [] -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).
% 13.27/13.21 ** KEPT (pick-wt=60): 52 [] -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).
% 13.27/13.21 ** KEPT (pick-wt=60): 53 [] -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)).
% 13.27/13.21 Following clause subsumed by 49 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)).
% 13.27/13.21 Following clause subsumed by 50 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)).
% 13.27/13.21 Following clause subsumed by 51 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)).
% 13.34/13.22 ** KEPT (pick-wt=60): 55 [copy,54,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)).
% 13.34/13.22 ** KEPT (pick-wt=51): 56 [] -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)).
% 13.34/13.22 Following clause subsumed by 56 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)).
% 13.34/13.22 ** KEPT (pick-wt=42): 57 [] 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).
% 13.34/13.22 ** KEPT (pick-wt=42): 58 [] 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).
% 13.34/13.22 Following clause subsumed by 57 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).
% 13.34/13.22 Following clause subsumed by 58 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).
% 13.34/13.22 ** KEPT (pick-wt=49): 59 [] 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).
% 13.34/13.22 ** KEPT (pick-wt=35): 60 [] -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))).
% 13.34/13.22 ** KEPT (pick-wt=38): 61 [] 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)))).
% 13.34/13.22 ** KEPT (pick-wt=71): 62 [] -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)).
% 13.34/13.22 ** KEPT (pick-wt=18): 63 [] -ab_sem1668676832m_mult(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)=ti(A,B).
% 13.34/13.22 Following clause subsumed by 63 during input processing: 0 [] -ab_sem1668676832m_mult(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)=ti(A,B).
% 13.34/13.22 ** KEPT (pick-wt=27): 64 [] -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).
% 13.34/13.22 ** KEPT (pick-wt=38): 65 [] -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).
% 13.34/13.22 ** KEPT (pick-wt=49): 66 [] -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)).
% 13.34/13.22 ** KEPT (pick-wt=49): 68 [copy,67,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)).
% 13.34/13.22 Following clause subsumed by 68 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)).
% 13.34/13.22 ** KEPT (pick-wt=49): 69 [] -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).
% 13.34/13.22 Following clause subsumed by 68 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))).
% 13.34/13.22 Following clause subsumed by 66 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)).
% 13.34/13.22 ** KEPT (pick-wt=71): 70 [] -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)).
% 13.34/13.22 ** KEPT (pick-wt=27): 71 [] -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).
% 13.34/13.22 ** KEPT (pick-wt=49): 72 [] -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)).
% 13.34/13.22 ** KEPT (pick-wt=49): 74 [copy,73,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)).
% 13.34/13.22 Following clause subsumed by 74 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)).
% 13.34/13.22 ** KEPT (pick-wt=49): 75 [] -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).
% 13.34/13.22 ** KEPT (pick-wt=38): 76 [] -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)))).
% 13.34/13.22 ** KEPT (pick-wt=35): 77 [] hBOOL(hAPP(product_prod(A,B),bool,C,$f8(A,B,C)))| -hBOOL(hAPP(product_prod(A,B),bool,C,hAPP(B,product_prod(A,B),hAPP(A,fun(B,product_prod(A,B)),product_Pair(A,B),D),E))).
% 13.34/13.22 ** KEPT (pick-wt=260): 78 [] -hBOOL(hAPP(product_prod(A,product_prod(B,product_prod(C,product_prod(D,product_prod(E,F))))),bool,G,hAPP(product_prod(B,product_prod(C,product_prod(D,product_prod(E,F)))),product_prod(A,product_prod(B,product_prod(C,product_prod(D,product_prod(E,F))))),hAPP(A,fun(product_prod(B,product_prod(C,product_prod(D,product_prod(E,F)))),product_prod(A,product_prod(B,product_prod(C,product_prod(D,product_prod(E,F)))))),product_Pair(A,product_prod(B,product_prod(C,product_prod(D,product_prod(E,F))))),$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)),$f9(A,B,C,D,E,F,H,G))))))))|hBOOL(hAPP(product_prod(A,product_prod(B,product_prod(C,product_prod(D,product_prod(E,F))))),bool,G,H)).
