TSTP Solution File: SWW473+7 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWW473+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 13:22:40 EDT 2022
% Result : Unknown 32.85s 32.60s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWW473+7 : TPTP v8.1.0. Released v5.3.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 03:17:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 32.78/32.52 ----- Otter 3.3f, August 2004 -----
% 32.78/32.52 The process was started by sandbox2 on n027.cluster.edu,
% 32.78/32.52 Wed Jul 27 03:17:51 2022
% 32.78/32.52 The command was "./otter". The process ID is 16648.
% 32.78/32.52
% 32.78/32.52 set(prolog_style_variables).
% 32.78/32.52 set(auto).
% 32.78/32.52 dependent: set(auto1).
% 32.78/32.52 dependent: set(process_input).
% 32.78/32.52 dependent: clear(print_kept).
% 32.78/32.52 dependent: clear(print_new_demod).
% 32.78/32.52 dependent: clear(print_back_demod).
% 32.78/32.52 dependent: clear(print_back_sub).
% 32.78/32.52 dependent: set(control_memory).
% 32.78/32.52 dependent: assign(max_mem, 12000).
% 32.78/32.52 dependent: assign(pick_given_ratio, 4).
% 32.78/32.52 dependent: assign(stats_level, 1).
% 32.78/32.52 dependent: assign(max_seconds, 10800).
% 32.78/32.52 clear(print_given).
% 32.78/32.52
% 32.78/32.52 formula_list(usable).
% 32.78/32.52 all A (A=A).
% 32.78/32.52 all X_b X_c X_a (ti(fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),combb(X_b,X_c,X_a))=combb(X_b,X_c,X_a)).
% 32.78/32.52 all X_a X_b X_c (ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c))=combc(X_a,X_b,X_c)).
% 32.78/32.52 all X_a (ti(fun(X_a,X_a),combi(X_a))=combi(X_a)).
% 32.78/32.52 all X_a X_b (ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b))=combk(X_a,X_b)).
% 32.78/32.52 all X_a X_b X_c (ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c))=combs(X_a,X_b,X_c)).
% 32.78/32.52 ti(fun(pname,option(com)),body)=body.
% 32.78/32.52 all X_c (ti(fun(fun(X_c,bool),nat),finite_card(X_c))=finite_card(X_c)).
% 32.78/32.52 all X_b X_c (ti(fun(fun(X_b,fun(X_c,X_c)),bool),finite_comp_fun_idem(X_b,X_c))=finite_comp_fun_idem(X_b,X_c)).
% 32.78/32.52 all X_b (ti(fun(fun(X_b,bool),bool),finite_finite(X_b))=finite_finite(X_b)).
% 32.78/32.52 all X_b X_c (ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)))),finite_fold_image(X_b,X_c))=finite_fold_image(X_b,X_c)).
% 32.78/32.52 all X_b X_c (ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)))),finite1357897459simple(X_b,X_c))=finite1357897459simple(X_b,X_c)).
% 32.78/32.52 all X_b X_c (ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)))),finite908156982e_idem(X_b,X_c))=finite908156982e_idem(X_b,X_c)).
% 32.78/32.52 all X_b (ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite_folding_one(X_b))=finite_folding_one(X_b)).
% 32.78/32.52 all X_b (ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite2073411215e_idem(X_b))=finite2073411215e_idem(X_b)).
% 32.78/32.52 all X_a (ordere142940540dd_abs(X_a)->ti(fun(X_a,X_a),abs_abs(X_a))=abs_abs(X_a)).
% 32.78/32.52 all X_c (minus(X_c)->ti(fun(X_c,fun(X_c,X_c)),minus_minus(X_c))=minus_minus(X_c)).
% 32.78/32.52 all X_b (one(X_b)->ti(X_b,one_one(X_b))=one_one(X_b)).
% 32.78/32.52 all X_a (monoid_add(X_a)->ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a)).
% 32.78/32.52 all X_b (cancel_semigroup_add(X_b)->ti(fun(X_b,fun(X_b,X_b)),plus_plus(X_b))=plus_plus(X_b)).
% 32.78/32.52 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)).
% 32.78/32.52 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)).
% 32.78/32.52 all X_a (monoid_mult(X_a)->ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a)).
% 32.78/32.52 all X_a (semiring(X_a)->ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a)).
% 32.78/32.52 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)).
% 32.78/32.52 all X_a (mult_zero(X_a)->ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a)).
% 32.78/32.52 all X_b (zero(X_b)->ti(X_b,zero_zero(X_b))=zero_zero(X_b)).
% 32.78/32.52 all X_b (ti(fun(fun(X_b,bool),X_b),the(X_b))=the(X_b)).
% 32.78/32.52 all X_a (ti(X_a,undefined(X_a))=undefined(X_a)).
% 32.78/32.52 all X_a (ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a))=if(X_a)).
% 32.78/32.52 ti(fun(int,int),bit1)=bit1.
% 32.78/32.52 ti(int,pls)=pls.
% 32.78/32.52 all X_b (number(X_b)->ti(fun(int,X_b),number_number_of(X_b))=number_number_of(X_b)).
% 32.78/32.52 all X_b (ring_1(X_b)->ti(fun(X_b,bool),ring_1_Ints(X_b))=ring_1_Ints(X_b)).
% 32.78/32.52 ti(fun(int,int),succ)=succ.
% 32.78/32.52 ti(fun(nat,nat),suc)=suc.
% 32.78/32.52 all X_b (ti(fun(X_b,fun(fun(nat,X_b),fun(nat,X_b))),nat_case(X_b))=nat_case(X_b)).
% 32.78/32.52 all X_a (semiring_1(X_a)->ti(fun(nat,X_a),semiring_1_of_nat(X_a))=semiring_1_of_nat(X_a)).
% 32.78/32.52 all X_b (semiring_1(X_b)->ti(fun(fun(X_b,X_b),fun(nat,fun(X_b,X_b))),semiri532925092at_aux(X_b))=semiri532925092at_aux(X_b)).
% 32.78/32.52 ti(fun(int,bool),nat_neg)=nat_neg.
% 32.78/32.52 ti(fun(int,fun(int,int)),nat_tsub)=nat_tsub.
% 32.78/32.52 ti(fun(option(com),com),the_1(com))=the_1(com).
% 32.78/32.52 all X_b (bot(X_b)->ti(X_b,bot_bot(X_b))=bot_bot(X_b)).
% 32.78/32.52 all X_a (ord(X_a)->ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a)).
% 32.78/32.52 all X_a (ord(X_a)->ti(fun(X_a,fun(X_a,bool)),ord_less_e_q(X_a))=ord_less_e_q(X_a)).
% 32.78/32.52 all X_b (ti(fun(X_b,fun(fun(X_b,bool),X_b)),partial_flat_lub(X_b))=partial_flat_lub(X_b)).
% 32.78/32.52 all X_b (ti(fun(fun(X_b,bool),fun(X_b,bool)),collect(X_b))=collect(X_b)).
% 32.78/32.52 all X_b X_c (ti(fun(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool))),image(X_b,X_c))=image(X_b,X_c)).
% 32.78/32.52 all X_b (ti(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),insert(X_b))=insert(X_b)).
% 32.78/32.52 all X_b (ti(fun(fun(X_b,bool),X_b),the_elem(X_b))=the_elem(X_b)).
% 32.78/32.52 all X_b X_c (ti(fun(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool))),sum_Plus(X_b,X_c))=sum_Plus(X_b,X_c)).
% 32.78/32.52 ti(bool,fFalse)=fFalse.
% 32.78/32.52 ti(fun(bool,bool),fNot)=fNot.
% 32.78/32.52 ti(bool,fTrue)=fTrue.
% 32.78/32.52 ti(fun(bool,fun(bool,bool)),fconj)=fconj.
% 32.78/32.52 ti(fun(bool,fun(bool,bool)),fdisj)=fdisj.
% 32.78/32.52 all X_a (ti(fun(X_a,fun(X_a,bool)),fe_qual(X_a))=fe_qual(X_a)).
% 32.78/32.52 ti(fun(bool,fun(bool,bool)),fimplies)=fimplies.
% 32.78/32.52 all X_a X_c B_1_1 B_2_1 (hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1)=hAPP(X_a,X_c,B_1_1,B_2_1)).
% 32.78/32.52 all X_a X_c B_1_1 B_2_1 (hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1))=hAPP(X_a,X_c,B_1_1,B_2_1)).
% 32.78/32.52 all X_c X_a B_1_1 B_2_1 (ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1))=hAPP(X_a,X_c,B_1_1,B_2_1)).
% 32.78/32.52 all B_1_1 (hBOOL(ti(bool,B_1_1))<->hBOOL(B_1_1)).
% 32.78/32.52 all X_b (ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b))=member(X_b)).
% 32.78/32.52 ti(fun(x_a,bool),g)=g.
% 32.78/32.52 ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p)=p.
% 32.78/32.52 ti(fun(pname,bool),u)=u.
% 32.78/32.52 ti(fun(com,x_a),mgt)=mgt.
% 32.78/32.52 ti(fun(pname,x_a),mgt_call)=mgt_call.
% 32.78/32.52 ti(nat,na)=na.
% 32.78/32.52 ti(pname,pn)=pn.
% 32.78/32.52 ti(fun(com,bool),wt)=wt.
% 32.78/32.52 all Ts G_1 (hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_e_q(fun(x_a,bool)),Ts),G_1))->hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),Ts))).
% 32.78/32.52 all X_b A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))->hBOOL(hAPP(fun(fun(X_b,bool),bool),bool,finite_finite(fun(X_b,bool)),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,bool),bool),collect(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),combc(fun(X_b,bool),fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool))),A_3))))).
% 32.78/32.52 all X_c X_b H F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))->hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),H),F_1)))).
% 32.78/32.52 all X_b A_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)))).
% 32.78/32.52 all X_c X_b F A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(fun(X_c,bool),nat,finite_card(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))).
% 32.78/32.52 all X_b A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1))))).
% 32.78/32.52 all X_b A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))->ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_1)))).
% 32.78/32.52 all X_b X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))))).
% 32.78/32.52 all X_b X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))& (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))).
% 32.78/32.52 all X_b X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))).
% 32.78/32.52 all X_b Q_3 Pa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3)))->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),Pa)),Q_3))))).
% 32.78/32.52 all N M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),N)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N))).
% 32.78/32.52 all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_e_q(nat)),K)))).
% 32.78/32.52 all Na (hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_e_q(nat)),Na)))=hAPP(nat,nat,suc,Na)).
% 32.78/32.52 all X_b (finite_finite_1(X_b)-> (all A_3 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)))).
% 32.78/32.52 all X_b (finite_finite_1(X_b)-> (all A_3 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)))).
% 32.78/32.52 all X Y (hAPP(nat,nat,suc,X)=hAPP(nat,nat,suc,Y)->X=Y).
% 32.78/32.52 all Nat_3 Nat_4 (hAPP(nat,nat,suc,Nat_3)=hAPP(nat,nat,suc,Nat_4)<->Nat_3=Nat_4).
% 32.78/32.52 all N (hAPP(nat,nat,suc,N)!=N).
% 32.78/32.52 all N (N!=hAPP(nat,nat,suc,N)).
% 32.78/32.52 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1))->M_1=N)).
% 32.78/32.52 all K_1 I_2 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),K_1)))).
% 32.78/32.52 all M_1 N (M_1=N->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))).
% 32.78/32.52 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1))).
% 32.78/32.52 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),N)).
% 32.78/32.52 all I_2 J K_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),J)),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),K_1)),J)).
% 32.78/32.52 all X_b Pa Q_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Q_3))))<->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)))&hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3)))).
% 32.78/32.52 all X_b A_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)))<->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))).
% 32.78/32.52 all X_b A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)))).
% 32.78/32.52 all X_b A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)))).
% 32.78/32.52 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M_1)),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))).
% 32.78/32.52 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,suc,N)))-> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))->M_1=hAPP(nat,nat,suc,N))).
% 32.78/32.52 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,suc,N)))).
% 32.78/32.52 all Na M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Na),M))).
% 32.78/32.52 all M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,suc,Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))|M=hAPP(nat,nat,suc,Na)).
% 32.78/32.52 all M Na (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,Na)),M))).
% 32.78/32.52 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N)),N))).
% 32.78/32.52 all M_1 N K_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),N)),hAPP(nat,nat,suc,K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),K_1)).
% 32.78/32.52 all M_1 N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)).
% 32.78/32.52 all Na 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),Na))-> (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),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))))).
% 32.78/32.52 all N 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))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(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),K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N))).
% 32.78/32.52 all Na 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),Na))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K)<->M=Na))).
% 32.78/32.52 all I_2 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),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_2))=I_2).
% 32.78/32.52 all L_1 M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),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_1),L_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),L_1)))).
% 32.78/32.52 all L_1 M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),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_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M_1)))).
% 32.78/32.52 all M_1 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_1),N)),M_1)).
% 32.78/32.52 all X_c X_b B_1 F A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_e_q(fun(X_c,bool)),B_1),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))->hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1)))).
% 32.78/32.52 all X_c X_b F A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))-> (exists C_3 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_e_q(fun(X_c,bool)),C_3),A_3))&hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),C_3))&ti(fun(X_b,bool),B_1)=hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),C_3))))).
% 32.78/32.52 all X_b (order(X_b)-> (all Na N_3 F ((all N_1 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(nat,X_b,F,N_1)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_1)))))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Na),N_3))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,N_3))))))).
% 32.78/32.52 all X_c X_b F A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))-> (exists X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))& -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(X_c,fun(X_b,bool),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,bool))),combb(X_c,fun(X_c,bool),X_b),fe_qual(X_c)),F)),hAPP(X_b,X_c,F,X_2)))))))))).
% 32.78/32.52 all X_b X_c A_3 B_3 F X_1 (ti(X_b,B_3)=hAPP(X_c,X_b,F,X_1)-> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))))).
% 32.78/32.52 all X_b A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),A_3))->ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_1))).
% 32.78/32.52 all X_b C_1 A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1)))).
% 32.78/32.52 all X_b B_3 A_2 B_1 ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_1))->ti(X_b,A_2)=ti(X_b,B_3))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),B_1)))).
% 32.78/32.52 all X_b A_2 B_3 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),A_3)))-> (ti(X_b,A_2)!=ti(X_b,B_3)->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)))).
% 32.78/32.52 all I_1 Pa K (hBOOL(hAPP(nat,bool,Pa,K))-> ((all N_1 (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_1)))->hBOOL(hAPP(nat,bool,Pa,N_1))))->hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I_1))))).
% 32.78/32.52 all N M_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N)),M_4))-> (exists M_2 (M_4=hAPP(nat,nat,suc,M_2)))).
% 32.78/32.52 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)))).
% 32.78/32.52 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))))).
% 32.78/32.52 all X_b (order(X_b)-> (all X_1 Y_2 (ti(X_b,X_1)=ti(X_b,Y_2)<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))&hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_2),X_1))))).
% 32.78/32.52 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))))).
% 32.78/32.52 all X_b (order(X_b)-> (all Y_2 X_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_2),X_1))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))<->ti(X_b,X_1)=ti(X_b,Y_2))))).
% 32.78/32.52 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)))))).
% 32.78/32.52 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)))))).
% 32.78/32.52 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)))))).
% 32.78/32.52 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)))))).
% 32.78/32.52 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))))).
% 32.78/32.52 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)))))).
% 32.78/32.52 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))))).
% 32.78/32.52 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)))))).
% 32.78/32.52 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))))).
% 32.78/32.52 all X_b A_2 B_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1))).
% 32.78/32.52 all X_b A_2 B_1 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1)=hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),A_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_1)))).
% 32.78/32.52 all X_b A_2 Pa (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))=hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fimplies),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),A_2)))),Pa))).
% 32.78/32.52 all X_b X_c F G ((all X_2 (hAPP(X_b,X_c,F,X_2)=hAPP(X_b,X_c,G,X_2)))->ti(fun(X_b,X_c),F)=ti(fun(X_b,X_c),G)).
% 32.78/32.52 all X_b X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))<->hBOOL(hAPP(X_b,bool,A_3,X_1))).
% 32.78/32.52 all X_b Pa (hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)=ti(fun(X_b,bool),Pa)).
% 32.78/32.52 all X_b X_1 A_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)).
% 32.78/32.52 all X_b X_1 Y_2 A_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),A_3))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))).
% 32.78/32.52 all X_b A_2 B_3 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),A_3)))<->ti(X_b,A_2)=ti(X_b,B_3)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))).
% 32.78/32.52 all X_b Y_2 A_3 X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),A_3),X_1))<->ti(X_b,Y_2)=ti(X_b,X_1)|hBOOL(hAPP(X_b,bool,A_3,X_1))).
% 32.78/32.52 all X_b B_1 X_1 A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))-> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))-> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)<->ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_1)))).
% 32.78/32.52 all X_b B_3 A_2 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_1))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),B_1)))).
% 32.78/32.52 all X_b A_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))->hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)=ti(fun(X_b,bool),A_3)).
% 32.78/32.52 all X_b A_3 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),A_3)).
% 32.78/32.52 all X_b A_3 B_1 (ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_1)<->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))&hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),A_3))).
% 32.78/32.52 all X_b A_3 B_1 (ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_1)->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))).
% 32.78/32.52 all X_b A_3 B_1 (ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_1)->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),A_3))).
% 32.78/32.52 all X_b X_1 A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)))).
% 32.78/32.52 all X_b B_1 X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)))).
% 32.78/32.52 all X_b X_1 A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)))).
% 32.78/32.52 all X_b C_2 A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),C_2))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),C_2)))).
% 32.78/32.52 all X_b A_3 B_1 (ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_1)-> -(hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))-> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),A_3)))).
% 32.78/32.52 all X_b X_c Z_2 F A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))<-> (exists X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3))&ti(X_b,Z_2)=hAPP(X_c,X_b,F,X_2)))).
% 32.78/32.52 all X_c X_b F X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))).
% 32.78/32.52 all X_c X_b B_3 F X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))-> (ti(X_c,B_3)=hAPP(X_b,X_c,F,X_1)->hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B_3),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))))).
% 32.78/32.52 all X_b X_2 Xa (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),Xa)=hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),X_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),Xa)))).
% 32.78/32.52 all X_c X_b X_d F G A_3 (hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_d,bool),fun(X_c,bool),hAPP(fun(X_d,X_c),fun(fun(X_d,bool),fun(X_c,bool)),image(X_d,X_c),G),A_3))=hAPP(fun(X_d,bool),fun(X_b,bool),hAPP(fun(X_d,X_b),fun(fun(X_d,bool),fun(X_b,bool)),image(X_d,X_b),hAPP(fun(X_d,X_c),fun(X_d,X_b),hAPP(fun(X_c,X_b),fun(fun(X_d,X_c),fun(X_d,X_b)),combb(X_c,X_b,X_d),F),G)),A_3)).
% 32.78/32.52 all X_b Y_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),combi(X_b)),Y_3)=ti(fun(X_b,bool),Y_3)).
% 32.78/32.52 all X_b X_c (ord(X_c)-> (all F G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_e_q(fun(X_b,X_c)),F),G))<-> (all X_2 hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2))))))).
% 32.78/32.52 all X_b X_c (ord(X_c)-> (all X_1 F G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_e_q(fun(X_b,X_c)),F),G))->hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1)))))).
% 32.78/32.52 all X_b X_c (ord(X_c)-> (all X_1 F G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_e_q(fun(X_b,X_c)),F),G))->hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1)))))).
% 32.78/32.52 all X_b B_1 A_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1))).
% 32.78/32.52 all X_b X_1 A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_1))<->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))&hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))).
% 32.78/32.52 all X_b B_1 X_1 A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))<->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)))).
% 32.78/32.52 all X_b B_3 A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),B_1)))).
% 32.78/32.52 all X_b A_2 C_2 D_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),C_2),D_3))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),C_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),D_3)))).
% 32.78/32.52 all X_c X_b F A_2 B_1 (hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),A_2),B_1))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),hAPP(X_c,X_b,F,A_2)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_1))).
% 32.78/32.52 all X_c X_b F X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))=hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)).
% 32.78/32.52 all X_b X_c B_1 F A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))<-> (exists AA (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_e_q(fun(X_c,bool)),AA),A_3))&ti(fun(X_b,bool),B_1)=hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),AA)))).
% 32.78/32.52 all X_c X_b F A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))->hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_e_q(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),B_1)))).
% 32.78/32.52 all X_b X_c B_3 F A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))-> -(all X_2 (ti(X_b,B_3)=hAPP(X_c,X_b,F,X_2)-> -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3))))).
% 32.78/32.52 all X_b B_1 A_3 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_1))))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))).
% 32.78/32.52 all X_c X_b F B_1 A_3 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))->hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_2)),B_1))))->hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_e_q(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),B_1))).
% 32.78/32.52 all X_b X_c (ord(X_c)-> (all F G ((all X_2 hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2))))->hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_e_q(fun(X_b,X_c)),F),G))))).
% 32.78/32.52 all N_2 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2))<-> (exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_2),M_2))))).
% 32.78/32.52 all G_1 C_1 (hBOOL(hAPP(com,bool,wt,C_1))-> ((all X_2 (hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X_2),u))->hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X_2)),bot_bot(fun(x_a,bool)))))))->hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,C_1)),bot_bot(fun(x_a,bool))))))).
% 32.78/32.52 all X_b (ordered_ab_group_add(X_b)-> (all A_2 B_3 C_1 D_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1)-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C_1),D_1)))))).
% 32.78/32.52 all M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M)),Na))<->hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M)),Na))).
% 32.78/32.52 all X_c X_b B_1 A_3 F Z_2 G F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))-> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_e_q(fun(X_c,bool)),B_1),A_3))->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,B_1)),hAPP(fun(X_c,bool),X_b,F_1,A_3))=hAPP(fun(X_c,bool),X_b,F_1,A_3)))).
% 32.78/32.52 all X_c X_b X_1 A_3 F Z_2 G F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))->hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,A_3)))).
% 32.78/32.52 all X_b A_2 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),bot_bot(fun(X_b,bool))))).
% 32.78/32.52 all X_b B_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))).
% 32.78/32.52 all X_b hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),bot_bot(fun(X_b,bool)))).
% 32.78/32.52 all X_b A_3 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),bot_bot(fun(X_b,bool))),A_3)).
% 32.78/32.52 all X_b A_2 A_3 (ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))-> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))).
% 32.78/32.52 all X_b Pa (hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)=bot_bot(fun(X_b,bool))<-> (all X_2 (-hBOOL(hAPP(X_b,bool,Pa,X_2))))).
% 32.78/32.52 all X_b A_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),A_3)=bot_bot(fun(X_b,bool))).
% 32.78/32.52 all X_b A_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool)))=ti(fun(X_b,bool),A_3)).
% 32.78/32.52 all X_b C_1 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),bot_bot(fun(X_b,bool))))).
% 32.78/32.52 all X_b Pa (bot_bot(fun(X_b,bool))=hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)<-> (all X_2 (-hBOOL(hAPP(X_b,bool,Pa,X_2))))).
% 32.78/32.52 all X_b A_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),bot_bot(fun(X_b,bool))),A_3)=bot_bot(fun(X_b,bool))).
% 32.78/32.52 all X_b A_3 ((exists X_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)))<->ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))).
% 32.78/32.52 all X_b A_3 ((all X_2 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))))<->ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))).
% 32.78/32.52 all X_c X_b (bot(X_b)-> (all X_1 (hAPP(X_c,X_b,bot_bot(fun(X_c,X_b)),X_1)=bot_bot(X_b)))).
% 32.78/32.52 all X_b (bot_bot(fun(X_b,bool))=hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse))).
% 32.78/32.52 all X_b X_c (bot(X_c)-> (all X_2 (hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2)=bot_bot(X_c)))).
% 32.78/32.52 all X_b A_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))->hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))=ti(fun(X_b,bool),A_3)).
% 32.78/32.52 all X_b X_1 A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))=ti(fun(X_b,bool),A_3)).
% 32.78/32.52 all X_b A_2 A_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)).
% 32.78/32.52 all X_b A_3 A_2 B_1 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))),B_1)).
% 32.78/32.52 all X_b A_3 A_2 B_1 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))).
% 32.78/32.52 all X_c X_b X_1 F Z_2 G F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1))->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),X_1)=ti(X_b,X_1)).
% 32.78/32.52 all X_b A_3 X_1 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1))))).
% 32.78/32.52 all X_b A_3 X_1 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))<-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_1)))& (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)))).
% 32.78/32.52 all X_b A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))<->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)))).
% 32.78/32.52 all X_b A_3 X_1 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))->hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_1)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.52 all X_b A_3 X_1 B_1 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))->hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_1)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))& (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))->hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_1)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))).
% 32.78/32.52 all X_b C_2 A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),C_2))->hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C_2),A_3))=ti(fun(X_b,bool),A_3))).
% 32.78/32.52 all X_b D_3 B_1 A_3 C_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),C_2))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),D_3),B_1))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C_2),D_3))))).
% 32.78/32.52 all X_b A_3 B_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)),A_3)).
% 32.78/32.52 all X_b A_2 B_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool)))->ti(X_b,A_2)=ti(X_b,B_3)).
% 32.78/32.52 all X_b B_3 A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))->ti(X_b,B_3)=ti(X_b,A_2)).
% 32.78/32.52 all X_b A_2 B_3 C_1 D_1 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool))))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D_1),bot_bot(fun(X_b,bool))))<->ti(X_b,A_2)=ti(X_b,C_1)&ti(X_b,B_3)=ti(X_b,D_1)|ti(X_b,A_2)=ti(X_b,D_1)&ti(X_b,B_3)=ti(X_b,C_1)).
% 32.78/32.52 all X_b B_3 A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))<->ti(X_b,B_3)=ti(X_b,A_2)).
% 32.78/32.52 all X_b A_2 A_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)!=bot_bot(fun(X_b,bool))).
% 32.78/32.52 all X_b A_2 A_3 (bot_bot(fun(X_b,bool))!=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)).
% 32.78/32.52 all X_b A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))))<->ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))).
% 32.78/32.52 all X_c X_b F A_3 (hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)=bot_bot(fun(X_b,bool))<->ti(fun(X_c,bool),A_3)=bot_bot(fun(X_c,bool))).
% 32.78/32.52 all X_c X_b F (hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),bot_bot(fun(X_c,bool)))=bot_bot(fun(X_b,bool))).
% 32.78/32.52 all X_b X_c F A_3 (bot_bot(fun(X_b,bool))=hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)<->ti(fun(X_c,bool),A_3)=bot_bot(fun(X_c,bool))).
% 32.78/32.52 all X_a (bot(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),bot_bot(X_a)))->ti(X_a,A_1)=bot_bot(X_a)))).
% 32.78/32.52 all X_b (bot(X_b)-> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),bot_bot(X_b)))<->ti(X_b,A_2)=bot_bot(X_b)))).
% 32.78/32.52 all X_a (bot(X_a)-> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),bot_bot(X_a)),A_1)))).
% 32.78/32.52 all X_b Pa A_2 ((hBOOL(hAPP(X_b,bool,Pa,A_2))->hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),A_2))),Pa))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))& (-hBOOL(hAPP(X_b,bool,Pa,A_2))->hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),A_2))),Pa))=bot_bot(fun(X_b,bool)))).
% 32.78/32.52 all X_b Pa A_2 ((hBOOL(hAPP(X_b,bool,Pa,A_2))->hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fe_qual(X_b),A_2))),Pa))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))& (-hBOOL(hAPP(X_b,bool,Pa,A_2))->hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fe_qual(X_b),A_2))),Pa))=bot_bot(fun(X_b,bool)))).
% 32.78/32.52 all X_b A_2 (hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),A_2))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))).
% 32.78/32.52 all X_b A_2 (hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),fe_qual(X_b),A_2))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))).
% 32.78/32.52 all X_b X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))=hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))).
% 32.78/32.52 all X_b X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))->hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))).
% 32.78/32.52 all X_b X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))).
% 32.78/32.52 all X_b A_3 A_2 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1))))<->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))).
% 32.78/32.52 all X_b X_c F A_3 B_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_1))),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),B_1)))).
% 32.78/32.52 all X_b A_3 X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))->ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))|ti(fun(X_b,bool),A_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))).
% 32.78/32.52 all X_b F1 F2 Nat_3 (hAPP(nat,X_b,hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(X_b,fun(fun(nat,X_b),fun(nat,X_b)),nat_case(X_b),F1),F2),hAPP(nat,nat,suc,Nat_3))=hAPP(nat,X_b,F2,Nat_3)).
% 32.78/32.52 all X_c X_b C_1 X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3)=hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),C_1),bot_bot(fun(X_c,bool)))).
% 32.78/32.52 all X_c X_b C_1 A_3 ((ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3)=bot_bot(fun(X_c,bool)))& (ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3)=hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),C_1),bot_bot(fun(X_c,bool))))).
% 32.78/32.52 all X_c X_b X_1 A_3 F Z_2 G F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))-> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3))->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,A_3))=hAPP(fun(X_c,bool),X_b,F_1,A_3)))).
% 32.78/32.52 all X_b (ab_group_add(X_b)-> (all A_2 B_3 C_1 D_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1)-> (ti(X_b,A_2)=ti(X_b,B_3)<->ti(X_b,C_1)=ti(X_b,D_1))))).
% 32.78/32.52 all X_b A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),A_3))->hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1)))).
% 32.78/32.52 all X_b A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_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),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1))),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))))).
% 32.78/32.52 all X_b Pa A_3 F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),F_1),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))-> ((all A_4 F_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_3))-> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),F_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3))->hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),F_3))))))))->hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)))))).
% 32.78/32.52 all Pn G_1 (hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,Pn)),G_1)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,Pn)))),bot_bot(fun(x_a,bool)))))->hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,Pn)),bot_bot(fun(x_a,bool)))))).
% 32.78/32.52 all X_b Pa A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3))-> ((all A_4 A_5 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_5))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_5))-> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_5))->hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_5),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),bot_bot(fun(X_b,bool))))))))))->hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))))).
% 32.78/32.52 all X_b Pa F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))-> ((all X_2 F_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_3))-> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3))->hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),F_3)))))))->hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1))))).
% 32.78/32.52 all X_b A_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_2))<->ti(fun(X_b,bool),A_2)=bot_bot(fun(X_b,bool))| (exists A_5 A_4 (ti(fun(X_b,bool),A_2)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),A_5)&hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_5))))).
% 32.78/32.52 all U F ((all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),hAPP(nat,nat,F,N_1))))->hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_e_q(nat)),F)),U))))).
% 32.78/32.52 all X_b X_1 (hAPP(fun(X_b,bool),X_b,the_elem(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))=ti(X_b,X_1)).
% 32.78/32.52 all X_b A_3 (ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))<-> (exists X_2 B_4 (ti(fun(X_b,bool),A_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),B_4)& -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_4))))).
% 32.78/32.52 all Pn (hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),Pn),u))->hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,Pn))))).
% 32.78/32.52 all X_b C_1 A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))-> -(hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1)))).
% 32.78/32.52 all X_b B_1 C_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))-> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))))).
% 32.78/32.52 all X_b C_1 A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))-> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1))).
% 32.78/32.52 all X_b C_1 A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))).
% 32.78/32.52 all X_b A_3 B_1 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)),B_1)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.52 all X_b C_1 A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))<->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))& -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1))).
% 32.78/32.52 all X_b A_3 B_1 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)=hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_1))))).
% 32.78/32.52 all X_b X_1 A_3 F F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=ti(X_b,X_1))& (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))!=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))))).
% 32.78/32.52 all X_b X_1 A_3 F F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))-> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,F_1,A_3)=ti(X_b,X_1))& (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))!=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,F_1,A_3)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))))))).
% 32.78/32.52 all X_c X_b X_1 A_3 F Z_2 G F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))->hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool)))))))).
% 32.78/32.52 all X_c X_b X_1 A_3 F Z_2 G F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))-> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3))->hAPP(fun(X_c,bool),X_b,F_1,A_3)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool))))))))).
% 32.78/32.52 all X_b X_c (minus(X_c)-> (all A_3 B_1 X_2 (hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),fun(X_b,X_c)),minus_minus(fun(X_b,X_c)),A_3),B_1),X_2)=hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(X_b,X_c,A_3,X_2)),hAPP(X_b,X_c,B_1,X_2))))).
% 32.78/32.52 all X_c X_b (minus(X_b)-> (all A_3 B_1 X_1 (hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),minus_minus(fun(X_c,X_b)),A_3),B_1),X_1)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_c,X_b,A_3,X_1)),hAPP(X_c,X_b,B_1,X_1))))).
% 32.78/32.52 all X_b X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat)))& (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))=hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))).
% 32.78/32.52 all X_b X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat)))).
% 32.78/32.52 all X_b (one(X_b)-> (all X_1 (one_one(X_b)=ti(X_b,X_1)<->ti(X_b,X_1)=one_one(X_b)))).
% 32.78/32.52 all X_c X_b F Z_2 G F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1))->hAPP(fun(X_c,bool),X_b,F_1,bot_bot(fun(X_c,bool)))=ti(X_b,Z_2)).
% 32.78/32.52 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),one_one(nat))=N).
% 32.78/32.52 all M_1 N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,suc,N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),one_one(nat))),N)).
% 32.78/32.52 all X_b X_1 F F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1))->hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))=ti(X_b,X_1)).
% 32.78/32.52 all X_c X_b X_1 A_3 F Z_2 G F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))-> (-hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3))->hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,A_3))))).
% 32.78/32.52 all X_b B_1 A_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))-> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_1))->hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))),one_one(nat))))).
% 32.78/32.52 all X_b X_1 A_3 F F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))-> (ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,A_3)))))).
% 32.78/32.52 all X_b A_3 F F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))-> ((all X_2 Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool)))))))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,F_1,A_3)),A_3)))))).
% 32.78/32.52 all X_c X_b A_3 F Z_2 G F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))-> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3))->hAPP(X_c,X_b,G,X_2)=ti(X_b,Z_2)))->hAPP(fun(X_c,bool),X_b,F_1,A_3)=ti(X_b,Z_2)))).
% 32.78/32.52 all X_b X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))))).
% 32.78/32.52 all X_b X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))->hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))).
% 32.78/32.52 all X_b B_1 A_3 F F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (ti(fun(X_b,bool),B_1)!=bot_bot(fun(X_b,bool))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),A_3))->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,B_1)),hAPP(fun(X_b,bool),X_b,F_1,A_3))=hAPP(fun(X_b,bool),X_b,F_1,A_3))))).
% 32.78/32.52 all X_b X_1 A_3 F F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,A_3))))).
% 32.78/32.52 all X_b Pa F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))-> (ti(fun(X_b,bool),F_1)!=bot_bot(fun(X_b,bool))-> ((all X_2 hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool))))))-> ((all X_2 F_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_3))-> (ti(fun(X_b,bool),F_3)!=bot_bot(fun(X_b,bool))-> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3))->hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),F_3))))))))->hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)))))).
% 32.78/32.52 all X_b X_3 (hAPP(fun(X_b,bool),X_b,the_elem(X_b),X_3)=hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),fe_qual(fun(X_b,bool)),X_3)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool)))))).
% 32.78/32.52 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))))).
% 32.78/32.52 all X_b (cancel_semigroup_add(X_b)-> (all A_2 B_3 C_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B_3)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)<->ti(X_b,B_3)=ti(X_b,C_1)))).
% 32.78/32.52 all X_b (cancel_semigroup_add(X_b)-> (all B_3 A_2 C_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),A_2)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)<->ti(X_b,B_3)=ti(X_b,C_1)))).
% 32.78/32.52 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)))).
% 32.78/32.52 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)))).
% 32.78/32.52 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)))).
% 32.78/32.52 all X_b X_1 F F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1))->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),X_1)=ti(X_b,X_1)).
% 32.78/32.52 all M_1 N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1)).
% 32.78/32.52 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))).