% 13.34/13.22 ** KEPT (pick-wt=187): 79 [] -hBOOL(hAPP(product_prod(A,product_prod(B,product_prod(C,product_prod(D,E)))),bool,F,hAPP(product_prod(B,product_prod(C,product_prod(D,E))),product_prod(A,product_prod(B,product_prod(C,product_prod(D,E)))),hAPP(A,fun(product_prod(B,product_prod(C,product_prod(D,E))),product_prod(A,product_prod(B,product_prod(C,product_prod(D,E))))),product_Pair(A,product_prod(B,product_prod(C,product_prod(D,E)))),$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)).
% 13.34/13.22 ** KEPT (pick-wt=126): 80 [] -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)).
% 13.34/13.22 ** KEPT (pick-wt=77): 81 [] -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)),$f39(A,B,C,E,D)))))|hBOOL(hAPP(product_prod(A,product_prod(B,C)),bool,D,E)).
% 13.34/13.22 ** KEPT (pick-wt=30): 82 [] hAPP(A,B,C,$f47(A,B,C,D))!=hAPP(A,B,D,$f47(A,B,C,D))|ti(fun(A,B),C)=ti(fun(A,B),D).
% 13.34/13.22 ** KEPT (pick-wt=51): 83 [] -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)))|hBOOL(hAPP(B,bool,hAPP(A,fun(B,bool),hAPP(fun(product_prod(A,B),bool),fun(A,fun(B,bool)),product_curry(A,B,bool),C),D),E)).
% 13.34/13.22 ** KEPT (pick-wt=105): 84 [] -ordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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),E)),C)),D)),F)).
% 13.34/13.22 ** KEPT (pick-wt=105): 85 [] -ordered_ring(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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),E)),C)),D)),F)).
% 13.34/13.22 ** KEPT (pick-wt=105): 86 [] -ordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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))).
% 13.34/13.22 ** KEPT (pick-wt=105): 87 [] -ordered_ring(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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))).
% 13.34/13.22 ** KEPT (pick-wt=63): 89 [copy,88,flip.2] -ring_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),one_one(A))),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),one_one(A)))=hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),one_one(A)).
% 13.34/13.22 ** KEPT (pick-wt=105): 90 [] -ordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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),E)),C)),D)),F)).
% 13.34/13.22 ** KEPT (pick-wt=105): 91 [] -ordered_ring(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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),E)),C)),D)),F)).
% 13.34/13.22 ** KEPT (pick-wt=105): 92 [] -ordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))).
% 13.34/13.22 ** KEPT (pick-wt=105): 93 [] -ordered_ring(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))).
% 13.34/13.22 ** KEPT (pick-wt=14): 94 [] -one(A)|one_one(A)!=ti(A,B)|ti(A,B)=one_one(A).
% 13.34/13.22 ** KEPT (pick-wt=14): 95 [] -one(A)|one_one(A)=ti(A,B)|ti(A,B)!=one_one(A).
% 13.34/13.22 ** KEPT (pick-wt=38): 96 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 13.34/13.22 ** KEPT (pick-wt=38): 97 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 13.34/13.22 ** KEPT (pick-wt=38): 98 [] -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),A),one_one(int))),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 13.34/13.22 ** KEPT (pick-wt=38): 99 [] 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),A),one_one(int))),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 13.34/13.22 ** KEPT (pick-wt=35): 100 [] -linordered_idom(A)|ti(A,B)=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 Following clause subsumed by 99 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))),B)).
% 13.34/13.22 ** KEPT (pick-wt=35): 101 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|ti(A,B)=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)).
% 13.34/13.22 ** KEPT (pick-wt=41): 102 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|A=B.
% 13.34/13.22 ** KEPT (pick-wt=38): 103 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).
% 13.34/13.22 ** KEPT (pick-wt=28): 104 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))))|A!=B.
% 13.34/13.22 ** KEPT (pick-wt=61): 105 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),C),D))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))).
% 13.34/13.22 ** KEPT (pick-wt=63): 106 [] -ordere223160158up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),E))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),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))).
% 13.34/13.22 ** KEPT (pick-wt=63): 107 [] -ordere223160158up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),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))).
% 13.34/13.22 ** KEPT (pick-wt=27): 108 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A)))).
% 13.34/13.22 ** KEPT (pick-wt=55): 109 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))).
% 13.34/13.22 ** KEPT (pick-wt=38): 110 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),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),B)).
% 13.34/13.22 ** KEPT (pick-wt=38): 111 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),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),B)).
% 13.34/13.22 ** KEPT (pick-wt=50): 112 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 13.34/13.22 ** KEPT (pick-wt=50): 113 [] -ordere236663937imp_le(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 13.34/13.22 ** KEPT (pick-wt=50): 114 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 13.34/13.22 ** KEPT (pick-wt=50): 115 [] -ordere236663937imp_le(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 13.34/13.22 ** KEPT (pick-wt=50): 116 [] -ordere223160158up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),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),D))).
% 13.34/13.22 ** KEPT (pick-wt=50): 117 [] -ordere223160158up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))).
% 13.34/13.22 ** KEPT (pick-wt=63): 118 [] -ordere223160158up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),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))).
% 13.34/13.22 Following clause subsumed by 112 during input processing: 0 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 13.34/13.22 Following clause subsumed by 114 during input processing: 0 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 13.34/13.22 ** KEPT (pick-wt=19): 119 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B)=ti(A,B).
% 13.34/13.22 ** KEPT (pick-wt=19): 120 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A))=ti(A,B).
% 13.34/13.22 ** KEPT (pick-wt=19): 121 [] -monoid_mult(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B)=ti(A,B).
% 13.34/13.22 ** KEPT (pick-wt=19): 122 [] -comm_monoid_mult(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B)=ti(A,B).
% 13.34/13.22 ** KEPT (pick-wt=19): 123 [] -monoid_mult(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A))=ti(A,B).
% 13.34/13.22 ** KEPT (pick-wt=19): 124 [] -comm_monoid_mult(A)|hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A))=ti(A,B).
% 13.34/13.22 ** KEPT (pick-wt=53): 125 [] -ordered_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)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)).
% 13.34/13.22 ** KEPT (pick-wt=53): 126 [] -ordered_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)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)).
% 13.34/13.22 ** KEPT (pick-wt=50): 127 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),D)).
% 13.34/13.22 ** KEPT (pick-wt=50): 128 [] -ordere236663937imp_le(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),D)).
% 13.34/13.22 ** KEPT (pick-wt=50): 129 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D)).
% 13.34/13.22 ** KEPT (pick-wt=50): 130 [] -ordere236663937imp_le(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D)).
% 13.34/13.22 ** KEPT (pick-wt=50): 131 [] -ordere779506340up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),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),D))).
% 13.34/13.22 ** KEPT (pick-wt=50): 132 [] -ordere779506340up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))).
% 13.34/13.22 ** KEPT (pick-wt=63): 133 [] -ordere779506340up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),E))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),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))).
% 13.34/13.22 Following clause subsumed by 127 during input processing: 0 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),D)).
% 13.34/13.22 Following clause subsumed by 129 during input processing: 0 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D)).
% 13.34/13.22 ** KEPT (pick-wt=53): 134 [] -ordered_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)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),E)).
% 13.34/13.22 ** KEPT (pick-wt=53): 135 [] -ordered_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)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),E)).
% 13.34/13.22 ** KEPT (pick-wt=48): 136 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))).
% 13.34/13.22 ** KEPT (pick-wt=48): 137 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))).
% 13.34/13.22 ** KEPT (pick-wt=40): 138 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))),B).
% 13.34/13.22 ** KEPT (pick-wt=50): 139 [] -comm_semiring_1(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),one_one(A))),B).
% 13.34/13.22 ** KEPT (pick-wt=50): 140 [] -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)),C)=hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))),C).