% 32.78/32.52 all M_1 N K_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_1))).
% 32.78/32.52 all K M Na (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),Na)<->M=Na).
% 32.78/32.52 all M K Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K)<->M=Na).
% 32.78/32.52 all X_b (ordere236663937imp_le(X_b)-> (all A_2 C_1 B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),C_1)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3))))).
% 32.78/32.52 all X_b (ordere236663937imp_le(X_b)-> (all C_1 A_2 B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B_3)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3))))).
% 32.78/32.52 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)))))).
% 32.78/32.52 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)))))).
% 32.78/32.52 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))))))).
% 32.78/32.52 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))))).
% 32.78/32.52 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))))).
% 32.78/32.52 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)))).
% 32.78/32.52 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)))).
% 32.78/32.52 all M_1 N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,suc,N))=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N))).
% 32.78/32.52 all M_1 N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_1)),N)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N))).
% 32.78/32.52 all M_1 N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_1)),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,suc,N))).
% 32.78/32.52 all N M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N))).
% 32.78/32.52 all N M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1))).
% 32.78/32.52 all M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))<-> (exists K_2 (Na=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)))).
% 32.78/32.52 all K M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))).
% 32.78/32.52 all M_1 I_2 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M_1)))).
% 32.78/32.52 all M_1 I_2 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),J)))).
% 32.78/32.52 all K_1 I_2 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K_1)))).
% 32.78/32.52 all K_1 L_1 I_2 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1))))).
% 32.78/32.52 all M_1 K_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N))).
% 32.78/32.52 all M_1 K_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))).
% 32.78/32.52 all M_1 K_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),N))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N)))).
% 32.78/32.52 all M_1 N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),N)=M_1).
% 32.78/32.52 all N M_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1)),N)=M_1).
% 32.78/32.52 all I_2 J K_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),J)),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K_1))).
% 32.78/32.52 all K_1 M_1 N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)).
% 32.78/32.52 all M_1 K_1 N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),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),K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)).
% 32.78/32.52 all I_2 K_1 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),J)).
% 32.78/32.52 all J_1 K I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K)),I_1))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K)))).
% 32.78/32.52 all M_1 K_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1)),K_1)))).
% 32.78/32.52 all N M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N))=M_1).
% 32.78/32.52 all I_2 K_1 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),K_1)).
% 32.78/32.52 all I_1 K J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K)),J_1)))).
% 32.78/32.52 all N M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),N)=M_1).
% 32.78/32.52 all K I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)=K<->J_1=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),I_1))).
% 32.78/32.52 all I_2 K_1 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1))).
% 32.78/32.52 all I_2 K_1 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)),I_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),K_1)).
% 32.78/32.52 all I_2 K_1 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)),I_2)).
% 32.78/32.52 all N (hAPP(nat,nat,suc,N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N)).
% 32.78/32.52 all N (hAPP(nat,nat,suc,N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))).
% 32.78/32.52 all X_b X_1 A_3 F F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,A_3))=hAPP(fun(X_b,bool),X_b,F_1,A_3)))).
% 32.78/32.52 all M_1 K_1 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),hAPP(nat,nat,suc,J))).
% 32.78/32.52 all M_1 K_1 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1))),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1))).
% 32.78/32.52 all X_b X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))).
% 32.78/32.52 all X_b N_2 H F F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1))-> ((all X_2 Y_1 (hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_1))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1))))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),N_2))-> (ti(fun(X_b,bool),N_2)!=bot_bot(fun(X_b,bool))->hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,F_1,N_2))=hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_2)))))).
% 32.78/32.52 all Y X Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),Z))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))).
% 32.78/32.52 all Z X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))).
% 32.78/32.52 all X_b A_3 B_3 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool)))))->hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),B_3),A_3)=ti(X_b,B_3))& (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool)))))->hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),B_3),A_3)=hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool)))))))).
% 32.78/32.52 all X_b hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),combc(fun(X_b,bool),fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool)))))).
% 32.78/32.52 all X_b X_1 Y_2 Pa ((hBOOL(Pa)->ti(X_b,X_1)=hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),Y_2)))))& (-hBOOL(Pa)->ti(X_b,Y_2)=hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),Y_2)))))).
% 32.78/32.52 all X_b A_2 (hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),A_2))=ti(X_b,A_2)).
% 32.78/32.52 all X_b X_c X_1 Z_2 F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite_comp_fun_idem(X_b,X_c),F))->hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2))=hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)).
% 32.78/32.52 all X_b hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),insert(X_b))).
% 32.78/32.52 all X_b X_1 (hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),fe_qual(X_b),X_1))=ti(X_b,X_1)).
% 32.78/32.52 all X_b Pa A_2 (hBOOL(hAPP(X_b,bool,Pa,A_2))-> ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2))->ti(X_b,X_2)=ti(X_b,A_2)))->hAPP(fun(X_b,bool),X_b,the(X_b),Pa)=ti(X_b,A_2))).
% 32.78/32.52 all X_b Pa ((exists X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2))& (all Y_1 (hBOOL(hAPP(X_b,bool,Pa,Y_1))->ti(X_b,Y_1)=ti(X_b,X_2)))))->hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa)))).
% 32.78/32.53 all X_b A_2 Pa ((exists X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2))& (all Y_1 (hBOOL(hAPP(X_b,bool,Pa,Y_1))->ti(X_b,Y_1)=ti(X_b,X_2)))))-> (hBOOL(hAPP(X_b,bool,Pa,A_2))->hAPP(fun(X_b,bool),X_b,the(X_b),Pa)=ti(X_b,A_2))).
% 32.78/32.53 all X_b Pa A_2 (hBOOL(hAPP(X_b,bool,Pa,A_2))-> ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2))->ti(X_b,X_2)=ti(X_b,A_2)))->hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa))))).
% 32.78/32.53 all X_b Y_2 X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),A_3))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))))).
% 32.78/32.53 all X_b X_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))).
% 32.78/32.53 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,N))).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N)))).
% 32.78/32.53 all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),K)))).
% 32.78/32.53 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))).
% 32.78/32.53 all M Na (M!=Na<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))).
% 32.78/32.53 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)))).
% 32.78/32.53 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))).
% 32.78/32.53 all N M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1))->M_1!=N).
% 32.78/32.53 all S_1 T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S_1),T_4))->S_1!=T_4).
% 32.78/32.53 all Pa M Na ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M)))-> ((M=Na->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M)))-> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M))))).
% 32.78/32.53 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))))).
% 32.78/32.53 all X_b (linorder(X_b)-> (all X_1 Y_2 (ti(X_b,X_1)!=ti(X_b,Y_2)<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))))).
% 32.78/32.53 all X_b (linorder(X_b)-> (all X_1 Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))|ti(X_b,X_1)=ti(X_b,Y_2)))).
% 32.78/32.53 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))))).
% 32.78/32.53 all X_b (linorder(X_b)-> (all Y_2 X_1 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))-> (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))<->ti(X_b,X_1)=ti(X_b,Y_2))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))).
% 32.78/32.53 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))))).
% 32.78/32.53 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))))).
% 32.78/32.53 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)))).
% 32.78/32.53 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)))).
% 32.78/32.53 all X_b (preorder(X_b)-> (all Pa X_1 Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))->hBOOL(Pa))))).
% 32.78/32.53 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))))).
% 32.78/32.53 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))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 all X_b (linorder(X_b)-> (all X_1 Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_2),X_1))))).
% 32.78/32.53 all X_b (linorder(X_b)-> (all X_1 Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))))).
% 32.78/32.53 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))))).
% 32.78/32.53 all X_b (order(X_b)-> (all X_1 Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))&ti(X_b,X_1)!=ti(X_b,Y_2)))).
% 32.78/32.53 all X_b (preorder(X_b)-> (all X_1 Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))& -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_2),X_1))))).
% 32.78/32.53 all X_b (order(X_b)-> (all X_1 Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))|ti(X_b,X_1)=ti(X_b,Y_2)))).
% 32.78/32.53 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))))).
% 32.78/32.53 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))))).
% 32.78/32.53 all X_b (linorder(X_b)-> (all X_1 Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))<->ti(X_b,X_1)=ti(X_b,Y_2))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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))))).
% 32.78/32.53 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))))).
% 32.78/32.53 all X_b (linorder(X_b)-> (all X_1 Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))-> (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))<->ti(X_b,X_1)=ti(X_b,Y_2))))).
% 32.78/32.53 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)))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 all X_b (ordere236663937imp_le(X_b)-> (all A_2 C_1 B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),C_1)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))))).
% 32.78/32.53 all X_b (ordere236663937imp_le(X_b)-> (all C_1 A_2 B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B_3)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))).
% 32.78/32.53 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))))).
% 32.78/32.53 all X_a (bot(X_a)-> (all A_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),bot_bot(X_a)))))).
% 32.78/32.53 all X_b (bot(X_b)-> (all A_2 (ti(X_b,A_2)!=bot_bot(X_b)<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),bot_bot(X_b)),A_2))))).
% 32.78/32.53 all X_b (ordered_ab_group_add(X_b)-> (all A_2 B_3 C_1 D_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1)-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),D_1)))))).
% 32.78/32.53 all M Na (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M)))).
% 32.78/32.53 all M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))|M=Na).
% 32.78/32.53 all M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))).
% 32.78/32.53 all Na M (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M)))<->Na=M)).
% 32.78/32.53 all N M_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M_1)))->M_1=N)).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N)))).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))-> (hAPP(nat,nat,suc,M_1)!=N->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),N)))).
% 32.78/32.53 all K_1 I_2 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_2)),K_1)))).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N)))-> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))->M_1=N)).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))).
% 32.78/32.53 all I_2 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_2),J)),I_2))).
% 32.78/32.53 all J I_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),I_2))).
% 32.78/32.53 all K M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))).
% 32.78/32.53 all M_1 I_2 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M_1)))).
% 32.78/32.53 all M_1 I_2 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),J)))).
% 32.78/32.53 all K_1 I_2 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),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_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K_1)))).
% 32.78/32.53 all K_1 L_1 I_2 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1))))).
% 32.78/32.53 all M_1 N K_1 L_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_1))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),L_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))).
% 32.78/32.53 all I_2 J 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_2),J)),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1))).
% 32.78/32.53 all Z X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))).
% 32.78/32.53 all Y X Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))).
% 32.78/32.53 all M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))&M!=Na).
% 32.78/32.53 all M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))|M=Na).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))-> (M_1!=N->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))|M_1=N->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))).
% 32.78/32.53 all X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),Y))).
% 32.78/32.53 all N J K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K_1))->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_1))).
% 32.78/32.53 all L_1 M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),L_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M_1))))).
% 32.78/32.53 all N_2 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2))<-> (exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M_2))))).
% 32.78/32.53 all X_b A_3 F Na (ti(fun(X_b,bool),A_3)=hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),Na)))->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))).
% 32.78/32.53 all Na (hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),Na)))=Na).
% 32.78/32.53 all Pa I_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),Pa)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 all I_2 M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),M_1)))).
% 32.78/32.53 all I_2 M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),I_2)))).
% 32.78/32.53 all M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))<-> (exists K_2 (Na=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2))))).
% 32.78/32.53 all Na M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,Na)),M))).
% 32.78/32.53 all M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))).
% 32.78/32.53 all M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M)),Na))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N)))).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M_1)),N))).
% 32.78/32.53 all M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M)))<->Na=M)).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M_1)),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))).
% 32.78/32.53 all M_1 N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),hAPP(nat,nat,suc,M_1))).
% 32.78/32.53 all I_1 J_1 K (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)))<->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)),J_1))).
% 32.78/32.53 all M_1 N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),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_1),N))=M_1).
% 32.78/32.53 all C A_1 B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),A_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),C))))).
% 32.78/32.53 all Na 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),Na))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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),Na),K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))))).
% 32.78/32.53 all X_2 (hAPP(nat,fun(nat,bool),ord_less(nat),X_2)=hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,X_2))).
% 32.78/32.53 all M K F ((all M_2 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_2)),hAPP(nat,nat,F,N_1)))))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,M)),K)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K))))).
% 32.78/32.53 all Pa I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))-> (hBOOL(hAPP(nat,bool,Pa,J_1))-> ((all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1))-> (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,I)))->hBOOL(hAPP(nat,bool,Pa,I)))))->hBOOL(hAPP(nat,bool,Pa,I_1))))).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))-> (exists K_2 (N=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2))))).
% 32.78/32.53 all X_b (order(X_b)-> (all Na M F ((all N_1 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,N_1)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_1)))))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,M)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)))))).
% 32.78/32.53 all X_b (order(X_b)-> (all Na N_3 F ((all N_1 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,N_1)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_1)))))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),N_3))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,N_3))))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 all X_b X_c (ord(X_c)-> (all F G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less(fun(X_b,X_c)),F),G))<->hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_e_q(fun(X_b,X_c)),F),G))& -hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_e_q(fun(X_b,X_c)),G),F))))).
% 32.78/32.53 all X_b A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))))).
% 32.78/32.53 all X_b C_2 A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),B_1),C_2))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_2)))).
% 32.78/32.53 all X_b C_2 A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),C_2))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_2)))).
% 32.78/32.53 all X_b A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))).
% 32.78/32.53 all X_b A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))<->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))|ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_1)).
% 32.78/32.53 all X_b A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))<->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))&ti(fun(X_b,bool),A_3)!=ti(fun(X_b,bool),B_1)).
% 32.78/32.53 all X_b A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 all X_b A_3 X_1 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))<-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1)))& (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_1)))& (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))))).
% 32.78/32.53 all X_b A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1)))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))))).
% 32.78/32.53 all X_b A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))<-> (exists N_1 F_2 (ti(fun(X_b,bool),A_3)=hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F_2),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_1)))))).
% 32.78/32.53 all Na N_2 ((all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),Na))))->hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2))).
% 32.78/32.53 all I_1 J_1 F ((all I J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I)),hAPP(nat,nat,F,J_2)))))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_1))))).
% 32.78/32.53 all I_2 K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1))-> (K_1!=hAPP(nat,nat,suc,I_2)-> -(all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2))->K_1!=hAPP(nat,nat,suc,J_2))))).
% 32.78/32.53 all I_2 K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_2)),K_1))-> -(all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2))->K_1!=hAPP(nat,nat,suc,J_2)))).
% 32.78/32.53 all X_b C_1 A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1)))).
% 32.78/32.53 all X_b C_2 A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),B_1),C_2))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_2)))).
% 32.78/32.53 all X_b A_3 B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))-> (exists B_5 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_5),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_1),A_3))))).
% 32.78/32.53 all X_c X_b (order(X_b)&ord(X_c)-> (all C_1 F B_3 A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_c,X_b,F,B_3)),A_2))-> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),B_3))-> ((all X_2 Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Y_1),X_2))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,Y_1)),hAPP(X_c,X_b,F,X_2)))))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,C_1)),A_2))))))).
% 32.78/32.53 all X_c X_b (order(X_b)&order(X_c)-> (all C_1 F B_3 A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,B_3)),A_2))-> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),C_1),B_3))-> ((all X_2 Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),Y_1),X_2))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_c,X_b,F,Y_1)),hAPP(X_c,X_b,F,X_2)))))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,C_1)),A_2))))))).
% 32.78/32.53 all X_b X_c (order(X_c)&order(X_b)-> (all C_1 A_2 F B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),hAPP(X_c,X_b,F,B_3)))-> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),B_3),C_1))-> ((all X_2 Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),X_2),Y_1))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,F,Y_1)))))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,C_1)))))))).
% 32.78/32.53 all X_b X_c (order(X_c)&order(X_b)-> (all C_1 A_2 F B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,B_3)))-> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),B_3),C_1))-> ((all X_2 Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),X_2),Y_1))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,F,Y_1)))))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,C_1)))))))).
% 32.78/32.53 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))))).
% 32.78/32.53 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_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W_3))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W_3),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),W_3),Z)))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z)))))).
% 32.78/32.53 all X_c X_b (order(X_b)&order(X_c)-> (all C_1 F B_3 A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2))-> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),C_1),hAPP(X_b,X_c,F,B_3)))-> ((all X_2 Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2))->hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,Y_1)),hAPP(X_b,X_c,F,X_2)))))->hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,A_2)))))))).
% 32.78/32.53 all X_c X_b (order(X_b)&order(X_c)-> (all C_1 F B_3 A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_3),A_2))-> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,B_3)))-> ((all X_2 Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_1),X_2))->hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),hAPP(X_b,X_c,F,Y_1)),hAPP(X_b,X_c,F,X_2)))))->hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,A_2)))))))).
% 32.78/32.53 all X_b X_c (order(X_c)&order(X_b)-> (all F C_1 A_2 B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3))-> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,B_3)),C_1))-> ((all X_2 Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Y_1))->hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,F,Y_1)))))->hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),C_1))))))).
% 32.78/32.53 all X_b X_c (order(X_c)&order(X_b)-> (all F C_1 A_2 B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))-> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),hAPP(X_b,X_c,F,B_3)),C_1))-> ((all X_2 Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1))->hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,F,Y_1)))))->hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),C_1))))))).
% 32.78/32.53 all X_c X_b B_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))->hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_c,bool),nat,finite_card(X_c),B_1)))).
% 32.78/32.53 all X_c X_b F G M_3 N_2 (ti(fun(X_b,bool),M_3)=ti(fun(X_b,bool),N_2)-> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),N_2))->hAPP(X_b,X_c,F,X_2)=hAPP(X_b,X_c,G,X_2)))->hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),M_3)=hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),G),N_2))).
% 32.78/32.53 all X_b X_c A_3 B_1 (hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1)))->hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))).
% 32.78/32.53 all X_b X_c A_3 B_1 (hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1)))->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))).
% 32.78/32.53 all X_c X_b B_1 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))->hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1))))).
% 32.78/32.53 all X_b X_c A_3 B_1 (hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1)))<->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))&hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))).
% 32.78/32.53 all X_c X_b A_3 B_1 (hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1)=bot_bot(fun(sum_sum(X_b,X_c),bool))<->ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))&ti(fun(X_c,bool),B_1)=bot_bot(fun(X_c,bool))).
% 32.78/32.53 all X_c X_b B_1 A_3 ((hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))&hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))->hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_c,bool),nat,finite_card(X_c),B_1)))& (-(hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))&hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1)))->hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1))=zero_zero(nat))).
% 32.78/32.53 all X_b R_1 S (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),R_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S)))<->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),R_1),S))).
% 32.78/32.53 all X_b Q_3 Pa ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2))->hBOOL(hAPP(X_b,bool,Q_3,X_2))))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3)))).
% 32.78/32.53 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))).
% 32.78/32.53 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N)).
% 32.78/32.53 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N))).
% 32.78/32.53 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Na),zero_zero(nat)))<->Na=zero_zero(nat)).
% 32.78/32.53 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N)).
% 32.78/32.53 all M_1 N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)=zero_zero(nat)-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M_1)=zero_zero(nat)->M_1=N)).
% 32.78/32.53 all M_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),M_1)=zero_zero(nat)).
% 32.78/32.53 all M_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),zero_zero(nat))=M_1).
% 32.78/32.53 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N)=zero_zero(nat)).
% 32.78/32.53 all X_a (zero_ne_q_one(X_a)->one_one(X_a)!=zero_zero(X_a)).
% 32.78/32.53 all X_a (zero_ne_q_one(X_a)->zero_zero(X_a)!=one_one(X_a)).
% 32.78/32.53 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)))).
% 32.78/32.53 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)))).
% 32.78/32.53 all X_b (linord219039673up_add(X_b)-> (all A_2 (zero_zero(X_b)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)<->ti(X_b,A_2)=zero_zero(X_b)))).
% 32.78/32.53 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)))).
% 32.78/32.53 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)))).
% 32.78/32.53 all X_b (group_add(X_b)-> (all A_2 B_3 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)=zero_zero(X_b)<->ti(X_b,A_2)=ti(X_b,B_3)))).
% 32.78/32.53 all X_b (ab_group_add(X_b)-> (all A_2 B_3 (ti(X_b,A_2)=ti(X_b,B_3)<->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)=zero_zero(X_b)))).
% 32.78/32.53 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)))).
% 32.78/32.53 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)))).
% 32.78/32.53 all X_b (zero(X_b)-> (all X_1 (zero_zero(X_b)=ti(X_b,X_1)<->ti(X_b,X_1)=zero_zero(X_b)))).
% 32.78/32.53 bot_bot(nat)=zero_zero(nat).
% 32.78/32.53 all M_1 N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)=M_1->N=zero_zero(nat)).
% 32.78/32.53 all M Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)=zero_zero(nat)<->M=zero_zero(nat)&Na=zero_zero(nat)).
% 32.78/32.53 all M_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),zero_zero(nat))=M_1).
% 32.78/32.53 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N)=N).
% 32.78/32.53 all N (N!=zero_zero(nat)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))->N!=zero_zero(nat)).
% 32.78/32.53 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))).
% 32.78/32.53 all Na (Na!=zero_zero(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))).
% 32.78/32.53 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))).
% 32.78/32.53 all M_1 (hAPP(nat,nat,suc,M_1)!=zero_zero(nat)).
% 32.78/32.53 all M_1 (zero_zero(nat)!=hAPP(nat,nat,suc,M_1)).
% 32.78/32.53 all Nat_2 (hAPP(nat,nat,suc,Nat_2)!=zero_zero(nat)).
% 32.78/32.53 all M_1 (hAPP(nat,nat,suc,M_1)!=zero_zero(nat)).
% 32.78/32.53 all Nat_1 (zero_zero(nat)!=hAPP(nat,nat,suc,Nat_1)).
% 32.78/32.53 all M_1 (zero_zero(nat)!=hAPP(nat,nat,suc,M_1)).
% 32.78/32.53 all X_b F1 F2 (hAPP(nat,X_b,hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(X_b,fun(fun(nat,X_b),fun(nat,X_b)),nat_case(X_b),F1),F2),zero_zero(nat))=ti(X_b,F1)).
% 32.78/32.53 all X_b (linord219039673up_add(X_b)-> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),A_2))))).
% 32.78/32.53 all X_b (linord219039673up_add(X_b)-> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),zero_zero(X_b)))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 all X_b (ordere216010020id_add(X_b)-> (all Y_2 X_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),X_1))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),Y_2))-> (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),X_1),Y_2)=zero_zero(X_b)<->ti(X_b,X_1)=zero_zero(X_b)&ti(X_b,Y_2)=zero_zero(X_b)))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 all X_b (linord219039673up_add(X_b)-> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),A_2))))).
% 32.78/32.53 all X_b (linord219039673up_add(X_b)-> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b)))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 all X_b (ordered_ab_group_add(X_b)-> (all A_2 B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),zero_zero(X_b)))))).
% 32.78/32.53 all X_b (ordered_ab_group_add(X_b)-> (all A_2 B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),zero_zero(X_b)))))).
% 32.78/32.53 all X_a (linordered_semidom(X_a)-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),zero_zero(X_a)))).
% 32.78/32.53 all X_a (linordered_semidom(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),one_one(X_a)))).
% 32.78/32.53 all X_a (linordered_semidom(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a)))).
% 32.78/32.53 all X_a (linordered_semidom(X_a)-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a)))).
% 32.78/32.53 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))<-> (exists M_2 (Na=hAPP(nat,nat,suc,M_2)))).
% 32.78/32.53 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,zero_zero(nat))))<->Na=zero_zero(nat)).
% 32.78/32.53 all M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))<->M=zero_zero(nat)| (exists J_2 (M=hAPP(nat,nat,suc,J_2)&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),Na))))).
% 32.78/32.53 all M Na (hAPP(nat,nat,suc,zero_zero(nat))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)<->M=hAPP(nat,nat,suc,zero_zero(nat))&Na=zero_zero(nat)|M=zero_zero(nat)&Na=hAPP(nat,nat,suc,zero_zero(nat))).
% 32.78/32.53 all M Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)=hAPP(nat,nat,suc,zero_zero(nat))<->M=hAPP(nat,nat,suc,zero_zero(nat))&Na=zero_zero(nat)|M=zero_zero(nat)&Na=hAPP(nat,nat,suc,zero_zero(nat))).
% 32.78/32.53 all M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)))<->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),zero_zero(nat)),Na))).
% 32.78/32.53 all X_b (hAPP(fun(X_b,bool),nat,finite_card(X_b),bot_bot(fun(X_b,bool)))=zero_zero(nat)).
% 32.78/32.53 all X_b A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))->hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=zero_zero(nat)).
% 32.78/32.53 all Na M (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),Na),M)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))).
% 32.78/32.53 all M_1 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_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),M_1)))).
% 32.78/32.53 all N M_1 (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_1))=zero_zero(nat)).
% 32.78/32.53 all M Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),Na)=zero_zero(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)=zero_zero(nat)).
% 32.78/32.53 one_one(nat)=hAPP(nat,nat,suc,zero_zero(nat)).
% 32.78/32.53 all M Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,Na))=hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),combi(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),Na))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))).
% 32.78/32.53 all X_b X_2 (hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2))<->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool))))).
% 32.78/32.53 all X_b A_3 (hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=zero_zero(nat)<->ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))).
% 32.78/32.53 all X_b A_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))).
% 32.78/32.53 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))->hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat))))=N).
% 32.78/32.53 all I_2 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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,I_2))),N))).
% 32.78/32.53 all X_b Q_3 Pa X_1 (hBOOL(hAPP(X_b,bool,Pa,X_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),Pa),Q_3))->hBOOL(hAPP(X_b,bool,Q_3,X_1)))).
% 32.78/32.53 all X_b X_1 Pa Q_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),Pa),Q_3))-> (hBOOL(hAPP(X_b,bool,Pa,X_1))->hBOOL(hAPP(X_b,bool,Q_3,X_1)))).
% 32.78/32.53 all Pa A_2 B_3 (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))<-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_3))->hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))))& (all D_2 (A_2=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_3),D_2)->hBOOL(hAPP(nat,bool,Pa,D_2))))).
% 32.78/32.53 all Pa A_2 B_3 (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))<-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_3))& -hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))| (exists D_2 (A_2=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_3),D_2)& -hBOOL(hAPP(nat,bool,Pa,D_2)))))).
% 32.78/32.53 all I_1 M_3 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_3))->hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1)))))=hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I_1)))))).
% 32.78/32.53 all I_1 M_3 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_3))->hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I_1)))))!=zero_zero(nat)).
% 32.78/32.53 all I_1 M_3 (-hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_3))->hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1))))=hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I_1)))))).
% 32.78/32.53 all X_b A_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))<->ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))&hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))).
% 32.78/32.53 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))->hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))=N).
% 32.78/32.53 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))->N=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))).
% 32.78/32.53 all N M_1 ((M_1=zero_zero(nat)->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)=N)& (M_1!=zero_zero(nat)->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),one_one(nat))),N)))).
% 32.78/32.53 all Na Pa (-hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))-> (hBOOL(hAPP(nat,bool,Pa,Na))-> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),Na))& (all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),K_2))-> -hBOOL(hAPP(nat,bool,Pa,I))))&hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),one_one(nat)))))))).
% 32.78/32.53 all X_b A_3 K (hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=hAPP(nat,nat,suc,K)<-> (exists B_5 B_4 (ti(fun(X_b,bool),A_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_5),B_4)& -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_5),B_4))&hAPP(fun(X_b,bool),nat,finite_card(X_b),B_4)=K& (K=zero_zero(nat)->ti(fun(X_b,bool),B_4)=bot_bot(fun(X_b,bool)))))).
% 32.78/32.53 all X_b A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (((exists X_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)))->one_one(nat)=zero_zero(nat))->hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=zero_zero(nat))).
% 32.78/32.53 all Na Pa (-hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))-> (hBOOL(hAPP(nat,bool,Pa,Na))-> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),Na))& (all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_2))-> -hBOOL(hAPP(nat,bool,Pa,I))))&hBOOL(hAPP(nat,bool,Pa,K_2)))))).
% 32.78/32.53 all I_2 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))-> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2))&hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_2)=J))).
% 32.78/32.53 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))-> (exists M_2 (N=hAPP(nat,nat,suc,M_2)))).
% 32.78/32.53 all X_b (linordered_idom(X_b)-> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b)))))).
% 32.78/32.53 all X_b (linord219039673up_add(X_b)-> (all A_2 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)=zero_zero(X_b)<->ti(X_b,A_2)=zero_zero(X_b)))).
% 32.78/32.53 all X_b A_3 K (hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=hAPP(nat,nat,suc,K)-> (exists B_5 B_4 (ti(fun(X_b,bool),A_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_5),B_4)& -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_5),B_4))&hAPP(fun(X_b,bool),nat,finite_card(X_b),B_4)=K& (K=zero_zero(nat)->ti(fun(X_b,bool),B_4)=bot_bot(fun(X_b,bool)))))).
% 32.78/32.53 all Y (Y!=zero_zero(nat)-> -(all Nat (Y!=hAPP(nat,nat,suc,Nat)))).
% 32.78/32.53 all Pa K (hBOOL(hAPP(nat,bool,Pa,K))-> ((all N_1 (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_1)))->hBOOL(hAPP(nat,bool,Pa,N_1))))->hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))))).
% 32.78/32.53 all N (N!=zero_zero(nat)-> (exists M_2 (N=hAPP(nat,nat,suc,M_2)))).
% 32.78/32.53 all Na Pa (hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))-> ((all N_1 (hBOOL(hAPP(nat,bool,Pa,N_1))->hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_1)))))->hBOOL(hAPP(nat,bool,Pa,Na)))).
% 32.78/32.53 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)))).
% 32.78/32.53 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))))).
% 32.78/32.53 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)))).
% 32.78/32.53 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))))).
% 32.78/32.53 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)))).
% 32.78/32.53 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))))).
% 32.78/32.53 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)))).
% 32.78/32.53 all X_b (semiri456707255roduct(X_b)-> (all B_3 A_2 (ti(X_b,B_3)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),A_2)<->ti(X_b,A_2)=zero_zero(X_b)))).
% 32.78/32.53 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)))).
% 32.78/32.53 all X_a (linordered_field(X_a)-> (all X Y ((all E_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),E_2))->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_2)))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))))).
% 32.78/32.53 all X_b A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))->hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=hAPP(fun(X_b,bool),nat,hAPP(nat,fun(fun(X_b,bool),nat),hAPP(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat))),finite_fold_image(nat,X_b),plus_plus(nat)),hAPP(nat,fun(X_b,nat),combk(nat,X_b),one_one(nat))),zero_zero(nat)),A_3)).
% 32.78/32.53 all X_b A_3 ((hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))->hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=hAPP(fun(X_b,bool),nat,hAPP(nat,fun(fun(X_b,bool),nat),hAPP(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat))),finite_fold_image(nat,X_b),plus_plus(nat)),hAPP(nat,fun(X_b,nat),combk(nat,X_b),one_one(nat))),zero_zero(nat)),A_3))& (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))->hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=zero_zero(nat))).
% 32.78/32.53 all X_c X_b F G Z_2 (hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),F),G),Z_2),bot_bot(fun(X_c,bool)))=ti(X_b,Z_2)).
% 32.78/32.53 all X_c X_b A_3 F Z_2 G F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))->hAPP(fun(X_c,bool),X_b,F_1,A_3)=hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),F),G),Z_2),A_3))).
% 32.78/32.53 all X_b (linordered_idom(X_b)-> (all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b)))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),A_2)),A_2)),zero_zero(X_b)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))))))).
% 32.78/32.53 all V (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V)))->hAPP(int,nat,number_number_of(nat),V)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)))).
% 32.78/32.53 all X_a (linord626643107strict(X_a)-> (all V U_1 Y X A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),U_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),V))-> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U_1),V)=one_one(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1))))))))).
% 32.78/32.53 all X_b (ring_1(X_b)-> (all B_3 A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b)))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),ring_1_Ints(X_b)))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),ring_1_Ints(X_b))))))).
% 32.78/32.53 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)))).
% 32.78/32.53 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)))).
% 32.78/32.53 all X_b (ring_n68954251visors(X_b)-> (all A_2 B_3 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)=zero_zero(X_b)<->ti(X_b,A_2)=zero_zero(X_b)|ti(X_b,B_3)=zero_zero(X_b)))).
% 32.78/32.53 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))))).
% 32.78/32.53 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)))).
% 32.78/32.53 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N)=zero_zero(nat)).
% 32.78/32.53 all M_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),zero_zero(nat))=zero_zero(nat)).
% 32.78/32.53 all M Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)=zero_zero(nat)<->M=zero_zero(nat)|Na=zero_zero(nat)).
% 32.78/32.53 all K M Na (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),Na)<->M=Na|K=zero_zero(nat)).
% 32.78/32.53 all M K Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)<->M=Na|K=zero_zero(nat)).
% 32.78/32.53 all X_b (ab_sem1668676832m_mult(X_b)->hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),times_times(X_b)))).
% 32.78/32.53 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))))).
% 32.78/32.53 all X_a (semiring(X_a)-> (all A_1 E_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),E_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),B),E_1)),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_1)),C)))).
% 32.78/32.53 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)))).
% 32.78/32.53 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)))).
% 32.78/32.53 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)))).
% 32.78/32.53 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)))).
% 32.78/32.53 all K M Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)<->M=Na).
% 32.78/32.53 all M_1 N K_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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),K_1))).
% 32.78/32.53 all K_1 M_1 N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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))).
% 32.78/32.53 all K_1 L_1 I_2 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),L_1))))).
% 32.78/32.53 all K_1 I_2 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),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_1),I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),J)))).
% 32.78/32.53 all K_1 I_2 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),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_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K_1)))).
% 32.78/32.53 all M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),M_1)))).
% 32.78/32.53 all M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),M_1))).
% 32.78/32.53 all M_1 N K_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(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),K_1))).
% 32.78/32.53 all K_1 M_1 N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(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))).
% 32.78/32.53 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)))).
% 32.78/32.53 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)))).
% 32.78/32.53 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)))).
% 32.78/32.53 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))))).
% 32.78/32.53 all M Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)=one_one(nat)<->M=one_one(nat)&Na=one_one(nat)).
% 32.78/32.53 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),one_one(nat))=N).
% 32.78/32.53 all M Na (one_one(nat)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)<->M=one_one(nat)&Na=one_one(nat)).
% 32.78/32.53 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N)=N).
% 32.78/32.53 all X_b (number_ring(X_b)&linordered_idom(X_b)-> (all X_1 Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(int,X_b,number_number_of(X_b),X_1)),hAPP(int,X_b,number_number_of(X_b),Y_2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_2))))).
% 32.78/32.53 all X_b (number_ring(X_b)-> (all W_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(int,X_b,number_number_of(X_b),W_1)),ring_1_Ints(X_b))))).
% 32.78/32.53 all X_a (number_ring(X_a)-> (all V W (hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))))).
% 32.78/32.53 all X_b (number(X_b)-> (all W_1 X_1 (hAPP(int,X_b,number_number_of(X_b),W_1)=ti(X_b,X_1)<->ti(X_b,X_1)=hAPP(int,X_b,number_number_of(X_b),W_1)))).
% 32.78/32.53 all X_a (number_ring(X_a)-> (all V W (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W))))).
% 32.78/32.53 all X_b (number_ring(X_b)&ring_char_0(X_b)-> (all X_1 Y_2 (hAPP(int,X_b,number_number_of(X_b),X_1)=hAPP(int,X_b,number_number_of(X_b),Y_2)<->X_1=Y_2))).
% 32.78/32.53 all X_a (number_ring(X_a)-> (all V W Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W)),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W))),Z)))).
% 32.78/32.53 all X_b (ring_1(X_b)-> (all B_3 A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b)))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),ring_1_Ints(X_b)))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)),ring_1_Ints(X_b))))))).
% 32.78/32.53 all X_b (number_ring(X_b)&linordered_idom(X_b)-> (all X_1 Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(int,X_b,number_number_of(X_b),X_1)),hAPP(int,X_b,number_number_of(X_b),Y_2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_1),Y_2))))).