% 13.34/13.22 ** KEPT (pick-wt=51): 141 [] -hBOOL(hAPP(A,bool,hAPP(B,fun(A,bool),hAPP(fun(product_prod(B,A),bool),fun(B,fun(A,bool)),product_curry(B,A,bool),C),D),E))|hBOOL(hAPP(product_prod(B,A),bool,C,hAPP(A,product_prod(B,A),hAPP(B,fun(A,product_prod(B,A)),product_Pair(B,A),D),E))).
% 13.34/13.22 Following clause subsumed by 141 during input processing: 0 [] -hBOOL(hAPP(A,bool,hAPP(B,fun(A,bool),hAPP(fun(product_prod(B,A),bool),fun(B,fun(A,bool)),product_curry(B,A,bool),C),D),E))|hBOOL(hAPP(product_prod(B,A),bool,C,hAPP(A,product_prod(B,A),hAPP(B,fun(A,product_prod(B,A)),product_Pair(B,A),D),E))).
% 13.34/13.22 ** KEPT (pick-wt=15): 142 [] -preorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),B)).
% 13.34/13.22 ** KEPT (pick-wt=41): 143 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)).
% 13.34/13.22 ** KEPT (pick-wt=41): 144 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 13.34/13.22 ** KEPT (pick-wt=41): 145 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)).
% 13.34/13.22 ** KEPT (pick-wt=41): 146 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 13.34/13.22 ** KEPT (pick-wt=35): 147 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|ti(A,C)=ti(A,B)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)).
% 13.34/13.22 Following clause subsumed by 101 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|ti(A,B)=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)).
% 13.34/13.22 Following clause subsumed by 101 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)=ti(A,C).
% 13.34/13.22 ** KEPT (pick-wt=26): 148 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)).
% 13.34/13.22 ** KEPT (pick-wt=16): 149 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|A!=B.
% 13.34/13.22 ** KEPT (pick-wt=29): 150 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))|A=B.
% 13.34/13.22 ** KEPT (pick-wt=39): 151 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),C)).
% 13.34/13.22 ** KEPT (pick-wt=29): 152 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),A))|A=B.
% 13.34/13.22 ** KEPT (pick-wt=44): 153 [] -ord(A)| -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_e_q(fun(B,A)),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(B,A,C,E)),hAPP(B,A,D,E))).
% 13.34/13.22 ** KEPT (pick-wt=52): 154 [] -ord(A)|hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_e_q(fun(B,A)),C),D))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(B,A,C,$f50(B,A,C,D))),hAPP(B,A,D,$f50(B,A,C,D)))).
% 13.34/13.22 ** KEPT (pick-wt=28): 155 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)).
% 13.34/13.22 ** KEPT (pick-wt=22): 156 [] -order(A)|ti(A,B)!=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C)).
% 13.34/13.22 ** KEPT (pick-wt=22): 157 [] -order(A)|ti(A,B)!=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)).
% 13.34/13.22 ** KEPT (pick-wt=35): 158 [] -order(A)|ti(A,B)=ti(A,C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)).
% 13.34/13.22 ** KEPT (pick-wt=18): 159 [] -preorder(A)|B!=C|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C)).
% 13.34/13.22 Following clause subsumed by 153 during input processing: 0 [] -ord(A)| -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_e_q(fun(B,A)),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(B,A,C,E)),hAPP(B,A,D,E))).
% 13.34/13.22 Following clause subsumed by 158 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B))|ti(A,C)=ti(A,B).
% 13.34/13.22 Following clause subsumed by 156 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B))|ti(A,C)!=ti(A,B).
% 13.34/13.22 ** KEPT (pick-wt=31): 160 [] -ord(A)|B!=C| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),D)).
% 13.34/13.22 ** KEPT (pick-wt=35): 161 [] -order(A)|ti(A,B)!=ti(A,C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),B)).
% 13.34/13.22 ** KEPT (pick-wt=31): 162 [] -ord(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|C!=D|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),D)).
% 13.34/13.22 ** KEPT (pick-wt=35): 163 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|ti(A,B)!=ti(A,D)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),C)).
% 13.34/13.22 Following clause subsumed by 158 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B))|ti(A,B)=ti(A,C).
% 13.34/13.22 ** KEPT (pick-wt=41): 164 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),D)).