% 32.78/32.53 all X_a (number_ring(X_a)-> (all V W (hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),V),W))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))))).
% 32.78/32.53 all X_b (number(X_b)&ring(X_b)-> (all A_1 B V (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_1),B)),hAPP(int,X_b,number_number_of(X_b),V))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V)))))).
% 32.78/32.53 all X_b (number(X_b)&ring(X_b)-> (all V B C (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B),C))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C))))).
% 32.78/32.53 all X_b (ring_1(X_b)-> (all B_3 A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b)))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),ring_1_Ints(X_b)))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B_3)),ring_1_Ints(X_b))))))).
% 32.78/32.53 all X_a (number_ring(X_a)-> (all V W (hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))))).
% 32.78/32.53 all X_a (number_ring(X_a)-> (all V W (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))))).
% 32.78/32.53 all X_b (number(X_b)&semiring(X_b)-> (all V B C (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),C))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C))))).
% 32.78/32.53 all X_a (number_ring(X_a)-> (all V W Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),Z)))).
% 32.78/32.53 all X_b (number(X_b)&semiring(X_b)-> (all A_1 B V (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_1),B)),hAPP(int,X_b,number_number_of(X_b),V))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V)))))).
% 32.78/32.53 all X_b (ring_1(X_b)->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),zero_zero(X_b)),ring_1_Ints(X_b)))).
% 32.78/32.53 all X_b (ring_1(X_b)->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),one_one(X_b)),ring_1_Ints(X_b)))).
% 32.78/32.53 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)))).
% 32.78/32.53 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)))).
% 32.78/32.53 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)))).
% 32.78/32.53 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))))).
% 32.78/32.53 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)))).
% 32.78/32.53 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))))).
% 32.78/32.53 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)))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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))))).
% 32.78/32.53 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))))).
% 32.78/32.53 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))))).
% 32.78/32.53 all X_b (semiri456707255roduct(X_b)-> (all C_1 D_1 A_2 B_3 (ti(X_b,A_2)!=ti(X_b,B_3)&ti(X_b,C_1)!=ti(X_b,D_1)<->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),D_1))!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),D_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1))))).
% 32.78/32.53 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))))).
% 32.78/32.53 all X_a (comm_semiring_1(X_a)-> (all A_1 M_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),A_1),M_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),M_1))=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_1)))).
% 32.78/32.53 all X_b (semiri456707255roduct(X_b)-> (all W_1 Y_2 X_1 Z_2 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Y_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Z_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Z_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Y_2))<->ti(X_b,W_1)=ti(X_b,X_1)|ti(X_b,Y_2)=ti(X_b,Z_2)))).
% 32.78/32.53 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)))).
% 32.78/32.53 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)))).
% 32.78/32.53 all X_b (number(X_b)&linorder(X_b)-> (all V_3 W_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(int,X_b,number_number_of(X_b),V_3)),hAPP(int,X_b,number_number_of(X_b),W_1)))<-> -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(int,X_b,number_number_of(X_b),W_1)),hAPP(int,X_b,number_number_of(X_b),V_3)))))).
% 32.78/32.53 all X_a (number_ring(X_a)-> (all V W C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),C))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),C)))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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))))))))).
% 32.78/32.53 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))))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 all X_b (linord581940658strict(X_b)-> (all A_2 B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)),zero_zero(X_b)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),A_2))&hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_3),zero_zero(X_b)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),zero_zero(X_b)))&hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),B_3))))).
% 32.78/32.53 all X_b (linord581940658strict(X_b)-> (all A_2 B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),A_2))&hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),B_3))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),zero_zero(X_b)))&hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_3),zero_zero(X_b)))))).
% 32.78/32.53 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))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 all X_b (linord581940658strict(X_b)-> (all A_2 C_1 B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1))&hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b)))&hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2))))).
% 32.78/32.53 all X_b (linord581940658strict(X_b)-> (all C_1 A_2 B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1))&hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b)))&hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2))))).
% 32.78/32.53 all X_b (linord581940658strict(X_b)-> (all A_2 B_3 C_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 all X_b (linord581940658strict(X_b)-> (all A_2 B_3 C_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b)))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2)))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 all X_a (semiri456707255roduct(X_a)-> (all C D A_1 B R_3 (ti(X_a,R_3)!=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_3),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_3),D)))))).
% 32.78/32.53 all X_b (linord581940658strict(X_b)-> (all X_1 Y_2 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))=zero_zero(X_b)<->ti(X_b,X_1)=zero_zero(X_b)&ti(X_b,Y_2)=zero_zero(X_b)))).
% 32.78/32.53 all X_a (linordered_semidom(X_a)-> (all N M_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M_1))-> (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_1),N))))))).
% 32.78/32.53 all X_b (ring(X_b)-> (all A_2 E C_1 B_3 D_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)<->ti(X_b,C_1)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1)))).
% 32.78/32.53 all X_b (ring(X_b)-> (all A_2 E C_1 B_3 D_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)<->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1)=ti(X_b,D_1)))).
% 32.78/32.53 all X_a (comm_semiring_1(X_a)-> (all A_1 M_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),M_1)),M_1)=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_1)))).
% 32.78/32.53 all X_a (comm_semiring_1(X_a)-> (all M_1 A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M_1))=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_1)))).
% 32.78/32.53 all X_a (comm_semiring_1(X_a)-> (all M_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M_1),M_1)=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_1)))).
% 32.78/32.53 all M Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)=hAPP(nat,nat,suc,zero_zero(nat))<->M=hAPP(nat,nat,suc,zero_zero(nat))&Na=hAPP(nat,nat,suc,zero_zero(nat))).
% 32.78/32.53 all K_1 I_2 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),J))))).
% 32.78/32.53 all K_1 I_2 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K_1))))).
% 32.78/32.53 all M K Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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),Na),K)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))).
% 32.78/32.53 all K M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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),Na)))<->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),M),Na))).
% 32.78/32.53 all M Na (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),Na)))<->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),zero_zero(nat)),Na))).
% 32.78/32.53 all K M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))).
% 32.78/32.53 all M_1 N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),hAPP(nat,nat,suc,N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N))).
% 32.78/32.53 all M_1 N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,M_1)),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N))).
% 32.78/32.53 all K M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))).
% 32.78/32.53 all M_1 N (M_1=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)->N=one_one(nat)|M_1=zero_zero(nat)).
% 32.78/32.53 all X_b (ring_char_0(X_b)-> (all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b)))-> (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)=zero_zero(X_b)<->ti(X_b,A_2)=zero_zero(X_b))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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))))))))).
% 32.78/32.53 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))))))))).
% 32.78/32.53 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))))))))).
% 32.78/32.53 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))))))))).
% 32.78/32.53 all X_b (linord581940658strict(X_b)-> (all A_2 B_3 C_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b)))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_3),A_2)))))).
% 32.78/32.53 all X_b (linord581940658strict(X_b)-> (all A_2 B_3 C_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3)))))).
% 32.78/32.53 all X_b (linord581940658strict(X_b)-> (all X_1 Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))),zero_zero(X_b)))<->ti(X_b,X_1)=zero_zero(X_b)&ti(X_b,Y_2)=zero_zero(X_b)))).
% 32.78/32.53 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)))))).
% 32.78/32.53 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)))))).
% 32.78/32.53 all X_b (linord581940658strict(X_b)-> (all X_1 Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))))<->ti(X_b,X_1)!=zero_zero(X_b)|ti(X_b,Y_2)!=zero_zero(X_b)))).
% 32.78/32.53 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))))))).
% 32.78/32.53 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))))))).
% 32.78/32.53 all X_b (ordered_ring(X_b)-> (all A_2 E C_1 B_3 D_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1)))))).
% 32.78/32.53 all X_b (ordered_ring(X_b)-> (all A_2 E C_1 B_3 D_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1)),D_1))))).
% 32.78/32.53 all X_b (ordered_ring(X_b)-> (all A_2 E C_1 B_3 D_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1)))))).
% 32.78/32.53 all X_b (ordered_ring(X_b)-> (all A_2 E C_1 B_3 D_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1)),D_1))))).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N))))).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M_1))))).
% 32.78/32.53 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N))))).
% 32.78/32.53 all M Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),M))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),Na))).
% 32.78/32.53 all K M Na (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),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))<-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)))).
% 32.78/32.53 all M K Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)))<-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)))).
% 32.78/32.53 all X_b X_c (ab_semigroup_mult(X_c)-> (all G Z_2 A_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))->hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3))=hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,G,A_2)),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_2),A_3)))))).
% 32.78/32.53 all X_b X_c (comm_monoid_mult(X_c)-> (all G H A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))->hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,X_c)),combs(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combb(X_c,fun(X_c,X_c),X_b),times_times(X_c)),G)),H)),one_one(X_c)),A_3)=hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),one_one(X_c)),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),H),one_one(X_c)),A_3))))).
% 32.78/32.53 all X_a (linord1278240602ring_1(X_a)-> (all V U_1 Y X A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),U_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),V))-> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U_1),V)=one_one(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1))))))))).
% 32.78/32.53 all N M_1 ((M_1=zero_zero(nat)->hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)=zero_zero(nat))& (M_1!=zero_zero(nat)->hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),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_1),one_one(nat))),N)))).
% 32.78/32.53 all X_b (ring_char_0(X_b)-> (all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b)))->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),A_2)),A_2)!=zero_zero(X_b)))).
% 32.78/32.53 all X_a (linord1117847801e_zero(X_a)-> (all X Y ((all Z_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Z_3))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),one_one(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_3),X)),Y)))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))))).
% 32.78/32.53 all X_b X_c (comm_monoid_mult(X_c)-> (all F S (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),S))-> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),S))->hAPP(X_b,X_c,F,X_2)=one_one(X_c)))->hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),F),one_one(X_c)),S)=one_one(X_c))))).
% 32.78/32.53 all U M Na I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),Na))))).
% 32.78/32.53 all M_1 N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M_1)).
% 32.78/32.53 all M_1 N K_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_1))).
% 32.78/32.53 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))).
% 32.78/32.53 all Z (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z)=Z).
% 32.78/32.53 all Z (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),one_one(int))=Z).
% 32.78/32.53 all Z W (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),W)=hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z)).
% 32.78/32.53 all V W (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W))=hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W))).
% 32.78/32.53 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))).
% 32.78/32.53 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L))).
% 32.78/32.53 all Z1 Z2 W (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)=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W))).
% 32.78/32.53 all W Z1 Z2 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),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),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z2))).
% 32.78/32.53 all W Z1 Z2 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),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),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z2))).
% 32.78/32.53 all V W (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W))=hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))).
% 32.78/32.53 all Z1 Z2 W (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)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W))).
% 32.78/32.53 all K_1 I_2 J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),I_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),J))))).
% 32.78/32.53 all Na M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))-> (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),Na)=one_one(int)<->M=one_one(int)&Na=one_one(int))).
% 32.78/32.53 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)).
% 32.78/32.53 all Z (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),zero_zero(int))=Z).
% 32.78/32.53 all Z (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),Z)=Z).
% 32.78/32.53 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))).
% 32.78/32.53 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_2))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2))).
% 32.78/32.53 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),L)),zero_zero(int)))).
% 32.78/32.53 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)))).
% 32.78/32.53 all Z_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),plus_plus(int),one_one(int)),Z_2)),Z_2)),zero_zero(int)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int)))).
% 32.78/32.53 all K_1 I_2 J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),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_1),I_2)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),J)))).
% 32.78/32.53 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))).
% 32.78/32.53 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))).
% 32.78/32.53 all Z W (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),W)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z)).
% 32.78/32.53 all W hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),W)).
% 32.78/32.53 all Z W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),W))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z))).
% 32.78/32.53 all K_1 I_2 J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),J))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),J),K_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),K_1)))).
% 32.78/32.53 all Z W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),W))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z))->Z=W)).
% 32.78/32.53 all W_1 Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_2),one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))).
% 32.78/32.53 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))).
% 32.78/32.53 all Z_2 W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_2),W_1))&Z_2!=W_1).
% 32.78/32.53 all K_1 I_2 J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),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_2),K_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),J),K_1)))).
% 32.78/32.53 all Z_4 Z W_2 W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),W))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_4),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_2),Z_4)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z))))).
% 32.78/32.53 all W_1 Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_2))).
% 32.78/32.53 all W_1 Z_2 (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_2))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))).
% 32.78/32.53 all W Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),one_one(int))),Z))).
% 32.78/32.53 all W_1 Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))|W_1=Z_2).
% 32.78/32.53 all K M Na (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),Na)<->K=zero_zero(nat)|M=Na).
% 32.78/32.53 all I_2 U_1 J K_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),U_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),U_1)),K_1)).
% 32.78/32.53 all M Na K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)<->M=Na)).
% 32.78/32.53 all M Na K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)))).
% 32.78/32.53 all M Na K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)))).
% 32.78/32.53 all U M Na J_1 I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),I_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M)),Na)))).
% 32.78/32.53 all U_1 M_1 N J I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),I_2))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),U_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),J)),U_1)),M_1)),N)).
% 32.78/32.53 all U M Na J_1 I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),I_1))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)<->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M)=Na)).
% 32.78/32.53 all U M Na I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),Na))))).
% 32.78/32.53 all U_1 M_1 N I_2 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),U_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I_2)),U_1)),N))).
% 32.78/32.53 all U M Na I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)<->M=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),Na))).
% 32.78/32.53 all U M Na J_1 I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),I_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M)),Na)))).
% 32.78/32.53 all B Q_2 R_3 B_2 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_2)),R_3)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),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_2),Q_1)),R_2)),zero_zero(int)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q_2)))))))).
% 32.78/32.53 all B Q_1 R_2 Q_2 R_3 (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_2)),R_3)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_3),zero_zero(int)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_2))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_2),Q_1)))))).
% 32.78/32.53 all K_1 (hAPP(int,int,number_number_of(int),K_1)=K_1).
% 32.78/32.53 zero_zero(int)!=one_one(int).
% 32.78/32.53 all R_3 Q_2 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_3),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),A_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Q_2))))).
% 32.78/32.53 all R_3 Q_2 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_3),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_3))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_2),one_one(int)))))).
% 32.78/32.53 all B_2 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_2),Q_1)),R_2)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Q_1))))).
% 32.78/32.53 all B_2 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_2),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_2))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),zero_zero(int)))))).
% 32.78/32.53 all B Q_1 R_2 Q_2 R_3 (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_2)),R_3)))-> (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_3),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q_2)))))).
% 32.78/32.53 all B Q_2 R_3 B_2 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_2)),R_3)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),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_2),Q_1)),R_2)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_3))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),B))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_2),Q_1)))))))).
% 32.78/32.53 all Pa I_1 K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K))-> (hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),one_one(int))))-> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),K))-> (hBOOL(hAPP(int,bool,Pa,I))->hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I),one_one(int)))))))->hBOOL(hAPP(int,bool,Pa,I_1))))).
% 32.78/32.53 all Pa I_1 K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),K))-> (hBOOL(hAPP(int,bool,Pa,K))-> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I),K))-> (hBOOL(hAPP(int,bool,Pa,I))->hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I),one_one(int)))))))->hBOOL(hAPP(int,bool,Pa,I_1))))).
% 32.78/32.53 all X_b X_c (ab_semigroup_mult(X_c)-> (all Z_2 G H A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))-> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))->hAPP(X_b,X_c,G,X_2)=hAPP(X_b,X_c,H,X_2)))->hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_2),A_3)=hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),H),Z_2),A_3))))).
% 32.78/32.53 all Pa K I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_1))-> (hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),one_one(int))))-> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I))-> (hBOOL(hAPP(int,bool,Pa,I))->hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),one_one(int)))))))->hBOOL(hAPP(int,bool,Pa,I_1))))).
% 32.78/32.53 all Pa K I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),I_1))-> (hBOOL(hAPP(int,bool,Pa,K))-> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),I))-> (hBOOL(hAPP(int,bool,Pa,I))->hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),one_one(int)))))))->hBOOL(hAPP(int,bool,Pa,I_1))))).
% 32.78/32.53 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))))).
% 32.78/32.53 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),zero_zero(int))).
% 32.78/32.53 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))))).
% 32.78/32.53 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),one_one(int))).
% 32.78/32.53 all P_1 Pa ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_2))-> (hBOOL(hAPP(int,bool,Pa,X_2))<->hBOOL(hAPP(int,bool,P_1,X_2)))))->hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)))),Pa))=hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)))),P_1))).
% 32.78/32.53 all K Pa 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,Pa,X_2))->hBOOL(hAPP(int,bool,Pa,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))-> (all X_2 (hBOOL(hAPP(int,bool,Pa,X_2))->hBOOL(hAPP(int,bool,Pa,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),D_1))))))))).
% 32.78/32.53 all P_1 Pa X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))-> (hBOOL(Pa)<->hBOOL(P_1)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))&hBOOL(Pa)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))&hBOOL(P_1))).
% 32.78/32.53 all P_1 Pa X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))-> (hBOOL(Pa)<->hBOOL(P_1)))-> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))->hBOOL(Pa))<-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))->hBOOL(P_1)))).
% 32.78/32.53 all K Pa 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,Pa,X_2))->hBOOL(hAPP(int,bool,Pa,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))-> (all X_2 (hBOOL(hAPP(int,bool,Pa,X_2))->hBOOL(hAPP(int,bool,Pa,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),D_1))))))))).
% 32.78/32.53 all X_a (linorder(X_a)-> (all T_4 exists Z_3 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_3))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),T_4),X_2))))).
% 32.78/32.53 all X_a (linorder(X_a)-> (all T_4 exists Z_3 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),X_2))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_2),T_4))))).
% 32.78/32.53 all X_a (linorder(X_a)-> (all T_4 exists Z_3 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_3))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_2),T_4))))).
% 32.78/32.53 all X_a (linorder(X_a)-> (all T_4 exists Z_3 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),X_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),T_4),X_2))))).
% 32.78/32.53 all I_1 Pa K (hBOOL(hAPP(int,bool,Pa,K))-> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),I))-> (hBOOL(hAPP(int,bool,Pa,I))->hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),one_one(int)))))))-> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I),K))-> (hBOOL(hAPP(int,bool,Pa,I))->hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I),one_one(int)))))))->hBOOL(hAPP(int,bool,Pa,I_1))))).
% 32.78/32.53 all Pa 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_3 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Z_3))-> (hBOOL(hAPP(int,bool,Pa,X_2))<->hBOOL(hAPP(int,bool,P1,X_2)))))-> ((exists X1 hBOOL(hAPP(int,bool,P1,X1)))-> (exists X1 hBOOL(hAPP(int,bool,Pa,X1))))))).
% 32.78/32.53 all Pa 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_3 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_3),X_2))-> (hBOOL(hAPP(int,bool,Pa,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,Pa,X1))))))).
% 32.78/32.53 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))).
% 32.78/32.53 all X_a (number_ring(X_a)-> (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V)))->hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,X_a,number_number_of(X_a),V))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V)))->hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))=zero_zero(X_a))))).
% 32.78/32.53 all X_a (number_semiring(X_a)-> (all N (hAPP(int,X_a,number_number_of(X_a),hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))).
% 32.78/32.53 all N hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N))).
% 32.78/32.53 all K_1 (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K_1)),zero_zero(int)))).
% 32.78/32.53 all X_a (linordered_semidom(X_a)-> (all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))).
% 32.78/32.53 all X_a (linordered_semidom(X_a)-> (all M_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1))))).
% 32.78/32.53 all X_a (linordered_semidom(X_a)-> (all M_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),zero_zero(X_a)))))).
% 32.78/32.53 all X_a (semiring_1(X_a)->hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat))=zero_zero(X_a)).
% 32.78/32.53 all X_a (semiring_1(X_a)->hAPP(nat,X_a,semiring_1_of_nat(X_a),one_one(nat))=one_one(X_a)).
% 32.78/32.53 hAPP(nat,int,semiring_1_of_nat(int),one_one(nat))=one_one(int).
% 32.78/32.53 hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat))=zero_zero(int).
% 32.78/32.53 all Na (hAPP(nat,int,semiring_1_of_nat(int),Na)=zero_zero(int)<->Na=zero_zero(nat)).
% 32.78/32.53 all X_b (ring_1(X_b)-> (all Na hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)),ring_1_Ints(X_b))))).
% 32.78/32.53 all X_b (semiring_char_0(X_b)-> (all M Na (hAPP(nat,X_b,semiring_1_of_nat(X_b),M)=hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)<->M=Na))).
% 32.78/32.53 all X_a (semiring_1(X_a)-> (all M_1 N (hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))).
% 32.78/32.53 all X_b (linordered_semidom(X_b)-> (all M Na (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))))).
% 32.78/32.53 all X_b (linordered_semidom(X_b)-> (all M Na (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))))).
% 32.78/32.53 all X_a (linordered_semidom(X_a)-> (all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))))).
% 32.78/32.53 all X_a (linordered_semidom(X_a)-> (all M_1 N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))))).
% 32.78/32.53 all M Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))).
% 32.78/32.53 all M Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))).
% 32.78/32.53 all M_1 N (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N))).
% 32.78/32.53 all M_1 N Z (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),N)),Z))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N))),Z)).
% 32.78/32.53 all W_1 Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_2))<-> (exists N_1 (Z_2=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),N_1))))).
% 32.78/32.53 all M_1 N (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N))).
% 32.78/32.53 all M_1 N (hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N))=hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N))).
% 32.78/32.53 all X_a (semiring_1(X_a)-> (all M_1 N (hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))).
% 32.78/32.53 all X Y (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y))).
% 32.78/32.53 all X_1 Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2))).
% 32.78/32.53 all X_1 Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_1),Y_2))).
% 32.78/32.53 all X Y (hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X),Y))).
% 32.78/32.53 all X Y (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Y))).
% 32.78/32.53 all A_3 (hAPP(fun(nat,bool),nat,finite_card(nat),A_3)=hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))).
% 32.78/32.53 all A_3 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),A_3))<->hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)))).
% 32.78/32.53 one_one(int)=hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)).
% 32.78/32.53 zero_zero(int)=hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)).
% 32.78/32.53 all Pa (hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)))),Pa))=hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,int),fun(nat,bool),hAPP(fun(int,bool),fun(fun(nat,int),fun(nat,bool)),combb(int,bool,nat),Pa),semiring_1_of_nat(int))))).
% 32.78/32.53 all Z hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Z))).
% 32.78/32.53 all Pa ((exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_2))&hBOOL(hAPP(int,bool,Pa,X_2))))<-> (exists X_2 hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2))))).
% 32.78/32.53 all Pa ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_2))->hBOOL(hAPP(int,bool,Pa,X_2))))<-> (all X_2 hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2))))).
% 32.78/32.53 all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)))<->Na=zero_zero(nat)).
% 32.78/32.53 hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,zero_zero(nat)))=one_one(int).
% 32.78/32.53 all W_1 Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))<-> (exists N_1 (Z_2=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_1)))))).
% 32.78/32.53 all M_1 (hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M_1))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M_1))).
% 32.78/32.53 all N M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1))->hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N))).
% 32.78/32.53 all X_a (semiring_1(X_a)-> (all M_1 (hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,M_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1))))).
% 32.78/32.53 all X_a (ring_1(X_a)-> (all N M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1))->hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))).
% 32.78/32.53 all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))).
% 32.78/32.53 all K_1 I_2 J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K_1)),I_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K_1)),J))))).
% 32.78/32.53 all X_b (linordered_semidom(X_b)-> (all Na (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))))).
% 32.78/32.53 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))))).
% 32.78/32.53 all Pa X_1 Y_2 (hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_2))))<-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Y_2),X_1))->hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2)))))& (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2))->hBOOL(hAPP(int,bool,Pa,zero_zero(int))))).
% 32.78/32.53 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)).
% 32.78/32.53 all K_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1))-> (exists N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))&K_1=hAPP(nat,int,semiring_1_of_nat(int),N_1)))).
% 32.78/32.53 all X_b (semiring_1(X_b)-> (all Na (hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)=hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),hAPP(X_b,fun(X_b,X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,X_b)),combc(X_b,X_b,X_b),plus_plus(X_b)),one_one(X_b))),Na),zero_zero(X_b))))).
% 32.78/32.53 all M Na (hAPP(nat,int,semiring_1_of_nat(int),M)=hAPP(nat,int,semiring_1_of_nat(int),Na)<->M=Na).
% 32.78/32.53 all A_3 B_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),A_3),B_1))<->hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1)))).
% 32.78/32.53 all A_3 B_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_e_q(fun(nat,bool)),A_3),B_1))<->hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_e_q(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1)))).
% 32.78/32.53 bot_bot(fun(int,bool))=hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),bot_bot(fun(nat,bool))).
% 32.78/32.53 all A_3 B_1 (A_3=B_1<->hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)=hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1)).
% 32.78/32.53 all X_1 A_3 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),A_3))<->hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)))).
% 32.78/32.53 all X_1 Y_2 Pa ((hBOOL(Pa)->hAPP(nat,int,semiring_1_of_nat(int),X_1)=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),Pa),X_1),Y_2)))& (-hBOOL(Pa)->hAPP(nat,int,semiring_1_of_nat(int),Y_2)=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),Pa),X_1),Y_2)))).
% 32.78/32.53 all X_1 Y_2 (hAPP(nat,int,semiring_1_of_nat(int),X_1)=hAPP(nat,int,semiring_1_of_nat(int),Y_2)<->X_1=Y_2).
% 32.78/32.53 all X_b (semiring_1(X_b)-> (all Inc I_1 (hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),Inc),zero_zero(nat)),I_1)=ti(X_b,I_1)))).
% 32.78/32.53 all X_b (semiring_1(X_b)-> (all Inc Na I_1 (hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),Inc),hAPP(nat,nat,suc,Na)),I_1)=hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),Inc),Na),hAPP(X_b,X_b,Inc,I_1))))).
% 32.78/32.53 all K_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K_1))-> -(all N_1 (K_1!=hAPP(nat,int,semiring_1_of_nat(int),N_1)))).
% 32.78/32.53 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))-> -(all M_2 (Z!=hAPP(nat,int,semiring_1_of_nat(int),M_2)))).
% 32.78/32.53 all K_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K_1))-> (exists N_1 (K_1=hAPP(nat,int,semiring_1_of_nat(int),N_1)))).
% 32.78/32.53 all Z (-(all M_2 N_1 (Z!=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_2)),hAPP(nat,int,semiring_1_of_nat(int),N_1))))).
% 32.78/32.53 all X_c X_b (comm_monoid_mult(X_b)-> (all H G S R_1 E (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,E),E))-> ((all X1 Y1 X2 Y2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,X1),X2))&hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,Y1),Y2))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X1),Y1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X2),Y2)))))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),S))-> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),S))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_c,X_b,H,X_2)),hAPP(X_c,X_b,G,X_2)))))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),H),E),S)),hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),G),E),S))))))))).
% 32.78/32.53 all X_c X_b X_d (comm_monoid_mult(X_d)-> (all E G F H K T_3 S (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),S))-> ((all Y_1 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Y_1),T_3))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_c,X_b,K,Y_1)),S))&hAPP(X_b,X_c,H,hAPP(X_c,X_b,K,Y_1))=ti(X_c,Y_1)))-> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),S))->hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,H,X_2)),T_3))&hAPP(X_c,X_b,K,hAPP(X_b,X_c,H,X_2))=ti(X_b,X_2)&hAPP(X_c,X_d,G,hAPP(X_b,X_c,H,X_2))=hAPP(X_b,X_d,F,X_2)))->hAPP(fun(X_b,bool),X_d,hAPP(X_d,fun(fun(X_b,bool),X_d),hAPP(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d))),finite_fold_image(X_d,X_b),times_times(X_d)),F),E),S)=hAPP(fun(X_c,bool),X_d,hAPP(X_d,fun(fun(X_c,bool),X_d),hAPP(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d))),finite_fold_image(X_d,X_c),times_times(X_d)),G),E),T_3)))))).
% 32.78/32.53 all X_a (number_ring(X_a)-> (all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))=zero_zero(X_a))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,X_a,number_number_of(X_a),V))))).
% 32.78/32.54 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))).
% 32.78/32.54 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)))))).
% 32.78/32.54 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))))))).
% 32.78/32.54 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z_2)),one_one(int)))<->Z_2=zero_zero(int)).
% 32.78/32.54 all Z_1 (hBOOL(hAPP(int,bool,nat_neg,Z_1))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),zero_zero(int)))).
% 32.78/32.54 all X_1 (-hBOOL(hAPP(int,bool,nat_neg,X_1))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))).
% 32.78/32.54 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)))).
% 32.78/32.54 all X_b (ordere142940540dd_abs(X_b)-> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,abs_abs(X_b),A_2)),zero_zero(X_b)))<->ti(X_b,A_2)=zero_zero(X_b)))).
% 32.78/32.54 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))))).
% 32.78/32.54 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)))))).
% 32.78/32.54 all X_b (ordere142940540dd_abs(X_b)-> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,abs_abs(X_b),A_2)))<->ti(X_b,A_2)!=zero_zero(X_b)))).
% 32.78/32.54 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)))).
% 32.78/32.54 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)))))).
% 32.78/32.54 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)))))).
% 32.78/32.54 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)))))).
% 32.78/32.54 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))))))).
% 32.78/32.54 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)))))).
% 32.78/32.54 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))))).
% 32.78/32.54 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))))).
% 32.78/32.54 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))))).
% 32.78/32.54 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))))).
% 32.78/32.54 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))))).
% 32.78/32.54 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)))).
% 32.78/32.54 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))))).
% 32.78/32.54 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))))).
% 32.78/32.54 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)))).
% 32.78/32.54 -hBOOL(hAPP(int,bool,nat_neg,one_one(int))).
% 32.78/32.54 all X_a (linordered_idom(X_a)->hAPP(X_a,X_a,abs_abs(X_a),one_one(X_a))=one_one(X_a)).
% 32.78/32.54 -hBOOL(hAPP(int,bool,nat_neg,zero_zero(int))).
% 32.78/32.54 all X_b (ordere142940540dd_abs(X_b)-> (all A_2 (hAPP(X_b,X_b,abs_abs(X_b),A_2)=zero_zero(X_b)<->ti(X_b,A_2)=zero_zero(X_b)))).
% 32.78/32.54 all X_a (ordere142940540dd_abs(X_a)->hAPP(X_a,X_a,abs_abs(X_a),zero_zero(X_a))=zero_zero(X_a)).
% 32.78/32.54 all M_1 N (hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N))=one_one(int)->hAPP(int,int,abs_abs(int),M_1)=one_one(int)).
% 32.78/32.54 all X_a (linordered_idom(X_a)-> (all N (hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))=hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))).
% 32.78/32.54 all N (-hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),N)))).
% 32.78/32.54 all M_1 (hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),M_1))=hAPP(nat,int,semiring_1_of_nat(int),M_1)).
% 32.78/32.54 all V (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(int,nat,number_number_of(nat),V)=zero_zero(nat)).
% 32.78/32.54 all V_3 V_2 (hAPP(int,nat,number_number_of(nat),V_3)=hAPP(int,nat,number_number_of(nat),V_2)<-> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_2)),zero_zero(int))))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3)))-> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2)))->hAPP(int,int,number_number_of(int),V_3)=zero_zero(int))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2)))->V_3=V_2))).
% 32.78/32.54 all V_1 K_1 V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),K_1))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))-> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1)))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),K_1))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1)))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_1))),K_1)))).
% 32.78/32.54 all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V))=zero_zero(int))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,int,number_number_of(int),V))).
% 32.78/32.54 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))))).
% 32.78/32.54 all K F Na ((all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),Na))->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),one_one(nat)))),hAPP(nat,int,F,I)))),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))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))-> (exists I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),Na))&hAPP(nat,int,F,I)=K))))).
% 32.78/32.54 all K F Na ((all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),Na))->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),one_one(nat)))),hAPP(nat,int,F,I)))),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))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))-> (exists I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),Na))&hAPP(nat,int,F,I)=K))))).
% 32.78/32.54 all K F Na M ((all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),I))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),Na))->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),one_one(nat)))),hAPP(nat,int,F,I)))),one_one(int)))))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M)),K))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))-> (exists I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),I))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),Na))&hAPP(nat,int,F,I)=K)))))).
% 32.78/32.54 all N V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))),N))).
% 32.78/32.54 all K_1 (hAPP(int,int,succ,K_1)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),one_one(int))).
% 32.78/32.54 all X_a (number_ring(X_a)-> (all K_1 (hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,K_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),K_1))))).
% 32.78/32.54 all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V))=one_one(nat))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))->hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V))=hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V)))).
% 32.78/32.54 all W ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W)))->hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W))=zero_zero(nat))& (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W)))->hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W))=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),W)),hAPP(int,nat,number_number_of(nat),W))))).
% 32.78/32.54 all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V))=one_one(nat))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V)))).
% 32.78/32.54 hAPP(int,int,succ,pls)=hAPP(int,int,bit1,pls).
% 32.78/32.54 all W_1 (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,W_1))))<->hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W_1)))).
% 32.78/32.54 -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),pls))).
% 32.78/32.54 hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))).
% 32.78/32.54 all X_a (number_ring(X_a)-> (all W (hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,W))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W))),hAPP(int,X_a,number_number_of(X_a),W))))).
% 32.78/32.54 hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls))=hAPP(nat,nat,suc,zero_zero(nat)).
% 32.78/32.54 hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))=hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))).
% 32.78/32.54 all N (hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,N)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),N)).
% 32.78/32.54 all X_a (number_ring(X_a)->one_one(X_a)=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))).
% 32.78/32.54 one_one(nat)=hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)).
% 32.78/32.54 hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls))=one_one(nat).
% 32.78/32.54 one_one(int)=hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)).
% 32.78/32.54 all X_a (number_ring(X_a)->hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))=one_one(X_a)).
% 32.78/32.54 all X_a (number_semiring(X_a)->hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))=one_one(X_a)).
% 32.78/32.54 all X_a (number_ring(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))=ti(X_a,A_1)))).
% 32.78/32.54 all X_a (number_ring(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))),A_1)=ti(X_a,A_1)))).
% 32.78/32.54 all X_a (number_ring(X_a)-> (all V (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,bit1,pls)))))).
% 32.78/32.54 all X_a (number_ring(X_a)-> (all W (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),W))))).
% 32.78/32.54 zero_zero(int)=hAPP(int,int,number_number_of(int),pls).
% 32.78/32.54 all K_1 (hAPP(int,int,bit1,K_1)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),K_1)),K_1)).
% 32.78/32.54 all X_a (number_semiring(X_a)->hAPP(int,X_a,number_number_of(X_a),pls)=zero_zero(X_a)).
% 32.78/32.54 all X_a (number_ring(X_a)->hAPP(int,X_a,number_number_of(X_a),pls)=zero_zero(X_a)).
% 32.78/32.54 all X_a (number_ring(X_a)->zero_zero(X_a)=hAPP(int,X_a,number_number_of(X_a),pls)).
% 32.78/32.54 all X_a (number_ring(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),pls)),A_1)=ti(X_a,A_1)))).
% 32.78/32.54 all X_a (number_ring(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),pls))=ti(X_a,A_1)))).
% 32.78/32.54 hAPP(int,nat,number_number_of(nat),pls)=zero_zero(nat).
% 32.78/32.54 zero_zero(nat)=hAPP(int,nat,number_number_of(nat),pls).
% 32.78/32.54 pls=zero_zero(int).
% 32.78/32.54 all K L (hAPP(int,int,bit1,K)=hAPP(int,int,bit1,L)<->K=L).
% 32.78/32.54 all K_1 (hAPP(int,int,bit1,K_1)!=pls).
% 32.78/32.54 all L_1 (pls!=hAPP(int,int,bit1,L_1)).
% 32.78/32.54 all K_1 (hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),pls)=K_1).
% 32.78/32.54 all K_1 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),K_1)=K_1).
% 32.78/32.54 all K_1 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),pls)=K_1).
% 32.78/32.54 all W (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),W)=pls).
% 32.78/32.54 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))).
% 32.78/32.54 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),pls)).
% 32.78/32.54 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),hAPP(int,int,bit1,K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K))).
% 32.78/32.54 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L))).
% 32.78/32.54 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2))).
% 32.78/32.54 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)).
% 32.78/32.54 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),pls))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls))).
% 32.78/32.54 all K L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))).
% 32.78/32.54 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2))).
% 32.78/32.54 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K)),pls))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls))).
% 32.78/32.54 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,K)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K))).
% 32.78/32.55 all T_2 T_1 (preorder(T_1)->preorder(fun(T_2,T_1))).
% 32.78/32.55 all T_2 T_1 (finite_finite_1(T_1)&finite_finite_1(T_2)->finite_finite_1(fun(T_2,T_1))).
% 32.78/32.55 all T_2 T_1 (order(T_1)->order(fun(T_2,T_1))).
% 32.78/32.55 all T_2 T_1 (ord(T_1)->ord(fun(T_2,T_1))).
% 32.78/32.55 all T_2 T_1 (bot(T_1)->bot(fun(T_2,T_1))).
% 32.78/32.55 all T_2 T_1 (minus(T_1)->minus(fun(T_2,T_1))).
% 32.78/32.55 semiri456707255roduct(int).
% 32.78/32.55 ordere223160158up_add(int).
% 32.78/32.55 ordere236663937imp_le(int).
% 32.78/32.55 linord893533164strict(int).
% 32.78/32.55 linord626643107strict(int).
% 32.78/32.55 linord20386208strict(int).
% 32.78/32.55 ordere779506340up_add(int).
% 32.78/32.55 ordere142940540dd_abs(int).
% 32.78/32.55 ordere216010020id_add(int).
% 32.78/32.55 linord219039673up_add(int).
% 32.78/32.55 cancel146912293up_add(int).
% 32.78/32.55 ordere453448008miring(int).
% 32.78/32.55 linord581940658strict(int).
% 32.78/32.55 ring_n68954251visors(int).
% 32.78/32.55 ordere1490568538miring(int).
% 32.78/32.55 linord1278240602ring_1(int).
% 32.78/32.55 ordered_ab_group_add(int).
% 32.78/32.55 cancel_semigroup_add(int).
% 32.78/32.55 linordered_semiring(int).
% 32.78/32.55 linordered_semidom(int).
% 32.78/32.55 ab_semigroup_mult(int).
% 32.78/32.55 comm_monoid_mult(int).
% 32.78/32.55 ab_semigroup_add(int).
% 32.78/32.55 ordered_semiring(int).
% 32.78/32.55 ordered_ring_abs(int).
% 32.78/32.55 no_zero_divisors(int).
% 32.78/32.55 comm_monoid_add(int).
% 32.78/32.55 linordered_ring(int).
% 32.78/32.55 linordered_idom(int).
% 32.78/32.55 comm_semiring_1(int).
% 32.78/32.55 comm_semiring(int).
% 32.78/32.55 semiring_char_0(int).
% 32.78/32.55 number_semiring(int).
% 32.78/32.55 ab_group_add(int).
% 32.78/32.55 zero_ne_q_one(int).
% 32.78/32.55 ordered_ring(int).
% 32.78/32.55 preorder(int).
% 32.78/32.55 linorder(int).
% 32.78/32.55 monoid_mult(int).
% 32.78/32.55 monoid_add(int).
% 32.78/32.55 semiring_1(int).
% 32.78/32.55 group_add(int).
% 32.78/32.55 mult_zero(int).
% 32.78/32.55 order(int).
% 32.78/32.55 ring_char_0(int).
% 32.78/32.55 number_ring(int).
% 32.78/32.55 semiring(int).
% 32.78/32.55 ord(int).
% 32.78/32.55 ring_1(int).
% 32.78/32.55 minus(int).
% 32.78/32.55 zero(int).
% 32.78/32.55 ring(int).
% 32.78/32.55 number(int).
% 32.78/32.55 one(int).
% 32.78/32.55 semiri456707255roduct(nat).
% 32.78/32.55 ordere223160158up_add(nat).
% 32.78/32.55 ordere236663937imp_le(nat).
% 32.78/32.55 linord893533164strict(nat).
% 32.78/32.55 linord20386208strict(nat).
% 32.78/32.55 ordere779506340up_add(nat).
% 32.78/32.55 ordere216010020id_add(nat).
% 32.78/32.55 cancel146912293up_add(nat).
% 32.78/32.55 ordere453448008miring(nat).
% 32.78/32.55 ordere1490568538miring(nat).
% 32.78/32.55 cancel_semigroup_add(nat).
% 32.78/32.55 linordered_semiring(nat).
% 32.78/32.55 linordered_semidom(nat).
% 32.78/32.55 ab_semigroup_mult(nat).
% 32.78/32.55 comm_monoid_mult(nat).
% 32.78/32.55 ab_semigroup_add(nat).
% 32.78/32.55 ordered_semiring(nat).
% 32.78/32.55 no_zero_divisors(nat).
% 32.78/32.55 comm_monoid_add(nat).
% 32.78/32.55 comm_semiring_1(nat).
% 32.78/32.55 comm_semiring(nat).
% 32.78/32.55 semiring_char_0(nat).
% 32.78/32.55 number_semiring(nat).
% 32.78/32.55 zero_ne_q_one(nat).
% 32.78/32.55 preorder(nat).
% 32.78/32.55 linorder(nat).
% 32.78/32.55 monoid_mult(nat).
% 32.78/32.55 monoid_add(nat).
% 32.78/32.55 semiring_1(nat).
% 32.78/32.55 mult_zero(nat).
% 32.78/32.55 order(nat).
% 32.78/32.55 semiring(nat).
% 32.78/32.55 ord(nat).
% 32.78/32.55 bot(nat).
% 32.78/32.55 minus(nat).
% 32.78/32.55 zero(nat).
% 32.78/32.55 number(nat).
% 32.78/32.55 one(nat).
% 32.78/32.55 preorder(bool).
% 32.78/32.55 finite_finite_1(bool).
% 32.78/32.55 order(bool).
% 32.78/32.55 ord(bool).
% 32.78/32.55 bot(bool).
% 32.78/32.55 minus(bool).
% 32.78/32.55 all T_2 T_1 (finite_finite_1(T_1)&finite_finite_1(T_2)->finite_finite_1(sum_sum(T_2,T_1))).
% 32.78/32.55 all T A (ti(T,ti(T,A))=ti(T,A)).
% 32.78/32.55 all X_a X Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y)=ti(X_a,X)).
% 32.78/32.55 all X_a X Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y)=ti(X_a,Y)).
% 32.78/32.55 all P (ti(bool,P)=fTrue|ti(bool,P)=fFalse).
% 32.78/32.55 all P (-hBOOL(hAPP(bool,bool,fNot,P))| -hBOOL(P)).
% 32.78/32.55 all P (hBOOL(P)|hBOOL(hAPP(bool,bool,fNot,P))).
% 32.78/32.55 all X_a X_c X_b P Q R (hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R)=hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R))).
% 32.78/32.55 all X_a X_c X_b P Q R (hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R)=hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)).
% 32.78/32.55 all X_a P (hAPP(X_a,X_a,combi(X_a),P)=ti(X_a,P)).
% 32.78/32.55 all X_b X_a P Q (hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q)=ti(X_a,P)).
% 32.78/32.55 all X_a X_c X_b P Q R (hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R)=hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R))).
% 32.78/32.55 all Q P (-hBOOL(P)| -hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))).
% 32.78/32.55 all P Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(P)).
% 32.78/32.55 all P Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(Q)).
% 32.78/32.55 all Q P (-hBOOL(P)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))).
% 32.78/32.55 all P Q (-hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))).
% 32.78/32.55 all P Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))|hBOOL(P)|hBOOL(Q)).
% 32.78/32.55 -hBOOL(fFalse).
% 32.78/32.55 all P (ti(bool,P)=fTrue|ti(bool,P)=fFalse).
% 32.78/32.55 all X_a X Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fe_qual(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y)).
% 32.78/32.55 all X_a X Y (ti(X_a,X)!=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fe_qual(X_a),X),Y))).
% 32.78/32.55 all Q P (hBOOL(P)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q))).
% 32.78/32.55 all P Q (-hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q))).
% 32.78/32.55 all P Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q))| -hBOOL(P)|hBOOL(Q)).
% 32.78/32.55 hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)).
% 32.78/32.55 hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_e_q(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))).
% 32.78/32.55 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,na)),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))).
% 32.78/32.55 hAPP(fun(x_a,bool),nat,finite_card(x_a),g)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),hAPP(nat,nat,suc,na)).
% 32.78/32.55 hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)).
% 32.78/32.55 -hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),g)).
% 32.78/32.55 -hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_e_q(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))).
% 32.78/32.55 end_of_list.
% 32.78/32.55
% 32.78/32.55 -------> usable clausifies to:
% 32.78/32.55
% 32.78/32.55 list(usable).
% 32.78/32.55 0 [] A=A.
% 32.78/32.55 0 [] ti(fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),combb(X_b,X_c,X_a))=combb(X_b,X_c,X_a).
% 32.78/32.55 0 [] ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c))=combc(X_a,X_b,X_c).
% 32.78/32.55 0 [] ti(fun(X_a,X_a),combi(X_a))=combi(X_a).
% 32.78/32.55 0 [] ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b))=combk(X_a,X_b).
% 32.78/32.55 0 [] ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c))=combs(X_a,X_b,X_c).
% 32.78/32.55 0 [] ti(fun(pname,option(com)),body)=body.
% 32.78/32.55 0 [] ti(fun(fun(X_c,bool),nat),finite_card(X_c))=finite_card(X_c).
% 32.78/32.55 0 [] ti(fun(fun(X_b,fun(X_c,X_c)),bool),finite_comp_fun_idem(X_b,X_c))=finite_comp_fun_idem(X_b,X_c).
% 32.78/32.55 0 [] ti(fun(fun(X_b,bool),bool),finite_finite(X_b))=finite_finite(X_b).
% 32.78/32.55 0 [] ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)))),finite_fold_image(X_b,X_c))=finite_fold_image(X_b,X_c).
% 32.78/32.55 0 [] ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)))),finite1357897459simple(X_b,X_c))=finite1357897459simple(X_b,X_c).
% 32.78/32.55 0 [] ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)))),finite908156982e_idem(X_b,X_c))=finite908156982e_idem(X_b,X_c).
% 32.78/32.55 0 [] ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite_folding_one(X_b))=finite_folding_one(X_b).
% 32.78/32.55 0 [] ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite2073411215e_idem(X_b))=finite2073411215e_idem(X_b).
% 32.78/32.55 0 [] -ordere142940540dd_abs(X_a)|ti(fun(X_a,X_a),abs_abs(X_a))=abs_abs(X_a).
% 32.78/32.55 0 [] -minus(X_c)|ti(fun(X_c,fun(X_c,X_c)),minus_minus(X_c))=minus_minus(X_c).
% 32.78/32.55 0 [] -one(X_b)|ti(X_b,one_one(X_b))=one_one(X_b).
% 32.78/32.55 0 [] -monoid_add(X_a)|ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a).
% 32.78/32.55 0 [] -cancel_semigroup_add(X_b)|ti(fun(X_b,fun(X_b,X_b)),plus_plus(X_b))=plus_plus(X_b).
% 32.78/32.55 0 [] -ab_semigroup_add(X_a)|ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a).
% 32.78/32.55 0 [] -ab_semigroup_mult(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 32.78/32.55 0 [] -monoid_mult(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 32.78/32.55 0 [] -semiring(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 32.78/32.55 0 [] -no_zero_divisors(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 32.78/32.55 0 [] -mult_zero(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 32.78/32.55 0 [] -zero(X_b)|ti(X_b,zero_zero(X_b))=zero_zero(X_b).
% 32.78/32.55 0 [] ti(fun(fun(X_b,bool),X_b),the(X_b))=the(X_b).
% 32.78/32.55 0 [] ti(X_a,undefined(X_a))=undefined(X_a).
% 32.78/32.55 0 [] ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a))=if(X_a).
% 32.78/32.55 0 [] ti(fun(int,int),bit1)=bit1.
% 32.78/32.55 0 [] ti(int,pls)=pls.
% 32.78/32.55 0 [] -number(X_b)|ti(fun(int,X_b),number_number_of(X_b))=number_number_of(X_b).
% 32.78/32.55 0 [] -ring_1(X_b)|ti(fun(X_b,bool),ring_1_Ints(X_b))=ring_1_Ints(X_b).
% 32.78/32.55 0 [] ti(fun(int,int),succ)=succ.
% 32.78/32.55 0 [] ti(fun(nat,nat),suc)=suc.
% 32.78/32.55 0 [] ti(fun(X_b,fun(fun(nat,X_b),fun(nat,X_b))),nat_case(X_b))=nat_case(X_b).
% 32.78/32.55 0 [] -semiring_1(X_a)|ti(fun(nat,X_a),semiring_1_of_nat(X_a))=semiring_1_of_nat(X_a).
% 32.78/32.55 0 [] -semiring_1(X_b)|ti(fun(fun(X_b,X_b),fun(nat,fun(X_b,X_b))),semiri532925092at_aux(X_b))=semiri532925092at_aux(X_b).
% 32.78/32.55 0 [] ti(fun(int,bool),nat_neg)=nat_neg.
% 32.78/32.55 0 [] ti(fun(int,fun(int,int)),nat_tsub)=nat_tsub.
% 32.78/32.55 0 [] ti(fun(option(com),com),the_1(com))=the_1(com).
% 32.78/32.55 0 [] -bot(X_b)|ti(X_b,bot_bot(X_b))=bot_bot(X_b).
% 32.78/32.55 0 [] -ord(X_a)|ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a).
% 32.78/32.55 0 [] -ord(X_a)|ti(fun(X_a,fun(X_a,bool)),ord_less_e_q(X_a))=ord_less_e_q(X_a).
% 32.78/32.55 0 [] ti(fun(X_b,fun(fun(X_b,bool),X_b)),partial_flat_lub(X_b))=partial_flat_lub(X_b).
% 32.78/32.55 0 [] ti(fun(fun(X_b,bool),fun(X_b,bool)),collect(X_b))=collect(X_b).
% 32.78/32.55 0 [] ti(fun(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool))),image(X_b,X_c))=image(X_b,X_c).
% 32.78/32.55 0 [] ti(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),insert(X_b))=insert(X_b).
% 32.78/32.55 0 [] ti(fun(fun(X_b,bool),X_b),the_elem(X_b))=the_elem(X_b).
% 32.78/32.55 0 [] ti(fun(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool))),sum_Plus(X_b,X_c))=sum_Plus(X_b,X_c).
% 32.78/32.55 0 [] ti(bool,fFalse)=fFalse.
% 32.78/32.55 0 [] ti(fun(bool,bool),fNot)=fNot.
% 32.78/32.55 0 [] ti(bool,fTrue)=fTrue.
% 32.78/32.55 0 [] ti(fun(bool,fun(bool,bool)),fconj)=fconj.
% 32.78/32.55 0 [] ti(fun(bool,fun(bool,bool)),fdisj)=fdisj.
% 32.78/32.55 0 [] ti(fun(X_a,fun(X_a,bool)),fe_qual(X_a))=fe_qual(X_a).
% 32.78/32.55 0 [] ti(fun(bool,fun(bool,bool)),fimplies)=fimplies.
% 32.78/32.55 0 [] hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1)=hAPP(X_a,X_c,B_1_1,B_2_1).
% 32.78/32.55 0 [] hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1))=hAPP(X_a,X_c,B_1_1,B_2_1).
% 32.78/32.55 0 [] ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1))=hAPP(X_a,X_c,B_1_1,B_2_1).
% 32.78/32.55 0 [] -hBOOL(ti(bool,B_1_1))|hBOOL(B_1_1).
% 32.78/32.55 0 [] hBOOL(ti(bool,B_1_1))| -hBOOL(B_1_1).
% 32.78/32.55 0 [] ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b))=member(X_b).
% 32.78/32.55 0 [] ti(fun(x_a,bool),g)=g.
% 32.78/32.55 0 [] ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p)=p.
% 32.78/32.55 0 [] ti(fun(pname,bool),u)=u.
% 32.78/32.55 0 [] ti(fun(com,x_a),mgt)=mgt.
% 32.78/32.55 0 [] ti(fun(pname,x_a),mgt_call)=mgt_call.
% 32.78/32.55 0 [] ti(nat,na)=na.
% 32.78/32.55 0 [] ti(pname,pn)=pn.
% 32.78/32.55 0 [] ti(fun(com,bool),wt)=wt.
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_e_q(fun(x_a,bool)),Ts),G_1))|hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),Ts)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hBOOL(hAPP(fun(fun(X_b,bool),bool),bool,finite_finite(fun(X_b,bool)),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,bool),bool),collect(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),combc(fun(X_b,bool),fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool))),A_3)))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))|hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),H),F_1))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(fun(X_c,bool),nat,finite_card(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))|ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_1).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),Pa)),Q_3)))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),Pa)),Q_3)))).
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),N)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_e_q(nat)),K)))).
% 32.78/32.55 0 [] hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_e_q(nat)),Na)))=hAPP(nat,nat,suc,Na).
% 32.78/32.55 0 [] -finite_finite_1(X_b)|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)).
% 32.78/32.55 0 [] -finite_finite_1(X_b)|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)).
% 32.78/32.55 0 [] hAPP(nat,nat,suc,X)!=hAPP(nat,nat,suc,Y)|X=Y.
% 32.78/32.55 0 [] hAPP(nat,nat,suc,Nat_3)!=hAPP(nat,nat,suc,Nat_4)|Nat_3=Nat_4.
% 32.78/32.55 0 [] hAPP(nat,nat,suc,Nat_3)=hAPP(nat,nat,suc,Nat_4)|Nat_3!=Nat_4.
% 32.78/32.55 0 [] hAPP(nat,nat,suc,N)!=N.
% 32.78/32.55 0 [] N!=hAPP(nat,nat,suc,N).
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1))|M_1=N.
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),K_1)).
% 32.78/32.55 0 [] M_1!=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N)).
% 32.78/32.55 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1)).
% 32.78/32.55 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),N)).
% 32.78/32.55 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),J)),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),K_1)),J).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Q_3))))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Q_3))))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3))).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Q_3))))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M_1)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N)).
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,suc,N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))|M_1=hAPP(nat,nat,suc,N).
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,suc,N))).
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Na),M)).
% 32.78/32.55 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Na),M)).
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,suc,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))|M=hAPP(nat,nat,suc,Na).
% 32.78/32.55 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,suc,Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.55 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,suc,Na)))|M!=hAPP(nat,nat,suc,Na).
% 32.78/32.55 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,Na)),M)).
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,Na)),M)).
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N)),N)).
% 32.78/32.55 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),N)),hAPP(nat,nat,suc,K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),K_1).
% 32.78/32.55 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N).
% 32.78/32.55 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),Na))| -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),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.55 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),Na))|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),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.55 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))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(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),K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N).
% 32.78/32.55 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),Na))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K)|M=Na.
% 32.78/32.55 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),Na))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K)|M!=Na.
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),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_2))=I_2.
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),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_1),L_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),L_1))).
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),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_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M_1))).
% 32.78/32.55 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_1),N)),M_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_e_q(fun(X_c,bool)),B_1),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))|hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_e_q(fun(X_c,bool)),$f1(X_c,X_b,F,A_3,B_1)),A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))|hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),$f1(X_c,X_b,F,A_3,B_1))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))|ti(fun(X_b,bool),B_1)=hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),$f1(X_c,X_b,F,A_3,B_1)).
% 32.78/32.55 0 [] -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(nat,X_b,F,$f2(X_b,Na,N_3,F))),hAPP(nat,X_b,F,hAPP(nat,nat,suc,$f2(X_b,Na,N_3,F)))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Na),N_3))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,N_3))).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f3(X_c,X_b,F,A_3)),A_3)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(X_c,fun(X_b,bool),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,bool))),combb(X_c,fun(X_c,bool),X_b),fe_qual(X_c)),F)),hAPP(X_b,X_c,F,$f3(X_c,X_b,F,A_3))))))).
% 32.78/32.55 0 [] ti(X_b,B_3)!=hAPP(X_c,X_b,F,X_1)| -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),A_3))|ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_1).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),B_1))).
% 32.78/32.55 0 [] ti(X_b,A_2)!=ti(X_b,B_3)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),B_1))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),A_3)))|ti(X_b,A_2)=ti(X_b,B_3)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,Pa,K))|hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,$f4(I_1,Pa,K))))|hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I_1))).
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,Pa,K))| -hBOOL(hAPP(nat,bool,Pa,$f4(I_1,Pa,K)))|hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I_1))).
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N)),M_4))|M_4=hAPP(nat,nat,suc,$f5(N,M_4)).
% 32.78/32.55 0 [] -preorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),X)).
% 32.78/32.55 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)).
% 32.78/32.55 0 [] -order(X_b)|ti(X_b,X_1)!=ti(X_b,Y_2)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2)).
% 32.78/32.55 0 [] -order(X_b)|ti(X_b,X_1)!=ti(X_b,Y_2)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_2),X_1)).
% 32.78/32.55 0 [] -order(X_b)|ti(X_b,X_1)=ti(X_b,Y_2)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_2),X_1)).
% 32.78/32.55 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)).
% 32.78/32.55 0 [] -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_2),X_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))|ti(X_b,X_1)=ti(X_b,Y_2).
% 32.78/32.55 0 [] -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_2),X_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))|ti(X_b,X_1)!=ti(X_b,Y_2).
% 32.78/32.55 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)).
% 32.78/32.55 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)).
% 32.78/32.55 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)).
% 32.78/32.55 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)).
% 32.78/32.55 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).
% 32.78/32.55 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)).
% 32.78/32.55 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).
% 32.78/32.55 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)).
% 32.78/32.55 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)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1))).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1)=hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),A_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_1))).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))=hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fimplies),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),A_2)))),Pa)).
% 32.78/32.55 0 [] hAPP(X_b,X_c,F,$f6(X_b,X_c,F,G))!=hAPP(X_b,X_c,G,$f6(X_b,X_c,F,G))|ti(fun(X_b,X_c),F)=ti(fun(X_b,X_c),G).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hBOOL(hAPP(X_b,bool,A_3,X_1)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))| -hBOOL(hAPP(X_b,bool,A_3,X_1)).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)=ti(fun(X_b,bool),Pa).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),A_3))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),A_3)))|ti(X_b,A_2)=ti(X_b,B_3)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),A_3)))|ti(X_b,A_2)!=ti(X_b,B_3).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),A_3)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),A_3),X_1))|ti(X_b,Y_2)=ti(X_b,X_1)|hBOOL(hAPP(X_b,bool,A_3,X_1)).
% 32.78/32.55 0 [] hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),A_3),X_1))|ti(X_b,Y_2)!=ti(X_b,X_1).
% 32.78/32.55 0 [] hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),A_3),X_1))| -hBOOL(hAPP(X_b,bool,A_3,X_1)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)!=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)|ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_1).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)|ti(fun(X_b,bool),A_3)!=ti(fun(X_b,bool),B_1).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),B_1))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)=ti(fun(X_b,bool),A_3).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),A_3)).
% 32.78/32.55 0 [] ti(fun(X_b,bool),A_3)!=ti(fun(X_b,bool),B_1)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.55 0 [] ti(fun(X_b,bool),A_3)!=ti(fun(X_b,bool),B_1)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),A_3)).
% 32.78/32.55 0 [] ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_1)| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),A_3)).
% 32.78/32.55 0 [] ti(fun(X_b,bool),A_3)!=ti(fun(X_b,bool),B_1)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.55 0 [] ti(fun(X_b,bool),A_3)!=ti(fun(X_b,bool),B_1)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),C_2))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),C_2)).
% 32.78/32.55 0 [] ti(fun(X_b,bool),A_3)!=ti(fun(X_b,bool),B_1)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.55 0 [] ti(fun(X_b,bool),A_3)!=ti(fun(X_b,bool),B_1)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),$f7(X_b,X_c,Z_2,F,A_3)),A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))|ti(X_b,Z_2)=hAPP(X_c,X_b,F,$f7(X_b,X_c,Z_2,F,A_3)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))| -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3))|ti(X_b,Z_2)!=hAPP(X_c,X_b,F,X_2).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|ti(X_c,B_3)!=hAPP(X_b,X_c,F,X_1)|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B_3),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),Xa)=hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),X_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),Xa))).
% 32.78/32.55 0 [] hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_d,bool),fun(X_c,bool),hAPP(fun(X_d,X_c),fun(fun(X_d,bool),fun(X_c,bool)),image(X_d,X_c),G),A_3))=hAPP(fun(X_d,bool),fun(X_b,bool),hAPP(fun(X_d,X_b),fun(fun(X_d,bool),fun(X_b,bool)),image(X_d,X_b),hAPP(fun(X_d,X_c),fun(X_d,X_b),hAPP(fun(X_c,X_b),fun(fun(X_d,X_c),fun(X_d,X_b)),combb(X_c,X_b,X_d),F),G)),A_3).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),combi(X_b)),Y_3)=ti(fun(X_b,bool),Y_3).
% 32.78/32.55 0 [] -ord(X_c)| -hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_e_q(fun(X_b,X_c)),F),G))|hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2))).
% 32.78/32.55 0 [] -ord(X_c)|hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_e_q(fun(X_b,X_c)),F),G))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),hAPP(X_b,X_c,F,$f8(X_b,X_c,F,G))),hAPP(X_b,X_c,G,$f8(X_b,X_c,F,G)))).
% 32.78/32.55 0 [] -ord(X_c)| -hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_e_q(fun(X_b,X_c)),F),G))|hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1))).
% 32.78/32.55 0 [] -ord(X_c)| -hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_e_q(fun(X_b,X_c)),F),G))|hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1))).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),B_1))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),C_2),D_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),C_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),D_3))).
% 32.78/32.55 0 [] hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),A_2),B_1))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),hAPP(X_c,X_b,F,A_2)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))=hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_e_q(fun(X_c,bool)),$f9(X_b,X_c,B_1,F,A_3)),A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))|ti(fun(X_b,bool),B_1)=hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),$f9(X_b,X_c,B_1,F,A_3)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))| -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_e_q(fun(X_c,bool)),AA),A_3))|ti(fun(X_b,bool),B_1)!=hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),AA).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_e_q(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),B_1))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))|ti(X_b,B_3)=hAPP(X_c,X_b,F,$f10(X_b,X_c,B_3,F,A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),$f10(X_b,X_c,B_3,F,A_3)),A_3)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f11(X_b,B_1,A_3)),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f11(X_b,B_1,A_3)),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f12(X_c,X_b,F,B_1,A_3)),A_3))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_e_q(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),B_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,$f12(X_c,X_b,F,B_1,A_3))),B_1))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_e_q(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),B_1)).
% 32.78/32.55 0 [] -ord(X_c)| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),hAPP(X_b,X_c,F,$f13(X_b,X_c,F,G))),hAPP(X_b,X_c,G,$f13(X_b,X_c,F,G))))|hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_e_q(fun(X_b,X_c)),F),G)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2))| -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_2),$f14(N_2))).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2))|hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),$f15(N_2,M_2)),N_2)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f15(N_2,M_2)),M_2)).
% 32.78/32.55 0 [] -hBOOL(hAPP(com,bool,wt,C_1))|hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),$f16(G_1,C_1)),u))|hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,C_1)),bot_bot(fun(x_a,bool))))).
% 32.78/32.55 0 [] -hBOOL(hAPP(com,bool,wt,C_1))| -hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,$f16(G_1,C_1))),bot_bot(fun(x_a,bool)))))|hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,C_1)),bot_bot(fun(x_a,bool))))).
% 32.78/32.55 0 [] -ordered_ab_group_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C_1),D_1)).
% 32.78/32.55 0 [] -ordered_ab_group_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C_1),D_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M)),Na))|hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M)),Na)).
% 32.78/32.55 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M)),Na))| -hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M)),Na)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_e_q(fun(X_c,bool)),B_1),A_3))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,B_1)),hAPP(fun(X_c,bool),X_b,F_1,A_3))=hAPP(fun(X_c,bool),X_b,F_1,A_3).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))|hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),bot_bot(fun(X_b,bool)))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),bot_bot(fun(X_b,bool)))).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),bot_bot(fun(X_b,bool))),A_3)).
% 32.78/32.55 0 [] ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)!=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(X_b,bool,Pa,X_2)).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)=bot_bot(fun(X_b,bool))|hBOOL(hAPP(X_b,bool,Pa,$f17(X_b,Pa))).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),A_3)=bot_bot(fun(X_b,bool)).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool)))=ti(fun(X_b,bool),A_3).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),bot_bot(fun(X_b,bool)))).
% 32.78/32.55 0 [] bot_bot(fun(X_b,bool))!=hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)| -hBOOL(hAPP(X_b,bool,Pa,X_2)).
% 32.78/32.55 0 [] bot_bot(fun(X_b,bool))=hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)|hBOOL(hAPP(X_b,bool,Pa,$f18(X_b,Pa))).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),bot_bot(fun(X_b,bool))),A_3)=bot_bot(fun(X_b,bool)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))|ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f19(X_b,A_3)),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f20(X_b,A_3)),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))|ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool)).
% 32.78/32.55 0 [] -bot(X_b)|hAPP(X_c,X_b,bot_bot(fun(X_c,X_b)),X_1)=bot_bot(X_b).
% 32.78/32.55 0 [] bot_bot(fun(X_b,bool))=hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)).
% 32.78/32.55 0 [] -bot(X_c)|hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2)=bot_bot(X_c).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))=ti(fun(X_b,bool),A_3).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))=ti(fun(X_b,bool),A_3).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))),B_1).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),X_1)=ti(X_b,X_1).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_1)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_1)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_1)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),C_2))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C_2),A_3))=ti(fun(X_b,bool),A_3).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),C_2))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),D_3),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C_2),D_3))).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)),A_3)).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))!=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool)))|ti(X_b,A_2)=ti(X_b,B_3).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))|ti(X_b,B_3)=ti(X_b,A_2).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool))))!=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D_1),bot_bot(fun(X_b,bool))))|ti(X_b,A_2)=ti(X_b,C_1)|ti(X_b,A_2)=ti(X_b,D_1).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool))))!=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D_1),bot_bot(fun(X_b,bool))))|ti(X_b,A_2)=ti(X_b,C_1)|ti(X_b,B_3)=ti(X_b,C_1).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool))))!=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D_1),bot_bot(fun(X_b,bool))))|ti(X_b,B_3)=ti(X_b,D_1)|ti(X_b,A_2)=ti(X_b,D_1).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool))))!=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D_1),bot_bot(fun(X_b,bool))))|ti(X_b,B_3)=ti(X_b,D_1)|ti(X_b,B_3)=ti(X_b,C_1).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool))))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D_1),bot_bot(fun(X_b,bool))))|ti(X_b,A_2)!=ti(X_b,C_1)|ti(X_b,B_3)!=ti(X_b,D_1).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool))))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D_1),bot_bot(fun(X_b,bool))))|ti(X_b,A_2)!=ti(X_b,D_1)|ti(X_b,B_3)!=ti(X_b,C_1).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))|ti(X_b,B_3)=ti(X_b,A_2).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))|ti(X_b,B_3)!=ti(X_b,A_2).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)!=bot_bot(fun(X_b,bool)).
% 32.78/32.55 0 [] bot_bot(fun(X_b,bool))!=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))))|ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool)).
% 32.78/32.55 0 [] hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)!=bot_bot(fun(X_b,bool))|ti(fun(X_c,bool),A_3)=bot_bot(fun(X_c,bool)).
% 32.78/32.55 0 [] hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)=bot_bot(fun(X_b,bool))|ti(fun(X_c,bool),A_3)!=bot_bot(fun(X_c,bool)).
% 32.78/32.55 0 [] hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),bot_bot(fun(X_c,bool)))=bot_bot(fun(X_b,bool)).
% 32.78/32.55 0 [] bot_bot(fun(X_b,bool))!=hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)|ti(fun(X_c,bool),A_3)=bot_bot(fun(X_c,bool)).
% 32.78/32.55 0 [] bot_bot(fun(X_b,bool))=hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)|ti(fun(X_c,bool),A_3)!=bot_bot(fun(X_c,bool)).
% 32.78/32.55 0 [] -bot(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),bot_bot(X_a)))|ti(X_a,A_1)=bot_bot(X_a).
% 32.78/32.55 0 [] -bot(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),bot_bot(X_b)))|ti(X_b,A_2)=bot_bot(X_b).
% 32.78/32.55 0 [] -bot(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),bot_bot(X_b)))|ti(X_b,A_2)!=bot_bot(X_b).
% 32.78/32.55 0 [] -bot(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),bot_bot(X_a)),A_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(X_b,bool,Pa,A_2))|hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),A_2))),Pa))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))).
% 32.78/32.55 0 [] hBOOL(hAPP(X_b,bool,Pa,A_2))|hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),A_2))),Pa))=bot_bot(fun(X_b,bool)).
% 32.78/32.55 0 [] -hBOOL(hAPP(X_b,bool,Pa,A_2))|hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fe_qual(X_b),A_2))),Pa))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))).
% 32.78/32.55 0 [] hBOOL(hAPP(X_b,bool,Pa,A_2))|hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fe_qual(X_b),A_2))),Pa))=bot_bot(fun(X_b,bool)).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),A_2))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),fe_qual(X_b),A_2))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))=hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1))))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1))))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_1))),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),B_1)))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))|ti(fun(X_b,bool),A_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))).
% 32.78/32.55 0 [] hAPP(nat,X_b,hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(X_b,fun(fun(nat,X_b),fun(nat,X_b)),nat_case(X_b),F1),F2),hAPP(nat,nat,suc,Nat_3))=hAPP(nat,X_b,F2,Nat_3).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3)=hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),C_1),bot_bot(fun(X_c,bool))).
% 32.78/32.55 0 [] ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3)=bot_bot(fun(X_c,bool)).
% 32.78/32.55 0 [] ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3)=hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),C_1),bot_bot(fun(X_c,bool))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,A_3))=hAPP(fun(X_c,bool),X_b,F_1,A_3).
% 32.78/32.55 0 [] -ab_group_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1)|ti(X_b,A_2)!=ti(X_b,B_3)|ti(X_b,C_1)=ti(X_b,D_1).
% 32.78/32.55 0 [] -ab_group_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1)|ti(X_b,A_2)=ti(X_b,B_3)|ti(X_b,C_1)!=ti(X_b,D_1).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_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),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1))),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),F_1),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),$f21(X_b,Pa,A_3,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),F_1),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f22(X_b,Pa,A_3,F_1)),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),F_1),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f22(X_b,Pa,A_3,F_1)),$f21(X_b,Pa,A_3,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),F_1),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,$f21(X_b,Pa,A_3,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),F_1),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f22(X_b,Pa,A_3,F_1)),$f21(X_b,Pa,A_3,F_1))))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,Pn)),G_1)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,Pn)))),bot_bot(fun(x_a,bool)))))|hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,Pn)),bot_bot(fun(x_a,bool))))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),$f23(X_b,Pa,A_3)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f24(X_b,Pa,A_3)),$f23(X_b,Pa,A_3)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,$f23(X_b,Pa,A_3)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),$f23(X_b,Pa,A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f24(X_b,Pa,A_3)),bot_bot(fun(X_b,bool))))))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),$f25(X_b,Pa,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f26(X_b,Pa,F_1)),$f25(X_b,Pa,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,$f25(X_b,Pa,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f26(X_b,Pa,F_1)),$f25(X_b,Pa,F_1))))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_2))|ti(fun(X_b,bool),A_2)=bot_bot(fun(X_b,bool))|ti(fun(X_b,bool),A_2)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f27(X_b,A_2)),$f28(X_b,A_2)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_2))|ti(fun(X_b,bool),A_2)=bot_bot(fun(X_b,bool))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),$f28(X_b,A_2))).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_2))|ti(fun(X_b,bool),A_2)!=bot_bot(fun(X_b,bool)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_2))|ti(fun(X_b,bool),A_2)!=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),A_5)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_5)).