% 13.34/13.22 Following clause subsumed by 158 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B))|ti(A,C)=ti(A,B).
% 13.34/13.22 ** KEPT (pick-wt=41): 165 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),C)).
% 13.34/13.22 Following clause subsumed by 153 during input processing: 0 [] -ord(A)| -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_e_q(fun(B,A)),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(B,A,C,E)),hAPP(B,A,D,E))).
% 13.34/13.22 Following clause subsumed by 155 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)).
% 13.34/13.22 ** KEPT (pick-wt=15): 166 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),B)).
% 13.34/13.22 ** KEPT (pick-wt=35): 167 [] -linorder(A)|ti(A,B)=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 ** KEPT (pick-wt=22): 168 [] -linorder(A)|ti(A,B)!=ti(A,C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)).
% 13.34/13.22 ** KEPT (pick-wt=22): 169 [] -linorder(A)|ti(A,B)!=ti(A,C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 Following clause subsumed by 167 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B))|ti(A,B)=ti(A,C).
% 13.34/13.22 ** KEPT (pick-wt=28): 170 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 Following clause subsumed by 168 during input processing: 0 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)!=ti(A,C).
% 13.34/13.22 Following clause subsumed by 167 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 Following clause subsumed by 167 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B))|ti(A,C)=ti(A,B).
% 13.34/13.22 Following clause subsumed by 168 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B))|ti(A,C)!=ti(A,B).
% 13.34/13.22 Following clause subsumed by 167 during input processing: 0 [] -linorder(A)|ti(A,B)=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 ** KEPT (pick-wt=22): 171 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)!=ti(A,C).
% 13.34/13.22 ** KEPT (pick-wt=28): 172 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 Following clause subsumed by 172 during input processing: 0 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 Following clause subsumed by 171 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)!=ti(A,C).
% 13.34/13.22 ** KEPT (pick-wt=22): 173 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,C)!=ti(A,B).
% 13.34/13.22 Following clause subsumed by 172 during input processing: 0 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B))|hBOOL(D).
% 13.34/13.22 Following clause subsumed by 172 during input processing: 0 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 ** KEPT (pick-wt=28): 174 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 ** KEPT (pick-wt=31): 175 [] -ord(A)|B!=C| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 13.34/13.22 ** KEPT (pick-wt=35): 176 [] -order(A)|ti(A,B)!=ti(A,C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)).
% 13.34/13.22 ** KEPT (pick-wt=31): 177 [] -ord(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|C!=D|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 13.34/13.22 ** KEPT (pick-wt=35): 178 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)!=ti(A,D)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)).
% 13.34/13.22 ** KEPT (pick-wt=41): 179 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 13.34/13.22 ** KEPT (pick-wt=41): 180 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)).
% 13.34/13.22 Following clause subsumed by 172 during input processing: 0 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 Following clause subsumed by 167 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 ** KEPT (pick-wt=28): 181 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)).
% 13.34/13.22 ** KEPT (pick-wt=28): 182 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)).
% 13.34/13.22 Following clause subsumed by 181 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 Following clause subsumed by 182 during input processing: 0 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 Following clause subsumed by 181 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 ** KEPT (pick-wt=28): 183 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C)).
% 13.34/13.22 Following clause subsumed by 171 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)!=ti(A,C).
% 13.34/13.22 Following clause subsumed by 101 during input processing: 0 [] -order(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|ti(A,B)=ti(A,C).
% 13.34/13.22 ** KEPT (pick-wt=28): 184 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C)).
% 13.34/13.22 ** KEPT (pick-wt=28): 185 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)).
% 13.34/13.22 ** KEPT (pick-wt=41): 186 [] -preorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)).
% 13.34/13.22 Following clause subsumed by 101 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)=ti(A,C).
% 13.34/13.22 Following clause subsumed by 183 during input processing: 0 [] -order(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)).
% 13.34/13.22 Following clause subsumed by 156 during input processing: 0 [] -order(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|ti(A,B)!=ti(A,C).
% 13.34/13.22 Following clause subsumed by 181 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)).