% 32.78/32.55 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f29(U,F)),hAPP(nat,nat,F,$f29(U,F))))|hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_e_q(nat)),F)),U)))).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),X_b,the_elem(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))=ti(X_b,X_1).
% 32.78/32.55 0 [] ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))|ti(fun(X_b,bool),A_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f31(X_b,A_3)),$f30(X_b,A_3)).
% 32.78/32.55 0 [] ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f31(X_b,A_3)),$f30(X_b,A_3))).
% 32.78/32.55 0 [] ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))|ti(fun(X_b,bool),A_3)!=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),B_4)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_4)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),Pn),u))|hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,Pn)))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)),B_1)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1)).
% 32.78/32.55 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1)).
% 32.78/32.55 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)=hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_1)))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))!=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=ti(X_b,X_1).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))).
% 32.78/32.55 0 [] -hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))!=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,F_1,A_3)=ti(X_b,X_1).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,F_1,A_3)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))|hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool)))))).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3))|hAPP(fun(X_c,bool),X_b,F_1,A_3)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool)))))).
% 32.78/32.56 0 [] -minus(X_c)|hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),fun(X_b,X_c)),minus_minus(fun(X_b,X_c)),A_3),B_1),X_2)=hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(X_b,X_c,A_3,X_2)),hAPP(X_b,X_c,B_1,X_2)).
% 32.78/32.56 0 [] -minus(X_b)|hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),minus_minus(fun(X_c,X_b)),A_3),B_1),X_1)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_c,X_b,A_3,X_1)),hAPP(X_c,X_b,B_1,X_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))=hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat)).
% 32.78/32.56 0 [] -one(X_b)|one_one(X_b)!=ti(X_b,X_1)|ti(X_b,X_1)=one_one(X_b).
% 32.78/32.56 0 [] -one(X_b)|one_one(X_b)=ti(X_b,X_1)|ti(X_b,X_1)!=one_one(X_b).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1))|hAPP(fun(X_c,bool),X_b,F_1,bot_bot(fun(X_c,bool)))=ti(X_b,Z_2).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),one_one(nat))=N.
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,suc,N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),one_one(nat))),N).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1))|hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))=ti(X_b,X_1).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3))|hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,A_3)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_1))|hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))),one_one(nat)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,A_3)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,$f33(X_b,A_3,F,F_1)),$f32(X_b,A_3,F,F_1))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f33(X_b,A_3,F,F_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f32(X_b,A_3,F,F_1)),bot_bot(fun(X_b,bool))))))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,F_1,A_3)),A_3)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),$f34(X_c,X_b,A_3,F,Z_2,G,F_1)),A_3))|hAPP(fun(X_c,bool),X_b,F_1,A_3)=ti(X_b,Z_2).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))|hAPP(X_c,X_b,G,$f34(X_c,X_b,A_3,F,Z_2,G,F_1))!=ti(X_b,Z_2)|hAPP(fun(X_c,bool),X_b,F_1,A_3)=ti(X_b,Z_2).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|ti(fun(X_b,bool),B_1)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),A_3))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,B_1)),hAPP(fun(X_b,bool),X_b,F_1,A_3))=hAPP(fun(X_b,bool),X_b,F_1,A_3).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,A_3)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))|ti(fun(X_b,bool),F_1)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f35(X_b,Pa,F_1)),bot_bot(fun(X_b,bool)))))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),$f36(X_b,Pa,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))|ti(fun(X_b,bool),F_1)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f35(X_b,Pa,F_1)),bot_bot(fun(X_b,bool)))))|ti(fun(X_b,bool),$f36(X_b,Pa,F_1))!=bot_bot(fun(X_b,bool))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))|ti(fun(X_b,bool),F_1)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f35(X_b,Pa,F_1)),bot_bot(fun(X_b,bool)))))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f37(X_b,Pa,F_1)),$f36(X_b,Pa,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))|ti(fun(X_b,bool),F_1)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f35(X_b,Pa,F_1)),bot_bot(fun(X_b,bool)))))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,$f36(X_b,Pa,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1))|ti(fun(X_b,bool),F_1)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f35(X_b,Pa,F_1)),bot_bot(fun(X_b,bool)))))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f37(X_b,Pa,F_1)),$f36(X_b,Pa,F_1))))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 32.78/32.56 0 [] hAPP(fun(X_b,bool),X_b,the_elem(X_b),X_3)=hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),fe_qual(fun(X_b,bool)),X_3)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool))))).
% 32.78/32.56 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)).
% 32.78/32.56 0 [] -cancel_semigroup_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B_3)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)|ti(X_b,B_3)=ti(X_b,C_1).
% 32.78/32.56 0 [] -cancel_semigroup_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B_3)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)|ti(X_b,B_3)!=ti(X_b,C_1).
% 32.78/32.56 0 [] -cancel_semigroup_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),A_2)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)|ti(X_b,B_3)=ti(X_b,C_1).
% 32.78/32.56 0 [] -cancel_semigroup_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),A_2)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)|ti(X_b,B_3)!=ti(X_b,C_1).
% 32.78/32.56 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).
% 32.78/32.56 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).
% 32.78/32.56 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).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),X_1)=ti(X_b,X_1).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1).
% 32.78/32.56 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)).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_1)).
% 32.78/32.56 0 [] 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),Na)|M=Na.
% 32.78/32.56 0 [] 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),Na)|M!=Na.
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K)|M=Na.
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K)|M!=Na.
% 32.78/32.56 0 [] -ordere236663937imp_le(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),C_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3)).
% 32.78/32.56 0 [] -ordere236663937imp_le(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),C_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3)).
% 32.78/32.56 0 [] -ordere236663937imp_le(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3)).
% 32.78/32.56 0 [] -ordere236663937imp_le(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B_3)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3)).
% 32.78/32.56 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))).
% 32.78/32.56 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))).
% 32.78/32.56 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))).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 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).
% 32.78/32.56 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).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,suc,N))=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_1)),N)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_1)),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,suc,N)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N))).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))|Na=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),$f38(M,Na)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))|Na!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M_1))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),J))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K_1))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N)).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),N)=M_1.
% 32.78/32.56 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_1)),N)=M_1.
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),J)),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K_1)).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),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),K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),J).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K)),I_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K))).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K)),I_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1)),K_1))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N))=M_1.
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),K_1).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K)),J_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K)),J_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),N)=M_1.
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)!=K|J_1=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),I_1).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)=K|J_1!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),I_1).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)),I_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),K_1).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)),I_2).
% 32.78/32.56 0 [] hAPP(nat,nat,suc,N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N).
% 32.78/32.56 0 [] hAPP(nat,nat,suc,N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,A_3))=hAPP(fun(X_b,bool),X_b,F_1,A_3).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),hAPP(nat,nat,suc,J)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1))),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1))|hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,$f40(X_b,N_2,H,F,F_1)),$f39(X_b,N_2,H,F,F_1)))!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_b,X_b,H,$f40(X_b,N_2,H,F,F_1))),hAPP(X_b,X_b,H,$f39(X_b,N_2,H,F,F_1)))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),N_2))|ti(fun(X_b,bool),N_2)=bot_bot(fun(X_b,bool))|hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,F_1,N_2))=hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_2)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),Z))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool)))))|hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),B_3),A_3)=ti(X_b,B_3).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool)))))|hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),B_3),A_3)=hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool)))))).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),combc(fun(X_b,bool),fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool)))))).
% 32.78/32.56 0 [] -hBOOL(Pa)|ti(X_b,X_1)=hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),Y_2)))).
% 32.78/32.56 0 [] hBOOL(Pa)|ti(X_b,Y_2)=hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),Y_2)))).
% 32.78/32.56 0 [] hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fe_qual(X_b)),A_2))=ti(X_b,A_2).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite_comp_fun_idem(X_b,X_c),F))|hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2))=hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),insert(X_b))).
% 32.78/32.56 0 [] hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),fe_qual(X_b),X_1))=ti(X_b,X_1).
% 32.78/32.56 0 [] -hBOOL(hAPP(X_b,bool,Pa,A_2))|hBOOL(hAPP(X_b,bool,Pa,$f41(X_b,Pa,A_2)))|hAPP(fun(X_b,bool),X_b,the(X_b),Pa)=ti(X_b,A_2).
% 32.78/32.56 0 [] -hBOOL(hAPP(X_b,bool,Pa,A_2))|ti(X_b,$f41(X_b,Pa,A_2))!=ti(X_b,A_2)|hAPP(fun(X_b,bool),X_b,the(X_b),Pa)=ti(X_b,A_2).
% 32.78/32.56 0 [] -hBOOL(hAPP(X_b,bool,Pa,X_2))|hBOOL(hAPP(X_b,bool,Pa,$f42(X_b,Pa,X_2)))|hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa))).
% 32.78/32.56 0 [] -hBOOL(hAPP(X_b,bool,Pa,X_2))|ti(X_b,$f42(X_b,Pa,X_2))!=ti(X_b,X_2)|hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa))).
% 32.78/32.56 0 [] -hBOOL(hAPP(X_b,bool,Pa,X_2))|hBOOL(hAPP(X_b,bool,Pa,$f43(X_b,A_2,Pa,X_2)))| -hBOOL(hAPP(X_b,bool,Pa,A_2))|hAPP(fun(X_b,bool),X_b,the(X_b),Pa)=ti(X_b,A_2).
% 32.78/32.56 0 [] -hBOOL(hAPP(X_b,bool,Pa,X_2))|ti(X_b,$f43(X_b,A_2,Pa,X_2))!=ti(X_b,X_2)| -hBOOL(hAPP(X_b,bool,Pa,A_2))|hAPP(fun(X_b,bool),X_b,the(X_b),Pa)=ti(X_b,A_2).
% 32.78/32.56 0 [] -hBOOL(hAPP(X_b,bool,Pa,A_2))|hBOOL(hAPP(X_b,bool,Pa,$f44(X_b,Pa,A_2)))|hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa))).
% 32.78/32.56 0 [] -hBOOL(hAPP(X_b,bool,Pa,A_2))|ti(X_b,$f44(X_b,Pa,A_2))!=ti(X_b,A_2)|hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa))).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),A_3))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,N))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N))).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),K)))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)).
% 32.78/32.56 0 [] M=Na|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)).
% 32.78/32.56 0 [] M!=Na| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.56 0 [] M!=Na| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)).
% 32.78/32.56 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)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1))|M_1!=N.
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S_1),T_4))|S_1!=T_4.
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))|M=Na|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M)).
% 32.78/32.56 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X)).
% 32.78/32.56 0 [] -linorder(X_b)|ti(X_b,X_1)=ti(X_b,Y_2)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)).
% 32.78/32.56 0 [] -linorder(X_b)|ti(X_b,X_1)!=ti(X_b,Y_2)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)).
% 32.78/32.56 0 [] -linorder(X_b)|ti(X_b,X_1)!=ti(X_b,Y_2)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)).
% 32.78/32.56 0 [] -linorder(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))|ti(X_b,X_1)=ti(X_b,Y_2).
% 32.78/32.56 0 [] -linorder(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)).
% 32.78/32.56 0 [] -linorder(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))|ti(X_b,X_1)!=ti(X_b,Y_2).
% 32.78/32.56 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)).
% 32.78/32.56 0 [] -linorder(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))|ti(X_b,X_1)=ti(X_b,Y_2).
% 32.78/32.56 0 [] -linorder(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))|ti(X_b,X_1)!=ti(X_b,Y_2).
% 32.78/32.56 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)).
% 32.78/32.56 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).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 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).
% 32.78/32.56 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).
% 32.78/32.56 0 [] -preorder(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))|hBOOL(Pa).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 0 [] -linorder(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_2),X_1)).
% 32.78/32.56 0 [] -linorder(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_2),X_1)).
% 32.78/32.56 0 [] -linorder(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)).
% 32.78/32.56 0 [] -linorder(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)).
% 32.78/32.56 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)).
% 32.78/32.56 0 [] -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2)).
% 32.78/32.56 0 [] -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))|ti(X_b,X_1)!=ti(X_b,Y_2).
% 32.78/32.56 0 [] -order(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))|ti(X_b,X_1)=ti(X_b,Y_2).
% 32.78/32.56 0 [] -preorder(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2)).
% 32.78/32.56 0 [] -preorder(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_2),X_1)).
% 32.78/32.56 0 [] -preorder(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_2),X_1)).
% 32.78/32.56 0 [] -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))|ti(X_b,X_1)=ti(X_b,Y_2).
% 32.78/32.56 0 [] -order(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)).
% 32.78/32.56 0 [] -order(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))|ti(X_b,X_1)!=ti(X_b,Y_2).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 0 [] -linorder(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))|ti(X_b,X_1)=ti(X_b,Y_2).
% 32.78/32.56 0 [] -linorder(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))|ti(X_b,X_1)!=ti(X_b,Y_2).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 0 [] -linorder(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))|ti(X_b,X_1)=ti(X_b,Y_2).
% 32.78/32.56 0 [] -linorder(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))|ti(X_b,X_1)!=ti(X_b,Y_2).
% 32.78/32.56 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).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 0 [] -ordere236663937imp_le(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),C_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)).
% 32.78/32.56 0 [] -ordere236663937imp_le(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),C_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)).
% 32.78/32.56 0 [] -ordere236663937imp_le(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)).
% 32.78/32.56 0 [] -ordere236663937imp_le(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B_3)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)).
% 32.78/32.56 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))).
% 32.78/32.56 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))).
% 32.78/32.56 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))).
% 32.78/32.56 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)).
% 32.78/32.56 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)).
% 32.78/32.56 0 [] -bot(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),bot_bot(X_a))).
% 32.78/32.56 0 [] -bot(X_b)|ti(X_b,A_2)=bot_bot(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),bot_bot(X_b)),A_2)).
% 32.78/32.56 0 [] -bot(X_b)|ti(X_b,A_2)!=bot_bot(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),bot_bot(X_b)),A_2)).
% 32.78/32.56 0 [] -ordered_ab_group_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),D_1)).
% 32.78/32.56 0 [] -ordered_ab_group_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),D_1)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))|M=Na.
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))|M!=Na.
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M)))|Na=M.
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M)))|Na!=M.
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M_1)))|M_1=N.
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))|hAPP(nat,nat,suc,M_1)=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),N)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_2)),K_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))|M_1=N.
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)).
% 32.78/32.56 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_2),J)),I_2)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),I_2)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M_1))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),J))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),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_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K_1))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),L_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)).
% 32.78/32.56 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_2),J)),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))|M!=Na.
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))|M=Na.
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))|M=Na.
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))|M!=Na.
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))|M_1=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N)).
% 32.78/32.56 0 [] M_1!=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),Y)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K_1))|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_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),L_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M_1))).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2))| -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),$f45(N_2))).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2))|hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),$f46(N_2,M_2)),N_2)).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f46(N_2,M_2)),M_2)).
% 32.78/32.56 0 [] ti(fun(X_b,bool),A_3)!=hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),Na)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)).
% 32.78/32.56 0 [] hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),Na)))=Na.
% 32.78/32.56 0 [] hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),Pa)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1))))).
% 32.78/32.56 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))).
% 32.78/32.56 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))).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),M_1)))).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),I_2)))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))|Na=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),$f47(M,Na))).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))|Na!=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,Na)),M)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,Na)),M)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M)),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M)),Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M_1)),N)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M)))|Na=M.
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M)))|Na!=M.
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M_1)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),hAPP(nat,nat,suc,M_1))).
% 32.78/32.56 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)))|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)),J_1)).
% 32.78/32.56 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)))| -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)),J_1)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),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_1),N))=M_1.
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),A_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),C))).
% 32.78/32.56 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),Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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),Na),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.56 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),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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),Na),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.56 0 [] hAPP(nat,fun(nat,bool),ord_less(nat),X_2)=hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,X_2)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f49(M,K,F)),$f48(M,K,F)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,M)),K)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,$f49(M,K,F))),hAPP(nat,nat,F,$f48(M,K,F))))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,M)),K)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))| -hBOOL(hAPP(nat,bool,Pa,J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f50(Pa,I_1,J_1)),J_1))|hBOOL(hAPP(nat,bool,Pa,I_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))| -hBOOL(hAPP(nat,bool,Pa,J_1))|hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,$f50(Pa,I_1,J_1))))|hBOOL(hAPP(nat,bool,Pa,I_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))| -hBOOL(hAPP(nat,bool,Pa,J_1))| -hBOOL(hAPP(nat,bool,Pa,$f50(Pa,I_1,J_1)))|hBOOL(hAPP(nat,bool,Pa,I_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))|N=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),$f51(M_1,N))).
% 32.78/32.56 0 [] -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,$f52(X_b,Na,M,F))),hAPP(nat,X_b,F,hAPP(nat,nat,suc,$f52(X_b,Na,M,F)))))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,M)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)).
% 32.78/32.56 0 [] -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,$f52(X_b,Na,M,F))),hAPP(nat,X_b,F,hAPP(nat,nat,suc,$f52(X_b,Na,M,F)))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,M)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)).
% 32.78/32.56 0 [] -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,$f53(X_b,Na,N_3,F))),hAPP(nat,X_b,F,hAPP(nat,nat,suc,$f53(X_b,Na,N_3,F)))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),N_3))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,N_3))).
% 32.78/32.56 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)))).
% 32.78/32.56 0 [] -ord(X_c)| -hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less(fun(X_b,X_c)),F),G))|hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_e_q(fun(X_b,X_c)),F),G)).
% 32.78/32.56 0 [] -ord(X_c)| -hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less(fun(X_b,X_c)),F),G))| -hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_e_q(fun(X_b,X_c)),G),F)).
% 32.78/32.56 0 [] -ord(X_c)|hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less(fun(X_b,X_c)),F),G))| -hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_e_q(fun(X_b,X_c)),F),G))|hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_e_q(fun(X_b,X_c)),G),F)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool)))).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),B_1),C_2))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_2)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_1),C_2))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_2)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))|ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_1).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))|ti(fun(X_b,bool),A_3)!=ti(fun(X_b,bool),B_1).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))|ti(fun(X_b,bool),A_3)!=ti(fun(X_b,bool),B_1).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))|ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_1).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1))).
% 32.78/32.56 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)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|ti(fun(X_b,bool),A_3)=hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),$f54(X_b,A_3)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),$f55(X_b,A_3)))).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|ti(fun(X_b,bool),A_3)!=hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F_2),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_1))).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),$f56(Na,N_2)),N_2))|hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f56(Na,N_2)),Na))|hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f58(I_1,J_1,F)),$f57(I_1,J_1,F)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_1))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,$f58(I_1,J_1,F))),hAPP(nat,nat,F,$f57(I_1,J_1,F))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_1))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1))|K_1=hAPP(nat,nat,suc,I_2)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),$f59(I_2,K_1))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1))|K_1=hAPP(nat,nat,suc,I_2)|K_1=hAPP(nat,nat,suc,$f59(I_2,K_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_2)),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),$f60(I_2,K_1))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_2)),K_1))|K_1=hAPP(nat,nat,suc,$f60(I_2,K_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),B_1),C_2))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_2)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f61(X_b,A_3,B_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_1),A_3))).
% 32.78/32.56 0 [] -order(X_b)| -ord(X_c)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_c,X_b,F,B_3)),A_2))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),B_3))|hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),$f62(X_c,X_b,C_1,F,B_3,A_2)),$f63(X_c,X_b,C_1,F,B_3,A_2)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,C_1)),A_2)).
% 32.78/32.56 0 [] -order(X_b)| -ord(X_c)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_c,X_b,F,B_3)),A_2))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),B_3))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,$f62(X_c,X_b,C_1,F,B_3,A_2))),hAPP(X_c,X_b,F,$f63(X_c,X_b,C_1,F,B_3,A_2))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,C_1)),A_2)).
% 32.78/32.56 0 [] -order(X_b)| -order(X_c)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,B_3)),A_2))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),C_1),B_3))|hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),$f64(X_c,X_b,C_1,F,B_3,A_2)),$f65(X_c,X_b,C_1,F,B_3,A_2)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,C_1)),A_2)).
% 32.78/32.56 0 [] -order(X_b)| -order(X_c)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,B_3)),A_2))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),C_1),B_3))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_c,X_b,F,$f64(X_c,X_b,C_1,F,B_3,A_2))),hAPP(X_c,X_b,F,$f65(X_c,X_b,C_1,F,B_3,A_2))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,C_1)),A_2)).
% 32.78/32.56 0 [] -order(X_c)| -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),hAPP(X_c,X_b,F,B_3)))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),B_3),C_1))|hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),$f67(X_b,X_c,C_1,A_2,F,B_3)),$f66(X_b,X_c,C_1,A_2,F,B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,C_1))).
% 32.78/32.56 0 [] -order(X_c)| -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),hAPP(X_c,X_b,F,B_3)))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),B_3),C_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,$f67(X_b,X_c,C_1,A_2,F,B_3))),hAPP(X_c,X_b,F,$f66(X_b,X_c,C_1,A_2,F,B_3))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,C_1))).
% 32.78/32.56 0 [] -order(X_c)| -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,B_3)))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),B_3),C_1))|hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),$f69(X_b,X_c,C_1,A_2,F,B_3)),$f68(X_b,X_c,C_1,A_2,F,B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,C_1))).
% 32.78/32.56 0 [] -order(X_c)| -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,B_3)))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),B_3),C_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_c,X_b,F,$f69(X_b,X_c,C_1,A_2,F,B_3))),hAPP(X_c,X_b,F,$f68(X_b,X_c,C_1,A_2,F,B_3))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,C_1))).
% 32.78/32.56 0 [] -dense_linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f70(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)).
% 32.78/32.56 0 [] -dense_linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),$f70(X_a,Z,Y)),Z))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z)).
% 32.78/32.56 0 [] -dense_linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),$f71(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)).
% 32.78/32.56 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),$f71(X_a,Z,X,Y)),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z)).
% 32.78/32.56 0 [] -dense_linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),$f71(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)).
% 32.78/32.56 0 [] -order(X_b)| -order(X_c)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),C_1),hAPP(X_b,X_c,F,B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),$f72(X_c,X_b,C_1,F,B_3,A_2)),$f73(X_c,X_b,C_1,F,B_3,A_2)))|hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,A_2))).
% 32.78/32.56 0 [] -order(X_b)| -order(X_c)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),C_1),hAPP(X_b,X_c,F,B_3)))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,$f72(X_c,X_b,C_1,F,B_3,A_2))),hAPP(X_b,X_c,F,$f73(X_c,X_b,C_1,F,B_3,A_2))))|hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,A_2))).
% 32.78/32.56 0 [] -order(X_b)| -order(X_c)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_3),A_2))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),$f74(X_c,X_b,C_1,F,B_3,A_2)),$f75(X_c,X_b,C_1,F,B_3,A_2)))|hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,A_2))).
% 32.78/32.56 0 [] -order(X_b)| -order(X_c)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_3),A_2))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,B_3)))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),hAPP(X_b,X_c,F,$f74(X_c,X_b,C_1,F,B_3,A_2))),hAPP(X_b,X_c,F,$f75(X_c,X_b,C_1,F,B_3,A_2))))|hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,A_2))).
% 32.78/32.56 0 [] -order(X_c)| -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,B_3)),C_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),$f77(X_b,X_c,F,C_1,A_2,B_3)),$f76(X_b,X_c,F,C_1,A_2,B_3)))|hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),C_1)).
% 32.78/32.56 0 [] -order(X_c)| -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,B_3)),C_1))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),hAPP(X_b,X_c,F,$f77(X_b,X_c,F,C_1,A_2,B_3))),hAPP(X_b,X_c,F,$f76(X_b,X_c,F,C_1,A_2,B_3))))|hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),C_1)).
% 32.78/32.56 0 [] -order(X_c)| -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),hAPP(X_b,X_c,F,B_3)),C_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),$f79(X_b,X_c,F,C_1,A_2,B_3)),$f78(X_b,X_c,F,C_1,A_2,B_3)))|hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),C_1)).
% 32.78/32.56 0 [] -order(X_c)| -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_e_q(X_c),hAPP(X_b,X_c,F,B_3)),C_1))| -hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,$f79(X_b,X_c,F,C_1,A_2,B_3))),hAPP(X_b,X_c,F,$f78(X_b,X_c,F,C_1,A_2,B_3))))|hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),C_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))|hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_c,bool),nat,finite_card(X_c),B_1)).
% 32.78/32.56 0 [] ti(fun(X_b,bool),M_3)!=ti(fun(X_b,bool),N_2)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f80(X_c,X_b,F,G,M_3,N_2)),N_2))|hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),M_3)=hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),G),N_2).
% 32.78/32.56 0 [] ti(fun(X_b,bool),M_3)!=ti(fun(X_b,bool),N_2)|hAPP(X_b,X_c,F,$f80(X_c,X_b,F,G,M_3,N_2))!=hAPP(X_b,X_c,G,$f80(X_c,X_b,F,G,M_3,N_2))|hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),M_3)=hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),G),N_2).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1)))|hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))|hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1))).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1)))|hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1)).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1)))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1)).
% 32.78/32.56 0 [] hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1)!=bot_bot(fun(sum_sum(X_b,X_c),bool))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool)).
% 32.78/32.56 0 [] hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1)!=bot_bot(fun(sum_sum(X_b,X_c),bool))|ti(fun(X_c,bool),B_1)=bot_bot(fun(X_c,bool)).
% 32.78/32.56 0 [] hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1)=bot_bot(fun(sum_sum(X_b,X_c),bool))|ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))|ti(fun(X_c,bool),B_1)!=bot_bot(fun(X_c,bool)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))|hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_c,bool),nat,finite_card(X_c),B_1)).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1))=zero_zero(nat).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))|hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1))=zero_zero(nat).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),R_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),R_1),S)).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),R_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),R_1),S)).
% 32.78/32.56 0 [] hBOOL(hAPP(X_b,bool,Pa,$f81(X_b,Q_3,Pa)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3))).
% 32.78/32.56 0 [] -hBOOL(hAPP(X_b,bool,Q_3,$f81(X_b,Q_3,Pa)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Na),zero_zero(nat)))|Na=zero_zero(nat).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Na),zero_zero(nat)))|Na!=zero_zero(nat).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N)).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)!=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M_1)!=zero_zero(nat)|M_1=N.
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),M_1)=zero_zero(nat).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),zero_zero(nat))=M_1.
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N)=zero_zero(nat).
% 32.78/32.56 0 [] -zero_ne_q_one(X_a)|one_one(X_a)!=zero_zero(X_a).
% 32.78/32.56 0 [] -zero_ne_q_one(X_a)|zero_zero(X_a)!=one_one(X_a).
% 32.78/32.56 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).
% 32.78/32.56 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).
% 32.78/32.56 0 [] -linord219039673up_add(X_b)|zero_zero(X_b)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)|ti(X_b,A_2)=zero_zero(X_b).
% 32.78/32.56 0 [] -linord219039673up_add(X_b)|zero_zero(X_b)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)|ti(X_b,A_2)!=zero_zero(X_b).
% 32.78/32.56 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).
% 32.78/32.56 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).
% 32.78/32.56 0 [] -group_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)!=zero_zero(X_b)|ti(X_b,A_2)=ti(X_b,B_3).
% 32.78/32.56 0 [] -group_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)=zero_zero(X_b)|ti(X_b,A_2)!=ti(X_b,B_3).
% 32.78/32.56 0 [] -ab_group_add(X_b)|ti(X_b,A_2)!=ti(X_b,B_3)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)=zero_zero(X_b).
% 32.78/32.56 0 [] -ab_group_add(X_b)|ti(X_b,A_2)=ti(X_b,B_3)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)!=zero_zero(X_b).
% 32.78/32.56 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).
% 32.78/32.56 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).
% 32.78/32.56 0 [] -zero(X_b)|zero_zero(X_b)!=ti(X_b,X_1)|ti(X_b,X_1)=zero_zero(X_b).
% 32.78/32.56 0 [] -zero(X_b)|zero_zero(X_b)=ti(X_b,X_1)|ti(X_b,X_1)!=zero_zero(X_b).
% 32.78/32.56 0 [] bot_bot(nat)=zero_zero(nat).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)!=M_1|N=zero_zero(nat).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)!=zero_zero(nat)|M=zero_zero(nat).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)!=zero_zero(nat)|Na=zero_zero(nat).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)=zero_zero(nat)|M!=zero_zero(nat)|Na!=zero_zero(nat).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),zero_zero(nat))=M_1.
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N)=N.
% 32.78/32.56 0 [] N=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))|N!=zero_zero(nat).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))).
% 32.78/32.56 0 [] Na=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)).
% 32.78/32.56 0 [] Na!=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))).
% 32.78/32.56 0 [] hAPP(nat,nat,suc,M_1)!=zero_zero(nat).
% 32.78/32.56 0 [] zero_zero(nat)!=hAPP(nat,nat,suc,M_1).
% 32.78/32.56 0 [] hAPP(nat,nat,suc,Nat_2)!=zero_zero(nat).
% 32.78/32.56 0 [] hAPP(nat,nat,suc,M_1)!=zero_zero(nat).
% 32.78/32.56 0 [] zero_zero(nat)!=hAPP(nat,nat,suc,Nat_1).
% 32.78/32.56 0 [] zero_zero(nat)!=hAPP(nat,nat,suc,M_1).
% 32.78/32.56 0 [] hAPP(nat,X_b,hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(X_b,fun(fun(nat,X_b),fun(nat,X_b)),nat_case(X_b),F1),F2),zero_zero(nat))=ti(X_b,F1).
% 32.78/32.56 0 [] -linord219039673up_add(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),A_2)).
% 32.78/32.56 0 [] -linord219039673up_add(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),A_2)).
% 32.78/32.56 0 [] -linord219039673up_add(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),zero_zero(X_b))).
% 32.78/32.56 0 [] -linord219039673up_add(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),zero_zero(X_b))).
% 32.78/32.56 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))).
% 32.78/32.56 0 [] -ordere216010020id_add(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),X_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),Y_2))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),X_1),Y_2)!=zero_zero(X_b)|ti(X_b,X_1)=zero_zero(X_b).
% 32.78/32.56 0 [] -ordere216010020id_add(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),X_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),Y_2))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),X_1),Y_2)!=zero_zero(X_b)|ti(X_b,Y_2)=zero_zero(X_b).
% 32.78/32.56 0 [] -ordere216010020id_add(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),X_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),Y_2))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),X_1),Y_2)=zero_zero(X_b)|ti(X_b,X_1)!=zero_zero(X_b)|ti(X_b,Y_2)!=zero_zero(X_b).
% 32.78/32.56 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))).
% 32.78/32.56 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))).
% 32.78/32.56 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))).
% 32.78/32.56 0 [] -linord219039673up_add(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),A_2)).
% 32.78/32.56 0 [] -linord219039673up_add(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),A_2)).
% 32.78/32.56 0 [] -linord219039673up_add(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))).
% 32.78/32.56 0 [] -linord219039673up_add(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))).
% 32.78/32.56 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))).
% 32.78/32.56 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))).
% 32.78/32.56 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))).
% 32.78/32.56 0 [] -ordered_ab_group_add(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),zero_zero(X_b))).
% 32.78/32.56 0 [] -ordered_ab_group_add(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),zero_zero(X_b))).
% 32.78/32.56 0 [] -ordered_ab_group_add(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),zero_zero(X_b))).
% 32.78/32.56 0 [] -ordered_ab_group_add(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),zero_zero(X_b))).
% 32.78/32.56 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),zero_zero(X_a))).
% 32.78/32.56 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),one_one(X_a))).
% 32.78/32.56 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a))).
% 32.78/32.56 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))|Na=hAPP(nat,nat,suc,$f82(Na)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))|Na!=hAPP(nat,nat,suc,M_2).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,zero_zero(nat))))|Na=zero_zero(nat).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,zero_zero(nat))))|Na!=zero_zero(nat).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))|M=zero_zero(nat)|M=hAPP(nat,nat,suc,$f83(M,Na)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))|M=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f83(M,Na)),Na)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))|M!=zero_zero(nat).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))|M!=hAPP(nat,nat,suc,J_2)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),Na)).
% 32.78/32.56 0 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)|M=hAPP(nat,nat,suc,zero_zero(nat))|M=zero_zero(nat).
% 32.78/32.56 0 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)|M=hAPP(nat,nat,suc,zero_zero(nat))|Na=hAPP(nat,nat,suc,zero_zero(nat)).
% 32.78/32.56 0 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)|Na=zero_zero(nat)|M=zero_zero(nat).
% 32.78/32.56 0 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)|Na=zero_zero(nat)|Na=hAPP(nat,nat,suc,zero_zero(nat)).
% 32.78/32.56 0 [] hAPP(nat,nat,suc,zero_zero(nat))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)|M!=hAPP(nat,nat,suc,zero_zero(nat))|Na!=zero_zero(nat).
% 32.78/32.56 0 [] hAPP(nat,nat,suc,zero_zero(nat))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)|M!=zero_zero(nat)|Na!=hAPP(nat,nat,suc,zero_zero(nat)).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)!=hAPP(nat,nat,suc,zero_zero(nat))|M=hAPP(nat,nat,suc,zero_zero(nat))|M=zero_zero(nat).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)!=hAPP(nat,nat,suc,zero_zero(nat))|M=hAPP(nat,nat,suc,zero_zero(nat))|Na=hAPP(nat,nat,suc,zero_zero(nat)).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)!=hAPP(nat,nat,suc,zero_zero(nat))|Na=zero_zero(nat)|M=zero_zero(nat).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)!=hAPP(nat,nat,suc,zero_zero(nat))|Na=zero_zero(nat)|Na=hAPP(nat,nat,suc,zero_zero(nat)).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)=hAPP(nat,nat,suc,zero_zero(nat))|M!=hAPP(nat,nat,suc,zero_zero(nat))|Na!=zero_zero(nat).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)=hAPP(nat,nat,suc,zero_zero(nat))|M!=zero_zero(nat)|Na!=hAPP(nat,nat,suc,zero_zero(nat)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)))|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),zero_zero(nat)),Na)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)).
% 32.78/32.56 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),bot_bot(fun(X_b,bool)))=zero_zero(nat).
% 32.78/32.56 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=zero_zero(nat).
% 32.78/32.56 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),Na),M)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.56 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),Na),M)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.56 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_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),M_1)).
% 32.78/32.56 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_1))=zero_zero(nat).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),Na)!=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),Na)=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)=zero_zero(nat).
% 32.78/32.56 0 [] one_one(nat)=hAPP(nat,nat,suc,zero_zero(nat)).
% 32.78/32.56 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,Na))=hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),combi(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),Na)).
% 32.78/32.56 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))).
% 32.78/32.56 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))).
% 32.78/32.56 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))).
% 32.78/32.56 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))).
% 32.78/32.56 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))).
% 32.78/32.56 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))).
% 32.78/32.56 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)))).
% 32.78/32.56 0 [] -hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))).
% 32.78/32.56 0 [] hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))).
% 32.78/32.56 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)!=zero_zero(nat)|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)).
% 32.78/32.56 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=zero_zero(nat)|ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool)).
% 32.78/32.56 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=zero_zero(nat)|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat))))=N.
% 32.78/32.56 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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,I_2))),N)).
% 32.78/32.56 0 [] -hBOOL(hAPP(X_b,bool,Pa,X_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),Pa),Q_3))|hBOOL(hAPP(X_b,bool,Q_3,X_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),Pa),Q_3))| -hBOOL(hAPP(X_b,bool,Pa,X_1))|hBOOL(hAPP(X_b,bool,Q_3,X_1)).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_3))|hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))|A_2!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_3),D_2)|hBOOL(hAPP(nat,bool,Pa,D_2)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_3))|A_2=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_3),$f84(Pa,A_2,B_3)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_3))| -hBOOL(hAPP(nat,bool,Pa,$f84(Pa,A_2,B_3))).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))| -hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))|A_2=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_3),$f84(Pa,A_2,B_3)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))| -hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,Pa,$f84(Pa,A_2,B_3))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_3))|hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))).
% 32.78/32.56 0 [] -hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))|A_2!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_3),D_2)|hBOOL(hAPP(nat,bool,Pa,D_2)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_3))|A_2=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_3),$f85(Pa,A_2,B_3)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_3))| -hBOOL(hAPP(nat,bool,Pa,$f85(Pa,A_2,B_3))).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))| -hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))|A_2=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_3),$f85(Pa,A_2,B_3)).
% 32.78/32.56 0 [] hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3)))| -hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,Pa,$f85(Pa,A_2,B_3))).
% 32.78/32.56 0 [] -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_3))|hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1)))))=hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I_1))))).
% 32.78/32.57 0 [] -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_3))|hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I_1)))))!=zero_zero(nat).
% 32.78/32.57 0 [] hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_3))|hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1))))=hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I_1))))).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))|ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)).
% 32.78/32.57 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))=N.
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|N=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))).
% 32.78/32.57 0 [] M_1!=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)=N.
% 32.78/32.57 0 [] M_1=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),one_one(nat))),N)).
% 32.78/32.57 0 [] hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,Pa,Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f86(Na,Pa)),Na)).
% 32.78/32.57 0 [] hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,Pa,Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),$f86(Na,Pa)))| -hBOOL(hAPP(nat,bool,Pa,I)).
% 32.78/32.57 0 [] hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,Pa,Na))|hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),$f86(Na,Pa)),one_one(nat)))).
% 32.78/32.57 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)!=hAPP(nat,nat,suc,K)|ti(fun(X_b,bool),A_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f88(X_b,A_3,K)),$f87(X_b,A_3,K)).
% 32.78/32.57 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)!=hAPP(nat,nat,suc,K)| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f88(X_b,A_3,K)),$f87(X_b,A_3,K))).
% 32.78/32.57 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)!=hAPP(nat,nat,suc,K)|hAPP(fun(X_b,bool),nat,finite_card(X_b),$f87(X_b,A_3,K))=K.
% 32.78/32.57 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)!=hAPP(nat,nat,suc,K)|K!=zero_zero(nat)|ti(fun(X_b,bool),$f87(X_b,A_3,K))=bot_bot(fun(X_b,bool)).
% 32.78/32.57 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=hAPP(nat,nat,suc,K)|ti(fun(X_b,bool),A_3)!=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_5),B_4)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_5),B_4))|hAPP(fun(X_b,bool),nat,finite_card(X_b),B_4)!=K|K=zero_zero(nat).
% 32.78/32.57 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=hAPP(nat,nat,suc,K)|ti(fun(X_b,bool),A_3)!=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_5),B_4)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_5),B_4))|hAPP(fun(X_b,bool),nat,finite_card(X_b),B_4)!=K|ti(fun(X_b,bool),B_4)!=bot_bot(fun(X_b,bool)).
% 32.78/32.57 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f89(X_b,A_3)),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=zero_zero(nat).
% 32.78/32.57 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|one_one(nat)!=zero_zero(nat)|hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=zero_zero(nat).
% 32.78/32.57 0 [] hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,Pa,Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f90(Na,Pa)),Na)).
% 32.78/32.57 0 [] hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,Pa,Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),$f90(Na,Pa)))| -hBOOL(hAPP(nat,bool,Pa,I)).
% 32.78/32.57 0 [] hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,Pa,Na))|hBOOL(hAPP(nat,bool,Pa,$f90(Na,Pa))).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),$f91(I_2,J))).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),$f91(I_2,J))=J.
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|N=hAPP(nat,nat,suc,$f92(N)).
% 32.78/32.57 0 [] -linordered_idom(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))).
% 32.78/32.57 0 [] -linordered_idom(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))).
% 32.78/32.57 0 [] -linord219039673up_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)!=zero_zero(X_b)|ti(X_b,A_2)=zero_zero(X_b).
% 32.78/32.57 0 [] -linord219039673up_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)=zero_zero(X_b)|ti(X_b,A_2)!=zero_zero(X_b).
% 32.78/32.57 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)!=hAPP(nat,nat,suc,K)|ti(fun(X_b,bool),A_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f94(X_b,A_3,K)),$f93(X_b,A_3,K)).
% 32.78/32.57 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)!=hAPP(nat,nat,suc,K)| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f94(X_b,A_3,K)),$f93(X_b,A_3,K))).
% 32.78/32.57 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)!=hAPP(nat,nat,suc,K)|hAPP(fun(X_b,bool),nat,finite_card(X_b),$f93(X_b,A_3,K))=K.
% 32.78/32.57 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)!=hAPP(nat,nat,suc,K)|K!=zero_zero(nat)|ti(fun(X_b,bool),$f93(X_b,A_3,K))=bot_bot(fun(X_b,bool)).
% 32.78/32.57 0 [] Y=zero_zero(nat)|Y=hAPP(nat,nat,suc,$f95(Y)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,Pa,K))|hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,$f96(Pa,K))))|hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,Pa,K))| -hBOOL(hAPP(nat,bool,Pa,$f96(Pa,K)))|hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))).
% 32.78/32.57 0 [] N=zero_zero(nat)|N=hAPP(nat,nat,suc,$f97(N)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))|hBOOL(hAPP(nat,bool,Pa,$f98(Na,Pa)))|hBOOL(hAPP(nat,bool,Pa,Na)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,$f98(Na,Pa))))|hBOOL(hAPP(nat,bool,Pa,Na)).
% 32.78/32.57 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).
% 32.78/32.57 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)).
% 32.78/32.57 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).
% 32.78/32.57 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)).
% 32.78/32.57 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).
% 32.78/32.57 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)).
% 32.78/32.57 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).
% 32.78/32.57 0 [] -semiri456707255roduct(X_b)|ti(X_b,B_3)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),A_2)|ti(X_b,A_2)=zero_zero(X_b).
% 32.78/32.57 0 [] -semiri456707255roduct(X_b)|ti(X_b,B_3)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),A_2)|ti(X_b,A_2)!=zero_zero(X_b).
% 32.78/32.57 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).
% 32.78/32.57 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)),$f99(X_a,X,Y)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)).
% 32.78/32.57 0 [] -linordered_field(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),$f99(X_a,X,Y))))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)).
% 32.78/32.57 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=hAPP(fun(X_b,bool),nat,hAPP(nat,fun(fun(X_b,bool),nat),hAPP(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat))),finite_fold_image(nat,X_b),plus_plus(nat)),hAPP(nat,fun(X_b,nat),combk(nat,X_b),one_one(nat))),zero_zero(nat)),A_3).
% 32.78/32.57 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=hAPP(fun(X_b,bool),nat,hAPP(nat,fun(fun(X_b,bool),nat),hAPP(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat))),finite_fold_image(nat,X_b),plus_plus(nat)),hAPP(nat,fun(X_b,nat),combk(nat,X_b),one_one(nat))),zero_zero(nat)),A_3).
% 32.78/32.57 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=zero_zero(nat).
% 32.78/32.57 0 [] hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),F),G),Z_2),bot_bot(fun(X_c,bool)))=ti(X_b,Z_2).
% 32.78/32.57 0 [] -hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))|hAPP(fun(X_c,bool),X_b,F_1,A_3)=hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),F),G),Z_2),A_3).
% 32.78/32.57 0 [] -linordered_idom(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),A_2)),A_2)),zero_zero(X_b)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))).
% 32.78/32.57 0 [] -linordered_idom(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),A_2)),A_2)),zero_zero(X_b)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V)))|hAPP(int,nat,number_number_of(nat),V)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))).
% 32.78/32.57 0 [] -linord626643107strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),U_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),V))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U_1),V)!=one_one(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)).
% 32.78/32.57 0 [] -ring_1(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),ring_1_Ints(X_b)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),ring_1_Ints(X_b))).
% 32.78/32.57 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).
% 32.78/32.57 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).
% 32.78/32.57 0 [] -ring_n68954251visors(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)!=zero_zero(X_b)|ti(X_b,A_2)=zero_zero(X_b)|ti(X_b,B_3)=zero_zero(X_b).
% 32.78/32.57 0 [] -ring_n68954251visors(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)=zero_zero(X_b)|ti(X_b,A_2)!=zero_zero(X_b).
% 32.78/32.57 0 [] -ring_n68954251visors(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)=zero_zero(X_b)|ti(X_b,B_3)!=zero_zero(X_b).
% 32.78/32.57 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).
% 32.78/32.57 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).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N)=zero_zero(nat).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),zero_zero(nat))=zero_zero(nat).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)!=zero_zero(nat)|M=zero_zero(nat)|Na=zero_zero(nat).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)=zero_zero(nat)|M!=zero_zero(nat).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)=zero_zero(nat)|Na!=zero_zero(nat).
% 32.78/32.57 0 [] 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),Na)|M=Na|K=zero_zero(nat).
% 32.78/32.57 0 [] 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),Na)|M!=Na.
% 32.78/32.57 0 [] 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),Na)|K!=zero_zero(nat).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)|M=Na|K=zero_zero(nat).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)|M!=Na.
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)|K!=zero_zero(nat).
% 32.78/32.57 0 [] -ab_sem1668676832m_mult(X_b)|hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),times_times(X_b))).
% 32.78/32.57 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)).
% 32.78/32.57 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_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),B),E_1)),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_1)),C).
% 32.78/32.57 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).
% 32.78/32.57 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).
% 32.78/32.57 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).
% 32.78/32.57 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).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)|M=Na.
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)|M!=Na.
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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),K_1)).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),L_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),L_1))).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),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_1),I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),J))).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),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_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K_1))).
% 32.78/32.57 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),M_1)))).
% 32.78/32.57 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),M_1))).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(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),K_1)).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(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)).
% 32.78/32.57 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).
% 32.78/32.57 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).
% 32.78/32.57 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).
% 32.78/32.57 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)).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)!=one_one(nat)|M=one_one(nat).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)!=one_one(nat)|Na=one_one(nat).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)=one_one(nat)|M!=one_one(nat)|Na!=one_one(nat).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),one_one(nat))=N.
% 32.78/32.57 0 [] one_one(nat)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)|M=one_one(nat).
% 32.78/32.57 0 [] one_one(nat)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)|Na=one_one(nat).
% 32.78/32.57 0 [] one_one(nat)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)|M!=one_one(nat)|Na!=one_one(nat).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N)=N.
% 32.78/32.57 0 [] -number_ring(X_b)| -linordered_idom(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(int,X_b,number_number_of(X_b),X_1)),hAPP(int,X_b,number_number_of(X_b),Y_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_2)).
% 32.78/32.57 0 [] -number_ring(X_b)| -linordered_idom(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(int,X_b,number_number_of(X_b),X_1)),hAPP(int,X_b,number_number_of(X_b),Y_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_2)).
% 32.78/32.57 0 [] -number_ring(X_b)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(int,X_b,number_number_of(X_b),W_1)),ring_1_Ints(X_b))).
% 32.78/32.57 0 [] -number_ring(X_a)|hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)).
% 32.78/32.57 0 [] -number(X_b)|hAPP(int,X_b,number_number_of(X_b),W_1)!=ti(X_b,X_1)|ti(X_b,X_1)=hAPP(int,X_b,number_number_of(X_b),W_1).
% 32.78/32.57 0 [] -number(X_b)|hAPP(int,X_b,number_number_of(X_b),W_1)=ti(X_b,X_1)|ti(X_b,X_1)!=hAPP(int,X_b,number_number_of(X_b),W_1).
% 32.78/32.57 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W)).
% 32.78/32.57 0 [] -number_ring(X_b)| -ring_char_0(X_b)|hAPP(int,X_b,number_number_of(X_b),X_1)!=hAPP(int,X_b,number_number_of(X_b),Y_2)|X_1=Y_2.
% 32.78/32.57 0 [] -number_ring(X_b)| -ring_char_0(X_b)|hAPP(int,X_b,number_number_of(X_b),X_1)=hAPP(int,X_b,number_number_of(X_b),Y_2)|X_1!=Y_2.
% 32.78/32.57 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W)),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W))),Z).
% 32.78/32.57 0 [] -ring_1(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),ring_1_Ints(X_b)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)),ring_1_Ints(X_b))).
% 32.78/32.57 0 [] -number_ring(X_b)| -linordered_idom(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(int,X_b,number_number_of(X_b),X_1)),hAPP(int,X_b,number_number_of(X_b),Y_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_1),Y_2)).
% 32.78/32.57 0 [] -number_ring(X_b)| -linordered_idom(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(int,X_b,number_number_of(X_b),X_1)),hAPP(int,X_b,number_number_of(X_b),Y_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X_1),Y_2)).
% 32.78/32.57 0 [] -number_ring(X_a)|hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),V),W))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)).
% 32.78/32.57 0 [] -number(X_b)| -ring(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_1),B)),hAPP(int,X_b,number_number_of(X_b),V))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V))).
% 32.78/32.57 0 [] -number(X_b)| -ring(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B),C))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C)).
% 32.78/32.57 0 [] -ring_1(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),ring_1_Ints(X_b)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B_3)),ring_1_Ints(X_b))).
% 32.78/32.57 0 [] -number_ring(X_a)|hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)).
% 32.78/32.57 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W)).
% 32.78/32.57 0 [] -number(X_b)| -semiring(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),C))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C)).
% 32.78/32.57 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),Z).
% 32.78/32.57 0 [] -number(X_b)| -semiring(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_1),B)),hAPP(int,X_b,number_number_of(X_b),V))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V))).
% 32.78/32.57 0 [] -ring_1(X_b)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),zero_zero(X_b)),ring_1_Ints(X_b))).
% 32.78/32.57 0 [] -ring_1(X_b)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),one_one(X_b)),ring_1_Ints(X_b))).
% 32.78/32.57 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).
% 32.78/32.57 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).
% 32.78/32.57 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).
% 32.78/32.57 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)).
% 32.78/32.57 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).
% 32.78/32.57 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)).
% 32.78/32.57 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).
% 32.78/32.57 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))).
% 32.78/32.57 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)).
% 32.78/32.57 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)).
% 32.78/32.57 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)).
% 32.78/32.57 0 [] -semiri456707255roduct(X_b)|ti(X_b,A_2)=ti(X_b,B_3)|ti(X_b,C_1)=ti(X_b,D_1)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),D_1))!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),D_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1)).
% 32.78/32.57 0 [] -semiri456707255roduct(X_b)|ti(X_b,A_2)!=ti(X_b,B_3)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),D_1))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),D_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1)).
% 32.78/32.57 0 [] -semiri456707255roduct(X_b)|ti(X_b,C_1)!=ti(X_b,D_1)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),D_1))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),D_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1)).
% 32.78/32.57 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)).
% 32.78/32.57 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_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),M_1))=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_1).
% 32.78/32.57 0 [] -semiri456707255roduct(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Y_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Z_2))!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Z_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Y_2))|ti(X_b,W_1)=ti(X_b,X_1)|ti(X_b,Y_2)=ti(X_b,Z_2).
% 32.78/32.57 0 [] -semiri456707255roduct(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Y_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Z_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Z_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Y_2))|ti(X_b,W_1)!=ti(X_b,X_1).
% 32.78/32.57 0 [] -semiri456707255roduct(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Y_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Z_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Z_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Y_2))|ti(X_b,Y_2)!=ti(X_b,Z_2).
% 32.78/32.57 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).
% 32.78/32.57 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).
% 32.78/32.57 0 [] -number(X_b)| -linorder(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(int,X_b,number_number_of(X_b),V_3)),hAPP(int,X_b,number_number_of(X_b),W_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(int,X_b,number_number_of(X_b),W_1)),hAPP(int,X_b,number_number_of(X_b),V_3))).
% 32.78/32.57 0 [] -number(X_b)| -linorder(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(int,X_b,number_number_of(X_b),V_3)),hAPP(int,X_b,number_number_of(X_b),W_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(int,X_b,number_number_of(X_b),W_1)),hAPP(int,X_b,number_number_of(X_b),V_3))).
% 32.78/32.57 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),C))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),C).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)),zero_zero(X_b)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),A_2))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),zero_zero(X_b))).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)),zero_zero(X_b)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),A_2))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),B_3)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)),zero_zero(X_b)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_3),zero_zero(X_b)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),zero_zero(X_b))).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)),zero_zero(X_b)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_3),zero_zero(X_b)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),B_3)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)),zero_zero(X_b)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),A_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_3),zero_zero(X_b))).
% 32.78/32.57 0 [] -linord581940658strict(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)),zero_zero(X_b)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),zero_zero(X_b)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),B_3)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),A_2))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),zero_zero(X_b))).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),A_2))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_3),zero_zero(X_b))).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),B_3))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),zero_zero(X_b))).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),B_3))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_3),zero_zero(X_b))).
% 32.78/32.57 0 [] -linord581940658strict(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),A_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),B_3)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),zero_zero(X_b)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_3),zero_zero(X_b))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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)).
% 32.78/32.57 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)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2)).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 0 [] -semiri456707255roduct(X_a)|ti(X_a,R_3)=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_3),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_3),D)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))!=zero_zero(X_b)|ti(X_b,X_1)=zero_zero(X_b).
% 32.78/32.57 0 [] -linord581940658strict(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))!=zero_zero(X_b)|ti(X_b,Y_2)=zero_zero(X_b).
% 32.78/32.57 0 [] -linord581940658strict(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))=zero_zero(X_b)|ti(X_b,X_1)!=zero_zero(X_b)|ti(X_b,Y_2)!=zero_zero(X_b).
% 32.78/32.57 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_1))| -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_1),N))).
% 32.78/32.57 0 [] -ring(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)|ti(X_b,C_1)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1).
% 32.78/32.57 0 [] -ring(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)|ti(X_b,C_1)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1).
% 32.78/32.57 0 [] -ring(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1)=ti(X_b,D_1).
% 32.78/32.57 0 [] -ring(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1)!=ti(X_b,D_1).
% 32.78/32.57 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_1)),M_1)=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_1).
% 32.78/32.57 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M_1))=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_1).
% 32.78/32.57 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M_1),M_1)=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_1).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)!=hAPP(nat,nat,suc,zero_zero(nat))|M=hAPP(nat,nat,suc,zero_zero(nat)).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)!=hAPP(nat,nat,suc,zero_zero(nat))|Na=hAPP(nat,nat,suc,zero_zero(nat)).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)=hAPP(nat,nat,suc,zero_zero(nat))|M!=hAPP(nat,nat,suc,zero_zero(nat))|Na!=hAPP(nat,nat,suc,zero_zero(nat)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),J))).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K_1))).
% 32.78/32.57 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),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)).
% 32.78/32.57 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),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.57 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),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.57 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),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)).
% 32.78/32.57 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),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.57 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),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))| -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),M),Na)).
% 32.78/32.57 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),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)).
% 32.78/32.57 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),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)).
% 32.78/32.57 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),Na)))| -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),zero_zero(nat)),Na)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.57 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),hAPP(nat,nat,suc,N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,M_1)),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.57 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.57 0 [] M_1!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)|N=one_one(nat)|M_1=zero_zero(nat).
% 32.78/32.57 0 [] -ring_char_0(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b)))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)!=zero_zero(X_b)|ti(X_b,A_2)=zero_zero(X_b).
% 32.78/32.57 0 [] -ring_char_0(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b)))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)=zero_zero(X_b)|ti(X_b,A_2)!=zero_zero(X_b).
% 32.78/32.57 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)).
% 32.78/32.57 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)).
% 32.78/32.57 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)).
% 32.78/32.57 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)).
% 32.78/32.57 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)).
% 32.78/32.57 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)).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 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))).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_3),A_2)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_3),A_2)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_3)).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))),zero_zero(X_b)))|ti(X_b,X_1)=zero_zero(X_b).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))),zero_zero(X_b)))|ti(X_b,Y_2)=zero_zero(X_b).
% 32.78/32.57 0 [] -linord581940658strict(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))),zero_zero(X_b)))|ti(X_b,X_1)!=zero_zero(X_b)|ti(X_b,Y_2)!=zero_zero(X_b).
% 32.78/32.57 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)))).
% 32.78/32.57 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))).
% 32.78/32.57 0 [] -linord581940658strict(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))))|ti(X_b,X_1)!=zero_zero(X_b)|ti(X_b,Y_2)!=zero_zero(X_b).
% 32.78/32.57 0 [] -linord581940658strict(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))))|ti(X_b,X_1)=zero_zero(X_b).
% 32.78/32.57 0 [] -linord581940658strict(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))))|ti(X_b,Y_2)=zero_zero(X_b).
% 32.78/32.57 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)).
% 32.78/32.57 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)).
% 32.78/32.57 0 [] -ordered_ring(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1))).
% 32.78/32.57 0 [] -ordered_ring(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1))).
% 32.78/32.57 0 [] -ordered_ring(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1)),D_1)).
% 32.78/32.57 0 [] -ordered_ring(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1)),D_1)).
% 32.78/32.57 0 [] -ordered_ring(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1))).
% 32.78/32.57 0 [] -ordered_ring(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1))).
% 32.78/32.57 0 [] -ordered_ring(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1)),D_1)).
% 32.78/32.57 0 [] -ordered_ring(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),E)),D_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1)),D_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N))).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M_1))).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N))).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),Na)).
% 32.78/32.57 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),M))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),Na)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.57 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)).
% 32.78/32.57 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.57 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)).
% 32.78/32.57 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.57 0 [] -ab_semigroup_mult(X_c)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))|hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3))=hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,G,A_2)),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_2),A_3)).
% 32.78/32.57 0 [] -comm_monoid_mult(X_c)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,X_c)),combs(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combb(X_c,fun(X_c,X_c),X_b),times_times(X_c)),G)),H)),one_one(X_c)),A_3)=hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),one_one(X_c)),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),H),one_one(X_c)),A_3)).
% 32.78/32.57 0 [] -linord1278240602ring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),U_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),V))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U_1),V)!=one_one(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)).
% 32.78/32.57 0 [] M_1!=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)=zero_zero(nat).
% 32.78/32.57 0 [] M_1=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),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_1),one_one(nat))),N)).
% 32.78/32.57 0 [] -ring_char_0(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b)))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),A_2)),A_2)!=zero_zero(X_b).
% 32.78/32.57 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)),$f100(X_a,X,Y)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)).
% 32.78/32.57 0 [] -linord1117847801e_zero(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f100(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)).
% 32.78/32.57 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),$f100(X_a,X,Y)),X)),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)).
% 32.78/32.57 0 [] -comm_monoid_mult(X_c)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),S))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f101(X_b,X_c,F,S)),S))|hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),F),one_one(X_c)),S)=one_one(X_c).
% 32.78/32.57 0 [] -comm_monoid_mult(X_c)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),S))|hAPP(X_b,X_c,F,$f101(X_b,X_c,F,S))!=one_one(X_c)|hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),F),one_one(X_c)),S)=one_one(X_c).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),Na))).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),Na))).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M_1).
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)).
% 32.78/32.57 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)).
% 32.78/32.57 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z)=Z.
% 32.78/32.57 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),one_one(int))=Z.
% 32.78/32.57 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),W)=hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z).
% 32.78/32.57 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W))=hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W)).
% 32.78/32.57 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)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)).
% 32.78/32.57 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)).
% 32.78/32.57 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)=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W)).
% 32.78/32.57 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),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),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z2)).
% 32.78/32.57 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),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),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z2)).
% 32.78/32.57 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W))=hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W)).
% 32.78/32.57 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)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),I_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),J))).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))|hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),Na)!=one_one(int)|M=one_one(int).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))|hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),Na)!=one_one(int)|Na=one_one(int).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M))|hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),Na)=one_one(int)|M!=one_one(int)|Na!=one_one(int).
% 32.78/32.57 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).
% 32.78/32.57 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),zero_zero(int))=Z.
% 32.78/32.57 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),Z)=Z.
% 32.78/32.57 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)).
% 32.78/32.57 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),L)),zero_zero(int))).
% 32.78/32.57 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),L)),zero_zero(int))).
% 32.78/32.57 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))).
% 32.78/32.57 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_2)),Z_2)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int))).
% 32.78/32.57 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_2)),Z_2)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int))).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),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_1),I_2)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),J))).
% 32.78/32.57 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)).
% 32.78/32.57 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)).
% 32.78/32.57 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),W)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z).
% 32.78/32.57 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),W)).
% 32.78/32.57 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),W))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),J))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),J),K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),K_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z),W))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W),Z))|Z=W.
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_2),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)).
% 32.78/32.57 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_2),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)).
% 32.78/32.57 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)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_2),W_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))|Z_2!=W_1.
% 32.78/32.57 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_2),W_1))|Z_2=W_1.
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),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_2),K_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),J),K_1))).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),W))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_4),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_2),Z_4)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z))).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_2)).
% 32.78/32.57 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_2)).
% 32.78/32.57 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_1),one_one(int))),Z_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)).
% 32.78/32.57 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_1),one_one(int))),Z_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),one_one(int))),Z)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))|W_1=Z_2.
% 32.78/32.57 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)).
% 32.78/32.57 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int))))|W_1!=Z_2.
% 32.78/32.57 0 [] 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),Na)|K=zero_zero(nat)|M=Na.
% 32.78/32.57 0 [] 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),Na)|K!=zero_zero(nat).
% 32.78/32.57 0 [] 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),Na)|M!=Na.
% 32.78/32.57 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),U_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),U_1)),K_1).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)|M=Na.
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)|M!=Na.
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),I_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M)),Na)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),I_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M)),Na)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J),I_2))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),U_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),J)),U_1)),M_1)),N).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),I_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M)=Na.
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),I_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M)!=Na.
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),Na))).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),Na))).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),U_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I_2)),U_1)),N)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)|M=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),Na).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)|M!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),Na).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),I_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M)),Na)).
% 32.78/32.57 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),I_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M)),Na)).
% 32.78/32.57 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_2)),R_3)!=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),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_2),Q_1)),R_2)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q_2)).
% 32.78/32.57 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_2)),R_3)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),R_3),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_2),Q_1)).
% 32.78/32.57 0 [] hAPP(int,int,number_number_of(int),K_1)=K_1.
% 32.78/32.57 0 [] zero_zero(int)!=one_one(int).
% 32.78/32.57 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_3),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),A_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Q_2)).
% 32.78/32.57 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_3),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_3))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_2),one_one(int))).
% 32.78/32.57 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_2),Q_1)),R_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Q_1)).
% 32.78/32.57 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_2),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_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),zero_zero(int))).
% 32.78/32.57 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_2)),R_3)))| -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_3),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_1),Q_2)).
% 32.78/32.57 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_2)),R_3)!=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),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_2),Q_1)),R_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),R_3))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B_2),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Q_2),Q_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f102(Pa,I_1,K)),K))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),one_one(int))))|hBOOL(hAPP(int,bool,Pa,$f102(Pa,I_1,K)))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),one_one(int))))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f102(Pa,I_1,K)),one_one(int))))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),K))| -hBOOL(hAPP(int,bool,Pa,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f103(Pa,I_1,K)),K))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),K))| -hBOOL(hAPP(int,bool,Pa,K))|hBOOL(hAPP(int,bool,Pa,$f103(Pa,I_1,K)))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_1),K))| -hBOOL(hAPP(int,bool,Pa,K))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f103(Pa,I_1,K)),one_one(int))))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -ab_semigroup_mult(X_c)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f104(X_b,X_c,Z_2,G,H,A_3)),A_3))|hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_2),A_3)=hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),H),Z_2),A_3).
% 32.78/32.57 0 [] -ab_semigroup_mult(X_c)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))|hAPP(X_b,X_c,G,$f104(X_b,X_c,Z_2,G,H,A_3))!=hAPP(X_b,X_c,H,$f104(X_b,X_c,Z_2,G,H,A_3))|hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_2),A_3)=hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),H),Z_2),A_3).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_1))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),$f105(Pa,K,I_1)))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_1))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),one_one(int))))|hBOOL(hAPP(int,bool,Pa,$f105(Pa,K,I_1)))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_1))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),one_one(int))))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f105(Pa,K,I_1)),one_one(int))))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),I_1))| -hBOOL(hAPP(int,bool,Pa,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),$f106(Pa,K,I_1)))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),I_1))| -hBOOL(hAPP(int,bool,Pa,K))|hBOOL(hAPP(int,bool,Pa,$f106(Pa,K,I_1)))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),I_1))| -hBOOL(hAPP(int,bool,Pa,K))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f106(Pa,K,I_1)),one_one(int))))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 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))).
% 32.78/32.57 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),zero_zero(int))).
% 32.78/32.57 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))).
% 32.78/32.57 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),one_one(int))).
% 32.78/32.57 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f107(P_1,Pa)))|hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)))),Pa))=hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)))),P_1)).
% 32.78/32.57 0 [] hBOOL(hAPP(int,bool,Pa,$f107(P_1,Pa)))|hBOOL(hAPP(int,bool,P_1,$f107(P_1,Pa)))|hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)))),Pa))=hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)))),P_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,Pa,$f107(P_1,Pa)))| -hBOOL(hAPP(int,bool,P_1,$f107(P_1,Pa)))|hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)))),Pa))=hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)))),P_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,Pa,$f108(K,Pa,D_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,Pa,X_2))|hBOOL(hAPP(int,bool,Pa,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),D_1)))).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f108(K,Pa,D_1)),D_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,Pa,X_2))|hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),D_1)))).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,Pa,$f109(K,Pa,D_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,Pa,X_2))|hBOOL(hAPP(int,bool,Pa,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),D_1)))).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f109(K,Pa,D_1)),D_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))| -hBOOL(hAPP(int,bool,Pa,X_2))|hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),D_1)))).
% 32.78/32.57 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),$f110(X_a,T_4)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),T_4),X_2)).
% 32.78/32.57 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f111(X_a,T_4)),X_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_2),T_4)).
% 32.78/32.57 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),$f112(X_a,T_4)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_2),T_4)).
% 32.78/32.57 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f113(X_a,T_4)),X_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),T_4),X_2)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,Pa,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),$f114(I_1,Pa,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f115(I_1,Pa,K)),K))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,Pa,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),$f114(I_1,Pa,K)))|hBOOL(hAPP(int,bool,Pa,$f115(I_1,Pa,K)))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,Pa,K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),$f114(I_1,Pa,K)))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f115(I_1,Pa,K)),one_one(int))))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,Pa,K))|hBOOL(hAPP(int,bool,Pa,$f114(I_1,Pa,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f115(I_1,Pa,K)),K))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,Pa,K))|hBOOL(hAPP(int,bool,Pa,$f114(I_1,Pa,K)))|hBOOL(hAPP(int,bool,Pa,$f115(I_1,Pa,K)))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,Pa,K))|hBOOL(hAPP(int,bool,Pa,$f114(I_1,Pa,K)))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f115(I_1,Pa,K)),one_one(int))))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,Pa,K))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f114(I_1,Pa,K)),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),$f115(I_1,Pa,K)),K))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,Pa,K))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f114(I_1,Pa,K)),one_one(int))))|hBOOL(hAPP(int,bool,Pa,$f115(I_1,Pa,K)))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,Pa,K))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),$f114(I_1,Pa,K)),one_one(int))))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f115(I_1,Pa,K)),one_one(int))))|hBOOL(hAPP(int,bool,Pa,I_1)).
% 32.78/32.57 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,P1,$f117(Pa,P1,D_1)))|hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f117(Pa,P1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f116(Pa,P1,D_1)),D_1))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f118(Pa,P1,D_1,Z_3)),Z_3))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,Pa,$f119(Pa,P1,D_1))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,P1,$f117(Pa,P1,D_1)))|hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f117(Pa,P1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f116(Pa,P1,D_1)),D_1))))|hBOOL(hAPP(int,bool,Pa,$f118(Pa,P1,D_1,Z_3)))|hBOOL(hAPP(int,bool,P1,$f118(Pa,P1,D_1,Z_3)))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,Pa,$f119(Pa,P1,D_1))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,P1,$f117(Pa,P1,D_1)))|hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f117(Pa,P1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f116(Pa,P1,D_1)),D_1))))| -hBOOL(hAPP(int,bool,Pa,$f118(Pa,P1,D_1,Z_3)))| -hBOOL(hAPP(int,bool,P1,$f118(Pa,P1,D_1,Z_3)))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,Pa,$f119(Pa,P1,D_1))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))| -hBOOL(hAPP(int,bool,P1,$f117(Pa,P1,D_1)))| -hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f117(Pa,P1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f116(Pa,P1,D_1)),D_1))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),$f118(Pa,P1,D_1,Z_3)),Z_3))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,Pa,$f119(Pa,P1,D_1))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))| -hBOOL(hAPP(int,bool,P1,$f117(Pa,P1,D_1)))| -hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f117(Pa,P1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f116(Pa,P1,D_1)),D_1))))|hBOOL(hAPP(int,bool,Pa,$f118(Pa,P1,D_1,Z_3)))|hBOOL(hAPP(int,bool,P1,$f118(Pa,P1,D_1,Z_3)))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,Pa,$f119(Pa,P1,D_1))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))| -hBOOL(hAPP(int,bool,P1,$f117(Pa,P1,D_1)))| -hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f117(Pa,P1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f116(Pa,P1,D_1)),D_1))))| -hBOOL(hAPP(int,bool,Pa,$f118(Pa,P1,D_1,Z_3)))| -hBOOL(hAPP(int,bool,P1,$f118(Pa,P1,D_1,Z_3)))| -hBOOL(hAPP(int,bool,P1,X1))|hBOOL(hAPP(int,bool,Pa,$f119(Pa,P1,D_1))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,P_1,$f121(Pa,P_1,D_1)))|hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f121(Pa,P_1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f120(Pa,P_1,D_1)),D_1))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_3),$f122(Pa,P_1,D_1,Z_3)))| -hBOOL(hAPP(int,bool,P_1,X1))|hBOOL(hAPP(int,bool,Pa,$f123(Pa,P_1,D_1))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,P_1,$f121(Pa,P_1,D_1)))|hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f121(Pa,P_1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f120(Pa,P_1,D_1)),D_1))))|hBOOL(hAPP(int,bool,Pa,$f122(Pa,P_1,D_1,Z_3)))|hBOOL(hAPP(int,bool,P_1,$f122(Pa,P_1,D_1,Z_3)))| -hBOOL(hAPP(int,bool,P_1,X1))|hBOOL(hAPP(int,bool,Pa,$f123(Pa,P_1,D_1))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))|hBOOL(hAPP(int,bool,P_1,$f121(Pa,P_1,D_1)))|hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f121(Pa,P_1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f120(Pa,P_1,D_1)),D_1))))| -hBOOL(hAPP(int,bool,Pa,$f122(Pa,P_1,D_1,Z_3)))| -hBOOL(hAPP(int,bool,P_1,$f122(Pa,P_1,D_1,Z_3)))| -hBOOL(hAPP(int,bool,P_1,X1))|hBOOL(hAPP(int,bool,Pa,$f123(Pa,P_1,D_1))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))| -hBOOL(hAPP(int,bool,P_1,$f121(Pa,P_1,D_1)))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f121(Pa,P_1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f120(Pa,P_1,D_1)),D_1))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_3),$f122(Pa,P_1,D_1,Z_3)))| -hBOOL(hAPP(int,bool,P_1,X1))|hBOOL(hAPP(int,bool,Pa,$f123(Pa,P_1,D_1))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))| -hBOOL(hAPP(int,bool,P_1,$f121(Pa,P_1,D_1)))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f121(Pa,P_1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f120(Pa,P_1,D_1)),D_1))))|hBOOL(hAPP(int,bool,Pa,$f122(Pa,P_1,D_1,Z_3)))|hBOOL(hAPP(int,bool,P_1,$f122(Pa,P_1,D_1,Z_3)))| -hBOOL(hAPP(int,bool,P_1,X1))|hBOOL(hAPP(int,bool,Pa,$f123(Pa,P_1,D_1))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1))| -hBOOL(hAPP(int,bool,P_1,$f121(Pa,P_1,D_1)))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),$f121(Pa,P_1,D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),$f120(Pa,P_1,D_1)),D_1))))| -hBOOL(hAPP(int,bool,Pa,$f122(Pa,P_1,D_1,Z_3)))| -hBOOL(hAPP(int,bool,P_1,$f122(Pa,P_1,D_1,Z_3)))| -hBOOL(hAPP(int,bool,P_1,X1))|hBOOL(hAPP(int,bool,Pa,$f123(Pa,P_1,D_1))).