% 13.34/13.22 Following clause subsumed by 181 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 ** KEPT (pick-wt=35): 187 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|ti(A,B)=ti(A,C).
% 13.34/13.22 ** KEPT (pick-wt=35): 188 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|ti(A,B)!=ti(A,C).
% 13.34/13.22 Following clause subsumed by 101 during input processing: 0 [] -order(A)|ti(A,B)=ti(A,C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)).
% 13.34/13.22 Following clause subsumed by 147 during input processing: 0 [] -order(A)|ti(A,B)=ti(A,C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 Following clause subsumed by 182 during input processing: 0 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 13.34/13.22 Following clause subsumed by 184 during input processing: 0 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C)).
% 13.34/13.22 Following clause subsumed by 187 during input processing: 0 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)=ti(A,C).
% 13.34/13.22 Following clause subsumed by 168 during input processing: 0 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)!=ti(A,C).
% 13.34/13.22 Following clause subsumed by 110 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),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),B)).
% 13.34/13.22 ** KEPT (pick-wt=41): 189 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))| -hBOOL(hAPP(int,bool,C,B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f51(C,A,B)),B))|hBOOL(hAPP(int,bool,C,A)).
% 13.34/13.22 ** KEPT (pick-wt=34): 190 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))| -hBOOL(hAPP(int,bool,C,B))|hBOOL(hAPP(int,bool,C,$f51(C,A,B)))|hBOOL(hAPP(int,bool,C,A)).
% 13.34/13.22 ** KEPT (pick-wt=46): 191 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))| -hBOOL(hAPP(int,bool,C,B))| -hBOOL(hAPP(int,bool,C,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f51(C,A,B)),one_one(int))))|hBOOL(hAPP(int,bool,C,A)).
% 13.34/13.22 ** KEPT (pick-wt=53): 192 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,C,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),$f52(C,A,B)),B))|hBOOL(hAPP(int,bool,C,A)).
% 13.34/13.22 ** KEPT (pick-wt=46): 193 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,C,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int))))|hBOOL(hAPP(int,bool,C,$f52(C,A,B)))|hBOOL(hAPP(int,bool,C,A)).
% 13.34/13.22 ** KEPT (pick-wt=58): 194 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,C,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int))))| -hBOOL(hAPP(int,bool,C,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f52(C,A,B)),one_one(int))))|hBOOL(hAPP(int,bool,C,A)).
% 13.34/13.22 ** KEPT (pick-wt=41): 195 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))| -hBOOL(hAPP(int,bool,C,A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),$f53(C,A,B))
% 13.34/13.23 Search stopped in tp_alloc by max_mem option.
% 13.34/13.23 )|hBOOL(hAPP(int,bool,C,B)).
% 13.34/13.23 ** KEPT (pick-wt=34): 196 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))| -hBOOL(hAPP(int,bool,C,A))|hBOOL(hAPP(int,bool,C,$f53(C,A,B)))|hBOOL(hAPP(int,bool,C,B)).
% 13.34/13.23
% 13.34/13.23 Search stopped in tp_alloc by max_mem option.
% 13.34/13.23
% 13.34/13.23 ============ end of search ============
% 13.34/13.23
% 13.34/13.23 -------------- statistics -------------
% 13.34/13.23 clauses given 0
% 13.34/13.23 clauses generated 0
% 13.34/13.23 clauses kept 187
% 13.34/13.23 clauses forward subsumed 61
% 13.34/13.23 clauses back subsumed 0
% 13.34/13.23 Kbytes malloced 11718
% 13.34/13.23
% 13.34/13.23 ----------- times (seconds) -----------
% 13.34/13.23 user CPU time 0.16 (0 hr, 0 min, 0 sec)
% 13.34/13.23 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 13.34/13.23 wall-clock time 13 (0 hr, 0 min, 13 sec)
% 13.34/13.23
% 13.34/13.23 Process 20609 finished Wed Jul 27 09:55:51 2022
% 13.34/13.23 Otter interrupted
% 13.34/13.23 PROOF NOT FOUND
%------------------------------------------------------------------------------