% 32.78/32.58 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).
% 32.78/32.58 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).
% 32.78/32.58 0 [] -number_ring(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V)))|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,X_a,number_number_of(X_a),V).
% 32.78/32.58 0 [] -number_ring(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V)))|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))=zero_zero(X_a).
% 32.78/32.58 0 [] -number_semiring(X_a)|hAPP(int,X_a,number_number_of(X_a),hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,X_a,semiring_1_of_nat(X_a),N).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K_1)),zero_zero(int))).
% 32.78/32.58 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))).
% 32.78/32.58 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1))).
% 32.78/32.58 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),zero_zero(X_a))).
% 32.78/32.58 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat))=zero_zero(X_a).
% 32.78/32.58 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),one_one(nat))=one_one(X_a).
% 32.78/32.58 0 [] hAPP(nat,int,semiring_1_of_nat(int),one_one(nat))=one_one(int).
% 32.78/32.58 0 [] hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat))=zero_zero(int).
% 32.78/32.58 0 [] hAPP(nat,int,semiring_1_of_nat(int),Na)!=zero_zero(int)|Na=zero_zero(nat).
% 32.78/32.58 0 [] hAPP(nat,int,semiring_1_of_nat(int),Na)=zero_zero(int)|Na!=zero_zero(nat).
% 32.78/32.58 0 [] -ring_1(X_b)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)),ring_1_Ints(X_b))).
% 32.78/32.58 0 [] -semiring_char_0(X_b)|hAPP(nat,X_b,semiring_1_of_nat(X_b),M)!=hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)|M=Na.
% 32.78/32.58 0 [] -semiring_char_0(X_b)|hAPP(nat,X_b,semiring_1_of_nat(X_b),M)=hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)|M!=Na.
% 32.78/32.58 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)).
% 32.78/32.58 0 [] -linordered_semidom(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.58 0 [] -linordered_semidom(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.58 0 [] -linordered_semidom(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.58 0 [] -linordered_semidom(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.58 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))).
% 32.78/32.58 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),Na)).
% 32.78/32.58 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)).
% 32.78/32.58 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),N)),Z))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N))),Z).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_2))|Z_2=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),$f124(W_1,Z_2))).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_2))|Z_2!=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),N_1)).
% 32.78/32.58 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)).
% 32.78/32.58 0 [] hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N))=hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N)).
% 32.78/32.58 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)).
% 32.78/32.58 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2)).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_1),Y_2)).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_1),Y_2)).
% 32.78/32.58 0 [] hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X),Y)).
% 32.78/32.58 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Y)).
% 32.78/32.58 0 [] hAPP(fun(nat,bool),nat,finite_card(nat),A_3)=hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)).
% 32.78/32.58 0 [] -hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),A_3))|hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))).
% 32.78/32.58 0 [] hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),A_3))| -hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))).
% 32.78/32.58 0 [] one_one(int)=hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)).
% 32.78/32.58 0 [] zero_zero(int)=hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)).
% 32.78/32.58 0 [] hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)))),Pa))=hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,int),fun(nat,bool),hAPP(fun(int,bool),fun(fun(nat,int),fun(nat,bool)),combb(int,bool,nat),Pa),semiring_1_of_nat(int)))).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Z))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_2))| -hBOOL(hAPP(int,bool,Pa,X_2))|hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),$f125(Pa)))).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f126(Pa)))| -hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X3))).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,Pa,$f126(Pa)))| -hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X3))).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f127(Pa)))|hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,Pa,$f127(Pa)))|hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X4))|hBOOL(hAPP(int,bool,Pa,X4))| -hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),$f128(Pa)))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)))|Na=zero_zero(nat).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)))|Na!=zero_zero(nat).
% 32.78/32.58 0 [] hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,zero_zero(nat)))=one_one(int).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))|Z_2=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,$f129(W_1,Z_2)))).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2))|Z_2!=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_1))).
% 32.78/32.58 0 [] hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M_1))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M_1)).
% 32.78/32.58 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1))|hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)).
% 32.78/32.58 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,M_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)).
% 32.78/32.58 0 [] -ring_1(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1))|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K_1)),I_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K_1)),J))).
% 32.78/32.58 0 [] -linordered_semidom(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)).
% 32.78/32.58 0 [] -linordered_semidom(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)).
% 32.78/32.58 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))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_2))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Y_2),X_1))|hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2)))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_2))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2))|hBOOL(hAPP(int,bool,Pa,zero_zero(int))).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_2))))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Y_2),X_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2)).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_2))))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Y_2),X_1))| -hBOOL(hAPP(int,bool,Pa,zero_zero(int))).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_2))))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2))))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2)).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_2))))| -hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2))))| -hBOOL(hAPP(int,bool,Pa,zero_zero(int))).
% 32.78/32.58 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).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),$f130(K_1))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1))|K_1=hAPP(nat,int,semiring_1_of_nat(int),$f130(K_1)).
% 32.78/32.58 0 [] -semiring_1(X_b)|hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)=hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),hAPP(X_b,fun(X_b,X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,X_b)),combc(X_b,X_b,X_b),plus_plus(X_b)),one_one(X_b))),Na),zero_zero(X_b)).
% 32.78/32.58 0 [] hAPP(nat,int,semiring_1_of_nat(int),M)!=hAPP(nat,int,semiring_1_of_nat(int),Na)|M=Na.
% 32.78/32.58 0 [] hAPP(nat,int,semiring_1_of_nat(int),M)=hAPP(nat,int,semiring_1_of_nat(int),Na)|M!=Na.
% 32.78/32.58 0 [] -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),A_3),B_1))|hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1))).
% 32.78/32.58 0 [] hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),A_3),B_1))| -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1))).
% 32.78/32.58 0 [] -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_e_q(fun(nat,bool)),A_3),B_1))|hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_e_q(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1))).
% 32.78/32.58 0 [] hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_e_q(fun(nat,bool)),A_3),B_1))| -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_e_q(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1))).
% 32.78/32.58 0 [] bot_bot(fun(int,bool))=hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),bot_bot(fun(nat,bool))).
% 32.78/32.58 0 [] A_3!=B_1|hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)=hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1).
% 32.78/32.58 0 [] A_3=B_1|hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)!=hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1).
% 32.78/32.58 0 [] -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),A_3))|hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))).
% 32.78/32.58 0 [] hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),A_3))| -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))).
% 32.78/32.58 0 [] -hBOOL(Pa)|hAPP(nat,int,semiring_1_of_nat(int),X_1)=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),Pa),X_1),Y_2)).
% 32.78/32.58 0 [] hBOOL(Pa)|hAPP(nat,int,semiring_1_of_nat(int),Y_2)=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),Pa),X_1),Y_2)).
% 32.78/32.58 0 [] hAPP(nat,int,semiring_1_of_nat(int),X_1)!=hAPP(nat,int,semiring_1_of_nat(int),Y_2)|X_1=Y_2.
% 32.78/32.58 0 [] hAPP(nat,int,semiring_1_of_nat(int),X_1)=hAPP(nat,int,semiring_1_of_nat(int),Y_2)|X_1!=Y_2.
% 32.78/32.58 0 [] -semiring_1(X_b)|hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),Inc),zero_zero(nat)),I_1)=ti(X_b,I_1).
% 32.78/32.58 0 [] -semiring_1(X_b)|hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),Inc),hAPP(nat,nat,suc,Na)),I_1)=hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),Inc),Na),hAPP(X_b,X_b,Inc,I_1)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K_1))|K_1=hAPP(nat,int,semiring_1_of_nat(int),$f131(K_1)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z))|Z=hAPP(nat,int,semiring_1_of_nat(int),$f132(Z)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K_1))|K_1=hAPP(nat,int,semiring_1_of_nat(int),$f133(K_1)).
% 32.78/32.58 0 [] Z=hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),$f135(Z))),hAPP(nat,int,semiring_1_of_nat(int),$f134(Z))).
% 32.78/32.58 0 [] -comm_monoid_mult(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,E),E))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,$f139(X_c,X_b,H,G,S,R_1,E)),$f137(X_c,X_b,H,G,S,R_1,E)))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),S))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),$f140(X_c,X_b,H,G,S,R_1,E)),S))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),H),E),S)),hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),G),E),S))).
% 32.78/32.58 0 [] -comm_monoid_mult(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,E),E))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,$f139(X_c,X_b,H,G,S,R_1,E)),$f137(X_c,X_b,H,G,S,R_1,E)))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),S))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_c,X_b,H,$f140(X_c,X_b,H,G,S,R_1,E))),hAPP(X_c,X_b,G,$f140(X_c,X_b,H,G,S,R_1,E))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),H),E),S)),hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),G),E),S))).
% 32.78/32.58 0 [] -comm_monoid_mult(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,E),E))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,$f138(X_c,X_b,H,G,S,R_1,E)),$f136(X_c,X_b,H,G,S,R_1,E)))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),S))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),$f140(X_c,X_b,H,G,S,R_1,E)),S))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),H),E),S)),hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),G),E),S))).
% 32.78/32.58 0 [] -comm_monoid_mult(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,E),E))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,$f138(X_c,X_b,H,G,S,R_1,E)),$f136(X_c,X_b,H,G,S,R_1,E)))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),S))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_c,X_b,H,$f140(X_c,X_b,H,G,S,R_1,E))),hAPP(X_c,X_b,G,$f140(X_c,X_b,H,G,S,R_1,E))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),H),E),S)),hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),G),E),S))).
% 32.78/32.58 0 [] -comm_monoid_mult(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,E),E))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),$f139(X_c,X_b,H,G,S,R_1,E)),$f138(X_c,X_b,H,G,S,R_1,E))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),$f137(X_c,X_b,H,G,S,R_1,E)),$f136(X_c,X_b,H,G,S,R_1,E))))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),S))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),$f140(X_c,X_b,H,G,S,R_1,E)),S))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),H),E),S)),hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),G),E),S))).
% 32.78/32.58 0 [] -comm_monoid_mult(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,E),E))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),$f139(X_c,X_b,H,G,S,R_1,E)),$f138(X_c,X_b,H,G,S,R_1,E))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),$f137(X_c,X_b,H,G,S,R_1,E)),$f136(X_c,X_b,H,G,S,R_1,E))))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),S))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_c,X_b,H,$f140(X_c,X_b,H,G,S,R_1,E))),hAPP(X_c,X_b,G,$f140(X_c,X_b,H,G,S,R_1,E))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),H),E),S)),hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),G),E),S))).
% 32.78/32.58 0 [] -comm_monoid_mult(X_d)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),S))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),$f141(X_c,X_b,X_d,E,G,F,H,K,T_3,S)),T_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f142(X_c,X_b,X_d,E,G,F,H,K,T_3,S)),S))|hAPP(fun(X_b,bool),X_d,hAPP(X_d,fun(fun(X_b,bool),X_d),hAPP(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d))),finite_fold_image(X_d,X_b),times_times(X_d)),F),E),S)=hAPP(fun(X_c,bool),X_d,hAPP(X_d,fun(fun(X_c,bool),X_d),hAPP(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d))),finite_fold_image(X_d,X_c),times_times(X_d)),G),E),T_3).
% 32.78/32.58 0 [] -comm_monoid_mult(X_d)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),S))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),$f141(X_c,X_b,X_d,E,G,F,H,K,T_3,S)),T_3))| -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,H,$f142(X_c,X_b,X_d,E,G,F,H,K,T_3,S))),T_3))|hAPP(X_c,X_b,K,hAPP(X_b,X_c,H,$f142(X_c,X_b,X_d,E,G,F,H,K,T_3,S)))!=ti(X_b,$f142(X_c,X_b,X_d,E,G,F,H,K,T_3,S))|hAPP(X_c,X_d,G,hAPP(X_b,X_c,H,$f142(X_c,X_b,X_d,E,G,F,H,K,T_3,S)))!=hAPP(X_b,X_d,F,$f142(X_c,X_b,X_d,E,G,F,H,K,T_3,S))|hAPP(fun(X_b,bool),X_d,hAPP(X_d,fun(fun(X_b,bool),X_d),hAPP(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d))),finite_fold_image(X_d,X_b),times_times(X_d)),F),E),S)=hAPP(fun(X_c,bool),X_d,hAPP(X_d,fun(fun(X_c,bool),X_d),hAPP(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d))),finite_fold_image(X_d,X_c),times_times(X_d)),G),E),T_3).
% 32.78/32.58 0 [] -comm_monoid_mult(X_d)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),S))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_c,X_b,K,$f141(X_c,X_b,X_d,E,G,F,H,K,T_3,S))),S))|hAPP(X_b,X_c,H,hAPP(X_c,X_b,K,$f141(X_c,X_b,X_d,E,G,F,H,K,T_3,S)))!=ti(X_c,$f141(X_c,X_b,X_d,E,G,F,H,K,T_3,S))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f142(X_c,X_b,X_d,E,G,F,H,K,T_3,S)),S))|hAPP(fun(X_b,bool),X_d,hAPP(X_d,fun(fun(X_b,bool),X_d),hAPP(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d))),finite_fold_image(X_d,X_b),times_times(X_d)),F),E),S)=hAPP(fun(X_c,bool),X_d,hAPP(X_d,fun(fun(X_c,bool),X_d),hAPP(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d))),finite_fold_image(X_d,X_c),times_times(X_d)),G),E),T_3).
% 32.78/32.58 0 [] -comm_monoid_mult(X_d)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),S))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_c,X_b,K,$f141(X_c,X_b,X_d,E,G,F,H,K,T_3,S))),S))|hAPP(X_b,X_c,H,hAPP(X_c,X_b,K,$f141(X_c,X_b,X_d,E,G,F,H,K,T_3,S)))!=ti(X_c,$f141(X_c,X_b,X_d,E,G,F,H,K,T_3,S))| -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,H,$f142(X_c,X_b,X_d,E,G,F,H,K,T_3,S))),T_3))|hAPP(X_c,X_b,K,hAPP(X_b,X_c,H,$f142(X_c,X_b,X_d,E,G,F,H,K,T_3,S)))!=ti(X_b,$f142(X_c,X_b,X_d,E,G,F,H,K,T_3,S))|hAPP(X_c,X_d,G,hAPP(X_b,X_c,H,$f142(X_c,X_b,X_d,E,G,F,H,K,T_3,S)))!=hAPP(X_b,X_d,F,$f142(X_c,X_b,X_d,E,G,F,H,K,T_3,S))|hAPP(fun(X_b,bool),X_d,hAPP(X_d,fun(fun(X_b,bool),X_d),hAPP(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d))),finite_fold_image(X_d,X_b),times_times(X_d)),F),E),S)=hAPP(fun(X_c,bool),X_d,hAPP(X_d,fun(fun(X_c,bool),X_d),hAPP(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d))),finite_fold_image(X_d,X_c),times_times(X_d)),G),E),T_3).
% 32.78/32.58 0 [] -number_ring(X_a)| -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))=zero_zero(X_a).
% 32.78/32.58 0 [] -number_ring(X_a)|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,X_a,number_number_of(X_a),V).
% 32.78/32.58 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)).
% 32.78/32.58 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)))).
% 32.78/32.58 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))))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z_2)),one_one(int)))|Z_2=zero_zero(int).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z_2)),one_one(int)))|Z_2!=zero_zero(int).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,nat_neg,Z_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),zero_zero(int))).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,nat_neg,Z_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),zero_zero(int))).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,nat_neg,X_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,nat_neg,X_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1)).
% 32.78/32.58 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).
% 32.78/32.58 0 [] -ordere142940540dd_abs(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,abs_abs(X_b),A_2)),zero_zero(X_b)))|ti(X_b,A_2)=zero_zero(X_b).
% 32.78/32.58 0 [] -ordere142940540dd_abs(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_b,X_b,abs_abs(X_b),A_2)),zero_zero(X_b)))|ti(X_b,A_2)!=zero_zero(X_b).
% 32.78/32.58 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))).
% 32.78/32.58 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))).
% 32.78/32.58 0 [] -ordere142940540dd_abs(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,abs_abs(X_b),A_2)))|ti(X_b,A_2)!=zero_zero(X_b).
% 32.78/32.58 0 [] -ordere142940540dd_abs(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,abs_abs(X_b),A_2)))|ti(X_b,A_2)=zero_zero(X_b).
% 32.78/32.58 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).
% 32.78/32.58 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)))).
% 32.78/32.58 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)))).
% 32.78/32.58 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)))).
% 32.78/32.58 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))).
% 32.78/32.58 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)))).
% 32.78/32.58 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)).
% 32.78/32.58 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))).
% 32.78/32.58 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)).
% 32.78/32.58 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)).
% 32.78/32.58 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)).
% 32.78/32.58 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)).
% 32.78/32.58 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)).
% 32.78/32.58 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)).
% 32.78/32.58 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).
% 32.78/32.58 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)).
% 32.78/32.58 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)).
% 32.78/32.58 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).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,nat_neg,one_one(int))).
% 32.78/32.58 0 [] -linordered_idom(X_a)|hAPP(X_a,X_a,abs_abs(X_a),one_one(X_a))=one_one(X_a).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,nat_neg,zero_zero(int))).
% 32.78/32.58 0 [] -ordere142940540dd_abs(X_b)|hAPP(X_b,X_b,abs_abs(X_b),A_2)!=zero_zero(X_b)|ti(X_b,A_2)=zero_zero(X_b).
% 32.78/32.58 0 [] -ordere142940540dd_abs(X_b)|hAPP(X_b,X_b,abs_abs(X_b),A_2)=zero_zero(X_b)|ti(X_b,A_2)!=zero_zero(X_b).
% 32.78/32.58 0 [] -ordere142940540dd_abs(X_a)|hAPP(X_a,X_a,abs_abs(X_a),zero_zero(X_a))=zero_zero(X_a).
% 32.78/32.58 0 [] hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N))!=one_one(int)|hAPP(int,int,abs_abs(int),M_1)=one_one(int).
% 32.78/32.58 0 [] -linordered_idom(X_a)|hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))=hAPP(nat,X_a,semiring_1_of_nat(X_a),N).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),N))).
% 32.78/32.58 0 [] hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),M_1))=hAPP(nat,int,semiring_1_of_nat(int),M_1).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(int,nat,number_number_of(nat),V)=zero_zero(nat).
% 32.78/32.58 0 [] hAPP(int,nat,number_number_of(nat),V_3)!=hAPP(int,nat,number_number_of(nat),V_2)| -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_2)),zero_zero(int))).
% 32.78/32.58 0 [] hAPP(int,nat,number_number_of(nat),V_3)!=hAPP(int,nat,number_number_of(nat),V_2)|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3)))| -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2)))|hAPP(int,int,number_number_of(int),V_3)=zero_zero(int).
% 32.78/32.58 0 [] hAPP(int,nat,number_number_of(nat),V_3)!=hAPP(int,nat,number_number_of(nat),V_2)|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3)))|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2)))|V_3=V_2.
% 32.78/32.58 0 [] hAPP(int,nat,number_number_of(nat),V_3)=hAPP(int,nat,number_number_of(nat),V_2)|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3)))|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2)))|V_3!=V_2.
% 32.78/32.58 0 [] hAPP(int,nat,number_number_of(nat),V_3)=hAPP(int,nat,number_number_of(nat),V_2)|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3)))|hAPP(int,int,number_number_of(int),V_3)!=zero_zero(int)| -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))).
% 32.78/32.58 0 [] hAPP(int,nat,number_number_of(nat),V_3)=hAPP(int,nat,number_number_of(nat),V_2)|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3)))|hAPP(int,int,number_number_of(int),V_3)!=zero_zero(int)|V_3!=V_2.
% 32.78/32.58 0 [] hAPP(int,nat,number_number_of(nat),V_3)=hAPP(int,nat,number_number_of(nat),V_2)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_2)),zero_zero(int)))| -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))).
% 32.78/32.58 0 [] hAPP(int,nat,number_number_of(nat),V_3)=hAPP(int,nat,number_number_of(nat),V_2)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_2)),zero_zero(int)))|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2)))|V_3!=V_2.
% 32.78/32.58 0 [] hAPP(int,nat,number_number_of(nat),V_3)=hAPP(int,nat,number_number_of(nat),V_2)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_2)),zero_zero(int)))|hAPP(int,int,number_number_of(int),V_3)!=zero_zero(int)| -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))).
% 32.78/32.58 0 [] hAPP(int,nat,number_number_of(nat),V_3)=hAPP(int,nat,number_number_of(nat),V_2)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,number_number_of(int),V_2)),zero_zero(int)))|hAPP(int,int,number_number_of(int),V_3)!=zero_zero(int)|V_3!=V_2.
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),K_1).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))| -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1)))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),K_1).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1)))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),K_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_1))),K_1).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V))=zero_zero(int).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,int,number_number_of(int),V).
% 32.78/32.58 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)))).
% 32.78/32.58 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f143(K,F,Na)),Na))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f144(K,F,Na)),Na)).
% 32.78/32.58 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f143(K,F,Na)),Na))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hAPP(nat,int,F,$f144(K,F,Na))=K.
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),$f143(K,F,Na)),one_one(nat)))),hAPP(nat,int,F,$f143(K,F,Na))))),one_one(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f144(K,F,Na)),Na)).
% 32.78/32.58 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),$f143(K,F,Na)),one_one(nat)))),hAPP(nat,int,F,$f143(K,F,Na))))),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))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hAPP(nat,int,F,$f144(K,F,Na))=K.
% 32.78/32.58 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f145(K,F,Na)),Na))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f146(K,F,Na)),Na)).
% 32.78/32.58 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f145(K,F,Na)),Na))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hAPP(nat,int,F,$f146(K,F,Na))=K.
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),$f145(K,F,Na)),one_one(nat)))),hAPP(nat,int,F,$f145(K,F,Na))))),one_one(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,zero_zero(nat))),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f146(K,F,Na)),Na)).
% 32.78/32.58 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),$f145(K,F,Na)),one_one(nat)))),hAPP(nat,int,F,$f145(K,F,Na))))),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))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hAPP(nat,int,F,$f146(K,F,Na))=K.
% 32.78/32.58 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),$f147(K,F,Na,M)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M)),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),$f148(K,F,Na,M))).
% 32.78/32.58 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),$f147(K,F,Na,M)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M)),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f148(K,F,Na,M)),Na)).
% 32.78/32.58 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),$f147(K,F,Na,M)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M)),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hAPP(nat,int,F,$f148(K,F,Na,M))=K.
% 32.78/32.58 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f147(K,F,Na,M)),Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M)),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),$f148(K,F,Na,M))).
% 32.78/32.58 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f147(K,F,Na,M)),Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M)),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f148(K,F,Na,M)),Na)).
% 32.78/32.58 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f147(K,F,Na,M)),Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M)),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hAPP(nat,int,F,$f148(K,F,Na,M))=K.
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),$f147(K,F,Na,M)),one_one(nat)))),hAPP(nat,int,F,$f147(K,F,Na,M))))),one_one(int)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M)),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),$f148(K,F,Na,M))).
% 32.78/32.58 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),$f147(K,F,Na,M)),one_one(nat)))),hAPP(nat,int,F,$f147(K,F,Na,M))))),one_one(int)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M)),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f148(K,F,Na,M)),Na)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),$f147(K,F,Na,M)),one_one(nat)))),hAPP(nat,int,F,$f147(K,F,Na,M))))),one_one(int)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,F,M)),K))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),hAPP(nat,int,F,Na)))|hAPP(nat,int,F,$f148(K,F,Na,M))=K.
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))),N).
% 32.78/32.58 0 [] hAPP(int,int,succ,K_1)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),one_one(int)).
% 32.78/32.58 0 [] -number_ring(X_a)|hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,K_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),K_1)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V))=one_one(nat).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V)))|hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V))=hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W)))|hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W))=zero_zero(nat).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W)))|hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W))=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),W)),hAPP(int,nat,number_number_of(nat),W))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V))=one_one(nat).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V))=hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V)).
% 32.78/32.58 0 [] hAPP(int,int,succ,pls)=hAPP(int,int,bit1,pls).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,W_1))))|hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W_1))).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,W_1))))| -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W_1))).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),pls))).
% 32.78/32.58 0 [] hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))).
% 32.78/32.58 0 [] -number_ring(X_a)|hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,W))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W))),hAPP(int,X_a,number_number_of(X_a),W)).
% 32.78/32.58 0 [] hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls))=hAPP(nat,nat,suc,zero_zero(nat)).
% 32.78/32.58 0 [] hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))=hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))).
% 32.78/32.58 0 [] hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,N)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),N).
% 32.78/32.58 0 [] -number_ring(X_a)|one_one(X_a)=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)).
% 32.78/32.58 0 [] one_one(nat)=hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)).
% 32.78/32.58 0 [] hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls))=one_one(nat).
% 32.78/32.58 0 [] one_one(int)=hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)).
% 32.78/32.58 0 [] -number_ring(X_a)|hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))=one_one(X_a).
% 32.78/32.58 0 [] -number_semiring(X_a)|hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))=one_one(X_a).
% 32.78/32.58 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))=ti(X_a,A_1).
% 32.78/32.58 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))),A_1)=ti(X_a,A_1).
% 32.78/32.58 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,bit1,pls))).
% 32.78/32.58 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W))=hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),W)).
% 32.78/32.58 0 [] zero_zero(int)=hAPP(int,int,number_number_of(int),pls).
% 32.78/32.58 0 [] hAPP(int,int,bit1,K_1)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),K_1)),K_1).
% 32.78/32.58 0 [] -number_semiring(X_a)|hAPP(int,X_a,number_number_of(X_a),pls)=zero_zero(X_a).
% 32.78/32.58 0 [] -number_ring(X_a)|hAPP(int,X_a,number_number_of(X_a),pls)=zero_zero(X_a).
% 32.78/32.58 0 [] -number_ring(X_a)|zero_zero(X_a)=hAPP(int,X_a,number_number_of(X_a),pls).
% 32.78/32.58 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),pls)),A_1)=ti(X_a,A_1).
% 32.78/32.58 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),pls))=ti(X_a,A_1).
% 32.78/32.58 0 [] hAPP(int,nat,number_number_of(nat),pls)=zero_zero(nat).
% 32.78/32.58 0 [] zero_zero(nat)=hAPP(int,nat,number_number_of(nat),pls).
% 32.78/32.58 0 [] pls=zero_zero(int).
% 32.78/32.58 0 [] hAPP(int,int,bit1,K)!=hAPP(int,int,bit1,L)|K=L.
% 32.78/32.58 0 [] hAPP(int,int,bit1,K)=hAPP(int,int,bit1,L)|K!=L.
% 32.78/32.58 0 [] hAPP(int,int,bit1,K_1)!=pls.
% 32.78/32.58 0 [] pls!=hAPP(int,int,bit1,L_1).
% 32.78/32.58 0 [] hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),pls)=K_1.
% 32.78/32.58 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),K_1)=K_1.
% 32.78/32.58 0 [] hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),pls)=K_1.
% 32.78/32.58 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),W)=pls.
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),pls)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),hAPP(int,int,bit1,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K)).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),hAPP(int,int,bit1,K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K),L)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)).
% 32.78/32.58 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,K)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K)).
% 32.78/32.58 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,K)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K)).
% 32.78/32.58 0 [] -preorder(T_1)|preorder(fun(T_2,T_1)).
% 32.78/32.58 0 [] -finite_finite_1(T_1)| -finite_finite_1(T_2)|finite_finite_1(fun(T_2,T_1)).
% 32.78/32.58 0 [] -order(T_1)|order(fun(T_2,T_1)).
% 32.78/32.58 0 [] -ord(T_1)|ord(fun(T_2,T_1)).
% 32.78/32.58 0 [] -bot(T_1)|bot(fun(T_2,T_1)).
% 32.78/32.58 0 [] -minus(T_1)|minus(fun(T_2,T_1)).
% 32.78/32.58 0 [] semiri456707255roduct(int).
% 32.78/32.58 0 [] ordere223160158up_add(int).
% 32.78/32.58 0 [] ordere236663937imp_le(int).
% 32.78/32.58 0 [] linord893533164strict(int).
% 32.78/32.58 0 [] linord626643107strict(int).
% 32.78/32.58 0 [] linord20386208strict(int).
% 32.78/32.58 0 [] ordere779506340up_add(int).
% 32.78/32.58 0 [] ordere142940540dd_abs(int).
% 32.78/32.58 0 [] ordere216010020id_add(int).
% 32.78/32.58 0 [] linord219039673up_add(int).
% 32.78/32.58 0 [] cancel146912293up_add(int).
% 32.78/32.58 0 [] ordere453448008miring(int).
% 32.78/32.58 0 [] linord581940658strict(int).
% 32.78/32.58 0 [] ring_n68954251visors(int).
% 32.78/32.58 0 [] ordere1490568538miring(int).
% 32.78/32.58 0 [] linord1278240602ring_1(int).
% 32.78/32.58 0 [] ordered_ab_group_add(int).
% 32.78/32.58 0 [] cancel_semigroup_add(int).
% 32.78/32.58 0 [] linordered_semiring(int).
% 32.78/32.58 0 [] linordered_semidom(int).
% 32.78/32.58 0 [] ab_semigroup_mult(int).
% 32.78/32.58 0 [] comm_monoid_mult(int).
% 32.78/32.58 0 [] ab_semigroup_add(int).
% 32.78/32.58 0 [] ordered_semiring(int).
% 32.78/32.58 0 [] ordered_ring_abs(int).
% 32.78/32.58 0 [] no_zero_divisors(int).
% 32.78/32.58 0 [] comm_monoid_add(int).
% 32.78/32.58 0 [] linordered_ring(int).
% 32.78/32.58 0 [] linordered_idom(int).
% 32.78/32.58 0 [] comm_semiring_1(int).
% 32.78/32.58 0 [] comm_semiring(int).
% 32.78/32.58 0 [] semiring_char_0(int).
% 32.78/32.58 0 [] number_semiring(int).
% 32.78/32.58 0 [] ab_group_add(int).
% 32.78/32.58 0 [] zero_ne_q_one(int).
% 32.78/32.58 0 [] ordered_ring(int).
% 32.78/32.58 0 [] preorder(int).
% 32.78/32.58 0 [] linorder(int).
% 32.78/32.58 0 [] monoid_mult(int).
% 32.78/32.58 0 [] monoid_add(int).
% 32.78/32.58 0 [] semiring_1(int).
% 32.78/32.58 0 [] group_add(int).
% 32.78/32.58 0 [] mult_zero(int).
% 32.78/32.58 0 [] order(int).
% 32.78/32.58 0 [] ring_char_0(int).
% 32.78/32.58 0 [] number_ring(int).
% 32.78/32.58 0 [] semiring(int).
% 32.78/32.58 0 [] ord(int).
% 32.78/32.58 0 [] ring_1(int).
% 32.78/32.58 0 [] minus(int).
% 32.78/32.58 0 [] zero(int).
% 32.78/32.58 0 [] ring(int).
% 32.78/32.58 0 [] number(int).
% 32.78/32.58 0 [] one(int).
% 32.78/32.58 0 [] semiri456707255roduct(nat).
% 32.78/32.58 0 [] ordere223160158up_add(nat).
% 32.78/32.58 0 [] ordere236663937imp_le(nat).
% 32.78/32.58 0 [] linord893533164strict(nat).
% 32.78/32.58 0 [] linord20386208strict(nat).
% 32.78/32.58 0 [] ordere779506340up_add(nat).
% 32.78/32.58 0 [] ordere216010020id_add(nat).
% 32.78/32.58 0 [] cancel146912293up_add(nat).
% 32.78/32.58 0 [] ordere453448008miring(nat).
% 32.78/32.58 0 [] ordere1490568538miring(nat).
% 32.78/32.58 0 [] cancel_semigroup_add(nat).
% 32.78/32.58 0 [] linordered_semiring(nat).
% 32.78/32.58 0 [] linordered_semidom(nat).
% 32.78/32.58 0 [] ab_semigroup_mult(nat).
% 32.78/32.58 0 [] comm_monoid_mult(nat).
% 32.78/32.58 0 [] ab_semigroup_add(nat).
% 32.78/32.58 0 [] ordered_semiring(nat).
% 32.78/32.58 0 [] no_zero_divisors(nat).
% 32.78/32.58 0 [] comm_monoid_add(nat).
% 32.78/32.58 0 [] comm_semiring_1(nat).
% 32.78/32.58 0 [] comm_semiring(nat).
% 32.78/32.58 0 [] semiring_char_0(nat).
% 32.78/32.58 0 [] number_semiring(nat).
% 32.78/32.58 0 [] zero_ne_q_one(nat).
% 32.78/32.58 0 [] preorder(nat).
% 32.78/32.58 0 [] linorder(nat).
% 32.78/32.58 0 [] monoid_mult(nat).
% 32.78/32.58 0 [] monoid_add(nat).
% 32.78/32.58 0 [] semiring_1(nat).
% 32.78/32.58 0 [] mult_zero(nat).
% 32.78/32.58 0 [] order(nat).
% 32.78/32.58 0 [] semiring(nat).
% 32.78/32.58 0 [] ord(nat).
% 32.78/32.58 0 [] bot(nat).
% 32.78/32.58 0 [] minus(nat).
% 32.78/32.58 0 [] zero(nat).
% 32.78/32.58 0 [] number(nat).
% 32.78/32.58 0 [] one(nat).
% 32.78/32.58 0 [] preorder(bool).
% 32.78/32.58 0 [] finite_finite_1(bool).
% 32.78/32.58 0 [] order(bool).
% 32.78/32.58 0 [] ord(bool).
% 32.78/32.58 0 [] bot(bool).
% 32.78/32.58 0 [] minus(bool).
% 32.78/32.58 0 [] -finite_finite_1(T_1)| -finite_finite_1(T_2)|finite_finite_1(sum_sum(T_2,T_1)).
% 32.78/32.58 0 [] ti(T,ti(T,A))=ti(T,A).
% 32.78/32.58 0 [] hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y)=ti(X_a,X).
% 32.78/32.58 0 [] hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y)=ti(X_a,Y).
% 32.78/32.58 0 [] ti(bool,P)=fTrue|ti(bool,P)=fFalse.
% 32.78/32.58 0 [] -hBOOL(hAPP(bool,bool,fNot,P))| -hBOOL(P).
% 32.78/32.58 0 [] hBOOL(P)|hBOOL(hAPP(bool,bool,fNot,P)).
% 32.78/32.58 0 [] hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R)=hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R)).
% 32.78/32.58 0 [] hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R)=hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q).
% 32.78/32.58 0 [] hAPP(X_a,X_a,combi(X_a),P)=ti(X_a,P).
% 32.78/32.58 0 [] hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q)=ti(X_a,P).
% 32.78/32.58 0 [] hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R)=hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R)).
% 32.78/32.58 0 [] -hBOOL(P)| -hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)).
% 32.78/32.58 0 [] -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(P).
% 32.78/32.58 0 [] -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(Q).
% 32.78/32.58 0 [] -hBOOL(P)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)).
% 32.78/32.58 0 [] -hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)).
% 32.78/32.58 0 [] -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))|hBOOL(P)|hBOOL(Q).
% 32.78/32.58 0 [] -hBOOL(fFalse).
% 32.78/32.58 0 [] ti(bool,P)=fTrue|ti(bool,P)=fFalse.
% 32.78/32.58 0 [] -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fe_qual(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y).
% 32.78/32.58 0 [] ti(X_a,X)!=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fe_qual(X_a),X),Y)).
% 32.78/32.58 0 [] hBOOL(P)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)).
% 32.78/32.58 0 [] -hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)).
% 32.78/32.58 0 [] -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q))| -hBOOL(P)|hBOOL(Q).
% 32.78/32.58 0 [] hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)).
% 32.78/32.58 0 [] hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_e_q(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))).
% 32.78/32.58 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,na)),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))).
% 32.78/32.58 0 [] hAPP(fun(x_a,bool),nat,finite_card(x_a),g)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),hAPP(nat,nat,suc,na)).
% 32.78/32.58 0 [] hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)).
% 32.78/32.58 0 [] -hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),g)).
% 32.78/32.58 0 [] -hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_e_q(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))).
% 32.78/32.58 end_of_list.
% 32.78/32.58
% 32.78/32.58 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 32.78/32.58
% 32.78/32.58 This ia a non-Horn set with equality. The strategy will be
% 32.78/32.58 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 32.78/32.58 deletion, with positive clauses in sos and nonpositive
% 32.78/32.58 clauses in usable.
% 32.78/32.58
% 32.78/32.58 dependent: set(knuth_bendix).
% 32.78/32.58 dependent: set(anl_eq).
% 32.78/32.58 dependent: set(para_from).
% 32.78/32.58 dependent: set(para_into).
% 32.78/32.58 dependent: clear(para_from_right).
% 32.78/32.58 dependent: clear(para_into_right).
% 32.78/32.58 dependent: set(para_from_vars).
% 32.78/32.58 dependent: set(eq_units_both_ways).
% 32.78/32.58 dependent: set(dynamic_demod_all).
% 32.78/32.58 dependent: set(dynamic_demod).
% 32.78/32.58 dependent: set(order_eq).
% 32.78/32.58 dependent: set(back_demod).
% 32.78/32.58 dependent: set(lrpo).
% 32.78/32.58 dependent: set(hyper_res).
% 32.78/32.58 dependent: set(unit_deletion).
% 32.78/32.58 dependent: set(factor).
% 32.78/32.58
% 32.78/32.58 ------------> process usable:
% 32.78/32.58 ** KEPT (pick-wt=11): 1 [] -ordere142940540dd_abs(A)|ti(fun(A,A),abs_abs(A))=abs_abs(A).
% 32.78/32.58 ** KEPT (pick-wt=13): 2 [] -minus(A)|ti(fun(A,fun(A,A)),minus_minus(A))=minus_minus(A).
% 32.78/32.58 ** KEPT (pick-wt=9): 3 [] -one(A)|ti(A,one_one(A))=one_one(A).
% 32.78/32.58 ** KEPT (pick-wt=13): 4 [] -monoid_add(A)|ti(fun(A,fun(A,A)),plus_plus(A))=plus_plus(A).
% 32.78/32.58 ** KEPT (pick-wt=13): 5 [] -cancel_semigroup_add(A)|ti(fun(A,fun(A,A)),plus_plus(A))=plus_plus(A).
% 32.78/32.58 ** KEPT (pick-wt=13): 6 [] -ab_semigroup_add(A)|ti(fun(A,fun(A,A)),plus_plus(A))=plus_plus(A).
% 32.78/32.58 ** KEPT (pick-wt=13): 7 [] -ab_semigroup_mult(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 32.78/32.58 ** KEPT (pick-wt=13): 8 [] -monoid_mult(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 32.78/32.58 ** KEPT (pick-wt=13): 9 [] -semiring(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 32.78/32.58 ** KEPT (pick-wt=13): 10 [] -no_zero_divisors(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 32.78/32.58 ** KEPT (pick-wt=13): 11 [] -mult_zero(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 32.78/32.58 ** KEPT (pick-wt=9): 12 [] -zero(A)|ti(A,zero_zero(A))=zero_zero(A).
% 32.78/32.58 ** KEPT (pick-wt=11): 13 [] -number(A)|ti(fun(int,A),number_number_of(A))=number_number_of(A).
% 32.78/32.58 ** KEPT (pick-wt=11): 14 [] -ring_1(A)|ti(fun(A,bool),ring_1_Ints(A))=ring_1_Ints(A).
% 32.78/32.58 ** KEPT (pick-wt=11): 15 [] -semiring_1(A)|ti(fun(nat,A),semiring_1_of_nat(A))=semiring_1_of_nat(A).
% 32.78/32.58 ** KEPT (pick-wt=17): 16 [] -semiring_1(A)|ti(fun(fun(A,A),fun(nat,fun(A,A))),semiri532925092at_aux(A))=semiri532925092at_aux(A).
% 32.78/32.58 ** KEPT (pick-wt=9): 17 [] -bot(A)|ti(A,bot_bot(A))=bot_bot(A).
% 32.78/32.58 ** KEPT (pick-wt=13): 18 [] -ord(A)|ti(fun(A,fun(A,bool)),ord_less(A))=ord_less(A).
% 32.78/32.58 ** KEPT (pick-wt=13): 19 [] -ord(A)|ti(fun(A,fun(A,bool)),ord_less_e_q(A))=ord_less_e_q(A).
% 32.78/32.58 ** KEPT (pick-wt=6): 20 [] -hBOOL(ti(bool,A))|hBOOL(A).
% 32.78/32.58 ** KEPT (pick-wt=6): 21 [] hBOOL(ti(bool,A))| -hBOOL(A).
% 32.78/32.58 ** KEPT (pick-wt=39): 22 [] -hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_e_q(fun(x_a,bool)),A),B))|hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,B),A)).
% 32.78/32.58 ** KEPT (pick-wt=77): 23 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))|hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite(fun(A,bool)),hAPP(fun(fun(A,bool),bool),fun(fun(A,bool),bool),collect(fun(A,bool)),hAPP(fun(A,bool),fun(fun(A,bool),bool),hAPP(fun(fun(A,bool),fun(fun(A,bool),bool)),fun(fun(A,bool),fun(fun(A,bool),bool)),combc(fun(A,bool),fun(A,bool),bool),ord_less_e_q(fun(A,bool))),B)))).
% 32.78/32.58 ** KEPT (pick-wt=40): 24 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))|hBOOL(hAPP(fun(C,bool),bool,finite_finite(C),hAPP(fun(A,bool),fun(C,bool),hAPP(fun(A,C),fun(fun(A,bool),fun(C,bool)),image(A,C),D),B))).
% 32.78/32.58 ** KEPT (pick-wt=37): 25 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))|hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B))).
% 32.78/32.58 ** KEPT (pick-wt=58): 26 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(fun(C,bool),nat,finite_card(C),hAPP(fun(A,bool),fun(C,bool),hAPP(fun(A,C),fun(fun(A,bool),fun(C,bool)),image(A,C),D),B))),hAPP(fun(A,bool),nat,finite_card(A),B))).
% 32.78/32.58 ** KEPT (pick-wt=57): 27 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),C),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(fun(A,bool),nat,finite_card(A),C)),hAPP(fun(A,bool),nat,finite_card(A),B))).
% 32.78/32.58 ** KEPT (pick-wt=68): 28 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),C),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(fun(A,bool),nat,finite_card(A),B)),hAPP(fun(A,bool),nat,finite_card(A),C)))|ti(fun(A,bool),C)=ti(fun(A,bool),B).
% 32.78/32.58 ** KEPT (pick-wt=55): 29 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(fun(A,bool),nat,finite_card(A),B)),hAPP(fun(A,bool),nat,finite_card(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)))).
% 32.78/32.58 ** KEPT (pick-wt=62): 30 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B))|hAPP(fun(A,bool),nat,finite_card(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B))=hAPP(fun(A,bool),nat,finite_card(A),B).
% 32.78/32.58 ** KEPT (pick-wt=66): 31 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B))|hAPP(fun(A,bool),nat,finite_card(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B))=hAPP(nat,nat,suc,hAPP(fun(A,bool),nat,finite_card(A),B)).
% 32.78/32.58 Following clause subsumed by 31 during input processing: 0 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B))|hAPP(fun(A,bool),nat,finite_card(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B))=hAPP(nat,nat,suc,hAPP(fun(A,bool),nat,finite_card(A),B)).
% 32.78/32.59 ** KEPT (pick-wt=92): 32 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),hAPP(fun(A,bool),fun(A,bool),collect(A),B)))|hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),B)),C)))).
% 32.78/32.59 ** KEPT (pick-wt=92): 33 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),hAPP(fun(A,bool),fun(A,bool),collect(A),B)))|hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),C)),B)))).
% 32.78/32.59 ** KEPT (pick-wt=46): 34 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A)).
% 32.78/32.59 ** KEPT (pick-wt=11): 35 [] -finite_finite_1(A)|hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)).
% 32.78/32.59 Following clause subsumed by 35 during input processing: 0 [] -finite_finite_1(A)|hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)).
% 32.78/32.59 ** KEPT (pick-wt=14): 36 [] hAPP(nat,nat,suc,A)!=hAPP(nat,nat,suc,B)|A=B.
% 32.78/32.59 Following clause subsumed by 36 during input processing: 0 [] hAPP(nat,nat,suc,A)!=hAPP(nat,nat,suc,B)|A=B.
% 32.78/32.59 ** KEPT (pick-wt=14): 37 [] hAPP(nat,nat,suc,A)=hAPP(nat,nat,suc,B)|A!=B.
% 32.78/32.59 ** KEPT (pick-wt=7): 38 [] hAPP(nat,nat,suc,A)!=A.
% 32.78/32.59 Following clause subsumed by 38 during input processing: 0 [flip.1] hAPP(nat,nat,suc,A)!=A.
% 32.78/32.59 ** KEPT (pick-wt=29): 39 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),A))|A=B.
% 32.78/32.59 ** KEPT (pick-wt=39): 40 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),C)).
% 32.78/32.59 ** KEPT (pick-wt=16): 41 [] A!=B|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B)).
% 32.78/32.59 ** KEPT (pick-wt=92): 42 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fdisj),B)),C))))|hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),hAPP(fun(A,bool),fun(A,bool),collect(A),B))).
% 32.78/32.59 ** KEPT (pick-wt=92): 43 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fdisj),B)),C))))|hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),hAPP(fun(A,bool),fun(A,bool),collect(A),C))).
% 32.78/32.59 ** KEPT (pick-wt=110): 44 [] hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fdisj),B)),C))))| -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),hAPP(fun(A,bool),fun(A,bool),collect(A),B)))| -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),hAPP(fun(A,bool),fun(A,bool),collect(A),C))).
% 32.78/32.59 ** KEPT (pick-wt=37): 45 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),C)))|hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),C)).
% 32.78/32.59 Following clause subsumed by 25 during input processing: 0 [] hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),C)))| -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),C)).
% 32.78/32.59 ** KEPT (pick-wt=39): 46 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),C))| -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),C))|hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)).
% 32.78/32.59 Following clause subsumed by 46 during input processing: 0 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),C),B))|hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),C)).
% 32.78/32.59 ** KEPT (pick-wt=30): 47 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,A)),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B)).
% 32.78/32.59 ** KEPT (pick-wt=37): 48 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),hAPP(nat,nat,suc,B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))|A=hAPP(nat,nat,suc,B).
% 32.78/32.59 ** KEPT (pick-wt=30): 49 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),hAPP(nat,nat,suc,B))).
% 32.78/32.59 ** KEPT (pick-wt=34): 50 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,A)),hAPP(nat,nat,suc,B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B)).
% 32.78/32.59 ** KEPT (pick-wt=34): 51 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,A)),hAPP(nat,nat,suc,B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B)).
% 32.78/32.59 Following clause subsumed by 48 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),hAPP(nat,nat,suc,B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))|A=hAPP(nat,nat,suc,B).
% 32.78/32.59 Following clause subsumed by 49 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),hAPP(nat,nat,suc,B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B)).
% 32.78/32.59 Following clause subsumed by 41 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),hAPP(nat,nat,suc,B)))|A!=hAPP(nat,nat,suc,B).
% 32.78/32.59 ** KEPT (pick-wt=30): 52 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,B)),A)).
% 32.78/32.59 ** KEPT (pick-wt=17): 53 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,A)),A)).
% 32.78/32.59 ** KEPT (pick-wt=74): 54 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),C))| -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),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),A)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C)).
% 32.78/32.59 ** KEPT (pick-wt=74): 55 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),C))|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),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),A)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C)).
% 32.78/32.59 ** KEPT (pick-wt=73): 56 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),C))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),A))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),C).
% 32.78/32.59 ** KEPT (pick-wt=54): 57 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),C))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),A)|B=C.
% 32.78/32.59 ** KEPT (pick-wt=54): 58 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),C))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),A)|B!=C.
% 32.78/32.59 ** KEPT (pick-wt=38): 59 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))=A.
% 32.78/32.59 ** KEPT (pick-wt=48): 60 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))|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),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),C))).
% 32.78/32.59 ** KEPT (pick-wt=48): 61 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))|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),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),A))).
% 32.78/32.59 ** KEPT (pick-wt=61): 62 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))| -hBOOL(hAPP(fun(C,bool),bool,hAPP(fun(C,bool),fun(fun(C,bool),bool),ord_less_e_q(fun(C,bool)),D),hAPP(fun(A,bool),fun(C,bool),hAPP(fun(A,C),fun(fun(A,bool),fun(C,bool)),image(A,C),E),B)))|hBOOL(hAPP(fun(C,bool),bool,finite_finite(C),D)).
% 32.78/32.59 ** KEPT (pick-wt=78): 63 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),hAPP(fun(C,bool),fun(A,bool),hAPP(fun(C,A),fun(fun(C,bool),fun(A,bool)),image(C,A),D),E)))|hBOOL(hAPP(fun(C,bool),bool,hAPP(fun(C,bool),fun(fun(C,bool),bool),ord_less_e_q(fun(C,bool)),$f1(C,A,D,E,B)),E)).
% 32.78/32.59 ** KEPT (pick-wt=66): 64 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),hAPP(fun(C,bool),fun(A,bool),hAPP(fun(C,A),fun(fun(C,bool),fun(A,bool)),image(C,A),D),E)))|hBOOL(hAPP(fun(C,bool),bool,finite_finite(C),$f1(C,A,D,E,B))).
% 32.85/32.59 ** KEPT (pick-wt=86): 65 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),hAPP(fun(C,bool),fun(A,bool),hAPP(fun(C,A),fun(fun(C,bool),fun(A,bool)),image(C,A),D),E)))|ti(fun(A,bool),B)=hAPP(fun(C,bool),fun(A,bool),hAPP(fun(C,A),fun(fun(C,bool),fun(A,bool)),image(C,A),D),$f1(C,A,D,E,B)).
% 32.85/32.59 ** KEPT (pick-wt=69): 66 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,B,$f2(A,C,D,B))),hAPP(nat,A,B,hAPP(nat,nat,suc,$f2(A,C,D,B)))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,B,C)),hAPP(nat,A,B,D))).
% 32.85/32.59 ** KEPT (pick-wt=61): 67 [] hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))| -hBOOL(hAPP(fun(C,bool),bool,finite_finite(C),hAPP(fun(A,bool),fun(C,bool),hAPP(fun(A,C),fun(fun(A,bool),fun(C,bool)),image(A,C),D),B)))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),$f3(C,A,D,B)),B)).
% 32.85/32.59 ** KEPT (pick-wt=205): 68 [] hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))| -hBOOL(hAPP(fun(C,bool),bool,finite_finite(C),hAPP(fun(A,bool),fun(C,bool),hAPP(fun(A,C),fun(fun(A,bool),fun(C,bool)),image(A,C),D),B)))| -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))),hAPP(C,fun(A,bool),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),hAPP(fun(A,C),fun(A,fun(C,bool)),hAPP(fun(C,fun(C,bool)),fun(fun(A,C),fun(A,fun(C,bool))),combb(C,fun(C,bool),A),fe_qual(C)),D)),hAPP(A,C,D,$f3(C,A,D,B))))))).
% 32.85/32.59 ** KEPT (pick-wt=65): 69 [] ti(A,B)!=hAPP(C,A,D,E)| -hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),E),F))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(C,bool),fun(A,bool),hAPP(fun(C,A),fun(fun(C,bool),fun(A,bool)),image(C,A),D),F))).
% 32.85/32.59 ** KEPT (pick-wt=53): 70 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),C))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),C),B))|ti(fun(A,bool),B)=ti(fun(A,bool),C).
% 32.85/32.59 ** KEPT (pick-wt=55): 71 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),C))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),C)).
% 32.85/32.59 ** KEPT (pick-wt=53): 72 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),C))).
% 32.85/32.59 ** KEPT (pick-wt=43): 73 [] ti(A,B)!=ti(A,C)|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),D))).
% 32.85/32.59 ** KEPT (pick-wt=60): 74 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),D)))|ti(A,B)=ti(A,C)|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),D)).
% 32.85/32.59 ** KEPT (pick-wt=36): 75 [] -hBOOL(hAPP(nat,bool,A,B))|hBOOL(hAPP(nat,bool,A,hAPP(nat,nat,suc,$f4(C,A,B))))|hBOOL(hAPP(nat,bool,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),C))).
% 32.85/32.59 ** KEPT (pick-wt=32): 76 [] -hBOOL(hAPP(nat,bool,A,B))| -hBOOL(hAPP(nat,bool,A,$f4(C,A,B)))|hBOOL(hAPP(nat,bool,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),C))).
% 32.85/32.59 ** KEPT (pick-wt=26): 78 [copy,77,flip.2] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,A)),B))|hAPP(nat,nat,suc,$f5(A,B))=B.
% 32.85/32.59 ** KEPT (pick-wt=15): 79 [] -preorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),B)).
% 32.85/32.59 ** KEPT (pick-wt=28): 80 [] -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)).
% 32.85/32.59 ** KEPT (pick-wt=22): 81 [] -order(A)|ti(A,B)!=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C)).
% 32.85/32.59 ** KEPT (pick-wt=22): 82 [] -order(A)|ti(A,B)!=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)).
% 32.85/32.59 ** KEPT (pick-wt=35): 83 [] -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)).
% 32.85/32.59 ** KEPT (pick-wt=18): 84 [] -preorder(A)|B!=C|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C)).
% 32.85/32.59 Following clause subsumed by 83 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).
% 32.85/32.59 Following clause subsumed by 81 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).
% 32.85/32.59 ** KEPT (pick-wt=31): 85 [] -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)).
% 32.85/32.59 ** KEPT (pick-wt=35): 86 [] -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)).
% 32.85/32.59 ** KEPT (pick-wt=31): 87 [] -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)).
% 32.85/32.59 ** KEPT (pick-wt=35): 88 [] -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)).
% 32.85/32.59 Following clause subsumed by 83 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).
% 32.85/32.59 ** KEPT (pick-wt=41): 89 [] -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)).
% 32.85/32.59 Following clause subsumed by 83 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).
% 32.85/32.59 ** KEPT (pick-wt=41): 90 [] -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)).
% 32.85/32.59 Following clause subsumed by 80 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)).
% 32.85/32.59 ** KEPT (pick-wt=30): 91 [] hAPP(A,B,C,$f6(A,B,C,D))!=hAPP(A,B,D,$f6(A,B,C,D))|ti(fun(A,B),C)=ti(fun(A,B),D).
% 32.85/32.59 ** KEPT (pick-wt=23): 92 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|hBOOL(hAPP(A,bool,C,B)).
% 32.85/32.59 ** KEPT (pick-wt=23): 93 [] hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))| -hBOOL(hAPP(A,bool,C,B)).
% 32.85/32.59 Following clause subsumed by 74 during input processing: 0 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),D)))|ti(A,B)=ti(A,C)|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),D)).
% 32.85/32.59 Following clause subsumed by 73 during input processing: 0 [] hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),D)))|ti(A,B)!=ti(A,C).
% 32.85/32.59 Following clause subsumed by 72 during input processing: 0 [] hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),D)))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),D)).
% 32.85/32.59 ** KEPT (pick-wt=38): 94 [] -hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),C),D))|ti(A,B)=ti(A,D)|hBOOL(hAPP(A,bool,C,D)).
% 32.85/32.59 ** KEPT (pick-wt=32): 95 [] hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),C),D))|ti(A,B)!=ti(A,D).
% 32.85/32.59 ** KEPT (pick-wt=31): 96 [] hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),C),D))| -hBOOL(hAPP(A,bool,C,D)).
% 32.85/32.59 ** KEPT (pick-wt=86): 97 [] hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),D))|hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),C)!=hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),D)|ti(fun(A,bool),C)=ti(fun(A,bool),D).
% 32.85/32.59 ** KEPT (pick-wt=86): 98 [] hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),D))|hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),C)=hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),D)|ti(fun(A,bool),C)!=ti(fun(A,bool),D).
% 32.85/32.59 Following clause subsumed by 72 during input processing: 0 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),C))).
% 32.85/32.59 ** KEPT (pick-wt=43): 99 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),C)=ti(fun(A,bool),C).
% 32.85/32.59 ** KEPT (pick-wt=32): 100 [] ti(fun(A,bool),B)!=ti(fun(A,bool),C)|hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),C)).
% 32.85/32.59 ** KEPT (pick-wt=32): 101 [] ti(fun(A,bool),B)!=ti(fun(A,bool),C)|hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),C),B)).
% 32.85/32.59 Following clause subsumed by 70 during input processing: 0 [] ti(fun(A,bool),B)=ti(fun(A,bool),C)| -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),C))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),C),B)).
% 32.85/32.59 Following clause subsumed by 100 during input processing: 0 [] ti(fun(A,bool),B)!=ti(fun(A,bool),C)|hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),C)).
% 32.85/32.59 Following clause subsumed by 101 during input processing: 0 [] ti(fun(A,bool),B)!=ti(fun(A,bool),C)|hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),C),B)).
% 32.85/32.59 Following clause subsumed by 71 during input processing: 0 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),C))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),C)).
% 32.85/32.59 Following clause subsumed by 71 during input processing: 0 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),C),D))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),D)).
% 32.85/32.59 Following clause subsumed by 71 during input processing: 0 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),C))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),C)).
% 32.85/32.59 ** KEPT (pick-wt=63): 102 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),C))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),C),D))|hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),D)).
% 32.85/32.59 Following clause subsumed by 100 during input processing: 0 [] ti(fun(A,bool),B)!=ti(fun(A,bool),C)|hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),C)).
% 32.85/32.59 Following clause subsumed by 101 during input processing: 0 [] ti(fun(A,bool),B)!=ti(fun(A,bool),C)|hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),C),B)).
% 32.85/32.59 ** KEPT (pick-wt=61): 103 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(C,bool),fun(A,bool),hAPP(fun(C,A),fun(fun(C,bool),fun(A,bool)),image(C,A),D),E)))|hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),$f7(A,C,B,D,E)),E)).
% 32.85/32.59 ** KEPT (pick-wt=53): 104 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(C,bool),fun(A,bool),hAPP(fun(C,A),fun(fun(C,bool),fun(A,bool)),image(C,A),D),E)))|ti(A,B)=hAPP(C,A,D,$f7(A,C,B,D,E)).
% 32.85/32.59 Following clause subsumed by 69 during input processing: 0 [] hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(C,bool),fun(A,bool),hAPP(fun(C,A),fun(fun(C,bool),fun(A,bool)),image(C,A),D),E)))| -hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),F),E))|ti(A,B)!=hAPP(C,A,D,F).
% 32.85/32.59 ** KEPT (pick-wt=60): 105 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),hAPP(A,D,E,B)),hAPP(fun(A,bool),fun(D,bool),hAPP(fun(A,D),fun(fun(A,bool),fun(D,bool)),image(A,D),E),C))).
% 32.85/32.59 Following clause subsumed by 69 during input processing: 0 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|ti(D,E)!=hAPP(A,D,F,B)|hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),E),hAPP(fun(A,bool),fun(D,bool),hAPP(fun(A,D),fun(fun(A,bool),fun(D,bool)),image(A,D),F),C))).
% 32.85/32.59 ** KEPT (pick-wt=44): 106 [] -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))).
% 32.85/32.59 ** KEPT (pick-wt=52): 107 [] -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,$f8(B,A,C,D))),hAPP(B,A,D,$f8(B,A,C,D)))).
% 32.85/32.59 Following clause subsumed by 106 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))).
% 32.85/32.59 Following clause subsumed by 106 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))).
% 32.85/32.59 ** KEPT (pick-wt=57): 108 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),C)),D))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),D)).
% 32.85/32.59 ** KEPT (pick-wt=61): 109 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),C)),D))|hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),C),D)).
% 32.85/32.59 ** KEPT (pick-wt=78): 110 [] hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),C)),D))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),D))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),C),D)).
% 32.85/32.59 ** KEPT (pick-wt=78): 111 [] hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),D)))|hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),C),D)).
% 32.85/32.59 ** KEPT (pick-wt=78): 112 [] hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),D)))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),C),D)).
% 32.85/32.59 ** KEPT (pick-wt=61): 113 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),C))|hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),C))).
% 32.85/32.59 ** KEPT (pick-wt=80): 114 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),C))|hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),C))).
% 32.85/32.59 ** KEPT (pick-wt=87): 115 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|hAPP(fun(D,bool),fun(D,bool),hAPP(D,fun(fun(D,bool),fun(D,bool)),insert(D),hAPP(A,D,E,B)),hAPP(fun(A,bool),fun(D,bool),hAPP(fun(A,D),fun(fun(A,bool),fun(D,bool)),image(A,D),E),C))=hAPP(fun(A,bool),fun(D,bool),hAPP(fun(A,D),fun(fun(A,bool),fun(D,bool)),image(A,D),E),C).
% 32.85/32.59 ** KEPT (pick-wt=69): 116 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),hAPP(fun(C,bool),fun(A,bool),hAPP(fun(C,A),fun(fun(C,bool),fun(A,bool)),image(C,A),D),E)))|hBOOL(hAPP(fun(C,bool),bool,hAPP(fun(C,bool),fun(fun(C,bool),bool),ord_less_e_q(fun(C,bool)),$f9(A,C,B,D,E)),E)).
% 32.85/32.59 ** KEPT (pick-wt=77): 117 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),hAPP(fun(C,bool),fun(A,bool),hAPP(fun(C,A),fun(fun(C,bool),fun(A,bool)),image(C,A),D),E)))|ti(fun(A,bool),B)=hAPP(fun(C,bool),fun(A,bool),hAPP(fun(C,A),fun(fun(C,bool),fun(A,bool)),image(C,A),D),$f9(A,C,B,D,E)).
% 32.85/32.59 ** KEPT (pick-wt=93): 118 [] hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),hAPP(fun(C,bool),fun(A,bool),hAPP(fun(C,A),fun(fun(C,bool),fun(A,bool)),image(C,A),D),E)))| -hBOOL(hAPP(fun(C,bool),bool,hAPP(fun(C,bool),fun(fun(C,bool),bool),ord_less_e_q(fun(C,bool)),F),E))|ti(fun(A,bool),B)!=hAPP(fun(C,bool),fun(A,bool),hAPP(fun(C,A),fun(fun(C,bool),fun(A,bool)),image(C,A),D),F).
% 32.85/32.59 ** KEPT (pick-wt=86): 119 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),B),C))|hBOOL(hAPP(fun(D,bool),bool,hAPP(fun(D,bool),fun(fun(D,bool),bool),ord_less_e_q(fun(D,bool)),hAPP(fun(A,bool),fun(D,bool),hAPP(fun(A,D),fun(fun(A,bool),fun(D,bool)),image(A,D),E),B)),hAPP(fun(A,bool),fun(D,bool),hAPP(fun(A,D),fun(fun(A,bool),fun(D,bool)),image(A,D),E),C))).
% 32.85/32.59 ** KEPT (pick-wt=53): 120 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(C,bool),fun(A,bool),hAPP(fun(C,A),fun(fun(C,bool),fun(A,bool)),image(C,A),D),E)))|ti(A,B)=hAPP(C,A,D,$f10(A,C,B,D,E)).
% 32.85/32.59 ** KEPT (pick-wt=61): 121 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(C,bool),fun(A,bool),hAPP(fun(C,A),fun(fun(C,bool),fun(A,bool)),image(C,A),D),E)))|hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),$f10(A,C,B,D,E)),E)).
% 32.85/32.59 ** KEPT (pick-wt=41): 122 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),$f11(A,B,C)),B))|hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),C),B)).
% 32.85/32.59 ** KEPT (pick-wt=69): 123 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(B,A,C,$f12(A,B,C,D,E))),D))|hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),hAPP(fun(B,bool),fun(A,bool),hAPP(fun(B,A),fun(fun(B,bool),fun(A,bool)),image(B,A),C),E)),D)).
% 32.85/32.59 ** KEPT (pick-wt=52): 124 [] -ord(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(B,A,C,$f13(B,A,C,D))),hAPP(B,A,D,$f13(B,A,C,D))))|hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_e_q(fun(B,A)),C),D)).
% 32.85/32.59 ** KEPT (pick-wt=40): 125 [] -hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),A))| -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),$f14(A))).
% 32.85/32.59 ** KEPT (pick-wt=24): 126 [] hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),A))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f15(A,B)),B)).
% 32.85/32.59 ** KEPT (pick-wt=69): 127 [] -hBOOL(hAPP(com,bool,wt,A))|hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),$f16(B,A)),u))|hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,B),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,A)),bot_bot(fun(x_a,bool))))).
% 32.85/32.59 ** KEPT (pick-wt=96): 128 [] -hBOOL(hAPP(com,bool,wt,A))| -hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,B),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,$f16(B,A))),bot_bot(fun(x_a,bool)))))|hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,B),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,A)),bot_bot(fun(x_a,bool))))).
% 32.85/32.59 ** KEPT (pick-wt=53): 129 [] -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)).
% 32.85/32.59 ** KEPT (pick-wt=53): 130 [] -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)).
% 32.85/32.59 ** KEPT (pick-wt=49): 131 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,A)),B))|hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A)),B)).
% 32.85/32.59 ** KEPT (pick-wt=49): 132 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,A)),B))| -hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A)),B)).
% 32.85/32.59 ** KEPT (pick-wt=119): 133 [] -hBOOL(hAPP(fun(fun(A,bool),B),bool,hAPP(fun(A,B),fun(fun(fun(A,bool),B),bool),hAPP(B,fun(fun(A,B),fun(fun(fun(A,bool),B),bool)),hAPP(fun(B,fun(B,B)),fun(B,fun(fun(A,B),fun(fun(fun(A,bool),B),bool))),finite908156982e_idem(B,A),C),D),E),F))| -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),G))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_e_q(fun(A,bool)),H),G))|hAPP(B,B,hAPP(B,fun(B,B),C,hAPP(fun(A,bool),B,F,H)),hAPP(fun(A,bool),B,F,G))=hAPP(fun(A,bool),B,F,G).
% 32.85/32.59 ** KEPT (pick-wt=115): 134 [] -hBOOL(hAPP(fun(fun(A,bool),B),bool,hAPP(fun(A,B),fun(fun(fun(A,bool),B),bool),hAPP(B,fun(fun(A,B),fun(fun(fun(A,bool),B),bool)),hAPP(fun(B,fun(B,B)),fun(B,fun(fun(A,B),fun(fun(fun(A,bool),B),bool))),finite908156982e_idem(B,A),C),D),E),F))| -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),G))|hAPP(fun(A,bool),B,F,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),H),G))=hAPP(B,B,hAPP(B,fun(B,B),C,hAPP(A,B,E,H)),hAPP(fun(A,bool),B,F,G)).
% 32.85/32.59 ** KEPT (pick-wt=20): 135 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),bot_bot(fun(A,bool)))).
% 32.85/32.59 ** KEPT (pick-wt=41): 136 [] -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B))|hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),hAPP(fun(A,bool),fun(A,bool),hA
% 32.85/32.60 Search stopped in tp_alloc by max_mem option.
% 32.85/32.60 PP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))).
% 32.85/32.60 ** KEPT (pick-wt=27): 137 [] ti(fun(A,bool),B)!=bot_bot(fun(A,bool))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)).
% 32.85/32.60 ** KEPT (pick-wt=21): 138 [] hAPP(fun(A,bool),fun(A,bool),collect(A),B)!=bot_bot(fun(A,bool))| -hBOOL(hAPP(A,bool,B,C)).
% 32.85/32.60 Following clause subsumed by 135 during input processing: 0 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),bot_bot(fun(A,bool)))).
% 32.85/32.60 Following clause subsumed by 138 during input processing: 0 [flip.1] hAPP(fun(A,bool),fun(A,bool),collect(A),B)!=bot_bot(fun(A,bool))| -hBOOL(hAPP(A,bool,B,C)).
% 32.85/32.60 Following clause subsumed by 137 during input processing: 0 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|ti(fun(A,bool),C)!=bot_bot(fun(A,bool)).
% 32.85/32.60 Following clause subsumed by 137 during input processing: 0 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|ti(fun(A,bool),C)!=bot_bot(fun(A,bool)).
% 32.85/32.60 ** KEPT (pick-wt=13): 139 [] -bot(A)|hAPP(B,A,bot_bot(fun(B,A)),C)=bot_bot(A).
% 32.85/32.60 Following clause subsumed by 139 during input processing: 0 [] -bot(A)|hAPP(B,A,bot_bot(fun(B,A)),C)=bot_bot(A).
% 32.85/32.60 ** KEPT (pick-wt=88): 140 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool)))))=ti(fun(A,bool),C).
% 32.85/32.60 ** KEPT (pick-wt=73): 141 [] -hBOOL(hAPP(fun(fun(A,bool),B),bool,hAPP(fun(A,B),fun(fun(fun(A,bool),B),bool),hAPP(B,fun(fun(A,B),fun(fun(fun(A,bool),B),bool)),hAPP(fun(B,fun(B,B)),fun(B,fun(fun(A,B),fun(fun(fun(A,bool),B),bool))),finite908156982e_idem(B,A),C),D),E),F))|hAPP(B,B,hAPP(B,fun(B,B),C,G),G)=ti(B,G).
% 32.85/32.60
% 32.85/32.60 Search stopped in tp_alloc by max_mem option.
% 32.85/32.60
% 32.85/32.60 ============ end of search ============
% 32.85/32.60
% 32.85/32.60 -------------- statistics -------------
% 32.85/32.60 clauses given 0
% 32.85/32.60 clauses generated 0
% 32.85/32.60 clauses kept 140
% 32.85/32.60 clauses forward subsumed 35
% 32.85/32.60 clauses back subsumed 0
% 32.85/32.60 Kbytes malloced 11718
% 32.85/32.60
% 32.85/32.60 ----------- times (seconds) -----------
% 32.85/32.60 user CPU time 0.27 (0 hr, 0 min, 0 sec)
% 32.85/32.60 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 32.85/32.60 wall-clock time 32 (0 hr, 0 min, 32 sec)
% 32.85/32.60
% 32.85/32.60 Process 16648 finished Wed Jul 27 03:18:23 2022
% 32.85/32.60 Otter interrupted
% 32.85/32.60 PROOF NOT FOUND
%------------------------------------------------------------------------------